Group #14520976 — subgroups

Subgroups — #14520976

Order 1984.

170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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×(C₂×D₃₁)⋊C₄	C₂	1	2	yes	maximal
2	C₂×(C₂×D₃₁)⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁⋊#95	C₂	1	2	yes	maximal, complemented
6	C₂³×D₃₁	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₃₁	C₂²	1	2	yes	—
8	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₁	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃₁	C₂²	1	2	yes	—
11	(C₂×D₃₁)⋊C₄	—	2	4	no	—
12	(C₂×D₃₁)⋊C₄	—	2	2	no	—
13	C₄⋊Dic₃₁	—	2	2	no	—
14	C₂³×C₃₁	C₂³	1	1	yes	characteristic
15	C₂²×D₃₁	—	2	1	no	—
16	C₂²×D₃₁	—	2	2	no	—
17	C₂²×D₃₁	—	2	2	no	—
18	C₂²×D₃₁	—	2	1	no	—
19	C₂²×D₃₁	D₄	1	2	yes	—
20	C₂×C₄×C₃₁	—	2	2	no	—
21	C₂×C₄×C₃₁	—	2	2	no	—
22	C₂×C₄×C₃₁	—	2	2	no	—
23	C₂×C₄×C₃₁	—	2	2	no	—
24	C₂×C₄×C₃₁	D₄	1	2	yes	—
25	C₂×Dic₃₁	—	2	2	no	—
26	C₂×Dic₃₁	—	2	1	no	—
27	C₂×Dic₃₁	—	2	2	no	—
28	C₂×Dic₃₁	—	2	2	no	—
29	C₂×Dic₃₁	—	2	2	no	—
30	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₃₁	#41	1	2	yes	—
33	C₂²×C₃₁	#41	1	2	yes	—
34	C₂²×C₃₁	#41	1	1	yes	characteristic
35	C₂×D₃₁	—	2	2	no	—
36	C₂×D₃₁	—	2	4	no	—
37	C₂×D₃₁	—	4	1	no	—
38	C₂×D₃₁	—	4	1	no	—
39	C₂×D₃₁	—	4	2	no	—
40	C₄×C₃₁	—	2	2	no	—
41	C₄×C₃₁	—	4	2	no	—
42	Dic₃₁	—	4	2	no	—
43	Dic₃₁	—	4	1	no	—
44	#397	—	31	1	no	maximal, Sylow
45	C₂×C₃₁	#121	1	1	yes	characteristic
46	C₂×C₃₁	#123	1	2	yes	—
47	C₂×C₃₁	#123	1	1	yes	characteristic
48	C₂×C₃₁	#124	1	1	yes	characteristic
49	C₂×C₃₁	#126	1	2	yes	—
50	D₃₁	—	4	2	no	—
51	C₂×C₄⋊C₄	—	31	1	no	—
52	C₂×C₂²⋊C₄	—	31	2	no	—
53	C₂×C₂²⋊C₄	—	31	1	no	—
54	#95	—	31	2	no	—
55	#95	D₃₁	1	1	yes	characteristic, complemented
56	C₃₁	#397	1	1	yes	characteristic, complemented, Sylow
57	C₂⁴	—	31	1	no	—
58	C₂²×C₄	—	31	1	no	—
59	C₂²×C₄	—	31	2	no	—
60	C₂²×C₄	C₂×D₃₁	1	2	yes	—
61	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
62	C₄⋊C₄	—	62	2	no	—
63	C₂²⋊C₄	—	62	4	no	—
64	C₂²⋊C₄	—	62	2	no	—
65	C₂³	—	31	2	no	—
66	C₂³	—	62	1	no	—
67	C₂³	—	62	2	no	—
68	C₂³	—	62	2	no	—
69	C₂³	—	62	1	no	—
70	C₂³	C₂²×D₃₁	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	62	1	no	—
76	C₂×C₄	—	62	2	no	—
77	C₂×C₄	—	62	2	no	—
78	C₂×C₄	—	62	2	no	—
79	C₂×C₄	—	62	2	no	—
80	C₂×C₄	D₁₂₄	1	2	yes	—
81	C₂²	—	62	4	no	—
82	C₂²	—	62	2	no	—
83	C₂²	—	124	1	no	—
84	C₂²	—	124	1	no	—
85	C₂²	—	124	2	no	—
86	C₂²	C₂×D₁₂₄	1	1	yes	characteristic
87	C₂²	#92495	1	2	yes	—
88	C₂²	D₄×D₃₁	1	1	yes	characteristic
89	C₂²	#92497	1	2	yes	—
90	C₂²	#92499	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	4	2	no	—
93	C₄	—	124	1	no	—
94	C₄	—	124	2	no	—
95	C₂	—	124	2	no	—
96	C₂	#11758452	1	1	yes	characteristic
97	C₂	#11758460	1	2	yes	—
98	C₂	#11758463	1	1	yes	characteristic
99	C₂	#11758472	1	1	yes	characteristic
100	C₂	#11758475	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×(C₂×D₃₁)⋊C₄

