Subgroups — #22574246

Order 8576.

1124 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864114	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864105	C₂	1	2	yes	maximal, complemented
3	#16864088	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864085	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864077	C₂	1	2	yes	maximal, complemented
6	#16864075	C₂	1	2	yes	maximal, complemented
7	#16864059	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864053	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864052	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864046	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864045	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864033	C₂	1	2	yes	maximal, complemented
13	#16864014	C₂	1	2	yes	maximal, complemented
14	#16863989	C₂	1	2	yes	maximal, complemented
15	#16863988	C₂	1	2	yes	maximal, complemented
16	#16863948	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863927	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863906	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#14524022	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863875	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#525×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761627	C₂²	1	2	yes	—
25	C₂×#11761627	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
30	#14524042	C₂²	1	2	yes	complemented
31	#14524042	C₂²	1	1	yes	characteristic, complemented
32	#14524041	C₂²	1	1	yes	characteristic, complemented
33	#14524038	C₂²	1	2	yes	complemented
34	#14524037	C₂²	1	2	yes	complemented
35	#14524036	C₂²	1	2	yes	complemented
36	#14524036	C₂²	1	2	yes	complemented
37	#14524036	C₂²	1	2	yes	complemented
38	#14524035	C₂²	1	2	yes	complemented
39	#14524034	C₂²	1	1	yes	characteristic, complemented
40	#14524034	C₂²	1	2	yes	complemented
41	#14524033	C₂²	1	2	yes	complemented
42	#14524030	C₂²	1	2	yes	complemented
43	#14524030	C₂²	1	1	yes	characteristic, complemented
44	#14524029	C₂²	1	2	yes	—
45	#14524029	C₂²	1	2	yes	complemented
46	#14524027	C₂²	1	2	yes	—
47	#14524026	C₂²	1	2	yes	complemented
48	#14524025	C₂²	1	2	yes	—
49	#14524025	C₂²	1	2	yes	complemented
50	#14524025	C₂²	1	2	yes	complemented
51	#14524024	C₂²	1	2	yes	—
52	#14524024	C₂²	1	2	yes	complemented
53	#14524024	C₂²	1	2	yes	complemented
54	#14524023	C₂²	1	1	yes	characteristic, complemented
55	#14524023	C₂²	1	1	yes	characteristic, complemented
56	#14524022	C₂²	1	2	yes	—
57	#14524022	C₂²	1	1	yes	characteristic
58	#14524022	C₂²	1	1	yes	characteristic
59	#14524022	C₂²	1	2	yes	complemented
