Subgroups — C₂×#22574723 #31763159

Order 17152.

8122 conjugacy classes of subgroups.

The subgroup lattice has 1416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574723	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864141	C₂	1	2	yes	maximal, complemented
3	C₂×#16864139	C₂	1	2	yes	maximal, complemented
4	C₂×#16864132	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864129	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16864052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16864043	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16864040	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16864040	C₂	1	2	yes	maximal, complemented
11	C₂×#16864033	C₂	1	2	yes	maximal, complemented
12	C₂×D₄×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16864013	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16864011	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16863981	C₂	1	2	yes	maximal, complemented
16	C₂×#16863981	C₂	1	2	yes	maximal, complemented
17	C₂×#16863978	C₂	1	2	yes	maximal, complemented
18	C₂×#16863963	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16863959	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16863955	C₂	1	2	yes	maximal, complemented
21	C₂×#16863941	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863926	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂²×#14524030	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761628	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#11761627	C₂²	1	2	yes	complemented
27	C₂²×#11761627	C₂²	1	1	yes	characteristic, complemented
28	C₂³×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
29	C₂³×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
30	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
31	#16864141	C₂²	1	32	yes	complemented
32	#16864139	C₂²	1	32	yes	complemented
33	#16864132	C₂²	1	16	yes	complemented
34	#16864129	C₂²	1	16	yes	complemented
35	#16864055	C₂²	1	16	yes	complemented
36	#16864052	C₂²	1	16	yes	complemented
37	#16864043	C₂²	1	16	yes	complemented
38	#16864040	C₂²	1	16	yes	complemented
39	#16864040	C₂²	1	32	yes	complemented
40	#16864033	C₂²	1	32	yes	complemented
41	D₄×C₂²⋊D₆₇	C₂²	1	16	yes	complemented
42	#16864013	C₂²	1	16	yes	complemented
43	#16864011	C₂²	1	16	yes	complemented
44	#16863981	C₂²	1	32	yes	complemented
45	#16863981	C₂²	1	32	yes	complemented
46	#16863978	C₂²	1	32	yes	complemented
47	#16863963	C₂²	1	16	yes	complemented
48	#16863959	C₂²	1	16	yes	complemented
49	#16863955	C₂²	1	32	yes	complemented
50	#16863941	C₂²	1	16	yes	complemented
51	C₂×#14524042	C₂²	1	1	yes	characteristic, complemented
52	C₂×#14524039	C₂²	1	1	yes	characteristic
53	C₂×#14524039	C₂²	1	1	yes	characteristic, complemented
54	#16863926	C₂²	1	16	yes	complemented
55	C₂×#14524038	C₂²	1	1	yes	characteristic, complemented
56	C₂×#14524036	C₂²	1	2	yes	complemented
57	C₂×#14524036	C₂²	1	2	yes	complemented
58	C₂×#14524036	C₂²	1	1	yes	characteristic, complemented
59	C₂×#14524033	C₂²	1	1	yes	characteristic, complemented
60	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
61	C₂×#14524030	C₂²	1	1	yes	characteristic, complemented
62	C₂×#14524030	C₂²	1	2	yes	complemented
63	C₂×#14524030	C₂²	1	1	yes	characteristic, complemented
64	C₂×#14524030	C₂²	1	1	yes	characteristic, complemented
65	C₂×#14524030	C₂²	1	1	yes	characteristic, complemented
66	C₂×#14524030	C₂²	1	1	yes	characteristic, complemented
67	C₂×#14524030	C₂²	1	2	yes	complemented
68	C₂×#14524030	C₂²	1	2	yes	complemented
69	C₂×#14524030	C₂²	1	2	yes	complemented
70	C₂×#14524030	C₂²	1	16	yes	complemented
71	C₂×#14524029	C₂²	1	2	yes	complemented
72	C₂×#14524029	C₂²	1	2	yes	complemented
73	C₂×#14524029	C₂²	1	2	yes	complemented
74	C₂×#14524029	C₂²	1	1	yes	characteristic, complemented
75	C₂×#14524029	C₂²	1	2	yes	complemented
76	C₂×#14524029	C₂²	1	2	yes	complemented
77	C₂×#14524027	C₂²	1	1	yes	characteristic, complemented
78	C₂×#14524026	C₂²	1	2	yes	complemented
79	C₂×#14524026	C₂²	1	2	yes	complemented
80	C₂×#14524025	C₂²	1	2	yes	complemented
81	C₂×#14524025	C₂²	1	2	yes	complemented
82	C₂×#14524024	C₂²	1	2	yes	complemented
83	C₂×#14524024	C₂²	1	1	yes	characteristic, complemented
84	C₂×#14524024	C₂²	1	2	yes	complemented
85	C₂×#14524024	C₂²	1	2	yes	complemented
86	C₂×#14524024	C₂²	1	2	yes	complemented
87	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
88	C₂×#14524022	C₂²	1	2	yes	complemented
89	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
90	C₂×#14524021	C₂²	1	2	yes	complemented
91	C₂×#14524020	C₂²	1	2	yes	complemented
92	C₂×#14524020	C₂²	1	2	yes	complemented
93	C₂×#14524020	C₂²	1	1	yes	characteristic, complemented
94	C₂×#14524017	C₂²	1	1	yes	characteristic, complemented
95	C₂×#14524015	C₂²	1	1	yes	characteristic
96	C₂×#14524015	C₂²	1	2	yes	complemented
97	C₂×#14524015	C₂²	1	2	yes	complemented
98	C₂×#14524015	C₂²	1	2	yes	complemented
99	C₂×#14524015	C₂²	1	2	yes	complemented
100	C₂×#14524015	C₂²	1	2	yes	complemented
101	C₂×#14524015	C₂²	1	2	yes	complemented
102	C₂×#14524015	C₂²	1	2	yes	complemented
103	C₂×#14524014	C₂²	1	1	yes	characteristic
104	C₂×#14524014	C₂²	1	2	yes	complemented
105	C₂×#14524014	C₂²	1	2	yes	complemented
106	C₂×#14524014	C₂²	1	2	yes	complemented
107	C₂×#14524012	C₂²	1	2	yes	complemented
108	C₂×#14524012	C₂²	1	2	yes	complemented
109	C₂×#14524012	C₂²	1	2	yes	complemented
110	C₂×#14524012	C₂²	1	2	yes	complemented
111	C₂×#14524011	C₂²	1	2	yes	complemented
112	C₂×#14524011	C₂²	1	2	yes	complemented
113	C₂×#14524011	C₂²	1	2	yes	complemented
114	C₂×#14524011	C₂²	1	2	yes	complemented
115	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
117	C₂×#14524008	C₂²	1	1	yes	characteristic, complemented
118	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
120	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
121	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
123	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
126	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
127	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
128	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
129	C₂×#14524000	C₂²	1	1	yes	characteristic, complemented
130	C₂²×C₂²⋊Dic₆₇	C₂²	1	2	yes	complemented
131	C₂²×C₂²⋊Dic₆₇	C₂²	1	2	yes	complemented
132	C₂²×C₂²⋊Dic₆₇	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
134	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
136	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
137	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
138	D₄²×C₆₇	C₂²	1	16	yes	complemented
139	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
140	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
141	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
142	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
143	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
144	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
145	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
146	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₆₇	C₂³	1	2	yes	—
148	C₂×#11761628	—	4	4	no	—
