Subgroups — #31980910

Order 18176.

584 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22599677	C₂	1	2	yes	maximal
2	#22598926	C₂	1	1	yes	maximal, characteristic, complemented
3	#22587858	C₂	1	1	yes	maximal, characteristic, complemented
4	#22587853	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587834	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587829	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587770	C₂	1	2	yes	maximal, complemented
8	#22587763	C₂	1	2	yes	maximal, complemented
9	C₂×#17985750	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587041	C₂	1	2	yes	maximal, complemented
11	C₇₁×#2966	C₂	1	1	yes	maximal, characteristic
12	#17986556	C₂²	1	2	yes	—
13	#17986404	C₂²	1	1	yes	characteristic
14	#17986379	C₂²	1	1	yes	characteristic
15	#17986350	C₂²	1	2	yes	—
16	#17986303	—	2	2	no	—
17	#17986284	C₂²	1	2	yes	—
18	#17986279	C₂²	1	2	yes	—
19	#17986240	—	2	1	no	—
20	#17986240	—	2	1	no	—
21	#17986238	—	2	2	no	—
22	#17986226	—	2	2	no	—
23	#17986218	—	2	2	no	—
24	#17986209	C₂²	1	2	yes	—
25	#17986204	C₂²	1	2	yes	—
26	C₄×Dic₂₈₄	—	2	1	no	—
27	C₄×Dic₂₈₄	—	2	1	no	—
28	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
29	#17985750	C₂²	1	2	yes	—
30	#17985750	C₂²	1	1	yes	characteristic
31	#17985750	C₂²	1	1	yes	characteristic
32	#17985746	C₂²	1	2	yes	—
33	#17985746	C₂²	1	2	yes	—
34	#17985744	C₂²	1	2	yes	—
35	#17985744	C₂²	1	2	yes	—
36	#529×C₇₁	C₂²	1	1	yes	characteristic
37	#446×C₇₁	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic
39	#436×C₇₁	C₂²	1	1	yes	characteristic
40	#435×C₇₁	—	2	1	no	—
41	C₈×D₄×C₇₁	—	2	1	no	—
42	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
43	#433×C₇₁	—	2	1	no	—
44	#432×C₇₁	C₂²	1	1	yes	characteristic
45	#405×C₇₁	—	2	1	no	—
46	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
47	C₂×Dic₂₈₄	—	2	1	no	—
48	C₂×Dic₂₈₄	—	2	1	no	—
49	C₂×#11765855	—	2	2	no	—
50	C₂×#11765853	—	2	2	no	—
51	C₂²×C₇₁⋊C₈	—	2	2	no	—
52	#14556128	C₂³	1	2	yes	—
53	#14556128	C₂³	1	2	yes	—
54	#14556120	—	2	2	no	—
55	#14556107	—	2	2	no	—
56	#14556107	—	2	2	no	—
57	C₄×Dic₁₄₂	—	2	2	no	—
58	C₄×Dic₁₄₂	—	2	2	no	—
59	#14556087	—	2	2	no	—
60	#14556062	—	2	1	no	—
61	#14556062	—	2	1	no	—
62	#14556061	—	2	2	no	—
63	#14556059	—	2	2	no	—
64	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
65	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
67	#14556053	—	2	2	no	—
68	#14556053	—	2	2	no	—
69	#14556052	—	2	2	no	—
70	#14556051	—	2	2	no	—
71	#14556051	—	2	2	no	—
72	#14556049	—	2	2	no	—
73	C₂×M₁₆×C₇₁	—	2	1	no	—
74	C₂²×C₈×C₇₁	—	2	1	no	—
75	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
77	#126×C₇₁	—	2	1	no	—
78	#125×C₇₁	D₄	1	1	yes	characteristic
79	#124×C₇₁	D₄	1	1	yes	characteristic
80	#123×C₇₁	—	2	1	no	—
81	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
82	#121×C₇₁	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₇₁	—	2	1	no	—
85	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
86	#117×C₇₁	—	2	1	no	—
87	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₇₁	—	2	1	no	—
89	C₄⋊C₈×C₇₁	—	2	1	no	—
