Subgroups — C₂×#22574486 #31763124

Order 17152.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574486	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864138	C₂	1	2	yes	maximal, complemented
3	C₂×#16864136	C₂	1	2	yes	maximal, complemented
4	C₂×#16864130	C₂	1	2	yes	maximal, complemented
5	C₂×#16864117	C₂	1	2	yes	maximal, complemented
6	C₂×#16864109	C₂	1	2	yes	maximal, complemented
7	C₂×#16864076	C₂	1	2	yes	maximal, complemented
8	C₂×#16864057	C₂	1	2	yes	maximal, complemented
9	C₂×#16864037	C₂	1	2	yes	maximal, complemented
10	C₂×#16864020	C₂	1	4	yes	maximal, complemented
11	C₂×#16864019	C₂	1	2	yes	maximal, complemented
12	C₂×#16863982	C₂	1	4	yes	maximal, complemented
13	C₂×#16863960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16863909	C₂	1	2	yes	maximal, complemented
15	C₂×#16863903	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#536×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11761629	C₂²	1	2	yes	—
18	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
20	#16864138	C₂²	1	32	yes	complemented
21	#16864136	C₂²	1	32	yes	complemented
22	#16864130	C₂²	1	32	yes	complemented
23	#16864117	C₂²	1	32	yes	complemented
24	#16864109	C₂²	1	32	yes	complemented
25	#16864076	C₂²	1	32	yes	complemented
26	#16864057	C₂²	1	32	yes	complemented
27	#16864037	C₂²	1	32	yes	complemented
28	#16864020	C₂²	1	64	yes	complemented
29	#16864019	C₂²	1	32	yes	complemented
30	#16863982	C₂²	1	64	yes	complemented
31	#16863960	C₂²	1	16	yes	complemented
32	C₂×#14524042	C₂²	1	2	yes	complemented
33	C₂×#14524039	C₂²	1	2	yes	—
34	C₂×#14524038	C₂²	1	4	yes	complemented
35	C₂×#14524038	C₂²	1	4	yes	complemented
36	C₂×#14524036	C₂²	1	4	yes	complemented
37	C₂×#14524032	C₂²	1	2	yes	complemented
38	C₂×#14524032	C₂²	1	2	yes	complemented
39	C₂×#14524032	C₂²	1	4	yes	complemented
40	C₂×#14524031	C₂²	1	4	yes	complemented
41	C₂×#14524029	C₂²	1	4	yes	—
42	C₂×#14524029	C₂²	1	4	yes	complemented
43	C₂×#14524029	C₂²	1	4	yes	complemented
44	#16863909	C₂²	1	32	yes	complemented
45	#16863903	C₂²	1	16	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×#14524024	C₂²	1	1	yes	characteristic
50	C₂×#14524024	C₂²	1	1	yes	characteristic, complemented
51	C₂×#14524023	C₂²	1	4	yes	complemented
52	C₂×#14524019	C₂²	1	2	yes	complemented
53	C₂×#14524019	C₂²	1	4	yes	complemented
54	C₂×#14524019	C₂²	1	2	yes	complemented
55	C₂×#14524018	C₂²	1	4	yes	—
56	C₂×#14524018	C₂²	1	2	yes	—
57	C₂×#14524017	C₂²	1	2	yes	—
58	C₂×#14524017	C₂²	1	2	yes	complemented
59	C₂×#14524017	C₂²	1	4	yes	complemented
60	C₂×#14524016	C₂²	1	4	yes	complemented
61	C₂×#14524014	C₂²	1	2	yes	—
62	C₂×#14524013	C₂²	1	4	yes	—
63	C₂×#14524013	C₂²	1	4	yes	complemented
64	C₂×#14524011	C₂²	1	1	yes	characteristic
65	C₂×#14524011	C₂²	1	2	yes	—
66	C₂×#14524011	C₂²	1	1	yes	characteristic, complemented
67	C₂×#14524011	C₂²	1	2	yes	complemented
68	C₂×Q₈×Dic₆₇	C₂²	1	2	yes	complemented
69	C₂×#14524008	C₂²	1	4	yes	complemented
70	C₂×#14524005	C₂²	1	2	yes	complemented
71	C₂×#14524005	C₂²	1	4	yes	complemented
72	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
73	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
74	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
75	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
76	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
77	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
78	C₂×#14524001	C₂²	1	2	yes	complemented
79	C₂×#14524000	C₂²	1	4	yes	complemented
80	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
81	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
82	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#536×C₆₇	C₂²	1	16	yes	complemented
84	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
85	C₂×#124×C₆₇	C₂²	1	2	yes	—
86	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
90	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₆₇	C₂³	1	2	yes	—
92	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
93	C₂×#11761629	—	4	8	no	—
94	C₂×#11761629	C₂³	1	16	yes	—
95	C₂²×Dic₁₃₄	C₂³	1	4	yes	—
96	C₂²×D₂₆₈	—	4	4	no	—
97	C₂²×D₂₆₈	C₂³	1	2	yes	—
