Subgroups — #22573925

Order 8576.

1040 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864116	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864114	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864113	C₂	1	2	yes	maximal, complemented
4	#16864111	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864110	C₂	1	2	yes	maximal, complemented
6	#16864110	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864095	C₂	1	2	yes	maximal, complemented
8	#16864093	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864084	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864083	C₂	1	2	yes	maximal, complemented
11	#16864081	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864026	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863982	C₂	1	2	yes	maximal, complemented
14	#16863978	C₂	1	2	yes	maximal, complemented
15	#16863975	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863929	C₂	1	2	yes	maximal, complemented
17	#16863928	C₂	1	2	yes	maximal, complemented
18	#16863906	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863905	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863877	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863875	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761628	C₂²	1	1	yes	characteristic
25	C₂×#11761627	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
27	#14524043	C₂²	1	1	yes	characteristic, complemented
28	#14524042	C₂²	1	2	yes	complemented
29	#14524042	C₂²	1	1	yes	characteristic, complemented
30	#14524038	C₂²	1	2	yes	—
31	#14524038	C₂²	1	2	yes	—
32	#14524037	C₂²	1	2	yes	complemented
33	#14524036	C₂²	1	2	yes	—
34	#14524036	C₂²	1	2	yes	—
35	#14524036	C₂²	1	2	yes	complemented
36	#14524036	C₂²	1	2	yes	complemented
37	#14524034	C₂²	1	1	yes	characteristic, complemented
38	#14524034	C₂²	1	2	yes	complemented
39	#14524033	C₂²	1	2	yes	complemented
40	#14524033	C₂²	1	2	yes	complemented
41	#14524030	C₂²	1	2	yes	—
42	#14524030	C₂²	1	2	yes	complemented
43	#14524029	C₂²	1	2	yes	—
44	#14524029	C₂²	1	2	yes	—
45	#14524029	C₂²	1	2	yes	—
46	#14524029	C₂²	1	2	yes	complemented
47	#14524028	C₂²	1	2	yes	—
48	#14524028	C₂²	1	1	yes	characteristic
49	#14524026	C₂²	1	2	yes	—
50	#14524025	C₂²	1	1	yes	characteristic
51	#14524025	C₂²	1	2	yes	—
52	#14524024	C₂²	1	2	yes	—
53	#14524023	C₂²	1	2	yes	—
54	#14524023	C₂²	1	1	yes	characteristic
55	#14524023	C₂²	1	1	yes	characteristic, complemented
56	#14524022	C₂²	1	1	yes	characteristic
57	#14524022	C₂²	1	1	yes	characteristic, complemented
58	#14524021	C₂²	1	2	yes	—
59	#14524021	C₂²	1	1	yes	characteristic
60	#14524020	C₂²	1	1	yes	characteristic
61	#14524020	C₂²	1	2	yes	complemented
