Subgroups — C₂×#22573773 #31762869

Order 17152.

7954 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573773	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864119	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864111	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864096	C₂	1	2	yes	maximal, complemented
6	C₂×#16864087	C₂	1	2	yes	maximal, complemented
7	C₂×#16864086	C₂	1	2	yes	maximal, complemented
8	C₂×#16864075	C₂	1	4	yes	maximal, complemented
9	C₂×#16864051	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16864042	C₂	1	2	yes	maximal, complemented
11	C₂×#16863953	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16863930	C₂	1	2	yes	maximal, complemented
13	C₂×#16863924	C₂	1	4	yes	maximal, complemented
14	C₂×#16863903	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×#11761628	C₂	1	2	yes	maximal, complemented
16	C₂²×C₄×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#117×D₆₇	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11761628	C₂²	1	2	yes	—
20	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
21	C₂³×C₄×D₆₇	C₂²	1	2	yes	—
22	#16864119	C₂²	1	16	yes	complemented
23	#16864111	C₂²	1	16	yes	complemented
24	#16864106	C₂²	1	16	yes	complemented
25	#16864096	C₂²	1	32	yes	complemented
26	#16864087	C₂²	1	32	yes	complemented
27	#16864086	C₂²	1	32	yes	complemented
28	#16864075	C₂²	1	64	yes	complemented
29	#16864051	C₂²	1	16	yes	complemented
30	#16864042	C₂²	1	32	yes	complemented
31	#16863953	C₂²	1	16	yes	complemented
32	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
34	#16863930	C₂²	1	32	yes	complemented
35	#16863924	C₂²	1	64	yes	complemented
36	C₂×#14524038	C₂²	1	4	yes	complemented
37	C₂×#14524037	C₂²	1	4	yes	complemented
38	C₂×#14524036	C₂²	1	4	yes	complemented
39	C₂×#14524035	C₂²	1	2	yes	complemented
40	C₂×#14524035	C₂²	1	2	yes	complemented
41	C₂×#14524033	C₂²	1	4	yes	complemented
42	C₂×#14524031	C₂²	1	2	yes	—
43	C₂×#14524029	C₂²	1	4	yes	complemented
44	#16863903	C₂²	1	32	yes	complemented
45	C₂×#14524028	C₂²	1	4	yes	—
46	C₂×#14524026	C₂²	1	4	yes	complemented
47	C₂×#14524025	C₂²	1	4	yes	complemented
48	C₂×#14524024	C₂²	1	4	yes	—
49	C₂×#14524022	C₂²	1	2	yes	—
50	C₂×#14524022	C₂²	1	2	yes	—
51	C₂×#14524022	C₂²	1	2	yes	complemented
52	C₂×#14524021	C₂²	1	4	yes	complemented
53	C₂×#14524019	C₂²	1	2	yes	complemented
54	C₂×#14524019	C₂²	1	2	yes	complemented
55	C₂×#14524017	C₂²	1	2	yes	—
56	C₂×#14524016	C₂²	1	4	yes	—
57	C₂×#14524014	C₂²	1	2	yes	complemented
58	C₂×#14524014	C₂²	1	2	yes	complemented
59	C₂×#14524011	C₂²	1	4	yes	—
60	C₄×#11761628	C₂²	1	32	yes	complemented
61	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
62	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
63	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
64	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
65	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
66	C₂×C₄×D₂₆₈	C₂²	1	2	yes	—
67	C₂×C₄×D₂₆₈	C₂²	1	2	yes	—
68	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
69	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
70	C₂×C₄×D₂₆₈	C₂²	1	2	yes	—
71	C₂×C₄×D₂₆₈	C₂²	1	16	yes	complemented
72	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
73	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
74	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
75	C₂×#14524002	C₂²	1	2	yes	—
76	C₂×#14524002	C₂²	1	2	yes	complemented
77	C₂×#14524001	C₂²	1	2	yes	complemented
78	C₂×#14524001	C₂²	1	2	yes	complemented
79	C₂×#14524000	C₂²	1	4	yes	complemented
80	C₂×#14524000	C₂²	1	4	yes	complemented
81	C₂×#14523999	C₂²	1	4	yes	—
82	#117×D₆₇	C₂²	1	32	yes	complemented
83	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
84	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
85	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
86	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
87	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	—
88	C₂×C₄²×D₆₇	C₂²	1	4	yes	complemented
89	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
90	C₄×#41×C₆₇	C₂²	1	16	yes	complemented
91	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
94	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
95	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
98	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
99	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
100	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
101	C₂⁴×D₆₇	C₂³	1	2	yes	—
102	C₂×#11761628	—	2	16	no	—
