Subgroups — #22574559

Order 8576.

1060 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864150	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864140	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864138	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864110	C₂	1	2	yes	maximal, complemented
5	#16864073	C₂	1	2	yes	maximal, complemented
6	#16864073	C₂	1	2	yes	maximal, complemented
7	#16864069	C₂	1	2	yes	maximal, complemented
8	#16864043	C₂	1	2	yes	maximal, complemented
9	#16864038	C₂	1	2	yes	maximal, complemented
10	#16864019	C₂	1	2	yes	maximal, complemented
11	#16864014	C₂	1	2	yes	maximal, complemented
12	#16863983	C₂	1	2	yes	maximal, complemented
13	#16863982	C₂	1	2	yes	maximal, complemented
14	#16863969	C₂	1	2	yes	maximal, complemented
15	#16863954	C₂	1	2	yes	maximal, complemented
16	#16863931	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863925	C₂	1	1	yes	maximal, characteristic, complemented
18	#124×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	#562×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11761628	C₂²	1	2	yes	—
21	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
24	#14524042	C₂²	1	2	yes	complemented
25	#14524042	C₂²	1	2	yes	complemented
26	#14524038	C₂²	1	2	yes	complemented
27	#14524038	C₂²	1	2	yes	complemented
28	#14524038	C₂²	1	2	yes	complemented
29	#14524038	C₂²	1	2	yes	complemented
30	#14524038	C₂²	1	2	yes	complemented
31	#14524036	C₂²	1	2	yes	complemented
32	#14524035	C₂²	1	1	yes	characteristic, complemented
33	#14524032	C₂²	1	1	yes	characteristic
34	#14524032	C₂²	1	2	yes	complemented
35	#14524031	C₂²	1	1	yes	characteristic
36	#14524031	C₂²	1	1	yes	characteristic, complemented
37	#14524030	C₂²	1	2	yes	complemented
38	#14524030	C₂²	1	1	yes	characteristic, complemented
39	#14524029	C₂²	1	2	yes	complemented
40	#14524029	C₂²	1	2	yes	complemented
41	#14524029	C₂²	1	2	yes	complemented
42	#14524029	C₂²	1	2	yes	complemented
43	#14524029	C₂²	1	2	yes	complemented
44	#14524029	C₂²	1	2	yes	complemented
45	#14524028	C₂²	1	2	yes	—
46	#14524028	C₂²	1	2	yes	complemented
47	#14524028	C₂²	1	2	yes	complemented
48	#14524028	C₂²	1	2	yes	complemented
49	#14524027	C₂²	1	2	yes	complemented
50	#14524027	C₂²	1	2	yes	complemented
51	#14524025	C₂²	1	2	yes	complemented
52	#14524025	C₂²	1	2	yes	complemented
53	#14524025	C₂²	1	2	yes	complemented
54	#14524025	C₂²	1	2	yes	complemented
55	#14524023	C₂²	1	2	yes	complemented
56	#14524023	C₂²	1	2	yes	complemented
57	#14524023	C₂²	1	1	yes	characteristic, complemented
58	#14524022	C₂²	1	2	yes	complemented
59	#14524021	C₂²	1	2	yes	complemented
60	#14524020	C₂²	1	2	yes	complemented
61	#14524019	C₂²	1	1	yes	characteristic, complemented
62	#14524019	C₂²	1	2	yes	complemented
63	#14524018	C₂²	1	1	yes	characteristic
