Group #37572288 — subgroups

Subgroups — #37572288

Order 24448.

336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 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×#20259281	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊(C₁₉₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#20259232	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×Dic₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132417	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132417	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂²⋊C₈×C₁₉₁	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₁₉₁⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₁₉₁⋊C₈	C₂²	1	1	yes	characteristic
10	#20259281	—	2	2	no	—
11	#20259281	—	2	2	no	—
12	C₂×C₄⋊Dic₁₉₁	C₄	1	2	yes	—
13	C₂×C₂²⋊Dic₁₉₁	C₄	1	2	yes	—
14	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
16	C₂²⋊(C₁₉₁⋊C₈)	C₄	1	4	yes	complemented
17	#20259232	—	2	2	no	—
18	C₈×Dic₁₉₁	—	2	2	no	—
19	C₂³×C₄×C₁₉₁	C₂²	1	1	yes	characteristic
20	C₂²×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
22	C₂²⋊C₈×C₁₉₁	C₄	1	4	yes	complemented
23	C₂²×Dic₁₉₁	C₂×C₄	1	2	yes	—
24	C₂²×Dic₁₉₁	C₂×C₄	1	2	yes	—
25	C₂×C₁₉₁⋊C₈	—	2	1	no	—
26	C₂×C₁₉₁⋊C₈	—	2	1	no	—
27	C₂×C₁₉₁⋊C₈	—	2	1	no	—
28	C₂×C₁₉₁⋊C₈	—	2	1	no	—
29	C₂×C₁₉₁⋊C₈	C₂×C₄	1	2	yes	—
30	C₂×C₁₉₁⋊C₈	C₂×C₄	1	2	yes	—
31	C₄⋊Dic₁₉₁	—	2	4	no	—
32	C₂²⋊Dic₁₉₁	—	2	4	no	—
33	C₄×Dic₁₉₁	—	2	1	no	—
34	C₄×Dic₁₉₁	—	2	1	no	—
35	C₄×Dic₁₉₁	D₄	1	2	yes	—
36	C₄×Dic₁₉₁	D₄	1	2	yes	—
37	C₂⁴×C₁₉₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉₁	—	2	1	no	—
39	C₂²×C₄×C₁₉₁	—	2	1	no	—
40	C₂²×C₄×C₁₉₁	—	2	1	no	—
41	C₂²×C₄×C₁₉₁	—	2	1	no	—
42	C₂²×C₄×C₁₉₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉₁	C₂×C₄	1	2	yes	—
44	C₂²×C₄×C₁₉₁	C₂×C₄	1	2	yes	—
45	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
46	C₂×C₈×C₁₉₁	—	2	1	no	—
47	C₂×C₈×C₁₉₁	—	2	1	no	—
48	C₂×C₈×C₁₉₁	—	2	1	no	—
49	C₂×C₈×C₁₉₁	—	2	1	no	—
50	C₂×C₈×C₁₉₁	C₂×C₄	1	2	yes	—
51	C₂×C₈×C₁₉₁	C₂×C₄	1	2	yes	—
52	C₂×Dic₁₉₁	—	2	2	no	—
53	C₂×Dic₁₉₁	—	2	2	no	—
54	C₂×Dic₁₉₁	—	2	2	no	—
55	C₂×Dic₁₉₁	—	2	2	no	—
56	C₂×Dic₁₉₁	—	2	2	no	—
57	C₂×Dic₁₉₁	C₂²⋊C₄	1	4	yes	—
58	C₁₉₁⋊C₈	—	2	2	no	—
