Group #16845846 — subgroups

Subgroups — #16845846

Order 3968.

224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11758391	C₂	1	1	yes	maximal, characteristic
2	#14520915	C₂	1	1	yes	maximal, characteristic
3	#14520811	C₂	1	4	yes	maximal
4	C₃₁×#384	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
6	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
7	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	—
9	C₂²×C₃₁⋊C₈	C₂²	1	2	yes	—
10	C₃₁⋊#95	—	2	2	no	—
11	#11758391	C₄	1	4	yes	complemented
12	C₂²×C₄×C₃₁	—	2	2	no	—
13	C₂²×C₄×C₃₁	D₄	1	2	yes	—
14	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
15	C₂²×Dic₃₁	—	2	2	no	—
16	C₄⋊C₄×C₃₁	—	2	4	no	—
17	C₄⋊C₄×C₃₁	—	4	4	no	—
18	C₄²×C₃₁	C₂×C₄	1	2	yes	—
19	C₄²×C₃₁	Q₈	1	2	yes	—
20	C₄⋊Dic₃₁	—	2	4	no	—
21	C₂×C₃₁⋊C₈	—	2	2	no	—
22	C₂×C₃₁⋊C₈	—	2	2	no	—
23	C₂×C₃₁⋊C₈	C₂×C₄	1	4	yes	—
24	C₂³×C₃₁	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₃₁	—	2	2	no	—
26	C₂×C₄×C₃₁	—	2	2	no	—
27	C₂×C₄×C₃₁	—	4	2	no	—
28	C₂×C₄×C₃₁	—	4	4	no	—
29	C₂×C₄×C₃₁	C₄⋊C₄	1	4	yes	—
30	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₃₁	#41	1	2	yes	—
33	C₂×C₄×C₃₁	#41	1	2	yes	—
34	C₂×Dic₃₁	—	4	2	no	—
35	C₂×Dic₃₁	—	4	2	no	—
36	C₂×Dic₃₁	—	4	2	no	—
37	C₃₁⋊C₈	—	2	4	no	—
38	#1836	—	31	1	no	maximal, Sylow
39	C₂²×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₃₁	#124	1	1	yes	characteristic
41	C₂²×C₃₁	#124	1	1	yes	characteristic
42	C₂²×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
43	C₂²×C₃₁	#137	1	2	yes	—
44	C₄×C₃₁	—	2	4	no	—
45	C₄×C₃₁	—	8	2	no	—
46	C₄×C₃₁	#117	1	2	yes	—
47	C₄×C₃₁	#125	1	2	yes	—
48	Dic₃₁	—	8	2	no	—
49	C₂×#97	—	31	1	no	—
50	#384	D₃₁	1	1	yes	characteristic
51	#382	—	31	1	no	—
52	#340	—	31	4	no	—
53	C₂×C₃₁	#382	1	1	yes	characteristic
54	C₂×C₃₁	#428	1	2	yes	—
55	C₂×C₃₁	#489	1	2	yes	—
56	C₂×C₃₁	#490	1	1	yes	characteristic
57	C₂×C₃₁	#491	1	1	yes	characteristic
58	C₂²×C₈	—	31	2	no	—
59	C₂×C₄⋊C₄	—	2	2	no	—
60	C₂×C₄⋊C₄	—	31	2	no	—
61	C₂×C₄⋊C₄	C₂×D₃₁	1	2	yes	—
62	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
63	#97	—	31	4	no	—
64	#95	—	62	2	no	—
65	C₃₁	#1836	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	2	2	no	—
67	C₂²×C₄	—	62	2	no	—
68	C₂²×C₄	C₂²⋊D₃₁	1	2	yes	—
69	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
70	C₂×C₈	—	31	4	no	—
71	C₂×C₈	—	62	2	no	—
72	C₂×C₈	—	62	2	no	—
73	C₄⋊C₄	—	2	4	no	—
74	C₄⋊C₄	—	4	4	no	—
75	C₄⋊C₄	—	62	4	no	—
76	C₄²	Dic₆₂	1	2	yes	—
77	C₄²	C₄×D₃₁	1	2	yes	—
78	C₂³	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	4	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	124	2	no	—
84	C₂×C₄	—	124	2	no	—
85	C₂×C₄	—	124	2	no	—
86	C₂×C₄	Dic₃₁⋊C₄	1	4	yes	—
87	C₂×C₄	C₂×Dic₆₂	1	1	yes	characteristic
88	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
89	C₂×C₄	#92497	1	2	yes	—
90	C₂×C₄	#92499	1	2	yes	—
91	C₈	—	62	4	no	—
92	C₂²	C₂×Dic₃₁⋊C₄	1	1	yes	characteristic
93	C₂²	#11758509	1	2	yes	—
94	C₂²	#11758513	1	1	yes	characteristic
95	C₂²	#11758519	1	2	yes	—
96	C₂²	#11758524	1	1	yes	characteristic
97	C₄	—	2	4	no	—
98	C₄	—	8	2	no	—
99	C₄	—	248	2	no	—
100	C₄	#11758467	1	2	yes	—
101	C₄	#11758469	1	2	yes	—
102	C₂	#14520914	1	1	yes	characteristic
103	C₂	#14521089	1	2	yes	—
104	C₂	#14521411	1	2	yes	—
105	C₂	#14521413	1	1	yes	characteristic
106	C₂	#14521417	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11758391

