Subgroups — C₂×#22574779 #31763184

Order 17152.

7258 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574779	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864150	C₂	1	2	yes	maximal, complemented
3	C₂×#16864140	C₂	1	2	yes	maximal, complemented
4	C₂×#16864119	C₂	1	2	yes	maximal, complemented
5	C₂×#16864069	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×Dic₁₃₄	C₂	1	2	yes	maximal, complemented
7	C₂×#16864055	C₂	1	2	yes	maximal, complemented
8	C₂×#16864042	C₂	1	2	yes	maximal, complemented
9	C₂×#16864021	C₂	1	2	yes	maximal, complemented
10	C₂×#16864017	C₂	1	2	yes	maximal, complemented
11	C₂×#16864012	C₂	1	4	yes	maximal, complemented
12	C₂×#16863983	C₂	1	2	yes	maximal, complemented
13	C₂×#16863972	C₂	1	2	yes	maximal, complemented
14	C₂×#16863953	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#14524031	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11761628	C₂²	1	2	yes	—
18	C₂³×Dic₁₃₄	C₂²	1	1	yes	characteristic
19	C₂³×Dic₁₃₄	C₂²	1	2	yes	complemented
20	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
21	#16864150	C₂²	1	32	yes	complemented
22	#16864140	C₂²	1	32	yes	complemented
23	#16864119	C₂²	1	32	yes	complemented
24	#16864069	C₂²	1	64	yes	complemented
25	D₄×Dic₁₃₄	C₂²	1	32	yes	complemented
26	#16864055	C₂²	1	32	yes	complemented
27	#16864042	C₂²	1	32	yes	complemented
28	#16864021	C₂²	1	32	yes	complemented
29	#16864017	C₂²	1	32	yes	complemented
30	#16864012	C₂²	1	64	yes	complemented
31	#16863983	C₂²	1	32	yes	complemented
32	#16863972	C₂²	1	32	yes	complemented
33	#16863953	C₂²	1	16	yes	complemented
34	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14524043	C₂²	1	2	yes	complemented
36	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
37	C₂×#14524042	C₂²	1	4	yes	complemented
38	C₂×#14524038	C₂²	1	4	yes	complemented
39	C₂×#14524038	C₂²	1	4	yes	complemented
40	C₂×#14524038	C₂²	1	4	yes	complemented
41	C₂×#14524035	C₂²	1	2	yes	complemented
42	C₂×#14524031	C₂²	1	2	yes	—
43	C₂×#14524031	C₂²	1	2	yes	—
44	C₂×#14524031	C₂²	1	2	yes	—
45	C₂×#14524031	C₂²	1	2	yes	—
46	C₂×#14524031	C₂²	1	2	yes	—
47	C₂×#14524031	C₂²	1	16	yes	complemented
48	C₂×#14524029	C₂²	1	4	yes	complemented
49	C₂×#14524029	C₂²	1	4	yes	complemented
50	C₂×#14524028	C₂²	1	4	yes	—
51	C₂×#14524027	C₂²	1	4	yes	complemented
52	C₂×#14524027	C₂²	1	4	yes	complemented
53	C₂×#14524025	C₂²	1	4	yes	complemented
54	C₂×#14524023	C₂²	1	4	yes	complemented
55	C₂×#14524023	C₂²	1	4	yes	complemented
56	C₂×#14524022	C₂²	1	2	yes	—
57	C₂×#14524022	C₂²	1	2	yes	—
58	C₂×#14524022	C₂²	1	2	yes	complemented
59	C₂×#14524021	C₂²	1	4	yes	complemented
60	C₂×#14524021	C₂²	1	4	yes	complemented
61	C₂×#14524020	C₂²	1	4	yes	—
62	C₂×#14524020	C₂²	1	4	yes	complemented
63	C₂×#14524019	C₂²	1	4	yes	complemented
64	C₂×#14524017	C₂²	1	2	yes	—
65	C₂×#14524016	C₂²	1	4	yes	—
66	C₂×#14524015	C₂²	1	4	yes	complemented
67	C₂×#14524011	C₂²	1	4	yes	—
68	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
69	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
70	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
71	C₂×C₄×D₂₆₈	C₂²	1	2	yes	—
72	C₂×D₄×Dic₆₇	C₂²	1	4	yes	—
73	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
74	C₂×#14524002	C₂²	1	2	yes	—
75	C₂×#14524001	C₂²	1	4	yes	complemented
76	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
77	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
78	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	—
79	#529×C₆₇	C₂²	1	16	yes	complemented
80	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
81	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	C₂×#123×C₆₇	C₂²	1	2	yes	—
84	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
85	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
86	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
88	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
