Subgroups — C₂×#22573842 #31763710

Order 17152.

14438 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14524089	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573842	C₂	1	32	yes	maximal, direct product factor
4	C₂×#16864042	C₂	1	4	yes	maximal, complemented
5	C₂×#16864037	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×D₂₆₈	C₂	1	4	yes	maximal, complemented
7	C₂×#16864030	C₂	1	4	yes	maximal, complemented
8	C₂×#16863965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16863960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16863957	C₂	1	4	yes	maximal, complemented
11	C₂×#16863907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#120×D₆₇	C₂	1	4	yes	maximal, complemented
13	C₂×#16863870	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁵×D₆₇	C₂²	1	2	yes	complemented
16	C₂×#14524089	—	2	16	no	—
17	C₂×#14524089	C₂²	1	16	yes	complemented
18	C₂²×#11761629	C₂²	1	2	yes	complemented
19	C₂²×#11761628	C₂²	1	1	yes	characteristic, complemented
20	C₂²×#11761628	C₂²	1	2	yes	complemented
21	C₂³×D₂₆₈	—	2	16	no	—
22	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
23	C₂³×D₂₆₈	C₂²	1	4	yes	complemented
24	C₂³×D₂₆₈	C₂²	1	4	yes	complemented
25	C₂³×D₂₆₈	C₂²	1	2	yes	complemented
26	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
27	C₂³×D₂₆₈	C₂²	1	16	yes	complemented
28	C₂³×D₂₆₈	C₂²	1	2	yes	complemented
29	C₂²×D₄×D₆₇	C₂²	1	4	yes	complemented
30	C₂²×D₄×D₆₇	C₂²	1	8	yes	complemented
31	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
32	#16864042	C₂²	1	64	yes	complemented
33	#16864037	C₂²	1	64	yes	complemented
34	D₄×D₂₆₈	C₂²	1	64	yes	complemented
35	#16864030	C₂²	1	64	yes	complemented
36	#16863965	C₂²	1	16	yes	complemented
37	#16863960	C₂²	1	16	yes	complemented
38	#16863957	C₂²	1	64	yes	complemented
39	C₂×#14524040	C₂²	1	2	yes	complemented
40	C₂×#14524039	C₂²	1	2	yes	complemented
41	C₂×#14524032	C₂²	1	2	yes	complemented
42	C₂×#14524031	C₂²	1	2	yes	complemented
43	#16863907	C₂²	1	16	yes	complemented
44	C₂×#14524028	C₂²	1	8	yes	complemented
45	C₂×#14524026	C₂²	1	2	yes	complemented
46	C₂×#14524022	C₂²	1	2	yes	complemented
47	C₂×#14524018	C₂²	1	4	yes	complemented
48	C₂×#14524018	C₂²	1	8	yes	complemented
49	C₂×#14524017	C₂²	1	2	yes	complemented
50	C₂×#14524017	C₂²	1	4	yes	complemented
51	C₂×#14524016	C₂²	1	8	yes	complemented
52	C₂×#14524013	C₂²	1	8	yes	complemented
53	C₂×#14524013	C₂²	1	4	yes	complemented
54	C₂×#14524013	C₂²	1	8	yes	complemented
55	C₂×#14524012	C₂²	1	2	yes	complemented
56	C₂×#14524011	C₂²	1	8	yes	complemented
57	C₂×#14524011	C₂²	1	4	yes	complemented
58	#120×D₆₇	C₂²	1	64	yes	complemented
59	#16863870	C₂²	1	16	yes	complemented
60	C₂×C₄×D₂₆₈	C₂²	1	4	yes	complemented
61	C₂×#14524005	C₂²	1	4	yes	complemented
62	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
63	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
65	C₂×C₂²⋊C₄×D₆₇	C₂²	1	8	yes	complemented
66	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#525×C₆₇	C₂²	1	16	yes	complemented
69	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
70	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
71	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
72	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
73	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
74	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₂⁴×D₆₇	—	2	16	no	—
76	C₂⁴×D₆₇	—	4	16	no	—
77	C₂⁴×D₆₇	C₂³	1	8	yes	—
78	C₂⁴×D₆₇	C₂³	1	2	yes	—
79	C₂⁴×D₆₇	C₂³	1	2	yes	—
80	C₂⁴×D₆₇	C₂³	1	16	yes	complemented
81	C₂⁴×D₆₇	C₂³	1	4	yes	complemented
82	#14524089	—	2	128	no	—
83	C₂×#11761629	—	2	16	no	—
84	C₂×#11761629	C₂³	1	16	yes	complemented
85	C₂×#11761628	—	2	16	no	—
86	C₂×#11761628	—	2	8	no	—
87	C₂×#11761628	C₂³	1	8	yes	complemented
88	C₂×#11761628	C₂³	1	16	yes	complemented
89	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic, complemented
90	C₂²×D₂₆₈	—	2	16	no	—
91	C₂²×D₂₆₈	—	2	32	no	—
92	C₂²×D₂₆₈	—	2	32	no	—
93	C₂²×D₂₆₈	—	2	128	no	—
94	C₂²×D₂₆₈	—	2	16	no	—
95	C₂²×D₂₆₈	—	2	8	no	—
96	C₂²×D₂₆₈	D₄	1	16	yes	complemented
97	C₂²×D₂₆₈	C₂³	1	8	yes	—
98	C₂²×D₂₆₈	C₂³	1	2	yes	—
99	C₂²×D₂₆₈	C₂³	1	2	yes	—
100	C₂²×D₂₆₈	C₂³	1	2	yes	—
101	C₂²×D₂₆₈	C₂³	1	2	yes	—
102	C₂²×D₂₆₈	C₂³	1	8	yes	—
103	C₂²×D₂₆₈	C₂³	1	32	yes	complemented