90	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₇₁	—	2	1	no	—
93	C₂²⋊C₈×C₇₁	—	2	1	no	—
94	C₂²⋊C₈×C₇₁	—	2	1	no	—
95	#97×C₇₁	—	2	1	no	—
96	#97×C₇₁	—	2	1	no	—
97	C₄×C₈×C₇₁	—	2	1	no	—
98	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
99	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
100	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
102	C₂×Dic₁₄₂	—	2	2	no	—
103	C₂×Dic₁₄₂	—	2	2	no	—
104	Dic₂₈₄	—	4	2	no	—
105	Dic₂₈₄	—	4	2	no	—
106	#11765855	—	8	2	no	—
107	#11765853	—	8	2	no	—
108	C₂×C₇₁⋊C₈	—	2	2	no	—
109	C₂×C₇₁⋊C₈	—	2	2	no	—
110	C₂×C₇₁⋊C₈	—	8	2	no	—
111	C₄⋊Dic₇₁	—	2	2	no	—
112	C₄⋊Dic₇₁	—	2	2	no	—
113	C₄⋊Dic₇₁	—	2	2	no	—
114	C₄⋊Dic₇₁	—	2	2	no	—
115	Dic₇₁⋊C₄	—	4	2	no	—
116	Dic₇₁⋊C₄	—	4	2	no	—
117	C₂²⋊Dic₇₁	—	4	2	no	—
118	C₄×Dic₇₁	—	4	2	no	—
119	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
120	C₂×D₄×C₇₁	—	2	1	no	—
121	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₁	—	2	1	no	—
123	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
126	M₁₆×C₇₁	—	4	2	no	—
127	C₂×C₈×C₇₁	—	2	2	no	—
128	C₂×C₈×C₇₁	—	2	1	no	—
129	C₂×C₈×C₇₁	—	2	1	no	—
130	C₂×C₈×C₇₁	—	4	1	no	—
131	C₂×C₈×C₇₁	—	4	2	no	—
132	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
136	C₄⋊C₄×C₇₁	—	2	1	no	—
137	C₄⋊C₄×C₇₁	—	2	1	no	—
138	C₄⋊C₄×C₇₁	—	2	1	no	—
139	C₄⋊C₄×C₇₁	—	2	1	no	—
140	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
142	C₂²⋊C₄×C₇₁	—	2	1	no	—
143	C₂²⋊C₄×C₇₁	—	2	1	no	—
144	C₂²⋊C₄×C₇₁	—	2	1	no	—
145	C₂²⋊C₄×C₇₁	—	2	1	no	—
146	C₂²⋊C₄×C₇₁	—	2	1	no	—
147	C₄²×C₇₁	—	2	1	no	—
148	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₇₁	#41	1	1	yes	characteristic
151	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
152	C₂³×C₇₁	—	2	1	no	—
153	C₂³×C₇₁	#121	1	1	yes	characteristic
154	Q₈×C₇₁	—	2	2	no	—
155	D₄×C₇₁	—	2	2	no	—
156	D₄×C₇₁	—	4	2	no	—
157	C₂×C₄×C₇₁	—	2	2	no	—
158	C₂×C₄×C₇₁	—	2	1	no	—
159	C₂×C₄×C₇₁	—	2	1	no	—
160	C₂×C₄×C₇₁	—	2	2	no	—
161	C₂×C₄×C₇₁	—	2	1	no	—
162	C₂×C₄×C₇₁	—	2	1	no	—
163	C₂×C₄×C₇₁	—	2	1	no	—
164	C₂×C₄×C₇₁	—	4	1	no	—
165	C₂×C₄×C₇₁	—	4	1	no	—
166	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
167	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
168	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
172	C₂×Dic₇₁	—	4	2	no	—
173	C₂×Dic₇₁	—	4	2	no	—
174	Dic₁₄₂	—	4	2	no	—
175	Dic₁₄₂	—	4	2	no	—
176	Dic₁₄₂	—	4	2	no	—
177	Dic₁₄₂	—	4	2	no	—
178	C₈×C₇₁	—	2	1	no	—
179	C₈×C₇₁	—	2	1	no	—
180	C₈×C₇₁	—	2	1	no	—
181	C₈×C₇₁	—	4	1	no	—
182	C₈×C₇₁	—	4	1	no	—
183	C₈×C₇₁	#135	1	2	yes	—
184	C₇₁⋊C₈	—	4	2	no	—
185	C₇₁⋊C₈	—	4	2	no	—
186	C₂²×C₇₁	—	2	1	no	—
187	C₂²×C₇₁	—	2	1	no	—
188	C₂²×C₇₁	—	4	1	no	—
189	C₂²×C₇₁	—	4	1	no	—
190	C₂²×C₇₁	—	4	1	no	—
191	C₂²×C₇₁	#473	1	2	yes	—
192	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
193	C₄×C₇₁	—	2	1	no	—
194	C₄×C₇₁	—	2	1	no	—
195	C₄×C₇₁	—	2	1	no	—
196	C₄×C₇₁	—	2	1	no	—
197	C₄×C₇₁	—	4	1	no	—
198	C₄×C₇₁	—	4	1	no	—
199	C₄×C₇₁	—	4	1	no	—
200	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
201	C₄×C₇₁	#575	1	1	yes	characteristic
202	C₄×C₇₁	#577	1	2	yes	—
203	Dic₇₁	—	8	2	no	—
204	Dic₇₁	—	8	2	no	—
205	#19228	—	71	1	no	maximal, Sylow
