Subgroups — #22574906

Order 8576.

958 conjugacy classes of subgroups.

The subgroup lattice has 554 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	#16864150	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864138	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864120	C₂	1	2	yes	maximal, complemented
5	#16864117	C₂	1	2	yes	maximal, complemented
6	#16864113	C₂	1	2	yes	maximal, complemented
7	#16864073	C₂	1	2	yes	maximal, complemented
8	#16864071	C₂	1	2	yes	maximal, complemented
9	#16864069	C₂	1	2	yes	maximal, complemented
10	#16864020	C₂	1	2	yes	maximal, complemented
11	#16864019	C₂	1	2	yes	maximal, complemented
12	#16864012	C₂	1	2	yes	maximal, complemented
13	#16863986	C₂	1	2	yes	maximal, complemented
14	#16863985	C₂	1	2	yes	maximal, complemented
15	#16863982	C₂	1	2	yes	maximal, complemented
16	#16863931	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863931	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863925	C₂	1	1	yes	maximal, characteristic, complemented
19	#563×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#14524042	C₂²	1	2	yes	complemented
21	#14524042	C₂²	1	2	yes	complemented
22	#14524038	C₂²	1	2	yes	complemented
23	#14524038	C₂²	1	2	yes	complemented
24	#14524038	C₂²	1	2	yes	complemented
25	#14524038	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	#14524036	C₂²	1	2	yes	complemented
33	#14524035	C₂²	1	1	yes	characteristic, complemented
34	#14524032	C₂²	1	2	yes	—
35	#14524032	C₂²	1	2	yes	—
36	#14524032	C₂²	1	2	yes	complemented
37	#14524031	C₂²	1	1	yes	characteristic
38	#14524031	C₂²	1	1	yes	characteristic
39	#14524031	C₂²	1	2	yes	complemented
40	#14524029	C₂²	1	2	yes	—
41	#14524029	C₂²	1	2	yes	—
42	#14524029	C₂²	1	2	yes	—
43	#14524029	C₂²	1	2	yes	—
44	#14524029	C₂²	1	2	yes	complemented
45	#14524028	C₂²	1	2	yes	—
46	#14524028	C₂²	1	2	yes	—
47	#14524028	C₂²	1	2	yes	—
48	#14524028	C₂²	1	2	yes	complemented
49	#14524028	C₂²	1	2	yes	complemented
50	#14524027	C₂²	1	2	yes	—
51	#14524025	C₂²	1	2	yes	—
52	#14524025	C₂²	1	2	yes	complemented
53	#14524023	C₂²	1	1	yes	characteristic, complemented
54	#14524023	C₂²	1	1	yes	characteristic, complemented
55	#14524023	C₂²	1	2	yes	complemented
56	#14524023	C₂²	1	2	yes	complemented
57	#14524023	C₂²	1	2	yes	complemented
58	#14524021	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	2	yes	—
64	#14524018	C₂²	1	1	yes	characteristic
65	#14524018	C₂²	1	1	yes	characteristic
66	#14524017	C₂²	1	2	yes	—
67	#14524016	C₂²	1	2	yes	—
68	#14524014	C₂²	1	1	yes	characteristic
69	#14524013	C₂²	1	2	yes	—
70	#14524013	C₂²	1	2	yes	—
71	#14524013	C₂²	1	2	yes	complemented
72	#14524011	C₂²	1	2	yes	—
73	Q₈×Dic₆₇	C₂²	1	2	yes	complemented
74	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
76	#14524008	C₂²	1	2	yes	complemented
77	#14524008	C₂²	1	1	yes	characteristic, complemented
78	#14524008	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₂₆₈	C₂²	1	2	yes	—
80	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
81	#14524005	C₂²	1	1	yes	characteristic