98	C₂²×D₂₆₈	C₂³	1	4	yes	—
99	C₂²×D₂₆₈	C₂³	1	4	yes	—
100	C₂²×D₂₆₈	C₂³	1	2	yes	—
101	C₂²×D₂₆₈	C₂³	1	8	yes	complemented
102	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
103	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
104	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
105	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
106	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
107	C₂²×C₄×D₆₇	—	4	4	no	—
108	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
109	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
110	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
111	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
112	C₂²×C₄×D₆₇	C₂³	1	8	yes	complemented
113	#14524042	C₂³	1	16	yes	complemented
114	#14524039	C₂³	1	16	yes	—
115	#14524038	C₂³	1	32	yes	complemented
116	#14524038	C₂³	1	32	yes	complemented
117	#14524036	C₂³	1	32	yes	complemented
118	#14524032	C₂³	1	16	yes	complemented
119	#14524032	C₂³	1	16	yes	complemented
120	#14524032	C₂³	1	32	yes	complemented
121	#14524031	C₂³	1	32	yes	complemented
122	#14524029	C₂³	1	32	yes	—
123	#14524029	C₂³	1	32	yes	complemented
124	#14524029	C₂³	1	32	yes	complemented
125	#14524028	C₂³	1	32	yes	complemented
126	#14524028	C₂³	1	32	yes	complemented
127	#14524025	C₂³	1	32	yes	complemented
128	#14524024	C₂³	1	8	yes	—
129	#14524024	C₂³	1	8	yes	complemented
130	#14524023	C₂³	1	32	yes	complemented
131	#14524019	C₂³	1	16	yes	complemented
132	#14524019	C₂³	1	32	yes	complemented
133	#14524019	C₂³	1	16	yes	complemented
134	#14524018	C₂³	1	32	yes	—
135	#14524018	C₂³	1	16	yes	—
136	#14524017	C₂³	1	16	yes	—
137	#14524017	C₂³	1	16	yes	complemented
138	#14524017	C₂³	1	32	yes	complemented
139	#14524016	C₂³	1	32	yes	complemented
140	#14524014	C₂³	1	16	yes	—
141	#14524013	C₂³	1	32	yes	—
142	#14524013	C₂³	1	32	yes	complemented
143	#14524011	C₂³	1	16	yes	—
144	#14524011	C₂³	1	8	yes	—
145	#14524011	C₂³	1	8	yes	complemented
146	#14524011	C₂³	1	16	yes	complemented
147	Q₈×Dic₆₇	C₂³	1	16	yes	complemented
148	#14524008	C₂³	1	32	yes	complemented
149	#14524005	C₂³	1	16	yes	complemented
150	#14524005	C₂³	1	32	yes	complemented
151	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
152	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
153	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
154	(C₂²⋊D₆₇)⋊C₄	C₂³	1	32	yes	complemented
155	#14524002	C₂³	1	8	yes	complemented
156	#14524002	C₂³	1	8	yes	complemented
157	#14524001	C₂³	1	16	yes	complemented
158	#14524000	C₂³	1	32	yes	complemented
159	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
162	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
163	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
164	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
165	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
166	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
171	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
172	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
173	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
174	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
175	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
176	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
177	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
178	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
179	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
180	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
181	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
182	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
183	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
184	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
185	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
186	C₂×#41×C₆₇	—	4	4	no	—
187	C₂×#41×C₆₇	C₂³	1	8	yes	—
188	C₂²×Q₈×C₆₇	—	4	4	no	—
189	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
190	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
191	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
192	C₂²×Q₈×C₆₇	C₂³	1	8	yes	complemented
