Subgroups — C₂×#22574583 #31763470

Order 17152.

8046 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574583	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864136	C₂	1	4	yes	maximal, complemented
3	C₂×#16864119	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864099	C₂	1	2	yes	maximal, complemented
5	C₂×#16864068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864067	C₂	1	2	yes	maximal, complemented
7	C₂×#16864051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16864042	C₂	1	2	yes	maximal, complemented
9	C₂×#16864039	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16864017	C₂	1	2	yes	maximal, complemented
12	C₂×#16863985	C₂	1	4	yes	maximal, complemented
13	C₂×#16863976	C₂	1	2	yes	maximal, complemented
14	C₂×#16863965	C₂	1	2	yes	maximal, complemented
15	C₂×#16863962	C₂	1	2	yes	maximal, complemented
16	C₂×#16863946	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16863946	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11761629	C₂²	1	2	yes	complemented
20	C₂²×#11761628	C₂²	1	2	yes	complemented
21	C₂²×#11761628	C₂²	1	2	yes	complemented
22	C₂²×#11761628	C₂²	1	2	yes	complemented
23	C₂³×D₂₆₈	C₂²	1	2	yes	—
24	C₂²×D₄×D₆₇	C₂²	1	2	yes	—
25	#16864136	C₂²	1	64	yes	complemented
26	#16864119	C₂²	1	16	yes	complemented
27	#16864099	C₂²	1	32	yes	complemented
28	#16864068	C₂²	1	16	yes	complemented
29	#16864067	C₂²	1	32	yes	complemented
30	#16864051	C₂²	1	16	yes	complemented
31	#16864042	C₂²	1	32	yes	complemented
32	#16864039	C₂²	1	32	yes	complemented
33	D₄×D₂₆₈	C₂²	1	16	yes	complemented
34	#16864017	C₂²	1	32	yes	complemented
35	#16863985	C₂²	1	64	yes	complemented
36	#16863976	C₂²	1	32	yes	complemented
37	#16863965	C₂²	1	32	yes	complemented
38	#16863962	C₂²	1	32	yes	complemented
39	#16863946	C₂²	1	16	yes	complemented
40	#16863946	C₂²	1	16	yes	complemented
41	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
42	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
43	C₂×#14524040	C₂²	1	1	yes	characteristic
44	C₂×#14524040	C₂²	1	1	yes	characteristic
45	C₂×#14524040	C₂²	1	2	yes	complemented
46	C₂×#14524039	C₂²	1	4	yes	complemented
47	C₂×#14524038	C₂²	1	4	yes	complemented
48	C₂×#14524038	C₂²	1	4	yes	complemented
49	C₂×#14524031	C₂²	1	2	yes	—
50	C₂×#14524031	C₂²	1	2	yes	complemented
51	C₂×#14524031	C₂²	1	2	yes	complemented
52	C₂×#14524029	C₂²	1	4	yes	complemented
53	C₂×#14524028	C₂²	1	4	yes	complemented
54	C₂×#14524025	C₂²	1	4	yes	complemented
55	C₂×#14524025	C₂²	1	4	yes	complemented
56	C₂×#14524022	C₂²	1	2	yes	complemented
57	C₂×#14524021	C₂²	1	4	yes	complemented
58	C₂×#14524019	C₂²	1	2	yes	complemented
59	C₂×#14524018	C₂²	1	2	yes	—
60	C₂×#14524018	C₂²	1	2	yes	complemented
61	C₂×#14524018	C₂²	1	4	yes	complemented
62	C₂×#14524018	C₂²	1	4	yes	complemented
63	C₂×#14524018	C₂²	1	4	yes	complemented
64	C₂×#14524017	C₂²	1	2	yes	—
65	C₂×#14524017	C₂²	1	1	yes	characteristic
66	C₂×#14524017	C₂²	1	1	yes	characteristic, complemented
67	C₂×#14524017	C₂²	1	2	yes	complemented
68	C₂×#14524017	C₂²	1	2	yes	complemented
69	C₂×#14524017	C₂²	1	2	yes	complemented
70	C₂×#14524016	C₂²	1	4	yes	complemented
71	C₂×#14524016	C₂²	1	4	yes	complemented
72	C₂×#14524016	C₂²	1	4	yes	complemented
73	C₂×#14524014	C₂²	1	2	yes	—
74	C₂×#14524013	C₂²	1	4	yes	—
75	C₂×#14524013	C₂²	1	4	yes	complemented
76	C₂×#14524013	C₂²	1	4	yes	complemented
77	C₂×#14524011	C₂²	1	4	yes	complemented
78	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
79	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
80	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
81	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
82	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
83	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
85	C₂×#14524005	C₂²	1	4	yes	complemented
86	C₂×#14524001	C₂²	1	2	yes	complemented
87	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
89	#529×C₆₇	C₂²	1	16	yes	complemented
90	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
91	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
96	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
98	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
99	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
100	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₆₇	C₂³	1	4	yes	—
102	C₂×#11761629	—	4	8	no	—
103	C₂×#11761629	C₂³	1	16	yes	complemented
104	C₂×#11761628	—	4	8	no	—
105	C₂×#11761628	—	4	8	no	—
106	C₂×#11761628	—	4	8	no	—
107	C₂×#11761628	C₂³	1	16	yes	complemented
108	C₂×#11761628	C₂³	1	16	yes	complemented