90	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
91	C₂⁴×D₆₇	C₂³	1	2	yes	—
92	C₂×#11761628	—	4	8	no	—
93	C₂×#11761628	C₂³	1	16	yes	—
94	C₂²×Dic₁₃₄	—	4	4	no	—
95	C₂²×Dic₁₃₄	—	4	8	no	—
96	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
97	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
98	C₂²×Dic₁₃₄	C₂³	1	8	yes	—
99	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
100	C₂²×Dic₁₃₄	C₂³	1	4	yes	—
101	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
102	C₂²×Dic₁₃₄	C₂³	1	16	yes	complemented
103	C₂²×D₂₆₈	—	4	4	no	—
104	C₂²×D₂₆₈	C₂³	1	2	yes	—
105	C₂²×D₂₆₈	C₂³	1	8	yes	—
106	C₂²×D₂₆₈	C₂³	1	2	yes	—
107	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
108	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
109	C₂³×Dic₆₇	C₂³	1	2	yes	—
110	C₂³×Dic₆₇	C₂³	1	4	yes	—
111	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
112	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
113	#14524043	C₂³	1	8	yes	complemented
114	#14524043	C₂³	1	16	yes	complemented
115	#14524043	C₂³	1	8	yes	complemented
116	#14524042	C₂³	1	32	yes	complemented
117	#14524038	C₂³	1	32	yes	complemented
118	#14524038	C₂³	1	32	yes	complemented
119	#14524038	C₂³	1	32	yes	complemented
120	#14524035	C₂³	1	16	yes	complemented
121	#14524031	C₂³	1	16	yes	—
122	#14524031	C₂³	1	16	yes	—
123	#14524031	C₂³	1	16	yes	—
124	#14524031	C₂³	1	16	yes	—
125	#14524031	C₂³	1	16	yes	—
126	#14524029	C₂³	1	32	yes	complemented
127	#14524029	C₂³	1	32	yes	complemented
128	#14524028	C₂³	1	32	yes	—
129	#14524027	C₂³	1	32	yes	complemented
130	#14524027	C₂³	1	32	yes	complemented
131	#14524025	C₂³	1	32	yes	complemented
132	#14524023	C₂³	1	32	yes	complemented
133	#14524023	C₂³	1	32	yes	complemented
134	#14524022	C₂³	1	16	yes	—
135	#14524022	C₂³	1	16	yes	—
136	#14524022	C₂³	1	16	yes	complemented
137	#14524021	C₂³	1	32	yes	complemented
138	#14524021	C₂³	1	32	yes	complemented
139	#14524020	C₂³	1	32	yes	—
140	#14524020	C₂³	1	32	yes	complemented
141	#14524019	C₂³	1	32	yes	complemented
142	#14524017	C₂³	1	16	yes	—
143	#14524016	C₂³	1	32	yes	—
144	#14524015	C₂³	1	32	yes	complemented
145	#14524011	C₂³	1	32	yes	—
146	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
147	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
148	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
149	C₄×D₂₆₈	C₂³	1	16	yes	—
150	D₄×Dic₆₇	C₂³	1	32	yes	—
151	(C₂²⋊D₆₇)⋊C₄	C₂³	1	32	yes	complemented
152	#14524002	C₂³	1	16	yes	—
153	#14524001	C₂³	1	32	yes	complemented
154	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
155	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
158	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
160	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
161	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
162	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
163	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
164	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
165	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
166	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	—
167	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	—
168	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
169	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
170	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
171	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
172	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
173	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
174	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
175	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
176	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	—
177	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
178	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
179	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
