Subgroups — #22574462

Order 8576.

1050 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864134	C₂	1	2	yes	maximal, complemented
2	#16864134	C₂	1	2	yes	maximal, complemented
3	#16864098	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864094	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864093	C₂	1	2	yes	maximal, complemented
6	#16864089	C₂	1	2	yes	maximal, complemented
7	#16864088	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864081	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864065	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864064	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864048	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864045	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864006	C₂	1	1	yes	maximal, characteristic, complemented
14	#16863999	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863999	C₂	1	2	yes	maximal, complemented
16	#16863996	C₂	1	2	yes	maximal, complemented
17	#16863995	C₂	1	2	yes	maximal, complemented
18	#16863992	C₂	1	2	yes	maximal, complemented
19	#16863974	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863909	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863906	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863903	C₂	1	1	yes	maximal, characteristic, complemented
23	#537×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761629	C₂²	1	1	yes	characteristic
25	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11761627	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
28	#14524041	C₂²	1	1	yes	characteristic, complemented
29	#14524039	C₂²	1	2	yes	—
30	#14524039	C₂²	1	2	yes	—
31	#14524039	C₂²	1	1	yes	characteristic, complemented
32	#14524038	C₂²	1	2	yes	—
33	#14524038	C₂²	1	2	yes	—
34	#14524038	C₂²	1	2	yes	complemented
35	#14524036	C₂²	1	2	yes	—
36	#14524036	C₂²	1	2	yes	—
37	#14524036	C₂²	1	2	yes	complemented
38	#14524034	C₂²	1	1	yes	characteristic, complemented
39	#14524034	C₂²	1	2	yes	complemented
40	#14524034	C₂²	1	1	yes	characteristic, complemented
41	#14524034	C₂²	1	2	yes	complemented
42	#14524033	C₂²	1	2	yes	complemented
43	#14524033	C₂²	1	2	yes	complemented
44	#14524028	C₂²	1	2	yes	—
45	#14524028	C₂²	1	2	yes	—
46	#14524028	C₂²	1	2	yes	—
47	#14524027	C₂²	1	2	yes	—
48	#14524027	C₂²	1	2	yes	—
49	#14524027	C₂²	1	2	yes	complemented
50	#14524026	C₂²	1	2	yes	—
51	#14524026	C₂²	1	2	yes	—
52	#14524025	C₂²	1	2	yes	—
53	#14524025	C₂²	1	2	yes	complemented
54	#14524025	C₂²	1	2	yes	complemented
55	#14524024	C₂²	1	1	yes	characteristic
56	#14524024	C₂²	1	1	yes	characteristic
57	#14524024	C₂²	1	2	yes	complemented
58	#14524023	C₂²	1	1	yes	characteristic
59	#14524022	C₂²	1	1	yes	characteristic
60	#14524022	C₂²	1	1	yes	characteristic, complemented
