Group #37572499 — subgroups

Subgroups — #37572499

Order 24448.

400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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×C₄²×D₁₉₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₉₁⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂×(C₂×D₁₉₁)⋊C₈	C₂	1	2	yes	maximal
4	#27132418	C₂	1	1	yes	maximal, characteristic, complemented
5	#336×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₉₁	C₄	1	1	yes	characteristic
7	C₂²×C₄×D₁₉₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
9	C₂²×C₁₉₁⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×Dic₁₉₁	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₁₉₁	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
13	C₄²×D₁₉₁	—	2	4	no	—
14	Dic₁₉₁⋊C₈	—	2	4	no	—
15	(C₂×D₁₉₁)⋊C₈	—	2	4	no	—
16	C₂²×C₈×C₁₉₁	C₂²	1	2	yes	—
17	C₂×C₄²×C₁₉₁	C₂²	1	1	yes	characteristic
18	C₂³×D₁₉₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×D₁₉₁	—	2	2	no	—
23	C₂×C₄×D₁₉₁	—	2	2	no	—
24	C₂×C₄×D₁₉₁	—	2	2	no	—
25	C₂×C₄×D₁₉₁	—	2	2	no	—
26	C₂×C₄×D₁₉₁	—	2	2	no	—
27	C₂×C₄×D₁₉₁	—	2	2	no	—
28	C₂×C₄×D₁₉₁	—	2	2	no	—
29	C₂×C₄×D₁₉₁	C₈	1	4	yes	complemented
30	C₂×C₄×D₁₉₁	D₄	1	2	yes	—
31	C₂×C₄×D₁₉₁	Q₈	1	2	yes	—
32	C₂×C₁₉₁⋊C₈	—	2	2	no	—
33	C₂×C₁₉₁⋊C₈	—	2	2	no	—
34	C₂×C₁₉₁⋊C₈	—	2	2	no	—
35	C₄×Dic₁₉₁	—	2	2	no	—
36	C₄×Dic₁₉₁	—	2	2	no	—
37	C₄×Dic₁₉₁	D₄	1	4	yes	—
38	C₂²×C₄×C₁₉₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
41	C₂×C₈×C₁₉₁	—	2	2	no	—
42	C₂×C₈×C₁₉₁	—	2	2	no	—
43	C₂×C₈×C₁₉₁	—	2	2	no	—
44	C₄²×C₁₉₁	—	2	2	no	—
45	C₂²×D₁₉₁	—	2	1	no	—
46	C₂²×D₁₉₁	—	2	1	no	—
47	C₂²×D₁₉₁	—	2	1	no	—
48	C₂²×D₁₉₁	—	2	1	no	—
49	C₂²×D₁₉₁	C₄⋊C₄	1	2	yes	—
50	C₂²×D₁₉₁	C₂×C₈	1	2	yes	—
51	C₂²×D₁₉₁	M₁₆	1	2	yes	—
52	C₂×Dic₁₉₁	—	2	1	no	—
53	C₂×Dic₁₉₁	—	2	1	no	—
54	C₂×Dic₁₉₁	—	2	1	no	—
55	C₂×Dic₁₉₁	—	2	1	no	—
56	C₂×Dic₁₉₁	C₂²⋊C₄	1	2	yes	—
57	C₂×Dic₁₉₁	C₂²⋊C₄	1	2	yes	—
58	C₂×Dic₁₉₁	C₄⋊C₄	1	2	yes	—
59	C₂×Dic₁₉₁	C₂×C₈	1	2	yes	—
60	C₂×Dic₁₉₁	M₁₆	1	2	yes	—
61	C₄×D₁₉₁	—	2	8	no	—
62	C₄×D₁₉₁	—	2	4	no	—
63	C₄×D₁₉₁	—	2	4	no	—
64	C₄×D₁₉₁	—	2	8	no	—
65	C₁₉₁⋊C₈	—	4	2	no	—
66	C₂³×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉₁	—	2	1	no	—
68	C₂×C₄×C₁₉₁	—	2	1	no	—