149	C₂×#11761628	C₂³	1	8	yes	complemented
150	C₂×#11761627	—	4	4	no	—
151	C₂×#11761627	—	4	8	no	—
152	C₂×#11761627	C₂³	1	16	yes	complemented
153	C₂×#11761627	C₂³	1	8	yes	complemented
154	C₂²×Dic₁₃₄	—	4	4	no	—
155	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
156	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
157	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
158	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
159	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
160	C₂²×Dic₁₃₄	C₂³	1	8	yes	complemented
161	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
162	C₂²×C₂²⋊D₆₇	—	4	8	no	—
163	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
164	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
166	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
167	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
168	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
169	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
170	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
171	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
172	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
173	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
174	C₂²×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
175	C₂×D₄×D₆₇	—	4	4	no	—
176	C₂×D₄×D₆₇	C₂³	1	8	yes	complemented
177	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
178	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
179	C₂³×Dic₆₇	C₂³	1	2	yes	—
180	C₂³×Dic₆₇	C₂³	1	2	yes	—
181	C₂³×Dic₆₇	C₂³	1	2	yes	—
182	C₂³×Dic₆₇	C₂³	1	2	yes	—
183	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
184	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
185	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
186	#14524042	C₂³	1	8	yes	complemented
187	#14524039	C₂³	1	8	yes	—
188	#14524039	C₂³	1	8	yes	complemented
189	#14524038	C₂³	1	8	yes	complemented
190	#14524036	C₂³	1	16	yes	complemented
191	#14524036	C₂³	1	16	yes	complemented
192	#14524036	C₂³	1	8	yes	complemented
193	#14524033	C₂³	1	8	yes	complemented
194	#14524031	C₂³	1	8	yes	complemented
195	#14524030	C₂³	1	8	yes	complemented
196	#14524030	C₂³	1	16	yes	complemented
197	#14524030	C₂³	1	8	yes	complemented
198	#14524030	C₂³	1	8	yes	complemented
199	#14524030	C₂³	1	8	yes	complemented
200	#14524030	C₂³	1	8	yes	complemented
201	#14524030	C₂³	1	16	yes	complemented
202	#14524030	C₂³	1	16	yes	complemented
203	#14524030	C₂³	1	16	yes	complemented
204	#14524029	C₂³	1	16	yes	complemented
205	#14524029	C₂³	1	16	yes	complemented
206	#14524029	C₂³	1	16	yes	complemented
207	#14524029	C₂³	1	16	yes	complemented
208	#14524029	C₂³	1	8	yes	complemented
209	#14524029	C₂³	1	16	yes	complemented
210	#14524027	C₂³	1	8	yes	complemented
211	#14524026	C₂³	1	16	yes	complemented
212	#14524026	C₂³	1	16	yes	complemented
213	#14524025	C₂³	1	16	yes	complemented
214	#14524025	C₂³	1	16	yes	complemented
215	#14524024	C₂³	1	16	yes	complemented
216	#14524024	C₂³	1	8	yes	complemented
217	#14524024	C₂³	1	16	yes	complemented
218	#14524024	C₂³	1	16	yes	complemented
219	#14524024	C₂³	1	16	yes	complemented
220	#14524023	C₂³	1	8	yes	complemented
221	#14524022	C₂³	1	16	yes	complemented
222	#14524022	C₂³	1	8	yes	complemented
223	#14524021	C₂³	1	16	yes	complemented
224	#14524020	C₂³	1	16	yes	complemented
225	#14524020	C₂³	1	16	yes	complemented
226	#14524020	C₂³	1	8	yes	complemented
227	#14524017	C₂³	1	8	yes	complemented
228	#14524015	C₂³	1	8	yes	—
229	#14524015	C₂³	1	16	yes	complemented
230	#14524015	C₂³	1	16	yes	complemented
231	#14524015	C₂³	1	16	yes	complemented
232	#14524015	C₂³	1	16	yes	complemented
233	#14524015	C₂³	1	16	yes	complemented
234	#14524015	C₂³	1	16	yes	complemented
235	#14524015	C₂³	1	16	yes	complemented
236	#14524014	C₂³	1	8	yes	—
237	#14524014	C₂³	1	16	yes	complemented
238	#14524014	C₂³	1	16	yes	complemented
239	#14524014	C₂³	1	16	yes	complemented
240	#14524012	C₂³	1	16	yes	complemented
241	#14524012	C₂³	1	16	yes	complemented
242	#14524012	C₂³	1	16	yes	complemented
243	#14524012	C₂³	1	16	yes	complemented
244	#14524011	C₂³	1	16	yes	complemented
245	#14524011	C₂³	1	16	yes	complemented
246	#14524011	C₂³	1	16	yes	complemented
247	#14524011	C₂³	1	16	yes	complemented
248	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
249	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
250	#14524008	C₂³	1	8	yes	complemented
251	D₄×Dic₆₇	C₂³	1	8	yes	complemented
252	D₄×Dic₆₇	C₂³	1	16	yes	complemented
253	D₄×Dic₆₇	C₂³	1	16	yes	complemented
254	D₄×Dic₆₇	C₂³	1	8	yes	complemented
255	#14524005	C₂³	1	8	yes	complemented
256	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
257	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
258	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
259	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
260	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
261	#14524002	C₂³	1	8	yes	complemented
262	#14524000	C₂³	1	8	yes	complemented
263	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
268	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
271	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
272	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
276	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
278	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
279	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
281	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
282	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
283	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
284	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
285	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
286	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
287	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
288	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
289	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
293	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
294	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
295	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
296	C₂×C₂²⋊Dic₆₇	C₂³	1	16	yes	complemented
297	C₂×C₂²⋊Dic₆₇	C₂³	1	16	yes	complemented
298	C₂×C₂²⋊Dic₆₇	C₂³	1	16	yes	complemented
299	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
301	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
302	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
303	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
304	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
305	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
306	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
307	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
308	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
309	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
310	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
313	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
314	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
315	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