103	C₂×#11761628	C₂³	1	16	yes	—
104	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
105	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
106	C₂²×D₂₆₈	—	2	8	no	—
107	C₂²×D₂₆₈	C₂³	1	8	yes	—
108	C₂²×D₂₆₈	C₂³	1	2	yes	—
109	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
110	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
111	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
112	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
113	C₂³×Dic₆₇	C₂³	1	2	yes	—
114	C₂²×C₄×D₆₇	—	2	16	no	—
115	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
116	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
117	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
118	C₂²×C₄×D₆₇	C₂³	1	16	yes	—
119	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
120	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
121	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
122	#14524043	C₂³	1	8	yes	complemented
123	#14524043	C₂³	1	8	yes	complemented
124	#14524038	C₂³	1	32	yes	complemented
125	#14524037	C₂³	1	32	yes	complemented
126	#14524036	C₂³	1	32	yes	complemented
127	#14524035	C₂³	1	16	yes	complemented
128	#14524035	C₂³	1	16	yes	complemented
129	#14524033	C₂³	1	32	yes	complemented
130	#14524031	C₂³	1	16	yes	—
131	#14524029	C₂³	1	32	yes	complemented
132	#14524028	C₂³	1	32	yes	—
133	#14524026	C₂³	1	32	yes	complemented
134	#14524025	C₂³	1	32	yes	complemented
135	#14524024	C₂³	1	32	yes	—
136	#14524022	C₂³	1	16	yes	—
137	#14524022	C₂³	1	16	yes	—
138	#14524022	C₂³	1	16	yes	complemented
139	#14524021	C₂³	1	32	yes	complemented
140	#14524019	C₂³	1	16	yes	complemented
141	#14524019	C₂³	1	16	yes	complemented
142	#14524017	C₂³	1	16	yes	—
143	#14524016	C₂³	1	32	yes	—
144	#14524014	C₂³	1	16	yes	complemented
145	#14524014	C₂³	1	16	yes	complemented
146	#14524011	C₂³	1	32	yes	—
147	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
148	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
149	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
150	C₄×D₂₆₈	C₂³	1	16	yes	—
151	C₄×D₂₆₈	C₂³	1	8	yes	—
152	C₄×D₂₆₈	C₂³	1	16	yes	—
153	C₄×D₂₆₈	C₂³	1	8	yes	—
154	C₄×D₂₆₈	C₂³	1	8	yes	—
155	C₄×D₂₆₈	C₂³	1	16	yes	—
156	C₄×D₂₆₈	C₂³	1	8	yes	—
157	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
158	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
159	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
160	#14524002	C₂³	1	16	yes	—
161	#14524002	C₂³	1	16	yes	complemented
162	#14524001	C₂³	1	16	yes	complemented
163	#14524001	C₂³	1	16	yes	complemented
164	#14524000	C₂³	1	32	yes	complemented
165	#14524000	C₂³	1	32	yes	complemented
166	#14523999	C₂³	1	32	yes	—
167	C₂×C₄⋊Dic₆₇	C₂³	1	8	yes	—
168	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
173	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
174	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
175	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
176	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
177	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
178	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
179	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
180	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
181	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
182	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
183	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
184	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
185	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
186	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	—
187	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
188	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
189	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
190	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
192	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
193	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
194	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
195	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	—
196	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
197	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
198	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
199	C₄²×D₆₇	C₂³	1	32	yes	complemented
200	C₂×#41×C₆₇	—	2	8	no	—
201	C₂×#41×C₆₇	C₂³	1	8	yes	—
202	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
203	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
