Subgroups — #31980209

Order 18176.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598926	C₂	1	1	yes	maximal, characteristic, complemented
2	#22598411	C₂	1	2	yes	maximal
3	#22587894	C₂	1	2	yes	maximal, complemented
4	#22587887	C₂	1	2	yes	maximal, complemented
5	#22587858	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587853	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587834	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587829	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587088	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587004	C₂	1	2	yes	maximal, complemented
11	C₇₁×#2965	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	#17986340	—	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	#17986209	C₂²	1	2	yes	—
22	#17986204	C₂²	1	2	yes	—
23	#17986161	—	2	2	no	—
24	C₄×Dic₂₈₄	—	2	1	no	—
25	C₄×Dic₂₈₄	—	2	1	no	—
26	C₄×#11765855	—	2	2	no	—
27	C₄×#11765853	—	2	2	no	—
28	#17986052	C₂²	1	2	yes	—
29	#17985752	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	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
37	#446×C₇₁	C₂²	1	1	yes	characteristic
38	#446×C₇₁	C₂²	1	1	yes	characteristic
39	#436×C₇₁	C₂²	1	1	yes	characteristic
40	#436×C₇₁	C₂²	1	1	yes	characteristic
41	#435×C₇₁	—	2	1	no	—
42	#435×C₇₁	—	2	1	no	—
43	#431×C₇₁	—	2	1	no	—
44	#431×C₇₁	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×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	#14556128	C₂³	1	2	yes	—
52	#14556128	C₂³	1	2	yes	—
53	#14556120	—	2	2	no	—
54	#14556107	—	2	2	no	—
55	#14556107	—	2	2	no	—
56	C₄×Dic₁₄₂	—	2	2	no	—
57	C₄×Dic₁₄₂	—	2	2	no	—
58	#14556087	—	2	2	no	—
59	#14556062	—	2	1	no	—
60	#14556062	—	2	1	no	—
61	#14556061	—	2	2	no	—
62	#14556059	—	2	2	no	—
63	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
64	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
65	#14556053	—	2	2	no	—
66	#14556053	—	2	2	no	—
67	#14556052	—	2	2	no	—
68	#14556051	—	2	2	no	—
69	#14556051	—	2	2	no	—
70	#14556049	—	2	2	no	—
71	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
72	C₄×C₇₁⋊C₈	—	2	2	no	—
73	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
74	C₂×M₁₆×C₇₁	—	2	1	no	—
75	C₂×M₁₆×C₇₁	—	2	1	no	—
76	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₇₁	—	2	1	no	—
81	C₄×D₄×C₇₁	—	2	1	no	—
82	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
83	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
84	#117×C₇₁	—	2	1	no	—
85	#117×C₇₁	D₄	1	1	yes	characteristic
86	C₂×C₄²×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	—	4	4	no	—
107	#11765853	—	4	4	no	—
108	C₂×C₇₁⋊C₈	—	2	2	no	—
109	C₂×C₇₁⋊C₈	—	2	2	no	—
110	C₄⋊Dic₇₁	—	2	2	no	—
111	C₄⋊Dic₇₁	—	2	2	no	—
112	C₄⋊Dic₇₁	—	2	2	no	—
113	C₄⋊Dic₇₁	—	2	2	no	—
114	Dic₇₁⋊C₄	—	4	2	no	—
115	Dic₇₁⋊C₄	—	4	2	no	—
116	C₂²⋊Dic₇₁	—	4	2	no	—
117	C₄×Dic₇₁	—	4	2	no	—
118	#41×C₇₁	—	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	—	2	1	no	—
124	C₂²×C₄×C₇₁	—	2	1	no	—
125	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
128	M₁₆×C₇₁	—	4	2	no	—
129	M₁₆×C₇₁	—	4	2	no	—
130	C₂×C₈×C₇₁	—	2	2	no	—
131	C₂×C₈×C₇₁	—	2	1	no	—
132	C₂×C₈×C₇₁	—	2	1	no	—
133	C₂×C₈×C₇₁	—	4	1	no	—
134	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₇₁	—	2	1	no	—
146	C₄²×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	1	no	—
158	C₂×C₄×C₇₁	—	2	1	no	—
159	C₂×C₄×C₇₁	—	2	2	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	2	no	—