62	#14524017	C₂²	1	2	yes	—
63	#14524016	C₂²	1	1	yes	characteristic
64	#14524016	C₂²	1	2	yes	—
65	#14524015	C₂²	1	2	yes	—
66	#14524015	C₂²	1	1	yes	characteristic
67	#14524015	C₂²	1	2	yes	complemented
68	#14524014	C₂²	1	2	yes	—
69	#14524014	C₂²	1	1	yes	characteristic
70	#14524014	C₂²	1	2	yes	—
71	#14524014	C₂²	1	1	yes	characteristic, complemented
72	#14524013	C₂²	1	1	yes	characteristic
73	#14524011	C₂²	1	1	yes	characteristic
74	#14524011	C₂²	1	2	yes	—
75	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
77	#14524008	C₂²	1	1	yes	characteristic, complemented
78	#14524008	C₂²	1	2	yes	complemented
79	#14524008	C₂²	1	2	yes	complemented
80	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
81	D₄×Dic₆₇	C₂²	1	2	yes	—
82	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
83	#14524005	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
89	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
90	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
91	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
92	#14524002	C₂²	1	1	yes	characteristic
93	#14524002	C₂²	1	2	yes	complemented
94	#14524002	C₂²	1	2	yes	complemented
95	#14524002	C₂²	1	1	yes	characteristic, complemented
96	#14524001	C₂²	1	1	yes	characteristic
97	#14524001	C₂²	1	1	yes	characteristic
98	#14524001	C₂²	1	1	yes	characteristic
99	#14524001	C₂²	1	2	yes	complemented
100	#14524001	C₂²	1	1	yes	characteristic, complemented
101	#14524000	C₂²	1	1	yes	characteristic
102	#14524000	C₂²	1	2	yes	—
103	#14523999	C₂²	1	2	yes	—
104	#14523999	C₂²	1	2	yes	complemented
105	#14523999	C₂²	1	2	yes	complemented
106	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₄²×D₆₇	C₂²	1	2	yes	—
112	#126×C₆₇	C₂²	1	2	yes	complemented
113	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#123×C₆₇	C₂²	1	2	yes	—
115	#121×C₆₇	C₂²	1	1	yes	characteristic
116	#121×C₆₇	C₂²	1	2	yes	—
117	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
120	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#117×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	#11761628	—	2	4	no	—
125	#11761627	—	2	4	no	—
126	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₃₄	C₂³	1	2	yes	—
129	C₂×Dic₁₃₄	C₂³	1	2	yes	—
130	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
131	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
139	C₂²×Dic₆₇	C₂³	1	2	yes	—
140	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
141	C₂²×Dic₆₇	C₂³	1	2	yes	—
142	C₂×C₄×D₆₇	—	2	4	no	—
143	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₆₇	C₂³	1	2	yes	—
148	C₂×C₄×D₆₇	C₂³	1	2	yes	—
149	C₂×C₄×D₆₇	C₂³	1	2	yes	—
150	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₆₇	C₂³	1	2	yes	—
