Subgroups — #30744014

Order 17152.

550 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22560189	C₂	1	1	yes	maximal, characteristic
2	#22559903	C₂	1	1	yes	maximal, characteristic
3	#22558035	C₂	1	2	yes	maximal, complemented
4	#22558032	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11761612	—	2	1	no	—
7	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
9	#16863151	—	2	1	no	—
10	#16863151	C₂²	1	2	yes	—
11	#16863151	C₂²	1	2	yes	—
12	C₂×C₂²⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₆₇	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
15	#391×C₆₇	C₂²	1	1	yes	characteristic
16	#389×C₆₇	C₂²	1	1	yes	characteristic
17	#387×C₆₇	—	2	1	no	—
18	#385×C₆₇	—	2	1	no	—
19	#380×C₆₇	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
21	C₄×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
23	C₂×#11761612	—	2	4	no	—
24	C₂×#11761612	—	4	2	no	—
25	C₂×#11761612	—	4	2	no	—
26	C₂²×C₆₇⋊C₈	—	2	2	no	—
27	C₂²×C₆₇⋊C₈	—	2	2	no	—
28	C₄⋊(C₆₇⋊C₈)	—	4	2	no	—
29	C₂²⋊(C₆₇⋊C₈)	—	4	2	no	—
30	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
34	C₂²⋊Q₈×C₆₇	—	2	2	no	—
35	C₂²⋊Q₈×C₆₇	—	2	2	no	—
36	C₄×Q₈×C₆₇	—	4	2	no	—
37	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
38	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
39	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
40	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
45	C₂×C₄²×C₆₇	—	2	1	no	—
46	C₂×C₄²×C₆₇	—	2	1	no	—
47	C₂×C₄²×C₆₇	—	4	2	no	—
48	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
52	#95×C₆₇	—	2	1	no	—
53	#95×C₆₇	—	2	1	no	—
54	#95×C₆₇	—	2	1	no	—
55	#95×C₆₇	—	2	1	no	—
56	#95×C₆₇	—	2	1	no	—
57	#11761612	—	4	8	no	—
58	C₂×C₆₇⋊C₈	—	2	4	no	—
59	C₂×C₆₇⋊C₈	—	4	2	no	—
60	C₂×C₆₇⋊C₈	—	4	2	no	—
61	C₂×C₆₇⋊C₈	—	4	2	no	—
62	C₂×C₆₇⋊C₈	—	4	2	no	—
63	C₂×C₆₇⋊C₈	—	4	2	no	—
64	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×Q₈×C₆₇	—	2	1	no	—
66	C₂×Q₈×C₆₇	—	4	1	no	—
67	C₂×Q₈×C₆₇	—	4	1	no	—
68	C₂×Q₈×C₆₇	M₁₆	1	2	yes	complemented
69	C₂²×C₄×C₆₇	—	2	2	no	—
70	C₂²×C₄×C₆₇	—	2	2	no	—
71	C₂²×C₄×C₆₇	—	2	1	no	—
72	C₂²×C₄×C₆₇	—	2	1	no	—
73	C₂²×C₄×C₆₇	—	2	1	no	—
74	C₂²×C₄×C₆₇	—	2	1	no	—
75	C₂²×C₄×C₆₇	—	2	1	no	—
76	C₂²×C₄×C₆₇	—	2	1	no	—
77	C₂²×C₄×C₆₇	—	2	1	no	—
78	C₂²×C₄×C₆₇	—	2	1	no	—
79	C₂²×C₄×C₆₇	—	4	1	no	—
80	C₂²×C₄×C₆₇	—	4	1	no	—
81	C₂²×C₄×C₆₇	—	4	1	no	—
82	C₂²×C₄×C₆₇	—	4	1	no	—
83	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₆₇	Q₁₆	1	2	yes	—
88	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
91	C₄⋊C₄×C₆₇	—	2	4	no	—
92	C₄⋊C₄×C₆₇	—	2	1	no	—
93	C₄⋊C₄×C₆₇	—	4	1	no	—
94	C₄⋊C₄×C₆₇	—	4	1	no	—
95	C₄⋊C₄×C₆₇	—	4	2	no	—
96	C₄⋊C₄×C₆₇	—	4	1	no	—
97	C₄⋊C₄×C₆₇	—	4	1	no	—
98	C₄⋊C₄×C₆₇	M₁₆	1	2	yes	complemented
99	C₂²⋊C₄×C₆₇	—	2	4	no	—
100	C₂²⋊C₄×C₆₇	—	4	2	no	—
101	C₄²×C₆₇	—	2	2	no	—
102	C₄²×C₆₇	—	2	2	no	—
103	C₄²×C₆₇	—	4	1	no	—
104	C₄²×C₆₇	—	4	1	no	—
105	C₄²×C₆₇	—	4	2	no	—
106	C₄²×C₆₇	—	4	2	no	—
107	C₂³×C₆₇	—	2	1	no	—
108	C₂³×C₆₇	—	2	1	no	—
109	C₂³×C₆₇	—	2	1	no	—
110	C₂³×C₆₇	—	2	1	no	—
111	C₂³×C₆₇	—	2	1	no	—
112	C₂³×C₆₇	—	2	1	no	—
113	C₂³×C₆₇	#103	1	2	yes	—
114	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	Q₈×C₆₇	—	4	2	no	—
116	Q₈×C₆₇	—	4	2	no	—
117	C₂×C₄×C₆₇	—	2	1	no	—
