Group #31897090 — subgroups

Subgroups — #31897090

Order 18176.

402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 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	C₂×#17986351	C₂	1	1	yes	maximal, characteristic
2	#22589329	C₂	1	1	yes	maximal, characteristic
3	#22587095	C₂	1	1	yes	maximal, characteristic
4	#22587025	C₂	1	1	yes	maximal, characteristic
5	#22587022	C₂	1	1	yes	maximal, characteristic
6	#22586627	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1997	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556128	C₂²	1	1	yes	characteristic
9	#17986351	—	2	2	no	—
10	#17986351	—	2	2	no	—
11	#17986052	C₂²	1	1	yes	characteristic
12	#17986023	C₂²	1	1	yes	characteristic
13	C₂×#14556051	C₄	1	4	yes	—
14	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
15	#17985767	—	2	2	no	—
16	#17985749	—	2	2	no	—
17	#17985747	—	2	2	no	—
18	#17985745	—	2	2	no	—
19	#17985721	—	2	2	no	—
20	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
21	#423×C₇₁	C₂²	1	1	yes	characteristic
22	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
23	#343×C₇₁	—	2	2	no	—
24	C₂²×Dic₁₄₂	C₂×C₄	1	2	yes	—
25	C₂×#11765849	—	2	1	no	—
26	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
27	#14556128	—	2	1	no	—
28	#14556128	—	2	1	no	—
29	#14556128	—	2	1	no	—
30	#14556128	—	2	1	no	—
31	C₂×C₄⋊Dic₇₁	—	2	1	no	—
32	C₂×C₄⋊Dic₇₁	—	2	1	no	—
33	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
34	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
35	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
36	#14556051	—	2	8	no	—
37	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
38	C₄×C₇₁⋊C₈	—	2	1	no	—
39	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
40	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
41	C₂²×Q₈×C₇₁	—	2	1	no	—
42	C₂×M₁₆×C₇₁	—	2	1	no	—
43	C₂×M₁₆×C₇₁	D₄	1	2	yes	—
44	C₄⋊Q₈×C₇₁	—	2	1	no	—
45	C₄⋊Q₈×C₇₁	—	2	1	no	—
46	C₄⋊Q₈×C₇₁	—	2	1	no	—
47	C₄⋊Q₈×C₇₁	—	2	1	no	—
48	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
49	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
51	C₄⋊C₈×C₇₁	—	2	1	no	—
52	C₄⋊C₈×C₇₁	—	2	1	no	—
53	#97×C₇₁	—	2	1	no	—
54	C₄×C₈×C₇₁	—	2	1	no	—
55	C₂×Dic₁₄₂	—	2	2	no	—
56	C₂×Dic₁₄₂	—	2	2	no	—
57	C₂×Dic₁₄₂	—	4	4	no	—
58	C₂²×Dic₇₁	—	2	2	no	—
59	#11765849	—	4	2	no	—
60	C₂×C₇₁⋊C₈	—	2	2	no	—
61	C₂×C₇₁⋊C₈	—	4	2	no	—
62	C₂×C₇₁⋊C₈	—	4	1	no	—
63	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	4	yes	—
64	C₄⋊Dic₇₁	—	4	1	no	—
65	C₄⋊Dic₇₁	—	4	1	no	—
66	C₄⋊Dic₇₁	—	4	1	no	—
67	C₄⋊Dic₇₁	—	4	1	no	—
68	C₂×Q₈×C₇₁	—	4	1	no	—
69	C₂×Q₈×C₇₁	—	4	1	no	—
70	C₂×Q₈×C₇₁	—	8	2	no	—
71	C₂²×C₄×C₇₁	—	2	2	no	—