60	#14524022	C₂²	1	1	yes	characteristic, complemented
61	#14524022	C₂²	1	2	yes	complemented
62	#14524022	C₂²	1	1	yes	characteristic, complemented
63	#14524021	C₂²	1	2	yes	complemented
64	#14524021	C₂²	1	2	yes	complemented
65	#14524020	C₂²	1	2	yes	—
66	#14524020	C₂²	1	2	yes	—
67	#14524020	C₂²	1	2	yes	complemented
68	#14524020	C₂²	1	2	yes	complemented
69	#14524020	C₂²	1	2	yes	complemented
70	#14524019	C₂²	1	1	yes	characteristic, complemented
71	#14524015	C₂²	1	2	yes	—
72	#14524015	C₂²	1	2	yes	—
73	#14524014	C₂²	1	2	yes	—
74	#14524014	C₂²	1	1	yes	characteristic, complemented
75	#14524011	C₂²	1	2	yes	—
76	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
78	#14524008	C₂²	1	2	yes	complemented
79	#14524008	C₂²	1	1	yes	characteristic, complemented
80	#14524008	C₂²	1	1	yes	characteristic, complemented
81	D₄×Dic₆₇	C₂²	1	2	yes	—
82	D₄×Dic₆₇	C₂²	1	2	yes	—
83	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₆₇	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
94	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
95	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
96	#14524001	C₂²	1	1	yes	characteristic, complemented
97	#14524000	C₂²	1	2	yes	complemented
98	#14523999	C₂²	1	2	yes	—
99	#14523999	C₂²	1	2	yes	complemented
100	#14523999	C₂²	1	2	yes	complemented
101	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₂×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
103	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
104	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
107	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
108	C₂×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
109	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
112	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₂³×C₄×C₆₇	C₂²	1	1	yes	characteristic
114	#123×C₆₇	C₂²	1	2	yes	complemented
115	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#121×C₆₇	C₂²	1	1	yes	characteristic
118	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#120×C₆₇	C₂²	1	2	yes	—
120	C₄×D₄×C₆₇	C₂²	1	2	yes	—
121	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
122	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	#11761627	—	2	8	no	—
125	#11761627	—	4	2	no	—
126	C₂×Dic₁₃₄	—	4	2	no	—
127	C₂×Dic₁₃₄	C₂³	1	2	yes	—
128	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂×Dic₁₃₄	C₂³	1	2	yes	—
132	Q₈×D₆₇	—	4	2	no	—
133	C₂×C₂²⋊D₆₇	—	2	4	no	—
134	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
140	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
