Subgroups — #22574403

Order 8576.

1166 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864143	C₂	1	2	yes	maximal, complemented
2	#16864136	C₂	1	2	yes	maximal, complemented
3	#16864094	C₂	1	2	yes	maximal, complemented
4	#16864069	C₂	1	2	yes	maximal, complemented
5	#16864038	C₂	1	2	yes	maximal, complemented
6	#16864036	C₂	1	2	yes	maximal, complemented
7	#16864036	C₂	1	2	yes	maximal, complemented
8	D₄×C₂²⋊D₆₇	C₂	1	2	yes	maximal, complemented
9	#16863998	C₂	1	2	yes	maximal, complemented
10	#16863993	C₂	1	1	yes	maximal, characteristic, complemented
11	#16863990	C₂	1	2	yes	maximal, complemented
12	#16863984	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863982	C₂	1	2	yes	maximal, complemented
14	#16863977	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863958	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863957	C₂	1	2	yes	maximal, complemented
17	#16863907	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14524017	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11761628	C₂²	1	2	yes	complemented
21	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
25	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
26	#14524039	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	#14524036	C₂²	1	2	yes	complemented
31	#14524034	C₂²	1	2	yes	complemented
32	#14524033	C₂²	1	2	yes	complemented
33	#14524029	C₂²	1	2	yes	complemented
34	#14524029	C₂²	1	2	yes	complemented
35	#14524029	C₂²	1	2	yes	complemented
36	#14524028	C₂²	1	2	yes	complemented
37	#14524028	C₂²	1	2	yes	complemented
38	#14524028	C₂²	1	2	yes	complemented
39	#14524027	C₂²	1	2	yes	complemented
40	#14524027	C₂²	1	2	yes	complemented
41	#14524026	C₂²	1	2	yes	complemented
42	#14524026	C₂²	1	2	yes	complemented
43	#14524025	C₂²	1	2	yes	complemented
44	#14524025	C₂²	1	2	yes	complemented
45	#14524025	C₂²	1	2	yes	complemented
46	#14524023	C₂²	1	2	yes	complemented
47	#14524023	C₂²	1	2	yes	complemented
48	#14524022	C₂²	1	1	yes	characteristic, complemented
49	#14524022	C₂²	1	1	yes	characteristic, complemented
50	#14524021	C₂²	1	2	yes	complemented
51	#14524020	C₂²	1	2	yes	complemented
52	#14524020	C₂²	1	2	yes	complemented
53	#14524018	C₂²	1	2	yes	complemented
54	#14524018	C₂²	1	2	yes	complemented
55	#14524018	C₂²	1	2	yes	complemented
56	#14524017	C₂²	1	1	yes	characteristic
57	#14524017	C₂²	1	2	yes	complemented
58	#14524017	C₂²	1	2	yes	complemented
59	#14524017	C₂²	1	2	yes	complemented
60	#14524017	C₂²	1	1	yes	characteristic, complemented
61	#14524017	C₂²	1	2	yes	complemented
62	#14524017	C₂²	1	1	yes	characteristic, complemented
63	#14524017	C₂²	1	1	yes	characteristic, complemented
64	#14524017	C₂²	1	1	yes	characteristic, complemented
65	#14524017	C₂²	1	1	yes	characteristic, complemented
66	#14524016	C₂²	1	2	yes	complemented
