Group #31887905 — subgroups

Subgroups — #31887905

Order 18176.

330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 147 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	#22586632	C₂	1	2	yes	maximal
2	#22586171	C₂	1	2	yes	maximal
3	#22586169	C₂	1	2	yes	maximal
4	C₇₁×#1726	C₂	1	1	yes	maximal, characteristic
5	#17986052	C₂²	1	4	yes	—
6	#17985721	C₄	1	8	yes	complemented
7	C₂×#97×C₇₁	C₄	1	2	yes	—
8	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₇₁	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	#376×C₇₁	C₂²	1	1	yes	characteristic
12	C₄⋊(C₇₁⋊C₈)	—	2	4	no	—
13	C₂²⋊(C₇₁⋊C₈)	—	2	4	no	—
14	C₄×C₇₁⋊C₈	C₂×C₄	1	8	yes	—
15	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
20	#97×C₇₁	—	2	4	no	—
21	#97×C₇₁	—	2	2	no	—
22	C₄×C₈×C₇₁	—	2	4	no	—
23	C₄×C₈×C₇₁	C₂×C₄	1	4	yes	—
24	#95×C₇₁	—	2	2	no	—
25	C₂×C₇₁⋊C₈	—	2	8	no	—
26	C₂²×C₄×C₇₁	—	2	2	no	—
27	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₇₁	#41	1	2	yes	—
29	C₂×C₈×C₇₁	—	2	2	no	—
30	C₂×C₈×C₇₁	—	2	2	no	—
31	C₂×C₈×C₇₁	—	2	2	no	—
32	C₂×C₈×C₇₁	—	2	2	no	—
33	C₂×C₈×C₇₁	C₄²	1	2	yes	—
34	C₂×C₈×C₇₁	C₄²	1	2	yes	—
35	C₂×C₈×C₇₁	M₁₆	1	4	yes	—
36	C₄²×C₇₁	—	2	2	no	—
37	C₄²×C₇₁	M₁₆	1	4	yes	—
38	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
39	C₄²×C₇₁	#41	1	2	yes	—
40	C₂³×C₇₁	#117	1	1	yes	characteristic
41	C₂×C₄×C₇₁	—	2	4	no	—
42	C₂×C₄×C₇₁	—	4	2	no	—
43	C₂×C₄×C₇₁	—	4	4	no	—
44	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
45	C₂×C₄×C₇₁	#117	1	4	yes	—
46	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
47	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
48	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
49	C₈×C₇₁	—	2	2	no	—
50	C₈×C₇₁	—	2	2	no	—
51	C₈×C₇₁	—	2	4	no	—
52	C₇₁⋊C₈	—	4	8	no	—
53	C₂²×C₇₁	—	2	2	no	—
54	C₂²×C₇₁	#376	1	1	yes	characteristic
55	C₂²×C₇₁	#432	1	2	yes	—
56	C₄×C₇₁	—	2	4	no	—
57	C₄×C₇₁	—	4	4	no	—
58	C₄×C₇₁	C₄×M₁₆	1	1	yes	characteristic
59	C₄×C₇₁	C₄×M₁₆	1	1	yes	characteristic
60	C₄×C₇₁	#432	1	2	yes	—
61	#8140	—	71	1	no	maximal, Sylow
62	C₂×C₇₁	—	2	2	no	—
63	C₂×C₇₁	#1745	1	1	yes	characteristic
64	C₂×C₇₁	#1747	1	2	yes	—
65	#1726	D₇₁	1	1	yes	characteristic
66	#1452	—	71	2	no	—
67	#1275	—	71	2	no	—
68	#1274	—	71	2	no	—
69	C₇₁	#8140	1	1	yes	characteristic, complemented, Sylow
70	#431	—	71	4	no	—
71	C₂×#97	Dic₇₁	1	2	yes	—
72	C₂×#97	C₂×D₇₁	1	1	yes	characteristic
73	C₂×C₄×C₈	Dic₇₁	1	2	yes	—
74	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
75	#376	C₂×D₇₁	1	1	yes	characteristic
76	#322	—	71	8	no	—
77	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
78	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
79	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
80	C₂×C₄²	C₂×Dic₇₁	1	2	yes	—
81	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
82	C₄⋊C₈	—	142	4	no	—
83	C₂²⋊C₈	—	142	4	no	—
84	#97	—	2	4	no	—
85	#97	—	2	2	no	—
86	C₄×C₈	—	2	4	no	—
87	C₄×C₈	—	71	8	no	—
88	C₄×C₈	C₄×D₇₁	1	4	yes	—
89	#95	—	2	2	no	—
90	C₂²×C₄	—	2	2	no	—
91	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
92	C₂²×C₄	#11765865	1	2	yes	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	142	8	no	—
98	C₂×C₈	C₄×Dic₇₁	1	2	yes	—
99	C₂×C₈	C₄×Dic₇₁	1	2	yes	—
100	C₂×C₈	#11765849	1	4	yes	—
101	C₄²	—	2	2	no	—
102	C₄²	#11765849	1	4	yes	—
103	C₄²	C₂×C₄×D₇₁	1	2	yes	—
104	C₄²	#11765865	1	2	yes	—
105	C₂³	#14556087	1	1	yes	characteristic
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	4	no	—
109	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
110	C₂×C₄	#14556085	1	4	yes	—
111	C₂×C₄	#14556087	1	1	yes	characteristic
112	C₂×C₄	C₂×#11765849	1	2	yes	—
113	C₂×C₄	C₂×#11765849	1	2	yes	—
114	C₈	—	2	4	no	—
115	C₈	—	2	2	no	—
116	C₈	—	2	2	no	—
117	C₈	—	284	8	no	—
118	C₂²	—	2	2	no	—
119	C₂²	#17985845	1	1	yes	characteristic
120	C₂²	#17986056	1	2	yes	—
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	C₄×#11765849	1	1	yes	characteristic
124	C₄	C₄×#11765849	1	1	yes	characteristic
125	C₄	#17986056	1	2	yes	—
126	C₂	—	2	2	no	—
127	C₂	#22588089	1	1	yes	characteristic
128	C₂	#22588095	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22586632