206	C₂×C₇₁	—	2	2	no	—
207	C₂×C₇₁	—	8	1	no	—
208	C₂×C₇₁	#3035	1	1	yes	characteristic
209	C₂×C₇₁	#3060	1	1	yes	characteristic
210	C₂×C₇₁	C₂×#473	1	1	yes	characteristic
211	#3248	—	71	2	no	—
212	#3170	—	71	1	no	—
213	#2966	D₇₁	1	1	yes	characteristic
214	#1694	—	71	1	no	—
215	#1693	—	71	1	no	—
216	#1690	—	71	1	no	—
217	#1689	—	71	1	no	—
218	#1680	—	71	2	no	—
219	#1679	—	71	2	no	—
220	C₂×#334	—	71	1	no	—
221	#1552	—	71	2	no	—
222	C₇₁	#19228	1	1	yes	characteristic, complemented, Sylow
223	#533	—	71	2	no	—
224	#529	C₂×D₇₁	1	1	yes	characteristic
225	#500	—	71	1	no	—
226	#494	—	71	1	no	—
227	#487	—	71	2	no	—
228	#479	—	142	2	no	—
229	#475	—	71	2	no	—
230	#474	—	71	2	no	—
231	#467	—	142	1	no	—
232	#467	—	142	1	no	—
233	#467	—	142	2	no	—
234	#465	—	142	2	no	—
235	#464	—	142	2	no	—
236	#462	—	71	2	no	—
237	#461	—	71	2	no	—
238	#446	C₂×D₇₁	1	1	yes	characteristic
239	C₈×Q₈	C₂×D₇₁	1	1	yes	characteristic
240	C₄×Q₁₆	—	142	1	no	—
241	C₄×Q₁₆	—	142	1	no	—
242	#436	C₂×D₇₁	1	1	yes	characteristic
243	#435	—	2	1	no	—
244	C₈×D₄	—	2	1	no	—
245	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
246	#433	—	2	1	no	—
247	#432	C₂×D₇₁	1	1	yes	characteristic
248	C₂×C₄⋊C₈	—	71	2	no	—
249	#405	—	2	1	no	—
250	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
251	#334	—	71	2	no	—
252	#334	—	71	1	no	—
253	#334	—	71	1	no	—
254	#332	—	71	2	no	—
255	#332	—	71	2	no	—
256	#332	—	71	2	no	—
257	#332	—	71	2	no	—
258	C₂×Q₁₆	—	142	2	no	—
259	C₂×Q₁₆	—	142	1	no	—
260	C₂×Q₁₆	—	142	1	no	—
261	C₂×SD₁₆	—	142	2	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	142	2	no	—
265	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
266	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
267	C₄⋊Q₈	—	71	2	no	—
268	C₄⋊Q₈	—	71	2	no	—
269	#126	—	2	1	no	—
270	#125	—	142	2	no	—
271	#125	D₂₈₄	1	1	yes	characteristic
272	#124	D₂₈₄	1	1	yes	characteristic
273	#123	—	2	1	no	—
274	C₂²⋊Q₈	—	142	2	no	—
275	C₂²⋊Q₈	—	142	2	no	—
276	C₂²⋊Q₈	D₂₈₄	1	1	yes	characteristic
277	#121	D₂₈₄	1	1	yes	characteristic
278	C₄×Q₈	—	142	2	no	—
279	C₄×Q₈	—	142	2	no	—
280	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
283	#117	—	2	1	no	—
284	#117	—	142	2	no	—
285	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
286	#107	—	142	1	no	—
287	#107	—	142	1	no	—
288	#107	—	142	2	no	—
289	#106	—	142	2	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	71	2	no	—
293	C₄⋊C₈	—	71	2	no	—
294	C₄⋊C₈	—	142	2	no	—
295	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
296	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
297	#103	—	142	2	no	—
298	#103	—	142	2	no	—
299	#103	—	142	2	no	—
300	#103	—	142	2	no	—
301	#103	—	142	2	no	—
302	#102	—	142	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	#97	—	2	1	no	—
307	#97	—	2	1	no	—
308	C₄×C₈	—	2	1	no	—
309	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
310	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
313	C₂×Q₈	—	142	2	no	—
314	C₂×Q₈	—	142	2	no	—
315	C₂×Q₈	C₂×D₂₈₄	1	1	yes	characteristic
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	C₂×D₂₈₄	1	1	yes	characteristic