67	#14524016	C₂²	1	2	yes	complemented
68	#14524016	C₂²	1	2	yes	complemented
69	#14524016	C₂²	1	2	yes	complemented
70	#14524016	C₂²	1	2	yes	complemented
71	#14524015	C₂²	1	2	yes	—
72	#14524015	C₂²	1	2	yes	complemented
73	#14524014	C₂²	1	2	yes	complemented
74	#14524013	C₂²	1	2	yes	complemented
75	#14524013	C₂²	1	2	yes	complemented
76	#14524013	C₂²	1	2	yes	complemented
77	#14524013	C₂²	1	2	yes	complemented
78	#14524012	C₂²	1	2	yes	complemented
79	#14524012	C₂²	1	2	yes	complemented
80	#14524011	C₂²	1	2	yes	—
81	#14524011	C₂²	1	2	yes	complemented
82	D₄×Dic₆₇	C₂²	1	2	yes	complemented
83	#14524005	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
88	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
89	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
90	#14524002	C₂²	1	1	yes	characteristic, complemented
91	#14524001	C₂²	1	2	yes	complemented
92	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, 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×D₄×C₆₇	C₂²	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#123×C₆₇	C₂²	1	2	yes	complemented
99	#123×C₆₇	C₂²	1	2	yes	complemented
100	#123×C₆₇	C₂²	1	2	yes	complemented
101	#123×C₆₇	C₂²	1	2	yes	complemented
102	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₆₇	C₂³	1	2	yes	—
108	C₂³×D₆₇	C₂³	1	2	yes	—
109	#11761628	—	4	2	no	—
110	#11761628	—	4	4	no	—
111	C₂×Dic₁₃₄	C₂³	1	2	yes	—
112	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
113	C₂×D₂₆₈	—	4	2	no	—
114	C₂×D₂₆₈	C₂³	1	2	yes	—
115	C₂×D₂₆₈	C₂³	1	2	yes	—
116	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
117	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
118	C₂×D₂₆₈	C₂³	1	2	yes	—
119	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
120	C₂×D₂₆₈	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₆₇	—	4	4	no	—
122	C₂×C₂²⋊D₆₇	—	4	4	no	—
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	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
134	D₄×D₆₇	—	4	4	no	—
135	C₂²×Dic₆₇	C₂³	1	2	yes	—
136	C₂²×Dic₆₇	C₂³	1	2	yes	—
137	C₂×C₄×D₆₇	C₂³	1	2	yes	—
138	C₂×C₄×D₆₇	C₂³	1	2	yes	—
139	C₂×C₄×D₆₇	C₂³	1	2	yes	—
140	C₂×C₄×D₆₇	C₂³	1	2	yes	—
141	C₂×C₄×D₆₇	C₂³	1	2	yes	—
142	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₆₇	C₂³	1	2	yes	—
144	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₆₇	C₂³	1	2	yes	—
146	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₆₇	C₂³	1	2	yes	—
149	Dic₆₇⋊C₄	C₂³	1	2	yes	—
150	Dic₆₇⋊C₄	C₂³	1	2	yes	—
151	Dic₆₇⋊C₄	C₂³	1	2	yes	—
152	Dic₆₇⋊C₄	C₂³	1	2	yes	—
153	Dic₆₇⋊C₄	C₂³	1	2	yes	—
154	Dic₆₇⋊C₄	C₂³	1	2	yes	—
155	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
156	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
157	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
158	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
