Group #31906791 — subgroups

Subgroups — #31906791

Order 18176.

330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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×C₈×Dic₁₄₂	C₂	1	1	yes	maximal, characteristic
2	#22590143	C₂	1	1	yes	maximal, characteristic
3	#22586279	C₂	1	4	yes	maximal
4	C₇₁×#2163	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Dic₁₄₂	C₄	1	1	yes	characteristic
6	C₈×Dic₁₄₂	—	2	1	no	—
7	C₈×Dic₁₄₂	—	2	1	no	—
8	C₈×Dic₁₄₂	—	2	1	no	—
9	C₈×Dic₁₄₂	—	2	1	no	—
10	C₂×C₄⋊(C₇₁⋊C₈)	C₄	1	1	yes	characteristic
11	C₂×Dic₇₁⋊C₈	C₂²	1	2	yes	—
12	C₂×C₈×Dic₇₁	C₄	1	2	yes	—
13	C₄⋊(C₇₁⋊C₁₆)	—	2	1	no	—
14	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	—
15	#17985775	—	2	1	no	—
16	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₁₆×C₇₁	—	2	1	no	—
18	C₂²⋊C₁₆×C₇₁	C₂²	1	2	yes	—
19	#346×C₇₁	—	2	1	no	—
20	C₂²×Dic₁₄₂	C₈	1	1	yes	characteristic
21	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
22	C₄×Dic₁₄₂	—	2	1	no	—
23	C₄×Dic₁₄₂	—	2	1	no	—
24	C₄×Dic₁₄₂	—	2	1	no	—
25	C₄×Dic₁₄₂	—	2	1	no	—
26	C₂×C₄⋊Dic₇₁	C₈	1	1	yes	characteristic
27	C₂×Dic₇₁⋊C₄	C₈	1	2	yes	—
28	C₂×C₄×Dic₇₁	C₂×C₄	1	2	yes	—
29	C₂×C₇₁⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
31	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
32	Dic₇₁⋊C₈	—	2	2	no	—
33	Dic₇₁⋊C₈	—	2	2	no	—
34	C₈×Dic₇₁	—	2	2	no	—
35	C₈×Dic₇₁	—	2	2	no	—
36	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
38	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₆×C₇₁	—	2	2	no	—
40	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
41	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
43	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
44	C₂×Dic₁₄₂	—	2	1	no	—
45	C₂×Dic₁₄₂	—	2	1	no	—
46	C₂×Dic₁₄₂	—	2	4	no	—
47	C₂²×Dic₇₁	C₂×C₈	1	2	yes	—
48	C₂²×Dic₇₁	C₂×C₈	1	2	yes	—
49	C₂×C₇₁⋊C₈	—	2	2	no	—
50	C₂×C₇₁⋊C₈	—	4	2	no	—
51	C₄⋊Dic₇₁	—	2	1	no	—
52	C₄⋊Dic₇₁	—	2	1	no	—
53	Dic₇₁⋊C₄	—	2	2	no	—
54	Dic₇₁⋊C₄	—	2	2	no	—
55	C₄×Dic₇₁	—	2	2	no	—
56	C₄×Dic₇₁	—	2	2	no	—
57	C₇₁⋊C₁₆	—	4	2	no	—
58	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
59	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
60	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₈×C₇₁	—	2	2	no	—
62	C₂×C₈×C₇₁	—	4	1	no	—
63	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₇₁	M₁₆	1	1	yes	characteristic
70	C₄²×C₇₁	M₁₆	1	1	yes	characteristic
71	C₁₆×C₇₁	—	4	2	no	—
72	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
73	C₂×C₄×C₇₁	—	2	2	no	—
74	C₂×C₄×C₇₁	—	2	1	no	—
75	C₂×C₄×C₇₁	—	2	1	no	—
76	C₂×C₄×C₇₁	—	4	1	no	—
77	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
78	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
79	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
80	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
81	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
83	C₂×Dic₇₁	—	2	2	no	—
84	C₂×Dic₇₁	—	2	2	no	—
85	C₂×Dic₇₁	—	2	2	no	—
86	C₂×Dic₇₁	—	4	2	no	—
87	C₂×Dic₇₁	M₃₂	1	4	yes	—
88	Dic₁₄₂	—	2	4	no	—
89	Dic₁₄₂	—	2	4	no	—
90	C₈×C₇₁	—	2	1	no	—
91	C₈×C₇₁	—	2	1	no	—
92	C₈×C₇₁	—	2	1	no	—
93	C₈×C₇₁	#101	1	2	yes	—
94	C₇₁⋊C₈	—	4	2	no	—
95	C₂²×C₇₁	—	2	1	no	—
96	C₂²×C₇₁	—	2	1	no	—
97	C₂²×C₇₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
98	C₂²×C₇₁	C₂×M₃₂	1	2	yes	—
99	C₄×C₇₁	—	2	1	no	—
100	C₄×C₇₁	—	2	1	no	—
101	C₄×C₇₁	—	2	1	no	—
102	C₄×C₇₁	—	2	1	no	—
103	C₄×C₇₁	—	2	1	no	—
104	C₄×C₇₁	#410	1	1	yes	characteristic
105	C₄×C₇₁	C₂×#101	1	1	yes	characteristic
106	Dic₇₁	—	2	4	no	—
107	Dic₇₁	—	4	2	no	—
108	#11494	—	71	1	no	maximal, Sylow
109	C₂×C₇₁	—	2	2	no	—