61	#14524019	C₂²	1	1	yes	characteristic
62	#14524019	C₂²	1	1	yes	characteristic
63	#14524019	C₂²	1	1	yes	characteristic
64	#14524019	C₂²	1	2	yes	complemented
65	#14524018	C₂²	1	1	yes	characteristic
66	#14524017	C₂²	1	2	yes	—
67	#14524017	C₂²	1	2	yes	—
68	#14524017	C₂²	1	1	yes	characteristic
69	#14524017	C₂²	1	1	yes	characteristic, complemented
70	#14524016	C₂²	1	2	yes	—
71	#14524016	C₂²	1	2	yes	—
72	#14524015	C₂²	1	2	yes	—
73	#14524015	C₂²	1	2	yes	—
74	#14524015	C₂²	1	2	yes	—
75	#14524015	C₂²	1	2	yes	—
76	#14524015	C₂²	1	2	yes	complemented
77	#14524015	C₂²	1	2	yes	complemented
78	#14524014	C₂²	1	1	yes	characteristic
79	#14524014	C₂²	1	2	yes	—
80	#14524014	C₂²	1	2	yes	—
81	#14524014	C₂²	1	1	yes	characteristic
82	#14524014	C₂²	1	1	yes	characteristic
83	#14524014	C₂²	1	2	yes	complemented
84	#14524013	C₂²	1	2	yes	—
85	#14524011	C₂²	1	1	yes	characteristic
86	#14524011	C₂²	1	1	yes	characteristic
87	#14524011	C₂²	1	2	yes	—
88	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
89	#14524008	C₂²	1	1	yes	characteristic, complemented
90	D₄×Dic₆₇	C₂²	1	2	yes	—
91	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
92	D₄×Dic₆₇	C₂²	1	2	yes	complemented
93	#14524005	C₂²	1	2	yes	—
94	#14524005	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
101	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
102	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
103	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
104	#14524002	C₂²	1	1	yes	characteristic
105	#14524002	C₂²	1	2	yes	complemented
106	#14524001	C₂²	1	1	yes	characteristic
107	#14524001	C₂²	1	1	yes	characteristic
108	#14523999	C₂²	1	2	yes	complemented
109	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
110	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
111	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
112	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic
113	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
115	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
117	#121×C₆₇	C₂²	1	2	yes	—
118	#121×C₆₇	C₂²	1	2	yes	—
119	#121×C₆₇	C₂²	1	1	yes	characteristic
120	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#121×C₆₇	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	#11761629	—	4	2	no	—
125	#11761628	—	4	2	no	—
126	#11761627	—	4	2	no	—
127	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
128	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
129	C₂×D₂₆₈	C₂³	1	2	yes	—
130	C₂×D₂₆₈	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	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
140	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
142	C₂²×Dic₆₇	C₂³	1	2	yes	—
143	C₂²×Dic₆₇	C₂³	1	2	yes	—
144	C₂²×Dic₆₇	C₂³	1	2	yes	—
145	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₆₇	—	4	2	no	—