69	C₂×C₄×C₁₉₁	—	2	1	no	—
70	C₂×C₄×C₁₉₁	—	2	1	no	—
71	C₂×C₄×C₁₉₁	C₂×C₈	1	2	yes	—
72	C₂×C₄×C₁₉₁	M₁₆	1	2	yes	—
73	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉₁	C₂×D₄	1	2	yes	—
75	C₂×C₄×C₁₉₁	C₂×Q₈	1	1	yes	characteristic
76	C₂×C₄×C₁₉₁	#41	1	2	yes	—
77	C₈×C₁₉₁	—	4	2	no	—
78	C₂²×C₁₉₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₁₉₁	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₁₉₁	#117	1	1	yes	characteristic
81	C₂²×C₁₉₁	C₂²×C₈	1	1	yes	characteristic
82	C₂²×C₁₉₁	C₂×M₁₆	1	1	yes	characteristic
83	C₂²×C₁₉₁	C₂×M₁₆	1	1	yes	characteristic
84	C₂²×C₁₉₁	C₂×M₁₆	1	1	yes	characteristic
85	C₂×D₁₉₁	—	2	2	no	—
86	C₂×D₁₉₁	—	2	2	no	—
87	C₂×D₁₉₁	—	2	2	no	—
88	C₂×D₁₉₁	—	2	2	no	—
89	C₂×D₁₉₁	—	2	2	no	—
90	C₂×D₁₉₁	—	2	2	no	—
91	C₂×D₁₉₁	C₄⋊C₈	1	4	yes	complemented
92	C₄×C₁₉₁	—	2	2	no	—
93	C₄×C₁₉₁	—	2	2	no	—
94	C₄×C₁₉₁	#121	1	2	yes	—
95	C₄×C₁₉₁	C₂²⋊Q₈	1	2	yes	—
96	Dic₁₉₁	—	2	2	no	—
97	Dic₁₉₁	—	2	2	no	—
98	Dic₁₉₁	C₂²⋊C₈	1	4	yes	complemented
99	C₂×C₁₉₁	#380	1	1	yes	characteristic
100	C₂×C₁₉₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
101	C₂×C₁₉₁	#407	1	1	yes	characteristic
102	C₂×C₁₉₁	C₂×C₄⋊C₈	1	1	yes	characteristic
103	C₂×C₁₉₁	#423	1	1	yes	characteristic
104	C₂×C₁₉₁	#431	1	1	yes	characteristic
105	C₂×C₁₉₁	#432	1	1	yes	characteristic
106	D₁₉₁	—	2	4	no	—
107	C₁₉₁	#1797	1	1	yes	characteristic, complemented, Sylow
108	#1797	—	191	1	no	maximal, Sylow
109	C₂²×C₄²	—	191	1	no	—
110	C₂×C₄⋊C₈	—	191	2	no	—
111	C₂×C₂²⋊C₈	—	191	2	no	—
112	#336	—	191	1	no	—
113	#336	D₁₉₁	1	1	yes	characteristic, complemented
114	C₂³×C₄	—	191	1	no	—
115	C₂³×C₄	—	191	1	no	—
116	C₂³×C₄	—	191	1	no	—
117	C₂²×C₈	—	191	2	no	—
118	C₂²×C₈	C₂×D₁₉₁	1	2	yes	—
119	C₂×C₄²	—	382	4	no	—
120	C₂×C₄²	—	191	1	no	—
121	C₂×C₄²	—	191	1	no	—
122	C₂×C₄²	—	191	1	no	—
123	C₂×C₄²	C₂×D₁₉₁	1	1	yes	characteristic
124	C₄⋊C₈	—	382	4	no	—
125	C₂²⋊C₈	—	382	4	no	—
126	C₂⁴	—	191	1	no	—
127	C₂²×C₄	—	382	2	no	—
128	C₂²×C₄	—	382	2	no	—
129	C₂²×C₄	—	382	2	no	—
130	C₂²×C₄	—	382	2	no	—
131	C₂²×C₄	—	382	2	no	—
132	C₂²×C₄	—	382	2	no	—
133	C₂²×C₄	—	382	2	no	—
134	C₂²×C₄	—	191	1	no	—
135	C₂²×C₄	—	191	1	no	—
136	C₂²×C₄	—	191	4	no	—
137	C₂²×C₄	—	191	2	no	—