193	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
200	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
201	#124×C₆₇	C₂³	1	16	yes	—
202	#123×C₆₇	C₂³	1	16	yes	complemented
203	#123×C₆₇	C₂³	1	16	yes	complemented
204	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
205	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
206	#117×C₆₇	C₂³	1	8	yes	complemented
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
209	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
213	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
214	C₂³×D₆₇	—	4	2	no	—
215	C₂³×D₆₇	—	4	4	no	—
216	C₂³×D₆₇	—	4	4	no	—
217	C₂³×D₆₇	—	4	8	no	—
218	C₂³×D₆₇	C₂⁴	1	2	yes	—
219	C₂³×D₆₇	C₂⁴	1	4	yes	—
220	C₂³×D₆₇	C₂⁴	1	8	yes	—
221	C₂³×D₆₇	C₂⁴	1	4	yes	—
222	#11761629	—	4	32	no	—
223	C₂×Dic₁₃₄	—	4	8	no	—
224	C₂×Dic₁₃₄	C₂⁴	1	16	yes	—
225	C₂×D₂₆₈	—	2	8	no	—
226	C₂×D₂₆₈	—	4	16	no	—
227	C₂×D₂₆₈	—	4	4	no	—
228	C₂×D₂₆₈	—	4	8	no	—
229	C₂×D₂₆₈	—	4	8	no	—
230	C₂×D₂₆₈	C₂⁴	1	8	yes	—
231	C₂×D₂₆₈	C₂⁴	1	16	yes	—
232	C₂×D₂₆₈	C₂⁴	1	16	yes	—
233	C₂×D₂₆₈	C₂⁴	1	8	yes	—
234	C₂×C₂²⋊D₆₇	—	4	4	no	—
235	C₂×C₂²⋊D₆₇	—	4	8	no	—
236	C₂×C₂²⋊D₆₇	—	4	8	no	—
237	C₂×C₂²⋊D₆₇	—	4	4	no	—
238	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
239	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
240	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
241	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
242	C₂²×Dic₆₇	—	4	2	no	—
243	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
244	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
245	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
246	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
247	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
248	C₂×C₄×D₆₇	—	2	8	no	—
249	C₂×C₄×D₆₇	—	4	16	no	—
250	C₂×C₄×D₆₇	—	4	4	no	—
251	C₂×C₄×D₆₇	—	4	8	no	—
252	C₂×C₄×D₆₇	—	4	8	no	—
253	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
254	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
255	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
256	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
257	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
258	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
259	C₄⋊Dic₆₇	C₂⁴	1	16	yes	—
260	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
261	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
262	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
263	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
264	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
265	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
266	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
267	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
268	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
269	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
270	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
271	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
272	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
273	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
274	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
275	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
276	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
277	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
278	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
279	C₄×Dic₆₇	C₂⁴	1	16	yes	—
280	C₄×Dic₆₇	C₂⁴	1	8	yes	—
281	C₄×Dic₆₇	C₂⁴	1	8	yes	—
282	C₄×Dic₆₇	C₂⁴	1	16	yes	—
283	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
286	#41×C₆₇	—	4	16	no	—
287	C₂×Q₈×C₆₇	—	2	8	no	—
288	C₂×Q₈×C₆₇	—	4	4	no	—
289	C₂×Q₈×C₆₇	—	4	2	no	—
290	C₂×Q₈×C₆₇	—	4	16	no	—
291	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
292	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
293	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
294	C₂×D₄×C₆₇	—	4	2	no	—
295	C₂×D₄×C₆₇	—	4	2	no	—
296	C₂×D₄×C₆₇	—	4	2	no	—
297	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
298	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
299	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₆₇	—	2	4	no	—