141	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
142	C₂²×Dic₆₇	C₂³	1	2	yes	—
143	C₂²×Dic₆₇	C₂³	1	2	yes	—
144	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
145	C₂²×Dic₆₇	C₂³	1	2	yes	—
146	C₂²×Dic₆₇	C₂³	1	2	yes	—
147	C₂×C₄×D₆₇	—	4	2	no	—
148	C₂×C₄×D₆₇	C₂³	1	2	yes	—
149	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₆₇	C₂³	1	2	yes	—
152	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₆₇	C₂³	1	2	yes	—
156	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₆₇	C₂³	1	2	yes	—
158	C₄⋊Dic₆₇	C₂³	1	2	yes	—
159	C₄⋊Dic₆₇	C₂³	1	2	yes	—
160	C₄⋊Dic₆₇	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	1	yes	characteristic
165	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	Dic₆₇⋊C₄	C₂³	1	2	yes	—
170	Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	Dic₆₇⋊C₄	C₂³	1	2	yes	—
172	Dic₆₇⋊C₄	C₂³	1	2	yes	—
173	Dic₆₇⋊C₄	C₂³	1	2	yes	—
174	Dic₆₇⋊C₄	C₂³	1	2	yes	—
175	Dic₆₇⋊C₄	C₂³	1	2	yes	—
176	Dic₆₇⋊C₄	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	1	yes	characteristic
181	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
188	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
189	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
197	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₆₇	C₂³	1	2	yes	—
202	C₄×Dic₆₇	C₂³	1	2	yes	—
203	C₄×Dic₆₇	C₂³	1	2	yes	—
204	C₄×Dic₆₇	C₂³	1	2	yes	—
205	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
206	#41×C₆₇	—	4	2	no	—
207	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₆₇	C₂³	1	2	yes	—
209	C₂×D₄×C₆₇	C₂³	1	2	yes	—
210	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₆₇	C₂³	1	2	yes	—
212	C₂²×C₄×C₆₇	—	4	2	no	—
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	2	yes	—
218	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₄²×C₆₇	C₂³	1	2	yes	—
230	C₂³×C₆₇	—	2	2	no	—
231	C₂³×C₆₇	—	2	2	no	—
232	C₂³×C₆₇	—	4	1	no	—
233	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂³×C₆₇	C₂⁴	1	2	yes	—
235	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₂²×D₆₇	—	2	2	no	—
238	C₂²×D₆₇	—	2	2	no	—
239	C₂²×D₆₇	—	4	1	no	—
240	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
241	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
242	Q₈×C₆₇	—	2	2	no	—
243	D₄×C₆₇	—	2	4	no	—
244	D₄×C₆₇	—	2	4	no	—
245	D₄×C₆₇	—	2	2	no	—
246	D₄×C₆₇	—	4	2	no	—
247	C₂×C₄×C₆₇	—	2	2	no	—
248	C₂×C₄×C₆₇	—	2	2	no	—
249	C₂×C₄×C₆₇	—	2	2	no	—
250	C₂×C₄×C₆₇	—	4	1	no	—
251	C₂×C₄×C₆₇	—	4	1	no	—
252	C₂×C₄×C₆₇	—	4	1	no	—
253	C₂×C₄×C₆₇	—	4	2	no	—
254	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₆₇	—	2	2	no	—
262	C₂²⋊D₆₇	—	2	2	no	—
263	C₂²⋊D₆₇	—	2	4	no	—