104	C₂²×D₂₆₈	C₂³	1	32	yes	complemented
105	C₂²×D₂₆₈	C₂³	1	16	yes	complemented
106	C₂²×D₂₆₈	C₂³	1	8	yes	complemented
107	C₂²×D₂₆₈	C₂³	1	4	yes	complemented
108	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic, complemented
109	C₂²×D₂₆₈	C₂³	1	8	yes	complemented
110	C₂²×D₂₆₈	C₂³	1	16	yes	complemented
111	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
112	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
113	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
114	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
115	C₂×D₄×D₆₇	—	2	32	no	—
116	C₂×D₄×D₆₇	—	2	16	no	—
117	C₂×D₄×D₆₇	—	4	32	no	—
118	C₂×D₄×D₆₇	C₂³	1	32	yes	complemented
119	C₂×D₄×D₆₇	C₂³	1	64	yes	complemented
120	C₂×D₄×D₆₇	C₂³	1	16	yes	complemented
121	C₂²×C₄×D₆₇	C₂³	1	4	yes	complemented
122	C₂²×C₄×D₆₇	C₂³	1	2	yes	complemented
123	C₂²×C₄×D₆₇	C₂³	1	8	yes	complemented
124	#14524040	C₂³	1	16	yes	complemented
125	#14524039	C₂³	1	16	yes	complemented
126	#14524032	C₂³	1	16	yes	complemented
127	#14524031	C₂³	1	16	yes	complemented
128	#14524028	C₂³	1	64	yes	complemented
129	#14524026	C₂³	1	16	yes	complemented
130	#14524022	C₂³	1	16	yes	complemented
131	#14524018	C₂³	1	32	yes	complemented
132	#14524018	C₂³	1	64	yes	complemented
133	#14524017	C₂³	1	16	yes	complemented
134	#14524017	C₂³	1	32	yes	complemented
135	#14524016	C₂³	1	64	yes	complemented
136	#14524013	C₂³	1	64	yes	complemented
137	#14524013	C₂³	1	32	yes	complemented
138	#14524013	C₂³	1	64	yes	complemented
139	#14524012	C₂³	1	16	yes	complemented
140	#14524011	C₂³	1	64	yes	complemented
141	#14524011	C₂³	1	32	yes	complemented
142	C₄×D₂₆₈	C₂³	1	32	yes	complemented
143	#14524005	C₂³	1	32	yes	complemented
144	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
145	#14524002	C₂³	1	8	yes	complemented
146	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	complemented
147	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	complemented
148	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
150	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
151	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
152	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
153	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	complemented
154	C₂²⋊C₄×D₆₇	C₂³	1	64	yes	complemented
155	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
156	C₂×C₄×Dic₆₇	C₂³	1	2	yes	complemented
157	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×#41×C₆₇	—	2	8	no	—
159	C₂×#41×C₆₇	C₂³	1	8	yes	complemented
160	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
161	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
162	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
163	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
164	C₂³×C₄×C₆₇	—	2	8	no	—
165	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
166	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
167	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂³×C₄×C₆₇	C₂³	1	8	yes	complemented
170	C₂³×C₄×C₆₇	C₂³	1	2	yes	complemented
171	#123×C₆₇	C₂³	1	16	yes	complemented
172	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
173	#121×C₆₇	C₂³	1	16	yes	complemented
174	#120×C₆₇	C₂³	1	16	yes	complemented
175	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
176	#117×C₆₇	C₂³	1	8	yes	complemented
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	complemented
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	complemented
183	C₂³×D₆₇	—	2	8	no	—
184	C₂³×D₆₇	—	2	32	no	—
185	C₂³×D₆₇	—	2	32	no	—
186	C₂³×D₆₇	—	2	64	no	—
187	C₂³×D₆₇	—	2	16	no	—
188	C₂³×D₆₇	—	4	8	no	—
189	C₂³×D₆₇	—	4	16	no	—
190	C₂³×D₆₇	—	4	8	no	—
191	C₂³×D₆₇	—	4	64	no	—
192	C₂³×D₆₇	—	4	16	no	—
193	C₂³×D₆₇	—	4	128	no	—
194	C₂³×D₆₇	C₂×D₄	1	16	yes	complemented
195	C₂³×D₆₇	C₂⁴	1	4	yes	—
196	C₂³×D₆₇	C₂⁴	1	2	yes	—
197	C₂³×D₆₇	C₂⁴	1	32	yes	—
198	C₂³×D₆₇	C₂⁴	1	4	yes	—
199	C₂³×D₆₇	C₂⁴	1	8	yes	—
200	C₂³×D₆₇	C₂⁴	1	8	yes	—
201	C₂³×D₆₇	C₂⁴	1	16	yes	complemented
202	#11761629	—	2	64	no	—
203	#11761628	—	2	32	no	—
204	#11761628	—	2	64	no	—
205	C₂×Dic₁₃₄	—	2	4	no	—
206	C₂×Dic₁₃₄	C₂⁴	1	4	yes	complemented
207	C₂×D₂₆₈	—	2	16	no	—
208	C₂×D₂₆₈	—	2	32	no	—
209	C₂×D₂₆₈	—	2	64	no	—
210	C₂×D₂₆₈	—	2	8	no	—
211	C₂×D₂₆₈	—	2	8	no	—
212	C₂×D₂₆₈	—	2	4	no	—
213	C₂×D₂₆₈	—	2	32	no	—