59	C₁₉₁⋊C₈	—	2	2	no	—
60	C₂³×C₁₉₁	—	2	1	no	—
61	C₂³×C₁₉₁	—	2	1	no	—
62	C₂³×C₁₉₁	—	2	2	no	—
63	C₂³×C₁₉₁	—	2	2	no	—
64	C₂³×C₁₉₁	C₄²	1	2	yes	—
65	C₂³×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉₁	—	2	1	no	—
67	C₂×C₄×C₁₉₁	—	2	1	no	—
68	C₂×C₄×C₁₉₁	—	2	2	no	—
69	C₂×C₄×C₁₉₁	—	2	2	no	—
70	C₂×C₄×C₁₉₁	—	2	2	no	—
71	C₂×C₄×C₁₉₁	—	2	2	no	—
72	C₂×C₄×C₁₉₁	C₄²	1	2	yes	—
73	C₂×C₄×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉₁	#41	1	1	yes	characteristic
78	C₂×C₄×C₁₉₁	#41	1	1	yes	characteristic
79	C₈×C₁₉₁	—	2	2	no	—
80	C₈×C₁₉₁	—	2	2	no	—
81	C₂²×C₁₉₁	—	2	2	no	—
82	C₂²×C₁₉₁	—	2	2	no	—
83	C₂²×C₁₉₁	—	2	2	no	—
84	C₂²×C₁₉₁	—	4	2	no	—
85	C₂²×C₁₉₁	—	4	2	no	—
86	C₂²×C₁₉₁	C₂×C₄²	1	1	yes	characteristic
87	C₂²×C₁₉₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₁₉₁	#117	1	1	yes	characteristic
89	C₂²×C₁₉₁	#131	1	2	yes	—
90	C₂²×C₁₉₁	#131	1	2	yes	—
91	C₄×C₁₉₁	—	2	2	no	—
92	C₄×C₁₉₁	C₄×D₄	1	1	yes	characteristic
93	C₄×C₁₉₁	C₄×D₄	1	1	yes	characteristic
94	C₄×C₁₉₁	C₄×D₄	1	1	yes	characteristic
95	C₄×C₁₉₁	C₄×D₄	1	1	yes	characteristic
96	Dic₁₉₁	—	2	4	no	—
97	Dic₁₉₁	—	4	2	no	—
98	C₂×C₁₉₁	—	4	2	no	—
99	C₂×C₁₉₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₁₉₁	#405	1	1	yes	characteristic
101	C₂×C₁₉₁	#405	1	1	yes	characteristic
102	C₂×C₁₉₁	#408	1	2	yes	—
103	C₂×C₁₉₁	#433	1	2	yes	—
104	C₁₉₁	#1750	1	1	yes	characteristic, complemented, Sylow
105	#1750	—	191	1	no	maximal, Sylow
106	C₂×#117	—	191	1	no	—
107	C₂×C₂²⋊C₈	—	191	1	no	—
108	C₂×C₂²⋊C₈	D₁₉₁	1	1	yes	characteristic
109	C₂×#97	—	191	1	no	—
110	C₂×C₄×C₈	—	191	1	no	—
111	#336	—	191	1	no	—
112	#336	—	191	1	no	—
113	C₂³×C₄	C₂×D₁₉₁	1	1	yes	characteristic
114	C₂²×C₈	—	191	1	no	—
115	C₂²×C₈	—	191	1	no	—
116	C₂²×C₈	C₂×D₁₉₁	1	1	yes	characteristic
117	C₂²×C₈	C₂×D₁₉₁	1	1	yes	characteristic
118	#117	—	382	2	no	—
119	#117	—	382	2	no	—
120	C₂×C₄⋊C₄	—	191	2	no	—
121	C₂×C₂²⋊C₄	—	191	2	no	—
122	C₂×C₄²	—	191	1	no	—
123	C₂×C₄²	—	191	1	no	—
124	C₂²⋊C₈	—	191	4	no	—
125	C₂²⋊C₈	Dic₁₉₁	1	4	yes	complemented
126	#97	—	382	2	no	—
127	C₄×C₈	—	382	2	no	—
128	C₂⁴	C₄×D₁₉₁	1	1	yes	characteristic
129	C₂²×C₄	—	2	1	no	—
130	C₂²×C₄	—	2	1	no	—
131	C₂²×C₄	—	2	1	no	—
132	C₂²×C₄	—	2	1	no	—
