Subgroups — C₂×#22574036 #31763747

Order 17152.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574036	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864096	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864093	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864093	C₂	1	2	yes	maximal, complemented
5	C₂×#16864091	C₂	1	2	yes	maximal, complemented
6	C₂×#16864088	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16864086	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16864077	C₂	1	2	yes	maximal, complemented
9	C₂×#16864072	C₂	1	2	yes	maximal, complemented
10	C₂×#16864054	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16864053	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16864040	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16863989	C₂	1	2	yes	maximal, complemented
14	C₂×#16863978	C₂	1	2	yes	maximal, complemented
15	C₂×#16863956	C₂	1	2	yes	maximal, complemented
16	C₂×#16863928	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16863925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16863906	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16863903	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂²⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#14524014	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863869	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×D₄×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761627	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂³×C₂²⋊D₆₇	C₂²	1	2	yes	—
28	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic
29	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic
30	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
31	#16864096	C₂²	1	16	yes	complemented
32	#16864093	C₂²	1	16	yes	complemented
33	#16864093	C₂²	1	32	yes	complemented
34	#16864091	C₂²	1	32	yes	complemented
35	#16864088	C₂²	1	16	yes	complemented
36	#16864086	C₂²	1	16	yes	complemented
37	#16864077	C₂²	1	32	yes	complemented
38	#16864072	C₂²	1	32	yes	complemented
39	#16864054	C₂²	1	16	yes	complemented
40	#16864053	C₂²	1	16	yes	complemented
41	#16864040	C₂²	1	16	yes	complemented
42	#16863989	C₂²	1	32	yes	complemented
43	#16863978	C₂²	1	32	yes	complemented
44	#16863956	C₂²	1	32	yes	complemented
45	#16863928	C₂²	1	16	yes	complemented
46	#16863925	C₂²	1	16	yes	complemented
47	C₂×#14524038	C₂²	1	2	yes	complemented
48	C₂×#14524036	C₂²	1	2	yes	complemented
49	C₂×#14524036	C₂²	1	2	yes	complemented
50	C₂×#14524036	C₂²	1	2	yes	complemented
51	C₂×#14524036	C₂²	1	2	yes	complemented
52	C₂×#14524036	C₂²	1	2	yes	complemented
53	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
54	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
55	C₂×#14524034	C₂²	1	2	yes	complemented
56	C₂×#14524033	C₂²	1	2	yes	complemented
57	C₂×#14524030	C₂²	1	1	yes	characteristic, complemented
58	C₂×#14524030	C₂²	1	2	yes	complemented
59	C₂×#14524029	C₂²	1	2	yes	complemented
60	#16863906	C₂²	1	16	yes	complemented
61	#16863903	C₂²	1	16	yes	complemented
62	C₂×#14524027	C₂²	1	2	yes	—
63	C₂×#14524026	C₂²	1	2	yes	complemented
64	C₂×#14524025	C₂²	1	2	yes	complemented
65	C₂×#14524025	C₂²	1	2	yes	complemented
66	C₂×#14524025	C₂²	1	2	yes	complemented
67	C₂×#14524024	C₂²	1	2	yes	—
68	C₂×#14524024	C₂²	1	2	yes	complemented
69	C₂×#14524024	C₂²	1	2	yes	complemented
70	C₂×#14524024	C₂²	1	2	yes	complemented
71	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
72	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
73	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
74	C₂×#14524022	C₂²	1	2	yes	complemented
75	C₂×#14524021	C₂²	1	2	yes	complemented
76	C₂×#14524020	C₂²	1	2	yes	complemented
77	C₂×#14524020	C₂²	1	2	yes	complemented
78	C₂×#14524019	C₂²	1	1	yes	characteristic, complemented
79	C₂×#14524019	C₂²	1	1	yes	characteristic, complemented
80	C₂²⋊Q₈×D₆₇	C₂²	1	16	yes	complemented
81	C₂×#14524016	C₂²	1	2	yes	complemented
82	C₂×#14524016	C₂²	1	2	yes	complemented
83	C₂×#14524015	C₂²	1	2	yes	complemented
84	C₂×#14524014	C₂²	1	1	yes	characteristic
85	C₂×#14524014	C₂²	1	1	yes	characteristic
86	C₂×#14524014	C₂²	1	2	yes	—
87	C₂×#14524014	C₂²	1	1	yes	characteristic, complemented
88	C₂×#14524014	C₂²	1	1	yes	characteristic, complemented
89	C₂×#14524014	C₂²	1	2	yes	complemented
90	C₂×#14524014	C₂²	1	1	yes	characteristic, complemented
91	C₂×#14524014	C₂²	1	2	yes	complemented
92	C₂×#14524014	C₂²	1	2	yes	complemented
93	C₂×#14524014	C₂²	1	16	yes	complemented
94	C₂×#14524012	C₂²	1	2	yes	—
95	C₂×#14524011	C₂²	1	2	yes	complemented
96	C₂×#14524011	C₂²	1	2	yes	complemented
97	#16863869	C₂²	1	32	yes	complemented
98	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
101	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
102	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
104	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
106	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
108	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
109	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
110	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
111	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
112	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
113	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
115	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
116	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
117	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
118	C₄×D₄×D₆₇	C₂²	1	16	yes	complemented
119	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
120	C₂×#14524002	C₂²	1	2	yes	complemented
121	C₂×#14524001	C₂²	1	1	yes	characteristic, complemented
122	C₂×#14523999	C₂²	1	2	yes	complemented
123	C₂×#14523999	C₂²	1	2	yes	complemented
124	C₂×#14523999	C₂²	1	2	yes	complemented
125	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
128	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₂²×C₂²⋊Dic₆₇	C₂²	1	2	yes	complemented
130	C₂²×C₂²⋊Dic₆₇	C₂²	1	2	yes	complemented
131	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
133	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	#546×C₆₇	C₂²	1	16	yes	complemented
138	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
140	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
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	—
144	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
145	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
146	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
147	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
148	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
149	C₂×#11761627	—	4	4	no	—
150	C₂×#11761627	C₂³	1	8	yes	complemented
151	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
152	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
153	C₂×Q₈×D₆₇	—	4	4	no	—
154	C₂×Q₈×D₆₇	C₂³	1	8	yes	complemented
155	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