159	C₂²⋊Dic₆₇	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	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
174	C₄×Dic₆₇	C₂³	1	2	yes	—
175	C₄×Dic₆₇	C₂³	1	2	yes	—
176	C₄×Dic₆₇	C₂³	1	2	yes	—
177	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
178	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₆₇	—	4	2	no	—
180	C₂×D₄×C₆₇	C₂³	1	2	yes	—
181	C₂×D₄×C₆₇	C₂³	1	2	yes	—
182	C₂²×C₄×C₆₇	—	4	2	no	—
183	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂³×C₆₇	—	2	2	no	—
203	C₂³×C₆₇	—	2	2	no	—
204	C₂³×C₆₇	—	2	2	no	—
205	C₂³×C₆₇	—	4	1	no	—
206	C₂³×C₆₇	—	4	1	no	—
207	C₂³×C₆₇	—	4	1	no	—
208	C₂³×C₆₇	C₂⁴	1	2	yes	—
209	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
212	C₂²×D₆₇	—	2	4	no	—
213	C₂²×D₆₇	—	4	2	no	—
214	C₂²×D₆₇	—	4	2	no	—
215	C₂²×D₆₇	—	4	2	no	—
216	C₂²×D₆₇	—	4	2	no	—
217	C₂²×D₆₇	—	4	2	no	—
218	C₂²×D₆₇	C₂⁴	1	2	yes	—
219	C₂²×D₆₇	C₂⁴	1	2	yes	—
220	C₂²×D₆₇	C₂⁴	1	2	yes	—
221	D₄×C₆₇	—	2	4	no	—
222	D₄×C₆₇	—	4	2	no	—
223	C₂×C₄×C₆₇	—	2	2	no	—
224	C₂×C₄×C₆₇	—	2	2	no	—
225	C₂×C₄×C₆₇	—	2	2	no	—
226	C₂×C₄×C₆₇	—	4	1	no	—
227	C₂×C₄×C₆₇	—	4	1	no	—
228	C₂×C₄×C₆₇	—	4	1	no	—
229	C₂×C₄×C₆₇	—	4	1	no	—
230	C₂×C₄×C₆₇	—	4	1	no	—
231	C₂×C₄×C₆₇	—	4	1	no	—
232	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
233	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
234	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²⋊D₆₇	—	2	4	no	—
240	C₂²⋊D₆₇	—	2	4	no	—
241	C₂²⋊D₆₇	—	2	4	no	—
242	C₂²⋊D₆₇	—	2	4	no	—
243	C₂²⋊D₆₇	—	4	2	no	—
244	C₂²⋊D₆₇	—	4	2	no	—
245	C₂²⋊D₆₇	—	4	2	no	—
246	C₂²⋊D₆₇	—	4	2	no	—
247	C₂²⋊D₆₇	—	4	2	no	—
248	C₂²⋊D₆₇	—	4	2	no	—
249	C₂²⋊D₆₇	—	4	2	no	—
250	C₂×Dic₆₇	—	4	2	no	—
251	C₂×Dic₆₇	—	4	2	no	—
252	C₂×Dic₆₇	C₂⁴	1	2	yes	—
253	C₂×Dic₆₇	C₂⁴	1	2	yes	—
254	C₂×Dic₆₇	C₂⁴	1	2	yes	—
255	C₂×Dic₆₇	C₂⁴	1	2	yes	—
256	C₂×Dic₆₇	C₂⁴	1	2	yes	—
257	D₂₆₈	—	4	2	no	—
258	D₂₆₈	—	4	1	no	—
259	D₂₆₈	—	4	2	no	—
260	D₂₆₈	—	4	1	no	—
261	D₂₆₈	—	4	2	no	—
262	D₂₆₈	—	4	2	no	—
263	D₂₆₈	—	4	1	no	—
264	C₄×D₆₇	—	4	2	no	—
265	C₄×D₆₇	—	4	2	no	—
266	C₄×D₆₇	—	4	2	no	—
267	C₄×D₆₇	—	4	2	no	—
268	C₄×D₆₇	—	4	2	no	—
269	Dic₁₃₄	—	4	1	no	—
270	Dic₁₃₄	—	4	2	no	—
271	C₂²×C₆₇	—	2	1	no	—
272	C₂²×C₆₇	—	2	1	no	—
273	C₂²×C₆₇	—	2	1	no	—
274	C₂²×C₆₇	—	2	1	no	—
275	C₂²×C₆₇	—	2	2	no	—
276	C₂²×C₆₇	—	2	1	no	—
277	C₂²×C₆₇	—	2	2	no	—
278	C₂²×C₆₇	—	2	1	no	—
279	C₂²×C₆₇	—	2	1	no	—
280	C₂²×C₆₇	—	2	2	no	—
281	C₂²×C₆₇	—	4	4	no	—
282	C₂²×C₆₇	—	8	2	no	—
283	C₂²×C₆₇	H(5,𝔽₂)	1	2	yes	—
284	C₂²×C₆₇	H(5,𝔽₂)	1	2	yes	—
285	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
286	C₂×D₆₇	—	2	2	no	—
287	C₂×D₆₇	—	2	2	no	—
288	C₂×D₆₇	—	2	2	no	—
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	C₂×D₆₇	—	8	4	no	—
296	C₂×D₆₇	—	8	4	no	—
297	C₄×C₆₇	—	2	2	no	—
298	C₄×C₆₇	—	2	1	no	—
299	C₄×C₆₇	—	2	1	no	—
300	C₄×C₆₇	—	2	2	no	—
301	C₄×C₆₇	—	2	1	no	—
302	C₄×C₆₇	—	2	1	no	—