64	#14524017	C₂²	1	2	yes	—
65	#14524016	C₂²	1	2	yes	complemented
66	#14524015	C₂²	1	2	yes	—
67	#14524015	C₂²	1	2	yes	complemented
68	#14524015	C₂²	1	2	yes	complemented
69	#14524014	C₂²	1	1	yes	characteristic
70	#14524014	C₂²	1	2	yes	complemented
71	#14524013	C₂²	1	2	yes	—
72	#14524013	C₂²	1	2	yes	—
73	#14524013	C₂²	1	2	yes	complemented
74	#14524011	C₂²	1	2	yes	—
75	#14524011	C₂²	1	2	yes	complemented
76	#14524011	C₂²	1	2	yes	complemented
77	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
78	#14524008	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₆₇	C₂²	1	2	yes	complemented
80	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
81	#14524005	C₂²	1	2	yes	complemented
82	#14524005	C₂²	1	2	yes	complemented
83	#14524005	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
86	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
87	#14524002	C₂²	1	2	yes	complemented
88	#14524001	C₂²	1	2	yes	complemented
89	#14524001	C₂²	1	2	yes	complemented
90	#14523999	C₂²	1	2	yes	complemented
91	#14523999	C₂²	1	2	yes	complemented
92	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
93	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
97	C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
98	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#123×C₆₇	C₂²	1	2	yes	complemented
102	#123×C₆₇	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
104	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
105	#121×C₆₇	C₂²	1	2	yes	complemented
106	#121×C₆₇	C₂²	1	2	yes	complemented
107	C₂³×D₆₇	C₂³	1	2	yes	—
108	C₂³×D₆₇	C₂³	1	2	yes	—
109	#11761628	—	4	4	no	—
110	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
111	C₂×Dic₁₃₄	C₂³	1	2	yes	—
112	C₂×Dic₁₃₄	C₂³	1	2	yes	—
113	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
114	Q₈×D₆₇	—	4	2	no	—
115	C₂×D₂₆₈	C₂³	1	2	yes	—
116	C₂×D₂₆₈	C₂³	1	2	yes	—
117	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
118	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
125	D₄×D₆₇	—	4	2	no	—
126	D₄×D₆₇	—	4	4	no	—
127	C₂²×Dic₆₇	C₂³	1	2	yes	—
128	C₂²×Dic₆₇	C₂³	1	2	yes	—
129	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₄×D₆₇	C₂³	1	2	yes	—
131	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₆₇	C₂³	1	2	yes	—
134	C₂×C₄×D₆₇	C₂³	1	2	yes	—
135	C₂×C₄×D₆₇	C₂³	1	2	yes	—
136	C₄⋊Dic₆₇	C₂³	1	2	yes	—
137	C₄⋊Dic₆₇	C₂³	1	2	yes	—
138	C₄⋊Dic₆₇	C₂³	1	2	yes	—
139	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₆₇	C₂³	1	2	yes	—
142	Dic₆₇⋊C₄	C₂³	1	2	yes	—
143	Dic₆₇⋊C₄	C₂³	1	2	yes	—
144	Dic₆₇⋊C₄	C₂³	1	2	yes	—
145	Dic₆₇⋊C₄	C₂³	1	2	yes	—
146	Dic₆₇⋊C₄	C₂³	1	2	yes	—
147	Dic₆₇⋊C₄	C₂³	1	2	yes	—
148	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
149	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
150	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