155	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₆₇	C₂³	1	2	yes	—
157	C₄⋊Dic₆₇	C₂³	1	2	yes	—
158	C₄⋊Dic₆₇	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	1	yes	characteristic
163	Dic₆₇⋊C₄	C₂³	1	2	yes	—
164	Dic₆₇⋊C₄	C₂³	1	2	yes	—
165	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₆₇⋊C₄	C₂³	1	2	yes	—
168	Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	Dic₆₇⋊C₄	C₂³	1	2	yes	—
170	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₆₇⋊C₄	C₂³	1	2	yes	—
172	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
174	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
181	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
193	C₄×Dic₆₇	C₂³	1	2	yes	—
194	C₄×Dic₆₇	C₂³	1	2	yes	—
195	C₄×Dic₆₇	C₂³	1	2	yes	—
196	C₄×Dic₆₇	C₂³	1	2	yes	—
197	C₄×Dic₆₇	C₂³	1	2	yes	—
198	C₄×Dic₆₇	C₂³	1	2	yes	—
199	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₆₇	C₂³	1	2	yes	—
201	C₄×Dic₆₇	C₂³	1	2	yes	—
202	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×D₄×C₆₇	C₂³	1	2	yes	—
205	C₂×D₄×C₆₇	C₂³	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
209	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
210	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₄²×C₆₇	C₂³	1	2	yes	—
224	C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂³×C₆₇	C₂⁴	1	2	yes	—
227	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂²×D₆₇	—	2	2	no	—
229	C₂²×D₆₇	—	4	1	no	—
230	C₂²×D₆₇	—	4	1	no	—
231	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
233	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
234	D₄×C₆₇	—	2	2	no	—
235	D₄×C₆₇	—	4	1	no	—
236	D₄×C₆₇	—	4	2	no	—
237	D₄×C₆₇	—	4	2	no	—
238	C₂×C₄×C₆₇	—	2	2	no	—
239	C₂×C₄×C₆₇	—	2	2	no	—
240	C₂×C₄×C₆₇	—	4	2	no	—
241	C₂×C₄×C₆₇	—	4	2	no	—
242	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
249	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₆₇	—	2	4	no	—
251	C₂²⋊D₆₇	—	2	2	no	—
252	C₂²⋊D₆₇	—	2	2	no	—
253	C₂²⋊D₆₇	—	4	1	no	—
254	C₂²⋊D₆₇	—	4	2	no	—
255	C₂²⋊D₆₇	—	4	2	no	—
256	C₂²⋊D₆₇	—	4	1	no	—
257	C₂×Dic₆₇	—	2	2	no	—
258	C₂×Dic₆₇	—	2	4	no	—
259	C₂×Dic₆₇	—	4	2	no	—
260	C₂×Dic₆₇	C₂⁴	1	2	yes	—
261	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₆₇	C₂⁴	1	2	yes	—
264	C₂×Dic₆₇	C₂⁴	1	2	yes	—
265	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₆₇	C₂⁴	1	2	yes	—
267	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
269	D₂₆₈	—	2	2	no	—
270	D₂₆₈	—	4	1	no	—
271	C₄×D₆₇	—	2	2	no	—
272	C₄×D₆₇	—	2	2	no	—
273	C₄×D₆₇	—	2	2	no	—
274	C₄×D₆₇	—	2	2	no	—
275	C₄×D₆₇	—	4	2	no	—
276	C₄×D₆₇	—	4	2	no	—
277	C₄×D₆₇	—	4	2	no	—
278	C₄×D₆₇	#41	1	4	yes	—
279	Dic₁₃₄	—	2	2	no	—
280	Dic₁₃₄	—	2	2	no	—