82	#14524005	C₂²	1	1	yes	characteristic
83	#14524005	C₂²	1	2	yes	complemented
84	#14524005	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
86	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
87	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
88	#14524002	C₂²	1	2	yes	complemented
89	#14524001	C₂²	1	2	yes	complemented
90	#14524001	C₂²	1	2	yes	complemented
91	#14524001	C₂²	1	2	yes	complemented
92	#14524000	C₂²	1	2	yes	complemented
93	#14523999	C₂²	1	2	yes	complemented
94	C₂×(C₂×D₆₇)⋊C₄	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	2	yes	complemented
99	#126×C₆₇	C₂²	1	2	yes	complemented
100	#126×C₆₇	C₂²	1	2	yes	complemented
101	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#124×C₆₇	C₂²	1	1	yes	characteristic
104	#123×C₆₇	C₂²	1	2	yes	—
105	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
106	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
107	C₂³×D₆₇	C₂³	1	2	yes	—
108	C₂×Dic₁₃₄	C₂³	1	2	yes	—
109	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
110	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
111	C₂×Dic₁₃₄	C₂³	1	2	yes	—
112	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
113	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
114	C₂×D₂₆₈	C₂³	1	2	yes	—
115	C₂×D₂₆₈	C₂³	1	2	yes	—
116	C₂×D₂₆₈	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
120	C₂²×Dic₆₇	C₂³	1	2	yes	—
121	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
123	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
124	C₂×C₄×D₆₇	C₂³	1	2	yes	—
125	C₂×C₄×D₆₇	C₂³	1	2	yes	—
126	C₂×C₄×D₆₇	C₂³	1	2	yes	—
127	C₂×C₄×D₆₇	C₂³	1	2	yes	—
128	C₄⋊Dic₆₇	C₂³	1	2	yes	—
129	C₄⋊Dic₆₇	C₂³	1	2	yes	—
130	C₄⋊Dic₆₇	C₂³	1	2	yes	—
131	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₆₇	C₂³	1	2	yes	—
133	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₆₇	C₂³	1	2	yes	—
135	Dic₆₇⋊C₄	C₂³	1	2	yes	—
136	Dic₆₇⋊C₄	C₂³	1	2	yes	—
137	Dic₆₇⋊C₄	C₂³	1	2	yes	—
138	Dic₆₇⋊C₄	C₂³	1	2	yes	—
139	Dic₆₇⋊C₄	C₂³	1	2	yes	—
140	Dic₆₇⋊C₄	C₂³	1	2	yes	—
141	Dic₆₇⋊C₄	C₂³	1	2	yes	—
142	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
143	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
144	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
145	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
146	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
147	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
148	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
149	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
150	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
151	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
152	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
153	(C₂×D₆₇)⋊C₄	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	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
165	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
166	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
167	C₄×Dic₆₇	C₂³	1	2	yes	—
168	C₄×Dic₆₇	C₂³	1	2	yes	—
169	C₄×Dic₆₇	C₂³	1	2	yes	—