147	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₆₇	C₂³	1	2	yes	—
150	C₂×C₄×D₆₇	C₂³	1	2	yes	—
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	2	yes	—
155	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₆₇	C₂³	1	2	yes	—
158	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₆₇	C₂³	1	2	yes	—
161	C₄⋊Dic₆₇	C₂³	1	2	yes	—
162	C₄⋊Dic₆₇	C₂³	1	2	yes	—
163	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₆₇⋊C₄	C₂³	1	2	yes	—
165	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₆₇⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
171	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₆₇⋊C₄	C₂³	1	2	yes	—
174	Dic₆₇⋊C₄	C₂³	1	2	yes	—
175	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
185	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
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	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
197	C₄×Dic₆₇	C₂³	1	2	yes	—
198	C₄×Dic₆₇	C₂³	1	2	yes	—
199	C₄×Dic₆₇	C₂³	1	2	yes	—
200	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₆₇	C₂³	1	2	yes	—
203	#41×C₆₇	—	4	2	no	—
204	#41×C₆₇	—	4	2	no	—
205	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₆₇	C₂³	1	2	yes	—
209	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₆₇	C₂³	1	2	yes	—
212	C₂×D₄×C₆₇	C₂³	1	2	yes	—
213	C₂×D₄×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	2	yes	—
219	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₇	C₂⁴	1	2	yes	—
230	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×D₆₇	—	4	1	no	—
233	C₂²×D₆₇	—	4	1	no	—
234	C₂²×D₆₇	—	4	1	no	—
235	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
236	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
237	C₂²×D₆₇	C₂⁴	1	2	yes	—
238	Q₈×C₆₇	—	2	2	no	—
239	Q₈×C₆₇	—	4	1	no	—
240	D₄×C₆₇	—	2	2	no	—
241	D₄×C₆₇	—	4	2	no	—
242	D₄×C₆₇	—	4	2	no	—
243	D₄×C₆₇	—	4	1	no	—
244	D₄×C₆₇	—	4	1	no	—
245	D₄×C₆₇	—	4	2	no	—
246	D₄×C₆₇	—	4	1	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	2	no	—
251	C₂×C₄×C₆₇	—	4	2	no	—
252	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
254	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²⋊D₆₇	—	4	1	no	—
260	C₂²⋊D₆₇	—	4	2	no	—
261	C₂²⋊D₆₇	—	4	1	no	—
262	C₂²⋊D₆₇	—	4	2	no	—
263	C₂²⋊D₆₇	—	4	2	no	—
264	C₂²⋊D₆₇	—	4	2	no	—
265	C₂²⋊D₆₇	—	4	2	no	—
266	C₂²⋊D₆₇	—	4	1	no	—
267	C₂²⋊D₆₇	—	4	1	no	—
268	C₂²⋊D₆₇	—	4	2	no	—
269	C₂²⋊D₆₇	—	4	2	no	—
270	C₂×Dic₆₇	—	4	1	no	—
271	C₂×Dic₆₇	—	4	2	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	1	yes	characteristic
277	C₂×Dic₆₇	C₂⁴	1	2	yes	—
278	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₆₇	C₂⁴	1	2	yes	—
280	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₆₇	C₂⁴	1	2	yes	—
283	D₂₆₈	—	2	2	no	—
284	D₂₆₈	—	4	2	no	—
285	D₂₆₈	—	4	2	no	—
286	C₄×D₆₇	—	2	2	no	—
287	C₄×D₆₇	—	2	2	no	—