138	C₂²×C₄	—	191	2	no	—
139	C₂²×C₄	—	191	1	no	—
140	C₂²×C₄	C₄×D₁₉₁	1	1	yes	characteristic
141	C₂²×C₄	C₄×D₁₉₁	1	1	yes	characteristic
142	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	2	2	no	—
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	382	2	no	—
147	C₂×C₈	—	382	2	no	—
148	C₂×C₈	—	382	2	no	—
149	C₄²	—	2	2	no	—
150	C₄²	—	382	2	no	—
151	C₄²	—	382	2	no	—
152	C₄²	—	191	4	no	—
153	C₂³	—	382	1	no	—
154	C₂³	—	382	1	no	—
155	C₂³	—	382	1	no	—
156	C₂³	—	382	1	no	—
157	C₂³	—	191	2	no	—
158	C₂³	—	191	2	no	—
159	C₂³	—	191	2	no	—
160	C₂³	C₂×C₄×D₁₉₁	1	1	yes	characteristic
161	C₂×C₄	—	2	1	no	—
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	382	8	no	—
166	C₂×C₄	—	382	8	no	—
167	C₂×C₄	—	382	1	no	—
168	C₂×C₄	—	382	1	no	—
169	C₂×C₄	—	382	1	no	—
170	C₂×C₄	—	382	1	no	—
171	C₂×C₄	—	382	4	no	—
172	C₂×C₄	—	382	4	no	—
173	C₂×C₄	—	191	2	no	—
174	C₂×C₄	—	191	2	no	—
175	C₂×C₄	—	191	2	no	—
176	C₂×C₄	—	191	2	no	—
177	C₂×C₄	—	191	2	no	—
178	C₂×C₄	C₈×D₁₉₁	1	2	yes	—
179	C₂×C₄	#15690270	1	2	yes	—
180	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
181	C₂×C₄	D₄×D₁₉₁	1	2	yes	—
182	C₂×C₄	Q₈×D₁₉₁	1	1	yes	characteristic
183	C₂×C₄	#15690287	1	2	yes	—
184	C₈	—	4	2	no	—
185	C₈	—	764	2	no	—
186	C₂²	—	382	2	no	—
187	C₂²	—	382	2	no	—
188	C₂²	—	382	2	no	—
189	C₂²	—	382	2	no	—
190	C₂²	—	382	2	no	—
191	C₂²	—	382	2	no	—
192	C₂²	—	191	4	no	—
193	C₂²	C₂²⋊C₄×D₁₉₁	1	1	yes	characteristic
194	C₂²	C₄⋊C₄×D₁₉₁	1	1	yes	characteristic
195	C₂²	#20259279	1	1	yes	characteristic
196	C₂²	C₂×C₈×D₁₉₁	1	1	yes	characteristic
197	C₂²	M₁₆×D₁₉₁	1	1	yes	characteristic
198	C₂²	M₁₆×D₁₉₁	1	1	yes	characteristic
199	C₂²	C₂×#15690270	1	1	yes	characteristic
200	C₄	—	2	2	no	—
201	C₄	—	2	2	no	—
202	C₄	—	382	2	no	—
203	C₄	—	382	2	no	—
204	C₄	—	191	4	no	—
205	C₄	#20259295	1	2	yes	—
206	C₄	#20259300	1	2	yes	—
207	C₂	—	382	4	no	—
208	C₂	#27132522	1	1	yes	characteristic
209	C₂	C₂²⋊C₈×D₁₉₁	1	1	yes	characteristic
210	C₂	#27132625	1	1	yes	characteristic
211	C₂	C₄⋊C₈×D₁₉₁	1	1	yes	characteristic
212	C₂	#27132685	1	1	yes	characteristic
213	C₂	#27132714	1	1	yes	characteristic
214	C₂	#27132718	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄²×D₁₉₁