170	C₄×Dic₆₇	C₂³	1	2	yes	—
171	C₄×Dic₆₇	C₂³	1	2	yes	—
172	C₄×Dic₆₇	C₂³	1	2	yes	—
173	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
174	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
177	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂²⋊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	C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₄²×C₆₇	C₂³	1	2	yes	—
194	C₂³×C₆₇	C₂⁴	1	2	yes	—
195	C₂²×D₆₇	—	4	2	no	—
196	C₂²×D₆₇	—	4	2	no	—
197	C₂²×D₆₇	—	4	2	no	—
198	C₂²×D₆₇	C₂⁴	1	2	yes	—
199	C₂²×D₆₇	C₂⁴	1	2	yes	—
200	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
201	Q₈×C₆₇	—	4	2	no	—
202	Q₈×C₆₇	—	4	1	no	—
203	D₄×C₆₇	—	4	1	no	—
204	C₂×C₄×C₆₇	—	4	2	no	—
205	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
206	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
208	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
209	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²⋊D₆₇	—	4	2	no	—
214	C₂²⋊D₆₇	—	4	2	no	—
215	C₂²⋊D₆₇	—	4	2	no	—
216	C₂×Dic₆₇	—	4	2	no	—
217	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
218	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
219	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
220	C₂×Dic₆₇	C₂⁴	1	2	yes	—
221	C₂×Dic₆₇	C₂⁴	1	2	yes	—
222	C₂×Dic₆₇	C₂⁴	1	2	yes	—
223	C₂×Dic₆₇	C₂⁴	1	2	yes	—
224	D₂₆₈	—	4	2	no	—
225	D₂₆₈	—	4	1	no	—
226	D₂₆₈	—	4	1	no	—
227	D₂₆₈	—	4	2	no	—
228	D₂₆₈	—	4	2	no	—
229	C₄×D₆₇	—	4	2	no	—
230	C₄×D₆₇	—	4	2	no	—
231	C₄×D₆₇	—	4	2	no	—
232	C₄×D₆₇	—	4	1	no	—
233	C₄×D₆₇	—	4	2	no	—
234	C₄×D₆₇	—	4	1	no	—
235	C₄×D₆₇	—	4	1	no	—
236	Dic₁₃₄	—	4	1	no	—
237	Dic₁₃₄	—	4	1	no	—
238	Dic₁₃₄	—	4	2	no	—
239	Dic₁₃₄	—	4	2	no	—
240	C₂²×C₆₇	—	2	2	no	—
241	C₂²×C₆₇	—	2	2	no	—
242	C₂²×C₆₇	—	2	2	no	—
243	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
244	C₂×D₆₇	—	2	1	no	—
245	C₂×D₆₇	—	2	1	no	—
246	C₂×D₆₇	—	2	2	no	—
247	C₂×D₆₇	—	2	2	no	—
248	C₂×D₆₇	—	2	2	no	—
249	C₂×D₆₇	—	2	1	no	—
250	C₂×D₆₇	—	2	2	no	—
251	C₂×D₆₇	—	2	2	no	—
252	C₂×D₆₇	—	2	2	no	—
253	C₂×D₆₇	—	8	4	no	—
254	C₄×C₆₇	—	2	2	no	—
255	C₄×C₆₇	—	2	1	no	—
256	C₄×C₆₇	—	2	2	no	—
257	C₄×C₆₇	—	2	1	no	—
258	C₄×C₆₇	—	2	2	no	—
259	C₄×C₆₇	—	2	1	no	—
260	C₄×C₆₇	—	2	2	no	—
261	C₄×C₆₇	—	2	2	no	—
262	Dic₆₇	—	2	2	no	—
263	Dic₆₇	—	2	2	no	—
264	Dic₆₇	—	2	2	no	—
265	Dic₆₇	—	2	2	no	—
266	Dic₆₇	—	2	1	no	—
267	Dic₆₇	—	2	1	no	—
268	Dic₆₇	—	2	1	no	—
269	C₂×C₆₇	—	4	2	no	—
270	C₂×C₆₇	#585	1	1	yes	characteristic
271	C₂×C₆₇	#585	1	1	yes	characteristic
272	C₂×C₆₇	#585	1	1	yes	characteristic
273	D₆₇	—	4	1	no	—
274	D₆₇	—	4	2	no	—
275	D₆₇	—	4	2	no	—
276	#3568	—	67	1	no	maximal, Sylow
277	C₆₇	#3568	1	1	yes	characteristic, complemented, Sylow
278	#563	—	67	1	no	—
279	#563	—	67	1	no	—
280	#563	D₆₇	1	1	yes	characteristic, complemented
281	H(3,𝔽₄)	—	67	1	no	—
282	#556	—	67	2	no	—
283	#556	—	67	2	no	—
284	#556	—	67	2	no	—
285	#551	—	67	2	no	—
286	#551	—	67	2	no	—
287	#551	—	67	2	no	—
288	#542	—	67	2	no	—
289	#542	—	67	2	no	—
290	#542	—	67	2	no	—
291	#538	—	67	2	no	—
292	#538	—	67	2	no	—
293	#538	—	67	2	no	—
294	#529	—	67	1	no	—