180	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
181	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
185	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
186	#126×C₆₇	C₂³	1	16	yes	complemented
187	#125×C₆₇	C₂³	1	8	yes	complemented
188	#124×C₆₇	C₂³	1	8	yes	complemented
189	#123×C₆₇	C₂³	1	16	yes	—
190	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
191	#121×C₆₇	C₂³	1	8	yes	—
192	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
193	C₄×D₄×C₆₇	C₂³	1	16	yes	—
194	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
195	#117×C₆₇	C₂³	1	16	yes	complemented
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
212	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
213	C₂³×D₆₇	—	2	8	no	—
214	C₂³×D₆₇	—	4	4	no	—
215	C₂³×D₆₇	—	4	4	no	—
216	C₂³×D₆₇	C₂⁴	1	4	yes	—
217	C₂³×D₆₇	C₂⁴	1	8	yes	—
218	#11761628	—	4	32	no	—
219	C₂×Dic₁₃₄	—	2	8	no	—
220	C₂×Dic₁₃₄	—	2	8	no	—
221	C₂×Dic₁₃₄	—	4	16	no	—
222	C₂×Dic₁₃₄	—	4	32	no	—
223	C₂×Dic₁₃₄	—	4	8	no	—
224	C₂×Dic₁₃₄	—	4	4	no	—
225	C₂×Dic₁₃₄	—	4	4	no	—
226	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
227	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
228	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
229	C₂×Dic₁₃₄	C₂⁴	1	16	yes	—
230	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
231	C₂×D₂₆₈	—	2	8	no	—
232	C₂×D₂₆₈	—	4	16	no	—
233	C₂×D₂₆₈	—	4	4	no	—
234	C₂×D₂₆₈	C₂⁴	1	8	yes	—
235	C₂×D₂₆₈	C₂⁴	1	8	yes	—
236	C₂×C₂²⋊D₆₇	—	4	8	no	—
237	C₂×C₂²⋊D₆₇	—	4	8	no	—
238	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
239	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
240	C₂²×Dic₆₇	—	4	8	no	—
241	C₂²×Dic₆₇	—	4	4	no	—
242	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
243	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
244	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
245	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
246	C₂²×Dic₆₇	C₂⁴	1	16	yes	—
247	C₂×C₄×D₆₇	—	4	8	no	—
248	C₂×C₄×D₆₇	—	4	8	no	—
249	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
250	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
251	C₄⋊Dic₆₇	C₂⁴	1	16	yes	—
252	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
253	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
254	C₄⋊Dic₆₇	C₂⁴	1	16	yes	—
255	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
256	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
257	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
258	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
259	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
260	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
261	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
262	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
263	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
264	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
265	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
266	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
267	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
268	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
269	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
270	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
271	C₄×Dic₆₇	C₂⁴	1	16	yes	—
272	C₄×Dic₆₇	C₂⁴	1	16	yes	—
273	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
274	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂×Q₈×C₆₇	—	4	2	no	—
276	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
277	C₂×D₄×C₆₇	—	2	8	no	—
278	C₂×D₄×C₆₇	—	4	2	no	—
279	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
280	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₆₇	—	2	4	no	—
282	C₂²×C₄×C₆₇	—	2	4	no	—
283	C₂²×C₄×C₆₇	—	2	8	no	—
284	C₂²×C₄×C₆₇	—	4	2	no	—
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
299	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
300	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