C₂

yes

maximal, characteristic

#14520915

C₂

yes

maximal, characteristic

#14520811

C₂

yes

maximal

C₃₁×#384

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

C₂²

yes

—

C₂×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂²×C₃₁⋊C₈

C₂²

yes

—

C₃₁⋊#95

—

#11758391

C₄

yes

complemented

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

D₄

yes

—

C₂²×C₄×C₃₁

C₂³

yes

characteristic

C₂²×Dic₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄²×C₃₁

C₂×C₄

yes

—

C₄²×C₃₁

Q₈

yes

—

C₄⋊Dic₃₁

—

C₂×C₃₁⋊C₈

—

C₂×C₃₁⋊C₈

—

C₂×C₃₁⋊C₈

C₂×C₄

yes

—

C₂³×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₄⋊C₄

yes

—

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₁

#41

yes

—

C₂×C₄×C₃₁

#41

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₃₁⋊C₈

—

#1836

—

maximal, Sylow

C₂²×C₃₁

C₂×C₄⋊C₄

yes

C₂²×C₃₁

yes

C₂²×C₃₁

yes

C₂²×C₃₁

yes

—

C₂²×C₃₁

#137

yes

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

#117

yes

—

C₄×C₃₁

#125

yes

—

Dic₃₁

—

C₂×#97

—

#384

D₃₁

yes

characteristic

#382

—

#340

—

C₂×C₃₁

#382

yes

characteristic

C₂×C₃₁

#428

yes

—

C₂×C₃₁

#489

yes

—

C₂×C₃₁

yes

C₂×C₃₁

yes

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₃₁

yes

—

C₂×C₄²

C₂×D₃₁

yes

characteristic

#97

—

#95

—

C₃₁

#1836

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₃₁

yes

—

C₂²×C₄

C₂²×D₃₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Dic₆₂

yes

—

C₄²

C₄×D₃₁

yes

—

C₂³

C₂×C₂²⋊D₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

124

—

C₂×C₄

—

124

—

C₂×C₄

—

124

—

C₂×C₄

Dic₃₁⋊C₄

yes

—

C₂×C₄

C₂×Dic₆₂

yes

characteristic

C₂×C₄

C₂×C₄×D₃₁

yes

characteristic

C₂×C₄

#92497

yes

—

C₂×C₄

#92499

yes

—

C₈

—

C₂²

C₂×Dic₃₁⋊C₄

yes

characteristic

C₂²

#11758509

yes

—

C₂²

#11758513

yes

characteristic

C₂²

#11758519

yes

—

C₂²

#11758524

yes

characteristic

C₄

—

C₄

—

C₄

—

248

—

100

C₄

#11758467

yes

—

101

C₄

#11758469

yes

—

102

C₂

#14520914

yes

characteristic

103

C₂

#14521089

yes

—

104

C₂

#14521411

yes

—

105

C₂

#14521413

yes

characteristic

106

C₂

#14521417

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₃₁
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₃₁×#384	C₂
socle, prime radical	C₂³×C₃₁	C₂×D₄
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	#384	D₃₁
hypocenter	C₃₁	#1836
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₃₁

commutator

C₂×C₄×C₃₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₁

Fitting

C₃₁×#384

C₂

socle, prime radical

C₂³×C₃₁

C₂×D₄

cosocle

C₂²×C₄×C₃₁

C₂³

D₃₁

C₃₁

G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
11. #11758391	C₄	semidirect
65. C₃₁	#1836	semidirect

H ≅ G/N

type

11. #11758391

C₄

semidirect

65. C₃₁

#1836

semidirect

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

subgroup	index
C₂×#11758391	2
#14520915	2
#14520811	2
C₃₁×#384	2
#1836	31

subgroup

index

C₃₁×#384

Subgroups — #16845846

Conjugacy classes of subgroups

Complements

Maximal subgroups