118	C₂×C₄×C₆₇	—	2	1	no	—
119	C₂×C₄×C₆₇	—	2	1	no	—
120	C₂×C₄×C₆₇	—	2	1	no	—
121	C₂×C₄×C₆₇	—	2	1	no	—
122	C₂×C₄×C₆₇	—	2	1	no	—
123	C₂×C₄×C₆₇	—	2	4	no	—
124	C₂×C₄×C₆₇	—	2	4	no	—
125	C₂×C₄×C₆₇	—	2	2	no	—
126	C₂×C₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	1	no	—
128	C₂×C₄×C₆₇	—	2	1	no	—
129	C₂×C₄×C₆₇	—	2	1	no	—
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	—	2	1	no	—
132	C₂×C₄×C₆₇	—	2	1	no	—
133	C₂×C₄×C₆₇	—	4	2	no	—
134	C₂×C₄×C₆₇	—	4	2	no	—
135	C₂×C₄×C₆₇	—	4	2	no	—
136	C₂×C₄×C₆₇	—	4	2	no	—
137	C₂×C₄×C₆₇	—	4	1	no	—
138	C₂×C₄×C₆₇	—	4	1	no	—
139	C₂×C₄×C₆₇	—	4	1	no	—
140	C₂×C₄×C₆₇	—	4	1	no	—
141	C₂×C₄×C₆₇	—	4	1	no	—
142	C₂×C₄×C₆₇	—	4	1	no	—
143	C₂×C₄×C₆₇	—	4	1	no	—
144	C₂×C₄×C₆₇	—	4	1	no	—
145	C₂×C₄×C₆₇	—	4	1	no	—
146	C₂×C₄×C₆₇	—	4	1	no	—
147	C₂×C₄×C₆₇	#99	1	2	yes	—
148	C₂×C₄×C₆₇	#103	1	2	yes	—
149	C₂×C₄×C₆₇	#104	1	2	yes	—
150	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
154	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₆₇	#137	1	1	yes	characteristic
156	C₆₇⋊C₈	—	4	4	no	—
157	C₆₇⋊C₈	—	8	2	no	—
158	C₂²×C₆₇	—	2	2	no	—
159	C₂²×C₆₇	—	2	2	no	—
160	C₂²×C₆₇	—	2	2	no	—
161	C₂²×C₆₇	—	4	1	no	—
162	C₂²×C₆₇	—	4	1	no	—
163	C₂²×C₆₇	—	4	1	no	—
164	C₂²×C₆₇	—	4	1	no	—
165	C₂²×C₆₇	#407	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×#99	1	1	yes	characteristic
167	C₂²×C₆₇	#413	1	1	yes	characteristic
168	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
169	C₂²×C₆₇	#417	1	1	yes	characteristic
170	C₂²×C₆₇	C₂×#104	1	1	yes	characteristic
171	C₂²×C₆₇	#421	1	1	yes	characteristic
172	C₄×C₆₇	—	2	1	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	—	2	1	no	—
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	2	1	no	—
178	C₄×C₆₇	—	4	1	no	—
179	C₄×C₆₇	—	4	2	no	—
180	C₄×C₆₇	—	4	2	no	—
181	C₄×C₆₇	—	4	1	no	—
182	C₄×C₆₇	—	8	1	no	—
183	C₄×C₆₇	—	8	1	no	—
184	C₄×C₆₇	#328	1	4	yes	—
185	#7617	—	67	1	no	maximal, Sylow
186	C₂×C₆₇	—	4	2	no	—
187	C₂×C₆₇	#1465	1	1	yes	characteristic
188	C₂×C₆₇	#1487	1	1	yes	characteristic
189	C₂×C₆₇	#1489	1	1	yes	characteristic
190	C₂×C₆₇	C₂×#328	1	1	yes	characteristic
191	C₂×C₆₇	#1513	1	1	yes	characteristic
192	C₂×C₆₇	#1529	1	1	yes	characteristic
193	C₂×C₆₇	#1550	1	1	yes	characteristic
194	C₄×C₂²⋊Q₈	D₆₇	1	1	yes	characteristic
195	#1797	—	67	1	no	—
196	#1728	—	67	1	no	—
197	#1272	—	67	2	no	—
198	#1271	—	67	2	no	—
199	C₆₇	#7617	1	1	yes	characteristic, complemented, Sylow
200	C₂²×M₁₆	—	134	1	no	—
201	C₂×C₂²⋊Q₈	Dic₆₇	1	1	yes	characteristic
202	C₂×C₄×Q₈	Dic₆₇	1	1	yes	characteristic
203	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
204	C₂×C₄⋊C₈	—	134	1	no	—
205	C₂×C₂²⋊C₈	—	134	1	no	—
206	#391	C₂×D₆₇	1	1	yes	characteristic
207	#389	C₂×D₆₇	1	1	yes	characteristic
208	#387	—	2	1	no	—
209	#385	—	2	1	no	—
210	#380	Dic₆₇	1	1	yes	characteristic
211	C₄×C₄⋊C₄	—	2	1	no	—
212	C₄×C₄⋊C₄	Dic₆₇	1	1	yes	characteristic
213	C₄×C₂²⋊C₄	—	2	1	no	—
214	#336	—	67	2	no	—
215	#336	—	67	2	no	—
216	#336	—	134	1	no	—
217	C₂²×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
218	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
219	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
220	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
