Subgroups — #22574555

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	#16864145	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864141	C₂	1	2	yes	maximal, complemented
3	#16864138	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864108	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864075	C₂	1	2	yes	maximal, complemented
6	#16864070	C₂	1	2	yes	maximal, complemented
7	#16864070	C₂	1	2	yes	maximal, complemented
8	#16864039	C₂	1	2	yes	maximal, complemented
9	#16864035	C₂	1	2	yes	maximal, complemented
10	#16864017	C₂	1	2	yes	maximal, complemented
11	#16864010	C₂	1	2	yes	maximal, complemented
12	#16863979	C₂	1	2	yes	maximal, complemented
13	#16863978	C₂	1	2	yes	maximal, complemented
14	#16863971	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863966	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863954	C₂	1	2	yes	maximal, complemented
17	#16863924	C₂	1	2	yes	maximal, complemented
18	#124×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	#555×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11761629	C₂²	1	1	yes	characteristic
21	C₂×#11761627	C₂²	1	1	yes	characteristic
22	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
24	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
25	#14524043	C₂²	1	1	yes	characteristic, complemented
26	#14524041	C₂²	1	1	yes	characteristic, complemented
27	#14524041	C₂²	1	1	yes	characteristic, complemented
28	#14524038	C₂²	1	2	yes	complemented
29	#14524038	C₂²	1	2	yes	complemented
30	#14524038	C₂²	1	2	yes	complemented
31	#14524037	C₂²	1	2	yes	complemented
32	#14524037	C₂²	1	2	yes	complemented
33	#14524036	C₂²	1	2	yes	complemented
34	#14524033	C₂²	1	2	yes	complemented
35	#14524032	C₂²	1	1	yes	characteristic
36	#14524032	C₂²	1	1	yes	characteristic, complemented
37	#14524031	C₂²	1	1	yes	characteristic
38	#14524031	C₂²	1	2	yes	complemented
39	#14524031	C₂²	1	1	yes	characteristic, complemented
40	#14524030	C₂²	1	1	yes	characteristic, complemented
41	#14524030	C₂²	1	1	yes	characteristic, complemented
42	#14524029	C₂²	1	2	yes	complemented
43	#14524029	C₂²	1	2	yes	complemented
44	#14524029	C₂²	1	2	yes	complemented
45	#14524029	C₂²	1	2	yes	complemented
46	#14524029	C₂²	1	2	yes	complemented
47	#14524028	C₂²	1	2	yes	—
48	#14524028	C₂²	1	2	yes	complemented
49	#14524028	C₂²	1	2	yes	complemented
50	#14524028	C₂²	1	2	yes	complemented
51	#14524026	C₂²	1	2	yes	complemented
52	#14524026	C₂²	1	2	yes	complemented
53	#14524025	C₂²	1	2	yes	complemented
54	#14524025	C₂²	1	2	yes	complemented
55	#14524025	C₂²	1	2	yes	complemented
56	#14524025	C₂²	1	2	yes	complemented
57	#14524024	C₂²	1	2	yes	complemented
58	#14524024	C₂²	1	2	yes	complemented
59	#14524022	C₂²	1	2	yes	complemented
60	#14524021	C₂²	1	2	yes	complemented
61	#14524021	C₂²	1	2	yes	complemented
62	#14524021	C₂²	1	2	yes	complemented
