Group #31830266 — subgroups

Subgroups — C₇₁×#9394 #31830266

Order 18176.

506 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#2982	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#2546	C₂	1	1	yes	maximal, characteristic
3	C₇₁×#1801	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#1546	C₂	1	2	yes	maximal
5	C₇₁×#1303	C₂	1	2	yes	maximal
6	C₂×C₄⋊Q₈×C₇₁	—	2	1	no	—
7	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
9	C₈×Q₈×C₇₁	—	2	4	no	—
10	#431×C₇₁	—	2	2	no	—
11	#431×C₇₁	C₂²	1	2	yes	—
12	#423×C₇₁	C₂²	1	2	yes	—
13	C₂×#101×C₇₁	—	2	1	no	—
14	#398×C₇₁	C₄	1	4	yes	—
15	#391×C₇₁	—	2	1	no	—
16	#389×C₇₁	—	2	2	no	—
17	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
18	#343×C₇₁	—	2	1	no	—
19	#332×C₇₁	—	2	4	no	—
20	C₂²×Q₈×C₇₁	—	2	1	no	—
21	C₂²×Q₈×C₇₁	D₄	1	1	yes	characteristic
22	C₂×M₁₆×C₇₁	—	2	2	no	—
23	C₄⋊Q₈×C₇₁	—	2	2	no	—
24	C₄⋊Q₈×C₇₁	—	2	2	no	—
25	C₄⋊Q₈×C₇₁	—	4	2	no	—
26	C₄⋊Q₈×C₇₁	—	4	2	no	—
27	C₄×Q₈×C₇₁	—	2	2	no	—
28	C₄×Q₈×C₇₁	—	2	2	no	—
29	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
30	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
31	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
32	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₇₁	—	2	1	no	—
36	C₂×C₄²×C₇₁	D₄	1	2	yes	—
37	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
38	C₄⋊C₈×C₇₁	—	2	4	no	—
39	C₄⋊C₈×C₇₁	—	2	2	no	—
40	C₄⋊C₈×C₇₁	—	2	2	no	—
41	C₄⋊C₈×C₇₁	D₄	1	4	yes	—
42	#101×C₇₁	—	4	2	no	—
43	C₂²⋊C₈×C₇₁	—	2	2	no	—
44	C₄×C₈×C₇₁	—	2	4	no	—
45	C₄×C₈×C₇₁	—	2	2	no	—
46	#95×C₇₁	—	2	4	no	—
47	#95×C₇₁	C₂×C₄	1	2	yes	—
48	C₂×Q₈×C₇₁	—	2	2	no	—
49	C₂×Q₈×C₇₁	—	2	2	no	—
50	C₂×Q₈×C₇₁	—	4	2	no	—
51	C₂×Q₈×C₇₁	—	4	1	no	—
52	C₂×Q₈×C₇₁	—	4	1	no	—
53	C₂×Q₈×C₇₁	—	4	2	no	—
54	C₂×Q₈×C₇₁	D₈	1	2	yes	—
55	C₂×Q₈×C₇₁	SD₁₆	1	2	yes	—
56	C₂²×C₄×C₇₁	—	2	2	no	—
57	C₂²×C₄×C₇₁	—	2	2	no	—
58	C₂²×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
63	M₁₆×C₇₁	—	4	2	no	—
64	M₁₆×C₇₁	—	4	2	no	—
65	C₂×C₈×C₇₁	—	2	4	no	—
66	C₂×C₈×C₇₁	—	4	2	no	—
67	C₄⋊C₄×C₇₁	—	2	4	no	—
68	C₄⋊C₄×C₇₁	—	2	4	no	—
69	C₄⋊C₄×C₇₁	—	2	2	no	—
70	C₄⋊C₄×C₇₁	—	2	4	no	—
71	C₄⋊C₄×C₇₁	—	4	8	no	—
72	C₄⋊C₄×C₇₁	—	4	1	no	—
73	C₄⋊C₄×C₇₁	—	4	1	no	—
74	C₄²×C₇₁	—	2	2	no	—
75	C₄²×C₇₁	—	2	2	no	—
76	C₄²×C₇₁	—	4	1	no	—
77	C₄²×C₇₁	—	4	1	no	—
78	C₄²×C₇₁	C₂×D₄	1	2	yes	—
79	C₄²×C₇₁	#41	1	2	yes	—
80	C₂³×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	Q₈×C₇₁	—	2	4	no	—
82	Q₈×C₇₁	—	2	4	no	—