281	Dic₁₃₄	—	4	2	no	—
282	Dic₁₃₄	—	4	2	no	—
283	C₂²×C₆₇	—	2	2	no	—
284	C₂²×C₆₇	—	2	1	no	—
285	C₂²×C₆₇	—	2	1	no	—
286	C₂²×C₆₇	—	2	2	no	—
287	C₂²×C₆₇	—	2	2	no	—
288	C₂²×C₆₇	—	2	1	no	—
289	C₂²×C₆₇	—	2	1	no	—
290	C₂²×C₆₇	—	2	1	no	—
291	C₂²×C₆₇	—	2	1	no	—
292	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
293	C₂×D₆₇	—	2	1	no	—
294	C₂×D₆₇	—	2	1	no	—
295	C₂×D₆₇	—	2	1	no	—
296	C₂×D₆₇	—	2	1	no	—
297	C₂×D₆₇	—	2	1	no	—
298	C₂×D₆₇	—	2	1	no	—
299	C₂×D₆₇	—	2	1	no	—
300	C₂×D₆₇	—	2	1	no	—
301	C₂×D₆₇	—	4	4	no	—
302	C₂×D₆₇	C₂×#41	1	2	yes	—
303	C₄×C₆₇	—	2	1	no	—
304	C₄×C₆₇	—	2	1	no	—
305	C₄×C₆₇	—	2	1	no	—
306	C₄×C₆₇	—	2	2	no	—
307	C₄×C₆₇	—	2	2	no	—
308	C₄×C₆₇	—	2	2	no	—
309	C₄×C₆₇	—	2	1	no	—
310	C₄×C₆₇	C₂×#41	1	2	yes	—
311	Dic₆₇	—	2	1	no	—
312	Dic₆₇	—	2	2	no	—
313	Dic₆₇	—	2	1	no	—
314	Dic₆₇	—	2	1	no	—
315	Dic₆₇	—	2	2	no	—
316	Dic₆₇	—	2	2	no	—
317	Dic₆₇	—	2	2	no	—
318	Dic₆₇	—	2	1	no	—
319	Dic₆₇	C₂×#41	1	2	yes	—
320	C₂×C₆₇	—	4	1	no	—
321	C₂×C₆₇	—	4	2	no	—
322	C₂×C₆₇	—	4	1	no	—
323	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
324	C₂×C₆₇	#585	1	1	yes	characteristic
325	C₂×C₆₇	#585	1	1	yes	characteristic
326	D₆₇	—	2	2	no	—
327	D₆₇	—	4	1	no	—
328	D₆₇	—	4	1	no	—
329	#3493	—	67	1	no	maximal, Sylow
330	C₆₇	#3493	1	1	yes	characteristic, complemented, Sylow
331	#556	—	67	2	no	—
332	#556	—	67	1	no	—
333	#556	—	67	1	no	—
334	#555	—	67	2	no	—
335	#555	—	67	1	no	—
336	#555	—	67	1	no	—
337	#553	—	67	1	no	—
338	#553	—	67	2	no	—
339	#553	D₆₇	1	1	yes	characteristic, complemented
340	#552	—	67	1	no	—
341	#552	—	67	2	no	—
342	#552	—	67	1	no	—
343	#544	—	67	1	no	—
344	#538	—	67	2	no	—
345	#538	—	67	2	no	—
346	#537	—	67	1	no	—
347	#529	—	67	2	no	—
348	#529	—	67	2	no	—
349	#525	—	67	1	no	—
350	#525	—	67	1	no	—
351	#520	—	67	1	no	—
352	#520	—	67	1	no	—
353	C₂×#117	—	67	1	no	—
354	C₂×#41	—	67	1	no	—
355	C₂×#41	—	67	1	no	—
356	C₂³×C₄	—	67	1	no	—
357	C₄⋊Q₈	—	67	2	no	—
358	C₄⋊Q₈	—	67	1	no	—
359	C₄⋊Q₈	—	67	1	no	—
360	#126	—	67	2	no	—
361	#126	—	67	2	no	—
362	#126	—	67	2	no	—
363	#126	—	67	2	no	—
364	#126	—	67	2	no	—
365	#126	—	67	2	no	—
366	#126	—	67	2	no	—
367	#126	C₂×D₆₇	1	2	yes	complemented
368	#125	—	67	2	no	—
369	#125	—	67	2	no	—
370	#125	—	67	2	no	—
371	#125	—	67	1	no	—
372	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
373	#124	—	67	2	no	—
374	#124	—	67	2	no	—
375	#124	—	67	2	no	—
376	#124	—	67	2	no	—
377	#124	—	67	2	no	—
378	#124	—	67	2	no	—
379	#123	—	67	2	no	—
380	#123	—	67	2	no	—
381	#123	—	67	1	no	—
382	#123	—	67	2	no	—
383	#123	—	67	2	no	—
384	#123	—	67	1	no	—
385	#123	C₂×D₆₇	1	2	yes	—
386	C₂²⋊Q₈	—	67	1	no	—
387	C₂²⋊Q₈	—	67	1	no	—
388	C₂²⋊Q₈	—	67	1	no	—
389	C₂²⋊Q₈	—	67	1	no	—
