Subgroups — C₂×#22574243 #31763828

Order 17152.

8774 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574243	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864111	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864099	C₂	1	2	yes	maximal, complemented
5	C₂×#16864092	C₂	1	2	yes	maximal, complemented
6	C₂×#16864068	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16864039	C₂	1	2	yes	maximal, complemented
8	C₂×#16864038	C₂	1	4	yes	maximal, complemented
9	C₂×D₄×D₂₆₈	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16864001	C₂	1	2	yes	maximal, complemented
12	C₂×#16863985	C₂	1	4	yes	maximal, complemented
13	C₂×#16863946	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16863909	C₂	1	2	yes	maximal, complemented
15	C₂×#121×D₆₇	C₂	1	2	yes	maximal, complemented
16	C₂×#16863870	C₂	1	2	yes	maximal, complemented
17	C₂²×C₄×D₂₆₈	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	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
22	C₂³×D₂₆₈	C₂²	1	2	yes	—
23	C₂²×D₄×D₆₇	C₂²	1	4	yes	complemented
24	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
25	C₂³×C₄×D₆₇	C₂²	1	2	yes	complemented
26	#16864111	C₂²	1	16	yes	complemented
27	#16864106	C₂²	1	16	yes	complemented
28	#16864099	C₂²	1	32	yes	complemented
29	#16864092	C₂²	1	32	yes	complemented
30	#16864068	C₂²	1	16	yes	complemented
31	#16864039	C₂²	1	32	yes	complemented
32	#16864038	C₂²	1	64	yes	complemented
33	D₄×D₂₆₈	C₂²	1	32	yes	complemented
34	D₄×D₂₆₈	C₂²	1	16	yes	complemented
35	#16864001	C₂²	1	32	yes	complemented
36	#16863985	C₂²	1	64	yes	complemented
37	#16863946	C₂²	1	16	yes	complemented
38	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
39	C₂×#14524040	C₂²	1	2	yes	complemented
40	C₂×#14524040	C₂²	1	1	yes	characteristic, complemented
41	C₂×#14524038	C₂²	1	4	yes	complemented
42	C₂×#14524035	C₂²	1	2	yes	complemented
43	C₂×#14524031	C₂²	1	2	yes	complemented
44	C₂×#14524029	C₂²	1	4	yes	complemented
45	#16863909	C₂²	1	32	yes	complemented
46	C₂×#14524028	C₂²	1	4	yes	complemented
47	C₂×#14524028	C₂²	1	4	yes	complemented
48	C₂×#14524025	C₂²	1	4	yes	complemented
49	C₂×#14524021	C₂²	1	4	yes	complemented
50	C₂×#14524019	C₂²	1	2	yes	complemented
51	C₂×#14524018	C₂²	1	2	yes	complemented
52	C₂×#14524018	C₂²	1	4	yes	complemented
53	C₂×#14524018	C₂²	1	4	yes	complemented
54	C₂×#14524018	C₂²	1	2	yes	complemented
55	C₂×#14524017	C₂²	1	2	yes	complemented
56	C₂×#14524017	C₂²	1	2	yes	complemented
57	C₂×#14524017	C₂²	1	2	yes	complemented
58	C₂×#14524017	C₂²	1	2	yes	complemented
59	C₂×#14524016	C₂²	1	4	yes	complemented
60	C₂×#14524016	C₂²	1	4	yes	complemented
61	C₂×#14524015	C₂²	1	4	yes	complemented
62	C₂×#14524014	C₂²	1	2	yes	complemented
63	#121×D₆₇	C₂²	1	32	yes	complemented
64	C₂×#14524013	C₂²	1	4	yes	complemented
65	C₂×#14524013	C₂²	1	4	yes	complemented
66	C₂×#14524013	C₂²	1	4	yes	complemented
67	#16863870	C₂²	1	32	yes	complemented
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	1	yes	characteristic, complemented
72	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
73	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
74	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
76	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
77	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
78	C₂×C₄×D₂₆₈	C₂²	1	16	yes	complemented
79	C₂×#14524005	C₂²	1	4	yes	complemented
80	C₂×#14524005	C₂²	1	4	yes	complemented
81	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
82	C₂×#14524002	C₂²	1	2	yes	complemented
83	C₂×#14524001	C₂²	1	2	yes	complemented
84	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
86	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
87	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	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, complemented
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	2	yes	complemented
98	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, 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	2	yes	—
102	C₂⁴×D₆₇	C₂³	1	4	yes	—
103	C₂×#11761629	—	4	8	no	—
104	C₂×#11761629	C₂³	1	16	yes	complemented
105	C₂×#11761628	—	4	8	no	—
106	C₂×#11761628	C₂³	1	16	yes	complemented
107	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
108	C₂²×D₂₆₈	—	2	8	no	—
109	C₂²×D₂₆₈	—	2	16	no	—
110	C₂²×D₂₆₈	C₂³	1	8	yes	—
111	C₂²×D₂₆₈	C₂³	1	16	yes	—
112	C₂²×D₂₆₈	C₂³	1	4	yes	—
113	C₂²×D₂₆₈	C₂³	1	2	yes	—
114	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
115	C₂²×D₂₆₈	C₂³	1	2	yes	—
116	C₂²×D₂₆₈	C₂³	1	2	yes	—
117	C₂²×D₂₆₈	C₂³	1	4	yes	—
118	C₂²×D₂₆₈	C₂³	1	2	yes	—
