Subgroups — #22574833

Order 8576.

936 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864148	C₂	1	2	yes	maximal, complemented
2	#16864148	C₂	1	2	yes	maximal, complemented
3	#16864113	C₂	1	2	yes	maximal, complemented
4	#16864101	C₂	1	2	yes	maximal, complemented
5	#16864082	C₂	1	2	yes	maximal, complemented
6	#16864081	C₂	1	2	yes	maximal, complemented
7	#16864072	C₂	1	2	yes	maximal, complemented
8	#16864072	C₂	1	2	yes	maximal, complemented
9	#16864027	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864022	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864012	C₂	1	2	yes	maximal, complemented
12	#16864003	C₂	1	2	yes	maximal, complemented
13	#16864003	C₂	1	2	yes	maximal, complemented
14	#16863993	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863987	C₂	1	2	yes	maximal, complemented
16	#16863984	C₂	1	1	yes	maximal, characteristic
17	#16863953	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863930	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#126×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#14524043	C₂²	1	1	yes	characteristic, complemented
21	#14524043	C₂²	1	1	yes	characteristic, complemented
22	#14524042	C₂²	1	2	yes	complemented
23	#14524042	C₂²	1	2	yes	complemented
24	#14524042	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	#14524037	C₂²	1	2	yes	complemented
29	#14524036	C₂²	1	2	yes	—
30	#14524036	C₂²	1	2	yes	—
31	#14524036	C₂²	1	2	yes	—
32	#14524036	C₂²	1	2	yes	—
33	#14524036	C₂²	1	2	yes	—
34	#14524035	C₂²	1	1	yes	characteristic, complemented
35	#14524035	C₂²	1	2	yes	complemented
36	#14524034	C₂²	1	2	yes	complemented
37	#14524034	C₂²	1	2	yes	complemented
38	#14524034	C₂²	1	2	yes	complemented
39	#14524033	C₂²	1	2	yes	complemented
40	#14524033	C₂²	1	2	yes	complemented
41	#14524033	C₂²	1	2	yes	complemented
42	#14524033	C₂²	1	2	yes	complemented
43	#14524033	C₂²	1	2	yes	complemented
44	#14524031	C₂²	1	1	yes	characteristic, complemented
45	#14524029	C₂²	1	2	yes	—
46	#14524029	C₂²	1	2	yes	—
47	#14524029	C₂²	1	2	yes	—
48	#14524028	C₂²	1	2	yes	complemented
49	#14524027	C₂²	1	2	yes	—
50	#14524027	C₂²	1	2	yes	—
51	#14524026	C₂²	1	2	yes	—
52	#14524026	C₂²	1	2	yes	—
53	#14524025	C₂²	1	2	yes	—
54	#14524025	C₂²	1	2	yes	—
55	#14524025	C₂²	1	2	yes	—
56	#14524023	C₂²	1	2	yes	complemented
57	#14524023	C₂²	1	2	yes	complemented
58	#14524022	C₂²	1	1	yes	characteristic
59	#14524022	C₂²	1	2	yes	—
60	#14524022	C₂²	1	1	yes	characteristic
61	#14524022	C₂²	1	2	yes	—
62	#14524022	C₂²	1	1	yes	characteristic
63	#14524022	C₂²	1	2	yes	—
64	#14524021	C₂²	1	2	yes	complemented
65	#14524021	C₂²	1	2	yes	complemented
66	#14524021	C₂²	1	2	yes	complemented
67	#14524020	C₂²	1	2	yes	—
68	#14524020	C₂²	1	2	yes	—
69	#14524020	C₂²	1	2	yes	—
70	#14524020	C₂²	1	2	yes	—
71	#14524020	C₂²	1	2	yes	—
72	#14524020	C₂²	1	2	yes	—
73	#14524017	C₂²	1	1	yes	characteristic
74	#14524016	C₂²	1	2	yes	—
75	#14524012	C₂²	1	2	yes	—
