Group #16845040 — subgroups

Subgroups — #16845040

Order 3968.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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	C₃₁⋊#564	C₂	1	1	yes	maximal, characteristic
2	#14521458	C₂	1	2	yes	maximal
3	#14521419	C₂	1	1	yes	maximal, characteristic
4	#14520790	C₂	1	2	yes	maximal
5	C₃₁×#330	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#125	C₂²	1	1	yes	characteristic
7	#11758467	—	2	2	no	—
8	#11758466	—	2	2	no	—
9	#11758466	—	2	2	no	—
10	#11758447	C₂²	1	2	yes	—
11	#11758446	C₂²	1	1	yes	characteristic
12	C₃₁×#97	C₂²	1	2	yes	—
13	#11758406	—	2	2	no	—
14	#11758405	—	2	2	no	—
15	#11758398	—	2	2	no	—
16	#11758391	C₂²	1	1	yes	characteristic
17	C₂×Dic₆₂	—	2	1	no	—
18	C₂×C₈×C₃₁	—	2	2	no	—
19	C₄⋊C₄×C₃₁	—	2	2	no	—
20	C₄⋊C₄×C₃₁	D₄	1	2	yes	—
21	C₄²×C₃₁	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₃₁	—	2	2	no	—
23	C₄⋊Dic₃₁	—	2	2	no	—
24	C₄⋊Dic₃₁	D₄	1	2	yes	—
25	C₄⋊Dic₃₁	D₄	1	2	yes	—
26	Dic₃₁⋊C₄	—	2	2	no	—
27	Dic₃₁⋊C₄	—	2	2	no	—
28	Dic₃₁⋊C₄	—	2	2	no	—
29	Dic₃₁⋊C₄	—	2	2	no	—
30	C₄×Dic₃₁	—	2	2	no	—
31	C₂×C₃₁⋊C₈	—	2	1	no	—
32	C₂×C₄×C₃₁	—	2	2	no	—
33	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
35	C₂×Dic₃₁	—	2	2	no	—
36	C₂×Dic₃₁	—	2	2	no	—
37	C₂×Dic₃₁	—	4	1	no	—
38	Dic₆₂	—	4	2	no	—
39	C₈×C₃₁	—	2	4	no	—
40	C₃₁⋊C₈	—	4	1	no	—
41	#1663	—	31	1	no	maximal, Sylow
42	C₂²×C₃₁	#120	1	1	yes	characteristic
43	C₄×C₃₁	—	2	1	no	—
44	C₄×C₃₁	—	2	2	no	—
45	C₄×C₃₁	—	4	2	no	—
46	Dic₃₁	—	4	2	no	—
47	Dic₃₁	—	4	2	no	—
48	Dic₃₁	—	8	1	no	—
49	#564	—	31	1	no	—
50	#501	—	31	2	no	—
51	#491	—	31	1	no	—
52	#330	—	31	2	no	—
53	#330	D₃₁	1	1	yes	characteristic
54	C₂×C₃₁	#454	1	1	yes	characteristic
55	C₂×C₃₁	#456	1	2	yes	—
56	C₄⋊Q₈	—	31	1	no	—
57	#125	—	31	2	no	—
58	#125	—	62	2	no	—
59	#125	—	62	2	no	—
60	#125	—	62	2	no	—
61	#125	C₂×D₃₁	1	1	yes	characteristic
62	#107	—	62	2	no	—
63	#106	—	62	2	no	—
64	#103	—	62	2	no	—
65	#97	—	31	1	no	—
66	#97	C₂×D₃₁	1	2	yes	—
67	C₃₁	#1663	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₈	—	62	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	62	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	31	2	no	—
73	C₄⋊C₄	—	31	2	no	—
74	C₄⋊C₄	—	62	2	no	—
75	C₄⋊C₄	—	62	2	no	—
76	C₄⋊C₄	—	62	2	no	—
77	C₄⋊C₄	—	62	2	no	—
78	C₄⋊C₄	—	62	2	no	—
79	C₄⋊C₄	—	62	2	no	—
80	C₄⋊C₄	D₁₂₄	1	2	yes	—
81	C₄²	—	62	2	no	—
82	C₄²	C₂²×D₃₁	1	1	yes	characteristic
83	Q₈	—	124	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	62	2	no	—
86	C₂×C₄	—	62	2	no	—
87	C₂×C₄	—	124	1	no	—
88	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
89	C₂×C₄	D₄×D₃₁	1	2	yes	—
90	C₈	—	2	4	no	—
91	C₈	—	124	1	no	—
92	C₂²	#11758459	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	124	2	no	—
97	C₄	—	124	2	no	—
98	C₄	—	248	1	no	—
99	C₂	#14521224	1	1	yes	characteristic
100	C₂	#14521233	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃₁⋊#564