214	C₂×D₂₆₈	—	2	128	no	—
215	C₂×D₂₆₈	—	2	128	no	—
216	C₂×D₂₆₈	—	2	64	no	—
217	C₂×D₂₆₈	—	4	16	no	—
218	C₂×D₂₆₈	C₂×D₄	1	16	yes	complemented
219	C₂×D₂₆₈	C₂×D₄	1	16	yes	complemented
220	C₂×D₂₆₈	C₂×D₄	1	64	yes	complemented
221	C₂×D₂₆₈	C₂⁴	1	32	yes	—
222	C₂×D₂₆₈	C₂⁴	1	8	yes	—
223	C₂×D₂₆₈	C₂⁴	1	8	yes	—
224	C₂×D₂₆₈	C₂⁴	1	8	yes	—
225	C₂×D₂₆₈	C₂⁴	1	8	yes	—
226	C₂×D₂₆₈	C₂⁴	1	16	yes	complemented
227	C₂×D₂₆₈	C₂⁴	1	4	yes	complemented
228	C₂×D₂₆₈	C₂⁴	1	32	yes	complemented
229	C₂×C₂²⋊D₆₇	—	2	8	no	—
230	C₂×C₂²⋊D₆₇	—	2	16	no	—
231	C₂×C₂²⋊D₆₇	—	2	16	no	—
232	C₂×C₂²⋊D₆₇	—	4	16	no	—
233	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
234	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
235	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	complemented
236	C₂×C₂²⋊D₆₇	C₂⁴	1	32	yes	complemented
237	D₄×D₆₇	—	2	128	no	—
238	D₄×D₆₇	—	2	64	no	—
239	D₄×D₆₇	—	4	128	no	—
240	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
241	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
242	C₂×C₄×D₆₇	—	2	16	no	—
243	C₂×C₄×D₆₇	—	2	8	no	—
244	C₂×C₄×D₆₇	—	4	16	no	—
245	C₂×C₄×D₆₇	C₂⁴	1	16	yes	complemented
246	C₂×C₄×D₆₇	C₂⁴	1	8	yes	complemented
247	C₂×C₄×D₆₇	C₂⁴	1	32	yes	complemented
248	C₄⋊Dic₆₇	C₂⁴	1	8	yes	complemented
249	Dic₆₇⋊C₄	C₂⁴	1	16	yes	complemented
250	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
251	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
252	(C₂×D₆₇)⋊C₄	C₂⁴	1	32	yes	complemented
253	(C₂×D₆₇)⋊C₄	C₂⁴	1	32	yes	complemented
254	(C₂×D₆₇)⋊C₄	C₂⁴	1	32	yes	complemented
255	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	complemented
256	C₄×Dic₆₇	C₂⁴	1	8	yes	complemented
257	C₂⁴×C₆₇	—	2	4	no	—
258	C₂⁴×C₆₇	—	2	8	no	—
259	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
260	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
261	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
263	#41×C₆₇	—	2	32	no	—
264	C₂×Q₈×C₆₇	—	2	4	no	—
265	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	complemented
266	C₂×D₄×C₆₇	—	2	8	no	—
267	C₂×D₄×C₆₇	—	2	16	no	—
268	C₂×D₄×C₆₇	—	2	4	no	—
269	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
270	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
271	C₂×D₄×C₆₇	C₂⁴	1	4	yes	complemented
272	C₂²×C₄×C₆₇	—	2	4	no	—
273	C₂²×C₄×C₆₇	—	2	8	no	—
274	C₂²×C₄×C₆₇	—	2	8	no	—
275	C₂²×C₄×C₆₇	—	2	8	no	—
276	C₂²×C₄×C₆₇	—	2	32	no	—
277	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	complemented
278	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
282	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	complemented
288	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	complemented
289	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	complemented
290	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
291	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
292	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	complemented
293	C₄²×C₆₇	C₂⁴	1	8	yes	complemented
294	C₂³×C₆₇	—	2	32	no	—
295	C₂³×C₆₇	—	2	8	no	—
296	C₂³×C₆₇	—	2	4	no	—
297	C₂³×C₆₇	—	2	4	no	—
298	C₂³×C₆₇	—	2	4	no	—
299	C₂³×C₆₇	—	2	16	no	—
300	C₂³×C₆₇	—	2	4	no	—
301	C₂³×C₆₇	—	2	8	no	—
302	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
303	C₂³×C₆₇	H(5,𝔽₂)	1	8	yes	complemented
304	C₂³×C₆₇	C₂⁵	1	4	yes	—
305	C₂³×C₆₇	C₂⁵	1	2	yes	—
306	C₂³×C₆₇	C₂⁵	1	4	yes	—
307	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
308	C₂²×D₆₇	—	2	16	no	—
309	C₂²×D₆₇	—	2	4	no	—
310	C₂²×D₆₇	—	2	16	no	—
311	C₂²×D₆₇	—	2	8	no	—
312	C₂²×D₆₇	—	2	8	no	—
313	C₂²×D₆₇	—	2	16	no	—
314	C₂²×D₆₇	—	2	64	no	—
315	C₂²×D₆₇	—	2	64	no	—
316	C₂²×D₆₇	—	2	32	no	—
317	C₂²×D₆₇	—	4	32	no	—
318	C₂²×D₆₇	—	4	16	no	—
319	C₂²×D₆₇	—	4	32	no	—
320	C₂²×D₆₇	—	4	16	no	—
321	C₂²×D₆₇	—	4	32	no	—
322	C₂²×D₆₇	—	4	128	no	—
323	C₂²×D₆₇	—	4	256	no	—
324	C₂²×D₆₇	—	4	32	no	—
325	C₂²×D₆₇	—	8	32	no	—
326	C₂²×D₆₇	C₂²×D₄	1	16	yes	—
327	C₂²×D₆₇	C₂²×D₄	1	32	yes	complemented
328	C₂²×D₆₇	C₂⁵	1	8	yes	—
329	C₂²×D₆₇	C₂⁵	1	4	yes	—
330	C₂²×D₆₇	C₂⁵	1	8	yes	—
331	Q₈×C₆₇	—	2	8	no	—
332	D₄×C₆₇	—	2	16	no	—
333	D₄×C₆₇	—	2	32	no	—
334	D₄×C₆₇	—	2	8	no	—
335	C₂×C₄×C₆₇	—	2	8	no	—
336	C₂×C₄×C₆₇	—	2	4	no	—
337	C₂×C₄×C₆₇	—	2	4	no	—
338	C₂×C₄×C₆₇	—	2	8	no	—
339	C₂×C₄×C₆₇	—	2	16	no	—
340	C₂×C₄×C₆₇	—	2	16	no	—
341	C₂×C₄×C₆₇	—	2	16	no	—