301	C₂²×C₄×C₆₇	—	2	4	no	—
302	C₂²×C₄×C₆₇	—	2	4	no	—
303	C₂²×C₄×C₆₇	—	4	4	no	—
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
306	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
310	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
311	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
312	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
313	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
315	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
317	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
318	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
319	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
320	C₄²×C₆₇	C₂⁴	1	8	yes	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	2	2	no	—
324	C₂³×C₆₇	—	2	4	no	—
325	C₂³×C₆₇	—	2	4	no	—
326	C₂³×C₆₇	—	2	4	no	—
327	C₂³×C₆₇	C₂⁵	1	2	yes	—
328	C₂³×C₆₇	C₂⁵	1	2	yes	—
329	C₂³×C₆₇	C₂⁵	1	2	yes	—
330	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
331	C₂²×D₆₇	—	2	4	no	—
332	C₂²×D₆₇	—	2	8	no	—
333	C₂²×D₆₇	—	2	8	no	—
334	C₂²×D₆₇	—	2	4	no	—
335	C₂²×D₆₇	—	2	8	no	—
336	C₂²×D₆₇	—	2	4	no	—
337	C₂²×D₆₇	—	4	4	no	—
338	C₂²×D₆₇	—	4	8	no	—
339	C₂²×D₆₇	—	4	8	no	—
340	C₂²×D₆₇	—	4	16	no	—
341	C₂²×D₆₇	—	4	16	no	—
342	C₂²×D₆₇	—	8	16	no	—
343	C₂²×D₆₇	C₂⁵	1	4	yes	—
344	C₂²×D₆₇	C₂⁵	1	8	yes	—
345	Q₈×C₆₇	—	2	16	no	—
346	Q₈×C₆₇	—	4	8	no	—
347	Q₈×C₆₇	—	4	4	no	—
348	D₄×C₆₇	—	4	4	no	—
349	D₄×C₆₇	—	4	4	no	—
350	D₄×C₆₇	—	4	4	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	8	no	—
355	C₂×C₄×C₆₇	—	2	8	no	—
356	C₂×C₄×C₆₇	—	2	8	no	—
357	C₂×C₄×C₆₇	—	2	8	no	—
358	C₂×C₄×C₆₇	—	2	8	no	—
359	C₂×C₄×C₆₇	—	4	8	no	—
360	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
361	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
362	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
363	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
364	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
365	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
366	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
367	C₂²⋊D₆₇	—	4	8	no	—
368	C₂²⋊D₆₇	—	4	16	no	—
369	C₂²⋊D₆₇	—	4	16	no	—
370	C₂²⋊D₆₇	—	4	8	no	—
371	C₂×Dic₆₇	—	2	4	no	—
372	C₂×Dic₆₇	—	2	4	no	—
373	C₂×Dic₆₇	—	2	8	no	—
374	C₂×Dic₆₇	—	2	4	no	—
375	C₂×Dic₆₇	—	4	4	no	—
376	C₂×Dic₆₇	C₂⁵	1	4	yes	—
377	C₂×Dic₆₇	C₂⁵	1	8	yes	—
378	C₂×Dic₆₇	C₂⁵	1	4	yes	—
379	C₂×Dic₆₇	C₂⁵	1	4	yes	—
380	D₂₆₈	—	2	16	no	—
381	D₂₆₈	—	4	8	no	—
382	D₂₆₈	—	4	16	no	—
383	D₂₆₈	—	4	16	no	—
384	C₄×D₆₇	—	2	16	no	—
385	C₄×D₆₇	—	4	8	no	—
386	C₄×D₆₇	—	4	16	no	—
387	C₄×D₆₇	—	4	16	no	—
388	Dic₁₃₄	—	4	16	no	—
389	C₂²×C₆₇	—	2	2	no	—
390	C₂²×C₆₇	—	2	2	no	—
391	C₂²×C₆₇	—	2	2	no	—
392	C₂²×C₆₇	—	2	4	no	—
393	C₂²×C₆₇	—	2	4	no	—
394	C₂²×C₆₇	—	2	4	no	—
395	C₂²×C₆₇	—	4	4	no	—
396	C₂²×C₆₇	—	4	4	no	—
397	C₂²×C₆₇	—	4	4	no	—
398	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
399	C₂²×C₆₇	#585	1	4	yes	—
400	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
401	C₂×D₆₇	—	2	4	no	—
402	C₂×D₆₇	—	2	8	no	—
403	C₂×D₆₇	—	2	8	no	—
404	C₂×D₆₇	—	2	4	no	—
405	C₂×D₆₇	—	2	8	no	—
406	C₂×D₆₇	—	2	4	no	—
407	C₂×D₆₇	—	4	16	no	—
408	C₂×D₆₇	—	4	8	no	—
409	C₂×D₆₇	—	4	16	no	—
410	C₂×D₆₇	—	8	16	no	—
411	C₄×C₆₇	—	2	2	no	—
412	C₄×C₆₇	—	2	8	no	—
413	C₄×C₆₇	—	2	2	no	—
414	C₄×C₆₇	—	2	2	no	—
415	C₄×C₆₇	—	2	8	no	—
416	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
417	Dic₆₇	—	2	4	no	—
418	Dic₆₇	—	2	4	no	—
419	Dic₆₇	—	2	8	no	—
420	Dic₆₇	—	2	4	no	—
421	C₂×#3540	—	67	1	no	maximal, Sylow
422	C₂×C₆₇	—	4	2	no	—
423	C₂×C₆₇	—	4	2	no	—
424	C₂×C₆₇	—	4	2	no	—
425	C₂×C₆₇	#3540	1	4	yes	complemented
426	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₆₇	C₂×#585	1	2	yes	—
428	D₆₇	—	4	4	no	—
429	D₆₇	—	4	8	no	—
430	#3540	—	67	32	no	—
431	C₂×H(3,𝔽₄)	—	67	2	no	—
432	C₂×#560	—	67	2	no	—
433	C₂×#559	—	67	2	no	—
434	C₂×#556	—	67	2	no	—
435	C₂×#555	—	67	2	no	—
436	C₂×#551	—	67	2	no	—
437	C₂×#548	—	67	2	no	—
438	C₂×#546	—	67	2	no	—
439	C₂×#542	—	67	4	no	—
440	C₂×#542	—	67	2	no	—
441	C₂×#538	—	67	4	no	—
442	C₂×#536	D₆₇	1	1	yes	characteristic, complemented
443	C₂×#535	—	67	1	no	—