288	C₄×D₆₇	—	4	1	no	—
289	C₄×D₆₇	—	4	1	no	—
290	C₄×D₆₇	—	4	2	no	—
291	C₄×D₆₇	—	4	2	no	—
292	C₄×D₆₇	—	4	2	no	—
293	Dic₁₃₄	—	2	2	no	—
294	C₂²×C₆₇	—	2	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	1	no	—
302	C₂²×C₆₇	—	2	1	no	—
303	C₂²×C₆₇	—	2	2	no	—
304	C₂²×C₆₇	—	2	1	no	—
305	C₂²×C₆₇	—	2	1	no	—
306	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
307	C₂×D₆₇	—	2	1	no	—
308	C₂×D₆₇	—	2	1	no	—
309	C₂×D₆₇	—	2	2	no	—
310	C₂×D₆₇	—	2	2	no	—
311	C₂×D₆₇	—	2	1	no	—
312	C₂×D₆₇	—	2	2	no	—
313	C₂×D₆₇	—	2	1	no	—
314	C₂×D₆₇	—	2	1	no	—
315	C₂×D₆₇	—	2	1	no	—
316	C₂×D₆₇	—	4	4	no	—
317	C₄×C₆₇	—	2	1	no	—
318	C₄×C₆₇	—	2	1	no	—
319	C₄×C₆₇	—	2	2	no	—
320	C₄×C₆₇	—	2	1	no	—
321	C₄×C₆₇	—	2	2	no	—
322	C₄×C₆₇	—	2	2	no	—
323	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
324	Dic₆₇	—	2	2	no	—
325	Dic₆₇	—	2	1	no	—
326	Dic₆₇	—	2	1	no	—
327	Dic₆₇	—	2	1	no	—
328	Dic₆₇	—	2	1	no	—
329	Dic₆₇	—	2	2	no	—
330	Dic₆₇	—	2	2	no	—
331	Dic₆₇	—	2	1	no	—
332	Dic₆₇	—	2	1	no	—
333	C₂×C₆₇	—	4	1	no	—
334	C₂×C₆₇	—	4	2	no	—
335	C₂×C₆₇	—	4	1	no	—
336	C₂×C₆₇	—	4	1	no	—
337	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₆₇	#585	1	1	yes	characteristic
339	C₂×C₆₇	#585	1	1	yes	characteristic
340	D₆₇	—	4	2	no	—
341	D₆₇	—	4	1	no	—
342	D₆₇	—	4	1	no	—
343	#3539	—	67	1	no	maximal, Sylow
344	C₆₇	#3539	1	1	yes	characteristic, complemented, Sylow
345	#560	—	67	2	no	—
346	#560	—	67	2	no	—
347	#553	—	67	2	no	—
348	#553	—	67	2	no	—
349	#553	—	67	1	no	—
350	#553	—	67	1	no	—
351	#552	—	67	1	no	—
352	#552	—	67	1	no	—
353	#550	—	67	1	no	—
354	#550	—	67	1	no	—
355	#547	—	67	1	no	—
356	#547	—	67	1	no	—
357	#541	—	67	1	no	—
358	#540	—	67	1	no	—
359	#540	—	67	2	no	—
360	#540	—	67	2	no	—
361	#539	—	67	2	no	—
362	#539	—	67	2	no	—
363	#537	—	67	1	no	—
364	#537	D₆₇	1	1	yes	characteristic, complemented
365	#525	—	67	1	no	—
366	#525	—	67	1	no	—
367	#525	—	67	1	no	—
368	C₂×#41	—	67	1	no	—
369	C₂×#41	—	67	1	no	—
370	C₂×#41	—	67	1	no	—
371	C₂×#41	C₂×D₆₇	1	1	yes	characteristic
372	C₂×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
373	C₂³×C₄	—	67	1	no	—
374	C₄⋊Q₈	—	67	1	no	—
375	#127	—	67	1	no	—
376	#127	—	67	2	no	—
377	#127	—	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	#126	—	67	2	no	—
384	#125	—	67	2	no	—
385	#125	—	67	2	no	—
386	#125	—	67	2	no	—
387	#125	—	67	2	no	—
388	#125	—	67	1	no	—
389	#125	—	67	1	no	—
390	#123	—	67	1	no	—
391	#123	—	67	1	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	—	67	2	no	—
400	#123	—	67	2	no	—
401	#123	—	67	2	no	—
402	#123	—	67	2	no	—
403	#123	—	67	2	no	—
404	C₂²⋊Q₈	—	67	1	no	—
405	C₂²⋊Q₈	—	67	1	no	—
406	C₂²⋊Q₈	—	67	1	no	—
407	C₂²⋊Q₈	—	67	2	no	—
408	C₂²⋊Q₈	—	67	1	no	—
409	C₂²⋊Q₈	—	67	1	no	—
410	C₂²⋊Q₈	—	67	1	no	—
411	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