C₂

yes

maximal

C₂×(C₂×D₃₁)⋊C₄

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₃₁

C₂

yes

maximal, characteristic, complemented

C₃₁×#95

C₂

yes

maximal, characteristic, complemented

C₃₁⋊#95

C₂

yes

maximal, complemented

C₂³×D₃₁

C₂²

yes

characteristic

C₂²×C₄×C₃₁

C₂²

yes

—

C₂²×C₄×C₃₁

C₂²

yes

characteristic

C₂²×Dic₃₁

C₂²

yes

characteristic

C₂²×Dic₃₁

C₂²

yes

—

(C₂×D₃₁)⋊C₄

—

(C₂×D₃₁)⋊C₄

—

C₄⋊Dic₃₁

—

C₂³×C₃₁

C₂³

yes

characteristic

C₂²×D₃₁

—

C₂²×D₃₁

—

C₂²×D₃₁

—

C₂²×D₃₁

—

C₂²×D₃₁

D₄

yes

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

D₄

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂²×C₃₁

C₂×D₄

yes

characteristic

C₂²×C₃₁

C₂×D₄

yes

characteristic

C₂²×C₃₁

#41

yes

—

C₂²×C₃₁

#41

yes

—

C₂²×C₃₁

#41

yes

characteristic

C₂×D₃₁

—

C₂×D₃₁

—

C₂×D₃₁

—

C₂×D₃₁

—

C₂×D₃₁

—

C₄×C₃₁

—

C₄×C₃₁

—

Dic₃₁

—

Dic₃₁

—

—

C₂×C₃₁

yes

C₂×C₃₁

yes

—

C₂×C₃₁

yes

C₂×C₃₁

yes

C₂×C₃₁

yes

—

D₃₁

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

#95

D₃₁

yes

characteristic, complemented

C₃₁

#397

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₃₁

yes

—

C₂²×C₄

C₂×D₃₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²×D₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₂₄

yes

—

C₂²

—

C₂²

—

C₂²

—

124

—

C₂²

—

124

—

C₂²

—

124

—

C₂²

C₂×D₁₂₄

yes

characteristic

C₂²

#92495

yes

—

C₂²

D₄×D₃₁

yes

characteristic

C₂²

#92497

yes

—

C₂²

#92499

yes

characteristic

C₄

—

C₄

—

C₄

—

124

—

C₄

—

124

—

C₂

—

124

—

C₂

#11758452

yes

characteristic

C₂

#11758460

yes

—

C₂

yes

C₂

yes

100

C₂

#11758475

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₁
commutator, socle, cosocle	C₂³×C₃₁	C₂³
Fitting	C₃₁×#95	C₂
prime radical	C₂³×D₃₁	C₂²
hypercenter	#95	D₃₁
hypocenter	C₃₁	#397
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×D₃₁

commutator, socle, cosocle

C₂³×C₃₁

C₂³

Fitting

C₃₁×#95

C₂

prime radical

C₂³×D₃₁

C₂²

D₃₁

C₃₁

G ▷ C₂³×C₃₁ ▷ C₃₁

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
3. C₂×C₄⋊Dic₃₁	C₂	semidirect
4. C₃₁×#95	C₂	semidirect
5. C₃₁⋊#95	C₂	semidirect
55. #95	D₃₁	semidirect
56. C₃₁	#397	semidirect

H ≅ G/N

type

3. C₂×C₄⋊Dic₃₁

C₂

semidirect

4. C₃₁×#95

C₂

semidirect

5. C₃₁⋊#95

C₂

semidirect

55. #95

D₃₁

semidirect

56. C₃₁

#397

semidirect

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

subgroup	index
C₂×(C₂×D₃₁)⋊C₄	2
C₂×C₄⋊Dic₃₁	2
C₃₁×#95	2
C₃₁⋊#95	2
#397	31

subgroup

index

C₂×(C₂×D₃₁)⋊C₄

C₂×C₄⋊Dic₃₁

C₃₁×#95

C₃₁⋊#95

#397

Subgroups — #14520976

Conjugacy classes of subgroups

Complements

Maximal subgroups