63	#14524021	C₂²	1	2	yes	complemented
64	#14524020	C₂²	1	2	yes	complemented
65	#14524020	C₂²	1	2	yes	complemented
66	#14524020	C₂²	1	2	yes	complemented
67	#14524019	C₂²	1	2	yes	complemented
68	#14524017	C₂²	1	2	yes	—
69	#14524016	C₂²	1	2	yes	—
70	#14524016	C₂²	1	2	yes	complemented
71	#14524015	C₂²	1	2	yes	—
72	#14524015	C₂²	1	2	yes	complemented
73	#14524015	C₂²	1	2	yes	complemented
74	#14524014	C₂²	1	2	yes	complemented
75	#14524013	C₂²	1	2	yes	—
76	#14524013	C₂²	1	2	yes	—
77	#14524013	C₂²	1	2	yes	complemented
78	#14524011	C₂²	1	2	yes	—
79	#14524011	C₂²	1	2	yes	complemented
80	#14524011	C₂²	1	2	yes	complemented
81	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
82	C₄×D₂₆₈	C₂²	1	2	yes	complemented
83	C₄×D₂₆₈	C₂²	1	2	yes	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	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
88	#14524000	C₂²	1	1	yes	characteristic, complemented
89	#14524000	C₂²	1	2	yes	complemented
90	#14524000	C₂²	1	1	yes	characteristic, 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	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#124×C₆₇	C₂²	1	2	yes	complemented
100	#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#121×C₆₇	C₂²	1	2	yes	complemented
103	#121×C₆₇	C₂²	1	2	yes	complemented
104	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
105	#117×C₆₇	C₂²	1	2	yes	complemented
106	#117×C₆₇	C₂²	1	2	yes	complemented
107	C₂³×D₆₇	C₂³	1	2	yes	—
108	C₂³×D₆₇	C₂³	1	2	yes	—
109	#11761629	—	4	2	no	—
110	#11761627	—	4	2	no	—
111	C₂×Dic₁₃₄	C₂³	1	2	yes	—
112	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
113	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
114	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
115	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
116	Q₈×D₆₇	—	4	2	no	—
117	C₂×D₂₆₈	C₂³	1	2	yes	—
118	C₂×D₂₆₈	C₂³	1	2	yes	—
119	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
120	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
127	D₄×D₆₇	—	4	2	no	—
128	D₄×D₆₇	—	4	4	no	—
129	C₂²×Dic₆₇	C₂³	1	2	yes	—
130	C₂²×Dic₆₇	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	1	yes	characteristic
134	C₂×C₄×D₆₇	C₂³	1	2	yes	—
135	C₂×C₄×D₆₇	C₂³	1	2	yes	—
136	C₂×C₄×D₆₇	C₂³	1	2	yes	—
137	C₂×C₄×D₆₇	C₂³	1	2	yes	—
138	C₄⋊Dic₆₇	C₂³	1	2	yes	—
139	C₄⋊Dic₆₇	C₂³	1	2	yes	—
140	C₄⋊Dic₆₇	C₂³	1	2	yes	—
141	Dic₆₇⋊C₄	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	Dic₆₇⋊C₄	C₂³	1	2	yes	—
149	Dic₆₇⋊C₄	C₂³	1	2	yes	—
150	Dic₆₇⋊C₄	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	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
155	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
156	C₂²⋊Dic₆₇	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	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
173	C₄×Dic₆₇	C₂³	1	2	yes	—
174	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
