Group #16845397 — subgroups

Subgroups — #16845397

Order 3968.

328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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	C₂×#11758403	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₃₁	C₂	1	2	yes	maximal
4	#14520895	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₃₁	C₂²	1	2	yes	—
10	C₂²×C₃₁⋊C₈	C₂²	1	2	yes	—
11	C₄×C₈×C₃₁	C₄	1	4	yes	complemented
12	C₃₁⋊#95	C₄	1	4	yes	—
13	#11758403	C₄	1	8	yes	complemented
14	C₈×Dic₃₁	C₄	1	8	yes	complemented
15	#11758391	C₄	1	4	yes	complemented
16	C₂²×C₄×C₃₁	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
18	C₂²×Dic₃₁	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₃₁	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₃₁	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₃₁	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₃₁	C₂×C₄	1	2	yes	—
23	C₄²×C₃₁	C₂×C₄	1	2	yes	—
24	C₄²×C₃₁	C₂×C₄	1	2	yes	—
25	C₄×Dic₃₁	C₂×C₄	1	4	yes	—
26	C₄×Dic₃₁	C₂×C₄	1	4	yes	—
27	C₂×C₃₁⋊C₈	C₂×C₄	1	4	yes	—
28	C₂×C₃₁⋊C₈	C₂×C₄	1	4	yes	—
29	C₂×C₃₁⋊C₈	C₂×C₄	1	4	yes	—
30	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₃₁	—	2	4	no	—
32	C₂×C₄×C₃₁	C₄²	1	4	yes	—
33	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₃₁	C₂²×C₄	1	2	yes	—
35	C₂×C₄×C₃₁	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₃₁	—	2	8	no	—
38	C₂×Dic₃₁	C₄²	1	8	yes	—
39	C₈×C₃₁	C₄²	1	4	yes	—
40	C₈×C₃₁	C₄²	1	4	yes	—
41	C₃₁⋊C₈	C₄²	1	8	yes	—
42	#1726	—	31	1	no	maximal, Sylow
43	C₂²×C₃₁	C₂×C₄²	1	2	yes	—
44	C₂²×C₃₁	C₂×C₄²	1	1	yes	characteristic
45	C₂²×C₃₁	#131	1	4	yes	—
46	C₄×C₃₁	—	2	4	no	—
47	C₄×C₃₁	C₂×C₄²	1	2	yes	—
48	C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
49	C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
50	Dic₃₁	—	2	8	no	—
51	C₂×#97	—	31	2	no	—
52	C₂×#97	—	31	1	no	—
53	C₂×C₄×C₈	—	31	2	no	—
54	C₂×C₄×C₈	D₃₁	1	1	yes	characteristic
55	#376	—	31	1	no	—
56	C₂×C₃₁	C₄³	1	1	yes	characteristic
57	C₂×C₃₁	#405	1	4	yes	—
58	C₂×C₃₁	#405	1	2	yes	—
59	C₂²×C₈	—	31	2	no	—
60	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic
61	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic
62	C₂×C₄²	—	31	2	no	—
63	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
64	#97	—	31	8	no	—
65	#97	—	31	4	no	—
66	C₄×C₈	—	31	8	no	—
67	C₄×C₈	Dic₃₁	1	4	yes	complemented
68	#95	—	31	4	no	—
69	C₃₁	#1726	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₄	—	31	4	no	—
71	C₂²×C₄	C₄×D₃₁	1	2	yes	—
72	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
73	C₂×C₈	—	31	4	no	—
74	C₂×C₈	—	31	4	no	—
75	C₂×C₈	—	31	4	no	—
76	C₂×C₈	C₄×D₃₁	1	4	yes	—
77	C₂×C₈	C₄×D₃₁	1	4	yes	—
78	C₂×C₈	C₂×Dic₃₁	1	2	yes	—
79	C₂×C₈	C₂×Dic₃₁	1	2	yes	—
80	C₄²	—	31	4	no	—
81	C₄²	—	31	4	no	—
82	C₄²	C₄×D₃₁	1	2	yes	—
83	C₄²	C₂×Dic₃₁	1	2	yes	—
84	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	31	8	no	—
87	C₂×C₄	—	62	8	no	—
88	C₂×C₄	C₄×Dic₃₁	1	4	yes	—
89	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₃₁	1	2	yes	—
91	C₂×C₄	C₂×C₄×D₃₁	1	2	yes	—
92	C₂×C₄	C₂²×Dic₃₁	1	1	yes	characteristic
93	C₈	—	31	8	no	—
94	C₈	C₄×Dic₃₁	1	4	yes	—
95	C₈	C₄×Dic₃₁	1	4	yes	—
96	C₂²	C₄²×D₃₁	1	2	yes	—
97	C₂²	#11758478	1	4	yes	—
98	C₂²	C₂×C₄×Dic₃₁	1	1	yes	characteristic
99	C₄	—	2	4	no	—
100	C₄	—	62	8	no	—
101	C₄	C₄²×D₃₁	1	2	yes	—
102	C₄	C₂×C₄×Dic₃₁	1	1	yes	characteristic
103	C₄	C₂×C₄×Dic₃₁	1	1	yes	characteristic
104	C₂	C₄²×Dic₃₁	1	1	yes	characteristic
105	C₂	#14521003	1	4	yes	—
106	C₂	#14521004	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11758391

