Subgroups — #22574314

Order 8576.

1030 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864131	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864130	C₂	1	2	yes	maximal, complemented
3	#16864124	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864111	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864108	C₂	1	2	yes	maximal, complemented
6	#16864092	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864091	C₂	1	2	yes	maximal, complemented
8	#16864086	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864078	C₂	1	2	yes	maximal, complemented
10	#16864067	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864055	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864055	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864017	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864016	C₂	1	2	yes	maximal, complemented
15	#16864001	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863996	C₂	1	2	yes	maximal, complemented
17	#16863930	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863929	C₂	1	2	yes	maximal, complemented
19	#16863929	C₂	1	2	yes	maximal, complemented
20	#16863876	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863873	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#11761628	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761628	C₂²	1	1	yes	characteristic
25	C₂×#11761628	C₂²	1	1	yes	characteristic
26	C₂²×Dic₁₃₄	C₂²	1	1	yes	characteristic
27	#14524043	C₂²	1	1	yes	characteristic
28	#14524041	C₂²	1	2	yes	—
29	#14524040	C₂²	1	1	yes	characteristic
30	#14524039	C₂²	1	2	yes	—
31	#14524038	C₂²	1	2	yes	—
32	#14524038	C₂²	1	2	yes	—
33	#14524037	C₂²	1	2	yes	—
34	#14524036	C₂²	1	2	yes	—
35	#14524035	C₂²	1	1	yes	characteristic
36	#14524035	C₂²	1	1	yes	characteristic
37	#14524033	C₂²	1	2	yes	—
38	#14524033	C₂²	1	2	yes	—
39	#14524033	C₂²	1	2	yes	—
40	#14524032	C₂²	1	2	yes	—
41	#14524031	C₂²	1	1	yes	characteristic
42	#14524031	C₂²	1	1	yes	characteristic
43	#14524029	C₂²	1	2	yes	—
44	#14524029	C₂²	1	2	yes	—
45	#14524029	C₂²	1	2	yes	—
46	#14524029	C₂²	1	2	yes	—
47	#14524029	C₂²	1	2	yes	—
48	#14524028	C₂²	1	2	yes	—
49	#14524028	C₂²	1	2	yes	—
50	#14524028	C₂²	1	2	yes	—
51	#14524028	C₂²	1	2	yes	—
52	#14524026	C₂²	1	2	yes	—
53	#14524025	C₂²	1	2	yes	—
54	#14524025	C₂²	1	2	yes	—
55	#14524024	C₂²	1	2	yes	—
56	#14524022	C₂²	1	1	yes	characteristic
57	#14524022	C₂²	1	1	yes	characteristic
58	#14524021	C₂²	1	2	yes	—
59	#14524021	C₂²	1	2	yes	—
60	#14524021	C₂²	1	2	yes	—
61	#14524017	C₂²	1	1	yes	characteristic
62	#14524017	C₂²	1	1	yes	characteristic
63	#14524017	C₂²	1	1	yes	characteristic
64	#14524017	C₂²	1	1	yes	characteristic
65	#14524016	C₂²	1	2	yes	—
66	#14524016	C₂²	1	2	yes	—
67	#14524016	C₂²	1	2	yes	—
68	#14524016	C₂²	1	2	yes	—
69	#14524015	C₂²	1	2	yes	—