119	C₂²×D₂₆₈	C₂³	1	4	yes	—
120	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
121	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
122	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
123	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
124	C₂×D₄×D₆₇	—	4	8	no	—
125	C₂×D₄×D₆₇	—	4	16	no	—
126	C₂×D₄×D₆₇	C₂³	1	32	yes	complemented
127	C₂×D₄×D₆₇	C₂³	1	16	yes	complemented
128	C₂³×Dic₆₇	C₂³	1	2	yes	—
129	C₂²×C₄×D₆₇	—	4	8	no	—
130	C₂²×C₄×D₆₇	C₂³	1	2	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	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
137	C₂²×C₄×D₆₇	C₂³	1	16	yes	complemented
138	#14524043	C₂³	1	8	yes	complemented
139	#14524040	C₂³	1	16	yes	complemented
140	#14524040	C₂³	1	8	yes	complemented
141	#14524038	C₂³	1	32	yes	complemented
142	#14524035	C₂³	1	16	yes	complemented
143	#14524031	C₂³	1	16	yes	complemented
144	#14524029	C₂³	1	32	yes	complemented
145	#14524028	C₂³	1	32	yes	complemented
146	#14524028	C₂³	1	32	yes	complemented
147	#14524025	C₂³	1	32	yes	complemented
148	#14524021	C₂³	1	32	yes	complemented
149	#14524019	C₂³	1	16	yes	complemented
150	#14524018	C₂³	1	16	yes	complemented
151	#14524018	C₂³	1	32	yes	complemented
152	#14524018	C₂³	1	32	yes	complemented
153	#14524018	C₂³	1	16	yes	complemented
154	#14524017	C₂³	1	16	yes	complemented
155	#14524017	C₂³	1	16	yes	complemented
156	#14524017	C₂³	1	16	yes	complemented
157	#14524017	C₂³	1	16	yes	complemented
158	#14524016	C₂³	1	32	yes	complemented
159	#14524016	C₂³	1	32	yes	complemented
160	#14524015	C₂³	1	32	yes	complemented
161	#14524014	C₂³	1	16	yes	complemented
162	#14524013	C₂³	1	32	yes	complemented
163	#14524013	C₂³	1	32	yes	complemented
164	#14524013	C₂³	1	32	yes	complemented
165	C₄×D₂₆₈	C₂³	1	8	yes	—
166	C₄×D₂₆₈	C₂³	1	16	yes	—
167	C₄×D₂₆₈	C₂³	1	8	yes	—
168	C₄×D₂₆₈	C₂³	1	8	yes	complemented
169	C₄×D₂₆₈	C₂³	1	16	yes	complemented
170	C₄×D₂₆₈	C₂³	1	16	yes	complemented
171	C₄×D₂₆₈	C₂³	1	16	yes	complemented
172	C₄×D₂₆₈	C₂³	1	16	yes	complemented
173	C₄×D₂₆₈	C₂³	1	8	yes	complemented
174	C₄×D₂₆₈	C₂³	1	16	yes	complemented
175	#14524005	C₂³	1	32	yes	complemented
176	#14524005	C₂³	1	32	yes	complemented
177	(C₂²⋊D₆₇)⋊C₄	C₂³	1	32	yes	complemented
178	#14524002	C₂³	1	16	yes	complemented
179	#14524001	C₂³	1	16	yes	complemented
180	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
184	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊Dic₆₇	C₂³	1	8	yes	complemented
186	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
187	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
188	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
189	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
190	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	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	2	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	16	yes	complemented
201	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
202	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
203	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
204	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
206	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
211	#126×C₆₇	C₂³	1	16	yes	complemented
212	#125×C₆₇	C₂³	1	8	yes	complemented
213	#124×C₆₇	C₂³	1	8	yes	complemented
214	#123×C₆₇	C₂³	1	16	yes	complemented
215	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
216	#121×C₆₇	C₂³	1	8	yes	—
217	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
218	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
219	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
220	#117×C₆₇	C₂³	1	16	yes	complemented
221	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
236	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
237	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
238	C₂³×D₆₇	—	2	8	no	—
239	C₂³×D₆₇	—	2	8	no	—
240	C₂³×D₆₇	—	2	16	no	—
241	C₂³×D₆₇	—	4	4	no	—
242	C₂³×D₆₇	—	4	8	no	—
243	C₂³×D₆₇	—	4	8	no	—
244	C₂³×D₆₇	C₂⁴	1	2	yes	—
245	C₂³×D₆₇	C₂⁴	1	4	yes	—
246	C₂³×D₆₇	C₂⁴	1	8	yes	—
247	C₂³×D₆₇	C₂⁴	1	2	yes	—
248	C₂³×D₆₇	C₂⁴	1	16	yes	—
249	#11761629	—	4	32	no	—
250	#11761628	—	4	32	no	—
251	C₂×Dic₁₃₄	—	4	4	no	—
252	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
253	C₂×D₂₆₈	—	2	16	no	—
254	C₂×D₂₆₈	—	2	8	no	—
255	C₂×D₂₆₈	—	2	4	no	—
256	C₂×D₂₆₈	—	2	8	no	—
257	C₂×D₂₆₈	—	2	8	no	—
258	C₂×D₂₆₈	—	2	32	no	—
259	C₂×D₂₆₈	—	2	64	no	—
260	C₂×D₂₆₈	—	4	8	no	—
261	C₂×D₂₆₈	—	4	4	no	—
262	C₂×D₂₆₈	—	4	8	no	—
263	C₂×D₂₆₈	#41	1	8	yes	complemented
264	C₂×D₂₆₈	C₂⁴	1	16	yes	—
265	C₂×D₂₆₈	C₂⁴	1	8	yes	—
266	C₂×D₂₆₈	C₂⁴	1	4	yes	—