264	C₂²⋊D₆₇	—	2	2	no	—
265	C₂²⋊D₆₇	—	4	2	no	—
266	C₂²⋊D₆₇	#41	1	4	yes	complemented
267	C₂×Dic₆₇	—	2	4	no	—
268	C₂×Dic₆₇	—	2	2	no	—
269	C₂×Dic₆₇	—	2	2	no	—
270	C₂×Dic₆₇	—	2	4	no	—
271	C₂×Dic₆₇	—	4	1	no	—
272	C₂×Dic₆₇	—	4	2	no	—
273	C₂×Dic₆₇	—	4	2	no	—
274	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₆₇	C₂⁴	1	2	yes	—
277	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₆₇	C₂⁴	1	2	yes	—
280	C₂×Dic₆₇	C₂⁴	1	2	yes	—
281	C₂×Dic₆₇	C₂⁴	1	2	yes	—
282	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
284	C₄×D₆₇	—	2	4	no	—
285	C₄×D₆₇	—	2	2	no	—
286	C₄×D₆₇	—	2	2	no	—
287	C₄×D₆₇	—	4	1	no	—
288	C₄×D₆₇	—	4	1	no	—
289	C₄×D₆₇	—	4	2	no	—
290	Dic₁₃₄	—	2	2	no	—
291	Dic₁₃₄	—	2	2	no	—
292	Dic₁₃₄	—	2	4	no	—
293	Dic₁₃₄	—	4	2	no	—
294	Dic₁₃₄	—	4	2	no	—
295	C₂²×C₆₇	—	2	1	no	—
296	C₂²×C₆₇	—	2	1	no	—
297	C₂²×C₆₇	—	2	1	no	—
298	C₂²×C₆₇	—	2	1	no	—
299	C₂²×C₆₇	—	2	2	no	—
300	C₂²×C₆₇	—	2	1	no	—
301	C₂²×C₆₇	—	2	2	no	—
302	C₂²×C₆₇	—	2	1	no	—
303	C₂²×C₆₇	—	2	2	no	—
304	C₂²×C₆₇	—	2	1	no	—
305	C₂²×C₆₇	—	4	4	no	—
306	C₂²×C₆₇	C₂×#41	1	2	yes	—
307	C₂²×C₆₇	2₋¹⁺⁴	1	2	yes	—
308	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
309	C₂×D₆₇	—	2	1	no	—
310	C₂×D₆₇	—	2	1	no	—
311	C₂×D₆₇	—	2	1	no	—
312	C₂×D₆₇	—	2	1	no	—
313	C₂×D₆₇	—	2	1	no	—
314	C₂×D₆₇	—	4	4	no	—
315	C₂×D₆₇	C₂×#41	1	2	yes	—
316	C₄×C₆₇	—	2	2	no	—
317	C₄×C₆₇	—	2	1	no	—
318	C₄×C₆₇	—	2	2	no	—
319	C₄×C₆₇	—	2	1	no	—
320	C₄×C₆₇	—	2	1	no	—
321	C₄×C₆₇	—	2	2	no	—
322	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
323	Dic₆₇	—	2	2	no	—
324	Dic₆₇	—	2	2	no	—
325	Dic₆₇	—	2	1	no	—
326	Dic₆₇	—	2	2	no	—
327	Dic₆₇	—	2	2	no	—
328	Dic₆₇	—	2	1	no	—
329	Dic₆₇	—	2	1	no	—
330	Dic₆₇	—	2	1	no	—
331	Dic₆₇	—	2	1	no	—
332	Dic₆₇	C₂×#41	1	2	yes	—
333	C₂×C₆₇	—	2	2	no	—
334	C₂×C₆₇	—	2	2	no	—
335	C₂×C₆₇	—	4	2	no	—
336	C₂×C₆₇	—	4	1	no	—
337	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
338	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
340	D₆₇	—	2	2	no	—
341	D₆₇	—	4	1	no	—
342	#3520	—	67	1	no	maximal, Sylow
343	C₆₇	#3520	1	1	yes	characteristic, complemented, Sylow
344	#556	—	67	1	no	—
345	#554	—	67	2	no	—
346	#552	—	67	1	no	—
347	#552	—	67	1	no	—
348	#551	—	67	2	no	—
349	#551	—	67	2	no	—
350	D₄×Q₈	—	67	1	no	—
351	#548	—	67	1	no	—
352	#548	—	67	1	no	—
353	#547	—	67	1	no	—
354	#547	—	67	1	no	—
355	#546	—	67	2	no	—
356	#542	—	67	2	no	—
357	#539	—	67	2	no	—
358	#539	—	67	2	no	—
359	#533	—	67	1	no	—
360	#529	—	67	1	no	—
361	#525	—	67	1	no	—
362	#525	D₆₇	1	1	yes	characteristic, complemented
363	C₂×C₂²⋊Q₈	—	67	1	no	—
364	C₂×C₂²⋊Q₈	—	67	1	no	—