175	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
176	C₄×Dic₆₇	C₂³	1	2	yes	—
177	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
178	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₆₇	C₂³	1	2	yes	—
181	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×D₄×C₆₇	C₂³	1	2	yes	—
183	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
185	C₂²×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	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	C₄²×C₆₇	C₂³	1	2	yes	—
198	C₄²×C₆₇	C₂³	1	1	yes	characteristic
199	C₂³×C₆₇	C₂⁴	1	2	yes	—
200	C₂³×C₆₇	C₂⁴	1	2	yes	—
201	C₂²×D₆₇	—	2	4	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	—	4	2	no	—
207	C₂²×D₆₇	C₂⁴	1	2	yes	—
208	C₂²×D₆₇	C₂⁴	1	2	yes	—
209	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
210	Q₈×C₆₇	—	4	1	no	—
211	Q₈×C₆₇	—	4	1	no	—
212	D₄×C₆₇	—	4	2	no	—
213	D₄×C₆₇	—	4	1	no	—
214	D₄×C₆₇	—	4	2	no	—
215	D₄×C₆₇	—	4	1	no	—
216	C₂×C₄×C₆₇	—	4	2	no	—
217	C₂×C₄×C₆₇	—	4	2	no	—
218	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
219	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
221	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
223	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
224	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
225	C₂²⋊D₆₇	—	2	4	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	C₂²⋊D₆₇	—	4	2	no	—
231	C₂×Dic₆₇	—	4	2	no	—
232	C₂×Dic₆₇	—	4	2	no	—
233	C₂×Dic₆₇	C₂⁴	1	2	yes	—
234	C₂×Dic₆₇	C₂⁴	1	2	yes	—
235	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
236	C₂×Dic₆₇	C₂⁴	1	2	yes	—
237	C₂×Dic₆₇	C₂⁴	1	2	yes	—
238	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
239	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
240	D₂₆₈	—	2	4	no	—
241	D₂₆₈	—	4	1	no	—
242	D₂₆₈	—	4	2	no	—
243	D₂₆₈	—	4	1	no	—
244	C₄×D₆₇	—	2	2	no	—
245	C₄×D₆₇	—	2	2	no	—
246	C₄×D₆₇	—	2	2	no	—
247	C₄×D₆₇	—	4	2	no	—
248	C₄×D₆₇	—	4	2	no	—
249	C₄×D₆₇	—	4	2	no	—
250	C₄×D₆₇	—	4	2	no	—
251	Dic₁₃₄	—	4	1	no	—
252	Dic₁₃₄	—	4	1	no	—
253	Dic₁₃₄	—	4	1	no	—
254	Dic₁₃₄	—	4	2	no	—
255	Dic₁₃₄	—	4	1	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	—	2	2	no	—
261	C₂²×C₆₇	—	2	2	no	—
262	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
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	—	2	2	no	—
270	C₂×D₆₇	—	8	4	no	—
271	C₂×D₆₇	—	8	4	no	—
272	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
273	C₄×C₆₇	—	2	1	no	—
274	C₄×C₆₇	—	2	1	no	—
275	C₄×C₆₇	—	2	1	no	—
276	C₄×C₆₇	—	2	2	no	—
277	C₄×C₆₇	—	2	2	no	—
278	C₄×C₆₇	—	2	2	no	—
279	C₄×C₆₇	—	2	2	no	—
280	Dic₆₇	—	2	1	no	—
281	Dic₆₇	—	2	1	no	—
282	Dic₆₇	—	2	1	no	—
283	Dic₆₇	—	2	2	no	—
284	Dic₆₇	—	2	2	no	—
285	Dic₆₇	—	2	2	no	—
286	Dic₆₇	—	2	2	no	—
287	C₂×C₆₇	—	4	2	no	—
288	C₂×C₆₇	—	4	2	no	—
289	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₆₇	#585	1	2	yes	—
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	2	no	—
