Group #16845792 — subgroups

Subgroups — #16845792

Order 3968.

272 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 85 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×#11758503	C₂	1	1	yes	maximal, characteristic
2	#14521013	C₂	1	1	yes	maximal, characteristic
3	#14520817	C₂	1	4	yes	maximal, complemented
4	C₃₁×#407	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
6	C₂×M₁₆×C₃₁	C₂²	1	2	yes	—
7	C₂×C₂²⋊Dic₃₁	C₄	1	2	yes	—
8	#11758503	—	2	2	no	—
9	#11758503	—	2	2	no	—
10	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	—
11	C₂×C₄×Dic₃₁	C₄	1	2	yes	—
12	C₂×#92474	C₂²	1	2	yes	—
13	C₃₁×C₂²⋊C₈	—	2	2	no	—
14	C₂²⋊(C₃₁⋊C₈)	—	2	2	no	—
15	C₂⁴×C₃₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₃₁	—	2	4	no	—
17	C₂²×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₃₁	D₄	1	2	yes	—
19	C₂²×C₄×C₃₁	D₄	1	2	yes	—
20	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
21	C₂²×Dic₃₁	C₂×C₄	1	4	yes	—
22	M₁₆×C₃₁	—	2	4	no	—
23	C₂×C₈×C₃₁	—	2	2	no	—
24	C₂²⋊Dic₃₁	—	2	4	no	—
25	C₄⋊Dic₃₁	—	2	2	no	—
26	C₄⋊Dic₃₁	—	2	2	no	—
27	C₄×Dic₃₁	—	2	4	no	—
28	#92474	—	2	4	no	—
29	C₂×C₃₁⋊C₈	—	2	2	no	—
30	C₂³×C₃₁	—	2	2	no	—
31	C₂³×C₃₁	—	4	2	no	—
32	C₂³×C₃₁	C₂²⋊C₄	1	2	yes	—
33	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₃₁	—	2	2	no	—
35	C₂×C₄×C₃₁	—	2	4	no	—
36	C₂×C₄×C₃₁	—	2	4	no	—
37	C₂×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
38	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₃₁	#41	1	4	yes	—
41	C₂×Dic₃₁	—	2	4	no	—
42	C₂×Dic₃₁	—	4	4	no	—
43	C₈×C₃₁	—	4	2	no	—
44	C₃₁⋊C₈	—	4	2	no	—
45	#1822	—	31	1	no	maximal, Sylow
46	C₂²×C₃₁	—	2	2	no	—
47	C₂²×C₃₁	—	2	2	no	—
48	C₂²×C₃₁	—	2	4	no	—
49	C₂²×C₃₁	—	4	4	no	—
50	C₂²×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₃₁	#117	1	2	yes	—
52	C₄×C₃₁	—	2	2	no	—
53	C₄×C₃₁	#123	1	2	yes	—
54	C₄×C₃₁	#123	1	2	yes	—
55	Dic₃₁	—	4	4	no	—
56	C₂×#117	—	31	1	no	—
57	#407	—	31	1	no	—
58	#407	D₃₁	1	1	yes	characteristic
59	#343	—	31	4	no	—
60	C₂×C₃₁	—	2	2	no	—
61	C₂×C₃₁	—	4	2	no	—
62	C₂×C₃₁	#381	1	1	yes	characteristic
63	C₂×C₃₁	#413	1	2	yes	—
64	C₂³×C₄	C₂×D₃₁	1	1	yes	characteristic
65	C₂×M₁₆	—	31	2	no	—
66	C₂×M₁₆	C₂×D₃₁	1	2	yes	—
67	#117	—	62	2	no	—
68	#117	—	62	2	no	—
69	C₂×C₄⋊C₄	—	31	2	no	—
70	C₂×C₂²⋊C₄	—	31	2	no	—
71	C₂×C₄²	—	31	2	no	—
72	C₂²⋊C₈	—	2	2	no	—
73	C₂²⋊C₈	—	62	2	no	—
74	C₃₁	#1822	1	1	yes	characteristic, complemented, Sylow
75	C₂⁴	C₄×D₃₁	1	1	yes	characteristic
76	C₂²×C₄	—	2	4	no	—
77	C₂²×C₄	—	31	4	no	—
78	C₂²×C₄	C₄×D₃₁	1	1	yes	characteristic
79	C₂²×C₄	D₁₂₄	1	2	yes	—
80	C₂²×C₄	C₂²⋊D₃₁	1	2	yes	—
81	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
82	M₁₆	—	2	4	no	—
83	M₁₆	—	62	4	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	62	2	no	—
86	C₄⋊C₄	—	62	2	no	—
87	C₄⋊C₄	—	62	2	no	—
88	C₂²⋊C₄	—	62	4	no	—
89	C₄²	—	62	4	no	—
90	C₂³	—	2	2	no	—
91	C₂³	—	4	2	no	—
92	C₂³	(C₂×D₃₁)⋊C₄	1	2	yes	—
93	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	62	4	no	—
98	C₂×C₄	—	124	4	no	—
99	C₂×C₄	(C₂×D₃₁)⋊C₄	1	2	yes	—
100	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
101	C₂×C₄	#92497	1	4	yes	—
102	C₂×C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
103	C₈	—	4	2	no	—
104	C₈	—	124	2	no	—
105	C₂²	—	2	2	no	—
106	C₂²	—	2	2	no	—
107	C₂²	—	2	4	no	—
108	C₂²	—	4	4	no	—
109	C₂²	#11758454	1	2	yes	—
110	C₂²	C₂×(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	124	4	no	—
113	C₄	#11758463	1	2	yes	—
114	C₄	#11758512	1	2	yes	—
115	C₂	—	2	2	no	—
116	C₂	—	4	2	no	—
117	C₂	#14520910	1	1	yes	characteristic
118	C₂	#14521031	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11758503