76	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
78	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
80	#14524008	C₂²	1	2	yes	complemented
81	#14524008	C₂²	1	2	yes	complemented
82	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
86	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
87	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
88	#14524002	C₂²	1	2	yes	—
89	#14524002	C₂²	1	2	yes	—
90	#14524001	C₂²	1	2	yes	complemented
91	#14524000	C₂²	1	2	yes	complemented
92	#14523999	C₂²	1	2	yes	—
93	#14523999	C₂²	1	2	yes	—
94	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
95	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
96	#126×C₆₇	C₂²	1	2	yes	—
97	#126×C₆₇	C₂²	1	2	yes	—
98	#126×C₆₇	C₂²	1	2	yes	—
99	#126×C₆₇	C₂²	1	2	yes	—
100	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
106	C₂×C₄²×C₆₇	C₂²	1	1	yes	characteristic
107	C₂×Dic₁₃₄	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×Dic₁₃₄	C₂³	1	1	yes	characteristic
113	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
117	C₂²×Dic₆₇	C₂³	1	2	yes	—
118	C₂²×Dic₆₇	C₂³	1	2	yes	—
119	C₂×C₄×D₆₇	C₂³	1	2	yes	—
120	C₂×C₄×D₆₇	C₂³	1	2	yes	—
121	C₂×C₄×D₆₇	C₂³	1	2	yes	—
122	C₄⋊Dic₆₇	C₂³	1	2	yes	—
123	C₄⋊Dic₆₇	C₂³	1	2	yes	—
124	C₄⋊Dic₆₇	C₂³	1	2	yes	—
125	C₄⋊Dic₆₇	C₂³	1	2	yes	—
126	C₄⋊Dic₆₇	C₂³	1	2	yes	—
127	C₄⋊Dic₆₇	C₂³	1	2	yes	—
128	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
129	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₆₇	C₂³	1	2	yes	—
132	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
133	Dic₆₇⋊C₄	C₂³	1	2	yes	—
134	Dic₆₇⋊C₄	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	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	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	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
155	C₂²⋊Dic₆₇	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	2	yes	—
165	C₄×Dic₆₇	C₂³	1	2	yes	—
166	C₄×Dic₆₇	C₂³	1	2	yes	—
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	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂³×C₆₇	—	2	2	no	—
195	C₂³×C₆₇	—	4	1	no	—
196	C₂³×C₆₇	—	4	1	no	—
197	C₂³×C₆₇	C₂⁴	1	2	yes	—
198	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
199	C₂²×D₆₇	C₂⁴	1	2	yes	—
200	C₂×C₄×C₆₇	—	2	2	no	—
201	C₂×C₄×C₆₇	—	2	2	no	—
202	C₂×C₄×C₆₇	—	4	1	no	—
203	C₂×C₄×C₆₇	—	4	1	no	—
204	C₂×C₄×C₆₇	—	4	1	no	—
205	C₂×C₄×C₆₇	—	4	1	no	—
206	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
208	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²⋊D₆₇	—	2	4	no	—
216	C₂²⋊D₆₇	—	4	2	no	—
217	C₂²⋊D₆₇	—	4	2	no	—
218	C₂×Dic₆₇	—	4	2	no	—
219	C₂×Dic₆₇	—	4	2	no	—
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	C₂×Dic₆₇	C₂⁴	1	2	yes	—
225	C₂×Dic₆₇	C₂⁴	1	2	yes	—
226	C₂×Dic₆₇	C₂⁴	1	2	yes	—
227	D₂₆₈	—	4	1	no	—
228	C₄×D₆₇	—	4	2	no	—
229	C₄×D₆₇	—	4	2	no	—
230	C₄×D₆₇	—	4	2	no	—
231	Dic₁₃₄	—	4	1	no	—
232	Dic₁₃₄	—	4	2	no	—
233	Dic₁₃₄	—	4	2	no	—
234	Dic₁₃₄	—	4	2	no	—