267	C₂×D₂₆₈	C₂⁴	1	8	yes	—
268	C₂×D₂₆₈	C₂⁴	1	8	yes	—
269	C₂×D₂₆₈	C₂⁴	1	16	yes	—
270	C₂×D₂₆₈	C₂⁴	1	8	yes	—
271	C₂×D₂₆₈	C₂⁴	1	16	yes	—
272	C₂×D₂₆₈	C₂⁴	1	4	yes	—
273	C₂×C₂²⋊D₆₇	—	2	16	no	—
274	C₂×C₂²⋊D₆₇	—	4	8	no	—
275	C₂×C₂²⋊D₆₇	—	4	8	no	—
276	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
277	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
278	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
279	D₄×D₆₇	—	4	32	no	—
280	D₄×D₆₇	—	4	64	no	—
281	C₂²×Dic₆₇	—	4	4	no	—
282	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
283	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
284	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
285	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
286	C₂×C₄×D₆₇	—	2	8	no	—
287	C₂×C₄×D₆₇	—	2	8	no	—
288	C₂×C₄×D₆₇	—	4	32	no	—
289	C₂×C₄×D₆₇	—	4	4	no	—
290	C₂×C₄×D₆₇	—	4	4	no	—
291	C₂×C₄×D₆₇	—	4	8	no	—
292	C₂×C₄×D₆₇	—	4	8	no	—
293	C₂×C₄×D₆₇	—	4	8	no	—
294	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
295	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
296	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
297	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
298	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
299	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
300	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
301	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
302	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
303	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
304	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
305	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
306	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
307	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
308	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
309	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
310	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
311	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
312	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
313	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
314	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
315	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
316	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
317	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
318	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
319	C₄×Dic₆₇	C₂⁴	1	16	yes	—
320	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
321	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂×Q₈×C₆₇	—	2	4	no	—
323	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
324	C₂×D₄×C₆₇	—	2	8	no	—
325	C₂×D₄×C₆₇	—	2	4	no	—
326	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
327	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₆₇	—	2	4	no	—
329	C₂²×C₄×C₆₇	—	2	4	no	—
330	C₂²×C₄×C₆₇	—	2	8	no	—
331	C₂²×C₄×C₆₇	—	2	4	no	—
332	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
339	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
341	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
343	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
345	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
346	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
347	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
348	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
349	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
350	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
351	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
352	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
353	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
354	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
355	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
356	C₄²×C₆₇	C₂⁴	1	4	yes	—
357	C₄²×C₆₇	C₂⁴	1	4	yes	—
358	C₄²×C₆₇	C₂⁴	1	4	yes	—
359	C₄²×C₆₇	C₂⁴	1	4	yes	—
360	C₄²×C₆₇	C₂⁴	1	8	yes	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	4	no	—
364	C₂³×C₆₇	—	2	4	no	—
365	C₂³×C₆₇	—	2	4	no	—
366	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
367	C₂³×C₆₇	C₂⁵	1	4	yes	—
368	C₂³×C₆₇	C₂⁵	1	2	yes	—
369	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
370	C₂²×D₆₇	—	2	4	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	—	2	8	no	—
376	C₂²×D₆₇	—	2	8	no	—
377	C₂²×D₆₇	—	2	16	no	—
378	C₂²×D₆₇	—	2	4	no	—
379	C₂²×D₆₇	—	2	16	no	—
380	C₂²×D₆₇	—	2	32	no	—
381	C₂²×D₆₇	—	4	8	no	—
382	C₂²×D₆₇	—	4	16	no	—
383	C₂²×D₆₇	—	4	16	no	—
384	C₂²×D₆₇	—	4	32	no	—
385	C₂²×D₆₇	—	8	32	no	—
386	C₂²×D₆₇	C₂×#41	1	8	yes	—
387	C₂²×D₆₇	C₂⁵	1	4	yes	—
