Subgroups — #31967548

Order 18176.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598394	C₂	1	1	yes	maximal, characteristic
2	#22597449	C₂	1	1	yes	maximal, characteristic, complemented
3	#22597416	C₂	1	1	yes	maximal, characteristic, complemented
4	#22587221	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587207	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587186	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587172	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587161	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587149	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587143	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587132	C₂	1	1	yes	maximal, characteristic, complemented
12	#22587123	C₂	1	1	yes	maximal, characteristic, complemented
13	#22586775	C₂	1	1	yes	maximal, characteristic, complemented
14	#22586640	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#1480	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#11765865	C₂²	1	1	yes	characteristic
17	#17986320	C₄	1	1	yes	characteristic
18	#17986320	C₄	1	1	yes	characteristic
19	#17986291	C₄	1	1	yes	characteristic
20	#17986286	C₄	1	1	yes	characteristic
21	#17986196	C₄	1	1	yes	characteristic
22	#17986191	C₄	1	1	yes	characteristic
23	#17986142	C₄	1	1	yes	characteristic
24	#17986142	C₄	1	1	yes	characteristic
25	#17986123	C₂²	1	1	yes	characteristic
26	#17986123	C₂²	1	1	yes	characteristic
27	C₄×#11765853	C₂²	1	1	yes	characteristic
28	C₄×#11765853	C₂²	1	1	yes	characteristic
29	C₄×#11765850	C₂²	1	1	yes	characteristic
30	C₄×#11765850	C₂²	1	1	yes	characteristic
31	#17986077	C₂²	1	1	yes	characteristic
32	#17986077	C₂²	1	1	yes	characteristic
33	#17986071	—	2	1	no	—
34	#17986071	—	2	1	no	—
35	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
36	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
37	#17986064	C₂²	1	1	yes	characteristic
38	#17986064	C₂²	1	1	yes	characteristic
39	C₈×C₂²⋊D₇₁	—	2	1	no	—
40	C₈×C₂²⋊D₇₁	—	2	1	no	—
41	#17986056	C₂²	1	1	yes	characteristic
42	#17986052	C₂²	1	1	yes	characteristic
43	#17986052	C₂²	1	1	yes	characteristic
44	#17986051	—	2	1	no	—
45	C₄⋊C₈×D₇₁	—	2	1	no	—
46	#17985966	—	2	1	no	—
47	#17985966	—	2	1	no	—
48	#17985751	C₂²	1	1	yes	characteristic
49	#17985751	C₂²	1	1	yes	characteristic
50	#17985749	C₂²	1	1	yes	characteristic
51	#17985749	C₂²	1	1	yes	characteristic
52	#17985731	C₂²	1	1	yes	characteristic
53	#17985731	C₂²	1	1	yes	characteristic
54	#17985728	C₂²	1	1	yes	characteristic
55	#17985728	C₂²	1	1	yes	characteristic
56	#17985721	C₂²	1	1	yes	characteristic
57	#17985721	C₂²	1	1	yes	characteristic
58	#17985720	C₂²	1	1	yes	characteristic
59	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
60	#532×C₇₁	C₂²	1	1	yes	characteristic
61	#431×C₇₁	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
63	D₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
64	D₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
66	D₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