301	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
304	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
305	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
306	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
307	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
308	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
309	C₄²×C₆₇	C₂⁴	1	4	yes	—
310	C₄²×C₆₇	C₂⁴	1	4	yes	—
311	C₄²×C₆₇	C₂⁴	1	4	yes	—
312	C₄²×C₆₇	C₂⁴	1	4	yes	—
313	C₄²×C₆₇	C₂⁴	1	8	yes	—
314	C₂³×C₆₇	—	2	2	no	—
315	C₂³×C₆₇	—	2	2	no	—
316	C₂³×C₆₇	—	2	4	no	—
317	C₂³×C₆₇	—	2	4	no	—
318	C₂³×C₆₇	—	2	4	no	—
319	C₂³×C₆₇	2₋¹⁺⁴	1	4	yes	—
320	C₂³×C₆₇	C₂⁵	1	4	yes	—
321	C₂³×C₆₇	C₂⁵	1	2	yes	—
322	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
323	C₂²×D₆₇	—	2	8	no	—
324	C₂²×D₆₇	—	2	8	no	—
325	C₂²×D₆₇	—	2	8	no	—
326	C₂²×D₆₇	—	2	16	no	—
327	C₂²×D₆₇	—	4	8	no	—
328	C₂²×D₆₇	—	4	8	no	—
329	C₂²×D₆₇	—	8	16	no	—
330	C₂²×D₆₇	C₂⁵	1	8	yes	—
331	Q₈×C₆₇	—	4	4	no	—
332	D₄×C₆₇	—	2	16	no	—
333	D₄×C₆₇	—	4	4	no	—
334	C₂×C₄×C₆₇	—	2	4	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	8	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	4	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	4	no	—
343	C₂×C₄×C₆₇	—	2	8	no	—
344	C₂×C₄×C₆₇	—	2	16	no	—
345	C₂×C₄×C₆₇	—	4	4	no	—
346	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
347	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
348	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
349	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
350	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
351	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
352	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
353	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
354	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
355	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
356	C₂²⋊D₆₇	—	4	16	no	—
357	C₂²⋊D₆₇	—	4	16	no	—
358	C₂×Dic₆₇	—	2	8	no	—
359	C₂×Dic₆₇	—	2	8	no	—
360	C₂×Dic₆₇	—	2	8	no	—
361	C₂×Dic₆₇	—	4	8	no	—
362	C₂×Dic₆₇	—	4	16	no	—
363	C₂×Dic₆₇	C₂⁵	1	8	yes	—
364	C₂×Dic₆₇	C₂⁵	1	8	yes	—
365	C₂×Dic₆₇	C₂⁵	1	8	yes	—
366	D₂₆₈	—	2	16	no	—
367	D₂₆₈	—	4	8	no	—
368	C₄×D₆₇	—	4	16	no	—
369	C₄×D₆₇	—	4	16	no	—
370	Dic₁₃₄	—	2	16	no	—
371	Dic₁₃₄	—	2	16	no	—
372	Dic₁₃₄	—	4	8	no	—
373	Dic₁₃₄	—	4	16	no	—
374	Dic₁₃₄	—	4	8	no	—
375	C₂²×C₆₇	—	2	2	no	—
376	C₂²×C₆₇	—	2	2	no	—
377	C₂²×C₆₇	—	2	8	no	—
378	C₂²×C₆₇	—	2	4	no	—
379	C₂²×C₆₇	—	2	4	no	—
380	C₂²×C₆₇	—	2	4	no	—
381	C₂²×C₆₇	—	4	8	no	—
382	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
383	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
384	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
385	C₂²×C₆₇	#585	1	2	yes	—
386	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
387	C₂×D₆₇	—	2	8	no	—
388	C₂×D₆₇	—	2	8	no	—
389	C₂×D₆₇	—	2	8	no	—
390	C₂×D₆₇	—	4	16	no	—
391	C₂×D₆₇	—	8	16	no	—
392	C₄×C₆₇	—	2	4	no	—
393	C₄×C₆₇	—	2	2	no	—
394	C₄×C₆₇	—	2	2	no	—
395	C₄×C₆₇	—	2	2	no	—
396	C₄×C₆₇	—	2	4	no	—
397	C₄×C₆₇	—	2	2	no	—
398	C₄×C₆₇	—	2	4	no	—
399	C₄×C₆₇	—	2	2	no	—
400	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
401	Dic₆₇	—	2	8	no	—
402	Dic₆₇	—	2	8	no	—
403	Dic₆₇	—	2	8	no	—
404	C₂×#3561	—	67	1	no	maximal, Sylow
405	C₂×C₆₇	—	2	4	no	—
406	C₂×C₆₇	—	4	4	no	—
407	C₂×C₆₇	#3561	1	4	yes	complemented
408	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂×C₆₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
410	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
411	D₆₇	—	4	8	no	—
412	#3561	—	67	32	no	—
413	C₂×#563	—	67	2	no	—
414	C₂×#562	—	67	2	no	—
415	C₂×#556	—	67	2	no	—
416	C₂×#551	—	67	4	no	—
417	C₂×D₄×Q₈	—	67	2	no	—
418	C₂×#548	—	67	2	no	—
419	C₂×#546	—	67	2	no	—
420	C₂×#543	—	67	2	no	—
421	C₂×#542	—	67	4	no	—
422	C₂×#542	—	67	2	no	—
423	C₂×#538	—	67	2	no	—
424	C₂×#536	—	67	2	no	—
425	C₂×#533	—	67	1	no	—