83	Q₈×C₇₁	—	8	2	no	—
84	Q₈×C₇₁	—	8	2	no	—
85	C₂×C₄×C₇₁	—	2	2	no	—
86	C₂×C₄×C₇₁	—	2	2	no	—
87	C₂×C₄×C₇₁	—	2	2	no	—
88	C₂×C₄×C₇₁	—	2	4	no	—
89	C₂×C₄×C₇₁	—	2	2	no	—
90	C₂×C₄×C₇₁	—	4	1	no	—
91	C₂×C₄×C₇₁	—	4	2	no	—
92	C₂×C₄×C₇₁	—	4	2	no	—
93	C₂×C₄×C₇₁	—	4	2	no	—
94	C₂×C₄×C₇₁	—	4	2	no	—
95	C₂×C₄×C₇₁	—	4	2	no	—
96	C₂×C₄×C₇₁	—	4	2	no	—
97	C₂×C₄×C₇₁	#102	1	4	yes	—
98	C₂×C₄×C₇₁	C₄×D₄	1	2	yes	—
99	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
100	C₂×C₄×C₇₁	#121	1	2	yes	—
101	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
102	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
103	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
104	C₂×C₄×C₇₁	#135	1	2	yes	—
105	C₈×C₇₁	—	4	4	no	—
106	C₈×C₇₁	—	8	2	no	—
107	C₂²×C₇₁	—	2	1	no	—
108	C₂²×C₇₁	—	2	1	no	—
109	C₂²×C₇₁	#386	1	1	yes	characteristic
110	C₂²×C₇₁	C₂×#102	1	1	yes	characteristic
111	C₂²×C₇₁	#416	1	1	yes	characteristic
112	C₄×C₇₁	—	2	1	no	—
113	C₄×C₇₁	—	2	4	no	—
114	C₄×C₇₁	—	2	2	no	—
115	C₄×C₇₁	—	4	4	no	—
116	C₄×C₇₁	—	4	2	no	—
117	C₄×C₇₁	—	8	2	no	—
118	C₄×C₇₁	#456	1	2	yes	—
119	C₄×C₇₁	#465	1	2	yes	—
120	C₄×C₇₁	#466	1	2	yes	—
121	#9394	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂×C₇₁	—	2	1	no	—
123	C₂×C₇₁	—	2	1	no	—
124	C₂×C₇₁	#1886	1	1	yes	characteristic
125	C₂×C₇₁	#1893	1	1	yes	characteristic
126	C₂×C₇₁	#1915	1	1	yes	characteristic
127	#2982	C₂×C₇₁	1	1	yes	characteristic
128	#2546	C₂×C₇₁	1	1	yes	characteristic
129	#1801	C₂×C₇₁	1	1	yes	characteristic
130	#1546	C₂×C₇₁	1	2	yes	—
131	#1303	C₂×C₇₁	1	2	yes	—
132	C₇₁	#9394	1	1	yes	characteristic, direct product factor, Sylow
133	C₂×C₄⋊Q₈	—	2	1	no	—
134	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
135	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
136	C₈×Q₈	—	2	4	no	—
137	#431	—	2	2	no	—
138	#431	C₂²×C₇₁	1	2	yes	—
139	#423	C₂²×C₇₁	1	2	yes	—
140	C₂×#101	—	2	1	no	—
141	#398	C₄×C₇₁	1	4	yes	—
142	#391	—	2	1	no	—
143	#389	—	2	2	no	—
144	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
145	#343	—	2	1	no	—
146	#332	—	2	4	no	—
147	C₂²×Q₈	—	2	1	no	—
148	C₂²×Q₈	D₄×C₇₁	1	1	yes	characteristic
149	C₂×M₁₆	—	2	2	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄⋊Q₈	—	4	2	no	—
153	C₄⋊Q₈	—	4	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄⋊C₄	—	2	4	no	—
158	C₂×C₄⋊C₄	—	2	1	no	—
159	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	2	yes	—
160	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	2	yes	—