109	C₂×#11761628	C₂³	1	16	yes	complemented
110	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
111	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
112	C₂²×D₂₆₈	—	4	8	no	—
113	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
114	C₂²×D₂₆₈	C₂³	1	2	yes	—
115	C₂²×D₂₆₈	C₂³	1	2	yes	—
116	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
117	C₂²×D₂₆₈	C₂³	1	16	yes	—
118	C₂²×D₂₆₈	C₂³	1	4	yes	—
119	C₂²×D₂₆₈	C₂³	1	2	yes	—
120	C₂²×D₂₆₈	C₂³	1	2	yes	—
121	C₂²×D₂₆₈	C₂³	1	4	yes	—
122	C₂²×D₂₆₈	C₂³	1	2	yes	—
123	C₂²×D₂₆₈	C₂³	1	4	yes	—
124	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
125	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
126	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
127	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
128	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
129	C₂×D₄×D₆₇	—	4	8	no	—
130	C₂×D₄×D₆₇	C₂³	1	16	yes	—
131	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
132	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
133	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
134	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
135	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
136	#14524043	C₂³	1	8	yes	complemented
137	#14524043	C₂³	1	8	yes	complemented
138	#14524040	C₂³	1	8	yes	—
139	#14524040	C₂³	1	8	yes	—
140	#14524040	C₂³	1	16	yes	complemented
141	#14524039	C₂³	1	32	yes	complemented
142	#14524038	C₂³	1	32	yes	complemented
143	#14524038	C₂³	1	32	yes	complemented
144	#14524031	C₂³	1	16	yes	—
145	#14524031	C₂³	1	16	yes	complemented
146	#14524031	C₂³	1	16	yes	complemented
147	#14524029	C₂³	1	32	yes	complemented
148	#14524028	C₂³	1	32	yes	complemented
149	#14524025	C₂³	1	32	yes	complemented
150	#14524025	C₂³	1	32	yes	complemented
151	#14524022	C₂³	1	16	yes	complemented
152	#14524021	C₂³	1	32	yes	complemented
153	#14524019	C₂³	1	16	yes	complemented
154	#14524018	C₂³	1	16	yes	—
155	#14524018	C₂³	1	16	yes	complemented
156	#14524018	C₂³	1	32	yes	complemented
157	#14524018	C₂³	1	32	yes	complemented
158	#14524018	C₂³	1	32	yes	complemented
159	#14524017	C₂³	1	16	yes	—
160	#14524017	C₂³	1	8	yes	—
161	#14524017	C₂³	1	8	yes	complemented
162	#14524017	C₂³	1	16	yes	complemented
163	#14524017	C₂³	1	16	yes	complemented
164	#14524017	C₂³	1	16	yes	complemented
165	#14524016	C₂³	1	32	yes	complemented
166	#14524016	C₂³	1	32	yes	complemented
167	#14524016	C₂³	1	32	yes	complemented
168	#14524014	C₂³	1	16	yes	—
169	#14524013	C₂³	1	32	yes	—
170	#14524013	C₂³	1	32	yes	complemented
171	#14524013	C₂³	1	32	yes	complemented
172	#14524011	C₂³	1	32	yes	complemented
173	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
174	C₄×D₂₆₈	C₂³	1	8	yes	—
175	C₄×D₂₆₈	C₂³	1	16	yes	complemented
176	C₄×D₂₆₈	C₂³	1	16	yes	complemented
177	C₄×D₂₆₈	C₂³	1	16	yes	complemented
178	C₄×D₂₆₈	C₂³	1	8	yes	complemented
179	C₄×D₂₆₈	C₂³	1	16	yes	complemented
180	#14524005	C₂³	1	32	yes	complemented
181	#14524001	C₂³	1	16	yes	complemented
182	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
186	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
187	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
188	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
189	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
190	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
191	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
192	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
193	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
194	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
196	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
197	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
198	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
199	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
200	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
201	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
202	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
203	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
204	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
206	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
209	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
210	#126×C₆₇	C₂³	1	16	yes	complemented
211	#125×C₆₇	C₂³	1	8	yes	complemented
212	#124×C₆₇	C₂³	1	8	yes	—
213	#123×C₆₇	C₂³	1	16	yes	complemented
214	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
215	#121×C₆₇	C₂³	1	8	yes	—
216	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
217	C₄×D₄×C₆₇	C₂³	1	8	yes	—