426	C₂×#529	D₆₇	1	1	yes	characteristic, complemented
427	C₂²×#124	—	67	1	no	—
428	C₆₇	C₂×#3561	1	1	yes	characteristic, complemented, Sylow
429	C₂²×#41	—	67	2	no	—
430	C₂³×Q₈	—	67	1	no	—
431	C₂³×Q₈	—	67	2	no	—
432	C₂³×D₄	—	67	1	no	—
433	#563	—	67	32	no	—
434	#562	—	67	32	no	—
435	#556	—	67	32	no	—
436	#551	—	67	64	no	—
437	D₄×Q₈	—	67	32	no	—
438	#548	—	67	32	no	—
439	#546	—	67	32	no	—
440	#543	—	67	32	no	—
441	#542	—	67	64	no	—
442	#542	—	67	32	no	—
443	#538	—	67	32	no	—
444	#536	—	67	32	no	—
445	#533	—	67	16	no	—
446	C₂×C₄⋊Q₈	—	67	4	no	—
447	C₂×C₄⋊Q₈	—	67	1	no	—
448	C₂×C₄⋊Q₈	—	67	1	no	—
449	C₂×C₄⋊Q₈	—	67	2	no	—
450	#529	C₂×D₆₇	1	16	yes	complemented
451	C₂×#126	—	67	4	no	—
452	C₂×#126	—	67	4	no	—
453	C₂×#126	—	67	4	no	—
454	C₂×#126	C₂×D₆₇	1	2	yes	complemented
455	C₂×#125	—	67	2	no	—
456	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
457	C₂×#124	—	67	4	no	—
458	C₂×#124	—	67	4	no	—
459	C₂×#124	—	67	2	no	—
460	C₂×#124	—	67	2	no	—
461	C₂×#124	—	67	2	no	—
462	C₂×#124	—	67	2	no	—
463	C₂×#124	—	67	16	no	—
464	C₂×#124	—	67	2	no	—
465	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
466	C₂×#123	—	67	4	no	—
467	C₂×#123	—	67	4	no	—
468	C₂×#123	—	67	4	no	—
469	C₂×#123	—	67	4	no	—
470	C₂×#123	C₂×D₆₇	1	2	yes	—
471	C₂×C₂²⋊Q₈	—	67	4	no	—
472	C₂×C₂²⋊Q₈	—	67	2	no	—
473	C₂×C₂²⋊Q₈	—	67	2	no	—
474	C₂×C₂²⋊Q₈	—	67	2	no	—
475	C₂×C₂²⋊Q₈	—	67	4	no	—
476	C₂×C₂²⋊Q₈	—	67	4	no	—
477	C₂×C₂²⋊Q₈	—	67	4	no	—
478	C₂×C₂²⋊Q₈	—	67	4	no	—
479	C₂×C₂²⋊Q₈	—	67	4	no	—
480	C₂×C₂²⋊Q₈	—	67	4	no	—
481	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
482	C₂×#121	—	67	4	no	—
483	C₂×#121	—	67	2	no	—
484	C₂×#121	—	67	4	no	—
485	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
486	C₂×#120	—	67	4	no	—
487	C₂×C₄×Q₈	—	67	2	no	—
488	C₂×C₄×Q₈	—	67	2	no	—
489	C₂×C₄×Q₈	—	67	2	no	—
490	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
491	C₂×C₄×D₄	—	67	4	no	—
492	C₂×C₄×D₄	—	67	4	no	—
493	C₂×C₄×D₄	—	67	2	no	—
494	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	—
495	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
496	C₂×#117	—	67	2	no	—
497	C₂×#117	—	67	4	no	—
498	C₂×#117	C₂×D₆₇	1	2	yes	complemented
499	C₂²×C₂²⋊C₄	—	67	2	no	—
500	C₂²×C₂²⋊C₄	—	67	2	no	—
501	C₂²×C₂²⋊C₄	—	67	4	no	—
502	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
503	C₂⁵	—	67	2	no	—
504	C₂×#41	—	268	8	no	—
505	C₂×#41	—	67	16	no	—
506	C₂²×Q₈	—	268	4	no	—
507	C₂²×Q₈	—	268	8	no	—
508	C₂²×Q₈	—	67	2	no	—
509	C₂²×Q₈	—	67	4	no	—
510	C₂²×Q₈	—	67	2	no	—
511	C₂²×Q₈	—	67	8	no	—
512	C₂²×Q₈	—	67	16	no	—
513	C₂²×Q₈	—	67	2	no	—
514	C₂²×Q₈	—	67	2	no	—
515	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
516	C₂²×D₄	—	268	4	no	—
517	C₂²×D₄	—	67	4	no	—
518	C₂²×D₄	—	67	4	no	—
519	C₂²×D₄	—	67	2	no	—
520	C₂²×D₄	—	67	8	no	—
521	C₂²×D₄	—	67	2	no	—
522	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
523	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
524	C₂³×C₄	—	67	2	no	—
525	C₂³×C₄	—	67	4	no	—
526	C₂³×C₄	—	67	4	no	—
527	C₂³×C₄	—	67	4	no	—
528	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
529	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
530	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
531	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
532	C₄⋊Q₈	—	67	32	no	—
533	C₄⋊Q₈	—	67	8	no	—
534	C₄⋊Q₈	—	67	8	no	—
535	C₄⋊Q₈	—	67	16	no	—
536	#126	—	67	32	no	—
537	#126	—	67	32	no	—
538	#126	—	67	32	no	—
539	#126	C₂²×D₆₇	1	16	yes	complemented
540	#125	—	67	16	no	—
541	#125	C₂²×D₆₇	1	8	yes	complemented
542	#124	—	67	32	no	—
543	#124	—	67	32	no	—
544	#124	—	67	16	no	—
545	#124	—	67	16	no	—
546	#124	—	67	16	no	—
547	#124	—	67	16	no	—
548	#124	—	67	16	no	—
549	#124	C₂²×D₆₇	1	8	yes	complemented
550	#123	—	67	32	no	—
551	#123	—	67	32	no	—
552	#123	—	67	32	no	—
553	#123	—	67	32	no	—
554	#123	C₂²×D₆₇	1	16	yes	—
555	C₂²⋊Q₈	—	67	32	no	—
556	C₂²⋊Q₈	—	67	16	no	—