70	#14524015	C₂²	1	2	yes	—
71	#14524015	C₂²	1	2	yes	—
72	#14524014	C₂²	1	2	yes	—
73	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
74	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
75	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
76	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
77	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
78	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
79	#14524008	C₂²	1	2	yes	—
80	#14524008	C₂²	1	2	yes	—
81	#14524008	C₂²	1	2	yes	—
82	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
83	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
84	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
85	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
86	#14524005	C₂²	1	2	yes	—
87	#14524005	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
89	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
91	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
93	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
95	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
96	#14524002	C₂²	1	1	yes	characteristic
97	#14524002	C₂²	1	1	yes	characteristic
98	#14524001	C₂²	1	2	yes	—
99	#14524001	C₂²	1	2	yes	—
100	#14524000	C₂²	1	2	yes	—
101	#14524000	C₂²	1	2	yes	—
102	#14523999	C₂²	1	2	yes	—
103	#14523999	C₂²	1	2	yes	—
104	#14523999	C₂²	1	2	yes	—
105	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
107	C₄²×D₆₇	C₂²	1	2	yes	—
108	#126×C₆₇	C₂²	1	1	yes	characteristic
109	#126×C₆₇	C₂²	1	1	yes	characteristic
110	#125×C₆₇	C₂²	1	1	yes	characteristic
111	#124×C₆₇	C₂²	1	1	yes	characteristic
112	#123×C₆₇	C₂²	1	1	yes	characteristic
113	#123×C₆₇	C₂²	1	1	yes	characteristic
114	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
115	#121×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
120	#117×C₆₇	C₂²	1	1	yes	characteristic
121	#117×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄²×C₆₇	C₂²	1	1	yes	characteristic
123	#11761628	—	2	4	no	—
124	#11761628	—	2	4	no	—
125	C₂×Dic₁₃₄	—	2	4	no	—
126	C₂×Dic₁₃₄	C₂³	1	2	yes	—
127	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₃₄	C₂³	1	2	yes	—
129	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
130	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
131	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
132	C₂×D₂₆₈	C₂³	1	2	yes	—
133	C₂×D₂₆₈	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
140	C₂²×Dic₆₇	C₂³	1	2	yes	—
141	C₂²×Dic₆₇	C₂³	1	2	yes	—
142	C₂×C₄×D₆₇	C₂³	1	2	yes	—
143	C₂×C₄×D₆₇	C₂³	1	2	yes	—
144	C₂×C₄×D₆₇	C₂³	1	2	yes	—
145	C₂×C₄×D₆₇	C₂³	1	2	yes	—
146	C₂×C₄×D₆₇	C₂³	1	2	yes	—
147	C₂×C₄×D₆₇	C₂³	1	2	yes	—
148	C₄⋊Dic₆₇	C₂³	1	2	yes	—
149	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₆₇	C₂³	1	2	yes	—
152	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