388	C₂²×D₆₇	C₂⁵	1	8	yes	—
389	C₂²×D₆₇	C₂⁵	1	4	yes	—
390	Q₈×C₆₇	—	2	8	no	—
391	D₄×C₆₇	—	2	16	no	—
392	D₄×C₆₇	—	2	8	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	4	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	8	no	—
399	C₂×C₄×C₆₇	—	2	4	no	—
400	C₂×C₄×C₆₇	—	2	4	no	—
401	C₂×C₄×C₆₇	—	2	8	no	—
402	C₂×C₄×C₆₇	—	2	16	no	—
403	C₂×C₄×C₆₇	—	2	8	no	—
404	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
405	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
406	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
407	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
408	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
409	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
410	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
411	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
412	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
413	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
414	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
415	C₂²⋊D₆₇	—	2	32	no	—
416	C₂²⋊D₆₇	—	4	16	no	—
417	C₂²⋊D₆₇	—	4	16	no	—
418	C₂×Dic₆₇	—	2	4	no	—
419	C₂×Dic₆₇	—	2	4	no	—
420	C₂×Dic₆₇	—	2	8	no	—
421	C₂×Dic₆₇	—	4	8	no	—
422	C₂×Dic₆₇	C₂⁵	1	4	yes	—
423	C₂×Dic₆₇	C₂⁵	1	8	yes	—
424	C₂×Dic₆₇	C₂⁵	1	4	yes	—
425	D₂₆₈	—	2	32	no	—
426	D₂₆₈	—	2	16	no	—
427	D₂₆₈	—	2	8	no	—
428	D₂₆₈	—	2	16	no	—
429	D₂₆₈	—	2	16	no	—
430	D₂₆₈	—	4	16	no	—
431	D₂₆₈	—	4	8	no	—
432	D₂₆₈	—	4	16	no	—
433	D₂₆₈	C₂×#41	1	16	yes	complemented
434	C₄×D₆₇	—	2	16	no	—
435	C₄×D₆₇	—	2	16	no	—
436	C₄×D₆₇	—	4	8	no	—
437	C₄×D₆₇	—	4	8	no	—
438	C₄×D₆₇	—	4	16	no	—
439	C₄×D₆₇	—	4	16	no	—
440	C₄×D₆₇	—	4	16	no	—
441	Dic₁₃₄	—	4	8	no	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	8	no	—
445	C₂²×C₆₇	—	2	4	no	—
446	C₂²×C₆₇	—	2	4	no	—
447	C₂²×C₆₇	—	2	4	no	—
448	C₂²×C₆₇	—	4	8	no	—
449	C₂²×C₆₇	C₂²×#41	1	2	yes	—
450	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
451	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
452	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
453	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
454	C₂×D₆₇	—	2	4	no	—
455	C₂×D₆₇	—	2	4	no	—
456	C₂×D₆₇	—	2	16	no	—
457	C₂×D₆₇	—	2	4	no	—
458	C₂×D₆₇	—	2	8	no	—
459	C₂×D₆₇	—	2	4	no	—
460	C₂×D₆₇	—	2	8	no	—
461	C₂×D₆₇	—	2	8	no	—
462	C₂×D₆₇	—	2	4	no	—
463	C₂×D₆₇	—	4	32	no	—
464	C₂×D₆₇	—	4	8	no	—
465	C₂×D₆₇	—	4	16	no	—
466	C₂×D₆₇	—	8	32	no	—
467	C₂×D₆₇	C₂²×#41	1	8	yes	—
468	C₄×C₆₇	—	2	2	no	—
469	C₄×C₆₇	—	2	4	no	—
470	C₄×C₆₇	—	2	2	no	—
471	C₄×C₆₇	—	2	2	no	—
472	C₄×C₆₇	—	2	2	no	—
473	C₄×C₆₇	—	2	4	no	—
474	C₄×C₆₇	—	2	4	no	—
475	C₄×C₆₇	C₂²×#41	1	4	yes	—
476	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
477	Dic₆₇	—	2	8	no	—
478	Dic₆₇	—	2	4	no	—
479	Dic₆₇	—	2	4	no	—
480	C₂×#3519	—	67	1	no	maximal, Sylow
481	C₂×C₆₇	—	2	4	no	—
482	C₂×C₆₇	—	4	4	no	—
483	C₂×C₆₇	#3519	1	4	yes	complemented
484	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
485	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
486	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
487	D₆₇	—	2	8	no	—
488	D₆₇	—	4	4	no	—
489	D₆₇	—	4	8	no	—
490	#3519	—	67	32	no	—
491	C₂×#555	—	67	1	no	—
492	C₂×#554	—	67	1	no	—
493	C₂×#553	—	67	2	no	—
494	C₂×#553	—	67	2	no	—
495	C₂×#550	—	67	1	no	—
496	C₂×#546	—	67	2	no	—
497	C₂×#546	—	67	4	no	—
498	C₂×D₄²	—	67	1	no	—
499	C₂×D₄²	—	67	2	no	—
500	C₂×#540	—	67	2	no	—
501	C₂×#538	—	67	4	no	—
502	C₂×#532	—	67	1	no	—
503	C₂×#529	D₆₇	1	1	yes	characteristic, complemented
504	C₂×#525	—	67	2	no	—
505	C₂²×#121	—	67	2	no	—
506	C₂×#518	—	67	2	no	—
507	C₂²×C₄×D₄	—	67	1	no	—
508	C₆₇	C₂×#3519	1	1	yes	characteristic, complemented, Sylow
509	C₂²×#41	—	67	2	no	—
510	C₂²×#41	—	67	2	no	—
511	C₂³×D₄	—	67	4	no	—
512	C₂³×D₄	—	67	2	no	—
513	C₂³×D₄	—	67	1	no	—
514	C₂³×D₄	—	67	2	no	—
515	C₂⁴×C₄	—	67	2	no	—
516	#555	—	67	16	no	—
517	#554	—	67	16	no	—
518	#553	—	67	32	no	—
519	#553	—	67	32	no	—
520	#550	—	67	16	no	—
521	#546	—	67	32	no	—
522	#546	—	67	64	no	—
523	D₄²	—	67	16	no	—
524	D₄²	—	67	32	no	—
525	#540	—	67	32	no	—
526	#538	—	67	64	no	—
527	#532	—	67	16	no	—
528	C₂×C₄⋊Q₈	—	67	1	no	—
529	C₂×#127	—	67	1	no	—
530	C₂×#127	—	67	2	no	—
531	#529	C₂×D₆₇	1	16	yes	complemented
532	C₂×#126	—	67	4	no	—
533	C₂×#126	C₂×D₆₇	1	2	yes	complemented
534	C₂×#125	—	67	2	no	—
535	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
536	C₂×#124	—	67	4	no	—
537	C₂×#124	—	67	2	no	—
538	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
539	#525	—	67	32	no	—
540	C₂×#123	—	67	4	no	—
541	C₂×#123	—	67	4	no	—
542	C₂×#123	—	67	4	no	—
543	C₂×#123	C₂×D₆₇	1	2	yes	complemented