110	C₂×C₇₁	#1461	1	1	yes	characteristic
111	C₂×C₇₁	#2112	1	1	yes	characteristic
112	C₂×C₇₁	#2115	1	1	yes	characteristic
113	C₂×C₈×Q₈	—	71	1	no	—
114	#2163	—	71	1	no	—
115	#2163	D₇₁	1	1	yes	characteristic
116	#1322	—	71	4	no	—
117	C₇₁	#11494	1	1	yes	characteristic, complemented, Sylow
118	C₂×C₄×Q₈	—	71	1	no	—
119	C₈×Q₈	—	142	1	no	—
120	C₈×Q₈	—	142	1	no	—
121	C₈×Q₈	—	142	1	no	—
122	C₈×Q₈	—	142	1	no	—
123	C₂×C₄⋊C₈	—	71	2	no	—
124	C₂×C₄⋊C₈	—	71	1	no	—
125	C₂×C₄×C₈	—	71	2	no	—
126	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
127	C₄⋊C₁₆	—	2	1	no	—
128	C₄⋊C₁₆	—	142	1	no	—
129	C₂²⋊C₁₆	—	71	2	no	—
130	C₂²⋊C₁₆	C₂×D₇₁	1	2	yes	—
131	#346	—	2	1	no	—
132	#346	—	142	1	no	—
133	C₂²×Q₈	—	71	1	no	—
134	C₂²×C₈	—	71	2	no	—
135	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
136	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
137	C₄×Q₈	—	142	1	no	—
138	C₄×Q₈	—	142	1	no	—
139	C₄×Q₈	—	142	1	no	—
140	C₄×Q₈	—	142	1	no	—
141	C₂×C₄⋊C₄	—	71	2	no	—
142	C₂×C₄⋊C₄	—	71	1	no	—
143	C₂×C₄²	—	71	2	no	—
144	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
145	C₂×C₁₆	—	2	2	no	—
146	C₂×C₁₆	—	142	2	no	—
147	C₄⋊C₈	—	142	2	no	—
148	C₄⋊C₈	—	142	2	no	—
149	C₄⋊C₈	—	142	1	no	—
150	C₄⋊C₈	—	142	1	no	—
151	C₄×C₈	—	142	2	no	—
152	C₄×C₈	—	142	2	no	—
153	C₄×C₈	D₂₈₄	1	1	yes	characteristic
154	C₄×C₈	D₂₈₄	1	1	yes	characteristic
155	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
156	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
157	C₂×Q₈	—	142	4	no	—
158	C₂×Q₈	—	142	1	no	—
159	C₂×Q₈	—	142	1	no	—
160	C₂²×C₄	—	71	2	no	—
161	C₂²×C₄	—	71	2	no	—
162	C₂²×C₄	C₈×D₇₁	1	1	yes	characteristic
163	C₂²×C₄	C₈×D₇₁	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	284	2	no	—
168	C₂×C₈	—	142	2	no	—
169	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
170	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
171	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
172	C₂×C₈	C₂×D₂₈₄	1	1	yes	characteristic
173	C₄⋊C₄	—	142	2	no	—
174	C₄⋊C₄	—	142	2	no	—
175	C₄⋊C₄	—	142	1	no	—
176	C₄⋊C₄	—	142	1	no	—
177	C₄²	—	142	2	no	—
178	C₄²	—	142	2	no	—
179	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
180	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
181	C₄²	#11765848	1	1	yes	characteristic
182	C₄²	#11765848	1	1	yes	characteristic
183	C₁₆	—	4	2	no	—
184	C₁₆	—	284	2	no	—
185	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
186	Q₈	—	142	4	no	—
187	Q₈	—	142	4	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	284	2	no	—
193	C₂×C₄	—	71	4	no	—
194	C₂×C₄	—	142	2	no	—
195	C₂×C₄	—	142	2	no	—
196	C₂×C₄	—	142	2	no	—
197	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
198	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
199	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
200	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
201	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
202	C₂×C₄	C₂×#11765848	1	1	yes	characteristic
203	C₈	—	2	1	no	—
204	C₈	—	2	1	no	—
205	C₈	—	2	1	no	—
206	C₈	—	284	2	no	—
207	C₈	#14556046	1	2	yes	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	1	no	—
210	C₂²	C₂×(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
211	C₂²	M₃₂×D₇₁	1	2	yes	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	284	2	no	—
218	C₄	—	142	4	no	—
219	C₄	#17985972	1	1	yes	characteristic
220	C₄	C₂×#14556046	1	1	yes	characteristic
221	C₂	—	2	2	no	—
222	C₂	#22586663	1	1	yes	characteristic
223	C₂	#22589950	1	1	yes	characteristic
224	C₂	#22589960	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₄₂