154	Dic₆₇⋊C₄	C₂³	1	2	yes	—
155	Dic₆₇⋊C₄	C₂³	1	2	yes	—
156	Dic₆₇⋊C₄	C₂³	1	2	yes	—
157	Dic₆₇⋊C₄	C₂³	1	2	yes	—
158	Dic₆₇⋊C₄	C₂³	1	2	yes	—
159	Dic₆₇⋊C₄	C₂³	1	2	yes	—
160	Dic₆₇⋊C₄	C₂³	1	2	yes	—
161	Dic₆₇⋊C₄	C₂³	1	2	yes	—
162	Dic₆₇⋊C₄	C₂³	1	2	yes	—
163	Dic₆₇⋊C₄	C₂³	1	2	yes	—
164	Dic₆₇⋊C₄	C₂³	1	2	yes	—
165	Dic₆₇⋊C₄	C₂³	1	2	yes	—
166	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
167	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
168	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
169	C₂²⋊Dic₆₇	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	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
182	C₄×Dic₆₇	C₂³	1	2	yes	—
183	C₄×Dic₆₇	C₂³	1	2	yes	—
184	C₄×Dic₆₇	C₂³	1	2	yes	—
185	C₄×Dic₆₇	C₂³	1	2	yes	—
186	C₄×Dic₆₇	C₂³	1	2	yes	—
187	C₄×Dic₆₇	C₂³	1	2	yes	—
188	C₄×Dic₆₇	C₂³	1	2	yes	—
189	C₄×Dic₆₇	C₂³	1	2	yes	—
190	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
216	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₄²×C₆₇	C₂³	1	1	yes	characteristic
220	C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	C₄²×C₆₇	C₂³	1	1	yes	characteristic
223	C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂²×D₆₇	C₂⁴	1	2	yes	—
229	C₂²×D₆₇	C₂⁴	1	2	yes	—
230	Q₈×C₆₇	—	4	1	no	—
231	D₄×C₆₇	—	4	1	no	—
232	D₄×C₆₇	—	4	1	no	—
233	D₄×C₆₇	—	4	1	no	—
234	C₂×C₄×C₆₇	—	2	2	no	—
235	C₂×C₄×C₆₇	—	2	2	no	—
236	C₂×C₄×C₆₇	—	2	2	no	—
237	C₂×C₄×C₆₇	—	4	1	no	—
238	C₂×C₄×C₆₇	—	4	1	no	—
239	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₆₇	—	2	4	no	—
252	C₂²⋊D₆₇	—	2	4	no	—
253	C₂²⋊D₆₇	—	4	2	no	—
254	C₂²⋊D₆₇	—	4	2	no	—
255	C₂²⋊D₆₇	—	4	2	no	—
256	C₂²⋊D₆₇	—	4	2	no	—
257	C₂×Dic₆₇	—	2	4	no	—
258	C₂×Dic₆₇	—	4	2	no	—
259	C₂×Dic₆₇	C₂⁴	1	2	yes	—
260	C₂×Dic₆₇	C₂⁴	1	2	yes	—
261	C₂×Dic₆₇	C₂⁴	1	2	yes	—
262	C₂×Dic₆₇	C₂⁴	1	2	yes	—
263	C₂×Dic₆₇	C₂⁴	1	2	yes	—
264	C₂×Dic₆₇	C₂⁴	1	2	yes	—
265	D₂₆₈	—	2	2	no	—
266	D₂₆₈	—	2	2	no	—
267	D₂₆₈	—	4	2	no	—
268	D₂₆₈	—	4	2	no	—
269	C₄×D₆₇	—	2	4	no	—
270	C₄×D₆₇	—	2	4	no	—
271	C₄×D₆₇	—	4	2	no	—
272	C₄×D₆₇	—	4	2	no	—
273	C₄×D₆₇	—	4	2	no	—
274	C₄×D₆₇	—	4	2	no	—
275	Dic₁₃₄	—	2	2	no	—
276	Dic₁₃₄	—	2	4	no	—
277	Dic₁₃₄	—	4	2	no	—
278	Dic₁₃₄	#41	1	4	yes	—
279	C₂²×C₆₇	—	2	1	no	—
280	C₂²×C₆₇	—	2	1	no	—
281	C₂²×C₆₇	—	2	1	no	—
282	C₂²×C₆₇	—	2	1	no	—
283	C₂²×C₆₇	—	2	1	no	—
284	C₂²×C₆₇	—	2	1	no	—
285	C₂²×C₆₇	—	2	1	no	—
286	C₂²×C₆₇	—	2	1	no	—
287	C₂²×C₆₇	—	2	1	no	—
288	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
289	C₂×D₆₇	—	2	2	no	—
290	C₂×D₆₇	—	2	2	no	—
291	C₂×D₆₇	—	2	2	no	—
292	C₂×D₆₇	—	2	2	no	—
293	C₂×D₆₇	—	2	2	no	—
294	C₂×D₆₇	—	2	2	no	—
295	C₄×C₆₇	—	2	1	no	—
296	C₄×C₆₇	—	2	1	no	—
297	C₄×C₆₇	—	2	1	no	—
298	C₄×C₆₇	—	2	1	no	—
299	C₄×C₆₇	—	2	1	no	—
300	C₄×C₆₇	—	2	1	no	—
301	C₄×C₆₇	—	2	1	no	—
302	C₄×C₆₇	—	2	1	no	—
303	C₄×C₆₇	—	2	1	no	—
304	C₄×C₆₇	—	2	1	no	—
305	C₄×C₆₇	—	2	1	no	—
306	C₄×C₆₇	C₂×#41	1	2	yes	—