235	Dic₁₃₄	—	4	1	no	—
236	Dic₁₃₄	—	4	1	no	—
237	C₂²×C₆₇	—	2	1	no	—
238	C₂²×C₆₇	—	2	1	no	—
239	C₂²×C₆₇	—	2	2	no	—
240	C₂²×C₆₇	—	2	2	no	—
241	C₂²×C₆₇	—	2	2	no	—
242	C₂²×C₆₇	—	8	2	no	—
243	C₂²×C₆₇	2₋¹⁺⁴	1	2	yes	—
244	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
245	C₂×D₆₇	—	2	2	no	—
246	C₂×D₆₇	—	2	2	no	—
247	C₂×D₆₇	—	2	2	no	—
248	C₄×C₆₇	—	2	1	no	—
249	C₄×C₆₇	—	2	1	no	—
250	C₄×C₆₇	—	2	2	no	—
251	C₄×C₆₇	—	2	1	no	—
252	C₄×C₆₇	—	2	1	no	—
253	C₄×C₆₇	—	2	2	no	—
254	C₄×C₆₇	—	2	2	no	—
255	C₄×C₆₇	—	2	1	no	—
256	C₄×C₆₇	—	2	1	no	—
257	Dic₆₇	—	2	2	no	—
258	Dic₆₇	—	2	2	no	—
259	Dic₆₇	—	2	2	no	—
260	Dic₆₇	—	2	2	no	—
261	Dic₆₇	—	2	2	no	—
262	Dic₆₇	—	2	2	no	—
263	Dic₆₇	—	2	2	no	—
264	C₂×C₆₇	—	2	2	no	—
265	C₂×C₆₇	—	4	2	no	—
266	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
267	C₂×C₆₇	#585	1	1	yes	characteristic
268	C₂×C₆₇	#585	1	1	yes	characteristic
269	D₆₇	—	4	2	no	—
270	#3564	—	67	1	no	maximal, Sylow
271	C₆₇	#3564	1	1	yes	characteristic, complemented, Sylow
272	#563	—	67	2	no	—
273	#563	—	67	2	no	—
274	#556	—	67	2	no	—
275	#554	—	67	2	no	—
276	#552	—	67	2	no	—
277	#552	—	67	2	no	—
278	#551	—	67	2	no	—
279	#551	—	67	2	no	—
280	#544	—	67	1	no	—
281	#543	—	67	1	no	—
282	#542	—	67	2	no	—
283	#541	—	67	2	no	—
284	#541	—	67	2	no	—
285	#539	—	67	2	no	—
286	#539	—	67	1	no	—
287	#538	—	67	1	no	—
288	#533	—	67	1	no	—
289	#529	—	67	1	no	—
290	C₂×#126	D₆₇	1	1	yes	characteristic, complemented
291	C₄⋊Q₈	—	67	2	no	—
292	C₄⋊Q₈	—	67	2	no	—
293	C₄⋊Q₈	—	67	2	no	—
294	C₄⋊Q₈	—	67	1	no	—
295	C₄⋊Q₈	—	67	1	no	—
296	#126	—	67	2	no	—
297	#126	—	67	2	no	—
298	#126	—	67	2	no	—
299	#126	—	67	2	no	—
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	C₂×D₆₇	1	2	yes	—
306	#126	C₂×D₆₇	1	2	yes	—
307	#126	C₂×D₆₇	1	2	yes	—
308	#126	C₂×D₆₇	1	2	yes	—
309	#125	—	67	2	no	—
310	#125	—	67	2	no	—
311	#125	—	67	2	no	—
312	#125	—	67	2	no	—
313	#125	—	67	2	no	—
314	#125	—	67	2	no	—
315	#125	—	67	2	no	—
316	#125	—	67	2	no	—
317	#125	—	67	1	no	—
318	#125	—	67	2	no	—
319	#124	—	67	2	no	—
320	#124	—	67	2	no	—
321	#124	—	67	2	no	—
322	#124	—	67	1	no	—
323	#123	—	67	2	no	—
324	#123	—	67	2	no	—
325	#123	—	67	2	no	—
326	#123	—	67	2	no	—
327	#123	—	67	2	no	—
328	#123	—	67	2	no	—
329	#123	—	67	2	no	—
330	#123	—	67	2	no	—
331	C₂²⋊Q₈	—	67	1	no	—
332	C₂²⋊Q₈	—	67	1	no	—
333	C₂²⋊Q₈	—	67	1	no	—
334	C₂²⋊Q₈	—	67	2	no	—
335	C₂²⋊Q₈	—	67	2	no	—
336	C₂²⋊Q₈	—	67	2	no	—
337	C₂²⋊Q₈	—	67	2	no	—
338	C₂²⋊Q₈	—	67	2	no	—
339	C₂²⋊Q₈	—	67	2	no	—
340	C₂²⋊Q₈	—	67	2	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	—	67	2	no	—
348	#121	—	67	1	no	—
349	#121	—	67	2	no	—
350	#120	—	67	2	no	—
351	C₄×Q₈	—	67	2	no	—
352	C₄×Q₈	—	67	2	no	—
353	C₄×Q₈	—	67	1	no	—
354	C₄×Q₈	—	67	2	no	—
355	C₄×Q₈	—	67	1	no	—
356	C₄×Q₈	—	67	1	no	—
357	C₄×D₄	—	67	2	no	—
358	C₄×D₄	—	67	2	no	—
359	C₄×D₄	—	67	2	no	—
360	C₄×D₄	—	67	2	no	—
361	C₄×D₄	—	67	2	no	—
362	C₄×D₄	—	67	1	no	—
363	#117	—	67	2	no	—