365	#520	—	67	2	no	—
366	C₂×C₄×D₄	—	67	1	no	—
367	C₂×#41	—	67	1	no	—
368	C₂×#41	—	67	2	no	—
369	C₂×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
370	C₂²×Q₈	—	67	1	no	—
371	C₂²×Q₈	—	67	1	no	—
372	C₂²×D₄	—	67	1	no	—
373	C₂³×C₄	—	67	1	no	—
374	C₂³×C₄	C₂×D₆₇	1	1	yes	characteristic
375	C₄⋊Q₈	—	67	1	no	—
376	C₄⋊Q₈	—	67	1	no	—
377	C₄⋊Q₈	—	67	2	no	—
378	#126	—	67	2	no	—
379	#126	—	67	2	no	—
380	#126	—	67	2	no	—
381	#126	—	67	2	no	—
382	#126	—	67	2	no	—
383	#125	—	67	1	no	—
384	#125	—	67	2	no	—
385	#125	—	67	2	no	—
386	#125	—	67	2	no	—
387	#124	—	67	1	no	—
388	#124	—	67	2	no	—
389	#124	—	67	2	no	—
390	#124	—	67	2	no	—
391	#123	—	67	2	no	—
392	#123	—	67	2	no	—
393	#123	—	67	2	no	—
394	#123	—	67	2	no	—
395	#123	—	67	2	no	—
396	#123	—	67	2	no	—
397	#123	—	67	2	no	—
398	#123	—	67	2	no	—
399	#123	C₂×D₆₇	1	2	yes	complemented
400	C₂²⋊Q₈	—	67	1	no	—
401	C₂²⋊Q₈	—	67	1	no	—
402	C₂²⋊Q₈	—	67	1	no	—
403	C₂²⋊Q₈	—	67	2	no	—
404	C₂²⋊Q₈	—	67	1	no	—
405	C₂²⋊Q₈	—	67	1	no	—
406	C₂²⋊Q₈	—	67	2	no	—
407	C₂²⋊Q₈	—	67	2	no	—
408	C₂²⋊Q₈	—	67	2	no	—
409	C₂²⋊Q₈	—	67	1	no	—
410	C₂²⋊Q₈	—	67	1	no	—
411	C₂²⋊Q₈	—	67	2	no	—
412	C₂²⋊Q₈	—	67	2	no	—
413	C₂²⋊Q₈	—	67	2	no	—
414	C₂²⋊Q₈	—	67	2	no	—
415	C₂²⋊Q₈	—	67	2	no	—
416	C₂²⋊Q₈	—	67	2	no	—
417	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
418	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
419	#121	—	67	1	no	—
420	#121	—	67	2	no	—
421	#121	—	67	2	no	—
422	#121	—	67	2	no	—
423	#121	C₂×D₆₇	1	1	yes	characteristic
424	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
425	#120	—	67	2	no	—
426	#120	C₂×D₆₇	1	2	yes	—
427	C₄×Q₈	—	67	1	no	—
428	C₄×Q₈	—	67	2	no	—
429	C₄×Q₈	—	67	1	no	—
430	C₄×Q₈	—	67	1	no	—
431	C₄×Q₈	—	67	2	no	—
432	C₄×D₄	—	67	2	no	—
433	C₄×D₄	—	67	2	no	—
434	C₄×D₄	—	67	2	no	—
435	C₄×D₄	—	67	1	no	—
436	C₄×D₄	—	67	1	no	—
437	C₄×D₄	—	67	1	no	—
438	C₄×D₄	—	67	1	no	—
439	C₄×D₄	—	67	1	no	—
440	C₄×D₄	—	67	1	no	—
441	C₄×D₄	—	67	1	no	—
442	C₄×D₄	—	67	1	no	—
443	C₄×D₄	—	67	1	no	—
444	C₄×D₄	—	67	2	no	—
445	C₄×D₄	—	67	2	no	—
446	C₄×D₄	—	67	2	no	—
447	C₄×D₄	C₂×D₆₇	1	2	yes	—
448	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
449	#117	—	67	1	no	—
450	#117	—	67	2	no	—
451	#117	—	67	2	no	—
452	#117	—	67	2	no	—
453	#117	—	67	2	no	—
454	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	—	67	1	no	—
456	C₂×C₄⋊C₄	—	67	2	no	—
457	C₂×C₄⋊C₄	—	67	2	no	—
458	C₂×C₄⋊C₄	—	67	1	no	—
459	C₂×C₄⋊C₄	—	67	2	no	—
460	C₂×C₄⋊C₄	—	67	1	no	—
461	C₂×C₂²⋊C₄	—	67	1	no	—
462	C₂×C₂²⋊C₄	—	67	2	no	—
463	C₂×C₂²⋊C₄	—	67	1	no	—
464	C₂×C₂²⋊C₄	—	67	2	no	—
465	C₂×C₄²	—	67	1	no	—