165	C₂×C₄×C₇₁	—	4	1	no	—
166	C₂×C₄×C₇₁	—	4	1	no	—
167	C₂×C₄×C₇₁	—	4	2	no	—
168	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
170	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
171	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₇₁	—	4	2	no	—
175	C₂×Dic₇₁	—	4	2	no	—
176	Dic₁₄₂	—	4	2	no	—
177	Dic₁₄₂	—	4	2	no	—
178	Dic₁₄₂	—	4	2	no	—
179	Dic₁₄₂	—	4	2	no	—
180	C₈×C₇₁	—	2	1	no	—
181	C₈×C₇₁	—	2	1	no	—
182	C₈×C₇₁	—	2	1	no	—
183	C₈×C₇₁	—	4	1	no	—
184	C₈×C₇₁	—	4	1	no	—
185	C₈×C₇₁	#135	1	2	yes	—
186	C₇₁⋊C₈	—	4	2	no	—
187	C₇₁⋊C₈	—	4	2	no	—
188	C₂²×C₇₁	—	2	1	no	—
189	C₂²×C₇₁	—	2	1	no	—
190	C₂²×C₇₁	—	2	1	no	—
191	C₂²×C₇₁	—	4	1	no	—
192	C₂²×C₇₁	—	4	1	no	—
193	C₂²×C₇₁	—	4	1	no	—
194	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
195	C₄×C₇₁	—	2	1	no	—
196	C₄×C₇₁	—	2	1	no	—
197	C₄×C₇₁	—	2	1	no	—
198	C₄×C₇₁	—	4	1	no	—
199	C₄×C₇₁	—	4	1	no	—
200	C₄×C₇₁	—	4	1	no	—
201	C₄×C₇₁	#473	1	2	yes	—
202	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
203	C₄×C₇₁	#575	1	1	yes	characteristic
204	C₄×C₇₁	#575	1	2	yes	—
205	Dic₇₁	—	8	2	no	—
206	Dic₇₁	—	8	2	no	—
207	#19161	—	71	1	no	maximal, Sylow
208	C₂×C₇₁	—	4	1	no	—
209	C₂×C₇₁	—	8	1	no	—
210	C₂×C₇₁	#3035	1	1	yes	characteristic
211	C₂×C₇₁	#3054	1	1	yes	characteristic
212	C₂×C₇₁	C₂×#473	1	1	yes	characteristic
213	#3170	—	71	1	no	—
214	#3107	—	71	2	no	—
215	#2965	D₇₁	1	1	yes	characteristic
216	#1700	—	71	2	no	—
217	#1699	—	71	2	no	—
218	#1694	—	71	1	no	—
219	#1693	—	71	1	no	—
220	#1690	—	71	1	no	—
221	#1689	—	71	1	no	—
222	#1564	—	71	1	no	—
223	#1544	—	71	2	no	—
224	C₇₁	#19161	1	1	yes	characteristic, complemented, Sylow
225	#533	—	71	2	no	—
226	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
227	#500	—	71	1	no	—
228	#494	—	71	1	no	—
229	#487	—	71	2	no	—
230	#485	—	142	2	no	—
231	#475	—	71	2	no	—
232	#474	—	71	2	no	—
233	#467	—	142	1	no	—
234	#467	—	142	1	no	—
235	#462	—	71	2	no	—
236	#461	—	71	2	no	—
237	#452	—	142	2	no	—
238	#446	C₂×D₇₁	1	1	yes	characteristic
239	#446	C₂×D₇₁	1	1	yes	characteristic
240	C₄×Q₁₆	—	142	2	no	—
241	C₄×Q₁₆	—	142	1	no	—
242	C₄×Q₁₆	—	142	1	no	—
243	C₄×SD₁₆	—	142	2	no	—
244	#436	C₂×D₇₁	1	1	yes	characteristic
245	#436	C₂×D₇₁	1	1	yes	characteristic
246	#435	—	2	1	no	—
247	#435	—	2	1	no	—
248	#431	—	2	1	no	—
249	#431	—	71	2	no	—
250	#431	C₂×D₇₁	1	1	yes	characteristic
251	C₄×M₁₆	—	2	1	no	—
252	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
253	#335	—	71	2	no	—
254	#334	—	71	1	no	—
255	#334	—	71	1	no	—
256	#332	—	71	2	no	—
257	#332	—	71	2	no	—
258	#332	—	71	2	no	—
259	#332	—	71	2	no	—
260	C₂×#41	D₂₈₄	1	1	yes	characteristic
261	C₂×Q₁₆	—	142	2	no	—
262	C₂×Q₁₆	—	142	1	no	—
263	C₂×Q₁₆	—	142	1	no	—
264	C₂×SD₁₆	—	142	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
268	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
269	C₄⋊Q₈	—	71	2	no	—
270	C₄⋊Q₈	—	71	2	no	—
271	#125	—	142	2	no	—
272	C₂²⋊Q₈	—	142	2	no	—
273	C₂²⋊Q₈	—	142	2	no	—
274	C₄×Q₈	—	142	2	no	—
275	C₄×Q₈	—	142	2	no	—
276	C₄×Q₈	D₂₈₄	1	1	yes	characteristic
277	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	D₂₈₄	1	1	yes	characteristic
281	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	—	142	2	no	—
284	#117	D₂₈₄	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
287	#107	—	142	1	no	—
288	#107	—	142	1	no	—
289	#107	—	142	2	no	—
290	#106	—	142	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	71	2	no	—