218	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
219	#117×C₆₇	C₂³	1	16	yes	complemented
220	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
236	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
237	C₂³×D₆₇	—	4	8	no	—
238	C₂³×D₆₇	—	4	8	no	—
239	C₂³×D₆₇	—	4	8	no	—
240	C₂³×D₆₇	C₂⁴	1	2	yes	—
241	C₂³×D₆₇	C₂⁴	1	4	yes	—
242	C₂³×D₆₇	C₂⁴	1	2	yes	—
243	C₂³×D₆₇	C₂⁴	1	16	yes	—
244	#11761629	—	4	32	no	—
245	#11761628	—	4	32	no	—
246	#11761628	—	4	32	no	—
247	#11761628	—	4	32	no	—
248	C₂×Dic₁₃₄	—	2	8	no	—
249	C₂×Dic₁₃₄	—	4	4	no	—
250	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
251	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
252	C₂×D₂₆₈	—	2	8	no	—
253	C₂×D₂₆₈	—	2	4	no	—
254	C₂×D₂₆₈	—	2	8	no	—
255	C₂×D₂₆₈	—	2	4	no	—
256	C₂×D₂₆₈	—	4	32	no	—
257	C₂×D₂₆₈	—	4	8	no	—
258	C₂×D₂₆₈	—	4	4	no	—
259	C₂×D₂₆₈	—	4	4	no	—
260	C₂×D₂₆₈	—	4	8	no	—
261	C₂×D₂₆₈	—	4	4	no	—
262	C₂×D₂₆₈	—	4	8	no	—
263	C₂×D₂₆₈	C₂⁴	1	4	yes	—
264	C₂×D₂₆₈	C₂⁴	1	8	yes	—
265	C₂×D₂₆₈	C₂⁴	1	8	yes	—
266	C₂×D₂₆₈	C₂⁴	1	4	yes	—
267	C₂×D₂₆₈	C₂⁴	1	16	yes	—
268	C₂×D₂₆₈	C₂⁴	1	8	yes	—
269	C₂×D₂₆₈	C₂⁴	1	8	yes	—
270	C₂×D₂₆₈	C₂⁴	1	16	yes	—
271	C₂×D₂₆₈	C₂⁴	1	8	yes	—
272	C₂×D₂₆₈	C₂⁴	1	16	yes	—
273	C₂×C₂²⋊D₆₇	—	4	8	no	—
274	C₂×C₂²⋊D₆₇	—	4	4	no	—
275	C₂×C₂²⋊D₆₇	—	4	4	no	—
276	C₂×C₂²⋊D₆₇	—	4	8	no	—
277	C₂×C₂²⋊D₆₇	—	4	8	no	—
278	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
279	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
280	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
281	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
282	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
283	D₄×D₆₇	—	4	32	no	—
284	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
285	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
286	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
287	C₂×C₄×D₆₇	—	2	8	no	—
288	C₂×C₄×D₆₇	—	2	8	no	—
289	C₂×C₄×D₆₇	—	4	8	no	—
290	C₂×C₄×D₆₇	—	4	8	no	—
291	C₂×C₄×D₆₇	—	4	8	no	—
292	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
293	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
294	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
295	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
296	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
297	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
298	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
299	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
300	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
301	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
302	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
303	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
304	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
305	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
306	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
307	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
308	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
309	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
310	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
311	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
312	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
313	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
314	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
315	C₄×Dic₆₇	C₂⁴	1	16	yes	—
316	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
317	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂×Q₈×C₆₇	—	2	4	no	—
319	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
320	C₂×D₄×C₆₇	—	2	4	no	—
321	C₂×D₄×C₆₇	—	4	4	no	—
322	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
323	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
324	C₂²×C₄×C₆₇	—	2	8	no	—
325	C₂²×C₄×C₆₇	—	2	4	no	—
326	C₂²×C₄×C₆₇	—	2	4	no	—
327	C₂²×C₄×C₆₇	—	4	2	no	—
328	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
335	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
336	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
338	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
339	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
342	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
343	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
344	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
345	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
346	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
347	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
348	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
349	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