161	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
162	C₂×C₄²	—	2	1	no	—
163	C₂×C₄²	D₄×C₇₁	1	2	yes	—
164	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
165	C₄⋊C₈	—	2	4	no	—
166	C₄⋊C₈	—	2	2	no	—
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	D₄×C₇₁	1	4	yes	—
169	#101	—	4	2	no	—
170	C₂²⋊C₈	—	2	2	no	—
171	C₄×C₈	—	2	4	no	—
172	C₄×C₈	—	2	2	no	—
173	#95	—	2	4	no	—
174	#95	C₂×C₄×C₇₁	1	2	yes	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	2	2	no	—
177	C₂×Q₈	—	4	2	no	—
178	C₂×Q₈	—	4	1	no	—
179	C₂×Q₈	—	4	1	no	—
180	C₂×Q₈	—	4	2	no	—
181	C₂×Q₈	D₈×C₇₁	1	2	yes	—
182	C₂×Q₈	SD₁₆×C₇₁	1	2	yes	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
186	C₂²×C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
187	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
188	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
189	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
190	M₁₆	—	4	2	no	—
191	M₁₆	—	4	2	no	—
192	C₂×C₈	—	2	4	no	—
193	C₂×C₈	—	4	2	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	2	4	no	—
196	C₄⋊C₄	—	2	2	no	—
197	C₄⋊C₄	—	2	4	no	—
198	C₄⋊C₄	—	4	8	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	4	1	no	—
204	C₄²	—	4	1	no	—
205	C₄²	C₂×D₄×C₇₁	1	2	yes	—
206	C₄²	#41×C₇₁	1	2	yes	—
207	C₂³	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
208	Q₈	—	2	4	no	—
209	Q₈	—	2	4	no	—
210	Q₈	—	8	2	no	—
211	Q₈	—	8	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	4	1	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	#102×C₇₁	1	4	yes	—
225	C₂×C₄	C₄×D₄×C₇₁	1	2	yes	—
226	C₂×C₄	#120×C₇₁	1	1	yes	characteristic
227	C₂×C₄	#121×C₇₁	1	2	yes	—
228	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
229	C₂×C₄	C₂×D₈×C₇₁	1	1	yes	characteristic
230	C₂×C₄	C₂×SD₁₆×C₇₁	1	1	yes	characteristic
231	C₂×C₄	#135×C₇₁	1	2	yes	—
232	C₈	—	4	4	no	—
233	C₈	—	8	2	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	#386×C₇₁	1	1	yes	characteristic
237	C₂²	C₂×#102×C₇₁	1	1	yes	characteristic
238	C₂²	#416×C₇₁	1	1	yes	characteristic
239	C₄	—	2	1	no	—
240	C₄	—	2	4	no	—
241	C₄	—	2	2	no	—
242	C₄	—	4	4	no	—
243	C₄	—	4	2	no	—
244	C₄	—	8	2	no	—
245	C₄	#456×C₇₁	1	2	yes	—
246	C₄	#465×C₇₁	1	2	yes	—
247	C₄	#466×C₇₁	1	2	yes	—
248	C₂	—	2	1	no	—
249	C₂	—	2	1	no	—
250	C₂	C₇₁×#1886	1	1	yes	characteristic
251	C₂	C₇₁×#1893	1	1	yes	characteristic
252	C₂	C₇₁×#1915	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₁×#2982