204	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
207	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
208	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
210	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
212	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
213	C₄×D₄×C₆₇	C₂³	1	16	yes	—
214	C₄×D₄×C₆₇	C₂³	1	16	yes	—
215	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
216	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
217	#117×C₆₇	C₂³	1	8	yes	—
218	#117×C₆₇	C₂³	1	16	yes	complemented
219	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
234	C₂×C₄²×C₆₇	C₂³	1	16	yes	complemented
235	C₂³×D₆₇	—	2	8	no	—
236	C₂³×D₆₇	—	2	8	no	—
237	C₂³×D₆₇	—	4	4	no	—
238	C₂³×D₆₇	C₂⁴	1	2	yes	—
239	C₂³×D₆₇	C₂⁴	1	8	yes	—
240	C₂³×D₆₇	C₂⁴	1	2	yes	—
241	#11761628	—	2	64	no	—
242	C₂×Dic₁₃₄	—	2	8	no	—
243	C₂×Dic₁₃₄	—	4	4	no	—
244	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
245	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
246	C₂×D₂₆₈	—	2	8	no	—
247	C₂×D₂₆₈	—	2	4	no	—
248	C₂×D₂₆₈	—	2	32	no	—
249	C₂×D₂₆₈	#41	1	8	yes	complemented
250	C₂×D₂₆₈	C₂⁴	1	8	yes	—
251	C₂×D₂₆₈	C₂⁴	1	4	yes	—
252	C₂×D₂₆₈	C₂⁴	1	4	yes	—
253	C₂×C₂²⋊D₆₇	—	2	16	no	—
254	C₂×C₂²⋊D₆₇	—	4	8	no	—
255	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
256	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
257	C₂²×Dic₆₇	—	2	8	no	—
258	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
259	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
260	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
261	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
262	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
263	C₂×C₄×D₆₇	—	2	16	no	—
264	C₂×C₄×D₆₇	—	2	8	no	—
265	C₂×C₄×D₆₇	—	2	8	no	—
266	C₂×C₄×D₆₇	—	2	8	no	—
267	C₂×C₄×D₆₇	—	2	8	no	—
268	C₂×C₄×D₆₇	—	2	64	no	—
269	C₂×C₄×D₆₇	—	4	8	no	—
270	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
271	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
272	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
273	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
274	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
275	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
276	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
277	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
278	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
279	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
280	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
281	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
282	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
283	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
284	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
285	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
286	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
287	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
288	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
289	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
290	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
291	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
292	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
293	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
294	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
295	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
296	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
297	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
298	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
299	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
300	C₄×Dic₆₇	C₂⁴	1	16	yes	—
301	C₄×Dic₆₇	C₂⁴	1	16	yes	—
302	C₄×Dic₆₇	C₂⁴	1	16	yes	—
303	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
304	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
305	#41×C₆₇	—	2	32	no	—
306	C₂×Q₈×C₆₇	—	2	4	no	—
307	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
308	C₂×D₄×C₆₇	—	2	8	no	—
309	C₂×D₄×C₆₇	—	2	4	no	—
310	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
311	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
312	C₂²×C₄×C₆₇	—	2	8	no	—
313	C₂²×C₄×C₆₇	—	2	4	no	—
314	C₂²×C₄×C₆₇	—	2	8	no	—
315	C₂²×C₄×C₆₇	—	4	4	no	—
316	C₂²×C₄×C₆₇	—	4	2	no	—
317	C₂²×C₄×C₆₇	#41	1	8	yes	complemented
318	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
325	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
326	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