316	C₂×C₄×Dic₆₇	C₂³	1	8	yes	complemented
317	C₂⁵×C₆₇	C₂³	1	2	yes	—
318	C₂⁵×C₆₇	C₂³	1	2	yes	—
319	C₂²×D₄×C₆₇	—	4	4	no	—
320	C₂²×D₄×C₆₇	—	4	4	no	—
321	C₂²×D₄×C₆₇	—	4	8	no	—
322	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
325	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
328	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
329	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
330	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
331	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
332	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
333	C₂²×D₄×C₆₇	C₂³	1	16	yes	complemented
334	C₂²×D₄×C₆₇	C₂³	1	8	yes	complemented
335	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
338	#127×C₆₇	C₂³	1	8	yes	—
339	#121×C₆₇	C₂³	1	8	yes	—
340	#121×C₆₇	C₂³	1	8	yes	complemented
341	#121×C₆₇	C₂³	1	16	yes	complemented
342	#120×C₆₇	C₂³	1	16	yes	complemented
343	#120×C₆₇	C₂³	1	16	yes	complemented
344	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
345	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
346	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
347	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
350	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
352	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
353	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
354	C₂³×D₆₇	—	4	4	no	—
355	C₂³×D₆₇	—	4	4	no	—
356	C₂³×D₆₇	—	4	4	no	—
357	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
358	C₂³×D₆₇	C₂⁴	1	2	yes	—
359	C₂³×D₆₇	C₂⁴	1	8	yes	—
360	#11761628	—	4	16	no	—
361	#11761627	—	4	16	no	—
362	#11761627	—	4	32	no	—
363	C₂×Dic₁₃₄	—	2	4	no	—
364	C₂×Dic₁₃₄	—	2	4	no	—
365	C₂×Dic₁₃₄	—	4	16	no	—
366	C₂×Dic₁₃₄	—	4	4	no	—
367	C₂×Dic₁₃₄	—	4	2	no	—
368	C₂×Dic₁₃₄	—	4	4	no	—
369	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
370	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
371	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
372	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
373	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
374	C₂×D₂₆₈	—	2	4	no	—
375	C₂×D₂₆₈	C₂⁴	1	4	yes	—
376	C₂×C₂²⋊D₆₇	—	2	4	no	—
377	C₂×C₂²⋊D₆₇	—	2	8	no	—
378	C₂×C₂²⋊D₆₇	—	4	4	no	—
379	C₂×C₂²⋊D₆₇	—	4	4	no	—
380	C₂×C₂²⋊D₆₇	—	4	4	no	—
381	C₂×C₂²⋊D₆₇	—	4	4	no	—
382	C₂×C₂²⋊D₆₇	—	4	2	no	—
383	C₂×C₂²⋊D₆₇	—	4	4	no	—
384	C₂×C₂²⋊D₆₇	—	4	4	no	—
385	C₂×C₂²⋊D₆₇	—	4	4	no	—
386	C₂×C₂²⋊D₆₇	—	4	4	no	—
387	C₂×C₂²⋊D₆₇	—	4	32	no	—
388	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
389	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
390	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
391	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
392	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
393	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
394	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
395	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
396	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
397	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
398	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
399	D₄×D₆₇	—	4	16	no	—
400	C₂²×Dic₆₇	—	2	4	no	—
401	C₂²×Dic₆₇	—	4	2	no	—
402	C₂²×Dic₆₇	—	4	4	no	—
403	C₂²×Dic₆₇	—	4	4	no	—
404	C₂²×Dic₆₇	—	4	4	no	—
405	C₂²×Dic₆₇	—	4	4	no	—
406	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
412	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
413	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
414	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
416	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
418	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
419	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
420	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
421	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
422	C₂×C₄×D₆₇	—	2	4	no	—
423	C₂×C₄×D₆₇	—	4	4	no	—
424	C₂×C₄×D₆₇	—	4	4	no	—
425	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
426	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
427	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
428	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
429	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
430	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
431	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
432	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
433	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
434	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
435	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
436	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
437	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
438	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
439	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
440	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
441	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
442	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
443	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
444	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
445	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
446	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
447	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
448	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
449	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
450	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
451	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
452	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
453	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
454	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
455	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
456	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
457	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
458	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
459	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
460	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
461	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
462	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
463	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
464	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
465	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
466	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
467	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
468	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
469	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
470	C₄×Dic₆₇	C₂⁴	1	4	yes	—
471	C₄×Dic₆₇	C₂⁴	1	4	yes	—
472	C₄×Dic₆₇	C₂⁴	1	4	yes	—
473	C₄×Dic₆₇	C₂⁴	1	4	yes	—
474	C₄×Dic₆₇	C₂⁴	1	4	yes	—
475	C₄×Dic₆₇	C₂⁴	1	8	yes	—
476	C₄×Dic₆₇	C₂⁴	1	8	yes	—
477	C₂⁴×C₆₇	—	2	8	no	—
478	C₂⁴×C₆₇	—	4	4	no	—
479	C₂⁴×C₆₇	—	4	4	no	—
480	C₂⁴×C₆₇	—	4	4	no	—
481	C₂⁴×C₆₇	—	4	4	no	—
482	C₂⁴×C₆₇	—	4	4	no	—
483	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
484	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
485	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
486	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