307	Dic₆₇	—	2	2	no	—
308	Dic₆₇	—	2	2	no	—
309	Dic₆₇	—	2	2	no	—
310	Dic₆₇	—	2	2	no	—
311	Dic₆₇	—	2	2	no	—
312	Dic₆₇	C₂×#41	1	4	yes	—
313	C₂×C₆₇	—	4	1	no	—
314	C₂×C₆₇	—	4	1	no	—
315	C₂×C₆₇	—	4	1	no	—
316	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
317	C₂×C₆₇	#585	1	1	yes	characteristic
318	C₂×C₆₇	#585	1	1	yes	characteristic
319	D₆₇	—	4	2	no	—
320	D₆₇	—	4	2	no	—
321	#3524	—	67	1	no	maximal, Sylow
322	C₆₇	#3524	1	1	yes	characteristic, complemented, Sylow
323	#559	—	67	2	no	—
324	#559	—	67	1	no	—
325	#557	—	67	1	no	—
326	#555	—	67	2	no	—
327	#555	—	67	1	no	—
328	#553	—	67	2	no	—
329	#553	—	67	1	no	—
330	#552	—	67	2	no	—
331	#552	—	67	1	no	—
332	#550	—	67	1	no	—
333	#548	—	67	1	no	—
334	#548	—	67	1	no	—
335	#542	—	67	2	no	—
336	#542	—	67	1	no	—
337	#540	—	67	2	no	—
338	#540	—	67	1	no	—
339	#529	—	67	2	no	—
340	#529	—	67	2	no	—
341	#529	—	67	1	no	—
342	#529	D₆₇	1	1	yes	characteristic, complemented
343	#520	—	67	1	no	—
344	#519	—	67	1	no	—
345	C₄×#41	—	67	1	no	—
346	C₂×#41	—	67	1	no	—
347	C₂×#41	—	67	1	no	—
348	C₂²×Q₈	—	67	1	no	—
349	C₄⋊Q₈	—	67	2	no	—
350	C₄⋊Q₈	—	67	1	no	—
351	#127	—	67	2	no	—
352	#127	—	67	1	no	—
353	#126	—	67	2	no	—
354	#126	—	67	2	no	—
355	#126	—	67	2	no	—
356	#126	—	67	2	no	—
357	#126	C₂×D₆₇	1	1	yes	characteristic
358	#126	C₂×D₆₇	1	1	yes	characteristic
359	#125	—	67	2	no	—
360	#125	—	67	2	no	—
361	#125	—	67	2	no	—
362	#125	—	67	1	no	—
363	#125	—	67	1	no	—
364	#125	C₂×D₆₇	1	1	yes	characteristic
365	#124	—	67	2	no	—
366	#124	—	67	2	no	—
367	#124	—	67	2	no	—
368	#124	—	67	2	no	—
369	#124	—	67	2	no	—
370	#124	—	67	2	no	—
371	#124	—	67	1	no	—
372	#124	—	67	1	no	—
373	#124	C₂×D₆₇	1	1	yes	characteristic
374	#123	—	67	2	no	—
375	#123	—	67	2	no	—
376	#123	—	67	2	no	—
377	#123	—	67	2	no	—
378	#123	—	67	2	no	—
379	#123	—	67	2	no	—
380	#123	—	67	2	no	—
381	#123	—	67	2	no	—
382	#123	C₂×D₆₇	1	1	yes	characteristic
383	#123	C₂×D₆₇	1	1	yes	characteristic
384	C₂²⋊Q₈	—	67	1	no	—
385	C₂²⋊Q₈	—	67	1	no	—
386	C₂²⋊Q₈	—	67	2	no	—
387	C₂²⋊Q₈	—	67	2	no	—
388	C₂²⋊Q₈	—	67	2	no	—
389	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
390	#121	—	67	2	no	—
391	#121	—	67	2	no	—
392	#121	—	67	2	no	—
393	#121	—	67	2	no	—
394	#121	—	67	1	no	—
395	#121	—	67	1	no	—
396	#121	—	67	1	no	—
397	#121	—	67	1	no	—
398	#121	—	67	2	no	—
399	#121	—	67	2	no	—
400	#121	—	67	2	no	—
401	#121	—	67	2	no	—
402	#121	C₂×D₆₇	1	1	yes	characteristic
403	C₄×Q₈	—	67	2	no	—
404	C₄×Q₈	—	67	2	no	—
405	C₄×Q₈	—	67	2	no	—
406	C₄×Q₈	—	67	1	no	—
407	C₄×Q₈	—	67	1	no	—
408	C₄×Q₈	—	67	1	no	—
409	C₄×Q₈	—	67	1	no	—
410	C₄×Q₈	—	67	1	no	—
411	C₄×Q₈	—	67	1	no	—
412	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
413	C₄×D₄	—	67	2	no	—
414	C₄×D₄	—	67	2	no	—
415	C₄×D₄	—	67	2	no	—
416	C₄×D₄	—	67	2	no	—
417	C₄×D₄	—	67	2	no	—