444	C₂×#525	—	67	1	no	—
445	C₂×#525	—	67	2	no	—
446	C₆₇	C₂×#3540	1	1	yes	characteristic, complemented, Sylow
447	C₂²×#41	—	67	2	no	—
448	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
449	C₂³×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
450	C₂³×D₄	—	67	1	no	—
451	C₂⁴×C₄	—	67	1	no	—
452	H(3,𝔽₄)	—	67	32	no	—
453	#560	—	67	32	no	—
454	#559	—	67	32	no	—
455	#556	—	67	32	no	—
456	#555	—	67	32	no	—
457	#551	—	67	32	no	—
458	#548	—	67	32	no	—
459	#546	—	67	32	no	—
460	#542	—	67	64	no	—
461	#542	—	67	32	no	—
462	#538	—	67	64	no	—
463	#536	C₂×D₆₇	1	16	yes	complemented
464	#535	—	67	16	no	—
465	C₂×C₄⋊Q₈	—	67	2	no	—
466	C₂×C₄⋊Q₈	C₂×D₆₇	1	2	yes	complemented
467	C₂×#127	—	67	2	no	—
468	C₂×#126	—	67	4	no	—
469	C₂×#126	—	67	4	no	—
470	C₂×#126	—	67	4	no	—
471	C₂×#124	—	67	2	no	—
472	C₂×#124	—	67	2	no	—
473	C₂×#124	—	67	4	no	—
474	C₂×#124	—	67	4	no	—
475	C₂×#124	—	67	4	no	—
476	C₂×#124	—	67	4	no	—
477	C₂×#124	—	67	4	no	—
478	C₂×#124	C₂×D₆₇	1	2	yes	—
479	#525	—	67	16	no	—
480	#525	—	67	32	no	—
481	C₂×#123	—	67	1	no	—
482	C₂×#123	—	67	1	no	—
483	C₂×#123	—	67	4	no	—
484	C₂×#123	—	67	4	no	—
485	C₂×#123	—	67	4	no	—
486	C₂×#123	C₂×D₆₇	1	2	yes	complemented
487	C₂×#123	C₂×D₆₇	1	2	yes	complemented
488	C₂×C₂²⋊Q₈	—	67	2	no	—
489	C₂×C₂²⋊Q₈	—	67	2	no	—
490	C₂×C₂²⋊Q₈	—	67	4	no	—
491	C₂×C₂²⋊Q₈	—	67	4	no	—
492	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
493	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
494	C₂×#121	—	67	2	no	—
495	C₂×#121	—	67	2	no	—
496	C₂×#121	—	67	2	no	—
497	C₂×#121	—	67	4	no	—
498	C₂×#121	—	67	2	no	—
499	C₂×#121	—	67	4	no	—
500	C₂×#121	—	67	4	no	—
501	C₂×#120	—	67	1	no	—
502	C₂×#120	—	67	1	no	—
503	C₂×#120	—	67	2	no	—
504	C₂×#120	—	67	2	no	—
505	C₂×#120	—	67	4	no	—
506	C₂×#120	—	67	4	no	—
507	C₂×C₄×Q₈	—	67	2	no	—
508	C₂×C₄×Q₈	—	67	4	no	—
509	C₂×C₄×D₄	—	67	2	no	—
510	C₂×C₄×D₄	—	67	2	no	—
511	C₂×C₄×D₄	—	67	4	no	—
512	C₂×C₄×D₄	—	67	4	no	—
513	C₂×C₄×D₄	—	67	2	no	—
514	C₂×C₄×D₄	—	67	4	no	—
515	C₂×#117	—	67	1	no	—
516	C₂×#117	—	67	1	no	—
517	C₂×#117	—	67	2	no	—
518	C₂×#117	—	67	4	no	—
519	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
520	C₂²×C₂²⋊C₄	—	67	4	no	—
521	C₂⁵	—	67	2	no	—
522	C₂⁵	—	67	1	no	—
523	C₂×#41	—	4	4	no	—
524	C₂×#41	—	268	8	no	—
525	C₂×#41	—	67	16	no	—
526	C₂×#41	C₂²×D₆₇	1	8	yes	—
527	C₂²×Q₈	—	4	4	no	—
528	C₂²×Q₈	—	67	4	no	—
529	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
530	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
531	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
532	C₂²×Q₈	C₂²×D₆₇	1	8	yes	complemented
533	C₂²×D₄	—	268	4	no	—
534	C₂²×D₄	—	67	2	no	—
535	C₂²×D₄	—	67	4	no	—
536	C₂²×D₄	—	67	2	no	—
537	C₂²×D₄	—	67	4	no	—
538	C₂²×D₄	—	67	4	no	—
539	C₂²×D₄	—	67	4	no	—
540	C₂²×D₄	—	67	2	no	—
541	C₂²×D₄	—	67	8	no	—
542	C₂²×D₄	—	67	2	no	—
543	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
544	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
545	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
546	C₂³×C₄	—	268	4	no	—
547	C₂³×C₄	—	67	1	no	—
548	C₂³×C₄	—	67	4	no	—
549	C₂³×C₄	—	67	4	no	—
550	C₂³×C₄	—	67	2	no	—
551	C₂³×C₄	—	67	8	no	—
552	C₂³×C₄	—	67	2	no	—
553	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
554	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
555	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
556	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
557	C₄⋊Q₈	—	67	16	no	—
558	C₄⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
559	#127	—	67	16	no	—
560	#126	—	67	32	no	—
561	#126	—	67	32	no	—
562	#126	—	67	32	no	—
563	#124	—	67	16	no	—
564	#124	—	67	16	no	—
565	#124	—	67	32	no	—
566	#124	—	67	32	no	—
567	#124	—	67	32	no	—
568	#124	—	67	32	no	—
569	#124	—	67	32	no	—
570	#124	C₂²×D₆₇	1	16	yes	—
571	#123	—	67	8	no	—
572	#123	—	67	8	no	—
573	#123	—	67	32	no	—
574	#123	—	67	32	no	—
575	#123	—	67	32	no	—
576	#123	C₂²×D₆₇	1	16	yes	complemented
577	#123	C₂²×D₆₇	1	16	yes	complemented
578	C₂²⋊Q₈	—	67	16	no	—
579	C₂²⋊Q₈	—	67	16	no	—
580	C₂²⋊Q₈	—	67	32	no	—
581	C₂²⋊Q₈	—	67	32	no	—
582	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
