Group #16848817 — subgroups

Subgroups — #16848817

Order 3968.

448 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 221 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	#14520935	C₂	1	4	yes	maximal
2	#14520935	C₂	1	4	yes	maximal
3	C₄⋊C₄×Dic₃₁	C₂	1	4	yes	maximal
4	#14520895	C₂	1	2	yes	maximal
5	C₂×C₃₁×#125	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#125	C₄	1	8	yes	complemented
7	C₂×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
8	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
9	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₃₁	C₂²	1	4	yes	—
11	C₂×C₄×Dic₃₁	C₂²	1	4	yes	—
12	C₂×C₄×Dic₃₁	C₂²	1	4	yes	—
13	C₃₁⋊#95	C₂²	1	2	yes	—
14	C₃₁⋊#95	C₂²	1	2	yes	—
15	C₃₁⋊#95	C₂²	1	4	yes	—
16	C₃₁⋊#95	C₂²	1	4	yes	—
17	C₃₁⋊#95	C₂²	1	4	yes	—
18	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
20	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
21	C₂²×Dic₃₁	C₂³	1	4	yes	—
22	C₂²×Dic₃₁	C₂³	1	4	yes	—
23	C₄⋊C₄×C₃₁	C₂×C₄	1	16	yes	—
24	C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	—
25	C₄²×C₃₁	C₂×C₄	1	4	yes	—
26	C₄⋊Dic₃₁	—	2	8	no	—
27	C₄×Dic₃₁	—	2	8	no	—
28	C₄×Dic₃₁	—	2	8	no	—
29	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₃₁	—	2	4	no	—
31	C₂×C₄×C₃₁	—	2	4	no	—
32	C₂×C₄×C₃₁	—	2	4	no	—
33	C₂×C₄×C₃₁	—	2	2	no	—
34	C₂×C₄×C₃₁	C₂²×C₄	1	4	yes	—
35	C₂×C₄×C₃₁	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₃₁	C₂²×C₄	1	8	yes	—
37	C₂×Dic₃₁	—	2	4	no	—
38	C₂×Dic₃₁	—	2	4	no	—
39	C₂×Dic₃₁	—	2	4	no	—
40	C₂×Dic₃₁	—	2	4	no	—
41	C₂×Dic₃₁	—	2	4	no	—
42	C₂×Dic₃₁	#41	1	8	yes	—
43	#2371	—	31	1	no	maximal, Sylow
44	C₂²×C₃₁	C₂³×C₄	1	1	yes	characteristic
45	C₂²×C₃₁	C₂×#41	1	4	yes	—
46	C₂²×C₃₁	2₋¹⁺⁴	1	2	yes	—
47	C₄×C₃₁	—	2	4	no	—
48	C₄×C₃₁	—	2	8	no	—
49	C₄×C₃₁	—	2	2	no	—
50	Dic₃₁	—	2	8	no	—
51	Dic₃₁	—	4	4	no	—
52	C₂×#125	D₃₁	1	1	yes	characteristic
53	#387	—	31	4	no	—
54	#387	—	31	4	no	—
55	C₄×C₄⋊C₄	—	31	4	no	—
56	#376	—	31	2	no	—
57	C₂×C₃₁	C₄×#41	1	2	yes	—
58	C₂×C₃₁	#519	1	1	yes	characteristic
59	C₂×C₃₁	#552	1	4	yes	—
60	#125	Dic₃₁	1	8	yes	complemented
61	C₂×C₄⋊C₄	—	31	4	no	—
62	C₂×C₄⋊C₄	C₂×D₃₁	1	4	yes	—
63	C₂×C₄⋊C₄	C₂×D₃₁	1	2	yes	—
64	C₂×C₄²	—	31	4	no	—
65	C₂×C₄²	—	31	4	no	—
66	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
67	#95	—	31	2	no	—
68	#95	—	31	4	no	—
69	#95	—	31	2	no	—
70	#95	—	31	4	no	—
71	#95	—	31	4	no	—
72	C₃₁	#2371	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₄	—	31	4	no	—
74	C₂²×C₄	—	31	4	no	—
75	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
76	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
77	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
78	C₄⋊C₄	—	62	8	no	—
79	C₄⋊C₄	C₂×Dic₃₁	1	16	yes	—
80	C₄⋊C₄	C₂×Dic₃₁	1	8	yes	—
81	C₄²	—	62	8	no	—
82	C₄²	—	62	8	no	—
83	C₄²	C₂×Dic₃₁	1	4	yes	—
84	C₂³	C₂³×D₃₁	1	1	yes	characteristic
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	31	8	no	—
90	C₂×C₄	—	62	4	no	—
91	C₂×C₄	—	62	4	no	—
92	C₂×C₄	—	62	4	no	—
93	C₂×C₄	—	62	4	no	—
94	C₂×C₄	—	62	4	no	—
95	C₂×C₄	C₂²×Dic₃₁	1	4	yes	—
96	C₂×C₄	C₂²×Dic₃₁	1	2	yes	—
97	C₂×C₄	C₂²×Dic₃₁	1	8	yes	—
98	C₂²	#11758564	1	2	yes	—
99	C₂²	#41×D₃₁	1	4	yes	—
100	C₂²	C₂³×Dic₃₁	1	1	yes	characteristic
101	C₄	—	2	4	no	—
102	C₄	—	2	8	no	—
103	C₄	—	2	2	no	—
104	C₄	—	62	8	no	—
105	C₄	—	124	4	no	—
106	C₂	#41×Dic₃₁	1	2	yes	—
107	C₂	#14521527	1	1	yes	characteristic
108	C₂	#14521731	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14520935