133	C₂²×C₄	—	191	2	no	—
134	C₂²×C₄	—	191	2	no	—
135	C₂²×C₄	C₄×D₁₉₁	1	1	yes	characteristic
136	C₂²×C₄	C₄×D₁₉₁	1	2	yes	—
137	C₂²×C₄	C₂×Dic₁₉₁	1	2	yes	—
138	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
139	C₂×C₈	—	2	1	no	—
140	C₂×C₈	—	2	1	no	—
141	C₂×C₈	—	2	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	382	1	no	—
144	C₂×C₈	—	382	1	no	—
145	C₂×C₈	—	382	1	no	—
146	C₂×C₈	—	382	1	no	—
147	C₂×C₈	—	191	2	no	—
148	C₂×C₈	—	191	2	no	—
149	C₂×C₈	C₂×Dic₁₉₁	1	2	yes	—
150	C₂×C₈	C₂×Dic₁₉₁	1	2	yes	—
151	C₄⋊C₄	—	382	4	no	—
152	C₂²⋊C₄	—	382	4	no	—
153	C₄²	—	382	1	no	—
154	C₄²	—	382	1	no	—
155	C₄²	—	191	2	no	—
156	C₄²	—	191	2	no	—
157	C₂³	—	2	2	no	—
158	C₂³	—	2	2	no	—
159	C₂³	—	2	1	no	—
160	C₂³	—	2	1	no	—
161	C₂³	C₄×Dic₁₉₁	1	2	yes	—
162	C₂³	C₂×C₄×D₁₉₁	1	1	yes	characteristic
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	382	2	no	—
170	C₂×C₄	—	382	2	no	—
171	C₂×C₄	—	382	2	no	—
172	C₂×C₄	—	382	2	no	—
173	C₂×C₄	—	382	2	no	—
174	C₂×C₄	—	191	4	no	—
175	C₂×C₄	C₄×Dic₁₉₁	1	2	yes	—
176	C₂×C₄	C₂×C₄×D₁₉₁	1	1	yes	characteristic
177	C₂×C₄	C₂²×Dic₁₉₁	1	1	yes	characteristic
178	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
179	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
180	C₂×C₄	#15690286	1	1	yes	characteristic
181	C₂×C₄	#15690286	1	1	yes	characteristic
182	C₈	—	2	2	no	—
183	C₈	—	2	2	no	—
184	C₈	—	382	2	no	—
185	C₈	—	382	2	no	—
186	C₂²	—	2	2	no	—
187	C₂²	—	2	2	no	—
188	C₂²	—	2	2	no	—
189	C₂²	—	4	2	no	—
190	C₂²	—	4	2	no	—
191	C₂²	C₂×C₄×Dic₁₉₁	1	1	yes	characteristic
192	C₂²	C₂²⋊C₄×D₁₉₁	1	1	yes	characteristic
193	C₂²	#20259278	1	1	yes	characteristic
194	C₂²	#20259328	1	2	yes	—
195	C₂²	#20259330	1	2	yes	—
196	C₄	—	2	2	no	—
197	C₄	—	382	4	no	—
198	C₄	—	764	2	no	—
199	C₄	(C₂²⋊D₁₉₁)⋊C₄	1	1	yes	characteristic
200	C₄	(C₂²⋊D₁₉₁)⋊C₄	1	1	yes	characteristic
201	C₄	D₄×Dic₁₉₁	1	1	yes	characteristic
202	C₄	D₄×Dic₁₉₁	1	1	yes	characteristic
203	C₂	—	4	2	no	—
204	C₂	C₂²⋊C₄×Dic₁₉₁	1	1	yes	characteristic
205	C₂	#27132618	1	1	yes	characteristic
206	C₂	#27132621	1	1	yes	characteristic
207	C₂	#27132628	1	2	yes	—
208	C₂	#27132721	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#20259281