350	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
351	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
352	C₄²×C₆₇	C₂⁴	1	4	yes	—
353	C₄²×C₆₇	C₂⁴	1	4	yes	—
354	C₄²×C₆₇	C₂⁴	1	4	yes	—
355	C₄²×C₆₇	C₂⁴	1	4	yes	—
356	C₄²×C₆₇	C₂⁴	1	8	yes	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	4	no	—
360	C₂³×C₆₇	—	2	4	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	4	no	—
363	C₂³×C₆₇	C₂⁵	1	4	yes	—
364	C₂³×C₆₇	C₂⁵	1	2	yes	—
365	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
366	C₂²×D₆₇	—	2	4	no	—
367	C₂²×D₆₇	—	2	4	no	—
368	C₂²×D₆₇	—	2	4	no	—
369	C₂²×D₆₇	—	2	8	no	—
370	C₂²×D₆₇	—	2	8	no	—
371	C₂²×D₆₇	—	2	4	no	—
372	C₂²×D₆₇	—	2	4	no	—
373	C₂²×D₆₇	—	2	8	no	—
374	C₂²×D₆₇	—	2	4	no	—
375	C₂²×D₆₇	—	4	16	no	—
376	C₂²×D₆₇	—	4	16	no	—
377	C₂²×D₆₇	—	4	16	no	—
378	C₂²×D₆₇	—	8	32	no	—
379	C₂²×D₆₇	C₂⁵	1	4	yes	—
380	C₂²×D₆₇	C₂⁵	1	8	yes	—
381	C₂²×D₆₇	C₂⁵	1	4	yes	—
382	Q₈×C₆₇	—	2	8	no	—
383	D₄×C₆₇	—	2	8	no	—
384	D₄×C₆₇	—	4	8	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	4	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	4	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	4	no	—
392	C₂×C₄×C₆₇	—	2	16	no	—
393	C₂×C₄×C₆₇	—	2	8	no	—
394	C₂×C₄×C₆₇	—	2	8	no	—
395	C₂×C₄×C₆₇	—	4	4	no	—
396	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
397	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
398	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
399	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
400	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
401	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
402	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
403	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
404	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
405	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
406	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
407	C₂²⋊D₆₇	—	4	16	no	—
408	C₂²⋊D₆₇	—	4	16	no	—
409	C₂²⋊D₆₇	—	4	16	no	—
410	C₂²⋊D₆₇	—	4	8	no	—
411	C₂²⋊D₆₇	—	4	8	no	—
412	C₂×Dic₆₇	—	2	4	no	—
413	C₂×Dic₆₇	—	2	4	no	—
414	C₂×Dic₆₇	—	2	8	no	—
415	C₂×Dic₆₇	C₂⁵	1	4	yes	—
416	C₂×Dic₆₇	C₂⁵	1	8	yes	—
417	C₂×Dic₆₇	C₂⁵	1	4	yes	—
418	D₂₆₈	—	2	16	no	—
419	D₂₆₈	—	2	8	no	—
420	D₂₆₈	—	2	16	no	—
421	D₂₆₈	—	2	8	no	—
422	D₂₆₈	—	4	16	no	—
423	D₂₆₈	—	4	8	no	—
424	D₂₆₈	—	4	8	no	—
425	D₂₆₈	—	4	16	no	—
426	D₂₆₈	—	4	8	no	—
427	D₂₆₈	—	4	16	no	—
428	C₄×D₆₇	—	2	16	no	—
429	C₄×D₆₇	—	2	16	no	—
430	C₄×D₆₇	—	4	16	no	—
431	C₄×D₆₇	—	4	16	no	—
432	C₄×D₆₇	—	4	16	no	—
433	Dic₁₃₄	—	2	16	no	—
434	Dic₁₃₄	—	4	8	no	—
435	C₂²×C₆₇	—	2	2	no	—
436	C₂²×C₆₇	—	2	2	no	—
437	C₂²×C₆₇	—	2	4	no	—
438	C₂²×C₆₇	—	2	4	no	—
439	C₂²×C₆₇	—	2	2	no	—
440	C₂²×C₆₇	—	2	4	no	—
441	C₂²×C₆₇	—	4	8	no	—
442	C₂²×C₆₇	—	4	4	no	—
443	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
444	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
445	C₂²×C₆₇	#585	1	2	yes	—
446	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
447	C₂×D₆₇	—	2	4	no	—
448	C₂×D₆₇	—	2	4	no	—
449	C₂×D₆₇	—	2	4	no	—
450	C₂×D₆₇	—	2	8	no	—
451	C₂×D₆₇	—	2	8	no	—
452	C₂×D₆₇	—	2	4	no	—
453	C₂×D₆₇	—	2	4	no	—
454	C₂×D₆₇	—	2	8	no	—
455	C₂×D₆₇	—	2	4	no	—
456	C₂×D₆₇	—	4	8	no	—
457	C₂×D₆₇	—	4	16	no	—
458	C₂×D₆₇	—	4	8	no	—
459	C₂×D₆₇	—	8	32	no	—
460	C₄×C₆₇	—	2	2	no	—
461	C₄×C₆₇	—	2	2	no	—
462	C₄×C₆₇	—	2	4	no	—
463	C₄×C₆₇	—	2	4	no	—
464	C₄×C₆₇	—	2	2	no	—
465	C₄×C₆₇	—	2	2	no	—
466	C₄×C₆₇	—	2	4	no	—
467	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
468	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
469	Dic₆₇	—	2	8	no	—
470	Dic₆₇	—	2	4	no	—
471	Dic₆₇	—	2	4	no	—
472	C₂×#3546	—	67	1	no	maximal, Sylow
473	C₂×C₆₇	—	4	4	no	—
474	C₂×C₆₇	—	4	2	no	—
475	C₂×C₆₇	#3546	1	4	yes	complemented
476	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
479	D₆₇	—	4	4	no	—
480	D₆₇	—	4	8	no	—
481	D₆₇	—	4	4	no	—
482	#3546	—	67	32	no	—
483	C₂×#560	—	67	4	no	—
484	C₂×#556	—	67	1	no	—
485	C₂×#553	—	67	2	no	—
486	C₂×#550	—	67	1	no	—
487	C₂×#550	—	67	2	no	—
488	C₂×#547	—	67	1	no	—
489	C₂×#546	—	67	2	no	—
490	C₂×#546	—	67	2	no	—
491	C₂×D₄²	—	67	1	no	—
492	C₂×#542	—	67	2	no	—
493	C₂×#538	—	67	4	no	—
494	C₂×#537	—	67	2	no	—
495	C₂×#535	—	67	2	no	—
496	C₂×#535	—	67	2	no	—
497	C₂×#532	—	67	1	no	—
498	C₂×#532	—	67	1	no	—
499	C₂×#529	D₆₇	1	1	yes	characteristic, complemented
500	C₆₇	C₂×#3546	1	1	yes	characteristic, complemented, Sylow
501	C₂²×#41	—	67	2	no	—
502	C₂²×#41	—	67	2	no	—
503	C₂²×#41	—	67	2	no	—
504	C₂²×#41	—	67	2	no	—
505	C₂³×D₄	—	67	2	no	—
506	C₂³×D₄	—	67	2	no	—
507	#560	—	67	64	no	—
508	#556	—	67	16	no	—
