Group #16845829 — subgroups

Subgroups — #16845829

Order 3968.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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×Dic₃₁⋊C₈	C₂	1	2	yes	maximal
2	#14520895	C₂	1	1	yes	maximal, characteristic
3	#14520804	C₂	1	1	yes	maximal, characteristic
4	#14520803	C₂	1	2	yes	maximal
5	C₃₁×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₃₁	C₂²	1	2	yes	—
7	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic
10	C₂²×C₃₁⋊C₈	C₂²	1	2	yes	—
11	C₃₁⋊#95	C₄	1	2	yes	—
12	C₃₁⋊#95	C₄	1	2	yes	—
13	Dic₃₁⋊C₈	—	2	4	no	—
14	C₂²×C₄×C₃₁	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₃₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₃₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₃₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₃₁	—	2	2	no	—
20	C₂×C₈×C₃₁	—	2	2	no	—
21	C₂×C₈×C₃₁	—	2	2	no	—
22	C₄²×C₃₁	—	2	2	no	—
23	C₄×Dic₃₁	—	2	2	no	—
24	C₄×Dic₃₁	D₄	1	2	yes	—
25	C₄×Dic₃₁	Q₈	1	2	yes	—
26	C₂×C₃₁⋊C₈	—	2	2	no	—
27	C₂×C₃₁⋊C₈	—	2	2	no	—
28	C₂×C₃₁⋊C₈	—	2	2	no	—
29	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₃₁	—	2	2	no	—
31	C₂×C₄×C₃₁	—	2	2	no	—
32	C₂×C₄×C₃₁	—	2	2	no	—
33	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₃₁	#41	1	2	yes	—
36	C₂×C₄×C₃₁	#41	1	2	yes	—
37	C₂×Dic₃₁	—	2	2	no	—
38	C₂×Dic₃₁	—	2	2	no	—
39	C₂×Dic₃₁	—	2	1	no	—
40	C₂×Dic₃₁	—	2	1	no	—
41	C₂×Dic₃₁	—	2	2	no	—
42	C₂×Dic₃₁	—	2	2	no	—
43	C₂×Dic₃₁	C₄⋊C₄	1	4	yes	—
44	C₈×C₃₁	—	4	2	no	—
45	C₃₁⋊C₈	—	4	2	no	—
46	#1832	—	31	1	no	maximal, Sylow
47	C₂²×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₃₁	#117	1	1	yes	characteristic
49	C₂²×C₃₁	#117	1	1	yes	characteristic
50	C₂²×C₃₁	#131	1	2	yes	—
51	C₂²×C₃₁	#131	1	2	yes	—
52	C₄×C₃₁	—	4	2	no	—
53	C₄×C₃₁	#124	1	2	yes	—
54	C₄×C₃₁	#125	1	2	yes	—
55	Dic₃₁	—	2	4	no	—
56	Dic₃₁	—	4	1	no	—
57	Dic₃₁	—	4	1	no	—
58	C₂×C₄⋊C₈	—	31	2	no	—
59	#376	—	31	1	no	—
60	#336	—	31	2	no	—
61	#336	—	31	1	no	—
62	#336	D₃₁	1	1	yes	characteristic
63	C₂×C₃₁	#382	1	1	yes	characteristic
64	C₂×C₃₁	#424	1	2	yes	—
65	C₂×C₃₁	#433	1	2	yes	—
66	C₂×C₃₁	#433	1	1	yes	characteristic
67	C₂×C₃₁	#433	1	1	yes	characteristic
68	C₂²×C₈	—	31	2	no	—
69	C₂²×C₈	C₂×D₃₁	1	2	yes	—
70	C₂×C₄²	—	31	1	no	—
71	C₂×C₄²	—	31	1	no	—
72	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
73	C₄⋊C₈	—	62	4	no	—
74	#95	—	31	2	no	—
75	#95	—	31	2	no	—
76	C₃₁	#1832	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₄	—	31	2	no	—
78	C₂²×C₄	—	31	1	no	—
79	C₂²×C₄	—	31	1	no	—
80	C₂²×C₄	C₄×D₃₁	1	2	yes	—
81	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	62	2	no	—
86	C₂×C₈	—	62	2	no	—
87	C₂×C₈	—	62	2	no	—
88	C₄²	—	2	2	no	—
89	C₄²	—	31	2	no	—
90	C₄²	—	31	2	no	—
91	C₄²	—	62	2	no	—
92	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	31	4	no	—
97	C₂×C₄	—	62	2	no	—
98	C₂×C₄	—	62	2	no	—
99	C₂×C₄	—	62	1	no	—
100	C₂×C₄	—	62	1	no	—
101	C₂×C₄	—	62	2	no	—
102	C₂×C₄	—	62	2	no	—
103	C₂×C₄	#92495	1	2	yes	—
104	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
105	C₂×C₄	#92497	1	2	yes	—
106	C₂×C₄	Q₈×D₃₁	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	124	2	no	—
109	C₂²	#11758449	1	1	yes	characteristic
110	C₂²	#11758454	1	1	yes	characteristic
111	C₂²	C₄⋊C₄×D₃₁	1	1	yes	characteristic
112	C₂²	#11758478	1	2	yes	—
113	C₂²	#11758484	1	2	yes	—
114	C₄	—	4	2	no	—
115	C₄	—	62	4	no	—
116	C₄	—	124	1	no	—
117	C₄	—	124	1	no	—
118	C₄	#11758462	1	2	yes	—
119	C₄	#11758466	1	2	yes	—
120	C₂	#14520913	1	1	yes	characteristic
121	C₂	#14521074	1	2	yes	—
122	C₂	#14521107	1	2	yes	—
123	C₂	#14521108	1	1	yes	characteristic
124	C₂	#14521111	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₃₁⋊C₈