327	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
329	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
334	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
335	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
336	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
337	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
338	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
339	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
340	C₄²×C₆₇	C₂⁴	1	4	yes	—
341	C₄²×C₆₇	C₂⁴	1	4	yes	—
342	C₄²×C₆₇	C₂⁴	1	4	yes	—
343	C₄²×C₆₇	C₂⁴	1	4	yes	—
344	C₄²×C₆₇	C₂⁴	1	8	yes	—
345	C₄²×C₆₇	C₂⁴	1	8	yes	—
346	C₄²×C₆₇	C₂⁴	1	8	yes	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	2	4	no	—
350	C₂³×C₆₇	—	2	4	no	—
351	C₂³×C₆₇	—	2	4	no	—
352	C₂³×C₆₇	C₂×#41	1	4	yes	—
353	C₂³×C₆₇	C₂⁵	1	4	yes	—
354	C₂³×C₆₇	C₂⁵	1	2	yes	—
355	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
356	C₂²×D₆₇	—	2	4	no	—
357	C₂²×D₆₇	—	2	4	no	—
358	C₂²×D₆₇	—	2	16	no	—
359	C₂²×D₆₇	—	2	4	no	—
360	C₂²×D₆₇	—	2	4	no	—
361	C₂²×D₆₇	—	2	4	no	—
362	C₂²×D₆₇	—	2	16	no	—
363	C₂²×D₆₇	—	4	8	no	—
364	C₂²×D₆₇	—	4	32	no	—
365	C₂²×D₆₇	C₂×#41	1	8	yes	—
366	C₂²×D₆₇	C₂⁵	1	4	yes	—
367	C₂²×D₆₇	C₂⁵	1	4	yes	—
368	Q₈×C₆₇	—	2	8	no	—
369	D₄×C₆₇	—	2	16	no	—
370	D₄×C₆₇	—	2	8	no	—
371	C₂×C₄×C₆₇	—	2	4	no	—
372	C₂×C₄×C₆₇	—	2	4	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	4	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	16	no	—
378	C₂×C₄×C₆₇	—	2	8	no	—
379	C₂×C₄×C₆₇	—	2	16	no	—
380	C₂×C₄×C₆₇	—	4	4	no	—
381	C₂×C₄×C₆₇	—	4	8	no	—
382	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
383	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
384	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
385	C₂×C₄×C₆₇	C₂×#41	1	16	yes	complemented
386	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
387	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
388	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
389	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
390	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
391	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
392	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
393	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
394	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
395	C₂²⋊D₆₇	—	2	32	no	—
396	C₂²⋊D₆₇	—	4	16	no	—
397	C₂×Dic₆₇	—	2	16	no	—
398	C₂×Dic₆₇	—	2	4	no	—
399	C₂×Dic₆₇	—	2	4	no	—
400	C₂×Dic₆₇	—	2	8	no	—
401	C₂×Dic₆₇	—	2	8	no	—
402	C₂×Dic₆₇	C₂⁵	1	4	yes	—
403	C₂×Dic₆₇	C₂⁵	1	8	yes	—
404	C₂×Dic₆₇	C₂⁵	1	8	yes	—
405	C₂×Dic₆₇	C₂⁵	1	4	yes	—
406	D₂₆₈	—	2	16	no	—
407	D₂₆₈	—	2	8	no	—
408	D₂₆₈	C₂×#41	1	16	yes	complemented
409	C₄×D₆₇	—	2	32	no	—
410	C₄×D₆₇	—	2	16	no	—
411	C₄×D₆₇	—	2	16	no	—
412	C₄×D₆₇	—	2	16	no	—
413	C₄×D₆₇	—	2	16	no	—
414	C₄×D₆₇	—	4	16	no	—
415	Dic₁₃₄	—	2	16	no	—
416	Dic₁₃₄	—	4	8	no	—
417	C₂²×C₆₇	—	2	2	no	—
418	C₂²×C₆₇	—	2	2	no	—
419	C₂²×C₆₇	—	2	8	no	—
420	C₂²×C₆₇	—	2	4	no	—
421	C₂²×C₆₇	—	2	4	no	—
422	C₂²×C₆₇	—	2	4	no	—
423	C₂²×C₆₇	—	4	8	no	—
424	C₂²×C₆₇	C₂²×#41	1	2	yes	—
425	C₂²×C₆₇	C₂²×#41	1	4	yes	—
426	C₂²×C₆₇	C₂²×#41	1	2	yes	—
427	C₂²×C₆₇	#585	1	2	yes	—
428	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
429	C₂×D₆₇	—	2	4	no	—
430	C₂×D₆₇	—	2	4	no	—
431	C₂×D₆₇	—	2	16	no	—
432	C₂×D₆₇	—	2	4	no	—
433	C₂×D₆₇	—	2	4	no	—
434	C₂×D₆₇	—	2	4	no	—
435	C₂×D₆₇	—	4	32	no	—
436	C₂×D₆₇	—	4	8	no	—
437	C₂×D₆₇	C₂²×#41	1	8	yes	—
438	C₄×C₆₇	—	2	4	no	—
439	C₄×C₆₇	—	2	2	no	—
440	C₄×C₆₇	—	2	4	no	—
441	C₄×C₆₇	—	2	2	no	—
442	C₄×C₆₇	—	2	4	no	—
443	C₄×C₆₇	—	2	2	no	—
444	C₄×C₆₇	C₂²×#41	1	4	yes	—
445	C₄×C₆₇	C₂²×#41	1	4	yes	—
446	C₄×C₆₇	C₂²×#41	1	4	yes	—
447	Dic₆₇	—	2	8	no	—
448	Dic₆₇	—	2	4	no	—
449	Dic₆₇	—	2	4	no	—
450	Dic₆₇	—	2	8	no	—
451	C₂×#3475	—	67	1	no	maximal, Sylow
452	C₂×C₆₇	—	2	4	no	—
453	C₂×C₆₇	—	4	4	no	—
454	C₂×C₆₇	#3475	1	4	yes	complemented
455	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
456	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
457	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
458	D₆₇	—	2	8	no	—
459	D₆₇	—	4	4	no	—
460	#3475	—	67	32	no	—
461	C₂×#556	—	67	1	no	—
462	C₂×#555	—	67	1	no	—
463	C₂×#554	—	67	1	no	—
464	C₂×#553	—	67	2	no	—
465	C₂×#552	—	67	2	no	—
466	C₂×#552	—	67	2	no	—
467	C₂×#551	—	67	4	no	—
468	C₂×#547	—	67	1	no	—
469	C₂×#546	—	67	2	no	—
470	C₂×#533	—	67	1	no	—
471	C₂×#529	—	67	2	no	—
472	C₂×#529	—	67	4	no	—
473	C₂×#525	—	67	2	no	—
474	C₂×C₄×#41	—	67	2	no	—