418	C₄×D₄	—	67	2	no	—
419	C₄×D₄	—	67	2	no	—
420	C₄×D₄	—	67	2	no	—
421	C₄×D₄	—	67	2	no	—
422	C₄×D₄	—	67	2	no	—
423	C₄×D₄	—	67	1	no	—
424	C₄×D₄	—	67	1	no	—
425	C₄×D₄	—	67	1	no	—
426	C₄×D₄	—	67	1	no	—
427	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
428	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
429	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
430	#117	—	67	1	no	—
431	#117	—	67	1	no	—
432	#117	—	67	2	no	—
433	#117	—	67	2	no	—
434	#117	—	67	2	no	—
435	#117	—	67	2	no	—
436	#117	—	67	2	no	—
437	#117	—	67	2	no	—
438	#117	—	67	2	no	—
439	#117	C₂×D₆₇	1	1	yes	characteristic
440	#117	C₂×D₆₇	1	1	yes	characteristic
441	C₂×C₄⋊C₄	—	67	1	no	—
442	C₂×C₄⋊C₄	—	67	2	no	—
443	C₂×C₄²	—	67	2	no	—
444	C₂×C₄²	C₂×D₆₇	1	1	yes	characteristic
445	#41	—	134	4	no	—
446	#41	—	134	4	no	—
447	C₂×Q₈	—	67	2	no	—
448	C₂×Q₈	—	67	1	no	—
449	C₂×Q₈	—	67	2	no	—
450	C₂×Q₈	—	67	1	no	—
451	C₂×Q₈	—	134	4	no	—
452	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
453	C₂×D₄	—	67	2	no	—
454	C₂×D₄	—	67	2	no	—
455	C₂×D₄	—	67	2	no	—
456	C₂×D₄	—	67	2	no	—
457	C₂×D₄	—	67	2	no	—
458	C₂×D₄	—	67	2	no	—
459	C₂×D₄	—	67	2	no	—
460	C₂×D₄	—	67	2	no	—
461	C₂×D₄	—	67	1	no	—
462	C₂×D₄	—	67	1	no	—
463	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
464	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
465	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
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	C₂²×D₆₇	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
478	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
479	C₄⋊C₄	—	67	2	no	—
480	C₄⋊C₄	—	67	2	no	—
481	C₄⋊C₄	—	67	1	no	—
482	C₄⋊C₄	—	67	2	no	—
483	C₄⋊C₄	—	67	1	no	—
484	C₄⋊C₄	—	67	2	no	—
485	C₄⋊C₄	—	67	2	no	—
486	C₄⋊C₄	—	67	1	no	—
487	C₄⋊C₄	—	67	2	no	—
488	C₄⋊C₄	—	67	1	no	—
489	C₄⋊C₄	—	67	2	no	—
490	C₄⋊C₄	—	67	2	no	—
491	C₄⋊C₄	—	67	2	no	—
492	C₄⋊C₄	—	67	2	no	—
493	C₄⋊C₄	—	67	2	no	—
494	C₄⋊C₄	—	67	2	no	—
495	C₄⋊C₄	—	67	2	no	—
496	C₄⋊C₄	—	67	2	no	—
497	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
507	C₂²⋊C₄	—	67	2	no	—
508	C₂²⋊C₄	—	67	2	no	—
509	C₂²⋊C₄	—	67	2	no	—
510	C₂²⋊C₄	—	67	2	no	—
511	C₂²⋊C₄	—	67	2	no	—
512	C₂²⋊C₄	—	67	2	no	—
513	C₂²⋊C₄	—	67	2	no	—
514	C₂²⋊C₄	—	67	2	no	—
515	C₂²⋊C₄	—	67	2	no	—
516	C₂²⋊C₄	—	67	2	no	—
517	C₂²⋊C₄	—	67	2	no	—
518	C₂²⋊C₄	—	67	2	no	—
519	C₂²⋊C₄	—	67	2	no	—
520	C₂²⋊C₄	—	67	2	no	—
521	C₂²⋊C₄	—	67	2	no	—
522	C₂²⋊C₄	—	67	2	no	—
523	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
524	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
525	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
526	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
527	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
528	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
529	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