298	H(3,𝔽₄)	—	67	1	no	—
299	#555	—	67	1	no	—
300	#555	D₆₇	1	1	yes	characteristic, complemented
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	1	no	—
311	#536	—	67	1	no	—
312	#534	—	67	2	no	—
313	#529	—	67	2	no	—
314	C₂×#124	—	67	1	no	—
315	C₂×#41	—	67	1	no	—
316	C₂×#41	—	67	1	no	—
317	C₂²×Q₈	—	67	1	no	—
318	C₂²×D₄	—	67	1	no	—
319	C₂²×D₄	—	67	2	no	—
320	C₄⋊Q₈	—	67	1	no	—
321	C₄⋊Q₈	—	67	1	no	—
322	C₄⋊Q₈	—	67	1	no	—
323	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
324	#126	—	67	2	no	—
325	#126	—	67	2	no	—
326	#126	—	67	2	no	—
327	#126	—	67	2	no	—
328	#126	—	67	2	no	—
329	#126	—	67	2	no	—
330	#125	—	67	2	no	—
331	#124	—	67	1	no	—
332	#124	—	67	1	no	—
333	#124	—	67	1	no	—
334	#124	—	67	1	no	—
335	#124	—	67	2	no	—
336	#124	—	67	2	no	—
337	#124	—	67	2	no	—
338	#124	—	67	2	no	—
339	#124	—	67	2	no	—
340	#124	—	67	1	no	—
341	#124	—	67	1	no	—
342	#124	—	67	2	no	—
343	#124	C₂×D₆₇	1	1	yes	characteristic, complemented
344	#124	C₂×D₆₇	1	1	yes	characteristic, complemented
345	#124	C₂×D₆₇	1	2	yes	complemented
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	—	67	2	no	—
354	#123	—	67	2	no	—
355	#123	—	67	2	no	—
356	#123	—	67	2	no	—
357	#123	—	67	2	no	—
358	C₂²⋊Q₈	—	67	2	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	—	67	2	no	—
364	C₂²⋊Q₈	—	67	2	no	—
365	C₂²⋊Q₈	—	67	2	no	—
366	C₂²⋊Q₈	—	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	2	no	—
372	#121	—	67	2	no	—
373	#121	—	67	2	no	—
374	#121	C₂×D₆₇	1	2	yes	complemented
375	#121	C₂×D₆₇	1	2	yes	complemented
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	#120	—	67	2	no	—
382	C₄×Q₈	—	67	2	no	—
383	C₄×D₄	—	67	2	no	—
384	C₄×D₄	—	67	2	no	—
385	C₄×D₄	—	67	2	no	—
386	C₄×D₄	—	67	2	no	—
387	C₄×D₄	—	67	2	no	—
388	C₄×D₄	—	67	2	no	—
389	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
390	#117	—	67	2	no	—
391	#117	—	67	2	no	—
392	#117	—	67	1	no	—
393	#117	—	67	1	no	—
394	#117	C₂×D₆₇	1	2	yes	complemented
395	#117	C₂×D₆₇	1	2	yes	complemented
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	2	no	—
405	#41	—	268	2	no	—
406	C₂×Q₈	—	268	2	no	—
407	C₂×Q₈	—	67	2	no	—
408	C₂×Q₈	—	67	1	no	—
409	C₂×Q₈	—	67	1	no	—
410	C₂×Q₈	—	67	1	no	—
411	C₂×Q₈	—	67	1	no	—
412	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
413	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
414	C₂×D₄	—	268	4	no	—
415	C₂×D₄	—	268	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	2	no	—
422	C₂×D₄	—	67	2	no	—
423	C₂×D₄	—	67	1	no	—
424	C₂×D₄	—	67	1	no	—
425	C₂×D₄	—	67	2	no	—
426	C₂×D₄	C₂²×D₆₇	1	2	yes	—
427	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
428	C₂×D₄	C₂²×D₆₇	1	2	yes	—
429	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
430	C₂²×C₄	—	67	2	no	—
431	C₂²×C₄	—	67	2	no	—
432	C₂²×C₄	—	67	2	no	—
433	C₂²×C₄	—	67	2	no	—
434	C₂²×C₄	—	67	2	no	—
435	C₂²×C₄	—	67	2	no	—
436	C₂²×C₄	—	67	1	no	—
437	C₂²×C₄	—	67	1	no	—