303	C₄×C₆₇	—	2	2	no	—
304	Dic₆₇	—	2	2	no	—
305	Dic₆₇	—	2	2	no	—
306	Dic₆₇	—	2	2	no	—
307	Dic₆₇	—	2	2	no	—
308	Dic₆₇	—	2	2	no	—
309	C₂×C₆₇	—	2	2	no	—
310	C₂×C₆₇	—	2	2	no	—
311	C₂×C₆₇	—	4	2	no	—
312	C₂×C₆₇	—	4	1	no	—
313	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₆₇	#585	1	1	yes	characteristic
316	D₆₇	—	4	2	no	—
317	D₆₇	—	4	2	no	—
318	D₆₇	—	4	2	no	—
319	#3534	—	67	1	no	maximal, Sylow
320	C₆₇	#3534	1	1	yes	characteristic, complemented, Sylow
321	#562	—	67	2	no	—
322	#560	—	67	2	no	—
323	#553	—	67	2	no	—
324	#551	—	67	2	no	—
325	#546	—	67	2	no	—
326	#546	—	67	2	no	—
327	#546	—	67	2	no	—
328	D₄²	—	67	2	no	—
329	#540	—	67	2	no	—
330	#539	—	67	2	no	—
331	#539	—	67	1	no	—
332	#538	—	67	2	no	—
333	#538	—	67	1	no	—
334	#537	—	67	1	no	—
335	#534	—	67	2	no	—
336	#534	—	67	1	no	—
337	#525	—	67	1	no	—
338	C₂×#123	D₆₇	1	1	yes	characteristic, complemented
339	C₂×#121	—	67	1	no	—
340	C₂×#41	—	67	1	no	—
341	C₂×#41	—	67	2	no	—
342	C₂²×D₄	—	67	2	no	—
343	C₂²×D₄	—	67	2	no	—
344	C₂²×D₄	—	67	2	no	—
345	C₂²×D₄	—	67	1	no	—
346	C₂²×D₄	C₂×D₆₇	1	1	yes	characteristic
347	C₂³×C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
348	#127	—	67	2	no	—
349	#126	—	67	2	no	—
350	#126	—	67	2	no	—
351	#126	—	67	2	no	—
352	#126	—	67	2	no	—
353	#125	—	67	2	no	—
354	#125	—	67	2	no	—
355	#124	—	67	2	no	—
356	#124	—	67	2	no	—
357	#124	—	67	2	no	—
358	#123	—	67	2	no	—
359	#123	—	67	2	no	—
360	#123	—	67	2	no	—
361	#123	—	67	2	no	—
362	#123	—	67	2	no	—
363	#123	—	67	2	no	—
364	#123	—	67	2	no	—
365	#123	—	67	2	no	—
366	#123	—	67	2	no	—
367	#123	—	67	2	no	—
368	#123	C₂×D₆₇	1	2	yes	complemented
369	#123	C₂×D₆₇	1	2	yes	complemented
370	#123	C₂×D₆₇	1	2	yes	complemented
371	#123	C₂×D₆₇	1	2	yes	complemented
372	C₂²⋊Q₈	—	67	1	no	—
373	C₂²⋊Q₈	—	67	1	no	—
374	C₂²⋊Q₈	—	67	2	no	—
375	C₂²⋊Q₈	—	67	2	no	—
376	C₂²⋊Q₈	—	67	2	no	—
377	C₂²⋊Q₈	—	67	2	no	—
378	C₂²⋊Q₈	—	67	2	no	—
379	#121	—	67	2	no	—
380	#121	—	67	2	no	—
381	#121	—	67	2	no	—
382	#121	—	67	1	no	—
383	#121	—	67	1	no	—
384	#121	—	67	1	no	—
385	#121	—	67	1	no	—
386	#121	—	67	2	no	—
387	#121	—	67	2	no	—
388	#121	—	67	1	no	—
389	#121	—	67	1	no	—
390	#121	—	67	2	no	—
391	#121	—	67	2	no	—
392	#121	—	67	2	no	—
393	#121	—	67	2	no	—
394	#121	—	67	2	no	—
395	#121	—	67	2	no	—
396	#121	—	67	2	no	—
397	#121	—	67	2	no	—
398	#121	—	67	2	no	—
399	#121	—	67	2	no	—
400	#120	—	67	2	no	—
401	#120	—	67	2	no	—
402	#120	—	67	2	no	—
403	#120	—	67	2	no	—
404	#120	—	67	2	no	—
405	#120	—	67	2	no	—
406	#120	—	67	2	no	—
407	#120	—	67	2	no	—
408	C₄×D₄	—	67	2	no	—
409	C₄×D₄	—	67	2	no	—
410	C₄×D₄	—	67	2	no	—
411	C₄×D₄	—	67	2	no	—
412	C₄×D₄	—	67	2	no	—
413	C₄×D₄	—	67	2	no	—
414	C₄×D₄	—	67	2	no	—
415	C₄×D₄	—	67	2	no	—
416	#117	—	67	1	no	—
417	#117	—	67	2	no	—
418	C₂×C₄⋊C₄	—	67	1	no	—
419	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