156	C₂²×C₂²⋊D₆₇	—	2	16	no	—
157	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
158	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
159	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
160	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
161	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
162	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
163	C₂²×C₂²⋊D₆₇	C₂³	1	16	yes	—
164	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
165	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
166	C₂×D₄×D₆₇	—	2	8	no	—
167	C₂×D₄×D₆₇	C₂³	1	8	yes	—
168	C₂³×Dic₆₇	C₂³	1	2	yes	—
169	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
170	C₂³×Dic₆₇	C₂³	1	2	yes	—
171	C₂³×Dic₆₇	C₂³	1	2	yes	—
172	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
173	C₂²×C₄×D₆₇	—	4	4	no	—
174	C₂²×C₄×D₆₇	—	4	4	no	—
175	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
176	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
178	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
179	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
181	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
182	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
183	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
184	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
185	C₂²×C₄×D₆₇	C₂³	1	8	yes	—
186	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
187	C₂²×C₄×D₆₇	C₂³	1	8	yes	complemented
188	#14524038	C₂³	1	16	yes	complemented
189	#14524036	C₂³	1	16	yes	complemented
190	#14524036	C₂³	1	16	yes	complemented
191	#14524036	C₂³	1	16	yes	complemented
192	#14524036	C₂³	1	16	yes	complemented
193	#14524036	C₂³	1	16	yes	complemented
194	#14524035	C₂³	1	8	yes	complemented
195	#14524034	C₂³	1	8	yes	complemented
196	#14524034	C₂³	1	16	yes	complemented
197	#14524033	C₂³	1	16	yes	complemented
198	#14524030	C₂³	1	8	yes	complemented
199	#14524030	C₂³	1	16	yes	complemented
200	#14524029	C₂³	1	16	yes	complemented
201	#14524027	C₂³	1	16	yes	—
202	#14524026	C₂³	1	16	yes	complemented
203	#14524025	C₂³	1	16	yes	complemented
204	#14524025	C₂³	1	16	yes	complemented
205	#14524025	C₂³	1	16	yes	complemented
206	#14524024	C₂³	1	16	yes	—
207	#14524024	C₂³	1	16	yes	complemented
208	#14524024	C₂³	1	16	yes	complemented
209	#14524024	C₂³	1	16	yes	complemented
210	#14524023	C₂³	1	8	yes	complemented
211	#14524022	C₂³	1	8	yes	complemented
212	#14524022	C₂³	1	16	yes	complemented
213	#14524022	C₂³	1	8	yes	complemented
214	#14524021	C₂³	1	16	yes	complemented
215	#14524020	C₂³	1	16	yes	complemented
216	#14524020	C₂³	1	16	yes	complemented
217	#14524019	C₂³	1	8	yes	complemented
218	#14524019	C₂³	1	8	yes	complemented
219	#14524016	C₂³	1	16	yes	complemented
220	#14524016	C₂³	1	16	yes	complemented
221	#14524015	C₂³	1	16	yes	complemented
222	#14524014	C₂³	1	8	yes	—
223	#14524014	C₂³	1	8	yes	—
224	#14524014	C₂³	1	16	yes	—
225	#14524014	C₂³	1	8	yes	complemented
226	#14524014	C₂³	1	16	yes	complemented
227	#14524014	C₂³	1	8	yes	complemented
228	#14524014	C₂³	1	8	yes	complemented
229	#14524014	C₂³	1	16	yes	complemented
230	#14524014	C₂³	1	16	yes	complemented
231	#14524012	C₂³	1	16	yes	—
232	#14524011	C₂³	1	16	yes	complemented
233	#14524011	C₂³	1	16	yes	complemented
234	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
235	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
236	C₄×D₂₆₈	C₂³	1	8	yes	complemented
237	D₄×Dic₆₇	C₂³	1	8	yes	—
238	D₄×Dic₆₇	C₂³	1	8	yes	complemented
239	D₄×Dic₆₇	C₂³	1	16	yes	complemented
240	#14524005	C₂³	1	8	yes	complemented
241	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
242	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
243	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
244	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
245	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
246	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
247	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
248	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
249	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
250	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
251	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
252	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
253	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
254	#14524002	C₂³	1	16	yes	complemented
255	#14524002	C₂³	1	8	yes	complemented
256	#14524001	C₂³	1	8	yes	complemented
257	#14523999	C₂³	1	16	yes	complemented
258	#14523999	C₂³	1	16	yes	complemented
259	#14523999	C₂³	1	16	yes	complemented
260	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
262	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
266	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
267	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
268	C₂×C₄⋊Dic₆₇	C₂³	1	8	yes	complemented
269	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
270	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
273	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
274	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
275	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
276	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
277	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
278	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
279	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
280	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
281	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
282	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
283	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
285	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
290	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
291	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
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×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
302	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
303	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
304	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
305	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
306	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
307	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
308	C₂²⋊C₄×D₆₇	C₂³	1	8	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	2	yes	—
313	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
314	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
315	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
316	C₄²×D₆₇	C₂³	1	8	yes	complemented
317	C₂⁵×C₆₇	C₂³	1	2	yes	—
318	C₂×#41×C₆₇	—	4	4	no	—
319	C₂×#41×C₆₇	C₂³	1	8	yes	complemented
320	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
321	C₂²×D₄×C₆₇	—	4	4	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	1	yes	characteristic
325	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
326	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