C₂

yes

maximal

#14520935

C₂

yes

maximal

C₄⋊C₄×Dic₃₁

C₂

yes

maximal

#14520895

C₂

yes

maximal

C₂×C₃₁×#125

C₂

yes

maximal, characteristic

C₃₁×#125

C₄

yes

complemented

C₂×C₄⋊C₄×C₃₁

C₂²

yes

—

C₂×C₄⋊C₄×C₃₁

C₂²

yes

—

C₂×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂×C₄×Dic₃₁

C₂²

yes

—

C₂×C₄×Dic₃₁

C₂²

yes

—

C₃₁⋊#95

C₂²

yes

—

C₃₁⋊#95

C₂²

yes

—

C₃₁⋊#95

C₂²

yes

—

C₃₁⋊#95

C₂²

yes

—

C₃₁⋊#95

C₂²

yes

—

C₂²×C₄×C₃₁

C₂³

yes

characteristic

C₂²×C₄×C₃₁

C₂³

yes

—

C₂²×C₄×C₃₁

C₂³

yes

—

C₂²×Dic₃₁

C₂³

yes

—

C₂²×Dic₃₁

C₂³

yes

—

C₄⋊C₄×C₃₁

C₂×C₄

yes

—

C₄⋊C₄×C₃₁

C₂×C₄

yes

—

C₄²×C₃₁

C₂×C₄

yes

—

C₄⋊Dic₃₁

—

C₄×Dic₃₁

—

C₄×Dic₃₁

—

C₂³×C₃₁

C₂⁴

yes

characteristic

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂²×C₄

yes

—

C₂×C₄×C₃₁

C₂²×C₄

yes

—

C₂×C₄×C₃₁

C₂²×C₄

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

#41

yes

—

#2371

—

maximal, Sylow

C₂²×C₃₁

C₂³×C₄

yes

characteristic

C₂²×C₃₁

C₂×#41

yes

—

C₂²×C₃₁

2₋¹⁺⁴

yes

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

—

Dic₃₁

—

Dic₃₁

—

C₂×#125

D₃₁

yes

characteristic

#387

—

#387

—

C₄×C₄⋊C₄

—

#376

—

C₂×C₃₁

C₄×#41

yes

—

C₂×C₃₁

#519

yes

characteristic

C₂×C₃₁

#552

yes

—

#125

Dic₃₁

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₃₁

yes

—

C₂×C₄⋊C₄

C₂×D₃₁

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₃₁

yes

—

—

—

—

—

C₃₁

#2371

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₃₁

yes

characteristic

C₂²×C₄

C₂²×D₃₁

yes

—

C₂²×C₄

C₂²×D₃₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₃₁

yes

—

C₄⋊C₄

C₂×Dic₃₁

yes

—

C₄²

—

C₄²

—

C₄²

C₂×Dic₃₁

yes

—

C₂³

C₂³×D₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₃₁

yes

—

C₂×C₄

C₂²×Dic₃₁

yes

—

C₂×C₄

C₂²×Dic₃₁

yes

—

C₂²

#11758564

yes

—

C₂²

#41×D₃₁

yes

—

100

C₂²

C₂³×Dic₃₁

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

124

—

106

C₂

#41×Dic₃₁

yes

—

107

C₂

#14521527

yes

characteristic

108

C₂

#14521731

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₁
commutator	C₂²×C₃₁	C₂³×C₄
Fitting	C₂×C₃₁×#125	C₂
socle, prime radical, cosocle	C₂³×C₃₁	C₂⁴
hypercenter	C₂×#125	D₃₁
hypocenter	C₃₁	#2371
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₃₁

commutator

C₂²×C₃₁

C₂³×C₄

Fitting

C₂×C₃₁×#125

C₂

socle, prime radical, cosocle

C₂³×C₃₁

C₂⁴

D₃₁

C₃₁

G ▷ C₂²×C₃₁ ▷ C₃₁

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
6. C₃₁×#125	C₄	semidirect
60. #125	Dic₃₁	semidirect
72. C₃₁	#2371	semidirect

H ≅ G/N

type

6. C₃₁×#125

C₄

semidirect

60. #125

Dic₃₁

semidirect

72. C₃₁

#2371

semidirect

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

subgroup	index
#14520935	2
C₄⋊C₄×Dic₃₁	2
#14520895	2
C₂×C₃₁×#125	2
#2371	31

subgroup

index

#14520935

C₄⋊C₄×Dic₃₁

#14520895

C₂×C₃₁×#125

#2371

Subgroups — #16848817

Conjugacy classes of subgroups

Complements

Maximal subgroups