420	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
421	C₂×C₂²⋊C₄	—	67	2	no	—
422	C₂×C₂²⋊C₄	—	67	2	no	—
423	C₂×C₂²⋊C₄	—	67	2	no	—
424	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
425	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
426	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
427	C₂⁴	—	67	2	no	—
428	C₂⁴	—	67	2	no	—
429	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
430	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
431	#41	—	268	2	no	—
432	#41	—	268	4	no	—
433	C₂×Q₈	—	67	1	no	—
434	C₂×Q₈	—	67	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	268	2	no	—
437	C₂×D₄	—	268	4	no	—
438	C₂×D₄	—	268	4	no	—
439	C₂×D₄	—	268	4	no	—
440	C₂×D₄	—	67	2	no	—
441	C₂×D₄	—	67	2	no	—
442	C₂×D₄	—	67	2	no	—
443	C₂×D₄	—	67	2	no	—
444	C₂×D₄	—	67	2	no	—
445	C₂×D₄	—	67	2	no	—
446	C₂×D₄	—	67	2	no	—
447	C₂×D₄	—	67	2	no	—
448	C₂×D₄	—	67	2	no	—
449	C₂×D₄	—	67	2	no	—
450	C₂×D₄	—	67	2	no	—
451	C₂×D₄	—	67	2	no	—
452	C₂×D₄	—	67	1	no	—
453	C₂×D₄	—	67	2	no	—
454	C₂×D₄	—	67	1	no	—
455	C₂×D₄	—	67	2	no	—
456	C₂×D₄	—	67	1	no	—
457	C₂×D₄	—	67	2	no	—
458	C₂×D₄	C₂²×D₆₇	1	2	yes	—
459	C₂×D₄	C₂²×D₆₇	1	2	yes	—
460	C₂²×C₄	—	4	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	C₂²×D₆₇	1	1	yes	characteristic
469	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
470	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
471	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
472	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
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	C₄⋊C₄	—	67	1	no	—
478	C₄⋊C₄	—	67	2	no	—
479	C₄⋊C₄	—	67	1	no	—
480	C₄⋊C₄	—	67	1	no	—
481	C₄⋊C₄	—	67	2	no	—
482	C₄⋊C₄	—	67	1	no	—
483	C₄⋊C₄	—	67	2	no	—
484	C₄⋊C₄	—	67	2	no	—
485	C₄⋊C₄	—	67	2	no	—
486	C₄⋊C₄	—	67	2	no	—
487	C₄⋊C₄	—	67	2	no	—
488	C₄⋊C₄	—	67	2	no	—
489	C₄⋊C₄	—	67	2	no	—
490	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
491	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
492	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
493	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
494	C₂²⋊C₄	—	67	2	no	—
495	C₂²⋊C₄	—	67	2	no	—
496	C₂²⋊C₄	—	67	2	no	—
497	C₂²⋊C₄	—	67	2	no	—
498	C₂²⋊C₄	—	67	2	no	—
499	C₂²⋊C₄	—	67	2	no	—
500	C₂²⋊C₄	—	67	2	no	—
501	C₂²⋊C₄	—	67	2	no	—
502	C₂²⋊C₄	—	67	2	no	—
503	C₂²⋊C₄	—	67	2	no	—
504	C₂²⋊C₄	—	67	2	no	—
505	C₂²⋊C₄	—	67	2	no	—
506	C₂²⋊C₄	—	67	2	no	—
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	C₂²×D₆₇	1	2	yes	—
514	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
519	C₄²	—	67	2	no	—
520	C₄²	—	67	2	no	—
521	C₄²	—	67	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	268	2	no	—
529	C₂³	—	268	2	no	—
530	C₂³	—	268	2	no	—
531	C₂³	—	268	2	no	—
532	C₂³	—	268	2	no	—
533	C₂³	—	67	2	no	—
534	C₂³	—	67	2	no	—
535	C₂³	—	67	2	no	—