327	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
328	C₂²×D₄×C₆₇	C₂³	1	8	yes	complemented
329	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
332	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
333	#124×C₆₇	C₂³	1	8	yes	complemented
334	#123×C₆₇	C₂³	1	16	yes	complemented
335	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
336	#121×C₆₇	C₂³	1	8	yes	complemented
337	#121×C₆₇	C₂³	1	16	yes	complemented
338	#120×C₆₇	C₂³	1	16	yes	—
339	C₄×D₄×C₆₇	C₂³	1	8	yes	—
340	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
341	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
344	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
346	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
347	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
351	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
352	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
353	C₂³×D₆₇	—	2	4	no	—
354	C₂³×D₆₇	—	4	2	no	—
355	C₂³×D₆₇	—	4	2	no	—
356	C₂³×D₆₇	—	4	2	no	—
357	C₂³×D₆₇	—	4	2	no	—
358	C₂³×D₆₇	#41	1	8	yes	complemented
359	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
360	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
361	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
362	C₂³×D₆₇	C₂⁴	1	4	yes	—
363	C₂³×D₆₇	C₂⁴	1	4	yes	—
364	#11761627	—	4	16	no	—
365	C₂×Dic₁₃₄	—	2	4	no	—
366	C₂×Dic₁₃₄	—	4	4	no	—
367	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
368	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
369	Q₈×D₆₇	—	4	16	no	—
370	C₂×D₂₆₈	—	2	4	no	—
371	C₂×D₂₆₈	C₂⁴	1	4	yes	—
372	C₂×C₂²⋊D₆₇	—	2	4	no	—
373	C₂×C₂²⋊D₆₇	—	2	4	no	—
374	C₂×C₂²⋊D₆₇	—	2	8	no	—
375	C₂×C₂²⋊D₆₇	—	2	8	no	—
376	C₂×C₂²⋊D₆₇	—	2	8	no	—
377	C₂×C₂²⋊D₆₇	—	2	8	no	—
378	C₂×C₂²⋊D₆₇	—	2	64	no	—
379	C₂×C₂²⋊D₆₇	—	4	4	no	—
380	C₂×C₂²⋊D₆₇	—	4	4	no	—
381	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
382	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
383	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
384	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
385	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
386	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
387	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
388	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
389	D₄×D₆₇	—	2	32	no	—
390	C₂²×Dic₆₇	—	2	8	no	—
391	C₂²×Dic₆₇	—	4	2	no	—
392	C₂²×Dic₆₇	—	4	2	no	—
393	C₂²×Dic₆₇	—	4	4	no	—
394	C₂²×Dic₆₇	—	4	4	no	—
395	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
397	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
398	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
402	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
403	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
405	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
406	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
407	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
408	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
409	C₂×C₄×D₆₇	—	2	4	no	—
410	C₂×C₄×D₆₇	—	2	4	no	—
411	C₂×C₄×D₆₇	—	2	4	no	—
412	C₂×C₄×D₆₇	—	2	4	no	—
413	C₂×C₄×D₆₇	—	4	16	no	—
414	C₂×C₄×D₆₇	—	4	16	no	—
415	C₂×C₄×D₆₇	—	4	2	no	—
416	C₂×C₄×D₆₇	—	4	2	no	—
417	C₂×C₄×D₆₇	—	4	2	no	—
418	C₂×C₄×D₆₇	—	4	2	no	—
419	C₂×C₄×D₆₇	—	4	2	no	—
420	C₂×C₄×D₆₇	—	4	4	no	—
421	C₂×C₄×D₆₇	—	4	4	no	—
422	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
423	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
424	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
425	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
426	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
427	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
428	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
429	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
430	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
431	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
432	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
433	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
434	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
435	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
436	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
437	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
438	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
439	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
440	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
441	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
442	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
443	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
444	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
445	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
446	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
447	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
448	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
449	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
450	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
451	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
452	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
453	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
454	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
455	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
456	C₂²⋊Dic₆₇	C₂⁴	1	8	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	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
462	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
463	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
464	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
465	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
466	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
467	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
468	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
469	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
470	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
471	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
472	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
473	C₄×Dic₆₇	C₂⁴	1	4	yes	—
474	C₄×Dic₆₇	C₂⁴	1	4	yes	—
475	C₄×Dic₆₇	C₂⁴	1	4	yes	—
476	C₄×Dic₆₇	C₂⁴	1	8	yes	—
477	C₄×Dic₆₇	C₂⁴	1	8	yes	—
478	C₄×Dic₆₇	C₂⁴	1	8	yes	—
479	C₄×Dic₆₇	C₂⁴	1	8	yes	—
480	C₂⁴×C₆₇	—	2	8	no	—
481	C₂⁴×C₆₇	—	4	4	no	—
482	C₂⁴×C₆₇	—	4	4	no	—
483	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
484	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
485	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
486	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
487	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
488	#41×C₆₇	—	4	16	no	—
489	C₂×Q₈×C₆₇	—	2	4	no	—
490	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
491	C₂×D₄×C₆₇	—	2	4	no	—
492	C₂×D₄×C₆₇	—	2	4	no	—
493	C₂×D₄×C₆₇	—	2	4	no	—
494	C₂×D₄×C₆₇	—	4	16	no	—
495	C₂×D₄×C₆₇	—	4	4	no	—
496	C₂×D₄×C₆₇	—	4	4	no	—