487	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
488	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
489	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
490	C₂×D₄×C₆₇	—	2	4	no	—
491	C₂×D₄×C₆₇	—	2	8	no	—
492	C₂×D₄×C₆₇	—	2	4	no	—
493	C₂×D₄×C₆₇	—	2	4	no	—
494	C₂×D₄×C₆₇	—	2	4	no	—
495	C₂×D₄×C₆₇	—	4	16	no	—
496	C₂×D₄×C₆₇	—	4	16	no	—
497	C₂×D₄×C₆₇	—	4	4	no	—
498	C₂×D₄×C₆₇	—	4	4	no	—
499	C₂×D₄×C₆₇	—	4	4	no	—
500	C₂×D₄×C₆₇	—	4	4	no	—
501	C₂×D₄×C₆₇	—	4	4	no	—
502	C₂×D₄×C₆₇	—	4	32	no	—
503	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
504	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
505	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
506	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
507	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
508	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
509	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
510	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
511	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
512	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
513	C₂²×C₄×C₆₇	—	2	4	no	—
514	C₂²×C₄×C₆₇	—	2	4	no	—
515	C₂²×C₄×C₆₇	—	4	4	no	—
516	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
517	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
518	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
519	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
520	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
521	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
522	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
523	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
524	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
525	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
526	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
527	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
528	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
529	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
530	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
531	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
532	C₄²×C₆₇	C₂⁴	1	4	yes	—
533	C₂³×C₆₇	—	2	2	no	—
534	C₂³×C₆₇	—	2	2	no	—
535	C₂³×C₆₇	—	2	2	no	—
536	C₂³×C₆₇	—	2	4	no	—
537	C₂³×C₆₇	—	2	2	no	—
538	C₂³×C₆₇	—	2	4	no	—
539	C₂³×C₆₇	—	2	4	no	—
540	C₂³×C₆₇	—	2	4	no	—
541	C₂³×C₆₇	—	2	4	no	—
542	C₂³×C₆₇	—	2	4	no	—
543	C₂³×C₆₇	—	2	4	no	—
544	C₂³×C₆₇	—	2	4	no	—
545	C₂³×C₆₇	—	2	2	no	—
546	C₂³×C₆₇	—	2	4	no	—
547	C₂³×C₆₇	—	2	16	no	—
548	C₂³×C₆₇	—	4	8	no	—
549	C₂³×C₆₇	—	4	8	no	—
550	C₂³×C₆₇	—	4	8	no	—
551	C₂³×C₆₇	—	4	8	no	—
552	C₂³×C₆₇	—	4	8	no	—
553	C₂³×C₆₇	—	8	16	no	—
554	C₂³×C₆₇	—	8	16	no	—
555	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
556	C₂³×C₆₇	C₂⁵	1	2	yes	—
557	C₂³×C₆₇	C₂⁵	1	4	yes	—
558	C₂³×C₆₇	C₂⁵	1	4	yes	—
559	C₂³×C₆₇	C₂⁵	1	4	yes	—
560	C₂³×C₆₇	C₂⁵	1	2	yes	—
561	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
562	C₂²×D₆₇	—	2	2	no	—
563	C₂²×D₆₇	—	2	4	no	—
564	C₂²×D₆₇	—	2	4	no	—
565	C₂²×D₆₇	—	2	2	no	—
566	C₂²×D₆₇	—	2	4	no	—
567	C₂²×D₆₇	—	2	2	no	—
568	C₂²×D₆₇	—	4	8	no	—
569	C₂²×D₆₇	—	4	8	no	—
570	C₂²×D₆₇	—	4	8	no	—
571	C₂²×D₆₇	—	8	16	no	—
572	C₂²×D₆₇	C₂⁵	1	2	yes	—
573	C₂²×D₆₇	C₂⁵	1	4	yes	—
574	D₄×C₆₇	—	2	8	no	—
575	D₄×C₆₇	—	2	16	no	—
576	D₄×C₆₇	—	2	8	no	—
577	D₄×C₆₇	—	2	8	no	—
578	D₄×C₆₇	—	2	8	no	—
579	D₄×C₆₇	—	4	8	no	—
580	D₄×C₆₇	—	4	8	no	—
581	D₄×C₆₇	—	4	8	no	—
582	D₄×C₆₇	—	4	8	no	—
583	D₄×C₆₇	—	4	8	no	—
584	C₂×C₄×C₆₇	—	2	2	no	—
585	C₂×C₄×C₆₇	—	2	2	no	—
586	C₂×C₄×C₆₇	—	2	2	no	—
587	C₂×C₄×C₆₇	—	2	4	no	—
588	C₂×C₄×C₆₇	—	2	2	no	—
589	C₂×C₄×C₆₇	—	2	8	no	—
590	C₂×C₄×C₆₇	—	2	8	no	—
591	C₂×C₄×C₆₇	—	4	8	no	—
592	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
593	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
594	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
595	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
596	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
597	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
598	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
599	C₂²⋊D₆₇	—	2	8	no	—
600	C₂²⋊D₆₇	—	2	16	no	—
601	C₂²⋊D₆₇	—	4	8	no	—
602	C₂²⋊D₆₇	—	4	8	no	—
603	C₂²⋊D₆₇	—	4	8	no	—
604	C₂²⋊D₆₇	—	4	4	no	—
605	C₂²⋊D₆₇	—	4	8	no	—
606	C₂²⋊D₆₇	—	4	8	no	—
607	C₂²⋊D₆₇	—	4	8	no	—
608	C₂²⋊D₆₇	—	4	8	no	—
609	C₂²⋊D₆₇	—	4	8	no	—
610	C₂×Dic₆₇	—	2	2	no	—
611	C₂×Dic₆₇	—	2	2	no	—
612	C₂×Dic₆₇	—	2	4	no	—
613	C₂×Dic₆₇	—	2	2	no	—
614	C₂×Dic₆₇	—	2	8	no	—
615	C₂×Dic₆₇	—	2	2	no	—
616	C₂×Dic₆₇	—	2	4	no	—
617	C₂×Dic₆₇	—	2	4	no	—
618	C₂×Dic₆₇	—	2	2	no	—
619	C₂×Dic₆₇	—	2	2	no	—
620	C₂×Dic₆₇	—	2	2	no	—
621	C₂×Dic₆₇	—	4	4	no	—
622	C₂×Dic₆₇	—	4	8	no	—
623	C₂×Dic₆₇	—	4	8	no	—
624	C₂×Dic₆₇	—	4	8	no	—
625	C₂×Dic₆₇	—	4	8	no	—
626	C₂×Dic₆₇	C₂⁵	1	2	yes	—
627	C₂×Dic₆₇	C₂⁵	1	2	yes	—
628	C₂×Dic₆₇	C₂⁵	1	2	yes	—
629	C₂×Dic₆₇	C₂⁵	1	2	yes	—
630	C₂×Dic₆₇	C₂⁵	1	2	yes	—
631	C₂×Dic₆₇	C₂⁵	1	4	yes	—
632	C₂×Dic₆₇	C₂⁵	1	4	yes	—
633	C₂×Dic₆₇	C₂⁵	1	4	yes	—
634	C₂×Dic₆₇	C₂⁵	1	2	yes	—
635	C₂×Dic₆₇	C₂⁵	1	2	yes	—
636	D₂₆₈	—	2	8	no	—
637	C₄×D₆₇	—	2	8	no	—
638	C₄×D₆₇	—	4	8	no	—
639	C₄×D₆₇	—	4	8	no	—
640	Dic₁₃₄	—	2	8	no	—
641	Dic₁₃₄	—	2	8	no	—
642	Dic₁₃₄	—	4	8	no	—
643	Dic₁₃₄	—	4	4	no	—
644	Dic₁₃₄	—	4	8	no	—
645	C₂²×C₆₇	—	2	2	no	—
646	C₂²×C₆₇	—	2	2	no	—
647	C₂²×C₆₇	—	2	8	no	—
648	C₂²×C₆₇	—	2	4	no	—
649	C₂²×C₆₇	—	2	4	no	—
650	C₂²×C₆₇	—	2	4	no	—
651	C₂²×C₆₇	—	2	2	no	—
652	C₂²×C₆₇	—	2	4	no	—
653	C₂²×C₆₇	—	2	4	no	—
654	C₂²×C₆₇	—	2	2	no	—
655	C₂²×C₆₇	—	2	4	no	—
656	C₂²×C₆₇	—	2	4	no	—
657	C₂²×C₆₇	—	2	2	no	—
658	C₂²×C₆₇	—	2	4	no	—
659	C₂²×C₆₇	—	2	4	no	—
660	C₂²×C₆₇	—	4	8	no	—
661	C₂²×C₆₇	—	4	8	no	—
662	C₂²×C₆₇	—	4	4	no	—
663	C₂²×C₆₇	—	4	8	no	—
664	C₂²×C₆₇	—	8	16	no	—
665	C₂²×C₆₇	—	8	16	no	—
666	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
667	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
668	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
669	C₂²×C₆₇	#585	1	2	yes	—
670	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
671	C₂×D₆₇	—	2	2	no	—
672	C₂×D₆₇	—	2	4	no	—
673	C₂×D₆₇	—	2	4	no	—
674	C₂×D₆₇	—	2	2	no	—
675	C₂×D₆₇	—	2	4	no	—
676	C₂×D₆₇	—	2	2	no	—
677	C₂×D₆₇	—	4	8	no	—
678	C₂×D₆₇	—	4	4	no	—
679	C₂×D₆₇	—	8	16	no	—
680	C₄×C₆₇	—	2	2	no	—
681	C₄×C₆₇	—	2	4	no	—
682	C₄×C₆₇	—	2	2	no	—
683	C₄×C₆₇	—	2	2	no	—
684	C₄×C₆₇	—	2	2	no	—
685	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
686	Dic₆₇	—	2	4	no	—
687	Dic₆₇	—	2	4	no	—
688	Dic₆₇	—	2	2	no	—
689	Dic₆₇	—	2	4	no	—
690	Dic₆₇	—	2	2	no	—
691	Dic₆₇	—	2	2	no	—
692	Dic₆₇	—	2	2	no	—
693	Dic₆₇	—	2	2	no	—
694	Dic₆₇	—	2	2	no	—
695	Dic₆₇	—	2	2	no	—
696	C₂×#3558	—	67	1	no	maximal, Sylow
697	C₂×C₆₇	—	2	4	no	—
698	C₂×C₆₇	—	4	4	no	—
699	C₂×C₆₇	—	4	4	no	—
700	C₂×C₆₇	—	4	2	no	—
701	C₂×C₆₇	—	4	4	no	—
702	C₂×C₆₇	#3558	1	4	yes	complemented
703	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
706	D₆₇	—	4	4	no	—
707	D₆₇	—	4	2	no	—
708	#3558	—	67	32	no	—
709	C₂×#562	—	67	2	no	—
710	C₂×H(3,𝔽₄)	—	67	2	no	—
711	C₂×#559	—	67	1	no	—
712	C₂×#559	—	67	1	no	—
713	C₂×#548	—	67	1	no	—
714	C₂×#548	—	67	1	no	—
715	C₂×#546	—	67	2	no	—
716	C₂×#546	—	67	1	no	—