509	#553	—	67	32	no	—
510	#550	—	67	16	no	—
511	#550	—	67	32	no	—
512	#547	—	67	16	no	—
513	#546	—	67	32	no	—
514	#546	—	67	32	no	—
515	D₄²	—	67	16	no	—
516	#542	—	67	32	no	—
517	#538	—	67	64	no	—
518	#537	—	67	32	no	—
519	#535	—	67	32	no	—
520	#535	—	67	32	no	—
521	#532	—	67	16	no	—
522	#532	—	67	16	no	—
523	C₂×C₄⋊Q₈	—	67	1	no	—
524	C₂×C₄⋊Q₈	—	67	1	no	—
525	C₂×#127	—	67	4	no	—
526	C₂×#127	—	67	1	no	—
527	C₂×#127	—	67	1	no	—
528	C₂×#127	—	67	2	no	—
529	#529	C₂×D₆₇	1	16	yes	complemented
530	C₂×#126	—	67	4	no	—
531	C₂×#126	—	67	4	no	—
532	C₂×#126	C₂×D₆₇	1	2	yes	complemented
533	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
534	C₂×#124	—	67	4	no	—
535	C₂×#124	—	67	2	no	—
536	C₂×#124	—	67	2	no	—
537	C₂×#124	—	67	2	no	—
538	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
539	C₂×#123	—	67	4	no	—
540	C₂×#123	—	67	4	no	—
541	C₂×#123	—	67	4	no	—
542	C₂×#123	C₂×D₆₇	1	2	yes	complemented
543	C₂×C₂²⋊Q₈	—	67	2	no	—
544	C₂×C₂²⋊Q₈	—	67	2	no	—
545	C₂×C₂²⋊Q₈	—	67	4	no	—
546	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
547	C₂×#121	—	67	2	no	—
548	C₂×#121	—	67	2	no	—
549	C₂×#121	—	67	1	no	—
550	C₂×#121	—	67	1	no	—
551	C₂×#121	—	67	2	no	—
552	C₂×#121	—	67	2	no	—
553	C₂×#121	—	67	2	no	—
554	C₂×#121	—	67	4	no	—
555	C₂×#121	—	67	2	no	—
556	C₂×#121	—	67	4	no	—
557	C₂×#121	—	67	2	no	—
558	C₂×#121	—	67	4	no	—
559	C₂×#121	—	67	4	no	—
560	C₂×#121	—	67	4	no	—
561	C₂×#121	—	67	4	no	—
562	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
563	C₂×#120	—	67	4	no	—
564	C₂×#120	—	67	4	no	—
565	C₂×#120	—	67	4	no	—
566	C₂×#120	—	67	4	no	—
567	C₂×C₄×Q₈	—	67	2	no	—
568	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
569	C₂×C₄×D₄	—	67	4	no	—
570	C₂×C₄×D₄	—	67	1	no	—
571	C₂×C₄×D₄	—	67	2	no	—
572	C₂×C₄×D₄	—	67	2	no	—
573	C₂×C₄×D₄	—	67	2	no	—
574	C₂×C₄×D₄	—	67	1	no	—
575	C₂×C₄×D₄	—	67	2	no	—
576	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
577	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
578	C₂×#117	—	67	2	no	—
579	C₂×#117	C₂×D₆₇	1	2	yes	complemented
580	C₂²×C₄⋊C₄	—	67	2	no	—
581	C₂²×C₂²⋊C₄	—	67	4	no	—
582	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
583	C₂⁵	—	67	4	no	—
584	C₂×#41	—	268	8	no	—
585	C₂×#41	—	268	8	no	—
586	C₂×#41	—	268	8	no	—
587	C₂×#41	—	268	8	no	—
588	C₂×#41	—	67	16	no	—
589	C₂×#41	—	67	16	no	—
590	C₂×#41	—	67	16	no	—
591	C₂×#41	—	67	16	no	—
592	C₂²×Q₈	—	67	2	no	—
593	C₂²×Q₈	—	67	2	no	—
594	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
595	C₂²×D₄	—	268	8	no	—
596	C₂²×D₄	—	268	8	no	—
597	C₂²×D₄	—	67	2	no	—
598	C₂²×D₄	—	67	4	no	—
599	C₂²×D₄	—	67	4	no	—
600	C₂²×D₄	—	67	4	no	—
601	C₂²×D₄	—	67	2	no	—
602	C₂²×D₄	—	67	16	no	—
603	C₂²×D₄	—	67	2	no	—
604	C₂²×D₄	—	67	2	no	—
605	C₂²×D₄	—	67	4	no	—
606	C₂²×D₄	—	67	2	no	—
607	C₂²×D₄	—	67	4	no	—
608	C₂²×D₄	—	67	4	no	—
609	C₂²×D₄	—	67	16	no	—
610	C₂²×D₄	—	67	2	no	—
611	C₂²×D₄	—	67	1	no	—
612	C₂²×D₄	—	67	2	no	—
613	C₂²×D₄	—	67	1	no	—
614	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
615	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
616	C₂³×C₄	—	67	4	no	—
617	C₂³×C₄	—	67	4	no	—
618	C₂³×C₄	—	67	4	no	—
619	C₂³×C₄	—	67	2	no	—
620	C₂³×C₄	—	67	2	no	—
621	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
622	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
623	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
624	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
625	C₄⋊Q₈	—	67	8	no	—
626	C₄⋊Q₈	—	67	8	no	—
627	#127	—	67	32	no	—
628	#127	—	67	8	no	—
629	#127	—	67	8	no	—
630	#127	—	67	16	no	—
631	#126	—	67	32	no	—
632	#126	—	67	32	no	—
633	#126	C₂²×D₆₇	1	16	yes	complemented
634	#125	C₂²×D₆₇	1	8	yes	complemented
635	#124	—	67	32	no	—
636	#124	—	67	16	no	—
637	#124	—	67	16	no	—
638	#124	—	67	16	no	—
639	#124	C₂²×D₆₇	1	8	yes	—
640	#123	—	67	32	no	—
641	#123	—	67	32	no	—
642	#123	—	67	32	no	—
643	#123	C₂²×D₆₇	1	16	yes	complemented
644	C₂²⋊Q₈	—	67	16	no	—
645	C₂²⋊Q₈	—	67	16	no	—
646	C₂²⋊Q₈	—	67	32	no	—
647	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
648	#121	—	67	16	no	—
649	#121	—	67	16	no	—
650	#121	—	67	8	no	—
651	#121	—	67	8	no	—
652	#121	—	67	16	no	—
653	#121	—	67	16	no	—
654	#121	—	67	16	no	—
655	#121	—	67	32	no	—
656	#121	—	67	16	no	—
657	#121	—	67	32	no	—
658	#121	—	67	16	no	—
659	#121	—	67	32	no	—
660	#121	—	67	32	no	—
661	#121	—	67	32	no	—
662	#121	—	67	32	no	—
663	#121	C₂²×D₆₇	1	8	yes	—
664	#120	—	67	32	no	—
665	#120	—	67	32	no	—
666	#120	—	67	32	no	—
667	#120	—	67	32	no	—
668	C₄×Q₈	—	67	16	no	—
669	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