151	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
152	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
153	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
154	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
155	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
170	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
171	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
172	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
173	C₄×Dic₆₇	C₂³	1	2	yes	—
174	C₄×Dic₆₇	C₂³	1	2	yes	—
175	C₄×Dic₆₇	C₂³	1	2	yes	—
176	C₄×Dic₆₇	C₂³	1	2	yes	—
177	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₆₇	C₂³	1	2	yes	—
180	C₂×D₄×C₆₇	C₂³	1	2	yes	—
181	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
184	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
185	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₄²×C₆₇	C₂³	1	1	yes	characteristic
198	C₂³×C₆₇	C₂⁴	1	2	yes	—
199	C₂³×C₆₇	C₂⁴	1	2	yes	—
200	C₂²×D₆₇	—	2	4	no	—
201	C₂²×D₆₇	—	4	2	no	—
202	C₂²×D₆₇	—	4	2	no	—
203	C₂²×D₆₇	—	4	2	no	—
204	C₂²×D₆₇	—	4	2	no	—
205	C₂²×D₆₇	—	4	2	no	—
206	C₂²×D₆₇	C₂⁴	1	2	yes	—
207	C₂²×D₆₇	C₂⁴	1	2	yes	—
208	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
209	Q₈×C₆₇	—	4	1	no	—
210	Q₈×C₆₇	—	4	1	no	—
211	D₄×C₆₇	—	4	2	no	—
212	D₄×C₆₇	—	4	1	no	—
213	D₄×C₆₇	—	4	1	no	—
214	D₄×C₆₇	—	4	2	no	—
215	C₂×C₄×C₆₇	—	4	2	no	—
216	C₂×C₄×C₆₇	—	4	2	no	—
217	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
219	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
220	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
221	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
222	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
224	C₂²⋊D₆₇	—	2	4	no	—
225	C₂²⋊D₆₇	—	4	2	no	—
226	C₂²⋊D₆₇	—	4	2	no	—
227	C₂²⋊D₆₇	—	4	2	no	—
228	C₂²⋊D₆₇	—	4	2	no	—
229	C₂²⋊D₆₇	—	4	2	no	—
230	C₂×Dic₆₇	—	4	2	no	—
231	C₂×Dic₆₇	—	4	2	no	—
232	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
233	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
234	C₂×Dic₆₇	C₂⁴	1	2	yes	—
235	C₂×Dic₆₇	C₂⁴	1	2	yes	—
236	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
237	C₂×Dic₆₇	C₂⁴	1	2	yes	—
238	C₂×Dic₆₇	C₂⁴	1	2	yes	—
239	D₂₆₈	—	2	4	no	—
240	D₂₆₈	—	4	1	no	—
241	D₂₆₈	—	4	1	no	—
242	D₂₆₈	—	4	2	no	—
243	C₄×D₆₇	—	2	2	no	—
244	C₄×D₆₇	—	2	4	no	—
245	C₄×D₆₇	—	4	2	no	—
246	C₄×D₆₇	—	4	1	no	—
247	C₄×D₆₇	—	4	1	no	—
248	C₄×D₆₇	—	4	2	no	—
249	C₄×D₆₇	—	4	2	no	—
250	Dic₁₃₄	—	4	1	no	—
251	Dic₁₃₄	—	4	2	no	—
252	Dic₁₃₄	—	4	1	no	—
253	Dic₁₃₄	—	4	2	no	—
254	C₂²×C₆₇	—	2	2	no	—
255	C₂²×C₆₇	—	2	2	no	—
256	C₂²×C₆₇	—	2	2	no	—
257	C₂²×C₆₇	—	2	2	no	—
258	C₂²×C₆₇	—	2	2	no	—
259	C₂²×C₆₇	—	2	2	no	—
260	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
261	C₂×D₆₇	—	2	1	no	—
262	C₂×D₆₇	—	2	1	no	—
263	C₂×D₆₇	—	2	2	no	—
264	C₂×D₆₇	—	2	2	no	—