342	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
343	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	16	yes	complemented
345	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
346	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
347	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
348	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
349	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
350	C₂²⋊D₆₇	—	2	16	no	—
351	C₂²⋊D₆₇	—	2	32	no	—
352	C₂²⋊D₆₇	—	2	32	no	—
353	C₂²⋊D₆₇	—	4	32	no	—
354	C₂×Dic₆₇	—	2	4	no	—
355	C₂×Dic₆₇	—	2	8	no	—
356	C₂×Dic₆₇	C₂⁵	1	8	yes	—
357	C₂×Dic₆₇	C₂⁵	1	4	yes	—
358	D₂₆₈	—	2	32	no	—
359	D₂₆₈	—	2	64	no	—
360	D₂₆₈	—	2	16	no	—
361	D₂₆₈	—	2	16	no	—
362	D₂₆₈	—	2	8	no	—
363	D₂₆₈	—	4	32	no	—
364	D₂₆₈	C₂²×D₄	1	32	yes	complemented
365	D₂₆₈	C₂²×D₄	1	32	yes	complemented
366	C₄×D₆₇	—	2	32	no	—
367	C₄×D₆₇	—	2	16	no	—
368	C₄×D₆₇	—	4	32	no	—
369	Dic₁₃₄	—	2	8	no	—
370	C₂²×C₆₇	—	2	32	no	—
371	C₂²×C₆₇	—	2	4	no	—
372	C₂²×C₆₇	—	2	4	no	—
373	C₂²×C₆₇	—	2	4	no	—
374	C₂²×C₆₇	—	2	8	no	—
375	C₂²×C₆₇	—	2	16	no	—
376	C₂²×C₆₇	—	2	4	no	—
377	C₂²×C₆₇	—	2	8	no	—
378	C₂²×C₆₇	—	4	8	no	—
379	C₂²×C₆₇	C₂³×D₄	1	4	yes	—
380	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
381	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
382	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	8	yes	complemented
383	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
384	C₂×D₆₇	—	2	16	no	—
385	C₂×D₆₇	—	2	32	no	—
386	C₂×D₆₇	—	2	4	no	—
387	C₂×D₆₇	—	2	8	no	—
388	C₂×D₆₇	—	2	8	no	—
389	C₂×D₆₇	—	2	16	no	—
390	C₂×D₆₇	—	4	32	no	—
391	C₂×D₆₇	—	4	128	no	—
392	C₂×D₆₇	—	4	32	no	—
393	C₂×D₆₇	—	4	16	no	—
394	C₂×D₆₇	—	4	8	no	—
395	C₂×D₆₇	—	8	32	no	—
396	C₂×D₆₇	C₂³×D₄	1	16	yes	—
397	C₄×C₆₇	—	2	4	no	—
398	C₄×C₆₇	—	2	4	no	—
399	C₄×C₆₇	—	2	8	no	—
400	C₄×C₆₇	C₂³×D₄	1	4	yes	—
401	C₄×C₆₇	C₂³×D₄	1	4	yes	—
402	Dic₆₇	—	2	4	no	—
403	Dic₆₇	—	2	8	no	—
404	C₂×#3484	—	67	1	no	maximal, Sylow
405	C₂×C₆₇	—	2	4	no	—
406	C₂×C₆₇	—	2	8	no	—
407	C₂×C₆₇	—	4	4	no	—
408	C₂×C₆₇	#3484	1	4	yes	complemented
409	C₂×C₆₇	C₂⁴×D₄	1	1	yes	characteristic
410	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	2	yes	—
411	D₆₇	—	2	16	no	—
412	D₆₇	—	4	8	no	—
413	D₆₇	—	4	4	no	—
414	C₂²×H(5,𝔽₂)	—	67	1	no	—
415	C₂⁴×D₄	—	67	1	no	—
416	#3484	—	67	32	no	—
417	C₂×#546	—	67	4	no	—
418	C₂×#546	—	67	4	no	—
419	C₂×D₄²	—	67	4	no	—
420	C₂×D₄²	—	67	4	no	—
421	C₂×#535	—	67	1	no	—
422	C₂×#535	—	67	1	no	—
423	C₂×#534	—	67	4	no	—
424	C₂×#525	—	67	1	no	—
425	C₂×#525	D₆₇	1	1	yes	characteristic, complemented
426	C₂²×#120	—	67	4	no	—
427	C₂×#518	—	67	1	no	—
428	C₆₇	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
429	C₂⁶	—	67	2	no	—
430	C₂×H(5,𝔽₂)	—	67	16	no	—
431	C₂×H(5,𝔽₂)	—	134	16	no	—
432	C₂²×#41	—	67	2	no	—
433	C₂²×#41	—	67	1	no	—
434	C₂²×#41	—	67	2	no	—
435	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
436	C₂³×D₄	—	67	8	no	—
437	C₂³×D₄	—	67	4	no	—
438	C₂³×D₄	—	67	2	no	—
439	C₂³×D₄	—	67	1	no	—
440	C₂³×D₄	—	67	2	no	—
441	C₂³×D₄	—	67	1	no	—
442	C₂³×D₄	—	67	4	no	—
443	C₂³×D₄	—	67	4	no	—
444	C₂³×D₄	—	67	16	no	—
445	C₂³×D₄	—	67	2	no	—
446	C₂³×D₄	—	134	16	no	—
447	C₂⁴×C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
448	#546	—	67	64	no	—
449	#546	—	67	64	no	—
450	D₄²	—	67	64	no	—
451	D₄²	—	67	64	no	—
452	#535	—	67	16	no	—
453	#535	—	67	16	no	—
454	#534	—	67	64	no	—
455	C₂×#127	—	67	2	no	—
456	C₂×#127	—	67	2	no	—
457	C₂×#124	—	67	2	no	—
458	C₂×#124	—	67	2	no	—
459	#525	—	67	16	no	—
460	#525	C₂×D₆₇	1	16	yes	complemented
461	C₂×#123	—	67	2	no	—
462	C₂×#123	—	67	8	no	—
463	C₂×#123	C₂×D₆₇	1	2	yes	complemented
464	C₂×C₂²⋊Q₈	—	67	2	no	—
465	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
466	C₂×#121	—	67	2	no	—
467	C₂×#121	—	67	4	no	—
468	C₂×#121	—	67	8	no	—
469	C₂×#121	—	67	4	no	—
470	C₂×#121	—	67	8	no	—
471	C₂×#121	C₂×D₆₇	1	2	yes	complemented
472	C₂×#120	—	67	2	no	—
473	C₂×#120	—	67	4	no	—
474	C₂×#120	—	67	8	no	—
475	C₂×#120	—	67	64	no	—
476	C₂×#120	—	67	4	no	—
477	C₂×#120	—	67	8	no	—
478	C₂×#120	—	67	8	no	—
479	C₂×#120	C₂×D₆₇	1	2	yes	complemented
480	#518	—	67	16	no	—
481	C₂×C₄×D₄	—	67	4	no	—
482	C₂×C₄×D₄	—	67	4	no	—
483	C₂×C₄×D₄	—	67	4	no	—
484	C₂×C₄×D₄	C₂×D₆₇	1	4	yes	complemented
485	C₂×#117	—	67	1	no	—
486	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