294	C₄⋊C₈	—	71	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	C₂²⋊C₈	—	142	2	no	—
307	#97	—	2	1	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	142	2	no	—
311	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
312	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
315	#41	—	4	2	no	—
316	C₂×Q₈	—	142	2	no	—
317	C₂×Q₈	—	142	2	no	—
318	C₂×Q₈	C₂×D₂₈₄	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₂×D₂₈₄	1	1	yes	characteristic
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
326	C₂²×C₄	#11765865	1	1	yes	characteristic
327	Q₁₆	—	284	2	no	—
328	Q₁₆	—	284	4	no	—
329	Q₁₆	—	284	2	no	—
330	SD₁₆	—	284	4	no	—
331	M₁₆	—	4	2	no	—
332	M₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	142	2	no	—
338	C₂×C₈	—	142	2	no	—
339	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
340	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	284	2	no	—
346	C₄⋊C₄	—	284	2	no	—
347	C₄⋊C₄	—	142	2	no	—
348	C₄⋊C₄	—	142	2	no	—
349	C₄⋊C₄	—	142	2	no	—
350	C₄⋊C₄	—	142	2	no	—
351	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
352	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
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	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	284	2	no	—
361	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
362	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
363	C₄²	#11765865	1	1	yes	characteristic
364	C₄²	C₂³×D₇₁	1	1	yes	characteristic
365	C₂³	—	2	1	no	—
366	C₂³	#14556102	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	284	2	no	—
369	Q₈	—	284	2	no	—
370	Q₈	—	284	2	no	—
371	Q₈	—	284	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	284	2	no	—
386	C₂×C₄	—	284	2	no	—
387	C₂×C₄	#14556102	1	1	yes	characteristic
388	C₂×C₄	#14556102	1	1	yes	characteristic
389	C₂×C₄	#14556102	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₂²⋊D₇₁	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
392	C₂×C₄	C₂×#11765865	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	284	2	no	—
399	C₈	—	284	2	no	—
400	C₈	#14556148	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	C₂×#14556102	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	568	2	no	—
415	C₄	—	568	2	no	—
416	C₄	#17986274	1	2	yes	—
417	C₄	C₂×#14556148	1	1	yes	characteristic
418	C₄	#17986797	1	1	yes	characteristic
419	C₄	#17986799	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	8	1	no	—
422	C₂	#22597795	1	1	yes	characteristic
423	C₂	#22597949	1	1	yes	characteristic
424	C₂	C₂×#17986274	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14556102
commutator, cosocle	C₄²×C₇₁	C₂⁴
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#2965	C₂
socle	C₂²×C₇₁	C₂×#121
prime radical	C₂×#41×C₇₁	D₄
hypercenter	#2965	D₇₁
hypocenter	C₇₁	#19161
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2965

Complements

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

N	H ≅ G/N	type
1. #22598926	C₂	semidirect
3. #22587894	C₂	semidirect
4. #22587887	C₂	semidirect
5. #22587858	C₂	semidirect
6. #22587853	C₂	semidirect
7. #22587834	C₂	semidirect
8. #22587829	C₂	semidirect
9. #22587088	C₂	semidirect
10. #22587004	C₂	semidirect
224. C₇₁	#19161	semidirect

Maximal subgroups

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

subgroup	index
#22598926	2
#22598411	2
#22587894	2
#22587887	2
#22587858	2
#22587853	2
#22587834	2
#22587829	2
#22587088	2
#22587004	2
C₇₁×#2965	2
#19161	71