438	C₂²×C₄	—	67	1	no	—
439	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
440	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
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	2	no	—
448	C₄⋊C₄	—	67	2	no	—
449	C₄⋊C₄	—	67	2	no	—
450	C₄⋊C₄	—	67	2	no	—
451	C₄⋊C₄	—	67	2	no	—
452	C₄⋊C₄	—	67	2	no	—
453	C₄⋊C₄	—	67	2	no	—
454	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
455	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
456	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
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	2	no	—
486	C₄²	—	67	1	no	—
487	C₄²	—	67	1	no	—
488	C₄²	—	67	2	no	—
489	C₄²	—	67	1	no	—
490	C₄²	C₂²×D₆₇	1	1	yes	characteristic
491	C₄²	C₂²×D₆₇	1	1	yes	characteristic
492	C₄²	C₂²×D₆₇	1	1	yes	characteristic
493	C₄²	C₂²×D₆₇	1	2	yes	—
494	C₂³	—	268	2	no	—
495	C₂³	—	268	2	no	—
496	C₂³	—	268	2	no	—
497	C₂³	—	268	2	no	—
498	C₂³	—	268	2	no	—
499	C₂³	—	67	1	no	—
500	C₂³	—	67	2	no	—
501	C₂³	—	67	2	no	—
502	C₂³	—	134	4	no	—
503	C₂³	C₂³×D₆₇	1	2	yes	—
504	C₂³	C₂³×D₆₇	1	2	yes	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	268	1	no	—
508	Q₈	—	268	1	no	—
509	Q₈	—	268	1	no	—
510	Q₈	—	268	1	no	—
511	Q₈	—	268	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	2	no	—
516	D₄	—	268	1	no	—
517	D₄	—	268	1	no	—
518	D₄	—	268	2	no	—
519	D₄	—	268	2	no	—
520	D₄	—	268	2	no	—
521	D₄	—	268	2	no	—
522	D₄	—	268	2	no	—
523	D₄	—	268	2	no	—
524	D₄	—	134	4	no	—
525	D₄	—	134	4	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	268	2	no	—
529	C₂×C₄	—	268	2	no	—
530	C₂×C₄	—	268	2	no	—
531	C₂×C₄	—	268	2	no	—
532	C₂×C₄	—	268	2	no	—
533	C₂×C₄	—	268	2	no	—
534	C₂×C₄	—	67	2	no	—
535	C₂×C₄	—	67	2	no	—
536	C₂×C₄	—	67	1	no	—
537	C₂×C₄	—	67	2	no	—
538	C₂×C₄	—	67	2	no	—
539	C₂×C₄	—	67	1	no	—
540	C₂×C₄	—	67	1	no	—
541	C₂×C₄	—	134	2	no	—
542	C₂×C₄	—	134	2	no	—
543	C₂×C₄	—	134	2	no	—
544	C₂×C₄	C₂³×D₆₇	1	2	yes	—
545	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₆₇	1	2	yes	—
549	C₂×C₄	C₂³×D₆₇	1	2	yes	—
550	C₂×C₄	C₂³×D₆₇	1	2	yes	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	536	4	no	—
558	C₂²	—	536	4	no	—
559	C₂²	—	67	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	2	no	—
565	C₂²	—	134	2	no	—
566	C₂²	—	134	2	no	—
567	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	134	1	no	—
576	C₄	—	134	1	no	—
577	C₄	—	134	2	no	—
578	C₄	—	134	1	no	—
579	C₄	—	134	2	no	—
580	C₄	—	134	2	no	—
581	C₄	—	134	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	268	2	no	—
585	C₂	—	268	2	no	—
586	C₂	—	134	2	no	—
587	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
588	C₂	#16864232	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#555×C₆₇	C₂
hypercenter	#555	D₆₇
hypocenter	C₆₇	#3545
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. #16864145	C₂	semidirect
2. #16864141	C₂	semidirect
3. #16864138	C₂	semidirect