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	4	no	—
549	C₂×#121	—	67	2	no	—
550	C₂×#121	—	67	2	no	—
551	C₂×#121	—	67	2	no	—
552	C₂×#121	—	67	2	no	—
553	C₂×#121	—	67	32	no	—
554	C₂×#121	—	67	2	no	—
555	C₂×#121	—	67	2	no	—
556	C₂×#121	—	67	4	no	—
557	C₂×#121	—	67	4	no	—
558	C₂×#121	—	67	4	no	—
559	C₂×#121	—	67	4	no	—
560	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
561	C₂×#120	—	67	4	no	—
562	C₂×#120	—	67	4	no	—
563	C₂×#120	—	67	4	no	—
564	#518	—	67	32	no	—
565	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
566	C₂×C₄×D₄	—	67	4	no	—
567	C₂×C₄×D₄	—	67	4	no	—
568	C₂×C₄×D₄	—	67	4	no	—
569	C₂×C₄×D₄	—	67	1	no	—
570	C₂×C₄×D₄	—	67	1	no	—
571	C₂×C₄×D₄	—	67	2	no	—
572	C₂×C₄×D₄	—	67	1	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	—	67	2	no	—
577	C₂×C₄×D₄	—	67	2	no	—
578	C₂×C₄×D₄	—	67	2	no	—
579	C₂×C₄×D₄	—	67	16	no	—
580	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
581	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
582	C₂×#117	—	67	2	no	—
583	C₂×#117	—	67	2	no	—
584	C₂×#117	C₂×D₆₇	1	2	yes	complemented
585	C₂²×C₄⋊C₄	—	67	1	no	—
586	C₂²×C₄⋊C₄	—	67	2	no	—
587	C₂²×C₂²⋊C₄	—	67	2	no	—
588	C₂²×C₂²⋊C₄	—	67	4	no	—
589	C₂²×C₂²⋊C₄	—	67	4	no	—
590	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
591	C₂⁵	—	67	4	no	—
592	C₂⁵	—	67	2	no	—
593	C₂×#41	—	268	8	no	—
594	C₂×#41	—	268	8	no	—
595	C₂×#41	—	67	16	no	—
596	C₂×#41	—	67	16	no	—
597	C₂²×Q₈	—	67	2	no	—
598	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
599	C₂²×D₄	—	268	16	no	—
600	C₂²×D₄	—	268	8	no	—
601	C₂²×D₄	—	67	4	no	—
602	C₂²×D₄	—	67	4	no	—
603	C₂²×D₄	—	67	32	no	—
604	C₂²×D₄	—	67	16	no	—
605	C₂²×D₄	—	67	4	no	—
606	C₂²×D₄	—	67	4	no	—
607	C₂²×D₄	—	67	2	no	—
608	C₂²×D₄	—	67	4	no	—
609	C₂²×D₄	—	67	1	no	—
610	C₂²×D₄	—	67	4	no	—
611	C₂²×D₄	—	67	2	no	—
612	C₂²×D₄	—	67	1	no	—
613	C₂²×D₄	—	67	2	no	—
614	C₂²×D₄	—	67	8	no	—
615	C₂²×D₄	—	67	2	no	—
616	C₂²×D₄	—	67	16	no	—
617	C₂²×D₄	—	134	8	no	—
618	C₂²×D₄	—	134	16	no	—
619	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
620	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
621	C₂³×C₄	—	268	8	no	—
622	C₂³×C₄	—	67	2	no	—
623	C₂³×C₄	—	67	2	no	—
624	C₂³×C₄	—	67	4	no	—
625	C₂³×C₄	—	67	4	no	—
626	C₂³×C₄	—	67	4	no	—
627	C₂³×C₄	—	67	2	no	—
628	C₂³×C₄	—	67	16	no	—
629	C₂³×C₄	—	67	2	no	—
630	C₂³×C₄	—	67	2	no	—
631	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
632	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
633	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
634	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
635	C₄⋊Q₈	—	67	8	no	—
636	#127	—	67	8	no	—
637	#127	—	67	16	no	—
638	#126	—	67	32	no	—
639	#126	C₂²×D₆₇	1	16	yes	complemented
640	#125	—	67	16	no	—
641	#125	C₂²×D₆₇	1	8	yes	complemented
642	#124	—	67	32	no	—
643	#124	—	67	16	no	—
644	#124	C₂²×D₆₇	1	8	yes	complemented
645	#123	—	67	32	no	—
646	#123	—	67	32	no	—
647	#123	—	67	32	no	—
648	#123	C₂²×D₆₇	1	16	yes	complemented
649	C₂²⋊Q₈	—	67	16	no	—
650	C₂²⋊Q₈	—	67	32	no	—
651	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
652	#121	—	67	32	no	—
653	#121	—	67	16	no	—
654	#121	—	67	16	no	—
655	#121	—	67	16	no	—
656	#121	—	67	16	no	—
657	#121	—	67	16	no	—
658	#121	—	67	16	no	—
659	#121	—	67	16	no	—
660	#121	—	67	32	no	—
661	#121	—	67	32	no	—
662	#121	—	67	32	no	—
663	#121	—	67	32	no	—
664	#121	C₂²×D₆₇	1	8	yes	—
665	#120	—	67	32	no	—
666	#120	—	67	32	no	—
667	#120	—	67	32	no	—
668	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
669	C₄×D₄	—	67	32	no	—
670	C₄×D₄	—	67	32	no	—
671	C₄×D₄	—	67	32	no	—
672	C₄×D₄	—	67	8	no	—
673	C₄×D₄	—	67	16	no	—
674	C₄×D₄	—	67	8	no	—
675	C₄×D₄	—	67	8	no	—
676	C₄×D₄	—	67	16	no	—
677	C₄×D₄	—	67	8	no	—
678	C₄×D₄	—	67	16	no	—
679	C₄×D₄	—	67	16	no	—
680	C₄×D₄	—	67	16	no	—
681	C₄×D₄	—	67	16	no	—
682	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
683	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
684	#117	—	67	16	no	—
685	#117	—	67	16	no	—
686	#117	C₂²×D₆₇	1	16	yes	complemented
687	C₂×C₄⋊C₄	—	67	1	no	—
688	C₂×C₄⋊C₄	—	67	2	no	—
689	C₂×C₄⋊C₄	—	67	1	no	—
690	C₂×C₄⋊C₄	—	67	2	no	—
691	C₂×C₄⋊C₄	—	67	8	no	—
692	C₂×C₄⋊C₄	—	67	4	no	—
693	C₂×C₄⋊C₄	—	67	2	no	—
694	C₂×C₄⋊C₄	—	67	4	no	—
695	C₂×C₄⋊C₄	—	67	16	no	—
696	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
700	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
701	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
702	C₂×C₂²⋊C₄	—	67	4	no	—
703	C₂×C₂²⋊C₄	—	67	2	no	—
704	C₂×C₂²⋊C₄	—	67	4	no	—
705	C₂×C₂²⋊C₄	—	67	2	no	—
706	C₂×C₂²⋊C₄	—	67	4	no	—
707	C₂×C₂²⋊C₄	—	67	2	no	—
708	C₂×C₂²⋊C₄	—	67	4	no	—