497	C₂×D₄×C₆₇	—	4	4	no	—
498	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
499	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
500	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
501	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
502	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
503	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
504	C₂²×C₄×C₆₇	—	2	4	no	—
505	C₂²×C₄×C₆₇	—	2	4	no	—
506	C₂²×C₄×C₆₇	—	4	4	no	—
507	C₂²×C₄×C₆₇	—	4	4	no	—
508	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
510	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
511	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
512	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
513	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
515	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
516	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
517	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
518	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
519	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
520	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
521	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
522	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
523	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
524	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
525	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
526	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
527	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
528	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
529	C₄²×C₆₇	C₂⁴	1	4	yes	—
530	C₂³×C₆₇	—	2	2	no	—
531	C₂³×C₆₇	—	2	2	no	—
532	C₂³×C₆₇	—	2	2	no	—
533	C₂³×C₆₇	—	2	4	no	—
534	C₂³×C₆₇	—	2	4	no	—
535	C₂³×C₆₇	—	2	2	no	—
536	C₂³×C₆₇	—	2	4	no	—
537	C₂³×C₆₇	—	2	4	no	—
538	C₂³×C₆₇	—	2	4	no	—
539	C₂³×C₆₇	—	2	2	no	—
540	C₂³×C₆₇	—	2	4	no	—
541	C₂³×C₆₇	—	2	16	no	—
542	C₂³×C₆₇	—	4	8	no	—
543	C₂³×C₆₇	—	4	8	no	—
544	C₂³×C₆₇	—	8	16	no	—
545	C₂³×C₆₇	C₂×#41	1	4	yes	—
546	C₂³×C₆₇	C₂⁵	1	4	yes	—
547	C₂³×C₆₇	C₂⁵	1	4	yes	—
548	C₂³×C₆₇	C₂⁵	1	2	yes	—
549	C₂³×C₆₇	C₂⁵	1	2	yes	—
550	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
551	C₂²×D₆₇	—	2	2	no	—
552	C₂²×D₆₇	—	2	2	no	—
553	C₂²×D₆₇	—	2	2	no	—
554	C₂²×D₆₇	—	2	2	no	—
555	C₂²×D₆₇	—	2	2	no	—
556	C₂²×D₆₇	—	2	2	no	—
557	C₂²×D₆₇	—	2	2	no	—
558	C₂²×D₆₇	—	2	8	no	—
559	C₂²×D₆₇	—	4	4	no	—
560	C₂²×D₆₇	—	4	4	no	—
561	C₂²×D₆₇	—	4	16	no	—
562	C₂²×D₆₇	—	4	4	no	—
563	C₂²×D₆₇	—	4	4	no	—
564	C₂²×D₆₇	—	4	16	no	—
565	C₂²×D₆₇	C₂×#41	1	4	yes	—
566	C₂²×D₆₇	C₂×#41	1	4	yes	—
567	C₂²×D₆₇	C₂×#41	1	16	yes	complemented
568	C₂²×D₆₇	C₂⁵	1	2	yes	—
569	C₂²×D₆₇	C₂⁵	1	2	yes	—
570	C₂²×D₆₇	C₂⁵	1	2	yes	—
571	Q₈×C₆₇	—	2	8	no	—
572	D₄×C₆₇	—	2	8	no	—
573	D₄×C₆₇	—	2	8	no	—
574	D₄×C₆₇	—	2	8	no	—
575	D₄×C₆₇	—	4	8	no	—
576	D₄×C₆₇	—	4	8	no	—
577	D₄×C₆₇	—	4	8	no	—
578	C₂×C₄×C₆₇	—	2	2	no	—
579	C₂×C₄×C₆₇	—	2	2	no	—
580	C₂×C₄×C₆₇	—	2	2	no	—
581	C₂×C₄×C₆₇	—	2	4	no	—
582	C₂×C₄×C₆₇	—	2	2	no	—
583	C₂×C₄×C₆₇	—	2	4	no	—
584	C₂×C₄×C₆₇	—	2	8	no	—
585	C₂×C₄×C₆₇	—	2	8	no	—
586	C₂×C₄×C₆₇	—	4	8	no	—
587	C₂×C₄×C₆₇	—	4	8	no	—
588	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
589	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
590	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
591	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
592	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
593	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
594	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
595	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
596	C₂²⋊D₆₇	—	2	8	no	—
597	C₂²⋊D₆₇	—	2	8	no	—
598	C₂²⋊D₆₇	—	2	16	no	—
599	C₂²⋊D₆₇	—	2	16	no	—
600	C₂²⋊D₆₇	—	2	16	no	—
601	C₂²⋊D₆₇	—	2	16	no	—
602	C₂²⋊D₆₇	—	4	8	no	—
603	C₂²⋊D₆₇	—	4	8	no	—
604	C₂×Dic₆₇	—	2	2	no	—
605	C₂×Dic₆₇	—	2	16	no	—
606	C₂×Dic₆₇	—	2	4	no	—
607	C₂×Dic₆₇	—	2	4	no	—
608	C₂×Dic₆₇	—	2	2	no	—
609	C₂×Dic₆₇	—	2	2	no	—
610	C₂×Dic₆₇	—	2	2	no	—
611	C₂×Dic₆₇	—	2	4	no	—
612	C₂×Dic₆₇	—	2	2	no	—
613	C₂×Dic₆₇	—	2	4	no	—
614	C₂×Dic₆₇	—	4	4	no	—
615	C₂×Dic₆₇	—	4	4	no	—
616	C₂×Dic₆₇	—	4	8	no	—
617	C₂×Dic₆₇	—	4	8	no	—
618	C₂×Dic₆₇	C₂⁵	1	2	yes	—
619	C₂×Dic₆₇	C₂⁵	1	4	yes	—
620	C₂×Dic₆₇	C₂⁵	1	4	yes	—
621	C₂×Dic₆₇	C₂⁵	1	2	yes	—
622	C₂×Dic₆₇	C₂⁵	1	2	yes	—
623	C₂×Dic₆₇	C₂⁵	1	2	yes	—
624	C₂×Dic₆₇	C₂⁵	1	4	yes	—
625	C₂×Dic₆₇	C₂⁵	1	4	yes	—
626	C₂×Dic₆₇	C₂⁵	1	2	yes	—
627	D₂₆₈	—	2	8	no	—
628	C₄×D₆₇	—	2	8	no	—
629	C₄×D₆₇	—	2	8	no	—
630	C₄×D₆₇	—	2	8	no	—
631	C₄×D₆₇	—	2	8	no	—
632	C₄×D₆₇	—	4	4	no	—
633	C₄×D₆₇	—	4	4	no	—
634	C₄×D₆₇	—	4	4	no	—
635	C₄×D₆₇	—	4	4	no	—
636	C₄×D₆₇	—	4	4	no	—
637	C₄×D₆₇	—	4	8	no	—
638	C₄×D₆₇	—	4	8	no	—
639	Dic₁₃₄	—	2	8	no	—
640	Dic₁₃₄	—	4	8	no	—
641	C₂²×C₆₇	—	2	2	no	—
642	C₂²×C₆₇	—	2	2	no	—
643	C₂²×C₆₇	—	2	8	no	—
644	C₂²×C₆₇	—	2	4	no	—
645	C₂²×C₆₇	—	2	4	no	—
646	C₂²×C₆₇	—	2	2	no	—
647	C₂²×C₆₇	—	2	4	no	—
648	C₂²×C₆₇	—	2	2	no	—
649	C₂²×C₆₇	—	2	4	no	—
650	C₂²×C₆₇	—	2	4	no	—
651	C₂²×C₆₇	—	2	4	no	—
652	C₂²×C₆₇	—	2	2	no	—
653	C₂²×C₆₇	—	4	4	no	—
654	C₂²×C₆₇	—	4	8	no	—
655	C₂²×C₆₇	—	4	8	no	—
656	C₂²×C₆₇	—	8	16	no	—
657	C₂²×C₆₇	C₂²×#41	1	4	yes	—
658	C₂²×C₆₇	C₂²×#41	1	2	yes	—
659	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
660	C₂²×C₆₇	#585	1	2	yes	—
661	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
662	C₂×D₆₇	—	2	2	no	—
663	C₂×D₆₇	—	2	2	no	—
664	C₂×D₆₇	—	2	2	no	—
665	C₂×D₆₇	—	2	2	no	—
666	C₂×D₆₇	—	2	8	no	—
667	C₂×D₆₇	—	2	8	no	—
668	C₂×D₆₇	—	2	2	no	—
669	C₂×D₆₇	—	2	2	no	—
670	C₂×D₆₇	—	2	2	no	—
671	C₂×D₆₇	—	4	16	no	—
672	C₂×D₆₇	—	4	16	no	—
673	C₂×D₆₇	—	4	4	no	—
674	C₂×D₆₇	C₂²×#41	1	4	yes	—
675	C₂×D₆₇	C₂²×#41	1	4	yes	—
676	C₄×C₆₇	—	2	2	no	—
677	C₄×C₆₇	—	2	4	no	—
678	C₄×C₆₇	—	2	2	no	—
679	C₄×C₆₇	—	2	2	no	—
680	C₄×C₆₇	—	2	2	no	—
681	C₄×C₆₇	—	2	4	no	—
682	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
683	Dic₆₇	—	2	2	no	—
684	Dic₆₇	—	2	4	no	—
685	Dic₆₇	—	2	4	no	—
686	Dic₆₇	—	2	4	no	—
687	Dic₆₇	—	2	2	no	—
688	Dic₆₇	—	2	2	no	—
689	Dic₆₇	—	2	2	no	—
690	Dic₆₇	—	2	2	no	—
691	Dic₆₇	—	2	4	no	—
692	C₂×#3505	—	67	1	no	maximal, Sylow
693	C₂×C₆₇	—	2	4	no	—
694	C₂×C₆₇	—	4	2	no	—
695	C₂×C₆₇	—	4	4	no	—
696	C₂×C₆₇	—	4	4	no	—
697	C₂×C₆₇	#3505	1	4	yes	complemented
698	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
699	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
700	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
701	D₆₇	—	2	4	no	—
702	D₆₇	—	2	4	no	—
703	D₆₇	—	4	2	no	—
704	#3505	—	67	32	no	—
705	C₂×#553	—	67	2	no	—
706	C₂×#553	—	67	1	no	—
707	C₂×#553	—	67	2	no	—
708	C₂×#553	—	67	1	no	—
709	C₂×#552	—	67	1	no	—
710	C₂×#552	—	67	1	no	—
711	C₂×#551	—	67	2	no	—
712	C₂×#551	—	67	2	no	—
713	C₂×#548	—	67	1	no	—
714	C₂×#548	—	67	1	no	—
715	C₂×#546	—	67	1	no	—
716	C₂×#546	D₆₇	1	1	yes	characteristic, complemented
717	C₂×#539	—	67	2	no	—
718	C₂×#538	—	67	2	no	—
719	C₂×#534	—	67	2	no	—
720	C₂×#529	—	67	1	no	—
721	C₂×#529	—	67	1	no	—
722	C₂×#525	—	67	1	no	—
723	C₂×#525	—	67	1	no	—