531	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
533	C₄²	—	67	2	no	—
534	C₄²	—	67	2	no	—
535	C₄²	—	67	2	no	—
536	C₄²	—	67	2	no	—
537	C₄²	—	67	2	no	—
538	C₄²	—	67	2	no	—
539	C₄²	—	67	2	no	—
540	C₄²	—	67	2	no	—
541	C₄²	C₂²×D₆₇	1	1	yes	characteristic
542	C₄²	C₂²×D₆₇	1	1	yes	characteristic
543	C₄²	C₂²×D₆₇	1	1	yes	characteristic
544	C₄²	C₂²×D₆₇	1	1	yes	characteristic
545	C₄²	C₂²×D₆₇	1	1	yes	characteristic
546	C₄²	C₂²×D₆₇	1	1	yes	characteristic
547	C₂³	—	67	2	no	—
548	C₂³	—	67	2	no	—
549	C₂³	C₂³×D₆₇	1	1	yes	characteristic
550	C₂³	C₂³×D₆₇	1	1	yes	characteristic
551	C₂³	C₂³×D₆₇	1	1	yes	characteristic
552	Q₈	—	4	1	no	—
553	Q₈	—	268	2	no	—
554	Q₈	—	67	4	no	—
555	Q₈	—	134	4	no	—
556	Q₈	—	134	2	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	D₄	—	268	2	no	—
561	D₄	—	268	2	no	—
562	D₄	—	268	2	no	—
563	D₄	—	268	2	no	—
564	D₄	—	268	2	no	—
565	D₄	—	268	2	no	—
566	D₄	—	134	4	no	—
567	D₄	—	134	4	no	—
568	D₄	—	134	2	no	—
569	D₄	—	134	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	268	2	no	—
576	C₂×C₄	—	268	2	no	—
577	C₂×C₄	—	268	2	no	—
578	C₂×C₄	—	268	2	no	—
579	C₂×C₄	—	268	2	no	—
580	C₂×C₄	—	67	2	no	—
581	C₂×C₄	—	67	2	no	—
582	C₂×C₄	—	67	2	no	—
583	C₂×C₄	—	67	2	no	—
584	C₂×C₄	—	67	2	no	—
585	C₂×C₄	—	67	2	no	—
586	C₂×C₄	—	134	4	no	—
587	C₂×C₄	—	134	4	no	—
588	C₂×C₄	—	134	4	no	—
589	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	134	2	no	—
611	C₂²	—	134	2	no	—
612	C₂²	—	134	2	no	—
613	C₂²	—	134	2	no	—
614	C₂²	—	134	2	no	—
615	C₂²	—	134	2	no	—
616	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	67	4	no	—
629	C₄	—	134	2	no	—
630	C₄	—	134	2	no	—
631	C₄	—	134	2	no	—
632	C₄	—	134	2	no	—
633	C₄	—	134	2	no	—
634	C₄	#41×D₆₇	1	2	yes	—
635	C₂	—	4	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	4	1	no	—
638	C₂	—	268	2	no	—
639	C₂	—	268	2	no	—
640	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
641	C₂	#16864232	1	1	yes	characteristic
642	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#529×C₆₇	C₂
hypercenter	#529	D₆₇
hypocenter	C₆₇	#3524
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #16864131	C₂	semidirect
2. #16864130	C₂	semidirect
3. #16864124	C₂	semidirect
4. #16864111	C₂	semidirect
5. #16864108	C₂	semidirect
6. #16864092	C₂	semidirect
7. #16864091	C₂	semidirect
8. #16864086	C₂	semidirect
9. #16864078	C₂	semidirect
10. #16864067	C₂	semidirect
11. #16864055	C₂	semidirect
12. #16864055	C₂	semidirect
13. #16864017	C₂	semidirect
14. #16864016	C₂	semidirect
15. #16864001	C₂	semidirect
16. #16863996	C₂	semidirect
17. #16863930	C₂	semidirect
18. #16863929	C₂	semidirect
19. #16863929	C₂	semidirect
20. #16863876	C₂	semidirect
21. #16863873	C₂	semidirect
22. C₄×#11761628	C₂	semidirect
23. #529×C₆₇	C₂	semidirect
322. C₆₇	#3524	semidirect
342. #529	D₆₇	semidirect