709	C₂×C₂²⋊C₄	—	67	2	no	—
710	C₂×C₂²⋊C₄	—	67	16	no	—
711	C₂×C₂²⋊C₄	—	67	4	no	—
712	C₂×C₂²⋊C₄	—	67	4	no	—
713	C₂×C₂²⋊C₄	—	67	4	no	—
714	C₂×C₂²⋊C₄	—	67	32	no	—
715	C₂×C₂²⋊C₄	—	67	32	no	—
716	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
721	C₂×C₄²	—	67	4	no	—
722	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
723	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
724	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
725	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
726	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
727	C₂×C₄²	C₂²×D₆₇	1	8	yes	complemented
728	C₂⁴	—	268	4	no	—
729	C₂⁴	—	268	8	no	—
730	C₂⁴	—	268	8	no	—
731	C₂⁴	—	67	16	no	—
732	C₂⁴	—	67	8	no	—
733	C₂⁴	—	67	2	no	—
734	C₂⁴	—	67	2	no	—
735	C₂⁴	—	67	4	no	—
736	C₂⁴	—	134	8	no	—
737	C₂⁴	—	134	16	no	—
738	C₂⁴	—	134	8	no	—
739	C₂⁴	C₂³×D₆₇	1	2	yes	—
740	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
741	#41	—	268	32	no	—
742	#41	—	268	32	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	268	4	no	—
745	C₂×Q₈	—	67	8	no	—
746	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
747	C₂×D₄	—	2	8	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	—	268	8	no	—
750	C₂×D₄	—	268	4	no	—
751	C₂×D₄	—	268	8	no	—
752	C₂×D₄	—	268	64	no	—
753	C₂×D₄	—	268	32	no	—
754	C₂×D₄	—	268	8	no	—
755	C₂×D₄	—	268	8	no	—
756	C₂×D₄	—	67	16	no	—
757	C₂×D₄	—	67	16	no	—
758	C₂×D₄	—	67	16	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	4	no	—
764	C₂×D₄	—	67	16	no	—
765	C₂×D₄	—	67	8	no	—
766	C₂×D₄	—	67	4	no	—
767	C₂×D₄	—	67	8	no	—
768	C₂×D₄	—	67	8	no	—
769	C₂×D₄	—	134	32	no	—
770	C₂×D₄	—	134	64	no	—
771	C₂×D₄	—	134	16	no	—
772	C₂×D₄	—	134	8	no	—
773	C₂×D₄	—	134	16	no	—
774	C₂×D₄	—	134	4	no	—
775	C₂×D₄	—	134	8	no	—
776	C₂×D₄	—	134	8	no	—
777	C₂×D₄	C₂³×D₆₇	1	8	yes	—
778	C₂×D₄	C₂³×D₆₇	1	4	yes	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	8	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	268	4	no	—
784	C₂²×C₄	—	268	4	no	—
785	C₂²×C₄	—	268	8	no	—
786	C₂²×C₄	—	268	8	no	—
787	C₂²×C₄	—	268	8	no	—
788	C₂²×C₄	—	268	32	no	—
789	C₂²×C₄	—	268	4	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	—	67	16	no	—
795	C₂²×C₄	—	67	8	no	—
796	C₂²×C₄	—	67	2	no	—
797	C₂²×C₄	—	67	4	no	—
798	C₂²×C₄	—	67	2	no	—
799	C₂²×C₄	—	67	8	no	—
800	C₂²×C₄	—	67	8	no	—
801	C₂²×C₄	—	134	8	no	—
802	C₂²×C₄	—	134	8	no	—
803	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
804	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
805	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
806	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
807	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
808	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
809	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
810	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
811	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
812	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
813	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
814	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
815	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
816	C₄⋊C₄	—	67	4	no	—
817	C₄⋊C₄	—	67	8	no	—
818	C₄⋊C₄	—	67	4	no	—
819	C₄⋊C₄	—	67	8	no	—
820	C₄⋊C₄	—	67	16	no	—
821	C₄⋊C₄	—	67	8	no	—
822	C₄⋊C₄	—	67	16	no	—
823	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
824	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
825	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
826	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
827	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
828	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
829	C₂²⋊C₄	—	67	16	no	—
830	C₂²⋊C₄	—	67	8	no	—
831	C₂²⋊C₄	—	67	16	no	—
832	C₂²⋊C₄	—	67	8	no	—
833	C₂²⋊C₄	—	67	16	no	—
834	C₂²⋊C₄	—	67	8	no	—
835	C₂²⋊C₄	—	67	16	no	—
836	C₂²⋊C₄	—	67	8	no	—
837	C₂²⋊C₄	—	67	16	no	—
838	C₂²⋊C₄	—	67	16	no	—
839	C₂²⋊C₄	—	67	16	no	—
840	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
841	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
842	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
843	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
844	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
845	C₄²	—	67	16	no	—
846	C₄²	C₂³×D₆₇	1	4	yes	—
847	C₄²	C₂³×D₆₇	1	4	yes	—
848	C₄²	C₂³×D₆₇	1	4	yes	—
849	C₄²	C₂³×D₆₇	1	4	yes	—
850	C₄²	C₂³×D₆₇	1	8	yes	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	2	4	no	—
855	C₂³	—	2	4	no	—
856	C₂³	—	268	32	no	—
857	C₂³	—	268	8	no	—
858	C₂³	—	268	16	no	—
859	C₂³	—	268	16	no	—
860	C₂³	—	536	32	no	—
861	C₂³	—	67	8	no	—