C₂

yes

maximal, characteristic

C₂×Dic₁₉₁⋊C₈

C₂

yes

maximal, complemented

C₂×(C₂×D₁₉₁)⋊C₈

C₂

yes

maximal

#27132418

C₂

yes

maximal, characteristic, complemented

#336×C₁₉₁

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉₁

C₄

yes

characteristic

C₂²×C₄×D₁₉₁

C₄

yes

characteristic

C₂²×C₄×D₁₉₁

C₂²

yes

characteristic

C₂²×C₁₉₁⋊C₈

C₂²

yes

—

C₂×C₄×Dic₁₉₁

C₄

yes

characteristic

C₂×C₄×Dic₁₉₁

C₄

yes

characteristic

C₂×C₄×Dic₁₉₁

C₂²

yes

characteristic

C₄²×D₁₉₁

—

Dic₁₉₁⋊C₈

—

(C₂×D₁₉₁)⋊C₈

—

C₂²×C₈×C₁₉₁

C₂²

yes

—

C₂×C₄²×C₁₉₁

C₂²

yes

characteristic

C₂³×D₁₉₁

C₂×C₄

yes

characteristic

C₂²×Dic₁₉₁

C₂×C₄

yes

characteristic

C₂²×Dic₁₉₁

C₂×C₄

yes

characteristic

C₂²×Dic₁₉₁

C₂×C₄

yes

characteristic

C₂×C₄×D₁₉₁

—

C₂×C₄×D₁₉₁

—

C₂×C₄×D₁₉₁

—

C₂×C₄×D₁₉₁

—

C₂×C₄×D₁₉₁

—

C₂×C₄×D₁₉₁

—

C₂×C₄×D₁₉₁

—

C₂×C₄×D₁₉₁

C₈

yes

complemented

C₂×C₄×D₁₉₁

D₄

yes

—

C₂×C₄×D₁₉₁

Q₈

yes

—

C₂×C₁₉₁⋊C₈

—

C₂×C₁₉₁⋊C₈

—

C₂×C₁₉₁⋊C₈

—

C₄×Dic₁₉₁

—

C₄×Dic₁₉₁

—

C₄×Dic₁₉₁

D₄

yes

—

C₂²×C₄×C₁₉₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉₁

C₂³

yes

characteristic

C₂×C₈×C₁₉₁

—

C₂×C₈×C₁₉₁

—

C₂×C₈×C₁₉₁

—

C₄²×C₁₉₁

—

C₂²×D₁₉₁

—

C₂²×D₁₉₁

—

C₂²×D₁₉₁

—

C₂²×D₁₉₁

—

C₂²×D₁₉₁

C₄⋊C₄

yes

—

C₂²×D₁₉₁

C₂×C₈

yes

—

C₂²×D₁₉₁

M₁₆

yes

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

C₂²⋊C₄

yes

—

C₂×Dic₁₉₁

C₂²⋊C₄

yes

—

C₂×Dic₁₉₁

C₄⋊C₄

yes

—

C₂×Dic₁₉₁

C₂×C₈

yes

—

C₂×Dic₁₉₁

M₁₆

yes

—

C₄×D₁₉₁

—

C₄×D₁₉₁

—

C₄×D₁₉₁

—

C₄×D₁₉₁

—

C₁₉₁⋊C₈

—

C₂³×C₁₉₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

C₂×C₈

yes

—

C₂×C₄×C₁₉₁

M₁₆

yes

—

C₂×C₄×C₁₉₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉₁

C₂×D₄

yes

—

C₂×C₄×C₁₉₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉₁

#41

yes

—

C₈×C₁₉₁

—

C₂²×C₁₉₁

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉₁

#117

yes

characteristic

C₂²×C₁₉₁

C₂²×C₈

yes

characteristic

C₂²×C₁₉₁

C₂×M₁₆

yes

characteristic

C₂²×C₁₉₁

C₂×M₁₆

yes

characteristic

C₂²×C₁₉₁

C₂×M₁₆

yes

characteristic

C₂×D₁₉₁

—

C₂×D₁₉₁

—

C₂×D₁₉₁

—

C₂×D₁₉₁

—

C₂×D₁₉₁

—

C₂×D₁₉₁

—

C₂×D₁₉₁

C₄⋊C₈

yes

complemented

C₄×C₁₉₁

—

C₄×C₁₉₁

—

C₄×C₁₉₁

#121

yes

—

C₄×C₁₉₁

C₂²⋊Q₈

yes

—

Dic₁₉₁

—