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉₁⋊C₈)

C₂

yes

maximal, characteristic

C₂×#20259232

C₂

yes

maximal, characteristic, complemented

C₂×C₈×Dic₁₉₁

C₂

yes

maximal, characteristic, complemented

#27132417

C₂

yes

maximal, characteristic, complemented

#27132417

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊C₈×C₁₉₁

C₂

yes

maximal, characteristic

C₂²×C₁₉₁⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉₁⋊C₈

C₂²

yes

characteristic

#20259281

—

#20259281

—

C₂×C₄⋊Dic₁₉₁

C₄

yes

—

C₂×C₂²⋊Dic₁₉₁

C₄

yes

—

C₂×C₄×Dic₁₉₁

C₂²

yes

characteristic

C₂×C₄×Dic₁₉₁

C₂²

yes

characteristic

C₂²⋊(C₁₉₁⋊C₈)

C₄

yes

complemented

#20259232

—

C₈×Dic₁₉₁

—

C₂³×C₄×C₁₉₁

C₂²

yes

characteristic

C₂²×C₈×C₁₉₁

C₂²

yes

characteristic

C₂²×C₈×C₁₉₁

C₂²

yes

characteristic

C₂²⋊C₈×C₁₉₁

C₄

yes

complemented

C₂²×Dic₁₉₁

C₂×C₄

yes

—

C₂²×Dic₁₉₁

C₂×C₄

yes

—

C₂×C₁₉₁⋊C₈

—

C₂×C₁₉₁⋊C₈

—

C₂×C₁₉₁⋊C₈

—

C₂×C₁₉₁⋊C₈

—

C₂×C₁₉₁⋊C₈

C₂×C₄

yes

—

C₂×C₁₉₁⋊C₈

C₂×C₄

yes

—

C₄⋊Dic₁₉₁

—

C₂²⋊Dic₁₉₁

—

C₄×Dic₁₉₁

—

C₄×Dic₁₉₁

—

C₄×Dic₁₉₁

D₄

yes

—

C₄×Dic₁₉₁

D₄

yes

—

C₂⁴×C₁₉₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉₁

—

C₂²×C₄×C₁₉₁

—

C₂²×C₄×C₁₉₁

—

C₂²×C₄×C₁₉₁

—

C₂²×C₄×C₁₉₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉₁

C₂×C₄

yes

—

C₂²×C₄×C₁₉₁

C₂×C₄

yes

—

C₂²×C₄×C₁₉₁

C₂³

yes

characteristic

C₂×C₈×C₁₉₁

—

C₂×C₈×C₁₉₁

—

C₂×C₈×C₁₉₁

—

C₂×C₈×C₁₉₁

—

C₂×C₈×C₁₉₁

C₂×C₄

yes

—

C₂×C₈×C₁₉₁

C₂×C₄

yes

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

C₂²⋊C₄

yes

—

C₁₉₁⋊C₈

—

C₁₉₁⋊C₈

—

C₂³×C₁₉₁

—

C₂³×C₁₉₁

—

C₂³×C₁₉₁

—

C₂³×C₁₉₁

—

C₂³×C₁₉₁

C₄²

yes

—

C₂³×C₁₉₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

C₄²

yes

—

C₂×C₄×C₁₉₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉₁

C₂×D₄

yes

C₂×C₄×C₁₉₁

yes

C₂×C₄×C₁₉₁

yes

C₈×C₁₉₁

—

C₈×C₁₉₁

—

C₂²×C₁₉₁

—

C₂²×C₁₉₁

—

C₂²×C₁₉₁

—

C₂²×C₁₉₁

—

C₂²×C₁₉₁

—

C₂²×C₁₉₁

C₂×C₄²

yes

characteristic

C₂²×C₁₉₁

C₂×C₂²⋊C₄

yes

C₂²×C₁₉₁

yes

C₂²×C₁₉₁

yes

—

C₂²×C₁₉₁

#131

yes

—

C₄×C₁₉₁

—

C₄×C₁₉₁

C₄×D₄

yes

characteristic

C₄×C₁₉₁

C₄×D₄

yes

characteristic