862	C₂³	—	67	4	no	—
863	C₂³	—	67	4	no	—
864	C₂³	—	67	8	no	—
865	C₂³	—	134	16	no	—
866	C₂³	—	134	32	no	—
867	C₂³	—	134	4	no	—
868	C₂³	—	134	8	no	—
869	C₂³	—	134	4	no	—
870	C₂³	—	134	8	no	—
871	C₂³	—	134	8	no	—
872	C₂³	—	134	16	no	—
873	C₂³	—	134	4	no	—
874	C₂³	—	134	4	no	—
875	C₂³	—	134	4	no	—
876	C₂³	#14524089	1	4	yes	—
877	C₂³	C₂⁴×D₆₇	1	4	yes	—
878	C₂³	C₂⁴×D₆₇	1	2	yes	—
879	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
880	Q₈	—	2	8	no	—
881	Q₈	—	268	8	no	—
882	D₄	—	2	16	no	—
883	D₄	—	2	8	no	—
884	D₄	—	268	16	no	—
885	D₄	—	268	8	no	—
886	D₄	—	268	16	no	—
887	D₄	—	268	16	no	—
888	D₄	—	268	16	no	—
889	D₄	—	67	16	no	—
890	D₄	—	134	32	no	—
891	D₄	—	134	16	no	—
892	D₄	—	134	32	no	—
893	D₄	—	134	8	no	—
894	D₄	—	134	16	no	—
895	D₄	—	134	16	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	8	no	—
902	C₂×C₄	—	2	4	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	8	no	—
905	C₂×C₄	—	2	16	no	—
906	C₂×C₄	—	2	8	no	—
907	C₂×C₄	—	268	8	no	—
908	C₂×C₄	—	268	8	no	—
909	C₂×C₄	—	268	16	no	—
910	C₂×C₄	—	268	16	no	—
911	C₂×C₄	—	268	16	no	—
912	C₂×C₄	—	268	8	no	—
913	C₂×C₄	—	67	4	no	—
914	C₂×C₄	—	67	8	no	—
915	C₂×C₄	—	67	4	no	—
916	C₂×C₄	—	134	4	no	—
917	C₂×C₄	—	134	4	no	—
918	C₂×C₄	—	134	8	no	—
919	C₂×C₄	—	134	16	no	—
920	C₂×C₄	—	134	16	no	—
921	C₂×C₄	#41×D₆₇	1	4	yes	—
922	C₂×C₄	#14524089	1	4	yes	—
923	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
924	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
925	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
926	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
927	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
928	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
929	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
930	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
931	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	8	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	4	8	no	—
939	C₂²	—	268	32	no	—
940	C₂²	—	268	8	no	—
941	C₂²	—	268	16	no	—
942	C₂²	—	536	32	no	—
943	C₂²	—	67	8	no	—
944	C₂²	—	134	4	no	—
945	C₂²	—	134	8	no	—
946	C₂²	—	134	4	no	—
947	C₂²	—	134	8	no	—
948	C₂²	—	134	8	no	—
949	C₂²	—	134	4	no	—
950	C₂²	—	134	16	no	—
951	C₂²	—	134	4	no	—
952	C₂²	—	134	4	no	—
953	C₂²	C₂×#41×D₆₇	1	2	yes	—
954	C₂²	C₂×#14524089	1	4	yes	—
955	C₂²	C₂×#14524089	1	2	yes	—
956	C₂²	C₂×#14524089	1	2	yes	—
957	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
958	C₄	—	2	4	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	4	no	—
965	C₄	—	134	4	no	—
966	C₄	—	134	4	no	—
967	C₄	—	134	8	no	—
968	C₄	C₂×#41×D₆₇	1	4	yes	—
969	C₄	C₂×#14524089	1	4	yes	—
970	C₂	—	2	4	no	—
971	C₂	—	4	4	no	—
972	C₂	—	268	4	no	—
973	C₂	—	268	8	no	—
974	C₂	—	134	8	no	—
975	C₂	#22574243	1	4	yes	direct product factor
976	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
977	C₂	C₂²×#14524089	1	1	yes	characteristic
978	C₂	C₂²×#14524089	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×#3519
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. #22574243	C₂	direct (N × H)
2. C₂×#16864111	C₂	semidirect
3. C₂×#16864106	C₂	semidirect
4. C₂×#16864099	C₂	semidirect
5. C₂×#16864092	C₂	semidirect
6. C₂×#16864068	C₂	semidirect
7. C₂×#16864039	C₂	semidirect
8. C₂×#16864038	C₂	semidirect
9. C₂×D₄×D₂₆₈	C₂	semidirect
10. C₂×D₄×D₂₆₈	C₂	semidirect
11. C₂×#16864001	C₂	semidirect
12. C₂×#16863985	C₂	semidirect
13. C₂×#16863946	C₂	semidirect
14. C₂×#16863909	C₂	semidirect
15. C₂×#121×D₆₇	C₂	semidirect
16. C₂×#16863870	C₂	semidirect
17. C₂²×C₄×D₂₆₈	C₂	semidirect
18. C₂×#529×C₆₇	C₂	semidirect
19. C₂²×#11761629	C₂²	semidirect
20. C₂²×#11761628	C₂²	semidirect
23. C₂²×D₄×D₆₇	C₂²	semidirect
24. C₂²×D₄×D₆₇	C₂²	semidirect
25. C₂³×C₄×D₆₇	C₂²	semidirect
26. #16864111	C₂²	semidirect
27. #16864106	C₂²	semidirect
28. #16864099	C₂²	semidirect
29. #16864092	C₂²	semidirect
30. #16864068	C₂²	semidirect
31. #16864039	C₂²	semidirect
32. #16864038	C₂²	semidirect
33. D₄×D₂₆₈	C₂²	semidirect
34. D₄×D₂₆₈	C₂²	semidirect
35. #16864001	C₂²	semidirect
36. #16863985	C₂²	semidirect
37. #16863946	C₂²	semidirect
38. C₂×#14524043	C₂²	semidirect
39. C₂×#14524040	C₂²	semidirect
40. C₂×#14524040	C₂²	semidirect
41. C₂×#14524038	C₂²	semidirect
42. C₂×#14524035	C₂²	semidirect
43. C₂×#14524031	C₂²	semidirect
44. C₂×#14524029	C₂²	semidirect
45. #16863909	C₂²	semidirect
46. C₂×#14524028	C₂²	semidirect
47. C₂×#14524028	C₂²	semidirect
48. C₂×#14524025	C₂²	semidirect
49. C₂×#14524021	C₂²	semidirect
50. C₂×#14524019	C₂²	semidirect
51. C₂×#14524018	C₂²	semidirect
52. C₂×#14524018	C₂²	semidirect