67	C₂×#11765865	C₂×C₄	1	1	yes	characteristic
68	C₂×#11765853	C₂×C₄	1	1	yes	characteristic
69	C₂×#11765853	C₂×C₄	1	1	yes	characteristic
70	C₂×#11765850	C₂×C₄	1	1	yes	characteristic
71	C₂×#11765850	C₂×C₄	1	1	yes	characteristic
72	C₂×#11765849	—	2	1	no	—
73	C₂×#11765849	—	2	1	no	—
74	C₂²×C₇₁⋊C₈	—	2	1	no	—
75	C₂²×C₇₁⋊C₈	—	2	1	no	—
76	C₂×C₈×D₇₁	—	2	1	no	—
77	C₂×C₈×D₇₁	—	2	1	no	—
78	C₄×Dic₁₄₂	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
80	C₄×D₂₈₄	C₂×C₄	1	1	yes	characteristic
81	C₄×D₂₈₄	C₂³	1	1	yes	characteristic
82	C₄×C₂²⋊D₇₁	—	2	1	no	—
83	C₄×C₂²⋊D₇₁	—	2	1	no	—
84	#14556087	C₂×C₄	1	1	yes	characteristic
85	#14556085	—	2	1	no	—
86	C₄²×D₇₁	—	2	1	no	—
87	#14556061	C₂×C₄	1	1	yes	characteristic
88	#14556061	C₂×C₄	1	1	yes	characteristic
89	#14556059	C₂×C₄	1	1	yes	characteristic
90	#14556059	C₂×C₄	1	1	yes	characteristic
91	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
92	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
93	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
94	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
95	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
96	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
97	Dic₇₁⋊C₈	—	2	1	no	—
98	Dic₇₁⋊C₈	—	2	1	no	—
99	#14556051	C₂×C₄	1	1	yes	characteristic
100	#14556051	C₂×C₄	1	1	yes	characteristic
101	#14556049	C₂×C₄	1	1	yes	characteristic
102	#14556049	C₂×C₄	1	1	yes	characteristic
103	#14556049	C₂×C₄	1	1	yes	characteristic
104	#14556049	C₂×C₄	1	1	yes	characteristic
105	#14556048	C₂×C₄	1	1	yes	characteristic
106	#14556048	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
108	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
109	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
110	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
111	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
112	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
115	C₂²⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
116	(C₂×D₇₁)⋊C₈	—	2	1	no	—
117	(C₂×D₇₁)⋊C₈	—	2	1	no	—
118	#14556039	—	2	1	no	—
119	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
120	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
123	C₈×Dic₇₁	—	2	1	no	—
124	C₈×Dic₇₁	—	2	1	no	—
125	C₂×#41×C₇₁	—	2	1	no	—
126	C₂²×C₈×C₇₁	—	2	1	no	—
127	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
128	#127×C₇₁	C₂×C₄	1	1	yes	characteristic
129	#124×C₇₁	—	2	1	no	—
130	#121×C₇₁	—	2	1	no	—
131	#121×C₇₁	C₂×C₄	1	1	yes	characteristic
132	#121×C₇₁	C₂×C₄	1	1	yes	characteristic
133	C₄×D₄×C₇₁	—	2	1	no	—
134	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₇₁	—	2	1	no	—
138	C₄⋊C₈×C₇₁	—	2	1	no	—
139	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
140	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
141	C₂²⋊C₈×C₇₁	—	2	1	no	—
142	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
144	#11765865	—	2	2	no	—
145	#11765865	—	2	2	no	—
146	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₂₈₄	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₂²⋊D₇₁	—	2	1	no	—