C₂

yes

maximal, characteristic

C₇₁×#2546

C₂

yes

maximal, characteristic

C₇₁×#1801

C₂

yes

maximal, characteristic

C₇₁×#1546

C₂

yes

maximal

C₇₁×#1303

C₂

yes

maximal

C₂×C₄⋊Q₈×C₇₁

—

C₂×C₄⋊Q₈×C₇₁

C₂²

yes

characteristic

C₂×C₄×Q₈×C₇₁

C₂²

yes

characteristic

C₈×Q₈×C₇₁

—

#431×C₇₁

—

#431×C₇₁

C₂²

yes

—

#423×C₇₁

C₂²

yes

—

C₂×#101×C₇₁

—

#398×C₇₁

C₄

yes

—

#391×C₇₁

—

#389×C₇₁

—

C₄×C₄⋊C₄×C₇₁

C₂²

yes

characteristic

#343×C₇₁

—

#332×C₇₁

—

C₂²×Q₈×C₇₁

—

C₂²×Q₈×C₇₁

D₄

yes

characteristic

C₂×M₁₆×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄⋊C₄×C₇₁

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₁

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

—

C₂×C₄²×C₇₁

D₄

yes

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

D₄

yes

—

#101×C₇₁

—

C₂²⋊C₈×C₇₁

—

C₄×C₈×C₇₁

—

C₄×C₈×C₇₁

—

#95×C₇₁

—

#95×C₇₁

C₂×C₄

yes

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

D₈

yes

—

C₂×Q₈×C₇₁

SD₁₆

yes

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

—

C₄²×C₇₁

#41

yes

—

C₂³×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₁

—

Q₈×C₇₁

—

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

#102

yes

—

C₂×C₄×C₇₁

C₄×D₄

yes

—

C₂×C₄×C₇₁

#120

yes

characteristic

100

C₂×C₄×C₇₁

#121

yes

—

101

C₂×C₄×C₇₁

#123

yes

characteristic

102

C₂×C₄×C₇₁

C₂×D₈

yes

characteristic

103

C₂×C₄×C₇₁

C₂×SD₁₆

yes

characteristic

104

C₂×C₄×C₇₁

#135

yes

—

105

C₈×C₇₁

—

106

C₈×C₇₁

—

107

C₂²×C₇₁

—

108

C₂²×C₇₁

—

109

C₂²×C₇₁

#386

yes

characteristic

110

C₂²×C₇₁

C₂×#102

yes

characteristic

111

C₂²×C₇₁

#416

yes

characteristic

112

C₄×C₇₁

—

113

C₄×C₇₁

—

114

C₄×C₇₁

—

115

C₄×C₇₁

—

116

C₄×C₇₁

—

117

C₄×C₇₁

—

118

C₄×C₇₁

#456

yes

—

119

C₄×C₇₁

#465

yes

—

120

C₄×C₇₁

#466

yes

—

121

#9394

C₇₁

yes

maximal, characteristic, direct product factor, Sylow

122

C₂×C₇₁

—

123

C₂×C₇₁

—

124

C₂×C₇₁

#1886

yes

characteristic

125

C₂×C₇₁

#1893

yes

characteristic

126

C₂×C₇₁

#1915

yes

characteristic

127

#2982

C₂×C₇₁

yes

characteristic

128

#2546

C₂×C₇₁

yes

characteristic

129

#1801

C₂×C₇₁

yes

characteristic

130

#1546

C₂×C₇₁

yes

—

131

#1303

C₂×C₇₁

yes

—

132

C₇₁

#9394

yes

characteristic, direct product factor, Sylow

133

C₂×C₄⋊Q₈

—

134

C₂×C₄⋊Q₈

C₂²×C₇₁

yes

characteristic

135

C₂×C₄×Q₈

C₂²×C₇₁

yes

characteristic

136

C₈×Q₈

—

137

#431

—

138

#431

C₂²×C₇₁

yes

—

139

#423

C₂²×C₇₁

yes

—

140

C₂×#101

—

141

#398

C₄×C₇₁

yes

—

142

#391

—

143

#389

—

144

C₄×C₄⋊C₄

C₂²×C₇₁

yes

characteristic

145

#343

—

146

#332

—

147

C₂²×Q₈

—

148

C₂²×Q₈

D₄×C₇₁

yes

characteristic

149

C₂×M₁₆