72	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
75	M₁₆×C₇₁	—	2	2	no	—
76	M₁₆×C₇₁	—	2	2	no	—
77	M₁₆×C₇₁	—	4	2	no	—
78	C₂×C₈×C₇₁	—	2	2	no	—
79	C₂×C₈×C₇₁	—	4	1	no	—
80	C₄⋊C₄×C₇₁	—	2	2	no	—
81	C₄⋊C₄×C₇₁	—	2	2	no	—
82	C₄⋊C₄×C₇₁	—	4	1	no	—
83	C₄⋊C₄×C₇₁	—	4	1	no	—
84	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
86	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₇₁	#41	1	1	yes	characteristic
88	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
89	Q₈×C₇₁	—	8	2	no	—
90	Q₈×C₇₁	—	8	2	no	—
91	C₂×C₄×C₇₁	—	2	2	no	—
92	C₂×C₄×C₇₁	—	2	2	no	—
93	C₂×C₄×C₇₁	—	4	2	no	—
94	C₂×C₄×C₇₁	—	8	2	no	—
95	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
98	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
99	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
100	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
101	C₂×C₄×C₇₁	#137	1	2	yes	—
102	C₂×C₄×C₇₁	#137	1	2	yes	—
103	C₂×Dic₇₁	—	4	2	no	—
104	C₂×Dic₇₁	—	8	2	no	—
105	Dic₁₄₂	—	4	4	no	—
106	Dic₁₄₂	—	8	2	no	—
107	C₈×C₇₁	—	4	2	no	—
108	C₈×C₇₁	—	8	1	no	—
109	C₇₁⋊C₈	—	2	4	no	—
110	C₇₁⋊C₈	—	4	2	no	—
111	C₇₁⋊C₈	—	8	1	no	—
112	C₂²×C₇₁	—	2	1	no	—
113	C₂²×C₇₁	—	2	1	no	—
114	C₂²×C₇₁	#390	1	1	yes	characteristic
115	C₂²×C₇₁	#441	1	2	yes	—
116	C₄×C₇₁	—	2	1	no	—
117	C₄×C₇₁	—	2	1	no	—
118	C₄×C₇₁	—	8	2	no	—
119	C₄×C₇₁	#413	1	2	yes	—
120	C₄×C₇₁	#470	1	2	yes	—
121	C₄×C₇₁	#471	1	2	yes	—
122	C₄×C₇₁	#497	1	1	yes	characteristic
123	C₄×C₇₁	#497	1	1	yes	characteristic
124	Dic₇₁	—	8	2	no	—
125	#9803	—	71	1	no	maximal, Sylow
126	C₂×C₇₁	—	2	2	no	—
127	C₂×C₇₁	#1967	1	1	yes	characteristic
128	C₂×C₇₁	#1971	1	1	yes	characteristic
129	C₂×C₇₁	#1977	1	1	yes	characteristic
130	C₂×#487	—	71	1	no	—
131	#1997	—	71	1	no	—
132	#1997	D₇₁	1	1	yes	characteristic
133	#1566	—	71	1	no	—
134	#1549	—	71	1	no	—
135	#1548	—	71	1	no	—
136	#1451	—	71	1	no	—
137	C₇₁	#9803	1	1	yes	characteristic, complemented, Sylow
138	C₂×C₄⋊Q₈	—	71	1	no	—
139	C₂×C₄⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
140	#487	—	142	2	no	—
141	#487	—	142	2	no	—
142	#431	—	71	1	no	—
143	#423	—	71	1	no	—
144	#423	C₂×D₇₁	1	1	yes	characteristic
145	C₂×#103	—	71	4	no	—
146	C₄×M₁₆	C₂×D₇₁	1	1	yes	characteristic
147	C₂×C₄×C₈	—	71	1	no	—
148	#343	—	2	2	no	—
149	#343	—	142	2	no	—
150	#334	—	142	2	no	—
151	#333	—	142	2	no	—
152	#332	—	142	2	no	—
153	#322	—	142	2	no	—
154	C₂²×Q₈	—	2	1	no	—
155	C₂²×Q₈	—	71	2	no	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	142	1	no	—
158	C₂×M₁₆	C₂²⋊D₇₁	1	2	yes	—
159	C₂²×C₈	—	71	2	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	—	142	1	no	—
165	C₄⋊Q₈	—	142	1	no	—
166	C₄⋊Q₈	—	142	1	no	—