149	C₂×C₄×D₇₁	—	2	1	no	—
150	C₂×C₄×D₇₁	—	2	1	no	—
151	C₂×C₄×D₇₁	—	2	1	no	—
152	#11765853	—	2	2	no	—
153	#11765853	—	2	2	no	—
154	#11765850	—	2	2	no	—
155	#11765850	—	2	2	no	—
156	#11765849	—	8	1	no	—
157	#11765849	—	8	1	no	—
158	C₂×C₇₁⋊C₈	—	2	1	no	—
159	C₂×C₇₁⋊C₈	—	2	1	no	—
160	C₂×C₇₁⋊C₈	—	8	1	no	—
161	C₂×C₇₁⋊C₈	—	8	1	no	—
162	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₈×D₇₁	—	8	1	no	—
171	C₈×D₇₁	—	8	1	no	—
172	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
174	Dic₇₁⋊C₄	—	2	1	no	—
175	Dic₇₁⋊C₄	—	2	1	no	—
176	C₂²⋊Dic₇₁	—	2	1	no	—
177	(C₂×D₇₁)⋊C₄	—	2	1	no	—
178	(C₂×D₇₁)⋊C₄	—	2	1	no	—
179	C₄×Dic₇₁	—	2	1	no	—
180	C₄×Dic₇₁	—	2	1	no	—
181	C₄×Dic₇₁	—	2	1	no	—
182	#41×C₇₁	—	8	1	no	—
183	#41×C₇₁	—	8	1	no	—
184	C₂×Q₈×C₇₁	—	2	1	no	—
185	C₂×D₄×C₇₁	—	2	1	no	—
186	C₂×D₄×C₇₁	—	2	1	no	—
187	C₂×D₄×C₇₁	—	2	1	no	—
188	C₂×D₄×C₇₁	—	2	1	no	—
189	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
190	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₁	—	2	1	no	—
192	C₂²×C₄×C₇₁	—	2	1	no	—
193	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
196	C₂×C₈×C₇₁	—	2	1	no	—
197	C₂×C₈×C₇₁	—	2	1	no	—
198	C₂×C₈×C₇₁	—	2	1	no	—
199	C₂×C₈×C₇₁	—	2	1	no	—
200	C₂×C₈×C₇₁	—	8	1	no	—
201	C₄⋊C₄×C₇₁	—	2	1	no	—
202	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
204	C₂²⋊C₄×C₇₁	—	2	1	no	—
205	C₂²⋊C₄×C₇₁	—	2	1	no	—
206	C₂²⋊C₄×C₇₁	—	2	1	no	—
207	C₂²⋊C₄×C₇₁	—	2	1	no	—
208	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₇₁	#41	1	1	yes	characteristic
211	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
212	C₂³×C₇₁	—	2	1	no	—
213	C₂³×C₇₁	—	2	1	no	—
214	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
215	C₂²×D₇₁	—	2	1	no	—
216	Q₈×C₇₁	—	8	1	no	—
217	D₄×C₇₁	—	2	1	no	—
218	D₄×C₇₁	—	2	1	no	—
219	D₄×C₇₁	—	2	1	no	—
220	D₄×C₇₁	—	2	1	no	—
221	D₄×C₇₁	—	8	1	no	—
222	D₄×C₇₁	—	8	1	no	—
223	D₄×C₇₁	—	8	1	no	—
224	D₄×C₇₁	—	8	1	no	—
225	C₂×C₄×C₇₁	—	2	1	no	—
226	C₂×C₄×C₇₁	—	2	1	no	—
227	C₂×C₄×C₇₁	—	2	1	no	—
228	C₂×C₄×C₇₁	—	2	1	no	—
229	C₂×C₄×C₇₁	—	2	1	no	—
230	C₂×C₄×C₇₁	—	2	1	no	—
231	C₂×C₄×C₇₁	—	4	1	no	—
232	C₂×C₄×C₇₁	—	4	1	no	—
233	C₂×C₄×C₇₁	—	4	1	no	—
234	C₂×C₄×C₇₁	—	4	1	no	—
235	C₂×C₄×C₇₁	—	4	1	no	—
236	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
242	C₂²⋊D₇₁	—	2	4	no	—
243	C₂×Dic₇₁	—	2	1	no	—
244	C₂×Dic₇₁	—	2	1	no	—
245	C₂×Dic₇₁	—	2	1	no	—
246	D₂₈₄	—	2	1	no	—
247	D₂₈₄	#131	1	2	yes	—
248	C₄×D₇₁	—	2	4	no	—
249	C₄×D₇₁	—	4	1	no	—
250	C₄×D₇₁	—	4	1	no	—
251	C₄×D₇₁	—	8	1	no	—
252	Dic₁₄₂	—	2	1	no	—
253	Dic₁₄₂	#131	1	2	yes	—
254	C₈×C₇₁	—	4	1	no	—
255	C₈×C₇₁	—	4	1	no	—
256	C₈×C₇₁	—	4	1	no	—
257	C₈×C₇₁	—	4	1	no	—
258	C₇₁⋊C₈	—	2	1	no	—
259	C₇₁⋊C₈	—	2	1	no	—
260	C₇₁⋊C₈	—	2	1	no	—
261	C₇₁⋊C₈	—	2	1	no	—
262	C₇₁⋊C₈	—	2	1	no	—
263	C₇₁⋊C₈	—	2	1	no	—
264	C₇₁⋊C₈	—	2	1	no	—
265	C₇₁⋊C₈	—	2	1	no	—
266	C₇₁⋊C₈	—	4	1	no	—
267	C₇₁⋊C₈	—	4	1	no	—
268	C₂²×C₇₁	—	2	1	no	—
269	C₂²×C₇₁	—	2	1	no	—
270	C₂²×C₇₁	—	2	1	no	—
271	C₂²×C₇₁	—	4	1	no	—
272	C₂²×C₇₁	—	4	1	no	—
273	C₂²×C₇₁	—	4	1	no	—
274	C₂²×C₇₁	—	4	1	no	—
