Group #18010962 — subgroups

Subgroups — #18010962

Order 4736.

138 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 64 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	#14558454	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#10596927	C₂	1	2	yes	maximal
3	#14558422	C₂	1	1	yes	maximal, characteristic, complemented
4	#14558419	C₂	1	1	yes	maximal, characteristic, complemented
5	#14557491	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596927	C₂²	1	2	yes	—
7	C₂×#10596927	C₂²	1	2	yes	—
8	C₂²×#64436	C₂²	1	1	yes	characteristic
9	#11924495	C₄	1	1	yes	characteristic
10	#11924446	C₄	1	1	yes	characteristic
11	#11924446	C₄	1	1	yes	characteristic
12	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
13	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₃₇	C₄	1	1	yes	characteristic
15	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
16	M₁₆×C₃₇	—	2	2	no	—
17	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊Dic₃₇	C₈	1	2	yes	—
20	C₄⋊Dic₃₇	C₈	1	2	yes	—
21	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
23	C₂×#64436	—	2	2	no	—
24	C₂×#64436	C₂×C₄	1	1	yes	characteristic
25	C₂×#64436	C₂³	1	1	yes	characteristic
26	#10596927	—	2	2	no	—
27	#10596927	—	2	2	no	—
28	C₂³×C₃₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₃₇	—	2	1	no	—
30	C₂×C₄×C₃₇	—	2	1	no	—
31	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₃₇	C₂×C₈	1	2	yes	—
34	C₂×Dic₃₇	C₂×C₈	1	2	yes	—
35	C₈×C₃₇	—	2	1	no	—
36	C₈×C₃₇	M₁₆	1	2	yes	—
37	#64436	—	2	1	no	—
38	#64436	#41	1	2	yes	—
39	C₂²×C₃₇	—	2	1	no	—
40	C₂²×C₃₇	—	2	2	no	—
41	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₃₇	—	2	1	no	—
43	C₄×C₃₇	#117	1	1	yes	characteristic
44	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
45	Dic₃₇	—	2	2	no	—
46	Dic₃₇	—	2	2	no	—
47	#2164	—	37	1	no	maximal, Sylow
48	C₂×C₃₇	—	4	1	no	—
49	C₂×C₃₇	#431	1	1	yes	characteristic
50	C₂×C₃₇	#504	1	2	yes	—
51	#405	—	37	1	no	—
52	C₄⋊C₁₆	—	37	2	no	—
53	C₂²⋊C₁₆	—	37	2	no	—
54	#346	—	37	1	no	—
55	C₄×C₁₆	—	37	1	no	—
56	C₃₇	#2164	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	#3866	1	1	yes	characteristic
58	C₂²×C₈	—	37	1	no	—
59	#117	—	37	1	no	—
60	C₂×C₁₆	—	37	2	no	—
61	C₂×C₁₆	—	37	2	no	—
62	#97	—	37	1	no	—
63	#97	—	37	1	no	—
64	C₄×C₈	—	37	1	no	—
65	C₄×C₈	—	37	1	no	—
66	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	C₂×C₈	—	37	1	no	—
69	C₂×C₈	—	37	1	no	—
70	C₂×C₈	—	74	2	no	—
71	C₂×C₈	C₂×#3866	1	1	yes	characteristic
72	C₂×C₈	C₂×#3866	1	1	yes	characteristic
73	C₄⋊C₄	—	37	2	no	—
74	C₂²⋊C₄	—	37	2	no	—
75	C₄²	—	37	1	no	—
76	C₄²	—	37	1	no	—
77	C₁₆	—	74	2	no	—
78	C₁₆	—	74	2	no	—
79	C₂³	D₃₇⋊C₈	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	37	2	no	—
83	C₂×C₄	—	37	2	no	—
84	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
85	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	37	2	no	—
88	C₈	—	74	1	no	—
89	C₈	#10596957	1	2	yes	—
90	C₂²	—	2	1	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₂×D₃₇⋊C₈	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	74	2	no	—
95	C₄	—	74	2	no	—
96	C₄	#11924615	1	1	yes	characteristic
97	C₄	C₂×#10596957	1	1	yes	characteristic
98	C₂	—	4	1	no	—
99	C₂	#14558550	1	1	yes	characteristic
100	C₂	#14558592	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14558454

C₂

yes

maximal, complemented

C₂²⋊#10596927

C₂

yes

maximal

#14558422

C₂

yes

maximal, characteristic, complemented

#14558419

C₂

yes

maximal, characteristic, complemented

#14557491

C₂

yes

maximal, characteristic

C₂×#10596927

C₂²

yes

—

C₂×#10596927

C₂²

yes

—

C₂²×#64436

C₂²

yes

characteristic

#11924495

C₄

yes

characteristic

#11924446

C₄

yes

characteristic

#11924446

C₄

yes

characteristic

C₈×Dic₃₇

C₂²

yes

characteristic

C₈×Dic₃₇

C₂²

yes

characteristic

C₂×M₁₆×C₃₇

C₄

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

characteristic

M₁₆×C₃₇

—

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂²⋊Dic₃₇

C₈

yes

—

C₄⋊Dic₃₇

C₈

yes

—

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₂×#64436

—

C₂×#64436

C₂×C₄

yes

characteristic

C₂×#64436

C₂³

yes

characteristic

#10596927

—

#10596927

—

C₂³×C₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

—

C₂×Dic₃₇

C₂×C₈

yes

—

C₈×C₃₇

—

C₈×C₃₇

M₁₆

yes

—

#64436

—

#64436

#41

yes

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

C₂²×C₈

yes

characteristic

C₄×C₃₇

—

C₄×C₃₇

#117

yes

characteristic

C₄×C₃₇

C₂×M₁₆

yes

characteristic

Dic₃₇

—

Dic₃₇

—

#2164

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

#431

yes

characteristic

C₂×C₃₇

#504

yes

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₃₇

#2164

yes

characteristic, complemented, Sylow

C₂×M₁₆

#3866

yes

characteristic

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₂×#3866

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

D₃₇⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₃₇⋊C₈

yes

characteristic

C₂×C₄

C₂²×#3866

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

#10596957

yes

—

C₂²

—

C₂²

—

C₂²

C₂×D₃₇⋊C₈

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

#14558550

yes

characteristic

100

C₂

#14558592

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3866
commutator, socle	C₂²×C₃₇	C₂²×C₈
Fitting	C₂×M₁₆×C₃₇	C₄
prime radical	C₂³×C₃₇	C₂×C₈
cosocle	C₂×#64436	C₂³
hypercenter	C₂×M₁₆	#3866
hypocenter	C₃₇	#2164
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#3866

commutator, socle

C₂²×C₃₇

C₂²×C₈

Fitting

C₂×M₁₆×C₃₇

C₄

prime radical

C₂³×C₃₇

C₂×C₈

C₂³

C₂×M₁₆

C₃₇

G ▷ C₂²×C₃₇ ▷ C₃₇

C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. #14558454	C₂	semidirect
3. #14558422	C₂	semidirect
4. #14558419	C₂	semidirect
56. C₃₇	#2164	semidirect

H ≅ G/N

type

1. #14558454

C₂

semidirect

3. #14558422

C₂

semidirect

4. #14558419

C₂

semidirect

56. C₃₇

#2164

semidirect

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

subgroup	index
#14558454	2
C₂²⋊#10596927	2
#14558422	2
#14558419	2
#14557491	2
#2164	37

subgroup

index

Subgroups — #18010962

Conjugacy classes of subgroups

Complements

Maximal subgroups