Subgroups — #30869338

Order 17152.

714 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569144	C₂	1	1	yes	maximal, characteristic, complemented
2	#22568921	C₂	1	1	yes	maximal, characteristic
3	#22561187	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561038	C₂	1	1	yes	maximal, characteristic
5	#22560859	C₂	1	4	yes	maximal, complemented
6	#22560486	C₂	1	4	yes	maximal, complemented
7	#22560381	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3131	C₂	1	1	yes	maximal, characteristic
10	C₂×#14524050	C₂²	1	2	yes	—
11	#16863527	—	2	1	no	—
12	#16863527	—	2	1	no	—
13	Q₈×C₆₇⋊C₈	—	2	1	no	—
14	Q₈×C₆₇⋊C₈	—	2	1	no	—
15	#16863474	—	2	1	no	—
16	#16863474	—	2	1	no	—
17	D₄×C₆₇⋊C₈	—	2	1	no	—
18	D₄×C₆₇⋊C₈	—	2	1	no	—
19	C₂×#14523979	C₂²	1	4	yes	—
20	#16863423	C₂²	1	2	yes	—
21	#16863420	C₂²	1	1	yes	characteristic
22	#16863420	C₂²	1	1	yes	characteristic
23	C₂×#14523970	C₂²	1	4	yes	—
24	#16863363	C₂²	1	2	yes	—
25	#16863352	C₂²	1	2	yes	—
26	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
28	#16863155	C₂²	1	4	yes	—
29	#16863150	C₂²	1	2	yes	—
30	#16863150	C₂²	1	2	yes	—
31	#533×C₆₇	C₂²	1	1	yes	characteristic
32	#532×C₆₇	C₂²	1	1	yes	characteristic
33	#488×C₆₇	C₄	1	4	yes	complemented
34	#487×C₆₇	C₄	1	1	yes	characteristic, complemented
35	#487×C₆₇	C₄	1	1	yes	characteristic, complemented
36	#486×C₆₇	C₄	1	1	yes	characteristic, complemented
37	#486×C₆₇	C₄	1	1	yes	characteristic, complemented
38	#416×C₆₇	C₂²	1	4	yes	—
39	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
40	#14524050	—	4	4	no	—
41	C₂×#11761612	—	2	2	no	—
42	C₂×#11761612	C₂³	1	2	yes	—
43	C₂×#11761612	C₂³	1	2	yes	—
44	C₂²×C₆₇⋊C₈	—	2	2	no	—
45	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₄×Dic₆₇	—	2	1	no	—
48	C₂×C₄×Dic₆₇	—	2	1	no	—
49	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
50	#14523979	—	4	4	no	—
51	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
52	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
53	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
56	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
57	#14523970	—	4	4	no	—
58	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
60	#14523954	—	2	2	no	—
61	C₄×C₆₇⋊C₈	—	2	2	no	—
62	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
63	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
64	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
65	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
66	C₂×#41×C₆₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
71	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
72	#125×C₆₇	C₂×C₄	1	2	yes	—
73	#124×C₆₇	C₂×C₄	1	2	yes	—
74	C₂²⋊Q₈×C₆₇	—	2	1	no	—
75	C₂²⋊Q₈×C₆₇	—	2	1	no	—
76	#121×C₆₇	—	2	1	no	—
77	#121×C₆₇	—	2	1	no	—
78	C₄×Q₈×C₆₇	—	2	1	no	—
79	C₄×Q₈×C₆₇	—	2	1	no	—
80	C₄×D₄×C₆₇	—	2	1	no	—
81	C₄×D₄×C₆₇	—	2	1	no	—
82	#117×C₆₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
84	#103×C₆₇	C₂×C₄	1	4	yes	—
85	#103×C₆₇	C₂×C₄	1	4	yes	—
86	#102×C₆₇	C₂×C₄	1	4	yes	—
87	#102×C₆₇	C₂×C₄	1	4	yes	—