Dic₁₉₁

—

Dic₁₉₁

C₂²⋊C₈

yes

complemented

C₂×C₁₉₁

#380

yes

characteristic

100

C₂×C₁₉₁

C₂×C₂²⋊C₈

yes

characteristic

101

C₂×C₁₉₁

#407

yes

characteristic

102

C₂×C₁₉₁

C₂×C₄⋊C₈

yes

characteristic

103

C₂×C₁₉₁

#423

yes

characteristic

104

C₂×C₁₉₁

#431

yes

characteristic

105

C₂×C₁₉₁

#432

yes

characteristic

106

D₁₉₁

—

107

C₁₉₁

#1797

yes

characteristic, complemented, Sylow

108

#1797

—

191

maximal, Sylow

109

C₂²×C₄²

—

191

—

110

C₂×C₄⋊C₈

—

191

—

111

C₂×C₂²⋊C₈

—

191

—

112

#336

—

191

—

113

#336

D₁₉₁

yes

characteristic, complemented

114

C₂³×C₄

—

191

—

115

C₂³×C₄

—

191

—

116

C₂³×C₄

—

191

—

117

C₂²×C₈

—

191

—

118

C₂²×C₈

C₂×D₁₉₁

yes

—

119

C₂×C₄²

—

382

—

120

C₂×C₄²

—

191

—

121

C₂×C₄²

—

191

—

122

C₂×C₄²

—

191

—

123

C₂×C₄²

C₂×D₁₉₁

yes

characteristic

124

C₄⋊C₈

—

382

—

125

C₂²⋊C₈

—

382

—

126

C₂⁴

—

191

—

127

C₂²×C₄

—

382

—

128

C₂²×C₄

—

382

—

129

C₂²×C₄

—

382

—

130

C₂²×C₄

—

382

—

131

C₂²×C₄

—

382

—

132

C₂²×C₄

—

382

—

133

C₂²×C₄

—

382

—

134

C₂²×C₄

—

191

—

135

C₂²×C₄

—

191

—

136

C₂²×C₄

—

191

—

137

C₂²×C₄

—

191

—

138

C₂²×C₄

—

191

—

139

C₂²×C₄

—

191

—

140

C₂²×C₄

C₄×D₁₉₁

yes

characteristic

141

C₂²×C₄

C₄×D₁₉₁

yes

characteristic

142

C₂²×C₄

C₂²×D₁₉₁

yes

characteristic

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

382

—

147

C₂×C₈

—

382

—

148

C₂×C₈

—

382

—

149

C₄²

—

150

C₄²

—

382

—

151

C₄²

—

382

—

152

C₄²

—

191

—

153

C₂³

—

382

—

154

C₂³

—

382

—

155

C₂³

—

382

—

156

C₂³

—

382

—

157

C₂³

—

191

—

158

C₂³

—

191

—

159

C₂³

—

191

—

160

C₂³

C₂×C₄×D₁₉₁

yes

characteristic

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

382

—

166

C₂×C₄

—

382

—

167

C₂×C₄

—

382

—

168

C₂×C₄

—

382

—

169

C₂×C₄

—

382

—

170

C₂×C₄

—

382

—

171

C₂×C₄

—

382

—

172

C₂×C₄

—

382

—

173

C₂×C₄

—

191

—

174

C₂×C₄

—

191

—

175

C₂×C₄

—

191

—

176

C₂×C₄

—

191

—

177

C₂×C₄

—

191

—

178

C₂×C₄

C₈×D₁₉₁

yes

—

179

C₂×C₄

#15690270

yes

—

180

C₂×C₄

D₄×D₁₉₁

yes

characteristic

181

C₂×C₄

D₄×D₁₉₁

yes

—

182

C₂×C₄

Q₈×D₁₉₁

yes

characteristic

183