557	C₂²⋊Q₈	—	67	16	no	—
558	C₂²⋊Q₈	—	67	16	no	—
559	C₂²⋊Q₈	—	67	32	no	—
560	C₂²⋊Q₈	—	67	32	no	—
561	C₂²⋊Q₈	—	67	32	no	—
562	C₂²⋊Q₈	—	67	32	no	—
563	C₂²⋊Q₈	—	67	32	no	—
564	C₂²⋊Q₈	—	67	32	no	—
565	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	—
566	#121	—	67	32	no	—
567	#121	—	67	16	no	—
568	#121	—	67	32	no	—
569	#121	C₂²×D₆₇	1	8	yes	—
570	#120	—	67	32	no	—
571	C₄×Q₈	—	67	16	no	—
572	C₄×Q₈	—	67	16	no	—
573	C₄×Q₈	—	67	16	no	—
574	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
575	C₄×D₄	—	67	32	no	—
576	C₄×D₄	—	67	32	no	—
577	C₄×D₄	—	67	16	no	—
578	C₄×D₄	C₂²×D₆₇	1	16	yes	—
579	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
580	#117	—	67	16	no	—
581	#117	—	67	32	no	—
582	#117	C₂²×D₆₇	1	16	yes	complemented
583	C₂×C₄⋊C₄	—	67	4	no	—
584	C₂×C₄⋊C₄	—	67	2	no	—
585	C₂×C₄⋊C₄	—	67	2	no	—
586	C₂×C₄⋊C₄	—	67	2	no	—
587	C₂×C₄⋊C₄	—	67	4	no	—
588	C₂×C₄⋊C₄	—	67	4	no	—
589	C₂×C₄⋊C₄	—	67	4	no	—
590	C₂×C₄⋊C₄	—	67	4	no	—
591	C₂×C₄⋊C₄	—	67	4	no	—
592	C₂×C₄⋊C₄	—	67	2	no	—
593	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	—	67	4	no	—
600	C₂×C₂²⋊C₄	—	67	4	no	—
601	C₂×C₂²⋊C₄	—	67	4	no	—
602	C₂×C₂²⋊C₄	—	67	4	no	—
603	C₂×C₂²⋊C₄	—	67	4	no	—
604	C₂×C₂²⋊C₄	—	67	4	no	—
605	C₂×C₂²⋊C₄	—	67	4	no	—
606	C₂×C₂²⋊C₄	—	67	4	no	—
607	C₂×C₂²⋊C₄	—	67	16	no	—
608	C₂×C₂²⋊C₄	—	67	16	no	—
609	C₂×C₂²⋊C₄	—	67	4	no	—
610	C₂×C₂²⋊C₄	—	67	4	no	—
611	C₂×C₂²⋊C₄	—	67	32	no	—
612	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
617	C₂×C₄²	—	67	4	no	—
618	C₂×C₄²	—	67	4	no	—
619	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
620	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
621	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
622	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
623	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
624	C₂×C₄²	C₂²×D₆₇	1	8	yes	—
625	C₂⁴	—	268	4	no	—
626	C₂⁴	—	268	4	no	—
627	C₂⁴	—	67	8	no	—
628	C₂⁴	—	67	4	no	—
629	C₂⁴	—	134	8	no	—
630	C₂⁴	C₂³×D₆₇	1	2	yes	—
631	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
632	#41	—	268	32	no	—
633	C₂×Q₈	—	4	2	no	—
634	C₂×Q₈	—	268	16	no	—
635	C₂×Q₈	—	268	32	no	—
636	C₂×Q₈	—	268	8	no	—
637	C₂×Q₈	—	268	4	no	—
638	C₂×Q₈	—	268	4	no	—
639	C₂×Q₈	—	67	8	no	—
640	C₂×Q₈	—	67	16	no	—
641	C₂×Q₈	—	67	8	no	—
642	C₂×Q₈	—	67	8	no	—
643	C₂×Q₈	—	67	8	no	—
644	C₂×Q₈	—	134	8	no	—
645	C₂×Q₈	—	134	8	no	—
646	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	268	4	no	—
650	C₂×D₄	—	268	16	no	—
651	C₂×D₄	—	268	8	no	—
652	C₂×D₄	—	268	8	no	—
653	C₂×D₄	—	67	16	no	—
654	C₂×D₄	—	67	16	no	—
655	C₂×D₄	—	67	8	no	—
656	C₂×D₄	—	67	8	no	—
657	C₂×D₄	—	134	8	no	—
658	C₂×D₄	C₂³×D₆₇	1	8	yes	—
659	C₂×D₄	C₂³×D₆₇	1	4	yes	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	8	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	268	8	no	—
665	C₂²×C₄	—	268	8	no	—
666	C₂²×C₄	—	268	8	no	—
667	C₂²×C₄	—	268	4	no	—
668	C₂²×C₄	—	67	8	no	—
669	C₂²×C₄	—	67	16	no	—
670	C₂²×C₄	—	67	16	no	—
671	C₂²×C₄	—	67	16	no	—
672	C₂²×C₄	—	67	4	no	—
673	C₂²×C₄	—	67	4	no	—
674	C₂²×C₄	—	67	4	no	—
675	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
676	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
677	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
678	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
679	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
680	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
681	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
682	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
683	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
684	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
685	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
686	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
687	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
688	C₄⋊C₄	—	67	16	no	—
689	C₄⋊C₄	—	67	8	no	—
690	C₄⋊C₄	—	67	8	no	—
691	C₄⋊C₄	—	67	8	no	—