475	C₂×C₄×#41	D₆₇	1	1	yes	characteristic, complemented
476	C₂²×C₄×D₄	—	67	1	no	—
477	C₂²×#117	—	67	2	no	—
478	C₆₇	C₂×#3475	1	1	yes	characteristic, complemented, Sylow
479	C₂²×#41	—	67	2	no	—
480	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
481	C₂³×D₄	—	67	1	no	—
482	C₂⁴×C₄	—	67	2	no	—
483	#556	—	67	16	no	—
484	#555	—	67	16	no	—
485	#554	—	67	16	no	—
486	#553	—	67	32	no	—
487	#552	—	67	32	no	—
488	#552	—	67	32	no	—
489	#551	—	67	64	no	—
490	#547	—	67	16	no	—
491	#546	—	67	32	no	—
492	#533	—	67	16	no	—
493	C₂×C₄⋊Q₈	—	67	1	no	—
494	C₂×C₄⋊Q₈	—	67	1	no	—
495	#529	—	67	64	no	—
496	#529	—	67	32	no	—
497	C₂×#126	—	67	4	no	—
498	C₂×#126	—	67	4	no	—
499	C₂×#126	—	67	4	no	—
500	C₂×#125	—	67	4	no	—
501	C₂×#125	—	67	2	no	—
502	C₂×#125	—	67	2	no	—
503	C₂×#124	—	67	4	no	—
504	C₂×#124	—	67	2	no	—
505	#525	—	67	32	no	—
506	C₂×#123	—	67	4	no	—
507	C₂×#123	—	67	4	no	—
508	C₂×#123	—	67	4	no	—
509	C₂×#123	—	67	4	no	—
510	C₂×C₂²⋊Q₈	—	67	2	no	—
511	C₂×C₂²⋊Q₈	—	67	2	no	—
512	C₂×C₂²⋊Q₈	—	67	2	no	—
513	C₂×C₂²⋊Q₈	—	67	2	no	—
514	C₂×C₂²⋊Q₈	—	67	2	no	—
515	C₂×C₂²⋊Q₈	—	67	4	no	—
516	C₂×#121	—	67	2	no	—
517	C₂×#121	—	67	2	no	—
518	C₂×#121	—	67	2	no	—
519	C₂×#121	—	67	4	no	—
520	C₂×#120	—	67	4	no	—
521	C₄×#41	—	67	32	no	—
522	C₄×#41	C₂×D₆₇	1	16	yes	complemented
523	C₂×C₄×Q₈	—	67	2	no	—
524	C₂×C₄×Q₈	—	67	2	no	—
525	C₂×C₄×Q₈	—	67	2	no	—
526	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
527	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
528	C₂×C₄×D₄	—	67	4	no	—
529	C₂×C₄×D₄	—	67	4	no	—
530	C₂×C₄×D₄	—	67	4	no	—
531	C₂×C₄×D₄	—	67	1	no	—
532	C₂×C₄×D₄	—	67	2	no	—
533	C₂×C₄×D₄	—	67	1	no	—
534	C₂×C₄×D₄	—	67	1	no	—
535	C₂×C₄×D₄	—	67	2	no	—
536	C₂×C₄×D₄	—	67	1	no	—
537	C₂×C₄×D₄	—	67	16	no	—
538	C₂×C₄×D₄	—	67	2	no	—
539	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	—
540	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	—
541	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
542	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
543	C₂×#117	—	67	2	no	—
544	C₂×#117	—	67	2	no	—
545	C₂×#117	—	67	32	no	—
546	C₂×#117	—	67	2	no	—
547	C₂×#117	—	67	2	no	—
548	C₂×#117	—	67	4	no	—
549	C₂×#117	—	67	4	no	—
550	C₂×#117	—	67	4	no	—
551	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
552	C₂×#117	C₂×D₆₇	1	2	yes	complemented
553	C₂²×C₄⋊C₄	—	67	1	no	—
554	C₂²×C₄⋊C₄	—	67	2	no	—
555	C₂²×C₄⋊C₄	—	67	2	no	—
556	C₂²×C₂²⋊C₄	—	67	2	no	—
557	C₂²×C₂²⋊C₄	—	67	4	no	—
558	C₂²×C₄²	—	67	4	no	—
559	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
560	C₂²×C₄²	C₂×D₆₇	1	2	yes	complemented
561	C₂⁵	—	67	2	no	—
562	C₂×#41	—	2	8	no	—
563	C₂×#41	—	67	16	no	—
564	C₂×#41	—	134	16	no	—
565	C₂×#41	C₂²×D₆₇	1	8	yes	—
566	C₂²×Q₈	—	67	2	no	—
567	C₂²×Q₈	—	67	2	no	—
568	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
569	C₂²×D₄	—	67	4	no	—
570	C₂²×D₄	—	67	4	no	—
571	C₂²×D₄	—	67	1	no	—
572	C₂²×D₄	—	67	2	no	—
573	C₂²×D₄	—	67	1	no	—
574	C₂²×D₄	—	67	8	no	—
575	C₂²×D₄	—	134	8	no	—
576	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
577	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
578	C₂³×C₄	—	67	4	no	—
579	C₂³×C₄	—	67	2	no	—
580	C₂³×C₄	—	67	4	no	—
581	C₂³×C₄	—	67	2	no	—
582	C₂³×C₄	—	67	2	no	—
583	C₂³×C₄	—	67	16	no	—
584	C₂³×C₄	—	67	2	no	—
585	C₂³×C₄	—	67	2	no	—
586	C₂³×C₄	—	134	16	no	—
587	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
588	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
589	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
590	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
591	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
592	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
593	C₄⋊Q₈	—	67	8	no	—
594	C₄⋊Q₈	—	67	8	no	—
595	#126	—	67	32	no	—
596	#126	—	67	32	no	—
597	#126	—	67	32	no	—
598	#125	—	67	32	no	—
599	#125	—	67	16	no	—
600	#125	—	67	16	no	—
601	#124	—	67	32	no	—
602	#124	—	67	16	no	—
603	#123	—	67	32	no	—
604	#123	—	67	32	no	—
605	#123	—	67	32	no	—
606	#123	—	67	32	no	—
607	C₂²⋊Q₈	—	67	16	no	—
608	C₂²⋊Q₈	—	67	16	no	—
609	C₂²⋊Q₈	—	67	16	no	—
610	C₂²⋊Q₈	—	67	16	no	—
611	C₂²⋊Q₈	—	67	16	no	—
612	C₂²⋊Q₈	—	67	32	no	—
613	#121	—	67	16	no	—
614	#121	—	67	16	no	—
615	#121	—	67	16	no	—
616	#121	—	67	32	no	—
617	#120	—	67	32	no	—
618	C₄×Q₈	—	67	16	no	—
619	C₄×Q₈	—	67	16	no	—
620	C₄×Q₈	—	67	16	no	—
621	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
622	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
623	C₄×D₄	—	67	32	no	—
624	C₄×D₄	—	67	32	no	—
625	C₄×D₄	—	67	32	no	—