583	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
584	#121	—	67	16	no	—
585	#121	—	67	16	no	—
586	#121	—	67	16	no	—
587	#121	—	67	32	no	—
588	#121	—	67	16	no	—
589	#121	—	67	32	no	—
590	#121	—	67	32	no	—
591	#120	—	67	8	no	—
592	#120	—	67	8	no	—
593	#120	—	67	16	no	—
594	#120	—	67	16	no	—
595	#120	—	67	32	no	—
596	#120	—	67	32	no	—
597	C₄×Q₈	—	67	16	no	—
598	C₄×Q₈	—	67	32	no	—
599	C₄×D₄	—	67	16	no	—
600	C₄×D₄	—	67	16	no	—
601	C₄×D₄	—	67	32	no	—
602	C₄×D₄	—	67	32	no	—
603	C₄×D₄	—	67	16	no	—
604	C₄×D₄	—	67	32	no	—
605	#117	—	67	8	no	—
606	#117	—	67	8	no	—
607	#117	—	67	16	no	—
608	#117	—	67	32	no	—
609	#117	C₂²×D₆₇	1	8	yes	complemented
610	C₂×C₄⋊C₄	—	67	2	no	—
611	C₂×C₄⋊C₄	—	67	2	no	—
612	C₂×C₄⋊C₄	—	67	2	no	—
613	C₂×C₄⋊C₄	—	67	4	no	—
614	C₂×C₄⋊C₄	—	67	4	no	—
615	C₂×C₄⋊C₄	—	67	2	no	—
616	C₂×C₄⋊C₄	—	67	4	no	—
617	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
619	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
620	C₂×C₂²⋊C₄	—	67	2	no	—
621	C₂×C₂²⋊C₄	—	67	2	no	—
622	C₂×C₂²⋊C₄	—	67	1	no	—
623	C₂×C₂²⋊C₄	—	67	1	no	—
624	C₂×C₂²⋊C₄	—	67	2	no	—
625	C₂×C₂²⋊C₄	—	67	4	no	—
626	C₂×C₂²⋊C₄	—	67	4	no	—
627	C₂×C₂²⋊C₄	—	67	4	no	—
628	C₂×C₂²⋊C₄	—	67	4	no	—
629	C₂×C₂²⋊C₄	—	67	2	no	—
630	C₂×C₂²⋊C₄	—	67	4	no	—
631	C₂×C₂²⋊C₄	—	67	4	no	—
632	C₂×C₂²⋊C₄	—	67	4	no	—
633	C₂×C₂²⋊C₄	—	67	2	no	—
634	C₂×C₂²⋊C₄	—	67	4	no	—
635	C₂×C₂²⋊C₄	—	67	32	no	—
636	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
639	C₂×C₄²	—	67	4	no	—
640	C₂×C₄²	—	67	2	no	—
641	C₂×C₄²	—	67	2	no	—
642	C₂×C₄²	—	67	4	no	—
643	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
644	C₂⁴	—	268	2	no	—
645	C₂⁴	—	268	4	no	—
646	C₂⁴	—	268	4	no	—
647	C₂⁴	—	268	8	no	—
648	C₂⁴	—	67	8	no	—
649	C₂⁴	—	67	4	no	—
650	C₂⁴	—	67	2	no	—
651	C₂⁴	—	67	4	no	—
652	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
653	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
654	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
655	#41	—	4	16	no	—
656	#41	—	268	32	no	—
657	C₂×Q₈	—	2	8	no	—
658	C₂×Q₈	—	4	4	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×Q₈	—	4	16	no	—
661	C₂×Q₈	—	268	8	no	—
662	C₂×Q₈	—	67	16	no	—
663	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
664	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
665	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	268	4	no	—
670	C₂×D₄	—	268	8	no	—
671	C₂×D₄	—	268	8	no	—
672	C₂×D₄	—	268	16	no	—
673	C₂×D₄	—	268	4	no	—
674	C₂×D₄	—	268	8	no	—
675	C₂×D₄	—	268	8	no	—
676	C₂×D₄	—	268	4	no	—
677	C₂×D₄	—	67	8	no	—
678	C₂×D₄	—	67	16	no	—
679	C₂×D₄	—	67	8	no	—
680	C₂×D₄	—	67	16	no	—
681	C₂×D₄	—	67	16	no	—
682	C₂×D₄	—	67	16	no	—
683	C₂×D₄	—	67	8	no	—
684	C₂×D₄	—	67	8	no	—
685	C₂×D₄	—	134	8	no	—
686	C₂×D₄	C₂³×D₆₇	1	4	yes	—
687	C₂×D₄	C₂³×D₆₇	1	4	yes	—
688	C₂×D₄	C₂³×D₆₇	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	4	4	no	—
693	C₂²×C₄	—	268	4	no	—
694	C₂²×C₄	—	268	8	no	—
695	C₂²×C₄	—	268	8	no	—
696	C₂²×C₄	—	268	16	no	—
697	C₂²×C₄	—	268	2	no	—
698	C₂²×C₄	—	67	4	no	—
699	C₂²×C₄	—	67	16	no	—
700	C₂²×C₄	—	67	16	no	—
701	C₂²×C₄	—	67	8	no	—
702	C₂²×C₄	—	67	2	no	—
703	C₂²×C₄	—	67	4	no	—
704	C₂²×C₄	—	67	2	no	—
705	C₂²×C₄	—	67	2	no	—
706	C₂²×C₄	—	67	8	no	—
707	C₂²×C₄	—	134	8	no	—
708	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
709	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
710	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
711	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
712	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
713	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
714	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
715	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
716	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
717	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
718	C₄⋊C₄	—	67	8	no	—
719	C₄⋊C₄	—	67	8	no	—
720	C₄⋊C₄	—	67	8	no	—
721	C₄⋊C₄	—	67	16	no	—
722	C₄⋊C₄	—	67	16	no	—
723	C₄⋊C₄	—	67	8	no	—
724	C₄⋊C₄	—	67	16	no	—
725	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
726	C₄⋊C₄	C₂³×D₆₇	1	16	yes	—
727	C₄⋊C₄	C₂³×D₆₇	1	16	yes	—