670	C₄×D₄	—	67	32	no	—
671	C₄×D₄	—	67	16	no	—
672	C₄×D₄	—	67	8	no	—
673	C₄×D₄	—	67	16	no	—
674	C₄×D₄	—	67	16	no	—
675	C₄×D₄	—	67	8	no	—
676	C₄×D₄	—	67	16	no	—
677	C₄×D₄	C₂²×D₆₇	1	8	yes	—
678	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
679	#117	—	67	16	no	—
680	#117	C₂²×D₆₇	1	16	yes	complemented
681	C₂×C₄⋊C₄	—	67	2	no	—
682	C₂×C₄⋊C₄	—	67	4	no	—
683	C₂×C₄⋊C₄	—	67	1	no	—
684	C₂×C₄⋊C₄	—	67	1	no	—
685	C₂×C₄⋊C₄	—	67	2	no	—
686	C₂×C₄⋊C₄	—	67	2	no	—
687	C₂×C₄⋊C₄	—	67	4	no	—
688	C₂×C₄⋊C₄	—	67	16	no	—
689	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
692	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
693	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
694	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
695	C₂×C₂²⋊C₄	—	67	4	no	—
696	C₂×C₂²⋊C₄	—	67	2	no	—
697	C₂×C₂²⋊C₄	—	67	4	no	—
698	C₂×C₂²⋊C₄	—	67	4	no	—
699	C₂×C₂²⋊C₄	—	67	2	no	—
700	C₂×C₂²⋊C₄	—	67	2	no	—
701	C₂×C₂²⋊C₄	—	67	4	no	—
702	C₂×C₂²⋊C₄	—	67	4	no	—
703	C₂×C₂²⋊C₄	—	67	4	no	—
704	C₂×C₂²⋊C₄	—	67	4	no	—
705	C₂×C₂²⋊C₄	—	67	2	no	—
706	C₂×C₂²⋊C₄	—	67	32	no	—
707	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
712	C₂×C₄²	—	67	4	no	—
713	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
714	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
715	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
716	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
717	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
718	C₂×C₄²	C₂²×D₆₇	1	8	yes	complemented
719	C₂⁴	—	268	8	no	—
720	C₂⁴	—	268	8	no	—
721	C₂⁴	—	268	8	no	—
722	C₂⁴	—	67	16	no	—
723	C₂⁴	—	67	2	no	—
724	C₂⁴	—	67	4	no	—
725	C₂⁴	—	67	2	no	—
726	C₂⁴	C₂³×D₆₇	1	2	yes	—
727	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
728	#41	—	268	32	no	—
729	#41	—	268	32	no	—
730	#41	—	268	32	no	—
731	#41	—	268	32	no	—
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	268	4	no	—
734	C₂×Q₈	—	67	8	no	—
735	C₂×Q₈	—	67	8	no	—
736	C₂×Q₈	—	134	8	no	—
737	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	268	8	no	—
741	C₂×D₄	—	268	4	no	—
742	C₂×D₄	—	268	8	no	—
743	C₂×D₄	—	268	4	no	—
744	C₂×D₄	—	268	4	no	—
745	C₂×D₄	—	268	8	no	—
746	C₂×D₄	—	268	32	no	—
747	C₂×D₄	—	268	32	no	—
748	C₂×D₄	—	268	8	no	—
749	C₂×D₄	—	268	4	no	—
750	C₂×D₄	—	268	8	no	—
751	C₂×D₄	—	268	8	no	—
752	C₂×D₄	—	268	4	no	—
753	C₂×D₄	—	67	8	no	—
754	C₂×D₄	—	67	16	no	—
755	C₂×D₄	—	67	16	no	—
756	C₂×D₄	—	67	16	no	—
757	C₂×D₄	—	67	8	no	—
758	C₂×D₄	—	67	8	no	—
759	C₂×D₄	—	67	8	no	—
760	C₂×D₄	—	67	16	no	—
761	C₂×D₄	—	67	8	no	—
762	C₂×D₄	—	67	16	no	—
763	C₂×D₄	—	67	16	no	—
764	C₂×D₄	—	67	8	no	—
765	C₂×D₄	—	67	4	no	—
766	C₂×D₄	—	67	8	no	—
767	C₂×D₄	—	67	4	no	—
768	C₂×D₄	—	134	4	no	—
769	C₂×D₄	—	134	8	no	—
770	C₂×D₄	—	134	8	no	—
771	C₂×D₄	—	134	4	no	—
772	C₂×D₄	C₂³×D₆₇	1	4	yes	—
773	C₂×D₄	C₂³×D₆₇	1	8	yes	—
774	C₂²×C₄	—	2	8	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	268	8	no	—
779	C₂²×C₄	—	268	8	no	—
780	C₂²×C₄	—	268	8	no	—
781	C₂²×C₄	—	67	16	no	—
782	C₂²×C₄	—	67	16	no	—
783	C₂²×C₄	—	67	16	no	—
784	C₂²×C₄	—	67	2	no	—
785	C₂²×C₄	—	67	4	no	—
786	C₂²×C₄	—	67	2	no	—
787	C₂²×C₄	—	67	8	no	—
788	C₂²×C₄	—	67	8	no	—
789	C₂²×C₄	—	134	8	no	—
790	C₂²×C₄	—	134	8	no	—
791	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
792	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
793	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
794	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
795	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
796	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
797	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
798	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
799	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
800	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
801	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
802	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
803	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
804	C₄⋊C₄	—	67	8	no	—
805	C₄⋊C₄	—	67	16	no	—
806	C₄⋊C₄	—	67	4	no	—
807	C₄⋊C₄	—	67	4	no	—
808	C₄⋊C₄	—	67	8	no	—
809	C₄⋊C₄	—	67	8	no	—
810	C₄⋊C₄	—	67	16	no	—
811	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
812	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
813	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
814	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
815	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
816	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
817	C₂²⋊C₄	—	67	16	no	—
818	C₂²⋊C₄	—	67	8	no	—
819	C₂²⋊C₄	—	67	16	no	—
820	C₂²⋊C₄	—	67	16	no	—