4. #16864108	C₂	semidirect
5. #16864075	C₂	semidirect
6. #16864070	C₂	semidirect
7. #16864070	C₂	semidirect
8. #16864039	C₂	semidirect
9. #16864035	C₂	semidirect
10. #16864017	C₂	semidirect
11. #16864010	C₂	semidirect
12. #16863979	C₂	semidirect
13. #16863978	C₂	semidirect
14. #16863971	C₂	semidirect
15. #16863966	C₂	semidirect
16. #16863954	C₂	semidirect
17. #16863924	C₂	semidirect
18. #124×D₆₇	C₂	semidirect
19. #555×C₆₇	C₂	semidirect
22. C₂×Q₈×D₆₇	C₂²	semidirect
24. C₂×D₄×D₆₇	C₂²	semidirect
25. #14524043	C₂²	semidirect
26. #14524041	C₂²	semidirect
27. #14524041	C₂²	semidirect
28. #14524038	C₂²	semidirect
29. #14524038	C₂²	semidirect
30. #14524038	C₂²	semidirect
31. #14524037	C₂²	semidirect
32. #14524037	C₂²	semidirect
33. #14524036	C₂²	semidirect
34. #14524033	C₂²	semidirect
36. #14524032	C₂²	semidirect
38. #14524031	C₂²	semidirect
39. #14524031	C₂²	semidirect
40. #14524030	C₂²	semidirect
41. #14524030	C₂²	semidirect
42. #14524029	C₂²	semidirect
43. #14524029	C₂²	semidirect
44. #14524029	C₂²	semidirect
45. #14524029	C₂²	semidirect
46. #14524029	C₂²	semidirect
48. #14524028	C₂²	semidirect
49. #14524028	C₂²	semidirect
50. #14524028	C₂²	semidirect
51. #14524026	C₂²	semidirect
52. #14524026	C₂²	semidirect
53. #14524025	C₂²	semidirect
54. #14524025	C₂²	semidirect
55. #14524025	C₂²	semidirect
56. #14524025	C₂²	semidirect
57. #14524024	C₂²	semidirect
58. #14524024	C₂²	semidirect
59. #14524022	C₂²	semidirect
60. #14524021	C₂²	semidirect
61. #14524021	C₂²	semidirect
62. #14524021	C₂²	semidirect
63. #14524021	C₂²	semidirect
64. #14524020	C₂²	semidirect
65. #14524020	C₂²	semidirect
66. #14524020	C₂²	semidirect
67. #14524019	C₂²	semidirect
70. #14524016	C₂²	semidirect
72. #14524015	C₂²	semidirect
73. #14524015	C₂²	semidirect
74. #14524014	C₂²	semidirect
77. #14524013	C₂²	semidirect
79. #14524011	C₂²	semidirect
80. #14524011	C₂²	semidirect
81. C₄×Dic₁₃₄	C₂²	semidirect
82. C₄×D₂₆₈	C₂²	semidirect
83. C₄×D₂₆₈	C₂²	semidirect
84. C₄×C₂²⋊D₆₇	C₂²	semidirect
85. C₄×C₂²⋊D₆₇	C₂²	semidirect
86. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
87. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
88. #14524000	C₂²	semidirect
89. #14524000	C₂²	semidirect
90. #14524000	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. C₄⋊Q₈×C₆₇	C₂²	semidirect
99. #124×C₆₇	C₂²	semidirect
100. #124×C₆₇	C₂²	semidirect
101. #124×C₆₇	C₂²	semidirect
102. #121×C₆₇	C₂²	semidirect
103. #121×C₆₇	C₂²	semidirect
104. C₄×D₄×C₆₇	C₂²	semidirect
105. #117×C₆₇	C₂²	semidirect
106. #117×C₆₇	C₂²	semidirect
295. C₆₇	#3545	semidirect
300. #555	D₆₇	semidirect
323. C₄⋊Q₈	C₂×D₆₇	semidirect
343. #124	C₂×D₆₇	semidirect
344. #124	C₂×D₆₇	semidirect
345. #124	C₂×D₆₇	semidirect
374. #121	C₂×D₆₇	semidirect
375. #121	C₂×D₆₇	semidirect
389. C₄×D₄	C₂×D₆₇	semidirect
394. #117	C₂×D₆₇	semidirect
395. #117	C₂×D₆₇	semidirect