724	C₂²×C₂²⋊Q₈	—	67	1	no	—
725	C₂²×#121	—	67	1	no	—
726	C₂×#518	—	67	2	no	—
727	C₂²×C₄×D₄	—	67	1	no	—
728	C₆₇	C₂×#3505	1	1	yes	characteristic, complemented, Sylow
729	C₂²×#41	—	67	1	no	—
730	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
731	C₂³×Q₈	—	67	1	no	—
732	C₂³×D₄	—	67	2	no	—
733	C₂³×D₄	—	67	1	no	—
734	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
735	C₂⁴×C₄	—	67	1	no	—
736	C₂⁴×C₄	—	67	1	no	—
737	#553	—	67	32	no	—
738	#553	—	67	16	no	—
739	#553	—	67	32	no	—
740	#553	—	67	16	no	—
741	#552	—	67	16	no	—
742	#552	—	67	16	no	—
743	#551	—	67	32	no	—
744	#551	—	67	32	no	—
745	#548	—	67	16	no	—
746	#548	—	67	16	no	—
747	#546	—	67	16	no	—
748	#546	C₂×D₆₇	1	16	yes	complemented
749	#539	—	67	32	no	—
750	#538	—	67	32	no	—
751	#534	—	67	32	no	—
752	#529	—	67	16	no	—
753	#529	—	67	16	no	—
754	C₂×#126	—	67	2	no	—
755	C₂×#126	—	67	2	no	—
756	C₂×#126	—	67	2	no	—
757	C₂×#126	—	67	2	no	—
758	C₂×#126	—	67	2	no	—
759	C₂×#126	—	67	2	no	—
760	C₂×#125	—	67	1	no	—
761	C₂×#125	—	67	2	no	—
762	C₂×#125	—	67	2	no	—
763	C₂×#125	—	67	1	no	—
764	C₂×#124	—	67	1	no	—
765	C₂×#124	—	67	2	no	—
766	C₂×#124	—	67	2	no	—
767	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
768	#525	—	67	16	no	—
769	#525	—	67	16	no	—
770	C₂×#123	—	67	2	no	—
771	C₂×#123	—	67	2	no	—
772	C₂×#123	—	67	2	no	—
773	C₂×#123	—	67	2	no	—
774	C₂×#123	—	67	2	no	—
775	C₂×#123	—	67	2	no	—
776	C₂×#123	—	67	2	no	—
777	C₂×#123	—	67	2	no	—
778	C₂×#123	—	67	2	no	—
779	C₂×#123	C₂×D₆₇	1	2	yes	complemented
780	C₂×C₂²⋊Q₈	—	67	1	no	—
781	C₂×C₂²⋊Q₈	—	67	1	no	—
782	C₂×C₂²⋊Q₈	—	67	1	no	—
783	C₂×C₂²⋊Q₈	—	67	1	no	—
784	C₂×C₂²⋊Q₈	—	67	2	no	—
785	C₂×C₂²⋊Q₈	—	67	16	no	—
786	C₂×C₂²⋊Q₈	—	67	1	no	—
787	C₂×C₂²⋊Q₈	—	67	2	no	—
788	C₂×C₂²⋊Q₈	—	67	2	no	—
789	C₂×C₂²⋊Q₈	—	67	2	no	—
790	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
791	C₂×#121	—	67	1	no	—
792	C₂×#121	—	67	1	no	—
793	C₂×#121	—	67	2	no	—
794	C₂×#121	—	67	1	no	—
795	C₂×#121	—	67	1	no	—
796	C₂×#121	—	67	2	no	—
797	C₂×#121	—	67	1	no	—
798	C₂×#121	—	67	2	no	—
799	C₂×#121	—	67	2	no	—
800	C₂×#121	—	67	2	no	—
801	C₂×#121	—	67	16	no	—
802	C₂×#121	—	67	2	no	—
803	C₂×#121	—	67	2	no	—
804	C₂×#121	C₂×D₆₇	1	1	yes	characteristic, complemented
805	C₂×#121	C₂×D₆₇	1	2	yes	complemented
806	C₂×#120	—	67	2	no	—
807	C₂×#120	—	67	2	no	—
808	C₂×#120	—	67	2	no	—
809	C₂×#120	C₂×D₆₇	1	2	yes	—
810	#518	—	67	32	no	—
811	C₂×C₄×Q₈	—	67	1	no	—
812	C₂×C₄×Q₈	—	67	1	no	—
813	C₂×C₄×D₄	—	67	1	no	—
814	C₂×C₄×D₄	—	67	2	no	—
815	C₂×C₄×D₄	—	67	1	no	—
816	C₂×C₄×D₄	—	67	1	no	—
817	C₂×C₄×D₄	—	67	1	no	—
818	C₂×C₄×D₄	—	67	2	no	—
819	C₂×C₄×D₄	—	67	2	no	—
820	C₂×C₄×D₄	—	67	2	no	—
821	C₂×C₄×D₄	—	67	2	no	—
822	C₂×C₄×D₄	—	67	2	no	—
823	C₂×C₄×D₄	—	67	16	no	—
824	C₂×C₄×D₄	—	67	1	no	—
825	C₂×C₄×D₄	—	67	1	no	—
826	C₂×C₄×D₄	—	67	1	no	—
827	C₂×C₄×D₄	—	67	2	no	—
828	C₂×C₄×D₄	—	67	2	no	—
829	C₂×C₄×D₄	—	67	2	no	—
830	C₂×C₄×D₄	—	67	2	no	—
831	C₂×C₄×D₄	—	67	1	no	—
832	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
833	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
834	C₂×#117	—	67	1	no	—
835	C₂×#117	—	67	2	no	—
836	C₂×#117	—	67	1	no	—
837	C₂×#117	—	67	2	no	—
838	C₂×#117	—	67	2	no	—
839	C₂×#117	—	67	2	no	—
840	C₂²×C₄⋊C₄	—	67	1	no	—
841	C₂²×C₄⋊C₄	—	67	1	no	—
842	C₂²×C₄⋊C₄	—	67	1	no	—
843	C₂²×C₄⋊C₄	—	67	2	no	—
844	C₂²×C₂²⋊C₄	—	67	2	no	—
845	C₂²×C₂²⋊C₄	—	67	2	no	—
846	C₂²×C₂²⋊C₄	—	67	1	no	—
847	C₂²×C₂²⋊C₄	—	67	1	no	—
848	C₂²×C₂²⋊C₄	—	67	2	no	—
849	C₂²×C₂²⋊C₄	C₂×D₆₇	1	2	yes	complemented
850	C₂²×C₄²	—	67	1	no	—
851	C₂⁵	—	67	1	no	—
852	C₂⁵	—	67	1	no	—
853	C₂⁵	C₂²×D₆₇	1	2	yes	—
854	C₂×#41	—	4	4	no	—
855	C₂×#41	—	268	4	no	—
856	C₂×#41	—	67	8	no	—
857	C₂×#41	C₂²×D₆₇	1	8	yes	complemented
858	C₂²×Q₈	—	268	4	no	—
859	C₂²×Q₈	—	67	8	no	—
860	C₂²×Q₈	—	67	2	no	—
861	C₂²×Q₈	—	67	1	no	—
862	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
863	C₂²×D₄	—	4	4	no	—
864	C₂²×D₄	—	67	2	no	—
865	C₂²×D₄	—	67	2	no	—
866	C₂²×D₄	—	67	1	no	—
867	C₂²×D₄	—	67	2	no	—
868	C₂²×D₄	—	67	2	no	—
869	C₂²×D₄	—	67	1	no	—
870	C₂²×D₄	—	67	2	no	—
871	C₂²×D₄	—	67	2	no	—
872	C₂²×D₄	—	67	16	no	—
873	C₂²×D₄	—	67	8	no	—
874	C₂²×D₄	—	67	1	no	—
875	C₂²×D₄	—	134	8	no	—
876	C₂²×D₄	—	134	16	no	—
877	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
878	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
879	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
880	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
881	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
882	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
883	C₂²×D₄	C₂²×D₆₇	1	8	yes	complemented
884	C₂³×C₄	—	268	4	no	—
885	C₂³×C₄	—	268	4	no	—
886	C₂³×C₄	—	67	1	no	—
887	C₂³×C₄	—	67	2	no	—
888	C₂³×C₄	—	67	2	no	—
889	C₂³×C₄	—	67	1	no	—
890	C₂³×C₄	—	67	1	no	—
891	C₂³×C₄	—	67	2	no	—
892	C₂³×C₄	—	67	1	no	—
893	C₂³×C₄	—	67	2	no	—
894	C₂³×C₄	—	67	1	no	—
895	C₂³×C₄	—	67	1	no	—
896	C₂³×C₄	—	67	1	no	—
897	C₂³×C₄	—	67	8	no	—
898	C₂³×C₄	—	67	8	no	—
899	C₂³×C₄	—	67	2	no	—
900	C₂³×C₄	—	67	1	no	—
901	C₂³×C₄	—	67	1	no	—
902	C₂³×C₄	—	67	1	no	—
903	C₂³×C₄	—	67	1	no	—
904	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
905	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
906	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
907	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
908	#126	—	67	16	no	—
909	#126	—	67	16	no	—
910	#126	—	67	16	no	—
911	#126	—	67	16	no	—
912	#126	—	67	16	no	—
913	#126	—	67	16	no	—
914	#125	—	67	8	no	—
915	#125	—	67	16	no	—
916	#125	—	67	16	no	—
917	#125	—	67	8	no	—
918	#124	—	67	8	no	—
919	#124	—	67	16	no	—
920	#124	—	67	16	no	—
921	#124	C₂²×D₆₇	1	8	yes	complemented
922	#123	—	67	16	no	—
923	#123	—	67	16	no	—
924	#123	—	67	16	no	—
925	#123	—	67	16	no	—
926	#123	—	67	16	no	—
927	#123	—	67	16	no	—
928	#123	—	67	16	no	—
929	#123	—	67	16	no	—
930	#123	—	67	16	no	—
931	#123	C₂²×D₆₇	1	16	yes	complemented
932	C₂²⋊Q₈	—	67	8	no	—
933	C₂²⋊Q₈	—	67	8	no	—
934	C₂²⋊Q₈	—	67	8	no	—
935	C₂²⋊Q₈	—	67	8	no	—
936	C₂²⋊Q₈	—	67	16	no	—
937	C₂²⋊Q₈	—	67	8	no	—
938	C₂²⋊Q₈	—	67	16	no	—
939	C₂²⋊Q₈	—	67	16	no	—
940	C₂²⋊Q₈	—	67	16	no	—
941	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
942	#121	—	67	8	no	—
943	#121	—	67	8	no	—
944	#121	—	67	16	no	—
945	#121	—	67	8	no	—
946	#121	—	67	8	no	—
947	#121	—	67	16	no	—
948	#121	—	67	8	no	—
949	#121	—	67	16	no	—
950	#121	—	67	16	no	—
951	#121	—	67	16	no	—
952	#121	—	67	16	no	—
953	#121	—	67	16	no	—
954	#121	C₂²×D₆₇	1	8	yes	complemented
955	#121	C₂²×D₆₇	1	16	yes	complemented
956	#120	—	67	16	no	—
957	#120	—	67	16	no	—
958	#120	—	67	16	no	—
959	#120	C₂²×D₆₇	1	16	yes	—
960	C₄×Q₈	—	67	8	no	—
961	C₄×Q₈	—	67	8	no	—
962	C₄×D₄	—	67	8	no	—
963	C₄×D₄	—	67	16	no	—
964	C₄×D₄	—	67	8	no	—
965	C₄×D₄	—	67	8	no	—
966	C₄×D₄	—	67	8	no	—
967	C₄×D₄	—	67	16	no	—
968	C₄×D₄	—	67	16	no	—
969	C₄×D₄	—	67	16	no	—
970	C₄×D₄	—	67	16	no	—
971	C₄×D₄	—	67	16	no	—
972	C₄×D₄	—	67	8	no	—
973	C₄×D₄	—	67	8	no	—
974	C₄×D₄	—	67	8	no	—
975	C₄×D₄	—	67	16	no	—
976	C₄×D₄	—	67	16	no	—