536	C₂³	—	134	4	no	—
537	C₂³	C₂³×D₆₇	1	2	yes	—
538	C₂³	C₂³×D₆₇	1	1	yes	characteristic
539	C₂³	C₂³×D₆₇	1	1	yes	characteristic
540	C₂³	C₂³×D₆₇	1	1	yes	characteristic
541	Q₈	—	268	1	no	—
542	Q₈	—	268	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	4	2	no	—
545	D₄	—	268	1	no	—
546	D₄	—	268	2	no	—
547	D₄	—	268	1	no	—
548	D₄	—	268	2	no	—
549	D₄	—	268	1	no	—
550	D₄	—	268	2	no	—
551	D₄	—	268	2	no	—
552	D₄	—	268	2	no	—
553	D₄	—	268	2	no	—
554	D₄	—	268	2	no	—
555	D₄	—	268	2	no	—
556	D₄	—	268	2	no	—
557	D₄	—	268	2	no	—
558	D₄	—	268	2	no	—
559	D₄	—	134	4	no	—
560	D₄	—	134	4	no	—
561	D₄	—	134	4	no	—
562	D₄	—	134	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	268	2	no	—
573	C₂×C₄	—	268	2	no	—
574	C₂×C₄	—	268	2	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	—	67	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	C₂³×D₆₇	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₆₇	1	2	yes	—
586	C₂×C₄	C₂³×D₆₇	1	2	yes	—
587	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₆₇	1	2	yes	—
589	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	8	2	no	—
603	C₂²	—	536	4	no	—
604	C₂²	—	536	4	no	—
605	C₂²	—	134	2	no	—
606	C₂²	—	134	2	no	—
607	C₂²	—	134	2	no	—
608	C₂²	—	134	2	no	—
609	C₂²	—	134	2	no	—
610	C₂²	—	134	2	no	—
611	C₂²	—	134	2	no	—
612	C₂²	—	134	2	no	—
613	C₂²	—	134	2	no	—
614	C₂²	#14524088	1	2	yes	—
615	C₂²	#14524089	1	2	yes	—
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	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	134	2	no	—
625	C₄	—	134	2	no	—
626	C₄	—	134	2	no	—
627	C₄	—	134	2	no	—
628	C₄	—	134	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	2	2	no	—
631	C₂	—	4	1	no	—
632	C₂	—	4	2	no	—
633	C₂	—	268	2	no	—
634	C₂	—	268	2	no	—
635	C₂	—	268	2	no	—
636	C₂	C₂×#14524088	1	1	yes	characteristic
637	C₂	C₂×#14524089	1	1	yes	characteristic
638	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	C₂×#123×C₆₇	C₂
hypercenter	C₂×#123	D₆₇
hypocenter	C₆₇	#3534
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
1. #16864143	C₂	semidirect
2. #16864136	C₂	semidirect
3. #16864094	C₂	semidirect
4. #16864069	C₂	semidirect
5. #16864038	C₂	semidirect
6. #16864036	C₂	semidirect
7. #16864036	C₂	semidirect
8. D₄×C₂²⋊D₆₇	C₂	semidirect
9. #16863998	C₂	semidirect
10. #16863993	C₂	semidirect
11. #16863990	C₂	semidirect
12. #16863984	C₂	semidirect
13. #16863982	C₂	semidirect
14. #16863977	C₂	semidirect
15. #16863958	C₂	semidirect
16. #16863957	C₂	semidirect
17. #16863907	C₂	semidirect
18. C₂×#14524017	C₂	semidirect
19. C₂×#123×C₆₇	C₂	semidirect
20. C₂×#11761628	C₂²	semidirect
21. C₂×#11761628	C₂²	semidirect
22. C₂²×D₂₆₈	C₂²	semidirect
23. C₂²×C₂²⋊D₆₇	C₂²	semidirect
24. C₂²×C₂²⋊D₆₇	C₂²	semidirect
25. C₂×D₄×D₆₇	C₂²	semidirect
26. #14524039	C₂²	semidirect
27. #14524038	C₂²	semidirect