728	C₂²⋊C₄	—	67	8	no	—
729	C₂²⋊C₄	—	67	8	no	—
730	C₂²⋊C₄	—	67	4	no	—
731	C₂²⋊C₄	—	67	4	no	—
732	C₂²⋊C₄	—	67	8	no	—
733	C₂²⋊C₄	—	67	16	no	—
734	C₂²⋊C₄	—	67	16	no	—
735	C₂²⋊C₄	—	67	16	no	—
736	C₂²⋊C₄	—	67	16	no	—
737	C₂²⋊C₄	—	67	8	no	—
738	C₂²⋊C₄	—	67	16	no	—
739	C₂²⋊C₄	—	67	16	no	—
740	C₂²⋊C₄	—	67	16	no	—
741	C₂²⋊C₄	—	67	8	no	—
742	C₂²⋊C₄	—	67	16	no	—
743	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
744	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
745	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
746	C₄²	—	67	16	no	—
747	C₄²	—	67	8	no	—
748	C₄²	—	67	8	no	—
749	C₄²	—	67	16	no	—
750	C₄²	C₂³×D₆₇	1	8	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	4	no	—
757	C₂³	—	268	4	no	—
758	C₂³	—	268	8	no	—
759	C₂³	—	268	8	no	—
760	C₂³	—	268	16	no	—
761	C₂³	—	268	16	no	—
762	C₂³	—	536	16	no	—
763	C₂³	—	67	4	no	—
764	C₂³	—	67	8	no	—
765	C₂³	—	134	4	no	—
766	C₂³	—	134	8	no	—
767	C₂³	—	134	8	no	—
768	C₂³	—	134	4	no	—
769	C₂³	—	134	4	no	—
770	C₂³	—	134	8	no	—
771	C₂³	C₂⁴×D₆₇	1	2	yes	—
772	C₂³	C₂⁴×D₆₇	1	2	yes	—
773	C₂³	C₂⁴×D₆₇	1	2	yes	—
774	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
775	Q₈	—	2	16	no	—
776	Q₈	—	4	8	no	—
777	Q₈	—	4	4	no	—
778	Q₈	—	268	16	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	268	8	no	—
783	D₄	—	268	16	no	—
784	D₄	—	268	16	no	—
785	D₄	—	268	8	no	—
786	D₄	—	268	16	no	—
787	D₄	—	268	16	no	—
788	D₄	—	268	8	no	—
789	D₄	—	134	16	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	268	8	no	—
800	C₂×C₄	—	268	16	no	—
801	C₂×C₄	—	268	16	no	—
802	C₂×C₄	—	268	4	no	—
803	C₂×C₄	—	67	4	no	—
804	C₂×C₄	—	67	8	no	—
805	C₂×C₄	—	67	4	no	—
806	C₂×C₄	—	67	4	no	—
807	C₂×C₄	—	134	4	no	—
808	C₂×C₄	—	134	4	no	—
809	C₂×C₄	—	134	8	no	—
810	C₂×C₄	—	134	4	no	—
811	C₂×C₄	—	134	16	no	—
812	C₂×C₄	#14524088	1	4	yes	—
813	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
814	C₂×C₄	C₂⁴×D₆₇	1	8	yes	—
815	C₂×C₄	C₂⁴×D₆₇	1	8	yes	—
816	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
817	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
818	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	4	4	no	—
827	C₂²	—	4	4	no	—
828	C₂²	—	268	16	no	—
829	C₂²	—	268	8	no	—
830	C₂²	—	268	16	no	—
831	C₂²	—	536	16	no	—
832	C₂²	—	134	4	no	—
833	C₂²	—	134	8	no	—
834	C₂²	—	134	8	no	—
835	C₂²	—	134	4	no	—
836	C₂²	—	134	4	no	—
837	C₂²	—	134	8	no	—
838	C₂²	C₂×#14524088	1	2	yes	—
839	C₂²	#16864233	1	4	yes	—
840	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	8	no	—
845	C₄	—	2	8	no	—
846	C₄	—	134	4	no	—
847	C₄	—	134	4	no	—
848	C₄	—	134	8	no	—
849	C₄	—	134	4	no	—
850	C₄	C₂×#14524088	1	4	yes	—
851	C₂	—	4	2	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	2	no	—
854	C₂	—	268	4	no	—
855	C₂	—	268	8	no	—
856	C₂	#22574486	1	4	yes	direct product factor
857	C₂	C₂²×#14524088	1	1	yes	characteristic
858	C₂	C₂×#16864233	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#536×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#536	D₆₇
hypocenter	C₆₇	C₂×#3540
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#536

Complements

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

N	H ≅ G/N	type
1. #22574486	C₂	direct (N × H)
2. C₂×#16864138	C₂	semidirect
3. C₂×#16864136	C₂	semidirect
4. C₂×#16864130	C₂	semidirect
5. C₂×#16864117	C₂	semidirect
6. C₂×#16864109	C₂	semidirect
7. C₂×#16864076	C₂	semidirect
8. C₂×#16864057	C₂	semidirect
9. C₂×#16864037	C₂	semidirect
10. C₂×#16864020	C₂	semidirect
11. C₂×#16864019	C₂	semidirect
12. C₂×#16863982	C₂	semidirect
13. C₂×#16863960	C₂	semidirect
14. C₂×#16863909	C₂	semidirect
15. C₂×#16863903	C₂	semidirect
16. C₂×#536×C₆₇	C₂	semidirect
18. C₂³×D₂₆₈	C₂²	semidirect
19. C₂³×C₄×D₆₇	C₂²	semidirect
20. #16864138	C₂²	semidirect
21. #16864136	C₂²	semidirect
22. #16864130	C₂²	semidirect
23. #16864117	C₂²	semidirect
24. #16864109	C₂²	semidirect
25. #16864076	C₂²	semidirect
26. #16864057	C₂²	semidirect
27. #16864037	C₂²	semidirect
28. #16864020	C₂²	semidirect
29. #16864019	C₂²	semidirect
30. #16863982	C₂²	semidirect
31. #16863960	C₂²	semidirect
32. C₂×#14524042	C₂²	semidirect
34. C₂×#14524038	C₂²	semidirect