167	C₄⋊Q₈	—	142	1	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	—	142	1	no	—
170	C₂×C₄⋊C₄	—	142	1	no	—
171	C₂×C₄⋊C₄	C₄×D₇₁	1	2	yes	—
172	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
173	C₄⋊C₈	—	2	1	no	—
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	71	2	no	—
176	C₄⋊C₈	—	142	1	no	—
177	C₄⋊C₈	—	142	1	no	—
178	#103	—	142	8	no	—
179	C₂²⋊C₈	—	142	1	no	—
180	#97	—	2	1	no	—
181	C₄×C₈	—	2	1	no	—
182	C₄×C₈	—	71	2	no	—
183	C₄×C₈	—	71	2	no	—
184	C₄×C₈	—	142	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂×Q₈	—	8	2	no	—
188	C₂×Q₈	—	284	4	no	—
189	C₂×Q₈	—	142	2	no	—
190	C₂×Q₈	—	142	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	142	2	no	—
193	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
194	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
195	C₂²×C₄	#11765865	1	1	yes	characteristic
196	M₁₆	—	2	2	no	—
197	M₁₆	—	2	2	no	—
198	M₁₆	—	4	2	no	—
199	M₁₆	—	284	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	284	1	no	—
203	C₂×C₈	—	284	2	no	—
204	C₂×C₈	—	71	4	no	—
205	C₂×C₈	—	142	2	no	—
206	C₄⋊C₄	—	2	2	no	—
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	1	no	—
210	C₄⋊C₄	—	284	1	no	—
211	C₄⋊C₄	—	284	1	no	—
212	C₄⋊C₄	—	284	1	no	—
213	C₄⋊C₄	—	284	1	no	—
214	C₄²	D₄×D₇₁	1	1	yes	characteristic
215	C₄²	D₄×D₇₁	1	1	yes	characteristic
216	C₄²	D₄×D₇₁	1	1	yes	characteristic
217	C₄²	#11765864	1	1	yes	characteristic
218	C₂³	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
219	Q₈	—	8	2	no	—
220	Q₈	—	8	2	no	—
221	Q₈	—	284	4	no	—
222	Q₈	—	568	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	8	2	no	—
227	C₂×C₄	—	284	2	no	—
228	C₂×C₄	—	568	2	no	—
229	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
230	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
231	C₂×C₄	#14556100	1	1	yes	characteristic
232	C₂×C₄	#14556101	1	1	yes	characteristic
233	C₂×C₄	#14556114	1	1	yes	characteristic
234	C₂×C₄	#14556124	1	1	yes	characteristic
235	C₂×C₄	#14556158	1	2	yes	—
236	C₂×C₄	#14556159	1	2	yes	—
237	C₈	—	4	2	no	—
238	C₈	—	8	1	no	—
239	C₈	—	284	2	no	—
240	C₈	—	568	1	no	—
241	C₈	—	142	4	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	2	1	no	—
244	C₂²	#17985899	1	1	yes	characteristic
245	C₂²	#17986104	1	2	yes	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	8	2	no	—
249	C₄	—	568	2	no	—
250	C₄	#17985982	1	2	yes	—
251	C₄	#17986255	1	2	yes	—
252	C₄	#17986261	1	2	yes	—
253	C₄	#17986391	1	1	yes	characteristic
254	C₄	#17986394	1	1	yes	characteristic
255	C₂	—	2	2	no	—
256	C₂	#22589188	1	1	yes	characteristic
257	C₂	#22589210	1	1	yes	characteristic
258	C₂	#22589240	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17986351