692	C₄⋊C₄	—	67	16	no	—
693	C₄⋊C₄	—	67	16	no	—
694	C₄⋊C₄	—	67	16	no	—
695	C₄⋊C₄	—	67	16	no	—
696	C₄⋊C₄	—	67	16	no	—
697	C₄⋊C₄	—	67	8	no	—
698	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
699	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
700	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
701	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
702	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
703	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
704	C₂²⋊C₄	—	67	16	no	—
705	C₂²⋊C₄	—	67	16	no	—
706	C₂²⋊C₄	—	67	16	no	—
707	C₂²⋊C₄	—	67	16	no	—
708	C₂²⋊C₄	—	67	16	no	—
709	C₂²⋊C₄	—	67	16	no	—
710	C₂²⋊C₄	—	67	16	no	—
711	C₂²⋊C₄	—	67	16	no	—
712	C₂²⋊C₄	—	67	16	no	—
713	C₂²⋊C₄	—	67	16	no	—
714	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
715	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
716	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
717	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
718	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
719	C₄²	—	67	16	no	—
720	C₄²	—	67	16	no	—
721	C₄²	C₂³×D₆₇	1	4	yes	—
722	C₄²	C₂³×D₆₇	1	4	yes	—
723	C₄²	C₂³×D₆₇	1	4	yes	—
724	C₄²	C₂³×D₆₇	1	4	yes	—
725	C₄²	C₂³×D₆₇	1	8	yes	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	268	8	no	—
732	C₂³	—	268	8	no	—
733	C₂³	—	536	16	no	—
734	C₂³	—	67	8	no	—
735	C₂³	—	134	8	no	—
736	C₂³	—	134	8	no	—
737	C₂³	—	134	8	no	—
738	C₂³	—	134	16	no	—
739	C₂³	#14524090	1	4	yes	—
740	C₂³	C₂⁴×D₆₇	1	4	yes	—
741	C₂³	C₂⁴×D₆₇	1	2	yes	—
742	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
743	Q₈	—	4	4	no	—
744	Q₈	—	268	16	no	—
745	Q₈	—	268	8	no	—
746	Q₈	—	268	8	no	—
747	Q₈	—	134	16	no	—
748	Q₈	—	134	16	no	—
749	D₄	—	2	16	no	—
750	D₄	—	4	4	no	—
751	D₄	—	268	8	no	—
752	D₄	—	268	16	no	—
753	D₄	—	268	16	no	—
754	D₄	—	134	16	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	8	no	—
765	C₂×C₄	—	2	16	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	268	16	no	—
768	C₂×C₄	—	268	16	no	—
769	C₂×C₄	—	268	16	no	—
770	C₂×C₄	—	268	8	no	—
771	C₂×C₄	—	67	8	no	—
772	C₂×C₄	—	67	8	no	—
773	C₂×C₄	—	67	8	no	—
774	C₂×C₄	—	134	8	no	—
775	C₂×C₄	—	134	8	no	—
776	C₂×C₄	—	134	8	no	—
777	C₂×C₄	#14524089	1	4	yes	—
778	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
779	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
780	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
781	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
782	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
783	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
784	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
785	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
786	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	8	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	4	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	4	8	no	—
794	C₂²	—	268	16	no	—
795	C₂²	—	536	16	no	—
796	C₂²	—	134	8	no	—
797	C₂²	—	134	8	no	—
798	C₂²	—	134	8	no	—
799	C₂²	C₂×#14524089	1	2	yes	—
800	C₂²	C₂×#14524090	1	4	yes	—
801	C₂²	C₂×#14524090	1	2	yes	—
802	C₂²	#16864232	1	2	yes	—
803	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
804	C₄	—	2	4	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	4	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	2	no	—
811	C₄	—	2	4	no	—
812	C₄	—	134	8	no	—
813	C₄	—	134	8	no	—
814	C₄	—	134	8	no	—
815	C₄	C₂×#14524089	1	4	yes	—
816	C₂	—	2	4	no	—
817	C₂	—	4	4	no	—
818	C₂	—	268	8	no	—
819	C₂	#22574779	1	4	yes	direct product factor
820	C₂	C₂²×#14524089	1	1	yes	characteristic
821	C₂	C₂²×#14524090	1	1	yes	characteristic
822	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×#3561
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. #22574779	C₂	direct (N × H)
2. C₂×#16864150	C₂	semidirect
3. C₂×#16864140	C₂	semidirect
4. C₂×#16864119	C₂	semidirect
5. C₂×#16864069	C₂	semidirect