—

150

C₄⋊Q₈

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

C₄×Q₈

—

155

C₄×Q₈

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

C₂×C₄×C₇₁

yes

—

160

C₂×C₄⋊C₄

C₂×C₄×C₇₁

yes

—

161

C₂×C₄⋊C₄

D₄×C₇₁

yes

characteristic

162

C₂×C₄²

—

163

C₂×C₄²

D₄×C₇₁

yes

—

164

C₂×C₄²

C₂³×C₇₁

yes

characteristic

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

D₄×C₇₁

yes

—

169

#101

—

170

C₂²⋊C₈

—

171

C₄×C₈

—

172

C₄×C₈

—

173

#95

—

174

#95

C₂×C₄×C₇₁

yes

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

D₈×C₇₁

yes

—

182

C₂×Q₈

SD₁₆×C₇₁

yes

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

C₂²⋊C₄×C₇₁

yes

—

186

C₂²×C₄

C₂²⋊C₄×C₇₁

yes

—

187

C₂²×C₄

C₂²×C₄×C₇₁

yes

characteristic

188

C₂²×C₄

C₂×D₄×C₇₁

yes

characteristic

189

C₂²×C₄

C₂×D₄×C₇₁

yes

characteristic

190

M₁₆

—

191

M₁₆

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

C₂×D₄×C₇₁

yes

—

206

C₄²

#41×C₇₁

yes

—

207

C₂³

C₂×C₂²⋊C₄×C₇₁

yes

characteristic

208

Q₈

—

209

Q₈

—

210

Q₈

—

211

Q₈

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

#102×C₇₁

yes

—

225

C₂×C₄

C₄×D₄×C₇₁

yes

—

226

C₂×C₄

#120×C₇₁

yes

characteristic

227

C₂×C₄

#121×C₇₁

yes

—

228

C₂×C₄

#123×C₇₁

yes

characteristic

229

C₂×C₄

C₂×D₈×C₇₁

yes

characteristic

230

C₂×C₄

C₂×SD₁₆×C₇₁

yes

characteristic

231

C₂×C₄

#135×C₇₁

yes

—

232

C₈

—

233

C₈

—

234

C₂²

—

235

C₂²

—

236

C₂²

#386×C₇₁

yes

characteristic

237

C₂²

C₂×#102×C₇₁

yes

characteristic

238

C₂²

#416×C₇₁

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

#456×C₇₁

yes

—

246

C₄

#465×C₇₁

yes

—

247

C₄

#466×C₇₁

yes

—

248

C₂

—

249

C₂

—

250

C₂

C₇₁×#1886

yes

characteristic

251

C₂

C₇₁×#1893

yes

characteristic

252

C₂

C₇₁×#1915

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₇₁
Frattini, cosocle	C₂×C₄²	C₂³×C₇₁
prime radical	C₂³×C₇₁	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ G

subgroup

G/H

center, socle

C₂²×C₇₁

#386

commutator

C₂²×C₄

C₂²×C₄×C₇₁

Frattini, cosocle

C₂×C₄²

C₂³×C₇₁

prime radical

C₂³×C₇₁

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ G

N	H ≅ G/N	type
121. #9394	C₇₁	direct (N × H)
132. C₇₁	#9394	direct (N × H)

H ≅ G/N

type

121. #9394

C₇₁

direct (N × H)

132. C₇₁

#9394

direct (N × H)

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

subgroup	index
C₇₁×#2982	2
C₇₁×#2546	2
C₇₁×#1801	2
C₇₁×#1546	2
C₇₁×#1303	2
#9394	71

subgroup

index

C₇₁×#2982

C₇₁×#2546

C₇₁×#1801

C₇₁×#1546

C₇₁×#1303

#9394

Subgroups — C₇₁×#9394 #31830266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C71×#9394 #31830266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#9394 #31830266