977	C₄×D₄	—	67	16	no	—
978	C₄×D₄	—	67	16	no	—
979	C₄×D₄	—	67	8	no	—
980	C₄×D₄	C₂²×D₆₇	1	8	yes	—
981	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
982	#117	—	67	8	no	—
983	#117	—	67	16	no	—
984	#117	—	67	8	no	—
985	#117	—	67	16	no	—
986	#117	—	67	16	no	—
987	#117	—	67	16	no	—
988	C₂×C₄⋊C₄	—	67	1	no	—
989	C₂×C₄⋊C₄	—	67	2	no	—
990	C₂×C₄⋊C₄	—	67	2	no	—
991	C₂×C₄⋊C₄	—	67	1	no	—
992	C₂×C₄⋊C₄	—	67	1	no	—
993	C₂×C₄⋊C₄	—	67	1	no	—
994	C₂×C₄⋊C₄	—	67	1	no	—
995	C₂×C₄⋊C₄	—	67	1	no	—
996	C₂×C₄⋊C₄	—	67	2	no	—
997	C₂×C₄⋊C₄	—	67	8	no	—
998	C₂×C₄⋊C₄	—	67	2	no	—
999	C₂×C₄⋊C₄	—	67	2	no	—
1000	C₂×C₄⋊C₄	—	67	2	no	—
1001	C₂×C₄⋊C₄	—	67	2	no	—
1002	C₂×C₄⋊C₄	—	67	2	no	—
1003	C₂×C₄⋊C₄	—	67	2	no	—
1004	C₂×C₄⋊C₄	—	67	2	no	—
1005	C₂×C₄⋊C₄	—	67	2	no	—
1006	C₂×C₄⋊C₄	—	67	2	no	—
1007	C₂×C₄⋊C₄	—	67	2	no	—
1008	C₂×C₄⋊C₄	—	67	8	no	—
1009	C₂×C₄⋊C₄	—	67	8	no	—
1010	C₂×C₄⋊C₄	—	67	16	no	—
1011	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
1014	C₂×C₂²⋊C₄	—	67	1	no	—
1015	C₂×C₂²⋊C₄	—	67	2	no	—
1016	C₂×C₂²⋊C₄	—	67	2	no	—
1017	C₂×C₂²⋊C₄	—	67	2	no	—
1018	C₂×C₂²⋊C₄	—	67	2	no	—
1019	C₂×C₂²⋊C₄	—	67	2	no	—
1020	C₂×C₂²⋊C₄	—	67	1	no	—
1021	C₂×C₂²⋊C₄	—	67	16	no	—
1022	C₂×C₂²⋊C₄	—	67	2	no	—
1023	C₂×C₂²⋊C₄	—	67	2	no	—
1024	C₂×C₂²⋊C₄	—	67	16	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	2	no	—
1029	C₂×C₂²⋊C₄	—	67	1	no	—
1030	C₂×C₂²⋊C₄	—	67	1	no	—
1031	C₂×C₂²⋊C₄	—	67	2	no	—
1032	C₂×C₂²⋊C₄	—	67	2	no	—
1033	C₂×C₂²⋊C₄	—	67	1	no	—
1034	C₂×C₂²⋊C₄	—	67	1	no	—
1035	C₂×C₂²⋊C₄	—	67	2	no	—
1036	C₂×C₂²⋊C₄	—	67	2	no	—
1037	C₂×C₂²⋊C₄	—	67	8	no	—
1038	C₂×C₂²⋊C₄	—	67	8	no	—
1039	C₂×C₂²⋊C₄	—	67	16	no	—
1040	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1042	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1044	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1045	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1046	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1047	C₂×C₂²⋊C₄	C₂²×D₆₇	1	16	yes	complemented
1048	C₂×C₄²	—	67	2	no	—
1049	C₂×C₄²	—	67	2	no	—
1050	C₂×C₄²	—	67	2	no	—
1051	C₂×C₄²	—	67	2	no	—
1052	C₂×C₄²	—	67	1	no	—
1053	C₂×C₄²	—	67	1	no	—
1054	C₂×C₄²	—	67	1	no	—
1055	C₂×C₄²	—	67	8	no	—
1056	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1057	C₂⁴	—	2	8	no	—
1058	C₂⁴	—	4	4	no	—
1059	C₂⁴	—	4	4	no	—
1060	C₂⁴	—	268	2	no	—
1061	C₂⁴	—	268	2	no	—
1062	C₂⁴	—	268	2	no	—
1063	C₂⁴	—	268	2	no	—
1064	C₂⁴	—	67	8	no	—
1065	C₂⁴	—	67	4	no	—
1066	C₂⁴	—	67	4	no	—
1067	C₂⁴	—	67	1	no	—
1068	C₂⁴	—	67	1	no	—
1069	C₂⁴	—	67	1	no	—
1070	C₂⁴	—	134	4	no	—
1071	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1072	C₂⁴	C₂³×D₆₇	1	2	yes	—
1073	C₂⁴	C₂³×D₆₇	1	2	yes	—
1074	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1075	C₂⁴	C₂³×D₆₇	1	8	yes	—
1076	#41	—	4	16	no	—
1077	#41	—	268	16	no	—
1078	C₂×Q₈	—	2	4	no	—
1079	C₂×Q₈	—	268	4	no	—
1080	C₂×Q₈	—	268	16	no	—
1081	C₂×Q₈	—	67	8	no	—
1082	C₂×Q₈	—	67	4	no	—
1083	C₂×Q₈	—	134	4	no	—
1084	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1085	C₂×D₄	—	2	4	no	—
1086	C₂×D₄	—	2	4	no	—
1087	C₂×D₄	—	2	4	no	—
1088	C₂×D₄	—	4	16	no	—
1089	C₂×D₄	—	4	4	no	—
1090	C₂×D₄	—	4	4	no	—
1091	C₂×D₄	—	4	4	no	—
1092	C₂×D₄	—	268	4	no	—
1093	C₂×D₄	—	268	4	no	—
1094	C₂×D₄	—	67	8	no	—
1095	C₂×D₄	—	67	8	no	—
1096	C₂×D₄	—	67	4	no	—
1097	C₂×D₄	—	67	8	no	—
1098	C₂×D₄	—	67	8	no	—
1099	C₂×D₄	—	67	4	no	—
1100	C₂×D₄	—	67	8	no	—
1101	C₂×D₄	—	67	8	no	—
1102	C₂×D₄	—	67	4	no	—
1103	C₂×D₄	—	134	4	no	—
1104	C₂×D₄	—	134	32	no	—
1105	C₂×D₄	—	134	4	no	—
1106	C₂×D₄	—	134	8	no	—
1107	C₂×D₄	—	134	8	no	—
1108	C₂×D₄	—	134	8	no	—
1109	C₂×D₄	—	134	8	no	—
1110	C₂×D₄	—	134	64	no	—
1111	C₂×D₄	—	134	4	no	—
1112	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1113	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1114	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1115	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1116	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1117	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1118	C₂²×C₄	—	2	4	no	—
1119	C₂²×C₄	—	2	4	no	—
1120	C₂²×C₄	—	4	4	no	—
1121	C₂²×C₄	—	4	4	no	—
1122	C₂²×C₄	—	268	2	no	—
1123	C₂²×C₄	—	268	2	no	—
1124	C₂²×C₄	—	268	2	no	—
1125	C₂²×C₄	—	268	2	no	—
1126	C₂²×C₄	—	268	4	no	—
1127	C₂²×C₄	—	268	2	no	—
1128	C₂²×C₄	—	268	4	no	—
1129	C₂²×C₄	—	268	16	no	—
1130	C₂²×C₄	—	268	16	no	—
1131	C₂²×C₄	—	268	2	no	—
1132	C₂²×C₄	—	268	2	no	—
1133	C₂²×C₄	—	268	4	no	—
1134	C₂²×C₄	—	268	4	no	—
1135	C₂²×C₄	—	67	4	no	—
1136	C₂²×C₄	—	67	8	no	—
1137	C₂²×C₄	—	67	8	no	—
1138	C₂²×C₄	—	67	4	no	—
1139	C₂²×C₄	—	67	4	no	—
1140	C₂²×C₄	—	67	8	no	—
1141	C₂²×C₄	—	67	4	no	—
1142	C₂²×C₄	—	67	8	no	—
1143	C₂²×C₄	—	67	4	no	—
1144	C₂²×C₄	—	67	4	no	—
1145	C₂²×C₄	—	67	4	no	—
1146	C₂²×C₄	—	67	8	no	—
1147	C₂²×C₄	—	67	1	no	—
1148	C₂²×C₄	—	67	2	no	—
1149	C₂²×C₄	—	67	2	no	—
1150	C₂²×C₄	—	67	1	no	—
1151	C₂²×C₄	—	67	1	no	—
1152	C₂²×C₄	—	67	1	no	—
1153	C₂²×C₄	—	67	2	no	—
1154	C₂²×C₄	—	67	2	no	—
1155	C₂²×C₄	—	67	1	no	—
1156	C₂²×C₄	—	67	4	no	—
1157	C₂²×C₄	—	67	4	no	—
1158	C₂²×C₄	—	67	4	no	—
1159	C₂²×C₄	—	67	4	no	—
1160	C₂²×C₄	—	134	4	no	—
1161	C₂²×C₄	—	134	8	no	—
1162	C₂²×C₄	—	134	4	no	—
1163	C₂²×C₄	—	134	4	no	—
1164	C₂²×C₄	—	134	4	no	—
1165	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1166	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1167	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1168	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1169	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1170	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1171	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1172	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1173	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1174	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1175	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1176	C₄⋊C₄	—	67	4	no	—
1177	C₄⋊C₄	—	67	8	no	—
1178	C₄⋊C₄	—	67	8	no	—
1179	C₄⋊C₄	—	67	4	no	—
1180	C₄⋊C₄	—	67	4	no	—
1181	C₄⋊C₄	—	67	4	no	—
1182	C₄⋊C₄	—	67	4	no	—
1183	C₄⋊C₄	—	67	4	no	—
1184	C₄⋊C₄	—	67	8	no	—
1185	C₄⋊C₄	—	67	8	no	—
1186	C₄⋊C₄	—	67	8	no	—
1187	C₄⋊C₄	—	67	8	no	—
1188	C₄⋊C₄	—	67	8	no	—
1189	C₄⋊C₄	—	67	8	no	—
1190	C₄⋊C₄	—	67	8	no	—
1191	C₄⋊C₄	—	67	8	no	—
1192	C₄⋊C₄	—	67	8	no	—
1193	C₄⋊C₄	—	67	8	no	—
1194	C₄⋊C₄	—	67	8	no	—
1195	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1196	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1197	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1198	C₂²⋊C₄	—	67	4	no	—
1199	C₂²⋊C₄	—	67	8	no	—
1200	C₂²⋊C₄	—	67	8	no	—
1201	C₂²⋊C₄	—	67	8	no	—
1202	C₂²⋊C₄	—	67	8	no	—
1203	C₂²⋊C₄	—	67	8	no	—
1204	C₂²⋊C₄	—	67	4	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	4	no	—
1212	C₂²⋊C₄	—	67	4	no	—
1213	C₂²⋊C₄	—	67	8	no	—
1214	C₂²⋊C₄	—	67	8	no	—
1215	C₂²⋊C₄	—	67	4	no	—
1216	C₂²⋊C₄	—	67	4	no	—
1217	C₂²⋊C₄	—	67	8	no	—
1218	C₂²⋊C₄	—	67	8	no	—
