Group #16846676 — subgroups

Subgroups — #16846676

Order 3968.

252 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11758447	C₂	1	1	yes	maximal, characteristic
2	#14520915	C₂	1	1	yes	maximal, characteristic
3	#14520812	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₃₁	C₂²	1	2	yes	—
6	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	—
9	C₂×Dic₃₁⋊C₄	—	2	2	no	—
10	#11758447	—	2	2	no	—
11	#11758447	C₄	1	4	yes	complemented
12	C₄×C₈×C₃₁	—	2	2	no	—
13	C₃₁⋊#95	—	2	2	no	—
14	C₂²×C₄×C₃₁	D₄	1	2	yes	—
15	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₃₁	—	2	2	no	—
17	C₂²×Dic₃₁	—	2	2	no	—
18	C₂×C₈×C₃₁	—	2	2	no	—
19	C₂×C₈×C₃₁	—	2	2	no	—
20	C₂×C₈×C₃₁	Q₈	1	4	yes	—
21	C₄²×C₃₁	C₂×C₄	1	2	yes	—
22	C₄²×C₃₁	D₄	1	2	yes	—
23	C₄⋊Dic₃₁	—	2	2	no	—
24	C₄⋊Dic₃₁	—	2	4	no	—
25	C₄⋊Dic₃₁	C₂×C₄	1	4	yes	—
26	Dic₃₁⋊C₄	—	2	8	no	—
27	C₂³×C₃₁	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₁	—	2	4	no	—
29	C₂×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
30	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₃₁	C₂×Q₈	1	2	yes	—
33	C₂×C₄×C₃₁	#41	1	2	yes	—
34	C₂×Dic₃₁	—	2	4	no	—
35	C₂×Dic₃₁	—	4	4	no	—
36	C₂×Dic₃₁	—	4	2	no	—
37	C₂×Dic₃₁	—	4	4	no	—
38	C₈×C₃₁	—	2	4	no	—
39	#1991	—	31	1	no	maximal, Sylow
40	C₂²×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₃₁	#124	1	1	yes	characteristic
42	C₂²×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
43	C₂²×C₃₁	#135	1	4	yes	—
44	C₄×C₃₁	—	2	4	no	—
45	C₄×C₃₁	C₄×Q₈	1	2	yes	—
46	C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
47	Dic₃₁	—	4	4	no	—
48	Dic₃₁	—	8	2	no	—
49	C₂×#125	—	31	1	no	—
50	C₂×C₄×C₈	D₃₁	1	1	yes	characteristic
51	#382	—	31	1	no	—
52	#340	—	31	4	no	—
53	C₂×C₃₁	#391	1	1	yes	characteristic
54	C₂×C₃₁	#416	1	2	yes	—
55	C₂×C₃₁	#488	1	2	yes	—
56	C₂×C₃₁	#499	1	2	yes	—
57	C₂²×C₈	C₂×D₃₁	1	2	yes	—
58	#125	—	31	4	no	—
59	#125	—	62	2	no	—
60	C₂×C₄⋊C₄	—	31	2	no	—
61	C₂×C₄⋊C₄	—	31	2	no	—
62	C₂×C₄⋊C₄	—	62	2	no	—
63	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
64	C₄×C₈	—	2	2	no	—
65	#95	—	62	2	no	—
66	C₃₁	#1991	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	—	62	2	no	—
68	C₂²×C₄	—	62	2	no	—
69	C₂²×C₄	D₁₂₄	1	2	yes	—
70	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	Dic₆₂	1	4	yes	—
74	C₄⋊C₄	—	31	4	no	—
75	C₄⋊C₄	—	62	8	no	—
76	C₄⋊C₄	—	62	2	no	—
77	C₄⋊C₄	—	62	4	no	—
78	C₄²	C₄×D₃₁	1	2	yes	—
79	C₄²	C₂²⋊D₃₁	1	2	yes	—
80	C₂³	C₂×D₁₂₄	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	62	4	no	—
83	C₂×C₄	—	124	4	no	—
84	C₂×C₄	—	124	2	no	—
85	C₂×C₄	—	124	4	no	—
86	C₂×C₄	(C₂×D₃₁)⋊C₄	1	4	yes	—
87	C₂×C₄	C₂×Dic₆₂	1	2	yes	—
88	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
89	C₂×C₄	#92495	1	2	yes	—
90	C₂×C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
91	C₈	—	2	4	no	—
92	C₂²	#11758446	1	1	yes	characteristic
93	C₂²	#11758452	1	1	yes	characteristic
94	C₂²	#11758481	1	4	yes	—
95	C₂²	C₂×(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
96	C₄	—	2	4	no	—
97	C₄	—	124	4	no	—
98	C₄	—	248	2	no	—
99	C₄	C₄×Dic₆₂	1	2	yes	—
100	C₄	#11758501	1	2	yes	—
101	C₂	#14520955	1	1	yes	characteristic
102	C₂	#14521046	1	2	yes	—
103	C₂	#14521404	1	2	yes	—
104	C₂	#14521451	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11758447