466	C₂⁴	—	67	1	no	—
467	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
468	#41	—	4	2	no	—
469	#41	—	268	2	no	—
470	#41	—	134	8	no	—
471	C₂×Q₈	—	268	2	no	—
472	C₂×Q₈	—	268	2	no	—
473	C₂×Q₈	—	67	2	no	—
474	C₂×Q₈	—	67	2	no	—
475	C₂×Q₈	—	67	2	no	—
476	C₂×Q₈	—	67	1	no	—
477	C₂×Q₈	—	67	1	no	—
478	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
479	C₂×D₄	—	67	2	no	—
480	C₂×D₄	—	67	1	no	—
481	C₂×D₄	—	67	2	no	—
482	C₂×D₄	—	67	1	no	—
483	C₂×D₄	—	67	1	no	—
484	C₂×D₄	—	67	1	no	—
485	C₂×D₄	—	134	4	no	—
486	C₂×D₄	C₂²×D₆₇	1	2	yes	—
487	C₂×D₄	C₂²×D₆₇	1	2	yes	—
488	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₆₇	1	2	yes	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	268	2	no	—
492	C₂²×C₄	—	67	2	no	—
493	C₂²×C₄	—	67	1	no	—
494	C₂²×C₄	—	67	2	no	—
495	C₂²×C₄	—	67	2	no	—
496	C₂²×C₄	—	67	1	no	—
497	C₂²×C₄	—	67	1	no	—
498	C₂²×C₄	—	67	1	no	—
499	C₂²×C₄	—	67	1	no	—
500	C₂²×C₄	—	67	2	no	—
501	C₂²×C₄	—	67	2	no	—
502	C₂²×C₄	—	67	2	no	—
503	C₂²×C₄	—	67	1	no	—
504	C₂²×C₄	—	67	1	no	—
505	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
506	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
508	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
511	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
512	C₄⋊C₄	—	67	1	no	—
513	C₄⋊C₄	—	67	2	no	—
514	C₄⋊C₄	—	67	2	no	—
515	C₄⋊C₄	—	67	2	no	—
516	C₄⋊C₄	—	67	1	no	—
517	C₄⋊C₄	—	67	1	no	—
518	C₄⋊C₄	—	67	1	no	—
519	C₄⋊C₄	—	67	1	no	—
520	C₄⋊C₄	—	67	1	no	—
521	C₄⋊C₄	—	67	2	no	—
522	C₄⋊C₄	—	67	2	no	—
523	C₄⋊C₄	—	67	2	no	—
524	C₄⋊C₄	—	67	2	no	—
525	C₄⋊C₄	—	67	2	no	—
526	C₄⋊C₄	—	67	2	no	—
527	C₄⋊C₄	—	67	2	no	—
528	C₄⋊C₄	—	67	2	no	—
529	C₄⋊C₄	—	67	2	no	—
530	C₄⋊C₄	—	67	2	no	—
531	C₄⋊C₄	—	67	2	no	—
532	C₄⋊C₄	—	67	2	no	—
533	C₄⋊C₄	—	67	2	no	—
534	C₄⋊C₄	—	67	2	no	—
535	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
537	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
538	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
539	C₂²⋊C₄	—	67	2	no	—
540	C₂²⋊C₄	—	67	1	no	—
541	C₂²⋊C₄	—	67	2	no	—
542	C₂²⋊C₄	—	67	1	no	—
543	C₂²⋊C₄	—	67	1	no	—
544	C₂²⋊C₄	—	67	1	no	—
545	C₂²⋊C₄	—	67	2	no	—
546	C₂²⋊C₄	—	67	2	no	—
547	C₂²⋊C₄	—	67	2	no	—
548	C₂²⋊C₄	—	67	2	no	—
549	C₂²⋊C₄	—	67	2	no	—
550	C₂²⋊C₄	—	67	2	no	—
551	C₂²⋊C₄	—	67	1	no	—
552	C₂²⋊C₄	—	67	1	no	—
553	C₂²⋊C₄	—	67	1	no	—
554	C₂²⋊C₄	—	67	1	no	—
555	C₂²⋊C₄	—	67	2	no	—
556	C₂²⋊C₄	—	67	2	no	—
557	C₂²⋊C₄	—	67	2	no	—
558	C₂²⋊C₄	—	67	2	no	—
559	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
564	C₄²	—	67	1	no	—
565	C₄²	—	67	1	no	—
566	C₄²	—	67	1	no	—
567	C₄²	—	67	1	no	—
568	C₄²	—	67	2	no	—