1219	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1220	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1221	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1222	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1223	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1224	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1225	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1226	C₄²	—	67	4	no	—
1227	C₄²	—	67	4	no	—
1228	C₄²	—	67	4	no	—
1229	C₄²	—	67	8	no	—
1230	C₄²	—	67	8	no	—
1231	C₄²	—	67	8	no	—
1232	C₄²	—	67	8	no	—
1233	C₄²	C₂³×D₆₇	1	4	yes	—
1234	C₂³	—	2	2	no	—
1235	C₂³	—	2	2	no	—
1236	C₂³	—	2	2	no	—
1237	C₂³	—	2	4	no	—
1238	C₂³	—	2	4	no	—
1239	C₂³	—	2	2	no	—
1240	C₂³	—	2	4	no	—
1241	C₂³	—	2	4	no	—
1242	C₂³	—	2	4	no	—
1243	C₂³	—	2	4	no	—
1244	C₂³	—	2	2	no	—
1245	C₂³	—	2	16	no	—
1246	C₂³	—	4	8	no	—
1247	C₂³	—	4	8	no	—
1248	C₂³	—	8	16	no	—
1249	C₂³	—	268	4	no	—
1250	C₂³	—	268	4	no	—
1251	C₂³	—	268	4	no	—
1252	C₂³	—	268	16	no	—
1253	C₂³	—	268	4	no	—
1254	C₂³	—	268	16	no	—
1255	C₂³	—	67	16	no	—
1256	C₂³	—	67	4	no	—
1257	C₂³	—	67	4	no	—
1258	C₂³	—	67	2	no	—
1259	C₂³	—	67	2	no	—
1260	C₂³	—	67	2	no	—
1261	C₂³	—	134	8	no	—
1262	C₂³	—	134	2	no	—
1263	C₂³	—	134	2	no	—
1264	C₂³	—	134	2	no	—
1265	C₂³	—	134	2	no	—
1266	C₂³	—	134	2	no	—
1267	C₂³	—	134	2	no	—
1268	C₂³	—	134	2	no	—
1269	C₂³	#41×D₆₇	1	4	yes	—
1270	C₂³	C₂⁴×D₆₇	1	2	yes	—
1271	C₂³	C₂⁴×D₆₇	1	4	yes	—
1272	C₂³	C₂⁴×D₆₇	1	4	yes	—
1273	C₂³	C₂⁴×D₆₇	1	2	yes	—
1274	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1275	Q₈	—	2	8	no	—
1276	Q₈	—	268	8	no	—
1277	Q₈	—	134	8	no	—
1278	D₄	—	2	8	no	—
1279	D₄	—	2	8	no	—
1280	D₄	—	2	8	no	—
1281	D₄	—	4	8	no	—
1282	D₄	—	4	8	no	—
1283	D₄	—	4	8	no	—
1284	D₄	—	268	8	no	—
1285	D₄	—	268	8	no	—
1286	D₄	—	134	8	no	—
1287	D₄	—	134	8	no	—
1288	D₄	—	134	16	no	—
1289	D₄	—	134	16	no	—
1290	D₄	—	134	16	no	—
1291	D₄	—	134	16	no	—
1292	D₄	—	134	8	no	—
1293	C₂×C₄	—	2	2	no	—
1294	C₂×C₄	—	2	2	no	—
1295	C₂×C₄	—	2	2	no	—
1296	C₂×C₄	—	2	4	no	—
1297	C₂×C₄	—	2	2	no	—
1298	C₂×C₄	—	2	4	no	—
1299	C₂×C₄	—	2	8	no	—
1300	C₂×C₄	—	2	8	no	—
1301	C₂×C₄	—	4	8	no	—
1302	C₂×C₄	—	4	8	no	—
1303	C₂×C₄	—	268	4	no	—
1304	C₂×C₄	—	268	4	no	—
1305	C₂×C₄	—	268	4	no	—
1306	C₂×C₄	—	268	4	no	—
1307	C₂×C₄	—	268	8	no	—
1308	C₂×C₄	—	268	4	no	—
1309	C₂×C₄	—	268	8	no	—
1310	C₂×C₄	—	268	4	no	—
1311	C₂×C₄	—	268	4	no	—
1312	C₂×C₄	—	268	8	no	—
1313	C₂×C₄	—	268	8	no	—
1314	C₂×C₄	—	67	2	no	—
1315	C₂×C₄	—	67	2	no	—
1316	C₂×C₄	—	67	4	no	—
1317	C₂×C₄	—	67	4	no	—
1318	C₂×C₄	—	67	2	no	—
1319	C₂×C₄	—	67	2	no	—
1320	C₂×C₄	—	67	4	no	—
1321	C₂×C₄	—	67	4	no	—
1322	C₂×C₄	—	67	2	no	—
1323	C₂×C₄	—	134	8	no	—
1324	C₂×C₄	—	134	16	no	—
1325	C₂×C₄	—	134	2	no	—
1326	C₂×C₄	—	134	4	no	—
1327	C₂×C₄	—	134	4	no	—
1328	C₂×C₄	—	134	2	no	—
1329	C₂×C₄	—	134	2	no	—
1330	C₂×C₄	—	134	2	no	—
1331	C₂×C₄	—	134	4	no	—
1332	C₂×C₄	—	134	2	no	—
1333	C₂×C₄	—	134	4	no	—
1334	C₂×C₄	—	134	8	no	—
1335	C₂×C₄	—	134	8	no	—
1336	C₂×C₄	—	134	8	no	—
1337	C₂×C₄	#14524088	1	4	yes	—
1338	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1339	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1340	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1341	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1342	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1343	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1344	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1345	C₂²	—	2	2	no	—
1346	C₂²	—	2	2	no	—
1347	C₂²	—	2	8	no	—
1348	C₂²	—	2	2	no	—
1349	C₂²	—	2	4	no	—
1350	C₂²	—	2	4	no	—
1351	C₂²	—	2	2	no	—
1352	C₂²	—	2	4	no	—
1353	C₂²	—	2	4	no	—
1354	C₂²	—	2	4	no	—
1355	C₂²	—	2	4	no	—
1356	C₂²	—	2	2	no	—
1357	C₂²	—	4	8	no	—
1358	C₂²	—	4	8	no	—
1359	C₂²	—	4	4	no	—
1360	C₂²	—	8	16	no	—
1361	C₂²	—	268	16	no	—
1362	C₂²	—	268	16	no	—
1363	C₂²	—	268	4	no	—
1364	C₂²	—	67	4	no	—
1365	C₂²	—	67	4	no	—
1366	C₂²	—	134	2	no	—
1367	C₂²	—	134	2	no	—
1368	C₂²	—	134	2	no	—
1369	C₂²	—	134	2	no	—
1370	C₂²	—	134	2	no	—
1371	C₂²	—	134	2	no	—
1372	C₂²	—	134	2	no	—
1373	C₂²	—	134	8	no	—
1374	C₂²	—	134	8	no	—
1375	C₂²	C₂×#41×D₆₇	1	4	yes	—
1376	C₂²	C₂×#41×D₆₇	1	2	yes	—
1377	C₂²	C₂×#14524088	1	2	yes	—
1378	C₂²	#16864231	1	2	yes	—
1379	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1380	C₄	—	2	2	no	—
1381	C₄	—	2	2	no	—
1382	C₄	—	2	2	no	—
1383	C₄	—	2	4	no	—
1384	C₄	—	2	2	no	—
1385	C₄	—	2	4	no	—
1386	C₄	—	134	2	no	—
1387	C₄	—	134	4	no	—
1388	C₄	—	134	4	no	—
1389	C₄	—	134	2	no	—
1390	C₄	—	134	2	no	—
1391	C₄	—	134	2	no	—
1392	C₄	—	134	4	no	—
1393	C₄	—	134	2	no	—
1394	C₄	—	134	4	no	—
1395	C₄	C₂×#14524088	1	4	yes	—
1396	C₂	—	2	4	no	—
1397	C₂	—	4	4	no	—
1398	C₂	—	4	4	no	—
1399	C₂	—	4	2	no	—
1400	C₂	—	268	2	no	—
1401	C₂	—	134	4	no	—
1402	C₂	—	134	4	no	—
1403	C₂	#22574036	1	4	yes	direct product factor
1404	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1405	C₂	C₂²×#14524088	1	1	yes	characteristic
1406	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×#546×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#546	D₆₇
hypocenter	C₆₇	C₂×#3505
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#546

Complements

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

N	H ≅ G/N	type
1. #22574036	C₂	direct (N × H)
2. C₂×#16864096	C₂	semidirect
3. C₂×#16864093	C₂	semidirect
4. C₂×#16864093	C₂	semidirect
5. C₂×#16864091	C₂	semidirect
6. C₂×#16864088	C₂	semidirect
7. C₂×#16864086	C₂	semidirect
8. C₂×#16864077	C₂	semidirect
9. C₂×#16864072	C₂	semidirect
10. C₂×#16864054	C₂	semidirect
11. C₂×#16864053	C₂	semidirect
12. C₂×#16864040	C₂	semidirect
13. C₂×#16863989	C₂	semidirect
14. C₂×#16863978	C₂	semidirect
15. C₂×#16863956	C₂	semidirect
16. C₂×#16863928	C₂	semidirect
17. C₂×#16863925	C₂	semidirect
18. C₂×#16863906	C₂	semidirect
19. C₂×#16863903	C₂	semidirect
20. C₂×C₂²⋊Q₈×D₆₇	C₂	semidirect
21. C₂²×#14524014	C₂	semidirect
22. C₂×#16863869	C₂	semidirect
23. C₂×C₄×D₄×D₆₇	C₂	semidirect
24. C₂×#546×C₆₇	C₂	semidirect
25. C₂²×#11761627	C₂²	semidirect
26. C₂²×Q₈×D₆₇	C₂²	semidirect
30. C₂³×C₄×D₆₇	C₂²	semidirect
31. #16864096	C₂²	semidirect
32. #16864093	C₂²	semidirect
33. #16864093	C₂²	semidirect
34. #16864091	C₂²	semidirect
35. #16864088	C₂²	semidirect
36. #16864086	C₂²	semidirect
37. #16864077	C₂²	semidirect
38. #16864072	C₂²	semidirect
39. #16864054	C₂²	semidirect
40. #16864053	C₂²	semidirect
41. #16864040	C₂²	semidirect
42. #16863989	C₂²	semidirect
43. #16863978	C₂²	semidirect
44. #16863956	C₂²	semidirect
45. #16863928	C₂²	semidirect
46. #16863925	C₂²	semidirect
47. C₂×#14524038	C₂²	semidirect
48. C₂×#14524036	C₂²	semidirect
49. C₂×#14524036	C₂²	semidirect
50. C₂×#14524036	C₂²	semidirect
51. C₂×#14524036	C₂²	semidirect
52. C₂×#14524036	C₂²	semidirect
53. C₂×#14524035	C₂²	semidirect
54. C₂×#14524034	C₂²	semidirect
55. C₂×#14524034	C₂²	semidirect
56. C₂×#14524033	C₂²	semidirect
57. C₂×#14524030	C₂²	semidirect
58. C₂×#14524030	C₂²	semidirect
59. C₂×#14524029	C₂²	semidirect
60. #16863906	C₂²	semidirect
61. #16863903	C₂²	semidirect
63. C₂×#14524026	C₂²	semidirect