C₂

yes

maximal

#22586171

C₂

yes

maximal

#22586169

C₂

yes

maximal

C₇₁×#1726

C₂

yes

maximal, characteristic

#17986052

C₂²

yes

—

#17985721

C₄

yes

complemented

C₂×#97×C₇₁

C₄

yes

—

C₂×#97×C₇₁

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₁

C₄

yes

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

#376×C₇₁

C₂²

yes

characteristic

C₄⋊(C₇₁⋊C₈)

—

C₂²⋊(C₇₁⋊C₈)

—

C₄×C₇₁⋊C₈

C₂×C₄

yes

—

C₂²×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₁

C₂×C₄

yes

—

C₂×C₄²×C₇₁

C₂×C₄

yes

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

#97×C₇₁

—

#97×C₇₁

—

C₄×C₈×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

—

#95×C₇₁

—

C₂×C₇₁⋊C₈

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₁

#41

yes

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₄²

yes

—

C₂×C₈×C₇₁

C₄²

yes

—

C₂×C₈×C₇₁

M₁₆

yes

—

C₄²×C₇₁

—

C₄²×C₇₁

M₁₆

yes

—

C₄²×C₇₁

C₂²×C₄

yes

—

C₄²×C₇₁

#41

yes

—

C₂³×C₇₁

#117

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₁

#117

yes

—

C₂×C₄×C₇₁

#117

yes

characteristic

C₂×C₄×C₇₁

C₂×M₁₆

yes

—

C₂×C₄×C₇₁

C₂×M₁₆

yes

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

#376

yes

characteristic

C₂²×C₇₁

#432

yes

—

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

C₄×M₁₆

yes

characteristic

C₄×C₇₁

C₄×M₁₆

yes

characteristic

C₄×C₇₁

#432

yes

—

#8140

—

maximal, Sylow

C₂×C₇₁

—

C₂×C₇₁

#1745

yes

characteristic

C₂×C₇₁

#1747

yes

—

#1726

D₇₁

yes

—

—

—

C₇₁

#8140

yes

characteristic, complemented, Sylow

#431

—

C₂×#97

Dic₇₁

yes

—

C₂×#97

C₂×D₇₁

yes

characteristic

C₂×C₄×C₈

Dic₇₁

yes

—

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

#376

C₂×D₇₁

yes

characteristic

#322

—

C₂²×C₈

C₂×Dic₇₁

yes

characteristic

C₂²×C₈

C₂×Dic₇₁

yes

characteristic

C₂²×C₈

C₂×Dic₇₁

yes

—

C₂×C₄²

C₂×Dic₇₁

yes

—

C₂×C₄²

C₂²×D₇₁

yes

characteristic

C₄⋊C₈

—

142

—

C₂²⋊C₈

—

142

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₇₁

yes

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₂²×Dic₇₁

yes

characteristic

C₂²×C₄

#11765865

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

142

—

C₂×C₈

C₄×Dic₇₁

yes

—

C₂×C₈

C₄×Dic₇₁

yes

—

100

C₂×C₈

#11765849

yes

—

101

C₄²

—

102

C₄²

#11765849

yes

—

103

C₄²

C₂×C₄×D₇₁

yes

—

104

C₄²

#11765865

yes

—

105

C₂³

#14556087

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂×C₄×Dic₇₁

yes

characteristic

110

C₂×C₄

#14556085

yes

—

111

C₂×C₄

#14556087

yes

characteristic

112

C₂×C₄

C₂×#11765849

yes

—

113

C₂×C₄

C₂×#11765849

yes

—

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

284

—

118

C₂²

—

119

C₂²

#17985845

yes

characteristic

120

C₂²

#17986056

yes

—

121

C₄

—

122

C₄

—

123

C₄

C₄×#11765849

yes

characteristic

124

C₄

C₄×#11765849

yes

characteristic

125

C₄

#17986056

yes

—

126

C₂

—

127

C₂

#22588089

yes

characteristic

128

C₂

#22588095

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₇₁
commutator	C₂×C₄×C₇₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1726	C₂
socle	C₂²×C₇₁	#376
prime radical	C₂³×C₇₁	#117
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1726	D₇₁
hypocenter	C₇₁	#8140
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ #1726

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₇₁

commutator

C₂×C₄×C₇₁

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1726

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₇₁

C₁ ◁ C₂×C₄ ◁ #1726

N	H ≅ G/N	type
6. #17985721	C₄	semidirect
69. C₇₁	#8140	semidirect

H ≅ G/N

type

6. #17985721

C₄

semidirect

69. C₇₁

#8140

semidirect

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

subgroup	index
#22586632	2
#22586171	2
#22586169	2
C₇₁×#1726	2
#8140	71

subgroup

index

C₇₁×#1726

Subgroups — #31887905

Conjugacy classes of subgroups

Complements

Maximal subgroups