6. C₂×D₄×Dic₁₃₄	C₂	semidirect
7. C₂×#16864055	C₂	semidirect
8. C₂×#16864042	C₂	semidirect
9. C₂×#16864021	C₂	semidirect
10. C₂×#16864017	C₂	semidirect
11. C₂×#16864012	C₂	semidirect
12. C₂×#16863983	C₂	semidirect
13. C₂×#16863972	C₂	semidirect
14. C₂×#16863953	C₂	semidirect
15. C₂²×#14524031	C₂	semidirect
16. C₂×#529×C₆₇	C₂	semidirect
19. C₂³×Dic₁₃₄	C₂²	semidirect
21. #16864150	C₂²	semidirect
22. #16864140	C₂²	semidirect
23. #16864119	C₂²	semidirect
24. #16864069	C₂²	semidirect
25. D₄×Dic₁₃₄	C₂²	semidirect
26. #16864055	C₂²	semidirect
27. #16864042	C₂²	semidirect
28. #16864021	C₂²	semidirect
29. #16864017	C₂²	semidirect
30. #16864012	C₂²	semidirect
31. #16863983	C₂²	semidirect
32. #16863972	C₂²	semidirect
33. #16863953	C₂²	semidirect
34. C₂×#14524043	C₂²	semidirect
35. C₂×#14524043	C₂²	semidirect
36. C₂×#14524043	C₂²	semidirect
37. C₂×#14524042	C₂²	semidirect
38. C₂×#14524038	C₂²	semidirect
39. C₂×#14524038	C₂²	semidirect
40. C₂×#14524038	C₂²	semidirect
41. C₂×#14524035	C₂²	semidirect
47. C₂×#14524031	C₂²	semidirect
48. C₂×#14524029	C₂²	semidirect
49. C₂×#14524029	C₂²	semidirect
51. C₂×#14524027	C₂²	semidirect
52. C₂×#14524027	C₂²	semidirect
53. C₂×#14524025	C₂²	semidirect
54. C₂×#14524023	C₂²	semidirect
55. C₂×#14524023	C₂²	semidirect
58. C₂×#14524022	C₂²	semidirect
59. C₂×#14524021	C₂²	semidirect
60. C₂×#14524021	C₂²	semidirect
62. C₂×#14524020	C₂²	semidirect
63. C₂×#14524019	C₂²	semidirect
66. C₂×#14524015	C₂²	semidirect
68. C₂×C₄×Dic₁₃₄	C₂²	semidirect
69. C₂×C₄×Dic₁₃₄	C₂²	semidirect
70. C₂×C₄×Dic₁₃₄	C₂²	semidirect
73. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
75. C₂×#14524001	C₂²	semidirect
79. #529×C₆₇	C₂²	semidirect
80. C₂×#126×C₆₇	C₂²	semidirect
81. C₂×#125×C₆₇	C₂²	semidirect
82. C₂×#124×C₆₇	C₂²	semidirect
86. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
88. C₂×C₄×D₄×C₆₇	C₂²	semidirect
89. C₂×#117×C₆₇	C₂²	semidirect
102. C₂²×Dic₁₃₄	C₂³	semidirect
113. #14524043	C₂³	semidirect
114. #14524043	C₂³	semidirect
115. #14524043	C₂³	semidirect
116. #14524042	C₂³	semidirect
117. #14524038	C₂³	semidirect
118. #14524038	C₂³	semidirect
119. #14524038	C₂³	semidirect
120. #14524035	C₂³	semidirect
126. #14524029	C₂³	semidirect
127. #14524029	C₂³	semidirect
129. #14524027	C₂³	semidirect
130. #14524027	C₂³	semidirect
131. #14524025	C₂³	semidirect
132. #14524023	C₂³	semidirect
133. #14524023	C₂³	semidirect
136. #14524022	C₂³	semidirect
137. #14524021	C₂³	semidirect
138. #14524021	C₂³	semidirect
140. #14524020	C₂³	semidirect
141. #14524019	C₂³	semidirect
144. #14524015	C₂³	semidirect
146. C₄×Dic₁₃₄	C₂³	semidirect
147. C₄×Dic₁₃₄	C₂³	semidirect
148. C₄×Dic₁₃₄	C₂³	semidirect
151. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
153. #14524001	C₂³	semidirect
186. #126×C₆₇	C₂³	semidirect
187. #125×C₆₇	C₂³	semidirect
188. #124×C₆₇	C₂³	semidirect
192. C₄×Q₈×C₆₇	C₂³	semidirect
194. C₄×D₄×C₆₇	C₂³	semidirect
195. #117×C₆₇	C₂³	semidirect
407. C₂×C₆₇	#3561	semidirect
426. C₂×#529	D₆₇	semidirect
428. C₆₇	C₂×#3561	semidirect
450. #529	C₂×D₆₇	semidirect
454. C₂×#126	C₂×D₆₇	semidirect
456. C₂×#125	C₂×D₆₇	semidirect
465. C₂×#124	C₂×D₆₇	semidirect
490. C₂×C₄×Q₈	C₂×D₆₇	semidirect
495. C₂×C₄×D₄	C₂×D₆₇	semidirect
498. C₂×#117	C₂×D₆₇	semidirect
539. #126	C₂²×D₆₇	semidirect
541. #125	C₂²×D₆₇	semidirect
549. #124	C₂²×D₆₇	semidirect
574. C₄×Q₈	C₂²×D₆₇	semidirect
579. C₄×D₄	C₂²×D₆₇	semidirect
582. #117	C₂²×D₆₇	semidirect
819. C₂	#22574779	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574779	2
C₂×#16864150	2
C₂×#16864140	2
C₂×#16864119	2
C₂×#16864069	2
C₂×D₄×Dic₁₃₄	2
C₂×#16864055	2
C₂×#16864042	2
C₂×#16864021	2
C₂×#16864017	2
C₂×#16864012	2
C₂×#16863983	2
C₂×#16863972	2
C₂×#16863953	2
C₂²×#14524031	2
C₂×#529×C₆₇	2
C₂×#3561	67

Subgroups — C2×#22574779 #31763184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574779 #31763184