412	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
413	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
414	#121	—	67	1	no	—
415	#121	—	67	1	no	—
416	#121	—	67	1	no	—
417	#121	—	67	2	no	—
418	#121	—	67	2	no	—
419	#121	—	67	2	no	—
420	#121	—	67	2	no	—
421	#121	—	67	2	no	—
422	#121	—	67	2	no	—
423	#121	—	67	2	no	—
424	#121	—	67	2	no	—
425	#121	—	67	2	no	—
426	#121	—	67	1	no	—
427	#121	—	67	1	no	—
428	#121	—	67	2	no	—
429	#121	—	67	2	no	—
430	#121	—	67	1	no	—
431	#121	—	67	2	no	—
432	#121	—	67	2	no	—
433	#121	C₂×D₆₇	1	1	yes	characteristic
434	#121	C₂×D₆₇	1	2	yes	—
435	#121	C₂×D₆₇	1	2	yes	—
436	#121	C₂×D₆₇	1	2	yes	complemented
437	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
438	#120	—	67	1	no	—
439	#120	—	67	1	no	—
440	#120	—	67	2	no	—
441	#120	—	67	2	no	—
442	C₄×Q₈	—	67	1	no	—
443	C₄×Q₈	—	67	1	no	—
444	C₄×D₄	—	67	2	no	—
445	C₄×D₄	—	67	1	no	—
446	C₄×D₄	—	67	2	no	—
447	C₄×D₄	—	67	1	no	—
448	C₄×D₄	—	67	1	no	—
449	C₄×D₄	—	67	1	no	—
450	C₄×D₄	—	67	1	no	—
451	C₄×D₄	—	67	2	no	—
452	C₄×D₄	—	67	2	no	—
453	C₄×D₄	—	67	2	no	—
454	C₄×D₄	—	67	1	no	—
455	C₄×D₄	—	67	2	no	—
456	C₄×D₄	—	67	2	no	—
457	C₄×D₄	—	67	2	no	—
458	#117	—	67	1	no	—
459	#117	—	67	2	no	—
460	#117	—	67	1	no	—
461	#117	—	67	1	no	—
462	#117	—	67	2	no	—
463	C₂×C₄⋊C₄	—	67	1	no	—
464	C₂×C₄⋊C₄	—	67	2	no	—
465	C₂×C₄⋊C₄	—	67	2	no	—
466	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
467	C₂⁴	—	67	1	no	—
468	#41	—	4	2	no	—
469	#41	—	4	2	no	—
470	#41	—	268	2	no	—
471	#41	—	268	2	no	—
472	#41	—	268	2	no	—
473	C₂×Q₈	—	67	1	no	—
474	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
475	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
476	C₂×D₄	—	67	1	no	—
477	C₂×D₄	—	67	1	no	—
478	C₂×D₄	—	67	2	no	—
479	C₂×D₄	—	67	2	no	—
480	C₂×D₄	—	67	1	no	—
481	C₂×D₄	—	67	1	no	—
482	C₂×D₄	—	67	2	no	—
483	C₂×D₄	—	67	2	no	—
484	C₂×D₄	—	67	2	no	—
485	C₂×D₄	—	67	2	no	—
486	C₂×D₄	—	67	2	no	—
487	C₂×D₄	—	67	2	no	—
488	C₂×D₄	—	67	2	no	—
489	C₂×D₄	—	67	1	no	—
490	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
491	C₂×D₄	C₂²×D₆₇	1	2	yes	—
492	C₂×D₄	C₂²×D₆₇	1	2	yes	—
493	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
494	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₆₇	1	2	yes	—
497	C₂²×C₄	—	268	2	no	—
498	C₂²×C₄	—	67	2	no	—
499	C₂²×C₄	—	67	2	no	—
500	C₂²×C₄	—	67	2	no	—
501	C₂²×C₄	—	67	1	no	—
502	C₂²×C₄	—	67	2	no	—
503	C₂²×C₄	—	67	2	no	—
504	C₂²×C₄	—	67	2	no	—
505	C₂²×C₄	—	67	1	no	—
506	C₂²×C₄	—	67	1	no	—
507	C₂²×C₄	—	67	1	no	—
508	C₂²×C₄	—	67	1	no	—
509	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
513	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
514	C₄⋊C₄	—	67	1	no	—
515	C₄⋊C₄	—	67	1	no	—
516	C₄⋊C₄	—	67	1	no	—
517	C₄⋊C₄	—	67	2	no	—
518	C₄⋊C₄	—	67	2	no	—
519	C₄⋊C₄	—	67	1	no	—
520	C₄⋊C₄	—	67	2	no	—