88	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
91	C₂²×Dic₆₇	—	2	2	no	—
92	#11761612	—	2	4	no	—
93	#11761612	—	2	4	no	—
94	#11761612	—	4	4	no	—
95	C₂×C₆₇⋊C₈	—	2	2	no	—
96	C₂×C₆₇⋊C₈	—	2	2	no	—
97	C₂×C₆₇⋊C₈	—	2	2	no	—
98	C₂×C₆₇⋊C₈	—	2	2	no	—
99	C₂×C₆₇⋊C₈	—	4	4	no	—
100	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
101	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
102	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
103	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
104	C₄×Dic₆₇	—	2	4	no	—
105	C₄×Dic₆₇	—	2	2	no	—
106	C₄×Dic₆₇	—	2	2	no	—
107	C₄×Dic₆₇	—	4	2	no	—
108	#41×C₆₇	—	2	4	no	—
109	#41×C₆₇	—	2	4	no	—
110	C₂×Q₈×C₆₇	—	2	1	no	—
111	C₂×Q₈×C₆₇	—	2	1	no	—
112	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
113	C₂×D₄×C₆₇	—	2	2	no	—
114	C₂×D₄×C₆₇	—	2	1	no	—
115	C₂×D₄×C₆₇	—	2	1	no	—
116	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₆₇	—	2	2	no	—
118	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
120	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₆₇	—	2	2	no	—
122	C₂×C₈×C₆₇	—	2	2	no	—
123	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
125	C₄⋊C₄×C₆₇	—	2	1	no	—
126	C₄⋊C₄×C₆₇	—	2	1	no	—
127	C₄⋊C₄×C₆₇	—	2	2	no	—
128	C₄⋊C₄×C₆₇	—	2	2	no	—
129	C₄⋊C₄×C₆₇	—	2	1	no	—
130	C₄⋊C₄×C₆₇	—	2	1	no	—
131	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
132	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
133	C₂²⋊C₄×C₆₇	—	2	2	no	—
134	C₂²⋊C₄×C₆₇	—	2	2	no	—
135	C₂²⋊C₄×C₆₇	—	2	2	no	—
136	C₄²×C₆₇	—	2	2	no	—
137	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂³×C₆₇	—	2	2	no	—
142	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
143	Q₈×C₆₇	—	2	4	no	—
144	Q₈×C₆₇	—	4	2	no	—
145	Q₈×C₆₇	—	4	2	no	—
146	D₄×C₆₇	—	2	4	no	—
147	D₄×C₆₇	—	4	4	no	—
148	D₄×C₆₇	—	4	2	no	—
149	D₄×C₆₇	—	4	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	2	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	2	2	no	—
154	C₂×C₄×C₆₇	—	2	2	no	—
155	C₂×C₄×C₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	—	4	2	no	—
157	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
164	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
165	C₂×Dic₆₇	—	2	4	no	—
166	C₂×Dic₆₇	—	4	2	no	—
167	C₂×Dic₆₇	—	4	2	no	—
168	C₈×C₆₇	—	2	2	no	—
169	C₈×C₆₇	—	2	2	no	—
170	C₆₇⋊C₈	—	2	1	no	—
171	C₆₇⋊C₈	—	2	1	no	—
172	C₆₇⋊C₈	—	2	1	no	—
173	C₆₇⋊C₈	—	2	1	no	—
174	C₆₇⋊C₈	—	4	2	no	—
175	C₆₇⋊C₈	—	4	2	no	—
176	C₂²×C₆₇	—	2	1	no	—
177	C₂²×C₆₇	—	2	1	no	—
178	C₂²×C₆₇	—	4	2	no	—
179	C₂²×C₆₇	—	4	2	no	—
180	C₂²×C₆₇	—	4	2	no	—
181	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂²×C₆₇	#542	1	2	yes	—
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	4	2	no	—
186	C₄×C₆₇	—	4	2	no	—
187	C₄×C₆₇	—	4	2	no	—
188	C₄×C₆₇	#443	1	2	yes	—
189	C₄×C₆₇	#444	1	2	yes	—
190	C₄×C₆₇	#520	1	2	yes	—
191	C₄×C₆₇	#535	1	1	yes	characteristic
192	C₄×C₆₇	#536	1	1	yes	characteristic
193	Dic₆₇	—	4	4	no	—
194	#22234	—	67	1	no	maximal, Sylow
195	C₂×C₆₇	—	2	2	no	—
196	C₂×C₆₇	—	8	2	no	—