265	C₂×D₆₇	—	2	2	no	—
266	C₂×D₆₇	—	2	2	no	—
267	C₂×D₆₇	—	2	2	no	—
268	C₂×D₆₇	—	2	2	no	—
269	C₂×D₆₇	—	8	4	no	—
270	C₂×D₆₇	—	8	4	no	—
271	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
272	C₄×C₆₇	—	2	2	no	—
273	C₄×C₆₇	—	2	1	no	—
274	C₄×C₆₇	—	2	2	no	—
275	C₄×C₆₇	—	2	1	no	—
276	C₄×C₆₇	—	2	2	no	—
277	C₄×C₆₇	—	2	1	no	—
278	C₄×C₆₇	—	2	2	no	—
279	Dic₆₇	—	2	2	no	—
280	Dic₆₇	—	2	1	no	—
281	Dic₆₇	—	2	2	no	—
282	Dic₆₇	—	2	2	no	—
283	Dic₆₇	—	2	1	no	—
284	Dic₆₇	—	2	1	no	—
285	Dic₆₇	—	2	2	no	—
286	C₂×C₆₇	—	4	2	no	—
287	C₂×C₆₇	—	4	2	no	—
288	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₆₇	#585	1	1	yes	characteristic
290	C₂×C₆₇	#585	1	1	yes	characteristic
291	D₆₇	—	2	2	no	—
292	D₆₇	—	4	2	no	—
293	D₆₇	—	4	2	no	—
294	#3545	—	67	1	no	maximal, Sylow
295	C₆₇	#3545	1	1	yes	characteristic, complemented, Sylow
296	#563	—	67	1	no	—
297	#562	—	67	1	no	—
298	#562	D₆₇	1	1	yes	characteristic, complemented
299	H(3,𝔽₄)	—	67	1	no	—
300	#555	—	67	2	no	—
301	#551	—	67	2	no	—
302	#551	—	67	2	no	—
303	#551	—	67	2	no	—
304	#546	—	67	2	no	—
305	#546	—	67	2	no	—
306	#542	—	67	2	no	—
307	#542	—	67	2	no	—
308	#538	—	67	2	no	—
309	#538	—	67	2	no	—
310	#536	—	67	2	no	—
311	#534	—	67	2	no	—
312	#529	—	67	1	no	—
313	#529	—	67	1	no	—
314	C₂×#124	—	67	1	no	—
315	C₂×#41	—	67	2	no	—
316	C₂²×Q₈	—	67	1	no	—
317	C₂²×D₄	—	67	1	no	—
318	C₂²×D₄	—	67	2	no	—
319	C₄⋊Q₈	—	67	2	no	—
320	C₄⋊Q₈	—	67	2	no	—
321	#126	—	67	2	no	—
322	#126	—	67	2	no	—
323	#126	—	67	2	no	—
324	#126	—	67	2	no	—
325	#126	—	67	2	no	—
326	#126	—	67	2	no	—
327	#125	—	67	1	no	—
328	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
329	#124	—	67	1	no	—
330	#124	—	67	2	no	—
331	#124	—	67	1	no	—
332	#124	—	67	2	no	—
333	#124	—	67	2	no	—
334	#124	—	67	2	no	—
335	#124	—	67	2	no	—
336	#124	—	67	2	no	—
337	#124	—	67	2	no	—
338	#124	—	67	2	no	—
339	#124	—	67	1	no	—
340	#124	—	67	1	no	—
341	#124	C₂×D₆₇	1	1	yes	characteristic, complemented
342	#124	C₂×D₆₇	1	1	yes	characteristic, complemented
343	#123	—	67	2	no	—
344	#123	—	67	2	no	—
345	#123	—	67	2	no	—
346	#123	—	67	2	no	—
347	#123	—	67	2	no	—
348	#123	—	67	2	no	—
349	#123	—	67	2	no	—
350	#123	—	67	2	no	—
351	#123	—	67	2	no	—
352	#123	—	67	2	no	—
353	#123	C₂×D₆₇	1	2	yes	complemented
354	#123	C₂×D₆₇	1	2	yes	complemented
355	C₂²⋊Q₈	—	67	1	no	—
356	C₂²⋊Q₈	—	67	2	no	—
357	C₂²⋊Q₈	—	67	2	no	—
358	C₂²⋊Q₈	—	67	1	no	—
359	C₂²⋊Q₈	—	67	2	no	—
360	C₂²⋊Q₈	—	67	2	no	—
361	C₂²⋊Q₈	—	67	2	no	—
362	C₂²⋊Q₈	—	67	2	no	—
363	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
364	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
365	#121	—	67	1	no	—
366	#121	—	67	2	no	—
367	#121	—	67	2	no	—
368	#121	—	67	2	no	—
369	#121	—	67	2	no	—
370	#121	—	67	2	no	—
371	#121	—	67	1	no	—
372	#121	—	67	2	no	—
373	#121	C₂×D₆₇	1	2	yes	complemented