C₂

yes

maximal

#14520895

C₂

yes

maximal, characteristic

#14520804

C₂

yes

maximal, characteristic

#14520803

C₂

yes

maximal

C₃₁×#336

C₂

yes

maximal, characteristic

C₂²×C₈×C₃₁

C₂²

yes

—

C₂×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₄×Dic₃₁

C₂²

yes

characteristic

C₂×C₄×Dic₃₁

C₂²

yes

characteristic

C₂²×C₃₁⋊C₈

C₂²

yes

—

C₃₁⋊#95

C₄

yes

—

C₃₁⋊#95

C₄

yes

—

Dic₃₁⋊C₈

—

C₂²×C₄×C₃₁

C₂×C₄

yes

—

C₂²×C₄×C₃₁

C₂³

yes

characteristic

C₂²×Dic₃₁

C₂×C₄

yes

characteristic

C₂²×Dic₃₁

C₂×C₄

yes

characteristic

C₂²×Dic₃₁

C₂×C₄

yes

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₄²×C₃₁

—

C₄×Dic₃₁

—

C₄×Dic₃₁

D₄

yes

—

C₄×Dic₃₁

Q₈

yes

—

C₂×C₃₁⋊C₈

—

C₂×C₃₁⋊C₈

—

C₂×C₃₁⋊C₈

—

C₂³×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₁

#41

yes

—

C₂×C₄×C₃₁

#41

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

C₄⋊C₄

yes

—

C₈×C₃₁

—

C₃₁⋊C₈

—

#1832

—

maximal, Sylow

C₂²×C₃₁

C₂×C₄⋊C₄

yes

C₂²×C₃₁

yes

C₂²×C₃₁

yes

C₂²×C₃₁

yes

—

C₂²×C₃₁

#131

yes

—

C₄×C₃₁

—

C₄×C₃₁

#124

yes

—

C₄×C₃₁

#125

yes

—

Dic₃₁

—

Dic₃₁

—

Dic₃₁

—

C₂×C₄⋊C₈

—

—

—

—

D₃₁

yes

C₂×C₃₁

yes

C₂×C₃₁

yes

—

C₂×C₃₁

#433

yes

—

C₂×C₃₁

yes

C₂×C₃₁

yes

C₂²×C₈

—

C₂²×C₈

C₂×D₃₁

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₃₁

yes

characteristic

C₄⋊C₈

—

#95

—

#95

—

C₃₁

#1832

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₃₁

yes

—

C₂²×C₄

C₂²×D₃₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂×C₄×D₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#92495

yes

—

104

C₂×C₄

D₄×D₃₁

yes

characteristic

105

C₂×C₄

#92497

yes

—

106

C₂×C₄

Q₈×D₃₁

yes

characteristic

107

C₈

—

108

C₈

—

124

—

109

C₂²

#11758449

yes

characteristic

110

C₂²

#11758454

yes

characteristic

111

C₂²

C₄⋊C₄×D₃₁

yes

characteristic

112

C₂²

#11758478

yes

—

113

C₂²

#11758484

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

124

—

117

C₄

—

124

—

118

C₄

#11758462

yes

—

119

C₄

#11758466

yes

—

120

C₂

#14520913

yes

characteristic

121

C₂

#14521074

yes

—

122

C₂

#14521107

yes

—

123

C₂

#14521108

yes

characteristic

124

C₂

#14521111

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₁
commutator, socle, prime radical	C₂³×C₃₁	C₂²×C₄
Fitting	C₃₁×#336	C₂
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	#336	D₃₁
hypocenter	C₃₁	#1832
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₃₁

commutator, socle, prime radical

C₂³×C₃₁

C₂²×C₄

Fitting

C₃₁×#336

C₂

cosocle

C₂²×C₄×C₃₁

C₂³

D₃₁

C₃₁

G ▷ C₂³×C₃₁ ▷ C₃₁

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
76. C₃₁	#1832	semidirect

H ≅ G/N

type

76. C₃₁

#1832

semidirect

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

subgroup	index
C₂×Dic₃₁⋊C₈	2
#14520895	2
#14520804	2
#14520803	2
C₃₁×#336	2
#1832	31

subgroup

index

C₂×Dic₃₁⋊C₈

C₃₁×#336

Subgroups — #16845829

Conjugacy classes of subgroups

Complements

Maximal subgroups