221	C₂×M₁₆	—	268	2	no	—
222	C₂×M₁₆	—	268	2	no	—
223	C₂×M₁₆	—	134	4	no	—
224	C₂²×C₈	—	134	2	no	—
225	C₂²×C₈	—	134	2	no	—
226	C₂²⋊Q₈	—	2	2	no	—
227	C₂²⋊Q₈	—	2	2	no	—
228	C₄×Q₈	—	4	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	—	4	2	no	—
240	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
241	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
244	C₄⋊C₈	—	268	2	no	—
245	C₂²⋊C₈	—	268	2	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	C₂⁴	C₂²⋊Dic₆₇	1	1	yes	characteristic
252	C₂×Q₈	—	2	1	no	—
253	C₂×Q₈	—	4	1	no	—
254	C₂×Q₈	—	4	1	no	—
255	C₂×Q₈	#11761612	1	2	yes	complemented
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
273	C₂²×C₄	#11761615	1	2	yes	—
274	C₂²×C₄	#11761618	1	2	yes	—
275	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
278	M₁₆	—	268	8	no	—
279	C₂×C₈	—	268	2	no	—
280	C₂×C₈	—	268	2	no	—
281	C₂×C₈	—	268	2	no	—
282	C₂×C₈	—	268	2	no	—
283	C₂×C₈	—	268	2	no	—
284	C₂×C₈	—	134	4	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	#11761612	1	2	yes	complemented
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	4	1	no	—
298	C₄²	—	4	1	no	—
299	C₄²	—	4	2	no	—
300	C₄²	—	4	2	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	#14523967	1	2	yes	—
308	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
309	Q₈	—	4	2	no	—
310	Q₈	—	4	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	#14523958	1	2	yes	—
342	C₂×C₄	#14523967	1	2	yes	—
343	C₂×C₄	#14523970	1	2	yes	—
344	C₂×C₄	C₂×#11761612	1	1	yes	characteristic
345	C₂×C₄	C₂×#11761612	1	1	yes	characteristic
346	C₂×C₄	C₂×#11761615	1	1	yes	characteristic
347	C₂×C₄	C₂×#11761618	1	1	yes	characteristic
348	C₂×C₄	#14524068	1	1	yes	characteristic
349	C₂×C₄	#14524073	1	1	yes	characteristic
350	C₈	—	268	4	no	—
351	C₈	—	536	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	#16863360	1	1	yes	characteristic
360	C₂²	C₂×#14523958	1	1	yes	characteristic
361	C₂²	#16863380	1	1	yes	characteristic
362	C₂²	C₂×#14523967	1	1	yes	characteristic
363	C₂²	#16863397	1	1	yes	characteristic
364	C₂²	C₂×#14523970	1	1	yes	characteristic
365	C₂²	#16863413	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	2	no	—
376	C₄	—	8	1	no	—
377	C₄	—	8	1	no	—
378	C₄	#16863133	1	4	yes	—
379	C₂	—	4	2	no	—
380	C₂	#22558547	1	1	yes	characteristic
381	C₂	#22558638	1	1	yes	characteristic
382	C₂	#22558648	1	1	yes	characteristic
383	C₂	C₂×#16863133	1	1	yes	characteristic
384	C₂	#22558752	1	1	yes	characteristic
385	C₂	#22558816	1	1	yes	characteristic
386	C₂	#22558899	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₆₇
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₄×C₂²⋊Q₈×C₆₇	C₂
socle	C₂³×C₆₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₆₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₆₇
hypocenter	C₆₇	#7617
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
3. #22558035	C₂	semidirect
4. #22558032	C₂	semidirect
68. C₂×Q₈×C₆₇	M₁₆	semidirect
98. C₄⋊C₄×C₆₇	M₁₆	semidirect
199. C₆₇	#7617	semidirect
255. C₂×Q₈	#11761612	semidirect
292. C₄⋊C₄	#11761612	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22560189	2
#22559903	2
#22558035	2
#22558032	2
C₄×C₂²⋊Q₈×C₆₇	2
#7617	67