295	#529	—	67	1	no	—
296	#529	—	67	1	no	—
297	C₄⋊Q₈	—	67	2	no	—
298	C₄⋊Q₈	—	67	2	no	—
299	C₄⋊Q₈	C₂×D₆₇	1	2	yes	complemented
300	#126	—	67	2	no	—
301	#126	—	67	2	no	—
302	#126	—	67	2	no	—
303	#126	—	67	2	no	—
304	#126	—	67	2	no	—
305	#126	—	67	2	no	—
306	#126	—	67	2	no	—
307	#126	—	67	2	no	—
308	#126	—	67	2	no	—
309	#126	—	67	2	no	—
310	#126	—	67	2	no	—
311	#126	C₂×D₆₇	1	2	yes	complemented
312	#126	C₂×D₆₇	1	2	yes	complemented
313	#125	—	67	1	no	—
314	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
315	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
316	#124	—	67	2	no	—
317	#124	—	67	2	no	—
318	#124	—	67	2	no	—
319	#124	—	67	2	no	—
320	#124	—	67	2	no	—
321	#124	—	67	2	no	—
322	#124	—	67	2	no	—
323	#124	—	67	2	no	—
324	#124	—	67	1	no	—
325	#124	—	67	1	no	—
326	#124	—	67	2	no	—
327	#124	C₂×D₆₇	1	1	yes	characteristic
328	#123	—	67	2	no	—
329	#123	—	67	2	no	—
330	#123	—	67	2	no	—
331	#123	—	67	2	no	—
332	#123	—	67	2	no	—
333	#123	—	67	2	no	—
334	#123	—	67	2	no	—
335	#123	—	67	2	no	—
336	#123	C₂×D₆₇	1	2	yes	—
337	C₂²⋊Q₈	—	67	1	no	—
338	C₂²⋊Q₈	—	67	2	no	—
339	C₂²⋊Q₈	—	67	1	no	—
340	C₂²⋊Q₈	—	67	1	no	—
341	C₂²⋊Q₈	—	67	2	no	—
342	C₂²⋊Q₈	—	67	2	no	—
343	C₂²⋊Q₈	—	67	2	no	—
344	C₂²⋊Q₈	—	67	2	no	—
345	C₂²⋊Q₈	—	67	2	no	—
346	C₂²⋊Q₈	—	67	2	no	—
347	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
348	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
349	#121	—	67	1	no	—
350	#121	—	67	2	no	—
351	#121	—	67	1	no	—
352	#121	—	67	1	no	—
353	#121	—	67	2	no	—
354	#121	—	67	2	no	—
355	#120	—	67	2	no	—
356	#120	—	67	2	no	—
357	#120	—	67	2	no	—
358	#120	—	67	2	no	—
359	C₄×Q₈	—	67	1	no	—
360	C₄×Q₈	—	67	2	no	—
361	C₄×Q₈	—	67	1	no	—
362	C₄×Q₈	—	67	1	no	—
363	C₄×Q₈	—	67	2	no	—
364	C₄×Q₈	—	67	2	no	—
365	C₄×D₄	—	67	1	no	—
366	C₄×D₄	—	67	2	no	—
367	C₄×D₄	—	67	2	no	—
368	C₄×D₄	—	67	2	no	—
369	C₄×D₄	—	67	1	no	—
370	C₄×D₄	—	67	1	no	—
371	C₄×D₄	—	67	2	no	—
372	C₄×D₄	—	67	2	no	—
373	C₄×D₄	—	67	2	no	—
374	#117	—	67	2	no	—
375	#117	—	67	2	no	—
376	#117	—	67	2	no	—
377	#117	—	67	2	no	—
378	#117	—	67	2	no	—
379	#117	—	67	2	no	—
380	C₂×C₂²⋊C₄	—	67	2	no	—
381	C₂×C₂²⋊C₄	—	67	2	no	—
382	C₂×C₂²⋊C₄	—	67	2	no	—
383	C₂×C₄²	—	67	1	no	—
384	C₂⁴	—	67	2	no	—
385	C₂×Q₈	—	67	2	no	—
386	C₂×Q₈	—	67	2	no	—
387	C₂×Q₈	—	67	1	no	—
388	C₂×Q₈	—	67	1	no	—
389	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
390	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
391	C₂×D₄	—	67	2	no	—
392	C₂×D₄	—	67	2	no	—
393	C₂×D₄	—	67	2	no	—
394	C₂×D₄	—	67	1	no	—
395	C₂×D₄	—	67	1	no	—
396	C₂×D₄	—	67	2	no	—
397	C₂×D₄	—	67	2	no	—
398	C₂×D₄	—	67	2	no	—
399	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
400	C₂²×C₄	—	67	2	no	—
401	C₂²×C₄	—	67	1	no	—
402	C₂²×C₄	—	67	1	no	—
403	C₂²×C₄	—	67	1	no	—
404	C₂²×C₄	—	67	2	no	—
405	C₂²×C₄	—	67	2	no	—
406	C₂²×C₄	—	67	2	no	—
407	C₂²×C₄	—	67	2	no	—
408	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
409	C₄⋊C₄	—	67	2	no	—
410	C₄⋊C₄	—	67	2	no	—
411	C₄⋊C₄	—	67	2	no	—
412	C₄⋊C₄	—	67	2	no	—
413	C₄⋊C₄	—	67	2	no	—