197	C₂×C₆₇	#2326	1	1	yes	characteristic
198	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
199	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
200	#3131	D₆₇	1	1	yes	characteristic
201	#2960	—	67	1	no	—
202	#2931	—	67	1	no	—
203	#1994	—	67	1	no	—
204	#1962	—	67	1	no	—
205	#1929	—	67	4	no	—
206	#1866	—	67	4	no	—
207	#1848	—	67	1	no	—
208	#1744	—	67	1	no	—
209	C₆₇	#22234	1	1	yes	characteristic, complemented, Sylow
210	C₂×#131	—	67	2	no	—
211	#533	C₂×D₆₇	1	1	yes	characteristic
212	#532	C₂×D₆₇	1	1	yes	characteristic
213	#488	Dic₆₇	1	4	yes	complemented
214	#487	Dic₆₇	1	1	yes	characteristic, complemented
215	#487	Dic₆₇	1	1	yes	characteristic, complemented
216	#486	Dic₆₇	1	1	yes	characteristic, complemented
217	#486	Dic₆₇	1	1	yes	characteristic, complemented
218	#446	—	134	1	no	—
219	#446	—	134	1	no	—
220	C₈×Q₈	—	134	1	no	—
221	C₈×Q₈	—	134	1	no	—
222	#436	—	134	1	no	—
223	#436	—	134	1	no	—
224	C₈×D₄	—	134	1	no	—
225	C₈×D₄	—	134	1	no	—
226	C₂×#108	—	67	4	no	—
227	#424	—	67	2	no	—
228	#423	—	67	1	no	—
229	#423	—	67	1	no	—
230	C₂×#104	—	67	4	no	—
231	#416	C₂×D₆₇	1	4	yes	—
232	#408	—	67	2	no	—
233	#405	—	67	2	no	—
234	C₂×C₄×C₈	—	67	1	no	—
235	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
236	C₄³	—	67	1	no	—
237	#339	—	67	4	no	—
238	#336	—	67	2	no	—
239	#336	—	67	2	no	—
240	C₂×#41	C₂²×D₆₇	1	2	yes	—
241	#131	—	268	4	no	—
242	C₂×M₁₆	—	67	2	no	—
243	C₂×M₁₆	—	67	2	no	—
244	C₂×M₁₆	—	134	2	no	—
245	C₂²×C₈	—	67	1	no	—
246	C₂²×C₈	—	67	1	no	—
247	C₂²×C₈	—	134	2	no	—
248	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
249	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
250	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
251	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
252	#127	C₂×Dic₆₇	1	1	yes	characteristic
253	#125	C₂×Dic₆₇	1	2	yes	—
254	#124	C₂×Dic₆₇	1	2	yes	—
255	C₂²⋊Q₈	—	2	1	no	—
256	C₂²⋊Q₈	—	2	1	no	—
257	#121	—	2	1	no	—
258	#121	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	#117	C₂²×D₆₇	1	2	yes	—
264	C₂×C₄²	—	67	2	no	—
265	C₂×C₄²	—	134	1	no	—
266	C₂×C₄²	—	134	1	no	—
267	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
268	#108	—	268	4	no	—
269	C₄⋊C₈	—	134	2	no	—
270	C₄⋊C₈	—	134	2	no	—
271	C₄⋊C₈	—	134	1	no	—
272	C₄⋊C₈	—	134	1	no	—
273	C₄⋊C₈	—	134	1	no	—
274	C₄⋊C₈	—	134	1	no	—
275	#104	—	268	4	no	—
276	#103	C₂×Dic₆₇	1	4	yes	—
277	#103	C₂×Dic₆₇	1	4	yes	—
278	#102	C₂×Dic₆₇	1	4	yes	—
279	#102	C₂×Dic₆₇	1	4	yes	—
280	C₂²⋊C₈	—	134	2	no	—
281	C₂²⋊C₈	—	134	2	no	—
282	#97	—	134	2	no	—
283	C₄×C₈	—	67	1	no	—
284	C₄×C₈	—	67	1	no	—
285	C₄×C₈	—	67	1	no	—
286	C₄×C₈	—	67	1	no	—
287	C₄×C₈	—	134	2	no	—
288	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
289	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
290	C₄×C₈	C₂×Dic₆₇	1	2	yes	—
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	134	2	no	—
302	C₂²×C₄	#11761627	1	1	yes	characteristic
303	C₂²×C₄	#11761627	1	1	yes	characteristic
304	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
305	M₁₆	—	268	4	no	—