390	C₂²⋊Q₈	—	67	2	no	—
391	C₂²⋊Q₈	—	67	2	no	—
392	C₂²⋊Q₈	—	67	1	no	—
393	C₂²⋊Q₈	—	67	1	no	—
394	C₂²⋊Q₈	—	67	2	no	—
395	#121	—	67	1	no	—
396	#121	—	67	1	no	—
397	#121	—	67	2	no	—
398	#121	—	67	1	no	—
399	#121	—	67	2	no	—
400	#121	—	67	2	no	—
401	#121	—	67	2	no	—
402	#121	—	67	2	no	—
403	#121	—	67	1	no	—
404	#121	—	67	2	no	—
405	#121	C₂×D₆₇	1	1	yes	characteristic
406	#121	C₂×D₆₇	1	2	yes	—
407	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
408	#120	—	67	1	no	—
409	#120	—	67	2	no	—
410	#120	—	67	1	no	—
411	C₄×Q₈	—	67	2	no	—
412	C₄×Q₈	—	67	1	no	—
413	C₄×Q₈	—	67	2	no	—
414	C₄×Q₈	—	67	1	no	—
415	C₄×Q₈	—	67	2	no	—
416	C₄×D₄	—	67	1	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	1	no	—
422	C₄×D₄	—	67	1	no	—
423	C₄×D₄	—	67	2	no	—
424	C₄×D₄	—	67	2	no	—
425	C₄×D₄	—	67	2	no	—
426	C₄×D₄	—	67	2	no	—
427	C₄×D₄	—	67	1	no	—
428	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
429	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
430	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
431	#117	—	67	1	no	—
432	#117	—	67	1	no	—
433	#117	—	67	2	no	—
434	#117	—	67	2	no	—
435	#117	—	67	1	no	—
436	#117	—	67	1	no	—
437	#117	—	67	1	no	—
438	#117	—	67	1	no	—
439	#117	—	67	2	no	—
440	#117	—	67	2	no	—
441	#117	—	67	2	no	—
442	#117	—	67	2	no	—
443	#117	—	67	2	no	—
444	#117	—	67	1	no	—
445	#117	C₂×D₆₇	1	1	yes	characteristic
446	C₂×C₄⋊C₄	—	67	2	no	—
447	C₂×C₄⋊C₄	—	67	1	no	—
448	C₂×C₄⋊C₄	—	67	1	no	—
449	C₂×C₄⋊C₄	—	67	1	no	—
450	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
451	C₂×C₂²⋊C₄	—	67	2	no	—
452	C₂×C₄²	—	67	2	no	—
453	C₂⁴	—	67	1	no	—
454	#41	—	134	4	no	—
455	#41	—	134	4	no	—
456	C₂×Q₈	—	67	2	no	—
457	C₂×Q₈	—	67	2	no	—
458	C₂×Q₈	—	67	1	no	—
459	C₂×Q₈	—	67	1	no	—
460	C₂×D₄	—	67	1	no	—
461	C₂×D₄	—	67	2	no	—
462	C₂×D₄	—	67	1	no	—
463	C₂×D₄	—	67	2	no	—
464	C₂×D₄	—	67	1	no	—
465	C₂×D₄	—	67	2	no	—
466	C₂×D₄	—	67	1	no	—
467	C₂×D₄	—	67	1	no	—
468	C₂×D₄	—	67	1	no	—
469	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
470	C₂×D₄	C₂²×D₆₇	1	2	yes	—
471	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
472	C₂×D₄	C₂²×D₆₇	1	2	yes	—
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	1	no	—
478	C₂²×C₄	—	67	2	no	—
479	C₂²×C₄	—	67	1	no	—
480	C₂²×C₄	—	67	1	no	—
481	C₂²×C₄	—	67	1	no	—
482	C₂²×C₄	—	67	1	no	—
483	C₂²×C₄	—	67	1	no	—
484	C₂²×C₄	—	134	4	no	—
485	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
488	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
489	C₄⋊C₄	—	67	2	no	—
490	C₄⋊C₄	—	67	1	no	—
491	C₄⋊C₄	—	67	1	no	—
492	C₄⋊C₄	—	67	2	no	—
493	C₄⋊C₄	—	67	1	no	—
494	C₄⋊C₄	—	67	2	no	—
495	C₄⋊C₄	—	67	2	no	—
496	C₄⋊C₄	—	67	2	no	—
497	C₄⋊C₄	—	67	1	no	—