626	C₄×D₄	—	67	8	no	—
627	C₄×D₄	—	67	8	no	—
628	C₄×D₄	—	67	16	no	—
629	C₄×D₄	—	67	8	no	—
630	C₄×D₄	—	67	16	no	—
631	C₄×D₄	—	67	8	no	—
632	C₄×D₄	—	67	16	no	—
633	C₄×D₄	C₂²×D₆₇	1	16	yes	—
634	C₄×D₄	C₂²×D₆₇	1	16	yes	—
635	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
636	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
637	#117	—	67	16	no	—
638	#117	—	67	16	no	—
639	#117	—	67	16	no	—
640	#117	—	67	16	no	—
641	#117	—	67	32	no	—
642	#117	—	67	32	no	—
643	#117	—	67	32	no	—
644	#117	C₂²×D₆₇	1	8	yes	—
645	#117	C₂²×D₆₇	1	16	yes	complemented
646	C₂×C₄⋊C₄	—	67	1	no	—
647	C₂×C₄⋊C₄	—	67	2	no	—
648	C₂×C₄⋊C₄	—	67	2	no	—
649	C₂×C₄⋊C₄	—	67	4	no	—
650	C₂×C₄⋊C₄	—	67	4	no	—
651	C₂×C₄⋊C₄	—	67	1	no	—
652	C₂×C₄⋊C₄	—	67	2	no	—
653	C₂×C₄⋊C₄	—	67	8	no	—
654	C₂×C₄⋊C₄	—	67	2	no	—
655	C₂×C₄⋊C₄	—	67	4	no	—
656	C₂×C₄⋊C₄	—	67	4	no	—
657	C₂×C₄⋊C₄	—	67	4	no	—
658	C₂×C₄⋊C₄	—	67	4	no	—
659	C₂×C₄⋊C₄	—	67	2	no	—
660	C₂×C₄⋊C₄	—	67	16	no	—
661	C₂×C₄⋊C₄	—	67	16	no	—
662	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
665	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
666	C₂×C₂²⋊C₄	—	67	4	no	—
667	C₂×C₂²⋊C₄	—	67	4	no	—
668	C₂×C₂²⋊C₄	—	67	4	no	—
669	C₂×C₂²⋊C₄	—	67	2	no	—
670	C₂×C₂²⋊C₄	—	67	4	no	—
671	C₂×C₂²⋊C₄	—	67	4	no	—
672	C₂×C₂²⋊C₄	—	67	2	no	—
673	C₂×C₂²⋊C₄	—	67	2	no	—
674	C₂×C₂²⋊C₄	—	67	2	no	—
675	C₂×C₂²⋊C₄	—	67	16	no	—
676	C₂×C₂²⋊C₄	—	67	4	no	—
677	C₂×C₂²⋊C₄	—	67	4	no	—
678	C₂×C₂²⋊C₄	—	67	32	no	—
679	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
682	C₂×C₄²	—	67	4	no	—
683	C₂×C₄²	—	67	4	no	—
684	C₂×C₄²	—	67	4	no	—
685	C₂×C₄²	—	67	32	no	—
686	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
687	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
688	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
689	C₂×C₄²	C₂²×D₆₇	1	8	yes	—
690	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
691	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
692	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
693	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
694	C₂×C₄²	C₂²×D₆₇	1	16	yes	complemented
695	C₂⁴	—	268	4	no	—
696	C₂⁴	—	67	8	no	—
697	C₂⁴	—	67	2	no	—
698	C₂⁴	—	67	2	no	—
699	C₂⁴	—	134	8	no	—
700	C₂⁴	—	134	8	no	—
701	C₂⁴	C₂³×D₆₇	1	2	yes	—
702	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
703	#41	—	2	32	no	—
704	#41	—	134	64	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	268	4	no	—
707	C₂×Q₈	—	67	8	no	—
708	C₂×Q₈	—	67	8	no	—
709	C₂×Q₈	—	134	8	no	—
710	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
711	C₂×D₄	—	2	8	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	268	8	no	—
714	C₂×D₄	—	67	16	no	—
715	C₂×D₄	—	67	16	no	—
716	C₂×D₄	—	67	8	no	—
717	C₂×D₄	—	67	4	no	—
718	C₂×D₄	—	67	8	no	—
719	C₂×D₄	—	67	4	no	—
720	C₂×D₄	—	134	32	no	—
721	C₂×D₄	—	134	8	no	—
722	C₂×D₄	—	134	16	no	—
723	C₂×D₄	—	134	4	no	—
724	C₂×D₄	C₂³×D₆₇	1	8	yes	—
725	C₂×D₄	C₂³×D₆₇	1	4	yes	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	8	no	—
728	C₂²×C₄	—	2	8	no	—
729	C₂²×C₄	—	4	4	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	268	8	no	—
732	C₂²×C₄	—	67	16	no	—
733	C₂²×C₄	—	67	2	no	—
734	C₂²×C₄	—	67	4	no	—
735	C₂²×C₄	—	67	4	no	—
736	C₂²×C₄	—	67	2	no	—
737	C₂²×C₄	—	67	8	no	—
738	C₂²×C₄	—	67	8	no	—
739	C₂²×C₄	—	67	16	no	—
740	C₂²×C₄	—	67	8	no	—
741	C₂²×C₄	—	67	8	no	—
742	C₂²×C₄	—	67	8	no	—
743	C₂²×C₄	—	134	16	no	—
744	C₂²×C₄	—	134	8	no	—
745	C₂²×C₄	—	134	8	no	—
746	C₂²×C₄	—	134	8	no	—
747	C₂²×C₄	—	134	8	no	—
748	C₂²×C₄	—	134	8	no	—
749	C₂²×C₄	—	134	64	no	—
750	C₂²×C₄	#11761628	1	8	yes	complemented
751	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
752	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
753	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
754	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
755	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
756	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
758	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
759	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
760	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
761	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
762	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
763	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
764	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
765	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
766	C₄⋊C₄	—	67	4	no	—
767	C₄⋊C₄	—	67	8	no	—
768	C₄⋊C₄	—	67	8	no	—