C₂

yes

maximal, characteristic

#14521458

C₂

yes

maximal

#14521419

C₂

yes

maximal, characteristic

#14520790

C₂

yes

maximal

C₃₁×#330

C₂

yes

maximal, characteristic

C₃₁×#125

C₂²

yes

—

—

—

C₂²

yes

—

#11758446

C₂²

yes

characteristic

C₃₁×#97

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×Dic₆₂

—

C₂×C₈×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

D₄

yes

—

C₄²×C₃₁

C₂³

yes

characteristic

C₄⋊Dic₃₁

—

C₄⋊Dic₃₁

—

C₄⋊Dic₃₁

D₄

yes

—

C₄⋊Dic₃₁

D₄

yes

—

Dic₃₁⋊C₄

—

Dic₃₁⋊C₄

—

Dic₃₁⋊C₄

—

Dic₃₁⋊C₄

—

C₄×Dic₃₁

—

C₂×C₃₁⋊C₈

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

Dic₆₂

—

C₈×C₃₁

—

C₃₁⋊C₈

—

—

C₂²×C₃₁

yes

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

—

Dic₃₁

—

Dic₃₁

—

Dic₃₁

—

—

—

—

—

D₃₁

yes

C₂×C₃₁

yes

C₂×C₃₁

yes

—

C₄⋊Q₈

—

—

—

—

—

C₂×D₃₁

yes

—

—

—

—

C₂×D₃₁

yes

—

C₃₁

#1663

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₂₄

yes

—

C₄²

—

C₄²

C₂²×D₃₁

yes

characteristic

Q₈

—

124

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

124

—

C₂×C₄

C₂×D₁₂₄

yes

characteristic

C₂×C₄

D₄×D₃₁

yes

—

C₈

—

C₈

—

124

—

C₂²

#11758459

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

124

—

C₄

—

124

—

C₄

—

248

—

C₂

#14521224

yes

characteristic

100

C₂

#14521233

yes

—

	subgroup	G/H
center	C₂²	#11758459
commutator, cosocle	C₄²×C₃₁	C₂³
Frattini	C₄²	C₂²×D₃₁
Fitting	C₃₁×#330	C₂
socle, prime radical	C₂²×C₃₁	#120
hypercenter	#330	D₃₁
hypocenter	C₃₁	#1663
LCS	G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#11758459

commutator, cosocle

C₄²×C₃₁

C₂³

Frattini

C₄²

C₂²×D₃₁

Fitting

C₃₁×#330

C₂

C₂²×C₃₁

D₃₁

C₃₁

G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
67. C₃₁	#1663	semidirect

H ≅ G/N

type

67. C₃₁

#1663

semidirect

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

subgroup	index
C₃₁⋊#564	2
#14521458	2
#14521419	2
#14520790	2
C₃₁×#330	2
#1663	31

subgroup

index

C₃₁⋊#564

C₃₁×#330

Subgroups — #16845040

Conjugacy classes of subgroups

Complements

Maximal subgroups