Group #16844607 — subgroups

Subgroups — #16844607

Order 3968.

152 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14521176	C₂	1	2	yes	maximal
2	C₄×Dic₁₂₄	C₂	1	1	yes	maximal, characteristic
3	#14520779	C₂	1	2	yes	maximal
4	C₈×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₂₄	C₄	1	1	yes	characteristic
7	C₄×Dic₆₂	C₂²	1	2	yes	—
8	C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
9	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	#11758406	C₄	1	1	yes	characteristic
11	#11758404	C₄	1	2	yes	—
12	#11758403	—	2	2	no	—
13	Dic₃₁⋊C₈	—	2	2	no	—
14	C₄×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×Dic₆₂	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₃₁	—	2	2	no	—
18	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₃₁	C₂³	1	1	yes	characteristic
21	C₄⋊Dic₃₁	C₂×C₄	1	2	yes	—
22	Dic₃₁⋊C₄	—	2	2	no	—
23	C₄×Dic₃₁	—	2	2	no	—
24	C₂×C₃₁⋊C₈	—	2	1	no	—
25	C₂×C₃₁⋊C₈	D₄	1	1	yes	characteristic
26	C₂×C₃₁⋊C₈	D₄	1	1	yes	characteristic
27	Dic₁₂₄	—	2	2	no	—
28	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₃₁	#41	1	1	yes	characteristic
31	C₂×Dic₃₁	—	2	2	no	—
32	C₂×Dic₃₁	—	2	2	no	—
33	Dic₆₂	—	2	2	no	—
34	Dic₆₂	—	2	2	no	—
35	C₈×C₃₁	—	2	1	no	—
36	C₈×C₃₁	—	4	2	no	—
37	C₈×C₃₁	M₁₆	1	2	yes	—
38	C₃₁⋊C₈	—	2	2	no	—
39	C₃₁⋊C₈	—	2	1	no	—
40	C₃₁⋊C₈	Q₁₆	1	2	yes	complemented
41	#1591	—	31	1	no	maximal, Sylow
42	C₂²×C₃₁	C₄×D₄	1	1	yes	characteristic
43	C₄×C₃₁	—	2	1	no	—
44	C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
45	C₄×C₃₁	#131	1	1	yes	characteristic
46	C₄×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
47	C₄×C₃₁	#135	1	1	yes	characteristic
48	Dic₃₁	—	4	2	no	—
49	Dic₃₁	—	4	2	no	—
50	#446	—	31	2	no	—
51	C₄×Q₁₆	—	31	1	no	—
52	#335	D₃₁	1	1	yes	characteristic
53	Q₈⋊C₈	—	31	2	no	—
54	C₈²	—	31	1	no	—
55	C₂×C₃₁	#436	1	1	yes	characteristic
56	C₂×C₃₁	C₄×Q₁₆	1	1	yes	characteristic
57	C₂×C₃₁	#443	1	1	yes	characteristic
58	C₂×Q₁₆	—	31	1	no	—
59	C₄×Q₈	—	31	2	no	—
60	#107	—	31	1	no	—
61	C₄⋊C₈	—	62	2	no	—
62	C₄⋊C₈	C₂×D₃₁	1	2	yes	—
63	#103	—	31	2	no	—
64	#97	—	62	2	no	—
65	C₄×C₈	—	31	1	no	—
66	C₄×C₈	—	31	1	no	—
67	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
68	C₃₁	#1591	1	1	yes	characteristic, complemented, Sylow
69	C₂×Q₈	—	31	2	no	—
70	Q₁₆	—	62	2	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	31	1	no	—
73	C₂×C₈	—	31	1	no	—
74	C₂×C₈	—	62	1	no	—
75	C₂×C₈	C₄×D₃₁	1	1	yes	characteristic
76	C₂×C₈	C₄×D₃₁	1	1	yes	characteristic
77	C₄⋊C₄	—	31	2	no	—
78	C₄⋊C₄	—	62	2	no	—
79	C₄²	—	62	2	no	—
80	C₄²	C₂²×D₃₁	1	1	yes	characteristic
81	Q₈	—	62	2	no	—
82	Q₈	—	62	2	no	—
83	C₂×C₄	—	62	2	no	—
84	C₂×C₄	—	62	2	no	—
85	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
86	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
87	C₂×C₄	#92499	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	4	2	no	—
90	C₈	—	31	2	no	—
91	C₈	—	62	2	no	—
92	C₈	—	62	1	no	—
93	C₈	#92469	1	2	yes	—
94	C₂²	#11758470	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	124	2	no	—
97	C₄	—	124	2	no	—
98	C₄	C₂×#92469	1	1	yes	characteristic
99	C₄	#11758484	1	1	yes	characteristic
100	C₄	#11758489	1	1	yes	characteristic
101	C₄	Q₁₆×D₃₁	1	1	yes	characteristic
102	C₂	#14521126	1	1	yes	characteristic
103	C₂	#14521143	1	1	yes	characteristic
104	C₂	#14521165	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14521176