414	C₄⋊C₄	—	67	2	no	—
415	C₄⋊C₄	—	67	2	no	—
416	C₄⋊C₄	—	67	2	no	—
417	C₄⋊C₄	—	67	2	no	—
418	C₄⋊C₄	—	67	1	no	—
419	C₄⋊C₄	—	67	2	no	—
420	C₄⋊C₄	—	67	1	no	—
421	C₄⋊C₄	—	67	2	no	—
422	C₄⋊C₄	—	67	2	no	—
423	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
424	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
425	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
426	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
427	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
428	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
429	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
430	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
432	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
433	C₂²⋊C₄	—	67	2	no	—
434	C₂²⋊C₄	—	67	2	no	—
435	C₂²⋊C₄	—	67	2	no	—
436	C₂²⋊C₄	—	67	2	no	—
437	C₂²⋊C₄	—	67	2	no	—
438	C₂²⋊C₄	—	67	2	no	—
439	C₂²⋊C₄	—	67	2	no	—
440	C₂²⋊C₄	—	67	2	no	—
441	C₂²⋊C₄	—	67	2	no	—
442	C₂²⋊C₄	—	67	2	no	—
443	C₂²⋊C₄	—	67	2	no	—
444	C₂²⋊C₄	—	67	2	no	—
445	C₂²⋊C₄	—	67	2	no	—
446	C₂²⋊C₄	—	67	2	no	—
447	C₂²⋊C₄	—	67	2	no	—
448	C₂²⋊C₄	—	67	2	no	—
449	C₂²⋊C₄	—	67	2	no	—
450	C₂²⋊C₄	—	67	2	no	—
451	C₂²⋊C₄	—	67	2	no	—
452	C₂²⋊C₄	—	67	2	no	—
453	C₂²⋊C₄	—	67	2	no	—
454	C₂²⋊C₄	—	67	2	no	—
455	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
456	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
457	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
458	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
459	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
460	C₄²	—	67	1	no	—
461	C₄²	—	67	1	no	—
462	C₄²	—	67	1	no	—
463	C₄²	—	67	2	no	—
464	C₄²	—	67	2	no	—
465	C₄²	—	67	2	no	—
466	C₄²	—	67	2	no	—
467	C₄²	—	67	2	no	—
468	C₄²	—	67	2	no	—
469	C₄²	C₂²×D₆₇	1	1	yes	characteristic
470	C₄²	C₂²×D₆₇	1	2	yes	—
471	C₂³	—	268	2	no	—
472	C₂³	—	268	2	no	—
473	C₂³	—	268	2	no	—
474	C₂³	—	67	2	no	—
475	C₂³	—	67	2	no	—
476	C₂³	—	67	1	no	—
477	C₂³	C₂³×D₆₇	1	2	yes	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	268	2	no	—
481	Q₈	—	268	2	no	—
482	Q₈	—	268	1	no	—
483	Q₈	—	268	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	268	2	no	—
486	D₄	—	268	2	no	—
487	D₄	—	268	2	no	—
488	D₄	—	268	1	no	—
489	D₄	—	268	1	no	—
490	D₄	—	268	2	no	—
491	D₄	—	268	2	no	—
492	D₄	—	268	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	268	2	no	—
495	C₂×C₄	—	268	1	no	—
496	C₂×C₄	—	268	2	no	—
497	C₂×C₄	—	268	2	no	—
498	C₂×C₄	—	268	1	no	—
499	C₂×C₄	—	268	1	no	—
500	C₂×C₄	—	268	2	no	—
501	C₂×C₄	—	268	2	no	—
502	C₂×C₄	—	67	1	no	—
503	C₂×C₄	—	67	1	no	—
504	C₂×C₄	—	67	1	no	—
505	C₂×C₄	—	67	2	no	—
506	C₂×C₄	—	67	2	no	—
507	C₂×C₄	—	67	2	no	—
508	C₂×C₄	—	67	2	no	—
509	C₂×C₄	C₂³×D₆₇	1	2	yes	—
510	C₂×C₄	C₂³×D₆₇	1	2	yes	—
511	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
512	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
513	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
514	C₂×C₄	C₂³×D₆₇	1	2	yes	—
515	C₂×C₄	C₂³×D₆₇	1	2	yes	—
516	C₂×C₄	C₂³×D₆₇	1	2	yes	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	536	4	no	—