C₄×C₁₉₁

C₄×D₄

yes

characteristic

C₄×C₁₉₁

C₄×D₄

yes

characteristic

Dic₁₉₁

—

Dic₁₉₁

—

C₂×C₁₉₁

—

C₂×C₁₉₁

C₄×C₂²⋊C₄

yes

characteristic

100

C₂×C₁₉₁

#405

yes

characteristic

101

C₂×C₁₉₁

#405

yes

characteristic

102

C₂×C₁₉₁

#408

yes

—

103

C₂×C₁₉₁

#433

yes

—

104

C₁₉₁

#1750

yes

characteristic, complemented, Sylow

105

#1750

—

191

maximal, Sylow

106

C₂×#117

—

191

—

107

C₂×C₂²⋊C₈

—

191

—

108

C₂×C₂²⋊C₈

D₁₉₁

yes

characteristic

109

C₂×#97

—

191

—

110

C₂×C₄×C₈

—

191

—

111

#336

—

191

—

112

#336

—

191

—

113

C₂³×C₄

C₂×D₁₉₁

yes

characteristic

114

C₂²×C₈

—

191

—

115

C₂²×C₈

—

191

—

116

C₂²×C₈

C₂×D₁₉₁

yes

characteristic

117

C₂²×C₈

C₂×D₁₉₁

yes

characteristic

118

#117

—

382

—

119

#117

—

382

—

120

C₂×C₄⋊C₄

—

191

—

121

C₂×C₂²⋊C₄

—

191

—

122

C₂×C₄²

—

191

—

123

C₂×C₄²

—

191

—

124

C₂²⋊C₈

—

191

—

125

C₂²⋊C₈

Dic₁₉₁

yes

complemented

126

#97

—

382

—

127

C₄×C₈

—

382

—

128

C₂⁴

C₄×D₁₉₁

yes

characteristic

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

191

—

134

C₂²×C₄

—

191

—

135

C₂²×C₄

C₄×D₁₉₁

yes

characteristic

136

C₂²×C₄

C₄×D₁₉₁

yes

—

137

C₂²×C₄

C₂×Dic₁₉₁

yes

—

138

C₂²×C₄

C₂²×D₁₉₁

yes

characteristic

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

382

—

144

C₂×C₈

—

382

—

145

C₂×C₈

—

382

—

146

C₂×C₈

—

382

—

147

C₂×C₈

—

191

—

148

C₂×C₈

—

191

—

149

C₂×C₈

C₂×Dic₁₉₁

yes

—

150

C₂×C₈

C₂×Dic₁₉₁

yes

—

151

C₄⋊C₄

—

382

—

152

C₂²⋊C₄

—

382

—

153

C₄²

—

382

—

154

C₄²

—

382

—

155

C₄²

—

191

—

156

C₄²

—

191

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

C₄×Dic₁₉₁

yes

—

162

C₂³

C₂×C₄×D₁₉₁

yes

characteristic

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

382

—

170

C₂×C₄

—

382

—

171

C₂×C₄

—

382

—

172

C₂×C₄

—

382

—

173

C₂×C₄

—

382

—

174

C₂×C₄

—

191

—

175

C₂×C₄

C₄×Dic₁₉₁

yes

—

176

C₂×C₄

C₂×C₄×D₁₉₁

yes

characteristic

177

C₂×C₄

C₂²×Dic₁₉₁

yes

characteristic

178

C₂×C₄

D₄×D₁₉₁

yes

characteristic

179

C₂×C₄

D₄×D₁₉₁

yes

characteristic

180

C₂×C₄

#15690286