C₂

yes

maximal

C₄×Dic₁₂₄

C₂

yes

maximal, characteristic

#14520779

C₂

yes

maximal

C₈×C₃₁⋊C₈

C₂

yes

maximal, characteristic

C₃₁×#335

C₂

yes

maximal, characteristic

C₂×Dic₁₂₄

C₄

yes

characteristic

C₄×Dic₆₂

C₂²

yes

—

C₃₁×C₄⋊C₈

C₂²

yes

—

C₄×C₈×C₃₁

C₂²

yes

characteristic

#11758406

C₄

yes

characteristic

#11758404

C₄

yes

—

#11758403

—

Dic₃₁⋊C₈

—

C₄×C₃₁⋊C₈

C₂²

yes

characteristic

C₄×C₃₁⋊C₈

C₂²

yes

characteristic

C₂×Dic₆₂

C₂×C₄

yes

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

C₂×C₄

yes

characteristic

C₂×C₈×C₃₁

C₂×C₄

yes

characteristic

C₄²×C₃₁

C₂³

yes

characteristic

C₄⋊Dic₃₁

C₂×C₄

yes

—

Dic₃₁⋊C₄

—

C₄×Dic₃₁

—

C₂×C₃₁⋊C₈

—

C₂×C₃₁⋊C₈

D₄

yes

characteristic

C₂×C₃₁⋊C₈

D₄

yes

characteristic

Dic₁₂₄

—

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

#41

yes

characteristic

C₂×Dic₃₁

—

C₂×Dic₃₁

—

Dic₆₂

—

Dic₆₂

—

C₈×C₃₁

—

C₈×C₃₁

—

C₈×C₃₁

M₁₆

yes

—

C₃₁⋊C₈

—

C₃₁⋊C₈

—

C₃₁⋊C₈

Q₁₆

yes

complemented

#1591

—

maximal, Sylow

C₂²×C₃₁

C₄×D₄

yes

characteristic

C₄×C₃₁

—

C₄×C₃₁

C₂×M₁₆

yes

characteristic

C₄×C₃₁

#131

yes

characteristic

C₄×C₃₁

C₂×Q₁₆

yes

characteristic

C₄×C₃₁

#135

yes

characteristic

Dic₃₁

—

Dic₃₁

—

#446

—

C₄×Q₁₆

—

#335

D₃₁

yes

characteristic

Q₈⋊C₈

—

C₈²

—

C₂×C₃₁

#436

yes

characteristic

C₂×C₃₁

C₄×Q₁₆

yes

characteristic

C₂×C₃₁

#443

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₃₁

yes

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₃₁

yes

characteristic

C₃₁

#1591

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₃₁

yes

characteristic

C₂×C₈

C₄×D₃₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₃₁

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₃₁

yes

characteristic

C₂×C₄

D₄×D₃₁

yes

characteristic

C₂×C₄

#92499

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

C₈

#92469

yes

—

C₂²

#11758470

yes

characteristic

C₄

—

C₄

—

124

—

C₄

—

124

—

C₄

yes

C₄

yes

100

C₄

#11758489

yes

characteristic

101

C₄

Q₁₆×D₃₁

yes

characteristic

102

C₂

#14521126

yes

characteristic

103

C₂

#14521143

yes

characteristic

104

C₂

#14521165

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₃₁
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₄²	C₂²×D₃₁
Fitting	C₃₁×#335	C₂
socle, prime radical	C₂²×C₃₁	C₄×D₄
cosocle	C₄²×C₃₁	C₂³
hypercenter	#335	D₃₁
hypocenter	C₃₁	#1591
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

subgroup

G/H

center

C₂×C₄

D₄×D₃₁

commutator

C₂×C₄×C₃₁

C₂²×C₄

Frattini

C₄²

C₂²×D₃₁

Fitting

C₃₁×#335

C₂

socle, prime radical

C₂²×C₃₁

C₄×D₄

cosocle

C₄²×C₃₁

C₂³

D₃₁

C₃₁

G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

N	H ≅ G/N	type
40. C₃₁⋊C₈	Q₁₆	semidirect
68. C₃₁	#1591	semidirect

H ≅ G/N

type

40. C₃₁⋊C₈

Q₁₆

semidirect

68. C₃₁

#1591

semidirect

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

subgroup	index
#14521176	2
C₄×Dic₁₂₄	2
#14520779	2
C₈×C₃₁⋊C₈	2
C₃₁×#335	2
#1591	31

subgroup

index

#14521176

C₄×Dic₁₂₄

#14520779

C₈×C₃₁⋊C₈

C₃₁×#335

#1591

Subgroups — #16844607

Conjugacy classes of subgroups

Complements

Maximal subgroups