275	C₂²×C₇₁	—	4	1	no	—
276	C₂²×C₇₁	—	4	1	no	—
277	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
278	C₂×D₇₁	—	2	2	no	—
279	C₂×D₇₁	—	4	1	no	—
280	C₂×D₇₁	—	4	1	no	—
281	C₄×C₇₁	—	2	1	no	—
282	C₄×C₇₁	—	2	1	no	—
283	C₄×C₇₁	—	2	1	no	—
284	C₄×C₇₁	—	2	1	no	—
285	C₄×C₇₁	—	4	1	no	—
286	C₄×C₇₁	—	4	1	no	—
287	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
288	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
289	C₄×C₇₁	#576	1	1	yes	characteristic
290	C₄×C₇₁	#577	1	1	yes	characteristic
291	Dic₇₁	—	2	2	no	—
292	Dic₇₁	—	4	1	no	—
293	Dic₇₁	—	4	1	no	—
294	#17920	—	71	1	no	maximal, Sylow
295	C₂×C₇₁	—	4	1	no	—
296	C₂×C₇₁	—	8	1	no	—
297	C₂×C₇₁	—	8	1	no	—
298	C₂×C₇₁	#2929	1	1	yes	characteristic
299	C₂×C₇₁	#2946	1	1	yes	characteristic
300	C₂×C₇₁	#2957	1	1	yes	characteristic
301	D₇₁	—	4	2	no	—
302	#3106	—	71	1	no	—
303	#2988	—	71	1	no	—
304	#2981	—	71	1	no	—
305	#1588	—	71	1	no	—
306	#1586	—	71	1	no	—
307	#1583	—	71	1	no	—
308	#1581	—	71	1	no	—
309	#1580	—	71	1	no	—
310	SD₁₆⋊C₈	—	71	1	no	—
311	C₈×SD₁₆	—	71	1	no	—
312	C₈×D₈	—	71	1	no	—
313	#1573	—	71	1	no	—
314	#1488	—	71	1	no	—
315	#1480	D₇₁	1	1	yes	characteristic, complemented
316	#1454	—	71	1	no	—
317	C₇₁	#17920	1	1	yes	characteristic, complemented, Sylow
318	#532	C₂×D₇₁	1	1	yes	characteristic
319	C₄×#41	—	71	1	no	—
320	#482	—	71	1	no	—
321	#482	—	71	1	no	—
322	#477	—	71	1	no	—
323	#476	—	71	1	no	—
324	#460	—	71	1	no	—
325	#459	—	71	1	no	—
326	#449	—	71	1	no	—
327	#449	—	71	1	no	—
328	C₈×Q₈	—	71	1	no	—
329	C₈×Q₈	—	71	1	no	—
330	C₄×SD₁₆	—	71	1	no	—
331	C₄×SD₁₆	—	71	1	no	—
332	C₄×D₈	—	71	1	no	—
333	C₄×D₈	—	71	1	no	—
334	#436	—	71	1	no	—
335	#436	—	71	1	no	—
336	#435	—	142	1	no	—
337	#435	—	142	1	no	—
338	C₈×D₄	—	71	1	no	—
339	C₈×D₄	—	71	1	no	—
340	C₈×D₄	—	71	1	no	—
341	C₈×D₄	—	71	1	no	—
342	C₈×D₄	—	142	1	no	—
343	C₈×D₄	—	142	1	no	—
344	#432	—	71	1	no	—
345	#431	—	71	1	no	—
346	#431	—	71	1	no	—
347	#431	—	142	1	no	—
348	#431	C₂×D₇₁	1	1	yes	characteristic
349	C₂×C₄⋊C₈	—	142	1	no	—
350	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
351	#408	—	142	1	no	—
352	#408	—	142	1	no	—
353	#335	—	71	1	no	—
354	#335	—	71	1	no	—
355	#334	—	71	1	no	—
356	#334	—	71	1	no	—
357	Q₈⋊C₈	—	71	1	no	—
358	Q₈⋊C₈	—	71	1	no	—
359	D₄⋊C₈	—	71	1	no	—
360	D₄⋊C₈	—	71	1	no	—
361	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
362	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
363	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
364	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
365	#322	—	71	1	no	—
366	#322	—	71	1	no	—
367	#322	—	71	1	no	—
368	C₈²	—	71	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	71	1	no	—
371	C₂×SD₁₆	—	71	1	no	—
372	C₂×SD₁₆	—	71	1	no	—
373	C₂×D₈	—	71	1	no	—
374	C₂×D₈	—	71	1	no	—
375	C₂×M₁₆	—	142	1	no	—
376	C₂×M₁₆	—	142	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	142	1	no	—
379	C₂²×C₈	—	142	1	no	—
380	C₂²×C₈	—	142	1	no	—
381	C₂²×C₈	—	142	1	no	—
382	C₄⋊Q₈	C₄×D₇₁	1	1	yes	characteristic
383	#127	C₄×D₇₁	1	1	yes	characteristic