yes

characteristic

181

C₂×C₄

#15690286

yes

characteristic

182

C₈

—

183

C₈

—

184

C₈

—

382

—

185

C₈

—

382

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

C₂×C₄×Dic₁₉₁

yes

characteristic

192

C₂²

C₂²⋊C₄×D₁₉₁

yes

characteristic

193

C₂²

#20259278

yes

characteristic

194

C₂²

#20259328

yes

—

195

C₂²

#20259330

yes

—

196

C₄

—

197

C₄

—

382

—

198

C₄

—

764

—

199

C₄

(C₂²⋊D₁₉₁)⋊C₄

yes

characteristic

200

C₄

(C₂²⋊D₁₉₁)⋊C₄

yes

characteristic

201

C₄

D₄×Dic₁₉₁

yes

characteristic

202

C₄

D₄×Dic₁₉₁

yes

characteristic

203

C₂

—

204

C₂

C₂²⋊C₄×Dic₁₉₁

yes

characteristic

205

C₂

#27132618

yes

characteristic

206

C₂

#27132621

yes

characteristic

207

C₂

#27132628

yes

—

208

C₂

#27132721

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉₁
commutator	C₂²×C₁₉₁	C₂×C₄²
Fitting	C₂×C₂²⋊C₈×C₁₉₁	C₂
socle	C₂³×C₁₉₁	C₂²×C₄
prime radical	C₂⁴×C₁₉₁	C₂×C₄
cosocle	C₂²×C₄×C₁₉₁	C₂³
hypercenter	C₂×C₂²⋊C₈	D₁₉₁
hypocenter	C₁₉₁	#1750
LCS	G ▷ C₂²×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉₁

commutator

C₂²×C₁₉₁

C₂×C₄²

Fitting

C₂×C₂²⋊C₈×C₁₉₁

C₂

socle

C₂³×C₁₉₁

C₂²×C₄

prime radical

C₂⁴×C₁₉₁

C₂×C₄

cosocle

C₂²×C₄×C₁₉₁

C₂³

hypercenter

C₂×C₂²⋊C₈

D₁₉₁

C₁₉₁

G ▷ C₂²×C₁₉₁ ▷ C₁₉₁

C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
3. C₂×#20259232	C₂	semidirect
4. C₂×C₈×Dic₁₉₁	C₂	semidirect
5. #27132417	C₂	semidirect
6. #27132417	C₂	semidirect
16. C₂²⋊(C₁₉₁⋊C₈)	C₄	semidirect
22. C₂²⋊C₈×C₁₉₁	C₄	semidirect
104. C₁₉₁	#1750	semidirect
125. C₂²⋊C₈	Dic₁₉₁	semidirect

H ≅ G/N

type

3. C₂×#20259232

C₂

semidirect

4. C₂×C₈×Dic₁₉₁

C₂

semidirect

5. #27132417

C₂

semidirect

6. #27132417

C₂

semidirect

16. C₂²⋊(C₁₉₁⋊C₈)

C₄

semidirect

22. C₂²⋊C₈×C₁₉₁

C₄

semidirect

104. C₁₉₁

#1750

semidirect

125. C₂²⋊C₈

Dic₁₉₁

semidirect

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

subgroup	index
C₂×#20259281	2
C₂×C₂²⋊(C₁₉₁⋊C₈)	2
C₂×#20259232	2
C₂×C₈×Dic₁₉₁	2
#27132417	2
C₂×C₂²⋊C₈×C₁₉₁	2
#1750	191

subgroup

index

C₂×C₂²⋊(C₁₉₁⋊C₈)

C₂×C₈×Dic₁₉₁

C₂×C₂²⋊C₈×C₁₉₁

191

Subgroups — #37572288

Conjugacy classes of subgroups

Complements

Maximal subgroups