364	#117	—	67	2	no	—
365	#117	—	67	2	no	—
366	#117	—	67	2	no	—
367	#117	—	67	2	no	—
368	#117	—	67	2	no	—
369	C₂×C₄⋊C₄	—	67	2	no	—
370	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	—	67	2	no	—
374	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
377	C₂×C₄²	C₂×D₆₇	1	1	yes	characteristic
378	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
379	C₂×Q₈	—	67	2	no	—
380	C₂×Q₈	—	67	1	no	—
381	C₂×Q₈	—	67	2	no	—
382	C₂×Q₈	—	67	1	no	—
383	C₂×Q₈	—	67	2	no	—
384	C₂×Q₈	—	67	1	no	—
385	C₂×D₄	—	67	2	no	—
386	C₂×D₄	—	67	2	no	—
387	C₂×D₄	—	67	2	no	—
388	C₂×D₄	—	67	1	no	—
389	C₂²×C₄	—	67	2	no	—
390	C₂²×C₄	—	67	2	no	—
391	C₂²×C₄	—	67	2	no	—
392	C₂²×C₄	—	67	2	no	—
393	C₂²×C₄	—	67	2	no	—
394	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
395	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
396	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
397	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
398	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
399	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
400	C₄⋊C₄	—	67	2	no	—
401	C₄⋊C₄	—	67	2	no	—
402	C₄⋊C₄	—	67	2	no	—
403	C₄⋊C₄	—	67	2	no	—
404	C₄⋊C₄	—	67	2	no	—
405	C₄⋊C₄	—	67	2	no	—
406	C₄⋊C₄	—	67	2	no	—
407	C₄⋊C₄	—	67	2	no	—
408	C₄⋊C₄	—	67	2	no	—
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	1	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	2	no	—
419	C₄⋊C₄	—	67	1	no	—
420	C₄⋊C₄	—	67	2	no	—
421	C₄⋊C₄	—	67	2	no	—
422	C₄⋊C₄	—	67	1	no	—
423	C₄⋊C₄	—	67	2	no	—
424	C₄⋊C₄	—	67	1	no	—
425	C₄⋊C₄	—	67	2	no	—
426	C₄⋊C₄	—	67	2	no	—
427	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
428	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
429	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
430	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
431	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
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	C₂²×D₆₇	1	2	yes	—
449	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
450	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
451	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
452	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
453	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
454	C₄²	—	67	2	no	—
455	C₄²	—	67	2	no	—
456	C₄²	—	67	2	no	—
457	C₄²	—	67	2	no	—
458	C₄²	—	67	2	no	—
459	C₄²	—	67	2	no	—
460	C₄²	—	67	2	no	—
461	C₄²	C₂²×D₆₇	1	1	yes	characteristic
462	C₄²	C₂²×D₆₇	1	1	yes	characteristic
463	C₄²	C₂²×D₆₇	1	1	yes	characteristic
464	C₄²	C₂²×D₆₇	1	1	yes	characteristic
465	C₂³	—	2	2	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	67	2	no	—
469	C₂³	C₂³×D₆₇	1	2	yes	—
470	C₂³	C₂³×D₆₇	1	1	yes	characteristic
471	Q₈	—	268	2	no	—
472	Q₈	—	268	2	no	—
473	Q₈	—	268	1	no	—
474	Q₈	—	268	1	no	—
475	Q₈	—	268	2	no	—
476	Q₈	—	268	1	no	—
477	D₄	—	268	1	no	—
478	D₄	—	268	2	no	—
479	D₄	—	268	2	no	—
480	D₄	—	134	4	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	268	2	no	—