717	C₂×#546	—	67	1	no	—
718	C₂×#546	—	67	2	no	—
719	C₂×D₄²	—	67	1	no	—
720	C₂×D₄²	D₆₇	1	1	yes	characteristic, complemented
721	C₂×#542	—	67	1	no	—
722	C₂×#542	—	67	1	no	—
723	C₂×#538	—	67	2	no	—
724	C₂×#538	—	67	2	no	—
725	C₂×#538	—	67	2	no	—
726	C₂×#535	—	67	1	no	—
727	C₂×#535	—	67	1	no	—
728	C₂×#534	—	67	2	no	—
729	C₂×#532	—	67	1	no	—
730	C₂×#529	—	67	1	no	—
731	C₂²×#124	—	67	1	no	—
732	C₆₇	C₂×#3558	1	1	yes	characteristic, complemented, Sylow
733	C₂²×#41	—	67	2	no	—
734	C₂²×#41	—	67	1	no	—
735	C₂²×#41	—	67	1	no	—
736	C₂³×Q₈	—	67	1	no	—
737	C₂³×D₄	—	67	2	no	—
738	C₂³×D₄	—	67	1	no	—
739	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic
740	C₂³×D₄	C₂×D₆₇	1	2	yes	complemented
741	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
742	#562	—	67	32	no	—
743	H(3,𝔽₄)	—	67	32	no	—
744	#559	—	67	16	no	—
745	#559	—	67	16	no	—
746	#548	—	67	16	no	—
747	#548	—	67	16	no	—
748	#546	—	67	32	no	—
749	#546	—	67	16	no	—
750	#546	—	67	16	no	—
751	#546	—	67	32	no	—
752	D₄²	—	67	16	no	—
753	D₄²	C₂×D₆₇	1	16	yes	complemented
754	#542	—	67	16	no	—
755	#542	—	67	16	no	—
756	#538	—	67	32	no	—
757	#538	—	67	32	no	—
758	#538	—	67	32	no	—
759	#535	—	67	16	no	—
760	#535	—	67	16	no	—
761	#534	—	67	32	no	—
762	#532	—	67	16	no	—
763	C₂×C₄⋊Q₈	—	67	1	no	—
764	C₂×#127	—	67	1	no	—
765	C₂×#127	—	67	1	no	—
766	C₂×#127	C₂×D₆₇	1	1	yes	characteristic
767	#529	—	67	16	no	—
768	C₂×#126	—	67	1	no	—
769	C₂×#126	—	67	1	no	—
770	C₂×#126	—	67	2	no	—
771	C₂×#126	—	67	2	no	—
772	C₂×#125	—	67	1	no	—
773	C₂×#124	—	67	1	no	—
774	C₂×#124	—	67	1	no	—
775	C₂×#124	—	67	2	no	—
776	C₂×#124	—	67	1	no	—
777	C₂×#124	—	67	1	no	—
778	C₂×#124	—	67	2	no	—
779	C₂×#124	—	67	16	no	—
780	C₂×#124	—	67	1	no	—
781	C₂×#124	—	67	2	no	—
782	C₂×#124	—	67	2	no	—
783	C₂×#124	—	67	1	no	—
784	C₂×#124	—	67	2	no	—
785	C₂×#124	—	67	2	no	—
786	C₂×#124	—	67	2	no	—
787	C₂×#124	—	67	2	no	—
788	C₂×#124	—	67	2	no	—
789	C₂×#124	—	67	1	no	—
790	C₂×#123	—	67	1	no	—
791	C₂×#123	—	67	2	no	—
792	C₂×#123	—	67	2	no	—
793	C₂×#123	—	67	2	no	—
794	C₂×#123	—	67	2	no	—
795	C₂×#123	—	67	2	no	—
796	C₂×#123	—	67	2	no	—
797	C₂×#123	—	67	1	no	—
798	C₂×#123	—	67	2	no	—
799	C₂×#123	—	67	2	no	—
800	C₂×C₂²⋊Q₈	—	67	1	no	—
801	C₂×C₂²⋊Q₈	—	67	2	no	—
802	C₂×C₂²⋊Q₈	—	67	2	no	—
803	C₂×C₂²⋊Q₈	—	67	1	no	—
804	C₂×C₂²⋊Q₈	—	67	1	no	—
805	C₂×C₂²⋊Q₈	—	67	2	no	—
806	C₂×C₂²⋊Q₈	—	67	2	no	—
807	C₂×#121	—	67	1	no	—
808	C₂×#121	—	67	2	no	—
809	C₂×#121	—	67	2	no	—
810	C₂×#121	—	67	2	no	—
811	C₂×#121	—	67	2	no	—
812	C₂×#121	—	67	2	no	—
813	C₂×#121	—	67	2	no	—
814	C₂×#121	—	67	2	no	—
815	C₂×#121	—	67	2	no	—
816	C₂×#121	—	67	2	no	—
817	C₂×#121	—	67	2	no	—
818	C₂×#121	—	67	1	no	—
819	C₂×#121	—	67	1	no	—
820	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
821	C₂×#121	C₂×D₆₇	1	1	yes	characteristic, complemented
822	C₂×#121	C₂×D₆₇	1	2	yes	complemented
823	C₂×#120	—	67	2	no	—
824	C₂×#120	—	67	2	no	—
825	C₂×#120	—	67	2	no	—
826	C₂×#120	—	67	2	no	—
827	C₂×#120	—	67	2	no	—
828	C₂×#120	—	67	2	no	—
829	C₂×#120	—	67	2	no	—
830	C₂×#120	—	67	2	no	—
831	C₂×#120	C₂×D₆₇	1	2	yes	complemented
832	C₂×#120	C₂×D₆₇	1	2	yes	complemented
833	C₂×C₄×Q₈	—	67	1	no	—
834	C₂×C₄×Q₈	—	67	1	no	—
835	C₂×C₄×Q₈	—	67	1	no	—
836	C₂×C₄×D₄	—	67	1	no	—
837	C₂×C₄×D₄	—	67	2	no	—
838	C₂×C₄×D₄	—	67	2	no	—
839	C₂×C₄×D₄	—	67	1	no	—
840	C₂×C₄×D₄	—	67	1	no	—
841	C₂×C₄×D₄	—	67	1	no	—
842	C₂×C₄×D₄	—	67	2	no	—
843	C₂×C₄×D₄	—	67	1	no	—
844	C₂×C₄×D₄	—	67	2	no	—
845	C₂×C₄×D₄	—	67	2	no	—
846	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
847	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
848	C₂×#117	—	67	1	no	—
849	C₂×#117	—	67	1	no	—
850	C₂²×C₂²⋊C₄	—	67	2	no	—
851	C₂²×C₂²⋊C₄	—	67	2	no	—
852	C₂²×C₂²⋊C₄	—	67	2	no	—
853	C₂²×C₂²⋊C₄	—	67	2	no	—
854	C₂²×C₄²	—	67	1	no	—
855	C₂⁵	—	67	2	no	—
856	C₂⁵	C₂²×D₆₇	1	2	yes	—
857	C₂⁵	C₂²×D₆₇	1	2	yes	—
858	C₂×#41	—	268	4	no	—
859	C₂×#41	—	268	4	no	—
860	C₂×#41	—	268	8	no	—
861	C₂×#41	—	67	16	no	—
862	C₂×#41	—	67	8	no	—
863	C₂×#41	—	67	8	no	—
864	C₂²×Q₈	—	268	4	no	—
865	C₂²×Q₈	—	67	1	no	—
866	C₂²×Q₈	—	67	2	no	—
867	C₂²×Q₈	—	67	2	no	—
868	C₂²×Q₈	—	67	8	no	—
869	C₂²×Q₈	—	67	1	no	—
870	C₂²×Q₈	—	67	1	no	—
871	C₂²×D₄	—	4	4	no	—
872	C₂²×D₄	—	4	4	no	—
873	C₂²×D₄	—	4	8	no	—
874	C₂²×D₄	—	268	8	no	—
875	C₂²×D₄	—	268	4	no	—
876	C₂²×D₄	—	67	1	no	—
877	C₂²×D₄	—	67	2	no	—
878	C₂²×D₄	—	67	2	no	—
879	C₂²×D₄	—	67	2	no	—
880	C₂²×D₄	—	67	2	no	—
881	C₂²×D₄	—	67	2	no	—
882	C₂²×D₄	—	67	2	no	—
883	C₂²×D₄	—	67	2	no	—
884	C₂²×D₄	—	67	2	no	—
885	C₂²×D₄	—	67	16	no	—
886	C₂²×D₄	—	67	8	no	—
887	C₂²×D₄	—	67	2	no	—
888	C₂²×D₄	—	67	1	no	—
889	C₂²×D₄	—	67	1	no	—
890	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
891	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
892	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
893	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
894	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
895	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
896	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
897	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
898	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
899	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
900	C₂²×D₄	C₂²×D₆₇	1	8	yes	—
901	C₂²×D₄	C₂²×D₆₇	1	16	yes	complemented
902	C₂²×D₄	C₂²×D₆₇	1	8	yes	complemented
903	C₂³×C₄	—	67	2	no	—
904	C₂³×C₄	—	67	1	no	—
905	C₂³×C₄	—	67	2	no	—
906	C₂³×C₄	—	67	2	no	—
907	C₂³×C₄	—	67	2	no	—
908	C₂³×C₄	—	67	2	no	—
909	C₂³×C₄	—	67	2	no	—
910	C₂³×C₄	—	67	1	no	—
911	C₂³×C₄	—	67	1	no	—
912	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
913	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
914	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
915	C₄⋊Q₈	—	67	8	no	—
916	#127	—	67	8	no	—
917	#127	—	67	8	no	—
918	#127	C₂²×D₆₇	1	8	yes	—
919	#126	—	67	8	no	—
920	#126	—	67	8	no	—
921	#126	—	67	16	no	—
922	#126	—	67	16	no	—
923	#125	—	67	8	no	—
924	#124	—	67	8	no	—
925	#124	—	67	8	no	—
926	#124	—	67	16	no	—
927	#124	—	67	8	no	—
928	#124	—	67	8	no	—
929	#124	—	67	16	no	—
930	#124	—	67	8	no	—
931	#124	—	67	16	no	—
932	#124	—	67	16	no	—
933	#124	—	67	8	no	—
934	#124	—	67	16	no	—
935	#124	—	67	16	no	—
936	#124	—	67	16	no	—
937	#124	—	67	16	no	—
938	#124	—	67	16	no	—
939	#124	—	67	8	no	—
940	#123	—	67	8	no	—
941	#123	—	67	16	no	—
942	#123	—	67	16	no	—
943	#123	—	67	16	no	—
944	#123	—	67	16	no	—
945	#123	—	67	16	no	—
946	#123	—	67	16	no	—
947	#123	—	67	8	no	—
948	#123	—	67	16	no	—
949	#123	—	67	16	no	—
950	C₂²⋊Q₈	—	67	8	no	—
951	C₂²⋊Q₈	—	67	16	no	—
952	C₂²⋊Q₈	—	67	16	no	—
953	C₂²⋊Q₈	—	67	8	no	—
954	C₂²⋊Q₈	—	67	8	no	—
955	C₂²⋊Q₈	—	67	16	no	—
956	C₂²⋊Q₈	—	67	16	no	—
957	#121	—	67	8	no	—
958	#121	—	67	16	no	—
959	#121	—	67	16	no	—
960	#121	—	67	16	no	—
961	#121	—	67	16	no	—
962	#121	—	67	16	no	—
963	#121	—	67	16	no	—
964	#121	—	67	16	no	—
965	#121	—	67	16	no	—
966	#121	—	67	16	no	—
967	#121	—	67	16	no	—
968	#121	—	67	8	no	—
969	#121	—	67	8	no	—
970	#121	C₂²×D₆₇	1	8	yes	—
971	#121	C₂²×D₆₇	1	8	yes	complemented
972	#121	C₂²×D₆₇	1	16	yes	complemented
973	#120	—	67	16	no	—
974	#120	—	67	16	no	—
975	#120	—	67	16	no	—