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
321	C₂²×C₄	#11765865	1	1	yes	characteristic
322	Q₁₆	—	284	2	no	—
323	Q₁₆	—	284	2	no	—
324	Q₁₆	—	568	2	no	—
325	SD₁₆	—	568	2	no	—
326	M₁₆	—	4	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	2	no	—
332	C₂×C₈	—	568	2	no	—
333	C₂×C₈	—	142	2	no	—
334	C₂×C₈	—	142	2	no	—
335	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
336	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
337	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
338	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	284	2	no	—
344	C₄⋊C₄	—	284	2	no	—
345	C₄⋊C₄	—	142	2	no	—
346	C₄⋊C₄	—	142	2	no	—
347	C₄⋊C₄	—	142	2	no	—
348	C₄⋊C₄	—	142	2	no	—
349	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
350	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	284	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	284	2	no	—
359	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
360	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
361	C₄²	#11765865	1	1	yes	characteristic
362	C₄²	C₂³×D₇₁	1	1	yes	characteristic
363	C₂³	—	2	1	no	—
364	C₂³	#14556102	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	284	2	no	—
367	Q₈	—	284	2	no	—
368	Q₈	—	284	2	no	—
369	Q₈	—	284	2	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	284	2	no	—
382	C₂×C₄	—	284	2	no	—
383	C₂×C₄	#14556102	1	1	yes	characteristic
384	C₂×C₄	#14556102	1	1	yes	characteristic
385	C₂×C₄	#14556102	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₂²⋊D₇₁	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
388	C₂×C₄	C₂×#11765865	1	1	yes	characteristic
389	C₈	—	2	1	no	—
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	284	2	no	—
395	C₈	—	284	2	no	—
396	C₈	#14556148	1	2	yes	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	#17986274	1	2	yes	—
403	C₂²	C₂×#14556102	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	568	2	no	—
412	C₄	—	568	2	no	—
413	C₄	C₂×#14556148	1	1	yes	characteristic
414	C₄	#17986797	1	1	yes	characteristic
415	C₄	#17986811	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	8	1	no	—
418	C₂	#22597795	1	1	yes	characteristic
419	C₂	#22598002	1	1	yes	characteristic
420	C₂	C₂×#17986274	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14556102
commutator, cosocle	C₄²×C₇₁	C₂⁴
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#2966	C₂
socle	C₂²×C₇₁	C₂×#121
prime radical	#121×C₇₁	D₄
hypercenter	#2966	D₇₁
hypocenter	C₇₁	#19228
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2966

Complements

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

N	H ≅ G/N	type
2. #22598926	C₂	semidirect
3. #22587858	C₂	semidirect
4. #22587853	C₂	semidirect
5. #22587834	C₂	semidirect
6. #22587829	C₂	semidirect
7. #22587770	C₂	semidirect
8. #22587763	C₂	semidirect
9. C₂×#17985750	C₂	semidirect
10. #22587041	C₂	semidirect
222. C₇₁	#19228	semidirect

Maximal subgroups

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

subgroup	index
#22599677	2
#22598926	2
#22587858	2
#22587853	2
#22587834	2
#22587829	2
#22587770	2
#22587763	2
C₂×#17985750	2
#22587041	2
C₇₁×#2966	2
#19228	71