488	C₂×C₄	—	268	2	no	—
489	C₂×C₄	—	268	2	no	—
490	C₂×C₄	—	268	2	no	—
491	C₂×C₄	—	268	2	no	—
492	C₂×C₄	—	67	2	no	—
493	C₂×C₄	—	67	2	no	—
494	C₂×C₄	—	67	2	no	—
495	C₂×C₄	—	67	2	no	—
496	C₂×C₄	—	67	2	no	—
497	C₂×C₄	—	67	2	no	—
498	C₂×C₄	—	67	2	no	—
499	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
500	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
501	C₂×C₄	C₂³×D₆₇	1	2	yes	—
502	C₂×C₄	C₂³×D₆₇	1	2	yes	—
503	C₂×C₄	C₂³×D₆₇	1	2	yes	—
504	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
505	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
506	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
507	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	134	2	no	—
515	C₂²	—	134	2	no	—
516	C₂²	—	134	2	no	—
517	C₂²	#14524090	1	2	yes	—
518	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	134	2	no	—
529	C₄	—	134	2	no	—
530	C₄	—	134	2	no	—
531	C₄	—	134	2	no	—
532	C₄	—	134	2	no	—
533	C₄	—	134	2	no	—
534	C₄	—	134	2	no	—
535	C₂	—	2	2	no	—
536	C₂	—	4	2	no	—
537	C₂	—	268	2	no	—
538	C₂	C₂×#14524090	1	1	yes	characteristic
539	C₂	#16864232	1	1	yes	characteristic
540	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	C₂×#126×C₆₇	C₂
hypercenter	C₂×#126	D₆₇
hypocenter	C₆₇	#3564
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. #16864148	C₂	semidirect
2. #16864148	C₂	semidirect
3. #16864113	C₂	semidirect
4. #16864101	C₂	semidirect
5. #16864082	C₂	semidirect
6. #16864081	C₂	semidirect
7. #16864072	C₂	semidirect
8. #16864072	C₂	semidirect
9. #16864027	C₂	semidirect
10. #16864022	C₂	semidirect
11. #16864012	C₂	semidirect
12. #16864003	C₂	semidirect
13. #16864003	C₂	semidirect
14. #16863993	C₂	semidirect
15. #16863987	C₂	semidirect
17. #16863953	C₂	semidirect
18. #16863930	C₂	semidirect
19. C₂×#126×C₆₇	C₂	semidirect
20. #14524043	C₂²	semidirect
21. #14524043	C₂²	semidirect
22. #14524042	C₂²	semidirect
23. #14524042	C₂²	semidirect
24. #14524042	C₂²	semidirect
25. #14524038	C₂²	semidirect
26. #14524038	C₂²	semidirect
27. #14524038	C₂²	semidirect
28. #14524037	C₂²	semidirect
34. #14524035	C₂²	semidirect
35. #14524035	C₂²	semidirect
36. #14524034	C₂²	semidirect
37. #14524034	C₂²	semidirect
38. #14524034	C₂²	semidirect
39. #14524033	C₂²	semidirect
40. #14524033	C₂²	semidirect
41. #14524033	C₂²	semidirect
42. #14524033	C₂²	semidirect
43. #14524033	C₂²	semidirect
44. #14524031	C₂²	semidirect
48. #14524028	C₂²	semidirect
56. #14524023	C₂²	semidirect
57. #14524023	C₂²	semidirect
64. #14524021	C₂²	semidirect
65. #14524021	C₂²	semidirect
66. #14524021	C₂²	semidirect
76. C₄×Dic₁₃₄	C₂²	semidirect
77. C₄×Dic₁₃₄	C₂²	semidirect
78. C₄×Dic₁₃₄	C₂²	semidirect
79. C₄×Dic₁₃₄	C₂²	semidirect
80. #14524008	C₂²	semidirect
81. #14524008	C₂²	semidirect
82. C₄×D₂₆₈	C₂²	semidirect
90. #14524001	C₂²	semidirect
91. #14524000	C₂²	semidirect
94. C₄⋊C₄×D₆₇	C₂²	semidirect
271. C₆₇	#3564	semidirect
290. C₂×#126	D₆₇	semidirect