569	C₄²	—	67	2	no	—
570	C₄²	—	67	2	no	—
571	C₄²	—	67	2	no	—
572	C₄²	C₂²×D₆₇	1	2	yes	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	268	1	no	—
577	C₂³	—	67	1	no	—
578	C₂³	—	67	1	no	—
579	C₂³	—	134	2	no	—
580	C₂³	—	134	2	no	—
581	C₂³	C₂³×D₆₇	1	1	yes	characteristic
582	C₂³	C₂³×D₆₇	1	2	yes	—
583	C₂³	C₂³×D₆₇	1	1	yes	characteristic
584	C₂³	C₂³×D₆₇	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	268	2	no	—
587	Q₈	—	268	2	no	—
588	Q₈	—	134	4	no	—
589	Q₈	—	134	2	no	—
590	Q₈	—	134	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	268	2	no	—
596	D₄	—	67	4	no	—
597	D₄	—	134	2	no	—
598	D₄	—	134	2	no	—
599	D₄	—	134	4	no	—
600	D₄	—	134	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	268	1	no	—
609	C₂×C₄	—	268	1	no	—
610	C₂×C₄	—	268	2	no	—
611	C₂×C₄	—	268	1	no	—
612	C₂×C₄	—	268	2	no	—
613	C₂×C₄	—	268	2	no	—
614	C₂×C₄	—	67	1	no	—
615	C₂×C₄	—	67	1	no	—
616	C₂×C₄	—	67	1	no	—
617	C₂×C₄	—	67	2	no	—
618	C₂×C₄	—	67	1	no	—
619	C₂×C₄	—	67	1	no	—
620	C₂×C₄	—	67	2	no	—
621	C₂×C₄	—	67	2	no	—
622	C₂×C₄	—	67	2	no	—
623	C₂×C₄	—	67	1	no	—
624	C₂×C₄	—	134	4	no	—
625	C₂×C₄	—	134	2	no	—
626	C₂×C₄	—	134	4	no	—
627	C₂×C₄	—	134	4	no	—
628	C₂×C₄	—	134	2	no	—
629	C₂×C₄	—	134	2	no	—
630	C₂×C₄	—	134	2	no	—
631	C₂×C₄	C₂³×D₆₇	1	2	yes	—
632	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₆₇	1	2	yes	—
634	C₂×C₄	C₂³×D₆₇	1	2	yes	—
635	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	4	4	no	—
649	C₂²	—	268	4	no	—
650	C₂²	—	67	2	no	—
651	C₂²	—	134	1	no	—
652	C₂²	—	134	1	no	—
653	C₂²	—	134	1	no	—
654	C₂²	—	134	1	no	—
655	C₂²	—	134	1	no	—
656	C₂²	#41×D₆₇	1	2	yes	—
657	C₂²	#14524090	1	2	yes	—
658	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
659	C₄	—	2	2	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	67	2	no	—
666	C₄	—	134	2	no	—
667	C₄	—	134	1	no	—
668	C₄	—	134	2	no	—
669	C₄	—	134	1	no	—
670	C₄	—	134	1	no	—
671	C₄	—	134	2	no	—
672	C₄	—	134	2	no	—
673	C₄	—	134	1	no	—
674	C₄	—	134	1	no	—
675	C₄	#14524088	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	2	2	no	—
678	C₂	—	4	1	no	—
679	C₂	—	4	2	no	—
680	C₂	—	268	1	no	—
681	C₂	—	134	2	no	—
682	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
683	C₂	C₂×#14524088	1	1	yes	characteristic
684	C₂	C₂×#14524090	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#525×C₆₇	C₂
hypercenter	#525	D₆₇
hypocenter	C₆₇	#3520
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #16864114	C₂	semidirect
2. #16864105	C₂	semidirect
3. #16864088	C₂	semidirect
4. #16864085	C₂	semidirect
5. #16864077	C₂	semidirect
6. #16864075	C₂	semidirect