521	C₂²	—	134	1	no	—
522	C₂²	—	134	2	no	—
523	C₂²	—	134	2	no	—
524	C₂²	—	134	1	no	—
525	C₂²	—	134	1	no	—
526	C₂²	—	134	2	no	—
527	C₂²	—	134	2	no	—
528	C₂²	—	134	2	no	—
529	C₂²	—	134	2	no	—
530	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	134	1	no	—
540	C₄	—	134	1	no	—
541	C₄	—	134	1	no	—
542	C₄	—	134	2	no	—
543	C₄	—	134	2	no	—
544	C₄	—	134	2	no	—
545	C₄	—	134	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	268	2	no	—
548	C₂	—	268	2	no	—
549	C₂	—	268	1	no	—
550	C₂	#16864231	1	1	yes	characteristic
551	C₂	#16864233	1	1	yes	characteristic
552	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#563×C₆₇	C₂
hypercenter	#563	D₆₇
hypocenter	C₆₇	#3568
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #16864150	C₂	semidirect
2. #16864150	C₂	semidirect
3. #16864138	C₂	semidirect
4. #16864120	C₂	semidirect
5. #16864117	C₂	semidirect
6. #16864113	C₂	semidirect
7. #16864073	C₂	semidirect
8. #16864071	C₂	semidirect
9. #16864069	C₂	semidirect
10. #16864020	C₂	semidirect
11. #16864019	C₂	semidirect
12. #16864012	C₂	semidirect
13. #16863986	C₂	semidirect
14. #16863985	C₂	semidirect
15. #16863982	C₂	semidirect
16. #16863931	C₂	semidirect
17. #16863931	C₂	semidirect
18. #16863925	C₂	semidirect
19. #563×C₆₇	C₂	semidirect
20. #14524042	C₂²	semidirect
21. #14524042	C₂²	semidirect
22. #14524038	C₂²	semidirect
23. #14524038	C₂²	semidirect
24. #14524038	C₂²	semidirect
25. #14524038	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. #14524036	C₂²	semidirect
33. #14524035	C₂²	semidirect
36. #14524032	C₂²	semidirect
39. #14524031	C₂²	semidirect
44. #14524029	C₂²	semidirect
48. #14524028	C₂²	semidirect
49. #14524028	C₂²	semidirect
52. #14524025	C₂²	semidirect
53. #14524023	C₂²	semidirect
54. #14524023	C₂²	semidirect
55. #14524023	C₂²	semidirect
56. #14524023	C₂²	semidirect
57. #14524023	C₂²	semidirect
58. #14524021	C₂²	semidirect
59. #14524021	C₂²	semidirect
60. #14524020	C₂²	semidirect
61. #14524019	C₂²	semidirect
62. #14524019	C₂²	semidirect
71. #14524013	C₂²	semidirect
73. Q₈×Dic₆₇	C₂²	semidirect
74. Q₈×Dic₆₇	C₂²	semidirect
75. C₄×Dic₁₃₄	C₂²	semidirect
76. #14524008	C₂²	semidirect
77. #14524008	C₂²	semidirect
78. #14524008	C₂²	semidirect
83. #14524005	C₂²	semidirect
84. #14524005	C₂²	semidirect
87. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
88. #14524002	C₂²	semidirect
89. #14524001	C₂²	semidirect
90. #14524001	C₂²	semidirect
91. #14524001	C₂²	semidirect
92. #14524000	C₂²	semidirect
93. #14523999	C₂²	semidirect
94. C₂×(C₂×D₆₇)⋊C₄	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. #126×C₆₇	C₂²	semidirect
100. #126×C₆₇	C₂²	semidirect
101. #125×C₆₇	C₂²	semidirect
102. #125×C₆₇	C₂²	semidirect
105. C₂²⋊Q₈×C₆₇	C₂²	semidirect
106. C₂²⋊Q₈×C₆₇	C₂²	semidirect
277. C₆₇	#3568	semidirect
280. #563	D₆₇	semidirect
299. C₄⋊Q₈	C₂×D₆₇	semidirect
311. #126	C₂×D₆₇	semidirect
312. #126	C₂×D₆₇	semidirect
314. #125	C₂×D₆₇	semidirect
315. #125	C₂×D₆₇	semidirect
347. C₂²⋊Q₈	C₂×D₆₇	semidirect
348. C₂²⋊Q₈	C₂×D₆₇	semidirect