374	#121	C₂×D₆₇	1	2	yes	complemented
375	#120	—	67	2	no	—
376	#120	—	67	2	no	—
377	#120	—	67	2	no	—
378	#120	—	67	2	no	—
379	#120	—	67	2	no	—
380	#120	—	67	2	no	—
381	C₄×Q₈	—	67	1	no	—
382	C₄×Q₈	—	67	1	no	—
383	C₄×D₄	—	67	1	no	—
384	C₄×D₄	—	67	2	no	—
385	C₄×D₄	—	67	2	no	—
386	C₄×D₄	—	67	2	no	—
387	C₄×D₄	—	67	1	no	—
388	C₄×D₄	—	67	2	no	—
389	C₄×D₄	—	67	2	no	—
390	C₄×D₄	—	67	2	no	—
391	#117	—	67	2	no	—
392	#117	—	67	2	no	—
393	#117	—	67	2	no	—
394	#117	—	67	2	no	—
395	#117	—	67	2	no	—
396	C₂×C₂²⋊C₄	—	67	2	no	—
397	C₂×C₂²⋊C₄	—	67	2	no	—
398	C₂×C₂²⋊C₄	—	67	2	no	—
399	C₂×C₂²⋊C₄	—	67	2	no	—
400	C₂×C₂²⋊C₄	—	67	2	no	—
401	C₂×C₄²	—	67	1	no	—
402	C₂⁴	—	67	2	no	—
403	C₂⁴	—	67	2	no	—
404	#41	—	268	4	no	—
405	C₂×Q₈	—	268	2	no	—
406	C₂×Q₈	—	67	1	no	—
407	C₂×Q₈	—	67	2	no	—
408	C₂×Q₈	—	67	2	no	—
409	C₂×Q₈	—	67	1	no	—
410	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
411	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
412	C₂×D₄	—	268	4	no	—
413	C₂×D₄	—	268	2	no	—
414	C₂×D₄	—	67	2	no	—
415	C₂×D₄	—	67	2	no	—
416	C₂×D₄	—	67	2	no	—
417	C₂×D₄	—	67	2	no	—
418	C₂×D₄	—	67	2	no	—
419	C₂×D₄	—	67	2	no	—
420	C₂×D₄	—	67	2	no	—
421	C₂×D₄	—	67	1	no	—
422	C₂×D₄	—	67	1	no	—
423	C₂×D₄	—	67	2	no	—
424	C₂×D₄	C₂²×D₆₇	1	2	yes	—
425	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
426	C₂×D₄	C₂²×D₆₇	1	2	yes	—
427	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
428	C₂²×C₄	—	67	2	no	—
429	C₂²×C₄	—	67	2	no	—
430	C₂²×C₄	—	67	1	no	—
431	C₂²×C₄	—	67	1	no	—
432	C₂²×C₄	—	67	2	no	—
433	C₂²×C₄	—	67	2	no	—
434	C₂²×C₄	—	67	2	no	—
435	C₂²×C₄	—	67	1	no	—
436	C₂²×C₄	—	67	2	no	—
437	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
438	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
439	C₄⋊C₄	—	67	2	no	—
440	C₄⋊C₄	—	67	2	no	—
441	C₄⋊C₄	—	67	2	no	—
442	C₄⋊C₄	—	67	2	no	—
443	C₄⋊C₄	—	67	2	no	—
444	C₄⋊C₄	—	67	2	no	—
445	C₄⋊C₄	—	67	2	no	—
446	C₄⋊C₄	—	67	2	no	—
447	C₄⋊C₄	—	67	1	no	—
448	C₄⋊C₄	—	67	1	no	—
449	C₄⋊C₄	—	67	2	no	—
450	C₄⋊C₄	—	67	2	no	—
451	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
452	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
453	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
454	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
455	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
456	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
457	C₂²⋊C₄	—	67	2	no	—
458	C₂²⋊C₄	—	67	2	no	—
459	C₂²⋊C₄	—	67	2	no	—
460	C₂²⋊C₄	—	67	2	no	—
461	C₂²⋊C₄	—	67	2	no	—
462	C₂²⋊C₄	—	67	2	no	—
463	C₂²⋊C₄	—	67	2	no	—
464	C₂²⋊C₄	—	67	2	no	—
465	C₂²⋊C₄	—	67	2	no	—
466	C₂²⋊C₄	—	67	2	no	—
467	C₂²⋊C₄	—	67	2	no	—
468	C₂²⋊C₄	—	67	2	no	—
469	C₂²⋊C₄	—	67	2	no	—
470	C₂²⋊C₄	—	67	2	no	—
471	C₂²⋊C₄	—	67	2	no	—
472	C₂²⋊C₄	—	67	2	no	—
473	C₂²⋊C₄	—	67	2	no	—
474	C₂²⋊C₄	—	67	2	no	—