C₂

yes

maximal, characteristic

#22590143

C₂

yes

maximal, characteristic

#22586279

C₂

yes

maximal

C₇₁×#2163

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₄₂

C₄

yes

characteristic

C₈×Dic₁₄₂

—

C₈×Dic₁₄₂

—

C₈×Dic₁₄₂

—

C₈×Dic₁₄₂

—

C₂×C₄⋊(C₇₁⋊C₈)

C₄

yes

characteristic

C₂×Dic₇₁⋊C₈

C₂²

yes

—

C₂×C₈×Dic₇₁

C₄

yes

—

C₄⋊(C₇₁⋊C₁₆)

—

C₂²⋊(C₇₁⋊C₁₆)

C₂²

yes

—

#17985775

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₁

—

C₂²⋊C₁₆×C₇₁

C₂²

yes

—

#346×C₇₁

—

C₂²×Dic₁₄₂

C₈

yes

characteristic

C₂²×C₇₁⋊C₈

C₂×C₄

yes

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₂×C₄⋊Dic₇₁

C₈

yes

characteristic

C₂×Dic₇₁⋊C₄

C₈

yes

—

C₂×C₄×Dic₇₁

C₂×C₄

yes

—

C₂×C₇₁⋊C₁₆

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

Dic₇₁⋊C₈

—

Dic₇₁⋊C₈

—

C₈×Dic₇₁

—

C₈×Dic₇₁

—

C₂²×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₁

C₂³

yes

characteristic

C₂×C₄²×C₇₁

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₁

—

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

C₂×C₈

yes

—

C₂²×Dic₇₁

C₂×C₈

yes

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

M₁₆

yes

characteristic

C₄²×C₇₁

M₁₆

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂×M₁₆

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

M₃₂

yes

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

#101

yes

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₇₁

C₂×M₃₂

yes

—

C₄×C₇₁

—

100

C₄×C₇₁

—

101

C₄×C₇₁

—

102

C₄×C₇₁

—

103

C₄×C₇₁

—

104

C₄×C₇₁

#410

yes

characteristic

105

C₄×C₇₁

C₂×#101

yes

characteristic

106

Dic₇₁

—

107

Dic₇₁

—

108

#11494

—

maximal, Sylow

109

C₂×C₇₁

—

110

C₂×C₇₁

#1461

yes

characteristic

111

C₂×C₇₁

#2112

yes

characteristic

112

C₂×C₇₁

#2115

yes

characteristic

113

C₂×C₈×Q₈

—

114

#2163

—

115

#2163

D₇₁

yes

characteristic

116

#1322

—

117

C₇₁

#11494

yes

characteristic, complemented, Sylow

118

C₂×C₄×Q₈

—

119

C₈×Q₈

—

142

—

120

C₈×Q₈

—

142

—

121

C₈×Q₈

—

142

—

122

C₈×Q₈

—

142

—

123

C₂×C₄⋊C₈

—

124

C₂×C₄⋊C₈

—

125

C₂×C₄×C₈

—

126

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

127

C₄⋊C₁₆

—

128

C₄⋊C₁₆

—

142

—

129

C₂²⋊C₁₆

—

130

C₂²⋊C₁₆

C₂×D₇₁

yes

—

131

#346

—

132

#346

—

142

—

133

C₂²×Q₈

—

134

C₂²×C₈

—

135

C₂²×C₈

C₄×D₇₁

yes

characteristic

136

C₂²×C₈

C₂²×D₇₁

yes

characteristic

137

C₄×Q₈

—

142

—

138

C₄×Q₈

—

142

—

139

C₄×Q₈

—

142

—

140

C₄×Q₈

—

142

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄²

—

144

C₂×C₄²

C₄×D₇₁

yes

characteristic

145

C₂×C₁₆

—

146

C₂×C₁₆

—

142

—

147

C₄⋊C₈

—

142

—

148

C₄⋊C₈

—

142

—

149

C₄⋊C₈

—

142

—

150

C₄⋊C₈

—

142

—

151

C₄×C₈

—

142

—

152

C₄×C₈

—

142

—

153

C₄×C₈

D₂₈₄

yes

characteristic

154

C₄×C₈

D₂₈₄

yes

characteristic

155

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

156

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