C₂

yes

maximal, characteristic

#22589329

C₂

yes

maximal, characteristic

#22587095

C₂

yes

maximal, characteristic

#22587025

C₂

yes

maximal, characteristic

#22587022

C₂

yes

maximal, characteristic

#22586627

C₂

yes

maximal, characteristic

C₇₁×#1997

C₂

yes

maximal, characteristic

C₂×#14556128

C₂²

yes

—

—

C₂²

yes

characteristic

#17986023

C₂²

yes

characteristic

C₂×#14556051

C₄

yes

—

C₂×C₄×C₇₁⋊C₈

C₂²

yes

—

—

—

—

—

C₂×C₄⋊Q₈×C₇₁

C₂²

yes

characteristic

#423×C₇₁

C₂²

yes

characteristic

C₄×M₁₆×C₇₁

C₂²

yes

characteristic

#343×C₇₁

—

C₂²×Dic₁₄₂

C₂×C₄

yes

—

C₂×#11765849

—

C₂²×C₇₁⋊C₈

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₇₁

—

C₂×C₄⋊Dic₇₁

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

D₄

yes

—

#14556051

—

C₂²⋊(C₇₁⋊C₈)

—

C₄×C₇₁⋊C₈

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₂²×Q₈×C₇₁

—

C₂×M₁₆×C₇₁

—

C₂×M₁₆×C₇₁

D₄

yes

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄⋊C₄×C₇₁

C₂×C₄

yes

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

#97×C₇₁

—

C₄×C₈×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

#41

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

#41

yes

characteristic

C₂³×C₇₁

C₄×D₄

yes

characteristic

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

100

C₂×C₄×C₇₁

#127

yes

characteristic

101

C₂×C₄×C₇₁

#137

yes

—

102

C₂×C₄×C₇₁

#137

yes

—

103

C₂×Dic₇₁

—

104

C₂×Dic₇₁

—

105

Dic₁₄₂

—

106

Dic₁₄₂

—

107

C₈×C₇₁

—

108

C₈×C₇₁

—

109

C₇₁⋊C₈

—

110

C₇₁⋊C₈

—

111

C₇₁⋊C₈

—

112

C₂²×C₇₁

—

113

C₂²×C₇₁

—

114

C₂²×C₇₁

#390

yes

characteristic

115

C₂²×C₇₁

#441

yes

—

116

C₄×C₇₁

—

117

C₄×C₇₁

—

118

C₄×C₇₁

—

119

C₄×C₇₁

#413

yes

—

120

C₄×C₇₁

#470

yes

—

121

C₄×C₇₁

#471

yes

—

122

C₄×C₇₁

#497

yes

characteristic

123

C₄×C₇₁

#497

yes

characteristic

124

Dic₇₁

—

125

#9803

—

maximal, Sylow

126

C₂×C₇₁

—

127

C₂×C₇₁

#1967

yes

characteristic

128

C₂×C₇₁

#1971

yes

characteristic

129

C₂×C₇₁

#1977

yes

characteristic

130

C₂×#487

—

131

#1997

—

132

#1997

D₇₁

yes

characteristic

133

#1566

—

134

#1549

—

135

#1548

—

136

#1451

—

137

C₇₁

#9803

yes

characteristic, complemented, Sylow

138

C₂×C₄⋊Q₈

—

139

C₂×C₄⋊Q₈

C₂×D₇₁

yes

characteristic

140

#487

—

142

—

141

#487

—

142

—

142

#431

—

143

#423

—

144

#423

C₂×D₇₁

yes

characteristic

145

C₂×#103

—

146

C₄×M₁₆

C₂×D₇₁

yes

characteristic

147

C₂×C₄×C₈

—

148

#343

—

149

#343

—

142

—

150

#334

—

142

—

151

#333

—

142

—

152

#332

—

142

—

153

#322

—

142

—

154

C₂²×Q₈

—

155

C₂²×Q₈

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

142

—

158

C₂×M₁₆

C₂²⋊D₇₁

yes

—

159

C₂²×C₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

142

—

165

C₄⋊Q₈

—

142

—

166

C₄⋊Q₈

—

142

—

167

C₄⋊Q₈

—

142

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

142

—

170

C₂×C₄⋊C₄

—

142

—

171

C₂×C₄⋊C₄