28. #14524038	C₂²	semidirect
29. #14524038	C₂²	semidirect
30. #14524036	C₂²	semidirect
31. #14524034	C₂²	semidirect
32. #14524033	C₂²	semidirect
33. #14524029	C₂²	semidirect
34. #14524029	C₂²	semidirect
35. #14524029	C₂²	semidirect
36. #14524028	C₂²	semidirect
37. #14524028	C₂²	semidirect
38. #14524028	C₂²	semidirect
39. #14524027	C₂²	semidirect
40. #14524027	C₂²	semidirect
41. #14524026	C₂²	semidirect
42. #14524026	C₂²	semidirect
43. #14524025	C₂²	semidirect
44. #14524025	C₂²	semidirect
45. #14524025	C₂²	semidirect
46. #14524023	C₂²	semidirect
47. #14524023	C₂²	semidirect
48. #14524022	C₂²	semidirect
49. #14524022	C₂²	semidirect
50. #14524021	C₂²	semidirect
51. #14524020	C₂²	semidirect
52. #14524020	C₂²	semidirect
53. #14524018	C₂²	semidirect
54. #14524018	C₂²	semidirect
55. #14524018	C₂²	semidirect
57. #14524017	C₂²	semidirect
58. #14524017	C₂²	semidirect
59. #14524017	C₂²	semidirect
60. #14524017	C₂²	semidirect
61. #14524017	C₂²	semidirect
62. #14524017	C₂²	semidirect
63. #14524017	C₂²	semidirect
64. #14524017	C₂²	semidirect
65. #14524017	C₂²	semidirect
66. #14524016	C₂²	semidirect
67. #14524016	C₂²	semidirect
68. #14524016	C₂²	semidirect
69. #14524016	C₂²	semidirect
70. #14524016	C₂²	semidirect
72. #14524015	C₂²	semidirect
73. #14524014	C₂²	semidirect
74. #14524013	C₂²	semidirect
75. #14524013	C₂²	semidirect
76. #14524013	C₂²	semidirect
77. #14524013	C₂²	semidirect
78. #14524012	C₂²	semidirect
79. #14524012	C₂²	semidirect
81. #14524011	C₂²	semidirect
82. D₄×Dic₆₇	C₂²	semidirect
83. #14524005	C₂²	semidirect
84. C₄×C₂²⋊D₆₇	C₂²	semidirect
85. C₄×C₂²⋊D₆₇	C₂²	semidirect
86. C₄×C₂²⋊D₆₇	C₂²	semidirect
87. C₄×C₂²⋊D₆₇	C₂²	semidirect
88. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
89. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
90. #14524002	C₂²	semidirect
91. #14524001	C₂²	semidirect
92. C₂×C₄⋊Dic₆₇	C₂²	semidirect
93. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
94. C₂²⋊C₄×D₆₇	C₂²	semidirect
95. C₂²⋊C₄×D₆₇	C₂²	semidirect
97. C₂³×C₄×C₆₇	C₂²	semidirect
98. #123×C₆₇	C₂²	semidirect
99. #123×C₆₇	C₂²	semidirect
100. #123×C₆₇	C₂²	semidirect
101. #123×C₆₇	C₂²	semidirect
102. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
103. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
104. C₂×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. C₂×C₂²⋊C₄×C₆₇	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₆₇	C₂²	semidirect
320. C₆₇	#3534	semidirect
338. C₂×#123	D₆₇	semidirect
347. C₂³×C₄	C₂×D₆₇	semidirect
368. #123	C₂×D₆₇	semidirect
369. #123	C₂×D₆₇	semidirect
370. #123	C₂×D₆₇	semidirect
371. #123	C₂×D₆₇	semidirect
419. C₂×C₄⋊C₄	C₂×D₆₇	semidirect
420. C₂×C₄⋊C₄	C₂×D₆₇	semidirect
424. C₂×C₂²⋊C₄	C₂×D₆₇	semidirect
425. C₂×C₂²⋊C₄	C₂×D₆₇	semidirect
426. C₂×C₂²⋊C₄	C₂×D₆₇	semidirect