487	C₂²×C₂²⋊C₄	—	67	4	no	—
488	C₂²×C₂²⋊C₄	—	67	8	no	—
489	C₂⁵	—	268	16	no	—
490	C₂⁵	—	67	2	no	—
491	C₂⁵	—	67	2	no	—
492	C₂⁵	—	67	16	no	—
493	C₂⁵	—	67	4	no	—
494	C₂⁵	—	67	8	no	—
495	C₂⁵	—	134	16	no	—
496	C₂⁵	C₂²×D₆₇	1	1	yes	characteristic
497	H(5,𝔽₂)	—	134	128	no	—
498	C₂×#41	—	2	8	no	—
499	C₂×#41	—	67	16	no	—
500	C₂×#41	—	67	8	no	—
501	C₂×#41	—	67	16	no	—
502	C₂×#41	—	134	16	no	—
503	C₂×#41	—	134	16	no	—
504	C₂×#41	—	134	8	no	—
505	C₂×#41	C₂²×D₆₇	1	8	yes	complemented
506	C₂²×Q₈	—	67	1	no	—
507	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic, complemented
508	C₂²×D₄	—	268	32	no	—
509	C₂²×D₄	—	67	8	no	—
510	C₂²×D₄	—	67	64	no	—
511	C₂²×D₄	—	67	4	no	—
512	C₂²×D₄	—	67	2	no	—
513	C₂²×D₄	—	67	4	no	—
514	C₂²×D₄	—	67	32	no	—
515	C₂²×D₄	—	67	16	no	—
516	C₂²×D₄	—	67	16	no	—
517	C₂²×D₄	—	67	8	no	—
518	C₂²×D₄	—	67	2	no	—
519	C₂²×D₄	—	67	2	no	—
520	C₂²×D₄	—	67	8	no	—
521	C₂²×D₄	—	67	4	no	—
522	C₂²×D₄	—	67	8	no	—
523	C₂²×D₄	—	67	2	no	—
524	C₂²×D₄	—	67	2	no	—
525	C₂²×D₄	—	67	1	no	—
526	C₂²×D₄	—	67	16	no	—
527	C₂²×D₄	—	67	8	no	—
528	C₂²×D₄	—	67	32	no	—
529	C₂²×D₄	—	67	32	no	—
530	C₂²×D₄	—	67	16	no	—
531	C₂²×D₄	—	134	32	no	—
532	C₂²×D₄	—	134	32	no	—
533	C₂²×D₄	—	134	128	no	—
534	C₂²×D₄	—	134	16	no	—
535	C₂²×D₄	—	134	16	no	—
536	C₂²×D₄	—	134	16	no	—
537	C₂²×D₄	—	134	32	no	—
538	C₂²×D₄	—	134	8	no	—
539	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
540	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
541	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic, complemented
542	C₂³×C₄	—	2	8	no	—
543	C₂³×C₄	—	67	8	no	—
544	C₂³×C₄	—	67	4	no	—
545	C₂³×C₄	—	67	2	no	—
546	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
547	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
548	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
549	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
550	C₂³×C₄	C₂²×D₆₇	1	8	yes	complemented
551	C₂³×C₄	C₂²×D₆₇	1	2	yes	complemented
552	#127	—	67	16	no	—
553	#127	—	67	16	no	—
554	#124	—	67	16	no	—
555	#124	—	67	16	no	—
556	#123	—	67	16	no	—
557	#123	—	67	64	no	—
558	#123	C₂²×D₆₇	1	16	yes	complemented
559	C₂²⋊Q₈	—	67	16	no	—
560	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
561	#121	—	67	16	no	—
562	#121	—	67	32	no	—
563	#121	—	67	64	no	—
564	#121	—	67	32	no	—
565	#121	—	67	64	no	—
566	#121	C₂²×D₆₇	1	16	yes	complemented
567	#120	—	67	16	no	—
568	#120	—	67	32	no	—
569	#120	—	67	64	no	—
570	#120	—	67	32	no	—
571	#120	—	67	64	no	—
572	#120	—	67	64	no	—
573	#120	C₂²×D₆₇	1	16	yes	complemented
574	C₄×D₄	—	67	32	no	—
575	C₄×D₄	—	67	32	no	—
576	C₄×D₄	—	67	32	no	—
577	C₄×D₄	C₂²×D₆₇	1	32	yes	complemented
578	#117	—	67	8	no	—
579	#117	C₂²×D₆₇	1	8	yes	complemented
580	C₂×C₄⋊C₄	—	67	2	no	—
581	C₂×C₄⋊C₄	—	67	4	no	—
582	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	complemented
583	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	complemented
584	C₂×C₂²⋊C₄	—	67	2	no	—
585	C₂×C₂²⋊C₄	—	67	4	no	—
586	C₂×C₂²⋊C₄	—	67	8	no	—
587	C₂×C₂²⋊C₄	—	67	8	no	—
588	C₂×C₂²⋊C₄	—	67	8	no	—
589	C₂×C₂²⋊C₄	—	67	4	no	—
590	C₂×C₂²⋊C₄	—	67	32	no	—
591	C₂×C₂²⋊C₄	—	67	64	no	—
592	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	complemented
595	C₂×C₄²	—	67	2	no	—
596	C₂×C₄²	C₂²×D₆₇	1	2	yes	complemented
597	C₂⁴	—	2	4	no	—
598	C₂⁴	—	2	8	no	—
599	C₂⁴	—	268	128	no	—
600	C₂⁴	—	268	8	no	—
601	C₂⁴	—	268	16	no	—
602	C₂⁴	—	268	8	no	—
603	C₂⁴	—	268	64	no	—
604	C₂⁴	—	268	16	no	—
605	C₂⁴	—	67	16	no	—
606	C₂⁴	—	67	8	no	—
607	C₂⁴	—	67	8	no	—
608	C₂⁴	—	67	16	no	—
609	C₂⁴	—	67	32	no	—
610	C₂⁴	—	67	4	no	—
611	C₂⁴	—	67	4	no	—
612	C₂⁴	—	67	2	no	—
613	C₂⁴	—	134	64	no	—
614	C₂⁴	—	134	32	no	—
615	C₂⁴	—	134	16	no	—
616	C₂⁴	—	134	8	no	—
617	C₂⁴	—	134	32	no	—
618	C₂⁴	C₂³×D₆₇	1	4	yes	—
619	C₂⁴	C₂³×D₆₇	1	2	yes	—
620	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
621	C₂⁴	C₂³×D₆₇	1	2	yes	—
622	#41	—	2	32	no	—
623	#41	—	134	64	no	—
624	#41	—	134	64	no	—
625	#41	—	134	32	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	67	4	no	—
628	C₂×Q₈	—	134	4	no	—
629	C₂×Q₈	C₂³×D₆₇	1	4	yes	complemented
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	2	16	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	268	16	no	—
634	C₂×D₄	—	268	128	no	—
635	C₂×D₄	—	268	16	no	—