C₂

yes

maximal, characteristic

#14521013

C₂

yes

maximal, characteristic

#14520817

C₂

yes

maximal, complemented

C₃₁×#407

C₂

yes

maximal, characteristic

C₂³×C₄×C₃₁

C₂²

yes

characteristic

C₂×M₁₆×C₃₁

C₂²

yes

—

C₂×C₂²⋊Dic₃₁

C₄

yes

—

#11758503

—

#11758503

—

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂×C₄×Dic₃₁

C₄

yes

—

C₂×#92474

C₂²

yes

—

C₃₁×C₂²⋊C₈

—

C₂²⋊(C₃₁⋊C₈)

—

C₂⁴×C₃₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₃₁

D₄

yes

—

C₂²×C₄×C₃₁

D₄

yes

—

C₂²×C₄×C₃₁

C₂³

yes

characteristic

C₂²×Dic₃₁

C₂×C₄

yes

—

M₁₆×C₃₁

—

C₂×C₈×C₃₁

—

C₂²⋊Dic₃₁

—

C₄⋊Dic₃₁

—

C₄⋊Dic₃₁

—

C₄×Dic₃₁

—

#92474

—

C₂×C₃₁⋊C₈

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

C₂²⋊C₄

yes

—

C₂³×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂²⋊C₄

yes

—

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

#41

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₈×C₃₁

—

C₃₁⋊C₈

—

#1822

—

maximal, Sylow

C₂²×C₃₁

—

C₂²×C₃₁

—

C₂²×C₃₁

—

C₂²×C₃₁

—

C₂²×C₃₁

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₃₁

#117

yes

—

C₄×C₃₁

—

C₄×C₃₁

#123

yes

—

C₄×C₃₁

#123

yes

—

Dic₃₁

—

C₂×#117

—

#407

—

#407

D₃₁

yes

characteristic

#343

—

C₂×C₃₁

—

C₂×C₃₁

—

C₂×C₃₁

#381

yes

characteristic

C₂×C₃₁

#413

yes

—

C₂³×C₄

C₂×D₃₁

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₃₁

yes

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₃₁

#1822

yes

characteristic, complemented, Sylow

C₂⁴

C₄×D₃₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₃₁

yes

characteristic

C₂²×C₄

D₁₂₄

yes

—

C₂²×C₄

C₂²⋊D₃₁

yes

—

C₂²×C₄

C₂²×D₃₁

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

—

C₂³

(C₂×D₃₁)⋊C₄

yes

—

C₂³

C₂×C₄×D₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

124

—

C₂×C₄

(C₂×D₃₁)⋊C₄

yes

—

100

C₂×C₄

C₂×D₁₂₄

yes

characteristic

101

C₂×C₄

#92497

yes

—

102

C₂×C₄

C₂×C₂²⋊D₃₁

yes

characteristic

103

C₈

—

104

C₈

—

124

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

#11758454

yes

—

110

C₂²

C₂×(C₂×D₃₁)⋊C₄

yes

characteristic

111

C₄

—

112

C₄

—

124

—

113

C₄

#11758463

yes

—

114

C₄

#11758512

yes

—

115

C₂

—

116

C₂

—

117

C₂

#14520910

yes

characteristic

118

C₂

#14521031

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₃₁)⋊C₄
commutator	C₂³×C₃₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₃₁×#407	C₂
socle	C₂²×C₃₁	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃₁	C₂×C₄
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	#407	D₃₁
hypocenter	C₃₁	#1822
LCS	G ▷ C₂³×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂²

C₂×(C₂×D₃₁)⋊C₄

commutator

C₂³×C₃₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₁

Fitting

C₃₁×#407

C₂

socle

C₂²×C₃₁

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₃₁

C₂×C₄

cosocle

C₂²×C₄×C₃₁

C₂³

D₃₁

C₃₁

G ▷ C₂³×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
3. #14520817	C₂	semidirect
74. C₃₁	#1822	semidirect

H ≅ G/N

type

3. #14520817

C₂

semidirect

74. C₃₁

#1822

semidirect

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

subgroup	index
C₂×#11758503	2
#14521013	2
#14520817	2
C₃₁×#407	2
#1822	31

subgroup

index

C₃₁×#407

Subgroups — #16845792

Conjugacy classes of subgroups

Complements

Maximal subgroups