C₂

yes

maximal, characteristic

#14520915

C₂

yes

maximal, characteristic

#14520812

C₂

yes

maximal

C₂×C₄×C₈×C₃₁

C₂

yes

maximal, characteristic

C₂²×C₈×C₃₁

C₂²

yes

—

C₂×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂×Dic₃₁⋊C₄

—

#11758447

—

#11758447

C₄

yes

complemented

C₄×C₈×C₃₁

—

C₃₁⋊#95

—

C₂²×C₄×C₃₁

D₄

yes

—

C₂²×C₄×C₃₁

C₂³

yes

characteristic

C₂²×Dic₃₁

—

C₂²×Dic₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

Q₈

yes

—

C₄²×C₃₁

C₂×C₄

yes

—

C₄²×C₃₁

D₄

yes

—

C₄⋊Dic₃₁

—

C₄⋊Dic₃₁

—

C₄⋊Dic₃₁

C₂×C₄

yes

—

Dic₃₁⋊C₄

—

C₂³×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂²⋊C₄

yes

—

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

C₂×Q₈

yes

—

C₂×C₄×C₃₁

#41

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₈×C₃₁

—

#1991

—

maximal, Sylow

C₂²×C₃₁

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₃₁

#124

yes

characteristic

C₂²×C₃₁

C₄⋊Q₈

yes

characteristic

C₂²×C₃₁

#135

yes

—

C₄×C₃₁

—

C₄×C₃₁

C₄×Q₈

yes

—

C₄×C₃₁

C₂²⋊Q₈

yes

—

Dic₃₁

—

Dic₃₁

—

C₂×#125

—

C₂×C₄×C₈

D₃₁

yes

characteristic

#382

—

#340

—

C₂×C₃₁

#391

yes

characteristic

C₂×C₃₁

#416

yes

—

C₂×C₃₁

#488

yes

—

C₂×C₃₁

#499

yes

—

C₂²×C₈

C₂×D₃₁

yes

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₃₁

yes

characteristic

C₄×C₈

—

#95

—

C₃₁

#1991

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₂₄

yes

—

C₂²×C₄

C₂²×D₃₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₆₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₄×D₃₁

yes

—

C₄²

C₂²⋊D₃₁

yes

—

C₂³

C₂×D₁₂₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

124

—

C₂×C₄

—

124

—

C₂×C₄

—

124

—

C₂×C₄

(C₂×D₃₁)⋊C₄

yes

—

C₂×C₄

C₂×Dic₆₂

yes

—

C₂×C₄

C₂×C₄×D₃₁

yes

characteristic

C₂×C₄

#92495

yes

—

C₂×C₄

C₂×C₂²⋊D₃₁

yes

characteristic

C₈

—

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×(C₂×D₃₁)⋊C₄

yes

characteristic

C₄

—

C₄

—

124

—

C₄

—

248

—

C₄

C₄×Dic₆₂

yes

—

100

C₄

#11758501

yes

—

101

C₂

#14520955

yes

characteristic

102

C₂

#14521046

yes

—

103

C₂

#14521404

yes

—

104

C₂

#14521451

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₂₄
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₂×C₄×C₈×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂×D₄
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	C₂×C₄×C₈	D₃₁
hypocenter	C₃₁	#1991
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₁₂₄

commutator

C₂×C₄×C₃₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₁

Fitting

C₂×C₄×C₈×C₃₁

C₂

socle, prime radical

C₂³×C₃₁

C₂×D₄

cosocle

C₂²×C₄×C₃₁

C₂³

hypercenter

C₂×C₄×C₈

D₃₁

hypocenter

C₃₁

#1991

LCS

G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
11. #11758447	C₄	semidirect
66. C₃₁	#1991	semidirect

H ≅ G/N

type

11. #11758447

C₄

semidirect

66. C₃₁

#1991

semidirect

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

subgroup	index
C₂×#11758447	2
#14520915	2
#14520812	2
C₂×C₄×C₈×C₃₁	2
#1991	31

subgroup

index

C₂×C₄×C₈×C₃₁

Subgroups — #16846676

Conjugacy classes of subgroups

Complements

Maximal subgroups