475	C₂²⋊C₄	—	67	2	no	—
476	C₂²⋊C₄	—	67	2	no	—
477	C₂²⋊C₄	—	67	2	no	—
478	C₂²⋊C₄	—	67	2	no	—
479	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
480	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
485	C₄²	—	67	1	no	—
486	C₄²	—	67	1	no	—
487	C₄²	—	67	1	no	—
488	C₄²	—	67	2	no	—
489	C₄²	—	67	2	no	—
490	C₄²	—	67	2	no	—
491	C₄²	—	67	2	no	—
492	C₄²	C₂²×D₆₇	1	1	yes	characteristic
493	C₂³	—	268	2	no	—
494	C₂³	—	268	2	no	—
495	C₂³	—	268	2	no	—
496	C₂³	—	268	2	no	—
497	C₂³	—	268	2	no	—
498	C₂³	—	67	1	no	—
499	C₂³	—	67	2	no	—
500	C₂³	—	67	2	no	—
501	C₂³	—	134	4	no	—
502	C₂³	C₂³×D₆₇	1	2	yes	—
503	C₂³	C₂³×D₆₇	1	2	yes	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	268	2	no	—
507	Q₈	—	268	1	no	—
508	Q₈	—	268	2	no	—
509	Q₈	—	268	1	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	268	1	no	—
515	D₄	—	268	2	no	—
516	D₄	—	268	1	no	—
517	D₄	—	268	2	no	—
518	D₄	—	268	2	no	—
519	D₄	—	268	2	no	—
520	D₄	—	268	2	no	—
521	D₄	—	268	2	no	—
522	D₄	—	134	4	no	—
523	D₄	—	134	4	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	268	2	no	—
527	C₂×C₄	—	268	2	no	—
528	C₂×C₄	—	268	2	no	—
529	C₂×C₄	—	268	1	no	—
530	C₂×C₄	—	268	1	no	—
531	C₂×C₄	—	268	2	no	—
532	C₂×C₄	—	268	2	no	—
533	C₂×C₄	—	67	1	no	—
534	C₂×C₄	—	67	1	no	—
535	C₂×C₄	—	67	2	no	—
536	C₂×C₄	—	67	2	no	—
537	C₂×C₄	—	67	1	no	—
538	C₂×C₄	—	67	2	no	—
539	C₂×C₄	—	67	2	no	—
540	C₂×C₄	—	134	2	no	—
541	C₂×C₄	—	134	4	no	—
542	C₂×C₄	C₂³×D₆₇	1	2	yes	—
543	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₆₇	1	2	yes	—
547	C₂×C₄	C₂³×D₆₇	1	2	yes	—
548	C₂×C₄	C₂³×D₆₇	1	2	yes	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	536	4	no	—
556	C₂²	—	536	4	no	—
557	C₂²	—	67	2	no	—
558	C₂²	—	134	2	no	—
559	C₂²	—	134	2	no	—
560	C₂²	—	134	2	no	—
561	C₂²	—	134	2	no	—
562	C₂²	—	134	2	no	—
563	C₂²	—	134	2	no	—
564	C₂²	—	134	1	no	—
565	C₂²	—	134	1	no	—
566	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	134	2	no	—
575	C₄	—	134	1	no	—
576	C₄	—	134	2	no	—
577	C₄	—	134	1	no	—
578	C₄	—	134	1	no	—
579	C₄	—	134	2	no	—
580	C₄	—	134	2	no	—
581	C₂	—	4	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	268	2	no	—
584	C₂	—	268	2	no	—
585	C₂	—	134	2	no	—
586	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
587	C₂	#16864231	1	1	yes	characteristic
588	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#562×C₆₇	C₂
hypercenter	#562	D₆₇
hypocenter	C₆₇	#3545
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #16864150	C₂	semidirect
2. #16864140	C₂	semidirect
3. #16864138	C₂	semidirect
4. #16864110	C₂	semidirect
5. #16864073	C₂	semidirect
6. #16864073	C₂	semidirect
7. #16864069	C₂	semidirect
8. #16864043	C₂	semidirect
9. #16864038	C₂	semidirect
10. #16864019	C₂	semidirect
11. #16864014	C₂	semidirect
12. #16863983	C₂	semidirect
13. #16863982	C₂	semidirect