636	C₂×D₄	—	67	32	no	—
637	C₂×D₄	—	67	16	no	—
638	C₂×D₄	—	67	8	no	—
639	C₂×D₄	—	67	16	no	—
640	C₂×D₄	—	67	16	no	—
641	C₂×D₄	—	67	16	no	—
642	C₂×D₄	—	67	64	no	—
643	C₂×D₄	—	67	32	no	—
644	C₂×D₄	—	67	8	no	—
645	C₂×D₄	—	67	8	no	—
646	C₂×D₄	—	67	16	no	—
647	C₂×D₄	—	67	32	no	—
648	C₂×D₄	—	67	8	no	—
649	C₂×D₄	—	67	8	no	—
650	C₂×D₄	—	67	4	no	—
651	C₂×D₄	—	134	128	no	—
652	C₂×D₄	—	134	128	no	—
653	C₂×D₄	—	134	64	no	—
654	C₂×D₄	—	134	64	no	—
655	C₂×D₄	—	134	32	no	—
656	C₂×D₄	—	134	16	no	—
657	C₂×D₄	—	134	64	no	—
658	C₂×D₄	—	134	128	no	—
659	C₂×D₄	—	134	16	no	—
660	C₂×D₄	—	134	8	no	—
661	C₂×D₄	—	134	16	no	—
662	C₂×D₄	—	134	8	no	—
663	C₂×D₄	—	134	8	no	—
664	C₂×D₄	—	134	4	no	—
665	C₂×D₄	—	134	32	no	—
666	C₂×D₄	C₂³×D₆₇	1	16	yes	—
667	C₂×D₄	C₂³×D₆₇	1	8	yes	—
668	C₂×D₄	C₂³×D₆₇	1	4	yes	complemented
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	8	no	—
671	C₂²×C₄	—	2	8	no	—
672	C₂²×C₄	—	2	8	no	—
673	C₂²×C₄	—	2	32	no	—
674	C₂²×C₄	—	268	16	no	—
675	C₂²×C₄	—	67	32	no	—
676	C₂²×C₄	—	67	4	no	—
677	C₂²×C₄	—	67	2	no	—
678	C₂²×C₄	—	67	16	no	—
679	C₂²×C₄	—	67	8	no	—
680	C₂²×C₄	—	134	16	no	—
681	C₂²×C₄	—	134	8	no	—
682	C₂²×C₄	D₄×D₆₇	1	8	yes	complemented
683	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
684	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
685	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
686	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
687	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
688	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
689	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
691	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
692	C₂²×C₄	C₂³×D₆₇	1	8	yes	complemented
693	C₄⋊C₄	—	67	8	no	—
694	C₄⋊C₄	—	67	16	no	—
695	C₄⋊C₄	C₂³×D₆₇	1	8	yes	complemented
696	C₄⋊C₄	C₂³×D₆₇	1	16	yes	complemented
697	C₂²⋊C₄	—	67	8	no	—
698	C₂²⋊C₄	—	67	16	no	—
699	C₂²⋊C₄	—	67	32	no	—
700	C₂²⋊C₄	—	67	32	no	—
701	C₂²⋊C₄	—	67	32	no	—
702	C₂²⋊C₄	—	67	16	no	—
703	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
704	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
705	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	complemented
706	C₄²	—	67	8	no	—
707	C₄²	C₂³×D₆₇	1	8	yes	complemented
708	C₂³	—	2	32	no	—
709	C₂³	—	2	8	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	16	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	268	256	no	—
717	C₂³	—	268	32	no	—
718	C₂³	—	268	128	no	—
719	C₂³	—	268	32	no	—
720	C₂³	—	268	16	no	—
721	C₂³	—	268	32	no	—
722	C₂³	—	268	16	no	—
723	C₂³	—	268	32	no	—
724	C₂³	—	536	32	no	—
725	C₂³	—	67	32	no	—
726	C₂³	—	67	16	no	—
727	C₂³	—	67	8	no	—
728	C₂³	—	67	8	no	—
729	C₂³	—	67	4	no	—
730	C₂³	—	134	64	no	—
731	C₂³	—	134	32	no	—
732	C₂³	—	134	4	no	—
733	C₂³	—	134	16	no	—
734	C₂³	—	134	8	no	—
735	C₂³	—	134	8	no	—
736	C₂³	—	134	16	no	—
737	C₂³	—	134	64	no	—
738	C₂³	—	134	16	no	—
739	C₂³	C₂×D₄×D₆₇	1	4	yes	—
740	C₂³	#14524089	1	8	yes	complemented
741	C₂³	C₂⁴×D₆₇	1	4	yes	—
742	C₂³	C₂⁴×D₆₇	1	2	yes	—
743	C₂³	C₂⁴×D₆₇	1	4	yes	—
744	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
745	Q₈	—	2	8	no	—
746	Q₈	—	134	8	no	—
747	D₄	—	2	16	no	—
748	D₄	—	2	32	no	—
749	D₄	—	2	8	no	—
750	D₄	—	268	32	no	—
751	D₄	—	268	32	no	—
752	D₄	—	67	32	no	—
753	D₄	—	67	32	no	—
754	D₄	—	134	64	no	—
755	D₄	—	134	32	no	—
756	D₄	—	134	32	no	—
757	D₄	—	134	16	no	—
758	D₄	—	134	32	no	—
759	D₄	—	134	16	no	—
760	D₄	—	134	16	no	—
761	D₄	—	134	8	no	—
762	C₂×C₄	—	2	8	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	8	no	—
766	C₂×C₄	—	2	16	no	—
767	C₂×C₄	—	2	16	no	—
768	C₂×C₄	—	2	16	no	—
769	C₂×C₄	—	268	32	no	—
770	C₂×C₄	—	67	8	no	—
771	C₂×C₄	—	67	4	no	—
772	C₂×C₄	—	134	32	no	—
773	C₂×C₄	—	134	4	no	—
774	C₂×C₄	—	134	8	no	—
775	C₂×C₄	—	134	16	no	—
776	C₂×C₄	C₂×D₄×D₆₇	1	4	yes	—
777	C₂×C₄	C₂×D₄×D₆₇	1	4	yes	—
778	C₂×C₄	C₂×D₄×D₆₇	1	16	yes	complemented
779	C₂×C₄	C₂⁴×D₆₇	1	8	yes	—
780	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
781	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
782	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
783	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
784	C₂²	—	2	32	no	—
785	C₂²	—	2	8	no	—
786	C₂²	—	2	16	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	2	4	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	8	no	—