157

C₂×Q₈

—

142

—

158

C₂×Q₈

—

142

—

159

C₂×Q₈

—

142

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₈×D₇₁

yes

characteristic

163

C₂²×C₄

C₈×D₇₁

yes

characteristic

164

C₂²×C₄

C₂×C₄×D₇₁

yes

characteristic

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

284

—

168

C₂×C₈

—

142

—

169

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

170

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

171

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

172

C₂×C₈

C₂×D₂₈₄

yes

characteristic

173

C₄⋊C₄

—

142

—

174

C₄⋊C₄

—

142

—

175

C₄⋊C₄

—

142

—

176

C₄⋊C₄

—

142

—

177

C₄²

—

142

—

178

C₄²

—

142

—

179

C₄²

(C₂×D₇₁)⋊C₄

yes

characteristic

180

C₄²

(C₂×D₇₁)⋊C₄

yes

characteristic

181

C₄²

#11765848

yes

characteristic

182

C₄²

#11765848

yes

characteristic

183

C₁₆

—

184

C₁₆

—

284

—

185

C₂³

C₂×C₈×D₇₁

yes

characteristic

186

Q₈

—

142

—

187

Q₈

—

142

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

284

—

193

C₂×C₄

—

194

C₂×C₄

—

142

—

195

C₂×C₄

—

142

—

196

C₂×C₄

—

142

—

197

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

198

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

199

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

200

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

201

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

202

C₂×C₄

C₂×#11765848

yes

characteristic

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

284

—

207

C₈

#14556046

yes

—

208

C₂²

—

209

C₂²

—

210

C₂²

C₂×(C₂×D₇₁)⋊C₈

yes

characteristic

211

C₂²

M₃₂×D₇₁

yes

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

284

—

218

C₄

—

142

—

219

C₄

#17985972

yes

characteristic

220

C₄

C₂×#14556046

yes

characteristic

221

C₂

—

222

C₂

#22586663

yes

characteristic

223

C₂

#22589950

yes

characteristic

224

C₂

#22589960

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄
commutator, prime radical	C₂³×C₇₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₇₁×#2163	C₂
socle	C₂²×C₇₁	C₂×C₂²⋊C₈
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	#2163	D₇₁
hypocenter	C₇₁	#11494
LCS	G ▷ C₂³×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

subgroup

G/H

center

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

commutator, prime radical

C₂³×C₇₁

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₇₁×#2163

C₂

socle

C₂²×C₇₁

C₂×C₂²⋊C₈

cosocle

C₂²×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂³×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

N	H ≅ G/N	type
117. C₇₁	#11494	semidirect

H ≅ G/N

type

117. C₇₁

#11494

semidirect

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

subgroup	index
C₂×C₈×Dic₁₄₂	2
#22590143	2
#22586279	2
C₇₁×#2163	2
#11494	71

subgroup

index

C₂×C₈×Dic₁₄₂

#22590143

#22586279

C₇₁×#2163

#11494

Subgroups — #31906791

Conjugacy classes of subgroups

Complements

Maximal subgroups