C₂×C₄

#15690287

yes

—

184

C₈

—

185

C₈

—

764

—

186

C₂²

—

382

—

187

C₂²

—

382

—

188

C₂²

—

382

—

189

C₂²

—

382

—

190

C₂²

—

382

—

191

C₂²

—

382

—

192

C₂²

—

191

—

193

C₂²

C₂²⋊C₄×D₁₉₁

yes

characteristic

194

C₂²

C₄⋊C₄×D₁₉₁

yes

characteristic

195

C₂²

#20259279

yes

characteristic

196

C₂²

C₂×C₈×D₁₉₁

yes

characteristic

197

C₂²

M₁₆×D₁₉₁

yes

characteristic

198

C₂²

M₁₆×D₁₉₁

yes

characteristic

199

C₂²

C₂×#15690270

yes

characteristic

200

C₄

—

201

C₄

—

202

C₄

—

382

—

203

C₄

—

382

—

204

C₄

—

191

—

205

C₄

#20259295

yes

—

206

C₄

#20259300

yes

—

207

C₂

—

382

—

208

C₂

#27132522

yes

characteristic

209

C₂

C₂²⋊C₈×D₁₉₁

yes

characteristic

210

C₂

#27132625

yes

characteristic

211

C₂

C₄⋊C₈×D₁₉₁

yes

characteristic

212

C₂

#27132685

yes

characteristic

213

C₂

#27132714

yes

characteristic

214

C₂

#27132718

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉₁
commutator	C₂²×C₁₉₁	C₂²×C₈
Fitting	#336×C₁₉₁	C₂
socle	C₂³×C₁₉₁	C₂²×C₄
prime radical	C₂³×D₁₉₁	C₂×C₄
cosocle	C₂²×C₄×C₁₉₁	C₂³
hypercenter	#336	D₁₉₁
hypocenter	C₁₉₁	#1797
LCS	G ▷ C₂²×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉₁

commutator

C₂²×C₁₉₁

C₂²×C₈

Fitting

#336×C₁₉₁

C₂

socle

C₂³×C₁₉₁

C₂²×C₄

prime radical

C₂³×D₁₉₁

C₂×C₄

cosocle

C₂²×C₄×C₁₉₁

C₂³

D₁₉₁

C₁₉₁

G ▷ C₂²×C₁₉₁ ▷ C₁₉₁

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
2. C₂×Dic₁₉₁⋊C₈	C₂	semidirect
4. #27132418	C₂	semidirect
5. #336×C₁₉₁	C₂	semidirect
29. C₂×C₄×D₁₉₁	C₈	semidirect
91. C₂×D₁₉₁	C₄⋊C₈	semidirect
98. Dic₁₉₁	C₂²⋊C₈	semidirect
107. C₁₉₁	#1797	semidirect
113. #336	D₁₉₁	semidirect

H ≅ G/N

type

2. C₂×Dic₁₉₁⋊C₈

C₂

semidirect

4. #27132418

C₂

semidirect

5. #336×C₁₉₁

C₂

semidirect

29. C₂×C₄×D₁₉₁

C₈

semidirect

91. C₂×D₁₉₁

C₄⋊C₈

semidirect

98. Dic₁₉₁

C₂²⋊C₈

semidirect

107. C₁₉₁

#1797

semidirect

113. #336

D₁₉₁

semidirect

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

subgroup	index
C₂×C₄²×D₁₉₁	2
C₂×Dic₁₉₁⋊C₈	2
C₂×(C₂×D₁₉₁)⋊C₈	2
#27132418	2
#336×C₁₉₁	2
#1797	191

subgroup

index

C₂×C₄²×D₁₉₁

C₂×Dic₁₉₁⋊C₈

C₂×(C₂×D₁₉₁)⋊C₈

#27132418

#336×C₁₉₁

#1797

191

Subgroups — #37572499

Conjugacy classes of subgroups

Complements

Maximal subgroups