306	M₁₆	—	134	4	no	—
307	M₁₆	—	134	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	268	4	no	—
311	C₂×C₈	—	67	1	no	—
312	C₂×C₈	—	67	1	no	—
313	C₂×C₈	—	67	1	no	—
314	C₂×C₈	—	67	1	no	—
315	C₂×C₈	—	134	2	no	—
316	C₂×C₈	—	134	2	no	—
317	C₂×C₈	—	134	2	no	—
318	C₂×C₈	—	134	2	no	—
319	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
320	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
328	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	268	2	no	—
334	C₄²	—	134	4	no	—
335	C₄²	—	134	2	no	—
336	C₄²	—	134	2	no	—
337	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
338	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
339	C₄²	D₄×D₆₇	1	1	yes	characteristic
340	C₄²	D₄×D₆₇	1	1	yes	characteristic
341	C₂³	—	2	2	no	—
342	C₂³	C₂×#11761627	1	1	yes	characteristic
343	Q₈	—	2	4	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	D₄	—	2	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	268	2	no	—
358	C₂×C₄	—	268	2	no	—
359	C₂×C₄	—	134	4	no	—
360	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
361	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
362	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
363	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
364	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
365	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
366	C₂×C₄	#14524089	1	2	yes	—
367	C₂×C₄	#14524090	1	2	yes	—
368	C₈	—	2	2	no	—
369	C₈	—	2	2	no	—
370	C₈	—	268	2	no	—
371	C₈	—	268	2	no	—
372	C₈	—	134	1	no	—
373	C₈	—	134	1	no	—
374	C₈	—	134	1	no	—
375	C₈	—	134	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
382	C₂²	#16864015	1	2	yes	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	268	4	no	—
389	C₄	#16863513	1	2	yes	—
390	C₄	#16863518	1	2	yes	—
391	C₄	#16863879	1	2	yes	—
392	C₄	#16863964	1	1	yes	characteristic
393	C₄	#16863966	1	1	yes	characteristic
394	C₂	—	2	2	no	—
395	C₂	—	8	2	no	—
396	C₂	#22562922	1	1	yes	characteristic
397	C₂	C₂×#16863513	1	1	yes	characteristic
398	C₂	C₂×#16863518	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#3131	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#532×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#3131	D₆₇
hypocenter	C₆₇	#22234
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3131

Complements

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

N	H ≅ G/N	type
1. #22569144	C₂	semidirect
3. #22561187	C₂	semidirect
5. #22560859	C₂	semidirect
6. #22560486	C₂	semidirect
7. #22560381	C₂	semidirect
8. #22559954	C₂	semidirect
33. #488×C₆₇	C₄	semidirect
34. #487×C₆₇	C₄	semidirect
35. #487×C₆₇	C₄	semidirect
36. #486×C₆₇	C₄	semidirect
37. #486×C₆₇	C₄	semidirect
209. C₆₇	#22234	semidirect
213. #488	Dic₆₇	semidirect
214. #487	Dic₆₇	semidirect
215. #487	Dic₆₇	semidirect
216. #486	Dic₆₇	semidirect
217. #486	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22569144	2
#22568921	2
#22561187	2
#22561038	2
#22560859	2
#22560486	2
#22560381	2
#22559954	2
C₆₇×#3131	2
#22234	67