769	C₄⋊C₄	—	67	16	no	—
770	C₄⋊C₄	—	67	16	no	—
771	C₄⋊C₄	—	67	4	no	—
772	C₄⋊C₄	—	67	8	no	—
773	C₄⋊C₄	—	67	8	no	—
774	C₄⋊C₄	—	67	16	no	—
775	C₄⋊C₄	—	67	16	no	—
776	C₄⋊C₄	—	67	16	no	—
777	C₄⋊C₄	—	67	16	no	—
778	C₄⋊C₄	—	67	8	no	—
779	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
780	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
781	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
782	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
783	C₂²⋊C₄	—	67	16	no	—
784	C₂²⋊C₄	—	67	16	no	—
785	C₂²⋊C₄	—	67	16	no	—
786	C₂²⋊C₄	—	67	8	no	—
787	C₂²⋊C₄	—	67	16	no	—
788	C₂²⋊C₄	—	67	16	no	—
789	C₂²⋊C₄	—	67	8	no	—
790	C₂²⋊C₄	—	67	8	no	—
791	C₂²⋊C₄	—	67	8	no	—
792	C₂²⋊C₄	—	67	16	no	—
793	C₂²⋊C₄	—	67	16	no	—
794	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
795	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
796	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
797	C₄²	—	67	16	no	—
798	C₄²	—	67	16	no	—
799	C₄²	—	67	16	no	—
800	C₄²	C₂³×D₆₇	1	8	yes	—
801	C₄²	C₂³×D₆₇	1	4	yes	—
802	C₄²	C₂³×D₆₇	1	4	yes	—
803	C₄²	C₂³×D₆₇	1	4	yes	—
804	C₄²	C₂³×D₆₇	1	4	yes	—
805	C₄²	C₂³×D₆₇	1	8	yes	—
806	C₄²	C₂³×D₆₇	1	8	yes	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	4	no	—
811	C₂³	—	2	4	no	—
812	C₂³	—	268	32	no	—
813	C₂³	—	268	8	no	—
814	C₂³	—	67	8	no	—
815	C₂³	—	67	4	no	—
816	C₂³	—	67	4	no	—
817	C₂³	—	134	16	no	—
818	C₂³	—	134	4	no	—
819	C₂³	—	134	16	no	—
820	C₂³	—	134	4	no	—
821	C₂³	—	134	4	no	—
822	C₂³	—	134	4	no	—
823	C₂³	—	134	4	no	—
824	C₂³	C₂×#11761628	1	4	yes	—
825	C₂³	C₂⁴×D₆₇	1	4	yes	—
826	C₂³	C₂⁴×D₆₇	1	2	yes	—
827	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
828	Q₈	—	2	8	no	—
829	Q₈	—	268	8	no	—
830	Q₈	—	134	16	no	—
831	D₄	—	2	16	no	—
832	D₄	—	2	8	no	—
833	D₄	—	268	16	no	—
834	D₄	—	67	16	no	—
835	D₄	—	134	16	no	—
836	D₄	—	134	32	no	—
837	D₄	—	134	8	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	8	no	—
845	C₂×C₄	—	2	16	no	—
846	C₂×C₄	—	2	16	no	—
847	C₂×C₄	—	4	8	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	268	16	no	—
850	C₂×C₄	—	67	4	no	—
851	C₂×C₄	—	67	8	no	—
852	C₂×C₄	—	67	8	no	—
853	C₂×C₄	—	67	4	no	—
854	C₂×C₄	—	134	32	no	—
855	C₂×C₄	—	134	8	no	—
856	C₂×C₄	—	134	16	no	—
857	C₂×C₄	—	134	4	no	—
858	C₂×C₄	—	134	4	no	—
859	C₂×C₄	—	134	8	no	—
860	C₂×C₄	—	134	16	no	—
861	C₂×C₄	—	134	16	no	—
862	C₂×C₄	—	134	16	no	—
863	C₂×C₄	—	134	16	no	—
864	C₂×C₄	#41×D₆₇	1	4	yes	—
865	C₂×C₄	C₂×#11761628	1	4	yes	—
866	C₂×C₄	C₂×#11761628	1	4	yes	—
867	C₂×C₄	C₂×#11761628	1	16	yes	complemented
868	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
869	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
870	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
871	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
872	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
873	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
874	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
875	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
876	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	4	8	no	—
884	C₂²	—	268	32	no	—
885	C₂²	—	268	8	no	—
886	C₂²	—	67	8	no	—
887	C₂²	—	134	4	no	—
888	C₂²	—	134	4	no	—
889	C₂²	—	134	4	no	—
890	C₂²	—	134	4	no	—
891	C₂²	—	134	4	no	—
892	C₂²	—	134	16	no	—
893	C₂²	C₂×#41×D₆₇	1	2	yes	—
894	C₂²	C₂²×#11761628	1	4	yes	—
895	C₂²	C₂²×#11761628	1	2	yes	—
896	C₂²	#16864232	1	2	yes	—
897	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
898	C₄	—	2	4	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	134	8	no	—
905	C₄	—	134	4	no	—
906	C₄	—	134	4	no	—
907	C₄	—	134	8	no	—
908	C₄	C₂×#41×D₆₇	1	4	yes	—
909	C₄	C₂²×#11761628	1	4	yes	—
910	C₄	C₂²×#11761628	1	4	yes	—
911	C₂	—	2	4	no	—
912	C₂	—	4	4	no	—
913	C₂	—	268	4	no	—
914	C₂	—	134	8	no	—
915	C₂	#22573773	1	4	yes	direct product factor
916	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
917	C₂	C₂³×#11761628	1	1	yes	characteristic
918	C₂	C₂×#16864232	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×C₄×#41×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×C₄×#41	D₆₇
hypocenter	C₆₇	C₂×#3475
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #22573773	C₂	direct (N × H)
2. C₂×#16864119	C₂	semidirect
3. C₂×#16864111	C₂	semidirect
4. C₂×#16864106	C₂	semidirect
5. C₂×#16864096	C₂	semidirect
6. C₂×#16864087	C₂	semidirect
7. C₂×#16864086	C₂	semidirect
8. C₂×#16864075	C₂	semidirect
9. C₂×#16864051	C₂	semidirect
10. C₂×#16864042	C₂	semidirect
11. C₂×#16863953	C₂	semidirect