498	C₄⋊C₄	—	67	1	no	—
499	C₄⋊C₄	—	67	1	no	—
500	C₄⋊C₄	—	67	2	no	—
501	C₄⋊C₄	—	67	1	no	—
502	C₄⋊C₄	—	67	2	no	—
503	C₄⋊C₄	—	67	2	no	—
504	C₄⋊C₄	—	67	2	no	—
505	C₄⋊C₄	—	67	1	no	—
506	C₄⋊C₄	—	67	2	no	—
507	C₄⋊C₄	—	67	2	no	—
508	C₄⋊C₄	—	67	2	no	—
509	C₄⋊C₄	—	67	2	no	—
510	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
514	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
517	C₂²⋊C₄	—	67	2	no	—
518	C₂²⋊C₄	—	67	1	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	—	67	2	no	—
524	C₂²⋊C₄	—	67	1	no	—
525	C₂²⋊C₄	—	67	2	no	—
526	C₂²⋊C₄	—	67	2	no	—
527	C₂²⋊C₄	—	67	2	no	—
528	C₂²⋊C₄	—	67	1	no	—
529	C₂²⋊C₄	—	67	2	no	—
530	C₂²⋊C₄	—	67	1	no	—
531	C₂²⋊C₄	—	67	1	no	—
532	C₂²⋊C₄	—	67	2	no	—
533	C₂²⋊C₄	—	67	2	no	—
534	C₂²⋊C₄	—	67	1	no	—
535	C₂²⋊C₄	—	67	2	no	—
536	C₂²⋊C₄	—	67	1	no	—
537	C₂²⋊C₄	—	67	1	no	—
538	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
544	C₄²	—	67	2	no	—
545	C₄²	—	67	2	no	—
546	C₄²	—	67	2	no	—
547	C₄²	—	67	2	no	—
548	C₄²	—	67	2	no	—
549	C₄²	—	67	2	no	—
550	C₄²	—	67	2	no	—
551	C₄²	—	67	2	no	—
552	C₄²	—	67	1	no	—
553	C₄²	C₂²×D₆₇	1	2	yes	—
554	C₄²	C₂²×D₆₇	1	1	yes	characteristic
555	C₂³	—	268	1	no	—
556	C₂³	—	268	1	no	—
557	C₂³	—	67	1	no	—
558	C₂³	—	67	1	no	—
559	C₂³	—	67	1	no	—
560	C₂³	—	134	2	no	—
561	C₂³	C₂³×D₆₇	1	1	yes	characteristic
562	C₂³	C₂³×D₆₇	1	1	yes	characteristic
563	C₂³	C₂³×D₆₇	1	2	yes	—
564	Q₈	—	268	2	no	—
565	Q₈	—	268	2	no	—
566	Q₈	—	134	2	no	—
567	Q₈	—	134	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	1	no	—
572	D₄	—	268	1	no	—
573	D₄	—	268	1	no	—
574	D₄	—	268	2	no	—
575	D₄	—	268	2	no	—
576	D₄	—	268	1	no	—
577	D₄	—	134	2	no	—
578	D₄	—	134	2	no	—
579	D₄	—	134	2	no	—
580	D₄	—	134	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	268	2	no	—
586	C₂×C₄	—	268	2	no	—
587	C₂×C₄	—	268	2	no	—
588	C₂×C₄	—	268	2	no	—
589	C₂×C₄	—	67	1	no	—
590	C₂×C₄	—	67	4	no	—
591	C₂×C₄	—	67	1	no	—
592	C₂×C₄	—	67	2	no	—
593	C₂×C₄	—	67	1	no	—
594	C₂×C₄	—	67	2	no	—
595	C₂×C₄	—	67	1	no	—
596	C₂×C₄	—	67	2	no	—
597	C₂×C₄	—	67	2	no	—
598	C₂×C₄	—	67	1	no	—
599	C₂×C₄	—	134	2	no	—
600	C₂×C₄	—	134	2	no	—
601	C₂×C₄	—	134	2	no	—
602	C₂×C₄	—	134	4	no	—
603	C₂×C₄	—	134	2	no	—
604	C₂×C₄	—	134	2	no	—
605	C₂×C₄	C₂³×D₆₇	1	2	yes	—
606	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₆₇	1	2	yes	—
610	C₂×C₄	C₂³×D₆₇	1	2	yes	—
611	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	268	4	no	—
623	C₂²	—	67	2	no	—
624	C₂²	—	134	1	no	—
625	C₂²	—	134	1	no	—
626	C₂²	—	134	1	no	—
627	C₂²	—	134	1	no	—
628	C₂²	—	134	1	no	—
629	C₂²	—	134	1	no	—
630	C₂²	—	134	1	no	—
631	C₂²	—	134	1	no	—
632	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	67	2	no	—
641	C₄	—	134	1	no	—