384	#124	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	C₄×D₇₁	1	1	yes	characteristic
387	#121	C₄×D₇₁	1	1	yes	characteristic
388	C₄×Q₈	—	71	1	no	—
389	C₄×Q₈	—	71	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	71	1	no	—
392	C₄×D₄	—	71	1	no	—
393	C₄×D₄	—	142	1	no	—
394	C₄×D₄	—	142	1	no	—
395	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
396	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
397	#117	—	71	1	no	—
398	#117	—	142	1	no	—
399	C₂×C₄²	—	142	1	no	—
400	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
401	#107	—	71	1	no	—
402	#107	—	71	1	no	—
403	#106	—	71	1	no	—
404	#106	—	71	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	71	1	no	—
408	C₄⋊C₈	—	71	1	no	—
409	C₄⋊C₈	—	71	1	no	—
410	C₄⋊C₈	—	71	1	no	—
411	C₄⋊C₈	—	71	1	no	—
412	C₄⋊C₈	—	71	1	no	—
413	C₄⋊C₈	—	142	1	no	—
414	C₄⋊C₈	—	142	1	no	—
415	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
416	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
417	#103	—	71	1	no	—
418	#103	—	71	1	no	—
419	#102	—	71	1	no	—
420	#102	—	71	1	no	—
421	#102	—	71	1	no	—
422	#102	—	71	1	no	—
423	#102	—	71	1	no	—
424	#102	—	71	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	71	1	no	—
427	C₂²⋊C₈	—	71	1	no	—
428	C₂²⋊C₈	—	71	1	no	—
429	C₂²⋊C₈	—	71	1	no	—
430	C₂²⋊C₈	—	142	1	no	—
431	C₂²⋊C₈	—	142	1	no	—
432	C₂²⋊C₈	—	142	1	no	—
433	C₂²⋊C₈	—	142	1	no	—
434	C₂²⋊C₈	—	142	1	no	—
435	C₂²⋊C₈	—	142	1	no	—
436	C₂²⋊C₈	—	142	1	no	—
437	#97	—	142	1	no	—
438	C₄×C₈	—	71	1	no	—
439	C₄×C₈	—	71	1	no	—
440	C₄×C₈	—	71	1	no	—
441	C₄×C₈	—	71	1	no	—
442	C₄×C₈	—	142	1	no	—
443	C₄×C₈	—	142	1	no	—
444	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
445	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
446	#41	—	8	1	no	—
447	#41	—	8	1	no	—
448	#41	—	142	2	no	—
449	#41	—	142	2	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	71	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	71	1	no	—
457	C₂×D₄	—	142	1	no	—
458	C₂×D₄	C₂×C₄×D₇₁	1	1	yes	characteristic
459	C₂×D₄	C₂×C₄×D₇₁	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	142	1	no	—
463	C₂²×C₄	—	142	1	no	—
464	C₂²×C₄	—	142	1	no	—
465	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
466	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
467	C₂²×C₄	#11765864	1	1	yes	characteristic
468	SD₁₆	—	142	2	no	—
469	SD₁₆	—	142	2	no	—
470	D₈	—	142	2	no	—
471	D₈	—	142	2	no	—
472	M₁₆	—	568	1	no	—
473	M₁₆	—	568	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	8	1	no	—
479	C₂×C₈	—	568	1	no	—
480	C₂×C₈	—	568	1	no	—
481	C₂×C₈	—	568	1	no	—
482	C₂×C₈	—	568	1	no	—
483	C₂×C₈	—	71	1	no	—
484	C₂×C₈	—	71	1	no	—
485	C₂×C₈	—	71	1	no	—
486	C₂×C₈	—	71	1	no	—
487	C₂×C₈	—	71	1	no	—
488	C₂×C₈	—	71	1	no	—
489	C₂×C₈	—	71	1	no	—
490	C₂×C₈	—	71	1	no	—
491	C₂×C₈	—	142	1	no	—
492	C₂×C₈	—	142	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	71	1	no	—
495	C₄⋊C₄	—	71	1	no	—
496	C₄⋊C₄	—	142	1	no	—
497	C₄⋊C₄	—	142	1	no	—
498	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