53. C₂×#14524018	C₂²	semidirect
54. C₂×#14524018	C₂²	semidirect
55. C₂×#14524017	C₂²	semidirect
56. C₂×#14524017	C₂²	semidirect
57. C₂×#14524017	C₂²	semidirect
58. C₂×#14524017	C₂²	semidirect
59. C₂×#14524016	C₂²	semidirect
60. C₂×#14524016	C₂²	semidirect
61. C₂×#14524015	C₂²	semidirect
62. C₂×#14524014	C₂²	semidirect
63. #121×D₆₇	C₂²	semidirect
64. C₂×#14524013	C₂²	semidirect
65. C₂×#14524013	C₂²	semidirect
66. C₂×#14524013	C₂²	semidirect
67. #16863870	C₂²	semidirect
71. C₂×C₄×D₂₆₈	C₂²	semidirect
72. C₂×C₄×D₂₆₈	C₂²	semidirect
73. C₂×C₄×D₂₆₈	C₂²	semidirect
74. C₂×C₄×D₂₆₈	C₂²	semidirect
75. C₂×C₄×D₂₆₈	C₂²	semidirect
76. C₂×C₄×D₂₆₈	C₂²	semidirect
77. C₂×C₄×D₂₆₈	C₂²	semidirect
78. C₂×C₄×D₂₆₈	C₂²	semidirect
79. C₂×#14524005	C₂²	semidirect
80. C₂×#14524005	C₂²	semidirect
81. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
82. C₂×#14524002	C₂²	semidirect
83. C₂×#14524001	C₂²	semidirect
84. C₂²×C₄⋊Dic₆₇	C₂²	semidirect
85. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
86. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
87. C₂×C₂²⋊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
92. C₂×#124×C₆₇	C₂²	semidirect
93. C₂×#123×C₆₇	C₂²	semidirect
94. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
96. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
97. C₂×C₄×D₄×C₆₇	C₂²	semidirect
98. C₂×C₄×D₄×C₆₇	C₂²	semidirect
99. C₂×#117×C₆₇	C₂²	semidirect
100. C₂²×C₄²×C₆₇	C₂²	semidirect
104. C₂×#11761629	C₂³	semidirect
106. C₂×#11761628	C₂³	semidirect
126. C₂×D₄×D₆₇	C₂³	semidirect
127. C₂×D₄×D₆₇	C₂³	semidirect
137. C₂²×C₄×D₆₇	C₂³	semidirect
138. #14524043	C₂³	semidirect
139. #14524040	C₂³	semidirect
140. #14524040	C₂³	semidirect
141. #14524038	C₂³	semidirect
142. #14524035	C₂³	semidirect
143. #14524031	C₂³	semidirect
144. #14524029	C₂³	semidirect
145. #14524028	C₂³	semidirect
146. #14524028	C₂³	semidirect
147. #14524025	C₂³	semidirect
148. #14524021	C₂³	semidirect
149. #14524019	C₂³	semidirect
150. #14524018	C₂³	semidirect
151. #14524018	C₂³	semidirect
152. #14524018	C₂³	semidirect
153. #14524018	C₂³	semidirect
154. #14524017	C₂³	semidirect
155. #14524017	C₂³	semidirect
156. #14524017	C₂³	semidirect
157. #14524017	C₂³	semidirect
158. #14524016	C₂³	semidirect
159. #14524016	C₂³	semidirect
160. #14524015	C₂³	semidirect
161. #14524014	C₂³	semidirect
162. #14524013	C₂³	semidirect
163. #14524013	C₂³	semidirect
164. #14524013	C₂³	semidirect
168. C₄×D₂₆₈	C₂³	semidirect
169. C₄×D₂₆₈	C₂³	semidirect
170. C₄×D₂₆₈	C₂³	semidirect
171. C₄×D₂₆₈	C₂³	semidirect
172. C₄×D₂₆₈	C₂³	semidirect
173. C₄×D₂₆₈	C₂³	semidirect
174. C₄×D₂₆₈	C₂³	semidirect
175. #14524005	C₂³	semidirect
176. #14524005	C₂³	semidirect
177. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
178. #14524002	C₂³	semidirect
179. #14524001	C₂³	semidirect
185. C₂×C₄⋊Dic₆₇	C₂³	semidirect
188. C₄⋊C₄×D₆₇	C₂³	semidirect
200. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
201. C₂²⋊C₄×D₆₇	C₂³	semidirect
202. C₂²⋊C₄×D₆₇	C₂³	semidirect
211. #126×C₆₇	C₂³	semidirect
212. #125×C₆₇	C₂³	semidirect
213. #124×C₆₇	C₂³	semidirect
214. #123×C₆₇	C₂³	semidirect
215. C₂²⋊Q₈×C₆₇	C₂³	semidirect
217. C₄×Q₈×C₆₇	C₂³	semidirect
218. C₄×D₄×C₆₇	C₂³	semidirect
219. C₄×D₄×C₆₇	C₂³	semidirect
220. #117×C₆₇	C₂³	semidirect
237. C₂×C₄²×C₆₇	C₂³	semidirect
263. C₂×D₂₆₈	#41	semidirect
433. D₂₆₈	C₂×#41	semidirect
483. C₂×C₆₇	#3519	semidirect
503. C₂×#529	D₆₇	semidirect
508. C₆₇	C₂×#3519	semidirect
531. #529	C₂×D₆₇	semidirect
533. C₂×#126	C₂×D₆₇	semidirect
535. C₂×#125	C₂×D₆₇	semidirect
538. C₂×#124	C₂×D₆₇	semidirect
543. C₂×#123	C₂×D₆₇	semidirect
546. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
565. C₂×C₄×Q₈	C₂×D₆₇	semidirect
580. C₂×C₄×D₄	C₂×D₆₇	semidirect
581. C₂×C₄×D₄	C₂×D₆₇	semidirect
584. C₂×#117	C₂×D₆₇	semidirect
590. C₂²×C₄²	C₂×D₆₇	semidirect
639. #126	C₂²×D₆₇	semidirect
641. #125	C₂²×D₆₇	semidirect
644. #124	C₂²×D₆₇	semidirect
648. #123	C₂²×D₆₇	semidirect
651. C₂²⋊Q₈	C₂²×D₆₇	semidirect
668. C₄×Q₈	C₂²×D₆₇	semidirect
682. C₄×D₄	C₂²×D₆₇	semidirect
683. C₄×D₄	C₂²×D₆₇	semidirect
686. #117	C₂²×D₆₇	semidirect
727. C₂×C₄²	C₂²×D₆₇	semidirect
975. C₂	#22574243	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574243	2
C₂×#16864111	2
C₂×#16864106	2
C₂×#16864099	2
C₂×#16864092	2
C₂×#16864068	2
C₂×#16864039	2
C₂×#16864038	2
C₂×D₄×D₂₆₈	2
C₂×#16864001	2
C₂×#16863985	2
C₂×#16863946	2
C₂×#16863909	2
C₂×#121×D₆₇	2
C₂×#16863870	2
C₂²×C₄×D₂₆₈	2
C₂×#529×C₆₇	2
C₂×#3519	67

Subgroups — C2×#22574243 #31763828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574243 #31763828