976	#120	—	67	16	no	—
977	#120	—	67	16	no	—
978	#120	—	67	16	no	—
979	#120	—	67	16	no	—
980	#120	—	67	16	no	—
981	#120	C₂²×D₆₇	1	16	yes	complemented
982	#120	C₂²×D₆₇	1	16	yes	complemented
983	C₄×Q₈	—	67	8	no	—
984	C₄×Q₈	—	67	8	no	—
985	C₄×Q₈	—	67	8	no	—
986	C₄×D₄	—	67	8	no	—
987	C₄×D₄	—	67	16	no	—
988	C₄×D₄	—	67	16	no	—
989	C₄×D₄	—	67	8	no	—
990	C₄×D₄	—	67	8	no	—
991	C₄×D₄	—	67	8	no	—
992	C₄×D₄	—	67	16	no	—
993	C₄×D₄	—	67	8	no	—
994	C₄×D₄	—	67	16	no	—
995	C₄×D₄	—	67	16	no	—
996	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
997	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
998	#117	—	67	8	no	—
999	#117	—	67	8	no	—
1000	C₂×C₄⋊C₄	—	67	1	no	—
1001	C₂×C₄⋊C₄	—	67	1	no	—
1002	C₂×C₄⋊C₄	—	67	1	no	—
1003	C₂×C₄⋊C₄	—	67	1	no	—
1004	C₂×C₄⋊C₄	—	67	1	no	—
1005	C₂×C₄⋊C₄	—	67	1	no	—
1006	C₂×C₄⋊C₄	—	67	1	no	—
1007	C₂×C₄⋊C₄	—	67	1	no	—
1008	C₂×C₄⋊C₄	—	67	2	no	—
1009	C₂×C₄⋊C₄	—	67	2	no	—
1010	C₂×C₄⋊C₄	—	67	2	no	—
1011	C₂×C₄⋊C₄	—	67	1	no	—
1012	C₂×C₄⋊C₄	—	67	2	no	—
1013	C₂×C₄⋊C₄	—	67	2	no	—
1014	C₂×C₄⋊C₄	—	67	1	no	—
1015	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1016	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1017	C₂×C₂²⋊C₄	—	67	1	no	—
1018	C₂×C₂²⋊C₄	—	67	2	no	—
1019	C₂×C₂²⋊C₄	—	67	2	no	—
1020	C₂×C₂²⋊C₄	—	67	2	no	—
1021	C₂×C₂²⋊C₄	—	67	2	no	—
1022	C₂×C₂²⋊C₄	—	67	2	no	—
1023	C₂×C₂²⋊C₄	—	67	2	no	—
1024	C₂×C₂²⋊C₄	—	67	2	no	—
1025	C₂×C₂²⋊C₄	—	67	2	no	—
1026	C₂×C₂²⋊C₄	—	67	2	no	—
1027	C₂×C₂²⋊C₄	—	67	2	no	—
1028	C₂×C₂²⋊C₄	—	67	16	no	—
1029	C₂×C₂²⋊C₄	—	67	16	no	—
1030	C₂×C₂²⋊C₄	—	67	16	no	—
1031	C₂×C₂²⋊C₄	—	67	1	no	—
1032	C₂×C₂²⋊C₄	—	67	1	no	—
1033	C₂×C₂²⋊C₄	—	67	1	no	—
1034	C₂×C₂²⋊C₄	—	67	2	no	—
1035	C₂×C₂²⋊C₄	—	67	2	no	—
1036	C₂×C₂²⋊C₄	—	67	2	no	—
1037	C₂×C₂²⋊C₄	—	67	2	no	—
1038	C₂×C₂²⋊C₄	—	67	1	no	—
1039	C₂×C₂²⋊C₄	—	67	2	no	—
1040	C₂×C₂²⋊C₄	—	67	1	no	—
1041	C₂×C₂²⋊C₄	—	67	1	no	—
1042	C₂×C₂²⋊C₄	—	67	1	no	—
1043	C₂×C₂²⋊C₄	—	67	2	no	—
1044	C₂×C₂²⋊C₄	—	67	2	no	—
1045	C₂×C₂²⋊C₄	—	67	2	no	—
1046	C₂×C₂²⋊C₄	—	67	2	no	—
1047	C₂×C₂²⋊C₄	—	67	16	no	—
1048	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1049	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1050	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1051	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1052	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1053	C₂×C₄²	—	67	1	no	—
1054	C₂×C₄²	—	67	1	no	—
1055	C₂×C₄²	—	67	1	no	—
1056	C₂×C₄²	—	67	2	no	—
1057	C₂×C₄²	—	67	2	no	—
1058	C₂×C₄²	—	67	1	no	—
1059	C₂×C₄²	—	67	1	no	—
1060	C₂×C₄²	—	67	8	no	—
1061	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1062	C₂⁴	—	2	8	no	—
1063	C₂⁴	—	4	4	no	—
1064	C₂⁴	—	4	4	no	—
1065	C₂⁴	—	4	4	no	—
1066	C₂⁴	—	4	4	no	—
1067	C₂⁴	—	4	4	no	—
1068	C₂⁴	—	268	4	no	—
1069	C₂⁴	—	268	4	no	—
1070	C₂⁴	—	268	4	no	—
1071	C₂⁴	—	67	8	no	—
1072	C₂⁴	—	67	1	no	—
1073	C₂⁴	—	67	2	no	—
1074	C₂⁴	C₂³×D₆₇	1	2	yes	—
1075	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1076	C₂⁴	C₂³×D₆₇	1	2	yes	—
1077	C₂⁴	C₂³×D₆₇	1	2	yes	—
1078	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1079	C₂⁴	C₂³×D₆₇	1	8	yes	—
1080	C₂⁴	C₂³×D₆₇	1	8	yes	—
1081	#41	—	268	16	no	—
1082	#41	—	268	16	no	—
1083	#41	—	268	32	no	—
1084	C₂×Q₈	—	268	16	no	—
1085	C₂×Q₈	—	268	4	no	—
1086	C₂×Q₈	—	268	4	no	—
1087	C₂×Q₈	—	268	2	no	—
1088	C₂×Q₈	—	67	4	no	—
1089	C₂×Q₈	—	67	8	no	—
1090	C₂×Q₈	—	67	8	no	—
1091	C₂×Q₈	—	67	4	no	—
1092	C₂×Q₈	—	67	4	no	—
1093	C₂×Q₈	—	134	4	no	—
1094	C₂×Q₈	—	134	4	no	—
1095	C₂×D₄	—	2	4	no	—
1096	C₂×D₄	—	2	8	no	—
1097	C₂×D₄	—	2	4	no	—
1098	C₂×D₄	—	2	4	no	—
1099	C₂×D₄	—	2	4	no	—
1100	C₂×D₄	—	4	16	no	—
1101	C₂×D₄	—	4	16	no	—
1102	C₂×D₄	—	4	4	no	—
1103	C₂×D₄	—	4	4	no	—
1104	C₂×D₄	—	4	4	no	—
1105	C₂×D₄	—	4	4	no	—
1106	C₂×D₄	—	4	4	no	—
1107	C₂×D₄	—	4	32	no	—
1108	C₂×D₄	—	268	32	no	—
1109	C₂×D₄	—	268	16	no	—
1110	C₂×D₄	—	268	4	no	—
1111	C₂×D₄	—	268	4	no	—
1112	C₂×D₄	—	268	4	no	—
1113	C₂×D₄	—	268	4	no	—
1114	C₂×D₄	—	268	4	no	—
1115	C₂×D₄	—	268	4	no	—
1116	C₂×D₄	—	268	4	no	—
1117	C₂×D₄	—	268	2	no	—
1118	C₂×D₄	—	268	4	no	—
1119	C₂×D₄	—	67	4	no	—
1120	C₂×D₄	—	67	8	no	—
1121	C₂×D₄	—	67	8	no	—
1122	C₂×D₄	—	67	8	no	—
1123	C₂×D₄	—	67	8	no	—
1124	C₂×D₄	—	67	8	no	—
1125	C₂×D₄	—	67	8	no	—
1126	C₂×D₄	—	67	8	no	—
1127	C₂×D₄	—	67	8	no	—
1128	C₂×D₄	—	67	8	no	—
1129	C₂×D₄	—	67	4	no	—
1130	C₂×D₄	—	67	4	no	—
1131	C₂×D₄	—	134	4	no	—
1132	C₂×D₄	—	134	8	no	—
1133	C₂×D₄	—	134	4	no	—
1134	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1135	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1136	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1137	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1138	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1139	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1140	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1141	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1142	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1143	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1144	C₂²×C₄	—	2	4	no	—
1145	C₂²×C₄	—	2	4	no	—
1146	C₂²×C₄	—	4	4	no	—
1147	C₂²×C₄	—	268	4	no	—
1148	C₂²×C₄	—	268	4	no	—
1149	C₂²×C₄	—	268	4	no	—
1150	C₂²×C₄	—	268	4	no	—
1151	C₂²×C₄	—	268	4	no	—
1152	C₂²×C₄	—	268	4	no	—
1153	C₂²×C₄	—	268	2	no	—
1154	C₂²×C₄	—	67	4	no	—
1155	C₂²×C₄	—	67	8	no	—
1156	C₂²×C₄	—	67	8	no	—
1157	C₂²×C₄	—	67	8	no	—
1158	C₂²×C₄	—	67	8	no	—
1159	C₂²×C₄	—	67	8	no	—
1160	C₂²×C₄	—	67	8	no	—
1161	C₂²×C₄	—	67	4	no	—
1162	C₂²×C₄	—	67	1	no	—
1163	C₂²×C₄	—	67	1	no	—
1164	C₂²×C₄	—	67	1	no	—
1165	C₂²×C₄	—	67	1	no	—
1166	C₂²×C₄	—	67	1	no	—
1167	C₂²×C₄	—	67	2	no	—
1168	C₂²×C₄	—	67	2	no	—
1169	C₂²×C₄	—	67	2	no	—
1170	C₂²×C₄	—	67	1	no	—
1171	C₂²×C₄	—	67	1	no	—
1172	C₂²×C₄	—	67	4	no	—
1173	C₂²×C₄	—	134	4	no	—
1174	C₂²×C₄	—	134	4	no	—
1175	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1176	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1177	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1178	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1179	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1180	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1181	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1182	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1183	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1184	C₄⋊C₄	—	67	4	no	—
1185	C₄⋊C₄	—	67	4	no	—
1186	C₄⋊C₄	—	67	4	no	—
1187	C₄⋊C₄	—	67	4	no	—
1188	C₄⋊C₄	—	67	4	no	—
1189	C₄⋊C₄	—	67	4	no	—
1190	C₄⋊C₄	—	67	4	no	—
1191	C₄⋊C₄	—	67	4	no	—
1192	C₄⋊C₄	—	67	8	no	—
1193	C₄⋊C₄	—	67	8	no	—
1194	C₄⋊C₄	—	67	8	no	—
1195	C₄⋊C₄	—	67	4	no	—
1196	C₄⋊C₄	—	67	8	no	—
1197	C₄⋊C₄	—	67	8	no	—
1198	C₄⋊C₄	—	67	4	no	—
1199	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1200	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1201	C₂²⋊C₄	—	67	4	no	—
1202	C₂²⋊C₄	—	67	8	no	—
1203	C₂²⋊C₄	—	67	8	no	—
1204	C₂²⋊C₄	—	67	8	no	—
1205	C₂²⋊C₄	—	67	8	no	—
1206	C₂²⋊C₄	—	67	8	no	—
1207	C₂²⋊C₄	—	67	8	no	—
1208	C₂²⋊C₄	—	67	8	no	—
1209	C₂²⋊C₄	—	67	8	no	—
1210	C₂²⋊C₄	—	67	8	no	—
1211	C₂²⋊C₄	—	67	8	no	—
1212	C₂²⋊C₄	—	67	4	no	—
1213	C₂²⋊C₄	—	67	4	no	—
1214	C₂²⋊C₄	—	67	4	no	—
1215	C₂²⋊C₄	—	67	8	no	—