792	C₂²	—	4	8	no	—
793	C₂²	—	268	32	no	—
794	C₂²	—	268	128	no	—
795	C₂²	—	268	32	no	—
796	C₂²	—	268	16	no	—
797	C₂²	—	268	8	no	—
798	C₂²	—	536	32	no	—
799	C₂²	—	67	16	no	—
800	C₂²	—	134	4	no	—
801	C₂²	—	134	8	no	—
802	C₂²	—	134	8	no	—
803	C₂²	—	134	16	no	—
804	C₂²	—	134	32	no	—
805	C₂²	—	134	16	no	—
806	C₂²	C₂²×D₄×D₆₇	1	4	yes	—
807	C₂²	C₂²×D₄×D₆₇	1	2	yes	—
808	C₂²	C₂×#14524089	1	4	yes	—
809	C₂²	C₂×#14524089	1	8	yes	complemented
810	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
811	C₄	—	2	4	no	—
812	C₄	—	2	4	no	—
813	C₄	—	2	8	no	—
814	C₄	—	134	4	no	—
815	C₄	—	134	8	no	—
816	C₄	C₂²×D₄×D₆₇	1	4	yes	—
817	C₄	C₂²×D₄×D₆₇	1	4	yes	—
818	C₂	—	2	4	no	—
819	C₂	—	2	8	no	—
820	C₂	—	4	4	no	—
821	C₂	—	268	8	no	—
822	C₂	—	268	4	no	—
823	C₂	—	134	16	no	—
824	C₂	#22573842	1	4	yes	direct product factor
825	C₂	C₂³×D₄×D₆₇	1	1	yes	characteristic
826	C₂	C₂²×#14524089	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#525×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#525	D₆₇
hypocenter	C₆₇	C₂×#3484
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. C₂²×#14524089	C₂	semidirect
2. C₂⁴×D₂₆₈	C₂	semidirect
3. #22573842	C₂	direct (N × H)
4. C₂×#16864042	C₂	semidirect
5. C₂×#16864037	C₂	semidirect
6. C₂×D₄×D₂₆₈	C₂	semidirect
7. C₂×#16864030	C₂	semidirect
8. C₂×#16863965	C₂	semidirect
9. C₂×#16863960	C₂	semidirect
10. C₂×#16863957	C₂	semidirect
11. C₂×#16863907	C₂	semidirect
12. C₂×#120×D₆₇	C₂	semidirect
13. C₂×#16863870	C₂	semidirect
14. C₂×#525×C₆₇	C₂	semidirect
15. C₂⁵×D₆₇	C₂²	semidirect
17. C₂×#14524089	C₂²	semidirect
18. C₂²×#11761629	C₂²	semidirect
19. C₂²×#11761628	C₂²	semidirect
20. C₂²×#11761628	C₂²	semidirect
23. C₂³×D₂₆₈	C₂²	semidirect
24. C₂³×D₂₆₈	C₂²	semidirect
25. C₂³×D₂₆₈	C₂²	semidirect
26. C₂³×D₂₆₈	C₂²	semidirect
27. C₂³×D₂₆₈	C₂²	semidirect
28. C₂³×D₂₆₈	C₂²	semidirect
29. C₂²×D₄×D₆₇	C₂²	semidirect
30. C₂²×D₄×D₆₇	C₂²	semidirect
31. C₂²×D₄×D₆₇	C₂²	semidirect
32. #16864042	C₂²	semidirect
33. #16864037	C₂²	semidirect
34. D₄×D₂₆₈	C₂²	semidirect
35. #16864030	C₂²	semidirect
36. #16863965	C₂²	semidirect
37. #16863960	C₂²	semidirect
38. #16863957	C₂²	semidirect
39. C₂×#14524040	C₂²	semidirect
40. C₂×#14524039	C₂²	semidirect
41. C₂×#14524032	C₂²	semidirect
42. C₂×#14524031	C₂²	semidirect
43. #16863907	C₂²	semidirect
44. C₂×#14524028	C₂²	semidirect
45. C₂×#14524026	C₂²	semidirect
46. C₂×#14524022	C₂²	semidirect
47. C₂×#14524018	C₂²	semidirect
48. C₂×#14524018	C₂²	semidirect
49. C₂×#14524017	C₂²	semidirect
50. C₂×#14524017	C₂²	semidirect
51. C₂×#14524016	C₂²	semidirect
52. C₂×#14524013	C₂²	semidirect
53. C₂×#14524013	C₂²	semidirect
54. C₂×#14524013	C₂²	semidirect
55. C₂×#14524012	C₂²	semidirect
56. C₂×#14524011	C₂²	semidirect
57. C₂×#14524011	C₂²	semidirect
58. #120×D₆₇	C₂²	semidirect
59. #16863870	C₂²	semidirect
60. C₂×C₄×D₂₆₈	C₂²	semidirect
61. C₂×#14524005	C₂²	semidirect
62. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
63. C₂×#14524002	C₂²	semidirect
64. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
65. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
66. C₂²×#41×C₆₇	C₂²	semidirect
67. C₂⁴×C₄×C₆₇	C₂²	semidirect
68. #525×C₆₇	C₂²	semidirect
69. C₂×#123×C₆₇	C₂²	semidirect
70. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
71. C₂×#121×C₆₇	C₂²	semidirect
72. C₂×#120×C₆₇	C₂²	semidirect
73. C₂×C₄×D₄×C₆₇	C₂²	semidirect
74. C₂×#117×C₆₇	C₂²	semidirect
80. C₂⁴×D₆₇	C₂³	semidirect
81. C₂⁴×D₆₇	C₂³	semidirect
84. C₂×#11761629	C₂³	semidirect
87. C₂×#11761628	C₂³	semidirect
88. C₂×#11761628	C₂³	semidirect
89. C₂²×Dic₁₃₄	C₂³	semidirect
96. C₂²×D₂₆₈	D₄	semidirect
103. C₂²×D₂₆₈	C₂³	semidirect
104. C₂²×D₂₆₈	C₂³	semidirect
105. C₂²×D₂₆₈	C₂³	semidirect
106. C₂²×D₂₆₈	C₂³	semidirect
107. C₂²×D₂₆₈	C₂³	semidirect
108. C₂²×D₂₆₈	C₂³	semidirect
109. C₂²×D₂₆₈	C₂³	semidirect
110. C₂²×D₂₆₈	C₂³	semidirect
113. C₂²×C₂²⋊D₆₇	C₂³	semidirect
114. C₂²×C₂²⋊D₆₇	C₂³	semidirect
118. C₂×D₄×D₆₇	C₂³	semidirect
119. C₂×D₄×D₆₇	C₂³	semidirect
120. C₂×D₄×D₆₇	C₂³	semidirect
121. C₂²×C₄×D₆₇	C₂³	semidirect
122. C₂²×C₄×D₆₇	C₂³	semidirect
123. C₂²×C₄×D₆₇	C₂³	semidirect
124. #14524040	C₂³	semidirect
125. #14524039	C₂³	semidirect
126. #14524032	C₂³	semidirect
127. #14524031	C₂³	semidirect