821	C₂²⋊C₄	—	67	8	no	—
822	C₂²⋊C₄	—	67	8	no	—
823	C₂²⋊C₄	—	67	16	no	—
824	C₂²⋊C₄	—	67	16	no	—
825	C₂²⋊C₄	—	67	16	no	—
826	C₂²⋊C₄	—	67	16	no	—
827	C₂²⋊C₄	—	67	8	no	—
828	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
829	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
830	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
831	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
832	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
833	C₄²	—	67	16	no	—
834	C₄²	C₂³×D₆₇	1	4	yes	—
835	C₄²	C₂³×D₆₇	1	4	yes	—
836	C₄²	C₂³×D₆₇	1	4	yes	—
837	C₄²	C₂³×D₆₇	1	4	yes	—
838	C₄²	C₂³×D₆₇	1	8	yes	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	4	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	268	16	no	—
846	C₂³	—	268	16	no	—
847	C₂³	—	268	16	no	—
848	C₂³	—	536	32	no	—
849	C₂³	—	67	4	no	—
850	C₂³	—	67	8	no	—
851	C₂³	—	67	4	no	—
852	C₂³	—	134	4	no	—
853	C₂³	—	134	8	no	—
854	C₂³	—	134	8	no	—
855	C₂³	—	134	4	no	—
856	C₂³	—	134	4	no	—
857	C₂³	—	134	4	no	—
858	C₂³	—	134	4	no	—
859	C₂³	—	134	8	no	—
860	C₂³	—	134	4	no	—
861	C₂³	C₂⁴×D₆₇	1	4	yes	—
862	C₂³	C₂⁴×D₆₇	1	2	yes	—
863	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
864	Q₈	—	2	8	no	—
865	Q₈	—	268	8	no	—
866	Q₈	—	134	16	no	—
867	D₄	—	2	8	no	—
868	D₄	—	4	8	no	—
869	D₄	—	268	16	no	—
870	D₄	—	268	8	no	—
871	D₄	—	268	16	no	—
872	D₄	—	268	8	no	—
873	D₄	—	268	8	no	—
874	D₄	—	268	16	no	—
875	D₄	—	268	16	no	—
876	D₄	—	268	8	no	—
877	D₄	—	268	16	no	—
878	D₄	—	268	16	no	—
879	D₄	—	268	8	no	—
880	D₄	—	134	8	no	—
881	D₄	—	134	16	no	—
882	D₄	—	134	16	no	—
883	D₄	—	134	8	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	2	16	no	—
892	C₂×C₄	—	2	8	no	—
893	C₂×C₄	—	2	8	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	268	16	no	—
896	C₂×C₄	—	268	16	no	—
897	C₂×C₄	—	268	16	no	—
898	C₂×C₄	—	67	4	no	—
899	C₂×C₄	—	67	8	no	—
900	C₂×C₄	—	67	4	no	—
901	C₂×C₄	—	134	4	no	—
902	C₂×C₄	—	134	8	no	—
903	C₂×C₄	—	134	4	no	—
904	C₂×C₄	—	134	16	no	—
905	C₂×C₄	—	134	16	no	—
906	C₂×C₄	#14524089	1	4	yes	—
907	C₂×C₄	#14524089	1	4	yes	—
908	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
909	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
910	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
911	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
912	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
913	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
914	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
915	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
916	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	4	8	no	—
924	C₂²	—	4	4	no	—
925	C₂²	—	268	8	no	—
926	C₂²	—	268	16	no	—
927	C₂²	—	268	8	no	—
928	C₂²	—	536	32	no	—
929	C₂²	—	134	4	no	—
930	C₂²	—	134	8	no	—
931	C₂²	—	134	8	no	—
932	C₂²	—	134	4	no	—
933	C₂²	—	134	4	no	—
934	C₂²	—	134	4	no	—
935	C₂²	—	134	4	no	—
936	C₂²	—	134	8	no	—
937	C₂²	—	134	4	no	—
938	C₂²	C₂×#14524089	1	2	yes	—
939	C₂²	C₂×#14524089	1	2	yes	—
940	C₂²	#16864232	1	2	yes	—
941	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	4	no	—
949	C₄	—	134	4	no	—
950	C₄	—	134	8	no	—
951	C₄	—	134	4	no	—
952	C₄	C₂×#14524089	1	4	yes	—
953	C₄	C₂×#14524089	1	4	yes	—
954	C₂	—	4	4	no	—
955	C₂	—	4	2	no	—
956	C₂	—	268	4	no	—
957	C₂	—	268	8	no	—
958	C₂	—	268	4	no	—
959	C₂	#22574583	1	4	yes	direct product factor
960	C₂	C₂²×#14524089	1	1	yes	characteristic
961	C₂	C₂²×#14524089	1	1	yes	characteristic
962	C₂	C₂×#16864232	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#529×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#529	D₆₇
hypocenter	C₆₇	C₂×#3546
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #22574583	C₂	direct (N × H)
2. C₂×#16864136	C₂	semidirect
3. C₂×#16864119	C₂	semidirect
4. C₂×#16864099	C₂	semidirect
5. C₂×#16864068	C₂	semidirect
6. C₂×#16864067	C₂	semidirect
7. C₂×#16864051	C₂	semidirect
8. C₂×#16864042	C₂	semidirect
9. C₂×#16864039	C₂	semidirect
10. C₂×D₄×D₂₆₈	C₂	semidirect
11. C₂×#16864017	C₂	semidirect
12. C₂×#16863985	C₂	semidirect
13. C₂×#16863976	C₂	semidirect
14. C₂×#16863965	C₂	semidirect
15. C₂×#16863962	C₂	semidirect
16. C₂×#16863946	C₂	semidirect
17. C₂×#16863946	C₂	semidirect
18. C₂×#529×C₆₇	C₂	semidirect
19. C₂²×#11761629	C₂²	semidirect
20. C₂²×#11761628	C₂²	semidirect
21. C₂²×#11761628	C₂²	semidirect
22. C₂²×#11761628	C₂²	semidirect
25. #16864136	C₂²	semidirect
26. #16864119	C₂²	semidirect
27. #16864099	C₂²	semidirect
28. #16864068	C₂²	semidirect
29. #16864067	C₂²	semidirect
30. #16864051	C₂²	semidirect
31. #16864042	C₂²	semidirect
32. #16864039	C₂²	semidirect