1216	C₂²⋊C₄	—	67	8	no	—
1217	C₂²⋊C₄	—	67	8	no	—
1218	C₂²⋊C₄	—	67	8	no	—
1219	C₂²⋊C₄	—	67	4	no	—
1220	C₂²⋊C₄	—	67	8	no	—
1221	C₂²⋊C₄	—	67	4	no	—
1222	C₂²⋊C₄	—	67	4	no	—
1223	C₂²⋊C₄	—	67	4	no	—
1224	C₂²⋊C₄	—	67	8	no	—
1225	C₂²⋊C₄	—	67	8	no	—
1226	C₂²⋊C₄	—	67	8	no	—
1227	C₂²⋊C₄	—	67	8	no	—
1228	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1229	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1230	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1231	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1232	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1233	C₄²	—	67	4	no	—
1234	C₄²	—	67	4	no	—
1235	C₄²	—	67	4	no	—
1236	C₄²	—	67	4	no	—
1237	C₄²	—	67	4	no	—
1238	C₄²	—	67	8	no	—
1239	C₄²	—	67	8	no	—
1240	C₄²	C₂³×D₆₇	1	4	yes	—
1241	C₂³	—	2	2	no	—
1242	C₂³	—	2	2	no	—
1243	C₂³	—	2	2	no	—
1244	C₂³	—	2	4	no	—
1245	C₂³	—	2	4	no	—
1246	C₂³	—	2	4	no	—
1247	C₂³	—	2	4	no	—
1248	C₂³	—	2	2	no	—
1249	C₂³	—	2	4	no	—
1250	C₂³	—	2	4	no	—
1251	C₂³	—	2	4	no	—
1252	C₂³	—	2	4	no	—
1253	C₂³	—	2	2	no	—
1254	C₂³	—	2	4	no	—
1255	C₂³	—	2	16	no	—
1256	C₂³	—	4	8	no	—
1257	C₂³	—	4	8	no	—
1258	C₂³	—	4	8	no	—
1259	C₂³	—	4	8	no	—
1260	C₂³	—	4	8	no	—
1261	C₂³	—	8	16	no	—
1262	C₂³	—	8	16	no	—
1263	C₂³	—	268	8	no	—
1264	C₂³	—	268	8	no	—
1265	C₂³	—	268	8	no	—
1266	C₂³	—	536	16	no	—
1267	C₂³	—	67	2	no	—
1268	C₂³	—	67	4	no	—
1269	C₂³	—	134	4	no	—
1270	C₂³	—	134	4	no	—
1271	C₂³	—	134	2	no	—
1272	C₂³	—	134	2	no	—
1273	C₂³	—	134	4	no	—
1274	C₂³	—	134	2	no	—
1275	C₂³	#14524088	1	4	yes	—
1276	C₂³	C₂⁴×D₆₇	1	4	yes	—
1277	C₂³	C₂⁴×D₆₇	1	2	yes	—
1278	C₂³	C₂⁴×D₆₇	1	4	yes	—
1279	C₂³	C₂⁴×D₆₇	1	4	yes	—
1280	C₂³	C₂⁴×D₆₇	1	2	yes	—
1281	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1282	Q₈	—	268	8	no	—
1283	Q₈	—	268	8	no	—
1284	Q₈	—	268	4	no	—
1285	Q₈	—	134	8	no	—
1286	Q₈	—	134	8	no	—
1287	D₄	—	2	8	no	—
1288	D₄	—	2	16	no	—
1289	D₄	—	2	8	no	—
1290	D₄	—	2	8	no	—
1291	D₄	—	2	8	no	—
1292	D₄	—	4	8	no	—
1293	D₄	—	4	8	no	—
1294	D₄	—	4	8	no	—
1295	D₄	—	4	8	no	—
1296	D₄	—	4	8	no	—
1297	D₄	—	268	8	no	—
1298	D₄	—	268	8	no	—
1299	D₄	—	268	8	no	—
1300	D₄	—	268	8	no	—
1301	D₄	—	268	8	no	—
1302	D₄	—	268	8	no	—
1303	D₄	—	268	8	no	—
1304	D₄	—	268	4	no	—
1305	D₄	—	268	8	no	—
1306	D₄	—	134	8	no	—
1307	D₄	—	134	16	no	—
1308	D₄	—	134	8	no	—
1309	C₂×C₄	—	2	2	no	—
1310	C₂×C₄	—	2	2	no	—
1311	C₂×C₄	—	2	2	no	—
1312	C₂×C₄	—	2	4	no	—
1313	C₂×C₄	—	2	2	no	—
1314	C₂×C₄	—	2	8	no	—
1315	C₂×C₄	—	2	8	no	—
1316	C₂×C₄	—	4	8	no	—
1317	C₂×C₄	—	268	8	no	—
1318	C₂×C₄	—	268	8	no	—
1319	C₂×C₄	—	268	8	no	—
1320	C₂×C₄	—	268	8	no	—
1321	C₂×C₄	—	268	8	no	—
1322	C₂×C₄	—	268	8	no	—
1323	C₂×C₄	—	268	4	no	—
1324	C₂×C₄	—	67	2	no	—
1325	C₂×C₄	—	67	2	no	—
1326	C₂×C₄	—	67	2	no	—
1327	C₂×C₄	—	67	2	no	—
1328	C₂×C₄	—	67	2	no	—
1329	C₂×C₄	—	67	4	no	—
1330	C₂×C₄	—	67	4	no	—
1331	C₂×C₄	—	67	4	no	—
1332	C₂×C₄	—	67	2	no	—
1333	C₂×C₄	—	67	2	no	—
1334	C₂×C₄	—	134	2	no	—
1335	C₂×C₄	—	134	2	no	—
1336	C₂×C₄	—	134	2	no	—
1337	C₂×C₄	—	134	4	no	—
1338	C₂×C₄	—	134	4	no	—
1339	C₂×C₄	—	134	4	no	—
1340	C₂×C₄	—	134	2	no	—
1341	C₂×C₄	—	134	8	no	—
1342	C₂×C₄	—	134	2	no	—
1343	C₂×C₄	—	134	2	no	—
1344	C₂×C₄	—	134	2	no	—
1345	C₂×C₄	—	134	8	no	—
1346	C₂×C₄	#14524088	1	4	yes	—
1347	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1348	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1349	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1350	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1351	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1352	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1353	C₂²	—	2	8	no	—
1354	C₂²	—	2	2	no	—
1355	C₂²	—	2	2	no	—
1356	C₂²	—	2	2	no	—
1357	C₂²	—	2	4	no	—
1358	C₂²	—	2	4	no	—
1359	C₂²	—	2	4	no	—
1360	C₂²	—	2	4	no	—
1361	C₂²	—	2	2	no	—
1362	C₂²	—	2	4	no	—
1363	C₂²	—	2	4	no	—
1364	C₂²	—	2	4	no	—
1365	C₂²	—	2	4	no	—
1366	C₂²	—	2	2	no	—
1367	C₂²	—	2	4	no	—
1368	C₂²	—	4	4	no	—
1369	C₂²	—	4	8	no	—
1370	C₂²	—	4	8	no	—
1371	C₂²	—	4	8	no	—
1372	C₂²	—	8	16	no	—
1373	C₂²	—	8	16	no	—
1374	C₂²	—	268	4	no	—
1375	C₂²	—	268	8	no	—
1376	C₂²	—	536	16	no	—
1377	C₂²	—	134	4	no	—
1378	C₂²	—	134	4	no	—
1379	C₂²	—	134	2	no	—
1380	C₂²	—	134	2	no	—
1381	C₂²	—	134	4	no	—
1382	C₂²	—	134	2	no	—
1383	C₂²	C₂×#14524088	1	4	yes	—
1384	C₂²	C₂×#14524088	1	2	yes	—
1385	C₂²	C₂×#14524088	1	2	yes	—
1386	C₂²	#16864231	1	2	yes	—
1387	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1388	C₄	—	2	2	no	—
1389	C₄	—	2	2	no	—
1390	C₄	—	2	2	no	—
1391	C₄	—	2	4	no	—
1392	C₄	—	2	2	no	—
1393	C₄	—	134	2	no	—
1394	C₄	—	134	2	no	—
1395	C₄	—	134	2	no	—
1396	C₄	—	134	4	no	—
1397	C₄	—	134	4	no	—
1398	C₄	—	134	4	no	—
1399	C₄	—	134	2	no	—
1400	C₄	—	134	2	no	—
1401	C₄	—	134	2	no	—
1402	C₄	—	134	2	no	—
1403	C₄	C₂×#14524088	1	4	yes	—
1404	C₂	—	2	4	no	—
1405	C₂	—	4	2	no	—
1406	C₂	—	4	4	no	—
1407	C₂	—	4	4	no	—
1408	C₂	—	4	4	no	—
1409	C₂	—	268	2	no	—
1410	C₂	—	268	4	no	—
1411	C₂	#22574723	1	4	yes	direct product factor
1412	C₂	C₂²×#14524088	1	1	yes	characteristic
1413	C₂	C₂²×#14524088	1	1	yes	characteristic
1414	C₂	C₂×#16864231	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×D₄²×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×D₄²	D₆₇
hypocenter	C₆₇	C₂×#3558
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×D₄²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #22574723	C₂	direct (N × H)
2. C₂×#16864141	C₂	semidirect
3. C₂×#16864139	C₂	semidirect
4. C₂×#16864132	C₂	semidirect
5. C₂×#16864129	C₂	semidirect
6. C₂×#16864055	C₂	semidirect
7. C₂×#16864052	C₂	semidirect
8. C₂×#16864043	C₂	semidirect
9. C₂×#16864040	C₂	semidirect
10. C₂×#16864040	C₂	semidirect
11. C₂×#16864033	C₂	semidirect
12. C₂×D₄×C₂²⋊D₆₇	C₂	semidirect
13. C₂×#16864013	C₂	semidirect
14. C₂×#16864011	C₂	semidirect
15. C₂×#16863981	C₂	semidirect
16. C₂×#16863981	C₂	semidirect
17. C₂×#16863978	C₂	semidirect
18. C₂×#16863963	C₂	semidirect
19. C₂×#16863959	C₂	semidirect
20. C₂×#16863955	C₂	semidirect
21. C₂×#16863941	C₂	semidirect
22. C₂×#16863926	C₂	semidirect
23. C₂²×#14524030	C₂	semidirect
24. C₂×D₄²×C₆₇	C₂	semidirect
25. C₂²×#11761628	C₂²	semidirect
26. C₂²×#11761627	C₂²	semidirect
27. C₂²×#11761627	C₂²	semidirect
28. C₂³×Dic₁₃₄	C₂²	semidirect
29. C₂³×C₂²⋊D₆₇	C₂²	semidirect
30. C₂²×D₄×D₆₇	C₂²	semidirect
31. #16864141	C₂²	semidirect
32. #16864139	C₂²	semidirect
33. #16864132	C₂²	semidirect
34. #16864129	C₂²	semidirect
35. #16864055	C₂²	semidirect
36. #16864052	C₂²	semidirect
37. #16864043	C₂²	semidirect
38. #16864040	C₂²	semidirect
39. #16864040	C₂²	semidirect
40. #16864033	C₂²	semidirect
41. D₄×C₂²⋊D₆₇	C₂²	semidirect
42. #16864013	C₂²	semidirect
43. #16864011	C₂²	semidirect
44. #16863981	C₂²	semidirect
45. #16863981	C₂²	semidirect
46. #16863978	C₂²	semidirect
47. #16863963	C₂²	semidirect
48. #16863959	C₂²	semidirect
49. #16863955	C₂²	semidirect
50. #16863941	C₂²	semidirect
51. C₂×#14524042	C₂²	semidirect
53. C₂×#14524039	C₂²	semidirect
54. #16863926	C₂²	semidirect
55. C₂×#14524038	C₂²	semidirect
56. C₂×#14524036	C₂²	semidirect
57. C₂×#14524036	C₂²	semidirect
58. C₂×#14524036	C₂²	semidirect
59. C₂×#14524033	C₂²	semidirect