7. #16864059	C₂	semidirect
8. #16864053	C₂	semidirect
9. #16864052	C₂	semidirect
10. #16864046	C₂	semidirect
11. #16864045	C₂	semidirect
12. #16864033	C₂	semidirect
13. #16864014	C₂	semidirect
14. #16863989	C₂	semidirect
15. #16863988	C₂	semidirect
16. #16863948	C₂	semidirect
17. #16863927	C₂	semidirect
18. #16863906	C₂	semidirect
19. C₂×#14524022	C₂	semidirect
20. C₂²⋊Q₈×D₆₇	C₂	semidirect
21. #16863875	C₂	semidirect
22. C₂×C₄×C₂²⋊D₆₇	C₂	semidirect
23. #525×C₆₇	C₂	semidirect
25. C₂×#11761627	C₂²	semidirect
26. C₂²×Dic₁₃₄	C₂²	semidirect
27. C₂×Q₈×D₆₇	C₂²	semidirect
30. #14524042	C₂²	semidirect
31. #14524042	C₂²	semidirect
32. #14524041	C₂²	semidirect
33. #14524038	C₂²	semidirect
34. #14524037	C₂²	semidirect
35. #14524036	C₂²	semidirect
36. #14524036	C₂²	semidirect
37. #14524036	C₂²	semidirect
38. #14524035	C₂²	semidirect
39. #14524034	C₂²	semidirect
40. #14524034	C₂²	semidirect
41. #14524033	C₂²	semidirect
42. #14524030	C₂²	semidirect
43. #14524030	C₂²	semidirect
45. #14524029	C₂²	semidirect
47. #14524026	C₂²	semidirect
49. #14524025	C₂²	semidirect
50. #14524025	C₂²	semidirect
52. #14524024	C₂²	semidirect
53. #14524024	C₂²	semidirect
54. #14524023	C₂²	semidirect
55. #14524023	C₂²	semidirect
59. #14524022	C₂²	semidirect
60. #14524022	C₂²	semidirect
61. #14524022	C₂²	semidirect
62. #14524022	C₂²	semidirect
63. #14524021	C₂²	semidirect
64. #14524021	C₂²	semidirect
67. #14524020	C₂²	semidirect
68. #14524020	C₂²	semidirect
69. #14524020	C₂²	semidirect
70. #14524019	C₂²	semidirect
74. #14524014	C₂²	semidirect
76. Q₈×Dic₆₇	C₂²	semidirect
77. C₄×Dic₁₃₄	C₂²	semidirect
78. #14524008	C₂²	semidirect
79. #14524008	C₂²	semidirect
80. #14524008	C₂²	semidirect
83. D₄×Dic₆₇	C₂²	semidirect
84. D₄×Dic₆₇	C₂²	semidirect
93. C₄×C₂²⋊D₆₇	C₂²	semidirect
95. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
96. #14524001	C₂²	semidirect
97. #14524000	C₂²	semidirect
99. #14523999	C₂²	semidirect
100. #14523999	C₂²	semidirect
101. C₂×C₄⋊Dic₆₇	C₂²	semidirect
103. C₂×Dic₆₇⋊C₄	C₂²	semidirect
104. C₂×Dic₆₇⋊C₄	C₂²	semidirect
105. C₄⋊C₄×D₆₇	C₂²	semidirect
106. C₄⋊C₄×D₆₇	C₂²	semidirect
112. C₂×#41×C₆₇	C₂²	semidirect
114. #123×C₆₇	C₂²	semidirect
116. C₂²⋊Q₈×C₆₇	C₂²	semidirect
118. #121×C₆₇	C₂²	semidirect
121. C₄×D₄×C₆₇	C₂²	semidirect
122. #117×C₆₇	C₂²	semidirect
266. C₂²⋊D₆₇	#41	semidirect
343. C₆₇	#3520	semidirect
362. #525	D₆₇	semidirect
369. C₂×#41	C₂×D₆₇	semidirect
399. #123	C₂×D₆₇	semidirect
418. C₂²⋊Q₈	C₂×D₆₇	semidirect
424. #121	C₂×D₆₇	semidirect
448. C₄×D₄	C₂×D₆₇	semidirect
454. #117	C₂×D₆₇	semidirect