499	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	142	1	no	—
505	C₂²⋊C₄	—	142	1	no	—
506	C₂²⋊C₄	—	142	1	no	—
507	C₄²	—	142	1	no	—
508	C₄²	—	142	1	no	—
509	C₄²	—	142	1	no	—
510	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
511	C₄²	D₄×D₇₁	1	1	yes	characteristic
512	C₄²	#11765864	1	1	yes	characteristic
513	C₄²	C₂³×D₇₁	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	142	1	no	—
517	C₂³	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
518	Q₈	—	8	1	no	—
519	Q₈	—	71	2	no	—
520	Q₈	—	142	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	8	1	no	—
526	D₄	—	8	1	no	—
527	D₄	—	8	1	no	—
528	D₄	—	8	1	no	—
529	D₄	—	71	2	no	—
530	D₄	—	142	4	no	—
531	D₄	—	142	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	284	1	no	—
544	C₂×C₄	—	284	1	no	—
545	C₂×C₄	—	568	1	no	—
546	C₂×C₄	—	142	4	no	—
547	C₂×C₄	—	142	1	no	—
548	C₂×C₄	—	142	1	no	—
549	C₂×C₄	—	142	1	no	—
550	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
551	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
552	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
554	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
555	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	284	1	no	—
561	C₈	—	284	1	no	—
562	C₈	—	142	1	no	—
563	C₈	—	142	1	no	—
564	C₈	—	142	1	no	—
565	C₈	—	142	1	no	—
566	C₈	—	142	1	no	—
567	C₈	—	142	1	no	—
568	C₈	—	142	1	no	—
569	C₈	—	142	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	284	1	no	—
580	C₂²	—	284	1	no	—
581	C₂²	—	142	2	no	—
582	C₂²	C₂×(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	284	1	no	—
590	C₄	—	284	1	no	—
591	C₄	—	142	2	no	—
592	C₄	#131×D₇₁	1	1	yes	characteristic
593	C₄	#131×D₇₁	1	1	yes	characteristic
594	C₄	#17986800	1	1	yes	characteristic
595	C₄	#17986805	1	1	yes	characteristic
596	C₂	—	4	1	no	—
597	C₂	—	8	1	no	—
598	C₂	—	8	1	no	—
599	C₂	—	284	2	no	—
600	C₂	#22597037	1	1	yes	characteristic
601	C₂	#22597166	1	1	yes	characteristic
602	C₂	#22597253	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#1480	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	#22598394	C₂
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#1480	D₇₁
hypocenter	C₇₁	#17920
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1480

Complements

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

N	H ≅ G/N	type
2. #22597449	C₂	semidirect
3. #22597416	C₂	semidirect
4. #22587221	C₂	semidirect
5. #22587207	C₂	semidirect
6. #22587186	C₂	semidirect
7. #22587172	C₂	semidirect
8. #22587161	C₂	semidirect
9. #22587149	C₂	semidirect
10. #22587143	C₂	semidirect
11. #22587132	C₂	semidirect
12. #22587123	C₂	semidirect
13. #22586775	C₂	semidirect
14. #22586640	C₂	semidirect
15. C₇₁×#1480	C₂	semidirect
315. #1480	D₇₁	semidirect
317. C₇₁	#17920	semidirect

Maximal subgroups

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

subgroup	index
#22598394	2
#22597449	2
#22597416	2
#22587221	2
#22587207	2
#22587186	2
#22587172	2
#22587161	2
#22587149	2
#22587143	2
#22587132	2
#22587123	2
#22586775	2
#22586640	2
C₇₁×#1480	2
#17920	71