521	C₄⋊C₄	—	67	2	no	—
522	C₄⋊C₄	—	67	2	no	—
523	C₄⋊C₄	—	67	2	no	—
524	C₄⋊C₄	—	67	1	no	—
525	C₄⋊C₄	—	67	1	no	—
526	C₄⋊C₄	—	67	2	no	—
527	C₄⋊C₄	—	67	2	no	—
528	C₄⋊C₄	—	67	1	no	—
529	C₄⋊C₄	—	67	1	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	2	yes	—
536	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
537	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
538	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
539	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
540	C₂²⋊C₄	—	67	1	no	—
541	C₂²⋊C₄	—	67	1	no	—
542	C₂²⋊C₄	—	67	1	no	—
543	C₂²⋊C₄	—	67	1	no	—
544	C₂²⋊C₄	—	67	2	no	—
545	C₂²⋊C₄	—	67	2	no	—
546	C₂²⋊C₄	—	67	1	no	—
547	C₂²⋊C₄	—	67	1	no	—
548	C₂²⋊C₄	—	67	2	no	—
549	C₂²⋊C₄	—	67	2	no	—
550	C₂²⋊C₄	—	67	2	no	—
551	C₂²⋊C₄	—	67	2	no	—
552	C₂²⋊C₄	—	67	2	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	1	no	—
558	C₂²⋊C₄	—	67	1	no	—
559	C₂²⋊C₄	—	67	2	no	—
560	C₂²⋊C₄	—	67	2	no	—
561	C₂²⋊C₄	—	67	2	no	—
562	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
565	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
566	C₄²	—	67	2	no	—
567	C₄²	—	67	2	no	—
568	C₄²	—	67	1	no	—
569	C₄²	—	67	1	no	—
570	C₄²	—	67	2	no	—
571	C₄²	—	67	2	no	—
572	C₂³	—	268	1	no	—
573	C₂³	—	268	1	no	—
574	C₂³	—	268	1	no	—
575	C₂³	—	67	1	no	—
576	C₂³	—	67	1	no	—
577	C₂³	—	67	2	no	—
578	C₂³	C₂³×D₆₇	1	1	yes	characteristic
579	C₂³	C₂³×D₆₇	1	1	yes	characteristic
580	C₂³	C₂³×D₆₇	1	1	yes	characteristic
581	C₂³	C₂³×D₆₇	1	2	yes	—
582	Q₈	—	2	2	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	134	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	268	2	no	—
593	D₄	—	268	2	no	—
594	D₄	—	268	2	no	—
595	D₄	—	268	2	no	—
596	D₄	—	268	1	no	—
597	D₄	—	268	1	no	—
598	D₄	—	268	2	no	—
599	D₄	—	268	1	no	—
600	D₄	—	268	2	no	—
601	D₄	—	268	2	no	—
602	D₄	—	268	2	no	—
603	D₄	—	268	1	no	—
604	D₄	—	268	2	no	—
605	D₄	—	134	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	268	1	no	—
612	C₂×C₄	—	268	1	no	—
613	C₂×C₄	—	268	2	no	—
614	C₂×C₄	—	268	2	no	—
615	C₂×C₄	—	268	2	no	—
616	C₂×C₄	—	268	1	no	—
617	C₂×C₄	—	268	2	no	—
618	C₂×C₄	—	268	2	no	—
619	C₂×C₄	—	268	2	no	—
620	C₂×C₄	—	67	1	no	—
621	C₂×C₄	—	67	1	no	—
622	C₂×C₄	—	67	2	no	—
623	C₂×C₄	—	67	1	no	—
624	C₂×C₄	—	67	1	no	—
625	C₂×C₄	—	67	1	no	—
626	C₂×C₄	—	67	2	no	—
627	C₂×C₄	—	67	1	no	—
628	C₂×C₄	—	67	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	2	yes	—
633	C₂×C₄	C₂³×D₆₇	1	2	yes	—
634	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
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	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	268	4	no	—
651	C₂²	—	134	2	no	—
652	C₂²	—	134	1	no	—
653	C₂²	—	134	1	no	—
654	C₂²	—	134	2	no	—
655	C₂²	—	134	1	no	—
656	C₂²	—	134	1	no	—
657	C₂²	—	134	2	no	—
658	C₂²	—	134	1	no	—
659	C₂²	—	134	1	no	—