C₄×D₇₁

yes

—

172

C₂×C₄²

C₂²×D₇₁

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

142

—

177

C₄⋊C₈

—

142

—

178

#103

—

142

—

179

C₂²⋊C₈

—

142

—

180

#97

—

181

C₄×C₈

—

182

C₄×C₈

—

183

C₄×C₈

—

184

C₄×C₈

—

142

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

284

—

189

C₂×Q₈

—

142

—

190

C₂×Q₈

—

142

—

191

C₂²×C₄

—

192

C₂²×C₄

—

142

—

193

C₂²×C₄

C₂×C₄×D₇₁

yes

characteristic

194

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

195

C₂²×C₄

#11765865

yes

characteristic

196

M₁₆

—

197

M₁₆

—

198

M₁₆

—

199

M₁₆

—

284

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

284

—

203

C₂×C₈

—

284

—

204

C₂×C₈

—

205

C₂×C₈

—

142

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

284

—

211

C₄⋊C₄

—

284

—

212

C₄⋊C₄

—

284

—

213

C₄⋊C₄

—

284

—

214

C₄²

D₄×D₇₁

yes

characteristic

215

C₄²

D₄×D₇₁

yes

characteristic

216

C₄²

D₄×D₇₁

yes

characteristic

217

C₄²

#11765864

yes

characteristic

218

C₂³

C₄×C₂²⋊D₇₁

yes

characteristic

219

Q₈

—

220

Q₈

—

221

Q₈

—

284

—

222

Q₈

—

568

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

284

—

228

C₂×C₄

—

568

—

229

C₂×C₄

C₂²⋊C₄×D₇₁

yes

characteristic

230

C₂×C₄

(C₂²⋊D₇₁)⋊C₄

yes

characteristic

231

C₂×C₄

#14556100

yes

characteristic

232

C₂×C₄

#14556101

yes

characteristic

233

C₂×C₄

#14556114

yes

characteristic

234

C₂×C₄

#14556124

yes

characteristic

235

C₂×C₄

#14556158

yes

—

236

C₂×C₄

#14556159

yes

—

237

C₈

—

238

C₈

—

239

C₈

—

284

—

240

C₈

—

568

—

241

C₈

—

142

—

242

C₂²

—

243

C₂²

—

244

C₂²

#17985899

yes

characteristic

245

C₂²

#17986104

yes

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

568

—

250

C₄

#17985982

yes

—

251

C₄

#17986255

yes

—

252

C₄

#17986261

yes

—

253

C₄

#17986391

yes

characteristic

254

C₄

#17986394

yes

characteristic

255

C₂

—

256

C₂

#22589188

yes

characteristic

257

C₂

#22589210

yes

characteristic

258

C₂

#22589240

yes

characteristic

	subgroup	G/H
center	C₂²	#17985899
commutator	C₂²×C₄×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1997	C₂
socle	C₂²×C₇₁	#390
prime radical	C₂³×C₇₁	C₄×D₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1997	D₇₁
hypocenter	C₇₁	#9803
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1997

subgroup

G/H

center

C₂²

#17985899

commutator

C₂²×C₄×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1997

C₂

socle

C₂²×C₇₁

#390

prime radical

C₂³×C₇₁

C₄×D₄

cosocle

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1997

N	H ≅ G/N	type
137. C₇₁	#9803	semidirect

H ≅ G/N

type

137. C₇₁

#9803

semidirect

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

subgroup	index
C₂×#17986351	2
#22589329	2
#22587095	2
#22587025	2
#22587022	2
#22586627	2
C₇₁×#1997	2
#9803	71

subgroup

index

C₇₁×#1997

Subgroups — #31897090

Conjugacy classes of subgroups

Complements

Maximal subgroups