35. C₂×#14524038	C₂²	semidirect
36. C₂×#14524036	C₂²	semidirect
37. C₂×#14524032	C₂²	semidirect
38. C₂×#14524032	C₂²	semidirect
39. C₂×#14524032	C₂²	semidirect
40. C₂×#14524031	C₂²	semidirect
42. C₂×#14524029	C₂²	semidirect
43. C₂×#14524029	C₂²	semidirect
44. #16863909	C₂²	semidirect
45. #16863903	C₂²	semidirect
46. C₂×#14524028	C₂²	semidirect
47. C₂×#14524028	C₂²	semidirect
48. C₂×#14524025	C₂²	semidirect
50. C₂×#14524024	C₂²	semidirect
51. C₂×#14524023	C₂²	semidirect
52. C₂×#14524019	C₂²	semidirect
53. C₂×#14524019	C₂²	semidirect
54. C₂×#14524019	C₂²	semidirect
58. C₂×#14524017	C₂²	semidirect
59. C₂×#14524017	C₂²	semidirect
60. C₂×#14524016	C₂²	semidirect
63. C₂×#14524013	C₂²	semidirect
66. C₂×#14524011	C₂²	semidirect
67. C₂×#14524011	C₂²	semidirect
68. C₂×Q₈×Dic₆₇	C₂²	semidirect
69. C₂×#14524008	C₂²	semidirect
70. C₂×#14524005	C₂²	semidirect
71. C₂×#14524005	C₂²	semidirect
73. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
74. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
75. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
76. C₂×#14524002	C₂²	semidirect
77. C₂×#14524002	C₂²	semidirect
78. C₂×#14524001	C₂²	semidirect
79. C₂×#14524000	C₂²	semidirect
80. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
82. C₂³×Q₈×C₆₇	C₂²	semidirect
83. #536×C₆₇	C₂²	semidirect
84. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
86. C₂×#123×C₆₇	C₂²	semidirect
87. C₂×#123×C₆₇	C₂²	semidirect
88. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
89. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
90. C₂×#117×C₆₇	C₂²	semidirect
101. C₂²×D₂₆₈	C₂³	semidirect
112. C₂²×C₄×D₆₇	C₂³	semidirect
113. #14524042	C₂³	semidirect
115. #14524038	C₂³	semidirect
116. #14524038	C₂³	semidirect
117. #14524036	C₂³	semidirect
118. #14524032	C₂³	semidirect
119. #14524032	C₂³	semidirect
120. #14524032	C₂³	semidirect
121. #14524031	C₂³	semidirect
123. #14524029	C₂³	semidirect
124. #14524029	C₂³	semidirect
125. #14524028	C₂³	semidirect
126. #14524028	C₂³	semidirect
127. #14524025	C₂³	semidirect
129. #14524024	C₂³	semidirect
130. #14524023	C₂³	semidirect
131. #14524019	C₂³	semidirect
132. #14524019	C₂³	semidirect
133. #14524019	C₂³	semidirect
137. #14524017	C₂³	semidirect
138. #14524017	C₂³	semidirect
139. #14524016	C₂³	semidirect
142. #14524013	C₂³	semidirect
145. #14524011	C₂³	semidirect
146. #14524011	C₂³	semidirect
147. Q₈×Dic₆₇	C₂³	semidirect
148. #14524008	C₂³	semidirect
149. #14524005	C₂³	semidirect
150. #14524005	C₂³	semidirect
152. C₄×C₂²⋊D₆₇	C₂³	semidirect
153. C₄×C₂²⋊D₆₇	C₂³	semidirect
154. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
155. #14524002	C₂³	semidirect
156. #14524002	C₂³	semidirect
157. #14524001	C₂³	semidirect
158. #14524000	C₂³	semidirect
181. C₂²⋊C₄×D₆₇	C₂³	semidirect
192. C₂²×Q₈×C₆₇	C₂³	semidirect
200. C₄⋊Q₈×C₆₇	C₂³	semidirect
202. #123×C₆₇	C₂³	semidirect
203. #123×C₆₇	C₂³	semidirect
204. C₂²⋊Q₈×C₆₇	C₂³	semidirect
205. C₂²⋊Q₈×C₆₇	C₂³	semidirect
206. #117×C₆₇	C₂³	semidirect
425. C₂×C₆₇	#3540	semidirect
442. C₂×#536	D₆₇	semidirect
446. C₆₇	C₂×#3540	semidirect
449. C₂³×Q₈	C₂×D₆₇	semidirect
463. #536	C₂×D₆₇	semidirect
466. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
486. C₂×#123	C₂×D₆₇	semidirect
487. C₂×#123	C₂×D₆₇	semidirect
492. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
493. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
519. C₂×#117	C₂×D₆₇	semidirect
532. C₂²×Q₈	C₂²×D₆₇	semidirect
558. C₄⋊Q₈	C₂²×D₆₇	semidirect
576. #123	C₂²×D₆₇	semidirect
577. #123	C₂²×D₆₇	semidirect
582. C₂²⋊Q₈	C₂²×D₆₇	semidirect
583. C₂²⋊Q₈	C₂²×D₆₇	semidirect
609. #117	C₂²×D₆₇	semidirect
856. C₂	#22574486	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574486	2
C₂×#16864138	2
C₂×#16864136	2
C₂×#16864130	2
C₂×#16864117	2
C₂×#16864109	2
C₂×#16864076	2
C₂×#16864057	2
C₂×#16864037	2
C₂×#16864020	2
C₂×#16864019	2
C₂×#16863982	2
C₂×#16863960	2
C₂×#16863909	2
C₂×#16863903	2
C₂×#536×C₆₇	2
C₂×#3540	67

Subgroups — C2×#22574486 #31763124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574486 #31763124