14. #16863969	C₂	semidirect
15. #16863954	C₂	semidirect
16. #16863931	C₂	semidirect
17. #16863925	C₂	semidirect
18. #124×D₆₇	C₂	semidirect
19. #562×C₆₇	C₂	semidirect
21. C₂×Q₈×D₆₇	C₂²	semidirect
23. C₂×D₄×D₆₇	C₂²	semidirect
24. #14524042	C₂²	semidirect
25. #14524042	C₂²	semidirect
26. #14524038	C₂²	semidirect
27. #14524038	C₂²	semidirect
28. #14524038	C₂²	semidirect
29. #14524038	C₂²	semidirect
30. #14524038	C₂²	semidirect
31. #14524036	C₂²	semidirect
32. #14524035	C₂²	semidirect
34. #14524032	C₂²	semidirect
36. #14524031	C₂²	semidirect
37. #14524030	C₂²	semidirect
38. #14524030	C₂²	semidirect
39. #14524029	C₂²	semidirect
40. #14524029	C₂²	semidirect
41. #14524029	C₂²	semidirect
42. #14524029	C₂²	semidirect
43. #14524029	C₂²	semidirect
44. #14524029	C₂²	semidirect
46. #14524028	C₂²	semidirect
47. #14524028	C₂²	semidirect
48. #14524028	C₂²	semidirect
49. #14524027	C₂²	semidirect
50. #14524027	C₂²	semidirect
51. #14524025	C₂²	semidirect
52. #14524025	C₂²	semidirect
53. #14524025	C₂²	semidirect
54. #14524025	C₂²	semidirect
55. #14524023	C₂²	semidirect
56. #14524023	C₂²	semidirect
57. #14524023	C₂²	semidirect
58. #14524022	C₂²	semidirect
59. #14524021	C₂²	semidirect
60. #14524020	C₂²	semidirect
61. #14524019	C₂²	semidirect
62. #14524019	C₂²	semidirect
65. #14524016	C₂²	semidirect
67. #14524015	C₂²	semidirect
68. #14524015	C₂²	semidirect
70. #14524014	C₂²	semidirect
73. #14524013	C₂²	semidirect
75. #14524011	C₂²	semidirect
76. #14524011	C₂²	semidirect
77. Q₈×Dic₆₇	C₂²	semidirect
78. #14524008	C₂²	semidirect
79. D₄×Dic₆₇	C₂²	semidirect
80. D₄×Dic₆₇	C₂²	semidirect
81. #14524005	C₂²	semidirect
82. #14524005	C₂²	semidirect
83. #14524005	C₂²	semidirect
84. C₄×C₂²⋊D₆₇	C₂²	semidirect
85. C₄×C₂²⋊D₆₇	C₂²	semidirect
86. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
87. #14524002	C₂²	semidirect
88. #14524001	C₂²	semidirect
89. #14524001	C₂²	semidirect
90. #14523999	C₂²	semidirect
91. #14523999	C₂²	semidirect
92. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
93. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
94. C₂²⋊C₄×D₆₇	C₂²	semidirect
95. C₂²⋊C₄×D₆₇	C₂²	semidirect
96. C₂²⋊C₄×D₆₇	C₂²	semidirect
97. C₄²×D₆₇	C₂²	semidirect
98. #125×C₆₇	C₂²	semidirect
99. #124×C₆₇	C₂²	semidirect
100. #124×C₆₇	C₂²	semidirect
101. #123×C₆₇	C₂²	semidirect
102. #123×C₆₇	C₂²	semidirect
103. C₂²⋊Q₈×C₆₇	C₂²	semidirect
104. C₂²⋊Q₈×C₆₇	C₂²	semidirect
105. #121×C₆₇	C₂²	semidirect
106. #121×C₆₇	C₂²	semidirect
295. C₆₇	#3545	semidirect
298. #562	D₆₇	semidirect
328. #125	C₂×D₆₇	semidirect
341. #124	C₂×D₆₇	semidirect
342. #124	C₂×D₆₇	semidirect
353. #123	C₂×D₆₇	semidirect
354. #123	C₂×D₆₇	semidirect
363. C₂²⋊Q₈	C₂×D₆₇	semidirect
364. C₂²⋊Q₈	C₂×D₆₇	semidirect
373. #121	C₂×D₆₇	semidirect
374. #121	C₂×D₆₇	semidirect