60. C₂×#14524031	C₂²	semidirect
61. C₂×#14524030	C₂²	semidirect
62. C₂×#14524030	C₂²	semidirect
63. C₂×#14524030	C₂²	semidirect
64. C₂×#14524030	C₂²	semidirect
65. C₂×#14524030	C₂²	semidirect
66. C₂×#14524030	C₂²	semidirect
67. C₂×#14524030	C₂²	semidirect
68. C₂×#14524030	C₂²	semidirect
69. C₂×#14524030	C₂²	semidirect
70. C₂×#14524030	C₂²	semidirect
71. C₂×#14524029	C₂²	semidirect
72. C₂×#14524029	C₂²	semidirect
73. C₂×#14524029	C₂²	semidirect
74. C₂×#14524029	C₂²	semidirect
75. C₂×#14524029	C₂²	semidirect
76. C₂×#14524029	C₂²	semidirect
77. C₂×#14524027	C₂²	semidirect
78. C₂×#14524026	C₂²	semidirect
79. C₂×#14524026	C₂²	semidirect
80. C₂×#14524025	C₂²	semidirect
81. C₂×#14524025	C₂²	semidirect
82. C₂×#14524024	C₂²	semidirect
83. C₂×#14524024	C₂²	semidirect
84. C₂×#14524024	C₂²	semidirect
85. C₂×#14524024	C₂²	semidirect
86. C₂×#14524024	C₂²	semidirect
87. C₂×#14524023	C₂²	semidirect
88. C₂×#14524022	C₂²	semidirect
89. C₂×#14524022	C₂²	semidirect
90. C₂×#14524021	C₂²	semidirect
91. C₂×#14524020	C₂²	semidirect
92. C₂×#14524020	C₂²	semidirect
93. C₂×#14524020	C₂²	semidirect
94. C₂×#14524017	C₂²	semidirect
96. C₂×#14524015	C₂²	semidirect
97. C₂×#14524015	C₂²	semidirect
98. C₂×#14524015	C₂²	semidirect
99. C₂×#14524015	C₂²	semidirect
100. C₂×#14524015	C₂²	semidirect
101. C₂×#14524015	C₂²	semidirect
102. C₂×#14524015	C₂²	semidirect
104. C₂×#14524014	C₂²	semidirect
105. C₂×#14524014	C₂²	semidirect
106. C₂×#14524014	C₂²	semidirect
107. C₂×#14524012	C₂²	semidirect
108. C₂×#14524012	C₂²	semidirect
109. C₂×#14524012	C₂²	semidirect
110. C₂×#14524012	C₂²	semidirect
111. C₂×#14524011	C₂²	semidirect
112. C₂×#14524011	C₂²	semidirect
113. C₂×#14524011	C₂²	semidirect
114. C₂×#14524011	C₂²	semidirect
115. C₂×C₄×Dic₁₃₄	C₂²	semidirect
116. C₂×C₄×Dic₁₃₄	C₂²	semidirect
117. C₂×#14524008	C₂²	semidirect
118. C₂×D₄×Dic₆₇	C₂²	semidirect
119. C₂×D₄×Dic₆₇	C₂²	semidirect
120. C₂×D₄×Dic₆₇	C₂²	semidirect
121. C₂×D₄×Dic₆₇	C₂²	semidirect
122. C₂×#14524005	C₂²	semidirect
123. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
124. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
125. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
126. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
127. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
128. C₂×#14524002	C₂²	semidirect
129. C₂×#14524000	C₂²	semidirect
130. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
131. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
132. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
133. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
134. C₂²×C₄×Dic₆₇	C₂²	semidirect
136. C₂³×D₄×C₆₇	C₂²	semidirect
137. C₂³×D₄×C₆₇	C₂²	semidirect
138. D₄²×C₆₇	C₂²	semidirect
141. C₂×#121×C₆₇	C₂²	semidirect
142. C₂×#121×C₆₇	C₂²	semidirect
143. C₂×#120×C₆₇	C₂²	semidirect
144. C₂×#120×C₆₇	C₂²	semidirect
145. C₂×C₄×D₄×C₆₇	C₂²	semidirect
146. C₂×C₄×D₄×C₆₇	C₂²	semidirect
149. C₂×#11761628	C₂³	semidirect
152. C₂×#11761627	C₂³	semidirect
153. C₂×#11761627	C₂³	semidirect
160. C₂²×Dic₁₃₄	C₂³	semidirect
174. C₂²×C₂²⋊D₆₇	C₂³	semidirect
176. C₂×D₄×D₆₇	C₂³	semidirect
186. #14524042	C₂³	semidirect
188. #14524039	C₂³	semidirect
189. #14524038	C₂³	semidirect
190. #14524036	C₂³	semidirect
191. #14524036	C₂³	semidirect
192. #14524036	C₂³	semidirect
193. #14524033	C₂³	semidirect
194. #14524031	C₂³	semidirect
195. #14524030	C₂³	semidirect
196. #14524030	C₂³	semidirect
197. #14524030	C₂³	semidirect
198. #14524030	C₂³	semidirect
199. #14524030	C₂³	semidirect
200. #14524030	C₂³	semidirect
201. #14524030	C₂³	semidirect
202. #14524030	C₂³	semidirect
203. #14524030	C₂³	semidirect
204. #14524029	C₂³	semidirect
205. #14524029	C₂³	semidirect
206. #14524029	C₂³	semidirect
207. #14524029	C₂³	semidirect
208. #14524029	C₂³	semidirect
209. #14524029	C₂³	semidirect
210. #14524027	C₂³	semidirect
211. #14524026	C₂³	semidirect
212. #14524026	C₂³	semidirect
213. #14524025	C₂³	semidirect
214. #14524025	C₂³	semidirect
215. #14524024	C₂³	semidirect
216. #14524024	C₂³	semidirect
217. #14524024	C₂³	semidirect
218. #14524024	C₂³	semidirect
219. #14524024	C₂³	semidirect
220. #14524023	C₂³	semidirect
221. #14524022	C₂³	semidirect
222. #14524022	C₂³	semidirect
223. #14524021	C₂³	semidirect
224. #14524020	C₂³	semidirect
225. #14524020	C₂³	semidirect
226. #14524020	C₂³	semidirect
227. #14524017	C₂³	semidirect
229. #14524015	C₂³	semidirect
230. #14524015	C₂³	semidirect
231. #14524015	C₂³	semidirect
232. #14524015	C₂³	semidirect
233. #14524015	C₂³	semidirect
234. #14524015	C₂³	semidirect
235. #14524015	C₂³	semidirect
237. #14524014	C₂³	semidirect
238. #14524014	C₂³	semidirect
239. #14524014	C₂³	semidirect
240. #14524012	C₂³	semidirect
241. #14524012	C₂³	semidirect
242. #14524012	C₂³	semidirect
243. #14524012	C₂³	semidirect
244. #14524011	C₂³	semidirect
245. #14524011	C₂³	semidirect
246. #14524011	C₂³	semidirect
247. #14524011	C₂³	semidirect
248. C₄×Dic₁₃₄	C₂³	semidirect
249. C₄×Dic₁₃₄	C₂³	semidirect
250. #14524008	C₂³	semidirect
251. D₄×Dic₆₇	C₂³	semidirect
252. D₄×Dic₆₇	C₂³	semidirect
253. D₄×Dic₆₇	C₂³	semidirect
254. D₄×Dic₆₇	C₂³	semidirect
255. #14524005	C₂³	semidirect
256. C₄×C₂²⋊D₆₇	C₂³	semidirect
257. C₄×C₂²⋊D₆₇	C₂³	semidirect
258. C₄×C₂²⋊D₆₇	C₂³	semidirect
259. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
260. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
261. #14524002	C₂³	semidirect
262. #14524000	C₂³	semidirect
296. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
297. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
298. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
308. C₂²⋊C₄×D₆₇	C₂³	semidirect
316. C₂×C₄×Dic₆₇	C₂³	semidirect
333. C₂²×D₄×C₆₇	C₂³	semidirect
334. C₂²×D₄×C₆₇	C₂³	semidirect
340. #121×C₆₇	C₂³	semidirect
341. #121×C₆₇	C₂³	semidirect
342. #120×C₆₇	C₂³	semidirect
343. #120×C₆₇	C₂³	semidirect
344. C₄×D₄×C₆₇	C₂³	semidirect
345. C₄×D₄×C₆₇	C₂³	semidirect
702. C₂×C₆₇	#3558	semidirect
720. C₂×D₄²	D₆₇	semidirect
732. C₆₇	C₂×#3558	semidirect
740. C₂³×D₄	C₂×D₆₇	semidirect
741. C₂³×D₄	C₂×D₆₇	semidirect
753. D₄²	C₂×D₆₇	semidirect
821. C₂×#121	C₂×D₆₇	semidirect
822. C₂×#121	C₂×D₆₇	semidirect
831. C₂×#120	C₂×D₆₇	semidirect
832. C₂×#120	C₂×D₆₇	semidirect
846. C₂×C₄×D₄	C₂×D₆₇	semidirect
847. C₂×C₄×D₄	C₂×D₆₇	semidirect
901. C₂²×D₄	C₂²×D₆₇	semidirect
902. C₂²×D₄	C₂²×D₆₇	semidirect
971. #121	C₂²×D₆₇	semidirect
972. #121	C₂²×D₆₇	semidirect
981. #120	C₂²×D₆₇	semidirect
982. #120	C₂²×D₆₇	semidirect
996. C₄×D₄	C₂²×D₆₇	semidirect
997. C₄×D₄	C₂²×D₆₇	semidirect
1411. C₂	#22574723	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22574723	2
C₂×#16864141	2
C₂×#16864139	2
C₂×#16864132	2
C₂×#16864129	2
C₂×#16864055	2
C₂×#16864052	2
C₂×#16864043	2
C₂×#16864040	2
C₂×#16864033	2
C₂×D₄×C₂²⋊D₆₇	2
C₂×#16864013	2
C₂×#16864011	2
C₂×#16863981	2
C₂×#16863978	2
C₂×#16863963	2
C₂×#16863959	2
C₂×#16863955	2
C₂×#16863941	2
C₂×#16863926	2
C₂²×#14524030	2
C₂×D₄²×C₆₇	2
C₂×#3558	67

Subgroups — C2×#22574723 #31763159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574723 #31763159