642	C₄	—	134	2	no	—
643	C₄	—	134	1	no	—
644	C₄	—	134	2	no	—
645	C₄	—	134	1	no	—
646	C₄	—	134	2	no	—
647	C₄	—	134	1	no	—
648	C₄	—	134	2	no	—
649	C₄	#41×D₆₇	1	2	yes	—
650	C₂	—	4	1	no	—
651	C₂	—	4	1	no	—
652	C₂	—	4	2	no	—
653	C₂	—	268	1	no	—
654	C₂	—	268	1	no	—
655	C₂	—	134	2	no	—
656	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
657	C₂	#16864231	1	1	yes	characteristic
658	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#553×C₆₇	C₂
hypercenter	#553	D₆₇
hypocenter	C₆₇	#3493
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #16864116	C₂	semidirect
2. #16864114	C₂	semidirect
3. #16864113	C₂	semidirect
4. #16864111	C₂	semidirect
5. #16864110	C₂	semidirect
6. #16864110	C₂	semidirect
7. #16864095	C₂	semidirect
8. #16864093	C₂	semidirect
9. #16864084	C₂	semidirect
10. #16864083	C₂	semidirect
11. #16864081	C₂	semidirect
12. #16864026	C₂	semidirect
13. #16863982	C₂	semidirect
14. #16863978	C₂	semidirect
15. #16863975	C₂	semidirect
16. #16863929	C₂	semidirect
17. #16863928	C₂	semidirect
18. #16863906	C₂	semidirect
19. #16863905	C₂	semidirect
20. #16863877	C₂	semidirect
21. #16863875	C₂	semidirect
22. #117×D₆₇	C₂	semidirect
23. #553×C₆₇	C₂	semidirect
27. #14524043	C₂²	semidirect
28. #14524042	C₂²	semidirect
29. #14524042	C₂²	semidirect
32. #14524037	C₂²	semidirect
35. #14524036	C₂²	semidirect
36. #14524036	C₂²	semidirect
37. #14524034	C₂²	semidirect
38. #14524034	C₂²	semidirect
39. #14524033	C₂²	semidirect
40. #14524033	C₂²	semidirect
42. #14524030	C₂²	semidirect
46. #14524029	C₂²	semidirect
55. #14524023	C₂²	semidirect
57. #14524022	C₂²	semidirect
61. #14524020	C₂²	semidirect
67. #14524015	C₂²	semidirect
71. #14524014	C₂²	semidirect
75. C₄×Dic₁₃₄	C₂²	semidirect
76. C₄×Dic₁₃₄	C₂²	semidirect
77. #14524008	C₂²	semidirect
78. #14524008	C₂²	semidirect
79. #14524008	C₂²	semidirect
82. D₄×Dic₆₇	C₂²	semidirect
88. C₄×C₂²⋊D₆₇	C₂²	semidirect
91. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
93. #14524002	C₂²	semidirect
94. #14524002	C₂²	semidirect
95. #14524002	C₂²	semidirect
99. #14524001	C₂²	semidirect
100. #14524001	C₂²	semidirect
104. #14523999	C₂²	semidirect
105. #14523999	C₂²	semidirect
106. C₂×Dic₆₇⋊C₄	C₂²	semidirect
109. C₄⋊C₄×D₆₇	C₂²	semidirect
112. #126×C₆₇	C₂²	semidirect
113. #125×C₆₇	C₂²	semidirect
117. #121×C₆₇	C₂²	semidirect
119. C₄×D₄×C₆₇	C₂²	semidirect
120. C₄×D₄×C₆₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
330. C₆₇	#3493	semidirect
339. #553	D₆₇	semidirect
367. #126	C₂×D₆₇	semidirect
372. #125	C₂×D₆₇	semidirect
407. #121	C₂×D₆₇	semidirect
429. C₄×D₄	C₂×D₆₇	semidirect
430. C₄×D₄	C₂×D₆₇	semidirect
450. C₂×C₄⋊C₄	C₂×D₆₇	semidirect