64. C₂×#14524025	C₂²	semidirect
65. C₂×#14524025	C₂²	semidirect
66. C₂×#14524025	C₂²	semidirect
68. C₂×#14524024	C₂²	semidirect
69. C₂×#14524024	C₂²	semidirect
70. C₂×#14524024	C₂²	semidirect
71. C₂×#14524023	C₂²	semidirect
72. C₂×#14524022	C₂²	semidirect
73. C₂×#14524022	C₂²	semidirect
74. C₂×#14524022	C₂²	semidirect
75. C₂×#14524021	C₂²	semidirect
76. C₂×#14524020	C₂²	semidirect
77. C₂×#14524020	C₂²	semidirect
78. C₂×#14524019	C₂²	semidirect
79. C₂×#14524019	C₂²	semidirect
80. C₂²⋊Q₈×D₆₇	C₂²	semidirect
81. C₂×#14524016	C₂²	semidirect
82. C₂×#14524016	C₂²	semidirect
83. C₂×#14524015	C₂²	semidirect
87. C₂×#14524014	C₂²	semidirect
88. C₂×#14524014	C₂²	semidirect
89. C₂×#14524014	C₂²	semidirect
90. C₂×#14524014	C₂²	semidirect
91. C₂×#14524014	C₂²	semidirect
92. C₂×#14524014	C₂²	semidirect
93. C₂×#14524014	C₂²	semidirect
95. C₂×#14524011	C₂²	semidirect
96. C₂×#14524011	C₂²	semidirect
97. #16863869	C₂²	semidirect
98. C₂×Q₈×Dic₆₇	C₂²	semidirect
99. C₂×C₄×Dic₁₃₄	C₂²	semidirect
100. C₂×C₄×D₂₆₈	C₂²	semidirect
102. C₂×D₄×Dic₆₇	C₂²	semidirect
103. C₂×D₄×Dic₆₇	C₂²	semidirect
104. C₂×#14524005	C₂²	semidirect
106. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
107. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
108. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
109. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
110. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
111. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
113. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
114. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
115. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
116. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
117. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
118. C₄×D₄×D₆₇	C₂²	semidirect
119. C₂×#14524002	C₂²	semidirect
120. C₂×#14524002	C₂²	semidirect
121. C₂×#14524001	C₂²	semidirect
122. C₂×#14523999	C₂²	semidirect
123. C₂×#14523999	C₂²	semidirect
124. C₂×#14523999	C₂²	semidirect
125. C₂²×C₄⋊Dic₆₇	C₂²	semidirect
126. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
127. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
128. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
129. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
130. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
133. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
134. C₂×C₄²×D₆₇	C₂²	semidirect
135. C₂²×#41×C₆₇	C₂²	semidirect
136. C₂³×D₄×C₆₇	C₂²	semidirect
137. #546×C₆₇	C₂²	semidirect
138. C₂×#124×C₆₇	C₂²	semidirect
139. C₂×#123×C₆₇	C₂²	semidirect
140. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
141. C₂×#121×C₆₇	C₂²	semidirect
142. C₂×#121×C₆₇	C₂²	semidirect
145. C₂×C₄×D₄×C₆₇	C₂²	semidirect
146. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
150. C₂×#11761627	C₂³	semidirect
154. C₂×Q₈×D₆₇	C₂³	semidirect
187. C₂²×C₄×D₆₇	C₂³	semidirect
188. #14524038	C₂³	semidirect
189. #14524036	C₂³	semidirect
190. #14524036	C₂³	semidirect
191. #14524036	C₂³	semidirect
192. #14524036	C₂³	semidirect
193. #14524036	C₂³	semidirect
194. #14524035	C₂³	semidirect
195. #14524034	C₂³	semidirect
196. #14524034	C₂³	semidirect
197. #14524033	C₂³	semidirect
198. #14524030	C₂³	semidirect
199. #14524030	C₂³	semidirect
200. #14524029	C₂³	semidirect
202. #14524026	C₂³	semidirect
203. #14524025	C₂³	semidirect
204. #14524025	C₂³	semidirect
205. #14524025	C₂³	semidirect
207. #14524024	C₂³	semidirect
208. #14524024	C₂³	semidirect
209. #14524024	C₂³	semidirect
210. #14524023	C₂³	semidirect
211. #14524022	C₂³	semidirect
212. #14524022	C₂³	semidirect
213. #14524022	C₂³	semidirect
214. #14524021	C₂³	semidirect
215. #14524020	C₂³	semidirect
216. #14524020	C₂³	semidirect
217. #14524019	C₂³	semidirect
218. #14524019	C₂³	semidirect
219. #14524016	C₂³	semidirect
220. #14524016	C₂³	semidirect
221. #14524015	C₂³	semidirect
225. #14524014	C₂³	semidirect
226. #14524014	C₂³	semidirect
227. #14524014	C₂³	semidirect
228. #14524014	C₂³	semidirect
229. #14524014	C₂³	semidirect
230. #14524014	C₂³	semidirect
232. #14524011	C₂³	semidirect
233. #14524011	C₂³	semidirect
234. Q₈×Dic₆₇	C₂³	semidirect
235. C₄×Dic₁₃₄	C₂³	semidirect
236. C₄×D₂₆₈	C₂³	semidirect
238. D₄×Dic₆₇	C₂³	semidirect
239. D₄×Dic₆₇	C₂³	semidirect
240. #14524005	C₂³	semidirect
242. C₄×C₂²⋊D₆₇	C₂³	semidirect
243. C₄×C₂²⋊D₆₇	C₂³	semidirect
244. C₄×C₂²⋊D₆₇	C₂³	semidirect
245. C₄×C₂²⋊D₆₇	C₂³	semidirect
246. C₄×C₂²⋊D₆₇	C₂³	semidirect
247. C₄×C₂²⋊D₆₇	C₂³	semidirect
249. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
250. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
251. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
252. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
253. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
254. #14524002	C₂³	semidirect
255. #14524002	C₂³	semidirect
256. #14524001	C₂³	semidirect
257. #14523999	C₂³	semidirect
258. #14523999	C₂³	semidirect
259. #14523999	C₂³	semidirect
268. C₂×C₄⋊Dic₆₇	C₂³	semidirect
280. C₄⋊C₄×D₆₇	C₂³	semidirect
281. C₄⋊C₄×D₆₇	C₂³	semidirect
282. C₄⋊C₄×D₆₇	C₂³	semidirect
296. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
297. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
308. C₂²⋊C₄×D₆₇	C₂³	semidirect
316. C₄²×D₆₇	C₂³	semidirect
319. C₂×#41×C₆₇	C₂³	semidirect
328. C₂²×D₄×C₆₇	C₂³	semidirect
333. #124×C₆₇	C₂³	semidirect
334. #123×C₆₇	C₂³	semidirect
335. C₂²⋊Q₈×C₆₇	C₂³	semidirect
336. #121×C₆₇	C₂³	semidirect
337. #121×C₆₇	C₂³	semidirect
340. C₄×D₄×C₆₇	C₂³	semidirect
351. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
358. C₂³×D₆₇	#41	semidirect
567. C₂²×D₆₇	C₂×#41	semidirect
697. C₂×C₆₇	#3505	semidirect
716. C₂×#546	D₆₇	semidirect
728. C₆₇	C₂×#3505	semidirect
730. C₂²×#41	C₂×D₆₇	semidirect
734. C₂³×D₄	C₂×D₆₇	semidirect
748. #546	C₂×D₆₇	semidirect
767. C₂×#124	C₂×D₆₇	semidirect
779. C₂×#123	C₂×D₆₇	semidirect
790. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
804. C₂×#121	C₂×D₆₇	semidirect
805. C₂×#121	C₂×D₆₇	semidirect
833. C₂×C₄×D₄	C₂×D₆₇	semidirect
849. C₂²×C₂²⋊C₄	C₂×D₆₇	semidirect
857. C₂×#41	C₂²×D₆₇	semidirect
883. C₂²×D₄	C₂²×D₆₇	semidirect
921. #124	C₂²×D₆₇	semidirect
931. #123	C₂²×D₆₇	semidirect
941. C₂²⋊Q₈	C₂²×D₆₇	semidirect
954. #121	C₂²×D₆₇	semidirect
955. #121	C₂²×D₆₇	semidirect
981. C₄×D₄	C₂²×D₆₇	semidirect
1047. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
1403. C₂	#22574036	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574036	2
C₂×#16864096	2
C₂×#16864093	2
C₂×#16864091	2
C₂×#16864088	2
C₂×#16864086	2
C₂×#16864077	2
C₂×#16864072	2
C₂×#16864054	2
C₂×#16864053	2
C₂×#16864040	2
C₂×#16863989	2
C₂×#16863978	2
C₂×#16863956	2
C₂×#16863928	2
C₂×#16863925	2
C₂×#16863906	2
C₂×#16863903	2
C₂×C₂²⋊Q₈×D₆₇	2
C₂²×#14524014	2
C₂×#16863869	2
C₂×C₄×D₄×D₆₇	2
C₂×#546×C₆₇	2
C₂×#3505	67

Subgroups — C2×#22574036 #31763747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574036 #31763747