C₂

yes

maximal, characteristic

C₂×#11758403

C₂

yes

maximal

C₂×C₈×Dic₃₁

C₂

yes

maximal

#14520895

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₃₁

C₂

yes

maximal, characteristic

C₂²×C₈×C₃₁

C₂²

yes

characteristic

C₂²×C₈×C₃₁

C₂²

yes

characteristic

C₂×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₄×Dic₃₁

C₂²

yes

—

C₂²×C₃₁⋊C₈

C₂²

yes

—

C₄×C₈×C₃₁

C₄

yes

complemented

C₃₁⋊#95

C₄

yes

—

#11758403

C₄

yes

complemented

C₈×Dic₃₁

C₄

yes

complemented

#11758391

C₄

yes

complemented

C₂²×C₄×C₃₁

C₂×C₄

yes

—

C₂²×C₄×C₃₁

C₂³

yes

characteristic

C₂²×Dic₃₁

C₂×C₄

yes

—

C₂×C₈×C₃₁

C₂×C₄

yes

—

C₂×C₈×C₃₁

C₂×C₄

yes

—

C₂×C₈×C₃₁

C₂×C₄

yes

—

C₂×C₈×C₃₁

C₂×C₄

yes

—

C₄²×C₃₁

C₂×C₄

yes

—

C₄²×C₃₁

C₂×C₄

yes

—

C₄×Dic₃₁

C₂×C₄

yes

—

C₄×Dic₃₁

C₂×C₄

yes

—

C₂×C₃₁⋊C₈

C₂×C₄

yes

—

C₂×C₃₁⋊C₈

C₂×C₄

yes

—

C₂×C₃₁⋊C₈

C₂×C₄

yes

—

C₂³×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₄²

yes

—

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

C₂²×C₄

yes

—

C₂×C₄×C₃₁

C₂²×C₄

yes

—

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×Dic₃₁

—

C₂×Dic₃₁

C₄²

yes

—

C₈×C₃₁

C₄²

yes

—

C₈×C₃₁

C₄²

yes

—

C₃₁⋊C₈

C₄²

yes

—

#1726

—

maximal, Sylow

C₂²×C₃₁

C₂×C₄²

yes

—

C₂²×C₃₁

C₂×C₄²

yes

characteristic

C₂²×C₃₁

#131

yes

—

C₄×C₃₁

—

C₄×C₃₁

C₂×C₄²

yes

—

C₄×C₃₁

C₂×C₄²

yes

characteristic

C₄×C₃₁

C₂×C₄²

yes

characteristic

Dic₃₁

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₃₁

yes

characteristic

#376

—

C₂×C₃₁

C₄³

yes

characteristic

C₂×C₃₁

#405

yes

—

C₂×C₃₁

#405

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₃₁

yes

characteristic

C₂²×C₈

C₂×D₃₁

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₃₁

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₃₁

yes

complemented

#95

—

C₃₁

#1726

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₄×D₃₁

yes

—

C₂²×C₄

C₂²×D₃₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₃₁

yes

—

C₂×C₈

C₄×D₃₁

yes

—

C₂×C₈

C₂×Dic₃₁

yes

—

C₂×C₈

C₂×Dic₃₁

yes

—

C₄²

—

C₄²

—

C₄²

C₄×D₃₁

yes

—

C₄²

C₂×Dic₃₁

yes

—

C₂³

C₂×C₄×D₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₃₁

yes

—

C₂×C₄

C₂×C₄×D₃₁

yes

characteristic

C₂×C₄

C₂×C₄×D₃₁

yes

—

C₂×C₄

C₂×C₄×D₃₁

yes

—

C₂×C₄

C₂²×Dic₃₁

yes

characteristic

C₈

—

C₈

C₄×Dic₃₁

yes

—

C₈

C₄×Dic₃₁

yes

—

C₂²

C₄²×D₃₁

yes

—

C₂²

#11758478

yes

—

C₂²

C₂×C₄×Dic₃₁

yes

characteristic

C₄

—

100

C₄

—

101

C₄

C₄²×D₃₁

yes

—

102

C₄

C₂×C₄×Dic₃₁

yes

characteristic

103

C₄

C₂×C₄×Dic₃₁

yes

characteristic

104

C₂

C₄²×Dic₃₁

yes

characteristic

105

C₂

#14521003

yes

—

106

C₂

#14521004

yes

—

	subgroup	G/H
center	C₂²×C₈	C₂×D₃₁
commutator	C₂×C₃₁	C₄³
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₂×C₄×C₈×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂²×C₄
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	C₂×C₄×C₈	D₃₁
hypocenter	C₃₁	#1726
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂²×C₈

C₂×D₃₁

commutator

C₂×C₃₁

C₄³

Frattini

C₂²×C₄

C₂²×D₃₁

Fitting

C₂×C₄×C₈×C₃₁

C₂

socle, prime radical

C₂³×C₃₁

C₂²×C₄

cosocle

C₂²×C₄×C₃₁

C₂³

hypercenter

C₂×C₄×C₈

D₃₁

C₃₁

G ▷ C₂×C₃₁ ▷ C₃₁

C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
11. C₄×C₈×C₃₁	C₄	semidirect
13. #11758403	C₄	semidirect
14. C₈×Dic₃₁	C₄	semidirect
15. #11758391	C₄	semidirect
67. C₄×C₈	Dic₃₁	semidirect
69. C₃₁	#1726	semidirect

H ≅ G/N

type

11. C₄×C₈×C₃₁

C₄

semidirect

13. #11758403

C₄

semidirect

14. C₈×Dic₃₁

C₄

semidirect

15. #11758391

C₄

semidirect

67. C₄×C₈

Dic₃₁

semidirect

69. C₃₁

#1726

semidirect

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

subgroup	index
C₂×#11758391	2
C₂×#11758403	2
C₂×C₈×Dic₃₁	2
#14520895	2
C₂×C₄×C₈×C₃₁	2
#1726	31

subgroup

index

C₂×C₈×Dic₃₁

C₂×C₄×C₈×C₃₁

Subgroups — #16845397

Conjugacy classes of subgroups

Complements

Maximal subgroups