660	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	134	1	no	—
668	C₄	—	134	1	no	—
669	C₄	—	134	2	no	—
670	C₄	—	134	1	no	—
671	C₄	—	134	1	no	—
672	C₄	—	134	1	no	—
673	C₄	—	134	2	no	—
674	C₄	—	134	2	no	—
675	C₄	—	134	1	no	—
676	C₄	#14524088	1	2	yes	—
677	C₂	—	4	1	no	—
678	C₂	—	4	1	no	—
679	C₂	—	4	1	no	—
680	C₂	—	4	2	no	—
681	C₂	—	268	1	no	—
682	C₂	—	268	1	no	—
683	C₂	—	268	2	no	—
684	C₂	C₂×#14524088	1	1	yes	characteristic
685	C₂	#16864231	1	1	yes	characteristic
686	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#537×C₆₇	C₂
hypercenter	#537	D₆₇
hypocenter	C₆₇	#3539
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. #16864134	C₂	semidirect
2. #16864134	C₂	semidirect
3. #16864098	C₂	semidirect
4. #16864094	C₂	semidirect
5. #16864093	C₂	semidirect
6. #16864089	C₂	semidirect
7. #16864088	C₂	semidirect
8. #16864081	C₂	semidirect
9. #16864065	C₂	semidirect
10. #16864064	C₂	semidirect
11. #16864048	C₂	semidirect
12. #16864045	C₂	semidirect
13. #16864006	C₂	semidirect
14. #16863999	C₂	semidirect
15. #16863999	C₂	semidirect
16. #16863996	C₂	semidirect
17. #16863995	C₂	semidirect
18. #16863992	C₂	semidirect
19. #16863974	C₂	semidirect
20. #16863909	C₂	semidirect
21. #16863906	C₂	semidirect
22. #16863903	C₂	semidirect
23. #537×C₆₇	C₂	semidirect
25. C₂×#11761628	C₂²	semidirect
28. #14524041	C₂²	semidirect
31. #14524039	C₂²	semidirect
34. #14524038	C₂²	semidirect
37. #14524036	C₂²	semidirect
38. #14524034	C₂²	semidirect
39. #14524034	C₂²	semidirect
40. #14524034	C₂²	semidirect
41. #14524034	C₂²	semidirect
42. #14524033	C₂²	semidirect
43. #14524033	C₂²	semidirect
49. #14524027	C₂²	semidirect
53. #14524025	C₂²	semidirect
54. #14524025	C₂²	semidirect
57. #14524024	C₂²	semidirect
60. #14524022	C₂²	semidirect
64. #14524019	C₂²	semidirect
69. #14524017	C₂²	semidirect
76. #14524015	C₂²	semidirect
77. #14524015	C₂²	semidirect
83. #14524014	C₂²	semidirect
88. Q₈×Dic₆₇	C₂²	semidirect
89. #14524008	C₂²	semidirect
91. D₄×Dic₆₇	C₂²	semidirect
92. D₄×Dic₆₇	C₂²	semidirect
94. #14524005	C₂²	semidirect
99. C₄×C₂²⋊D₆₇	C₂²	semidirect
100. C₄×C₂²⋊D₆₇	C₂²	semidirect
103. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
105. #14524002	C₂²	semidirect
108. #14523999	C₂²	semidirect
109. C₂×C₄⋊Dic₆₇	C₂²	semidirect
110. C₂×Dic₆₇⋊C₄	C₂²	semidirect
111. C₄⋊C₄×D₆₇	C₂²	semidirect
113. C₂×#41×C₆₇	C₂²	semidirect
115. C₂²⋊Q₈×C₆₇	C₂²	semidirect
116. C₂²⋊Q₈×C₆₇	C₂²	semidirect
120. #121×C₆₇	C₂²	semidirect
121. #121×C₆₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
344. C₆₇	#3539	semidirect
364. #537	D₆₇	semidirect
372. C₂×#41	C₂×D₆₇	semidirect
412. C₂²⋊Q₈	C₂×D₆₇	semidirect
413. C₂²⋊Q₈	C₂×D₆₇	semidirect
436. #121	C₂×D₆₇	semidirect
437. #121	C₂×D₆₇	semidirect
466. C₂×C₄⋊C₄	C₂×D₆₇	semidirect