12. C₂×#16863930	C₂	semidirect
13. C₂×#16863924	C₂	semidirect
14. C₂×#16863903	C₂	semidirect
15. C₂×C₄×#11761628	C₂	semidirect
16. C₂²×C₄×D₂₆₈	C₂	semidirect
17. C₂×#117×D₆₇	C₂	semidirect
18. C₂×C₄×#41×C₆₇	C₂	semidirect
22. #16864119	C₂²	semidirect
23. #16864111	C₂²	semidirect
24. #16864106	C₂²	semidirect
25. #16864096	C₂²	semidirect
26. #16864087	C₂²	semidirect
27. #16864086	C₂²	semidirect
28. #16864075	C₂²	semidirect
29. #16864051	C₂²	semidirect
30. #16864042	C₂²	semidirect
31. #16863953	C₂²	semidirect
32. C₂×#14524043	C₂²	semidirect
33. C₂×#14524043	C₂²	semidirect
34. #16863930	C₂²	semidirect
35. #16863924	C₂²	semidirect
36. C₂×#14524038	C₂²	semidirect
37. C₂×#14524037	C₂²	semidirect
38. C₂×#14524036	C₂²	semidirect
39. C₂×#14524035	C₂²	semidirect
40. C₂×#14524035	C₂²	semidirect
41. C₂×#14524033	C₂²	semidirect
43. C₂×#14524029	C₂²	semidirect
44. #16863903	C₂²	semidirect
46. C₂×#14524026	C₂²	semidirect
47. C₂×#14524025	C₂²	semidirect
51. C₂×#14524022	C₂²	semidirect
52. C₂×#14524021	C₂²	semidirect
53. C₂×#14524019	C₂²	semidirect
54. C₂×#14524019	C₂²	semidirect
57. C₂×#14524014	C₂²	semidirect
58. C₂×#14524014	C₂²	semidirect
60. C₄×#11761628	C₂²	semidirect
61. C₂×C₄×Dic₁₃₄	C₂²	semidirect
62. C₂×C₄×Dic₁₃₄	C₂²	semidirect
63. C₂×C₄×Dic₁₃₄	C₂²	semidirect
71. C₂×C₄×D₂₆₈	C₂²	semidirect
72. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
73. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
74. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
76. C₂×#14524002	C₂²	semidirect
77. C₂×#14524001	C₂²	semidirect
78. C₂×#14524001	C₂²	semidirect
79. C₂×#14524000	C₂²	semidirect
80. C₂×#14524000	C₂²	semidirect
82. #117×D₆₇	C₂²	semidirect
84. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
85. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
88. C₂×C₄²×D₆₇	C₂²	semidirect
90. C₄×#41×C₆₇	C₂²	semidirect
91. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
92. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
95. C₂×C₄×D₄×C₆₇	C₂²	semidirect
96. C₂×C₄×D₄×C₆₇	C₂²	semidirect
98. C₂×#117×C₆₇	C₂²	semidirect
100. C₂²×C₄²×C₆₇	C₂²	semidirect
122. #14524043	C₂³	semidirect
123. #14524043	C₂³	semidirect
124. #14524038	C₂³	semidirect
125. #14524037	C₂³	semidirect
126. #14524036	C₂³	semidirect
127. #14524035	C₂³	semidirect
128. #14524035	C₂³	semidirect
129. #14524033	C₂³	semidirect
131. #14524029	C₂³	semidirect
133. #14524026	C₂³	semidirect
134. #14524025	C₂³	semidirect
138. #14524022	C₂³	semidirect
139. #14524021	C₂³	semidirect
140. #14524019	C₂³	semidirect
141. #14524019	C₂³	semidirect
144. #14524014	C₂³	semidirect
145. #14524014	C₂³	semidirect
147. C₄×Dic₁₃₄	C₂³	semidirect
148. C₄×Dic₁₃₄	C₂³	semidirect
149. C₄×Dic₁₃₄	C₂³	semidirect
157. C₄×C₂²⋊D₆₇	C₂³	semidirect
158. C₄×C₂²⋊D₆₇	C₂³	semidirect
159. C₄×C₂²⋊D₆₇	C₂³	semidirect
161. #14524002	C₂³	semidirect
162. #14524001	C₂³	semidirect
163. #14524001	C₂³	semidirect
164. #14524000	C₂³	semidirect
165. #14524000	C₂³	semidirect
181. C₄⋊C₄×D₆₇	C₂³	semidirect
182. C₄⋊C₄×D₆₇	C₂³	semidirect
199. C₄²×D₆₇	C₂³	semidirect
211. C₄×Q₈×C₆₇	C₂³	semidirect
212. C₄×Q₈×C₆₇	C₂³	semidirect
215. C₄×D₄×C₆₇	C₂³	semidirect
216. C₄×D₄×C₆₇	C₂³	semidirect
218. #117×C₆₇	C₂³	semidirect
234. C₂×C₄²×C₆₇	C₂³	semidirect
249. C₂×D₂₆₈	#41	semidirect
317. C₂²×C₄×C₆₇	#41	semidirect
385. C₂×C₄×C₆₇	C₂×#41	semidirect
408. D₂₆₈	C₂×#41	semidirect
454. C₂×C₆₇	#3475	semidirect
475. C₂×C₄×#41	D₆₇	semidirect
478. C₆₇	C₂×#3475	semidirect
522. C₄×#41	C₂×D₆₇	semidirect
526. C₂×C₄×Q₈	C₂×D₆₇	semidirect
527. C₂×C₄×Q₈	C₂×D₆₇	semidirect
541. C₂×C₄×D₄	C₂×D₆₇	semidirect
542. C₂×C₄×D₄	C₂×D₆₇	semidirect
552. C₂×#117	C₂×D₆₇	semidirect
560. C₂²×C₄²	C₂×D₆₇	semidirect
621. C₄×Q₈	C₂²×D₆₇	semidirect
622. C₄×Q₈	C₂²×D₆₇	semidirect
635. C₄×D₄	C₂²×D₆₇	semidirect
636. C₄×D₄	C₂²×D₆₇	semidirect
645. #117	C₂²×D₆₇	semidirect
694. C₂×C₄²	C₂²×D₆₇	semidirect
750. C₂²×C₄	#11761628	semidirect
867. C₂×C₄	C₂×#11761628	semidirect
915. C₂	#22573773	direct (N × H)

Maximal subgroups

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

subgroup	index
#22573773	2
C₂×#16864119	2
C₂×#16864111	2
C₂×#16864106	2
C₂×#16864096	2
C₂×#16864087	2
C₂×#16864086	2
C₂×#16864075	2
C₂×#16864051	2
C₂×#16864042	2
C₂×#16863953	2
C₂×#16863930	2
C₂×#16863924	2
C₂×#16863903	2
C₂×C₄×#11761628	2
C₂²×C₄×D₂₆₈	2
C₂×#117×D₆₇	2
C₂×C₄×#41×C₆₇	2
C₂×#3475	67

Subgroups — C2×#22573773 #31762869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22573773 #31762869