33. D₄×D₂₆₈	C₂²	semidirect
34. #16864017	C₂²	semidirect
35. #16863985	C₂²	semidirect
36. #16863976	C₂²	semidirect
37. #16863965	C₂²	semidirect
38. #16863962	C₂²	semidirect
39. #16863946	C₂²	semidirect
40. #16863946	C₂²	semidirect
41. C₂×#14524043	C₂²	semidirect
42. C₂×#14524043	C₂²	semidirect
45. C₂×#14524040	C₂²	semidirect
46. C₂×#14524039	C₂²	semidirect
47. C₂×#14524038	C₂²	semidirect
48. C₂×#14524038	C₂²	semidirect
50. C₂×#14524031	C₂²	semidirect
51. C₂×#14524031	C₂²	semidirect
52. C₂×#14524029	C₂²	semidirect
53. C₂×#14524028	C₂²	semidirect
54. C₂×#14524025	C₂²	semidirect
55. C₂×#14524025	C₂²	semidirect
56. C₂×#14524022	C₂²	semidirect
57. C₂×#14524021	C₂²	semidirect
58. C₂×#14524019	C₂²	semidirect
60. C₂×#14524018	C₂²	semidirect
61. C₂×#14524018	C₂²	semidirect
62. C₂×#14524018	C₂²	semidirect
63. C₂×#14524018	C₂²	semidirect
66. C₂×#14524017	C₂²	semidirect
67. C₂×#14524017	C₂²	semidirect
68. C₂×#14524017	C₂²	semidirect
69. C₂×#14524017	C₂²	semidirect
70. C₂×#14524016	C₂²	semidirect
71. C₂×#14524016	C₂²	semidirect
72. C₂×#14524016	C₂²	semidirect
75. C₂×#14524013	C₂²	semidirect
76. C₂×#14524013	C₂²	semidirect
77. C₂×#14524011	C₂²	semidirect
78. C₂×C₄×Dic₁₃₄	C₂²	semidirect
80. C₂×C₄×D₂₆₈	C₂²	semidirect
81. C₂×C₄×D₂₆₈	C₂²	semidirect
82. C₂×C₄×D₂₆₈	C₂²	semidirect
83. C₂×C₄×D₂₆₈	C₂²	semidirect
84. C₂×C₄×D₂₆₈	C₂²	semidirect
85. C₂×#14524005	C₂²	semidirect
86. C₂×#14524001	C₂²	semidirect
87. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
88. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
89. #529×C₆₇	C₂²	semidirect
90. C₂×#126×C₆₇	C₂²	semidirect
91. C₂×#125×C₆₇	C₂²	semidirect
93. C₂×#123×C₆₇	C₂²	semidirect
94. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
96. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
98. C₂×C₄×D₄×C₆₇	C₂²	semidirect
99. C₂×#117×C₆₇	C₂²	semidirect
100. C₂²×C₄²×C₆₇	C₂²	semidirect
103. C₂×#11761629	C₂³	semidirect
107. C₂×#11761628	C₂³	semidirect
108. C₂×#11761628	C₂³	semidirect
109. C₂×#11761628	C₂³	semidirect
136. #14524043	C₂³	semidirect
137. #14524043	C₂³	semidirect
140. #14524040	C₂³	semidirect
141. #14524039	C₂³	semidirect
142. #14524038	C₂³	semidirect
143. #14524038	C₂³	semidirect
145. #14524031	C₂³	semidirect
146. #14524031	C₂³	semidirect
147. #14524029	C₂³	semidirect
148. #14524028	C₂³	semidirect
149. #14524025	C₂³	semidirect
150. #14524025	C₂³	semidirect
151. #14524022	C₂³	semidirect
152. #14524021	C₂³	semidirect
153. #14524019	C₂³	semidirect
155. #14524018	C₂³	semidirect
156. #14524018	C₂³	semidirect
157. #14524018	C₂³	semidirect
158. #14524018	C₂³	semidirect
161. #14524017	C₂³	semidirect
162. #14524017	C₂³	semidirect
163. #14524017	C₂³	semidirect
164. #14524017	C₂³	semidirect
165. #14524016	C₂³	semidirect
166. #14524016	C₂³	semidirect
167. #14524016	C₂³	semidirect
170. #14524013	C₂³	semidirect
171. #14524013	C₂³	semidirect
172. #14524011	C₂³	semidirect
173. C₄×Dic₁₃₄	C₂³	semidirect
175. C₄×D₂₆₈	C₂³	semidirect
176. C₄×D₂₆₈	C₂³	semidirect
177. C₄×D₂₆₈	C₂³	semidirect
178. C₄×D₂₆₈	C₂³	semidirect
179. C₄×D₂₆₈	C₂³	semidirect
180. #14524005	C₂³	semidirect
181. #14524001	C₂³	semidirect
189. C₄⋊C₄×D₆₇	C₂³	semidirect
201. C₂²⋊C₄×D₆₇	C₂³	semidirect
210. #126×C₆₇	C₂³	semidirect
211. #125×C₆₇	C₂³	semidirect
213. #123×C₆₇	C₂³	semidirect
214. C₂²⋊Q₈×C₆₇	C₂³	semidirect
216. C₄×Q₈×C₆₇	C₂³	semidirect
218. C₄×D₄×C₆₇	C₂³	semidirect
219. #117×C₆₇	C₂³	semidirect
236. C₂×C₄²×C₆₇	C₂³	semidirect
475. C₂×C₆₇	#3546	semidirect
499. C₂×#529	D₆₇	semidirect
500. C₆₇	C₂×#3546	semidirect
529. #529	C₂×D₆₇	semidirect
532. C₂×#126	C₂×D₆₇	semidirect
533. C₂×#125	C₂×D₆₇	semidirect
542. C₂×#123	C₂×D₆₇	semidirect
546. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
568. C₂×C₄×Q₈	C₂×D₆₇	semidirect
577. C₂×C₄×D₄	C₂×D₆₇	semidirect
579. C₂×#117	C₂×D₆₇	semidirect
582. C₂²×C₄²	C₂×D₆₇	semidirect
633. #126	C₂²×D₆₇	semidirect
634. #125	C₂²×D₆₇	semidirect
643. #123	C₂²×D₆₇	semidirect
647. C₂²⋊Q₈	C₂²×D₆₇	semidirect
669. C₄×Q₈	C₂²×D₆₇	semidirect
678. C₄×D₄	C₂²×D₆₇	semidirect
680. #117	C₂²×D₆₇	semidirect
718. C₂×C₄²	C₂²×D₆₇	semidirect
959. C₂	#22574583	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574583	2
C₂×#16864136	2
C₂×#16864119	2
C₂×#16864099	2
C₂×#16864068	2
C₂×#16864067	2
C₂×#16864051	2
C₂×#16864042	2
C₂×#16864039	2
C₂×D₄×D₂₆₈	2
C₂×#16864017	2
C₂×#16863985	2
C₂×#16863976	2
C₂×#16863965	2
C₂×#16863962	2
C₂×#16863946	2
C₂×#529×C₆₇	2
C₂×#3546	67

Subgroups — C2×#22574583 #31763470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574583 #31763470