128. #14524028	C₂³	semidirect
129. #14524026	C₂³	semidirect
130. #14524022	C₂³	semidirect
131. #14524018	C₂³	semidirect
132. #14524018	C₂³	semidirect
133. #14524017	C₂³	semidirect
134. #14524017	C₂³	semidirect
135. #14524016	C₂³	semidirect
136. #14524013	C₂³	semidirect
137. #14524013	C₂³	semidirect
138. #14524013	C₂³	semidirect
139. #14524012	C₂³	semidirect
140. #14524011	C₂³	semidirect
141. #14524011	C₂³	semidirect
142. C₄×D₂₆₈	C₂³	semidirect
143. #14524005	C₂³	semidirect
144. C₄×C₂²⋊D₆₇	C₂³	semidirect
145. #14524002	C₂³	semidirect
146. C₂×C₄⋊Dic₆₇	C₂³	semidirect
147. C₂×Dic₆₇⋊C₄	C₂³	semidirect
150. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
151. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
152. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
153. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
154. C₂²⋊C₄×D₆₇	C₂³	semidirect
155. C₂²⋊C₄×D₆₇	C₂³	semidirect
156. C₂×C₄×Dic₆₇	C₂³	semidirect
159. C₂×#41×C₆₇	C₂³	semidirect
160. C₂²×Q₈×C₆₇	C₂³	semidirect
163. C₂²×D₄×C₆₇	C₂³	semidirect
169. C₂³×C₄×C₆₇	C₂³	semidirect
170. C₂³×C₄×C₆₇	C₂³	semidirect
171. #123×C₆₇	C₂³	semidirect
172. C₂²⋊Q₈×C₆₇	C₂³	semidirect
173. #121×C₆₇	C₂³	semidirect
174. #120×C₆₇	C₂³	semidirect
175. C₄×D₄×C₆₇	C₂³	semidirect
176. #117×C₆₇	C₂³	semidirect
177. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
178. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
181. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
182. C₂×C₄²×C₆₇	C₂³	semidirect
194. C₂³×D₆₇	C₂×D₄	semidirect
201. C₂³×D₆₇	C₂⁴	semidirect
206. C₂×Dic₁₃₄	C₂⁴	semidirect
218. C₂×D₂₆₈	C₂×D₄	semidirect
219. C₂×D₂₆₈	C₂×D₄	semidirect
220. C₂×D₂₆₈	C₂×D₄	semidirect
226. C₂×D₂₆₈	C₂⁴	semidirect
227. C₂×D₂₆₈	C₂⁴	semidirect
228. C₂×D₂₆₈	C₂⁴	semidirect
235. C₂×C₂²⋊D₆₇	C₂⁴	semidirect
236. C₂×C₂²⋊D₆₇	C₂⁴	semidirect
245. C₂×C₄×D₆₇	C₂⁴	semidirect
246. C₂×C₄×D₆₇	C₂⁴	semidirect
247. C₂×C₄×D₆₇	C₂⁴	semidirect
248. C₄⋊Dic₆₇	C₂⁴	semidirect
249. Dic₆₇⋊C₄	C₂⁴	semidirect
252. (C₂×D₆₇)⋊C₄	C₂⁴	semidirect
253. (C₂×D₆₇)⋊C₄	C₂⁴	semidirect
254. (C₂×D₆₇)⋊C₄	C₂⁴	semidirect
255. (C₂×D₆₇)⋊C₄	C₂⁴	semidirect
256. C₄×Dic₆₇	C₂⁴	semidirect
265. C₂×Q₈×C₆₇	C₂⁴	semidirect
271. C₂×D₄×C₆₇	C₂⁴	semidirect
277. C₂²×C₄×C₆₇	C₂×D₄	semidirect
287. C₂²×C₄×C₆₇	C₂⁴	semidirect
288. C₄⋊C₄×C₆₇	C₂⁴	semidirect
289. C₄⋊C₄×C₆₇	C₂⁴	semidirect
292. C₂²⋊C₄×C₆₇	C₂⁴	semidirect
293. C₄²×C₆₇	C₂⁴	semidirect
303. C₂³×C₆₇	H(5,𝔽₂)	semidirect
327. C₂²×D₆₇	C₂²×D₄	semidirect
344. C₂×C₄×C₆₇	C₂²×D₄	semidirect
364. D₂₆₈	C₂²×D₄	semidirect
365. D₂₆₈	C₂²×D₄	semidirect
382. C₂²×C₆₇	C₂×H(5,𝔽₂)	semidirect
408. C₂×C₆₇	#3484	semidirect
425. C₂×#525	D₆₇	semidirect
428. C₆₇	C₂×#3484	semidirect
435. C₂²×#41	C₂×D₆₇	semidirect
447. C₂⁴×C₄	C₂×D₆₇	semidirect
460. #525	C₂×D₆₇	semidirect
463. C₂×#123	C₂×D₆₇	semidirect
465. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
471. C₂×#121	C₂×D₆₇	semidirect
479. C₂×#120	C₂×D₆₇	semidirect
484. C₂×C₄×D₄	C₂×D₆₇	semidirect
486. C₂×#117	C₂×D₆₇	semidirect
505. C₂×#41	C₂²×D₆₇	semidirect
507. C₂²×Q₈	C₂²×D₆₇	semidirect
541. C₂²×D₄	C₂²×D₆₇	semidirect
550. C₂³×C₄	C₂²×D₆₇	semidirect
551. C₂³×C₄	C₂²×D₆₇	semidirect
558. #123	C₂²×D₆₇	semidirect
560. C₂²⋊Q₈	C₂²×D₆₇	semidirect
566. #121	C₂²×D₆₇	semidirect
573. #120	C₂²×D₆₇	semidirect
577. C₄×D₄	C₂²×D₆₇	semidirect
579. #117	C₂²×D₆₇	semidirect
582. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
583. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
594. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
596. C₂×C₄²	C₂²×D₆₇	semidirect
629. C₂×Q₈	C₂³×D₆₇	semidirect
668. C₂×D₄	C₂³×D₆₇	semidirect
682. C₂²×C₄	D₄×D₆₇	semidirect
692. C₂²×C₄	C₂³×D₆₇	semidirect
695. C₄⋊C₄	C₂³×D₆₇	semidirect
696. C₄⋊C₄	C₂³×D₆₇	semidirect
705. C₂²⋊C₄	C₂³×D₆₇	semidirect
707. C₄²	C₂³×D₆₇	semidirect
740. C₂³	#14524089	semidirect
778. C₂×C₄	C₂×D₄×D₆₇	semidirect
809. C₂²	C₂×#14524089	semidirect
824. C₂	#22573842	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14524089	2
C₂⁴×D₂₆₈	2
#22573842	2
C₂×#16864042	2
C₂×#16864037	2
C₂×D₄×D₂₆₈	2
C₂×#16864030	2
C₂×#16863965	2
C₂×#16863960	2
C₂×#16863957	2
C₂×#16863907	2
C₂×#120×D₆₇	2
C₂×#16863870	2
C₂×#525×C₆₇	2
C₂×#3484	67

Subgroups — C2×#22573842 #31763710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22573842 #31763710