Group #18010932 — subgroups

Subgroups — #18010932

Order 4736.

160 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 76 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×#11924611	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#14558454	C₂	1	2	yes	maximal, complemented
4	C₄⋊#10596927	C₂	1	2	yes	maximal, complemented
5	#14557490	C₂	1	1	yes	maximal, characteristic
6	#11924611	—	2	2	no	—
7	D₃₇⋊C₁₆	—	2	2	no	—
8	C₂×#10596927	C₂²	1	2	yes	—
9	C₂×#10596927	C₂²	1	2	yes	—
10	C₂×#10596929	C₄	1	1	yes	characteristic
11	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
12	#11924493	C₄	1	1	yes	characteristic
13	#11924446	C₄	1	1	yes	characteristic
14	C₄×#64436	C₂²	1	1	yes	characteristic
15	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
16	#97×C₃₇	C₄	1	1	yes	characteristic
17	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
21	#10596938	C₈	1	2	yes	—
22	#10596936	C₈	1	2	yes	—
23	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
24	C₂×#64436	C₂×C₄	1	1	yes	characteristic
25	C₂×#64436	C₂³	1	1	yes	characteristic
26	#10596929	—	2	2	no	—
27	C₈×D₃₇	D₄	1	2	yes	—
28	C₈×D₃₇	Q₈	1	2	yes	—
29	#10596927	—	2	2	no	—
30	#10596927	—	2	2	no	—
31	C₂²×D₃₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₃₇	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₃₇	C₂×C₈	1	2	yes	—
35	C₂×Dic₃₇	C₂×C₈	1	1	yes	characteristic
36	C₄×D₃₇	C₄⋊C₄	1	2	yes	—
37	C₄×D₃₇	M₁₆	1	2	yes	—
38	C₈×C₃₇	—	2	1	no	—
39	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
40	#64436	—	2	1	no	—
41	#64436	C₂×D₄	1	1	yes	characteristic
42	#64436	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
44	C₂×D₃₇	—	2	2	no	—
45	C₂×D₃₇	C₄⋊C₈	1	2	yes	—
46	C₄×C₃₇	—	2	2	no	—
47	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
49	Dic₃₇	—	2	2	no	—
50	Dic₃₇	C₄⋊C₈	1	2	yes	—
51	#2151	—	37	1	no	maximal, Sylow
52	C₂×C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic
53	C₂×C₃₇	#504	1	2	yes	—
54	D₃₇	—	2	2	no	—
55	C₂×M₃₂	—	37	1	no	—
56	C₂²×C₁₆	—	37	1	no	—
57	#405	—	37	1	no	—
58	C₄⋊C₁₆	—	37	2	no	—
59	C₄⋊C₁₆	—	37	2	no	—
60	C₃₇	#2151	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	37	1	no	—
62	C₂²×C₈	—	37	1	no	—
63	#117	—	37	1	no	—
64	M₃₂	—	74	2	no	—
65	C₂×C₁₆	—	37	2	no	—
66	C₂×C₁₆	—	37	2	no	—
67	C₂×C₁₆	—	74	2	no	—
68	#97	—	37	1	no	—
69	#97	#3866	1	1	yes	characteristic
70	C₄×C₈	—	37	1	no	—
71	C₄×C₈	—	37	1	no	—
72	C₂²×C₄	—	37	1	no	—
73	M₁₆	—	74	2	no	—
74	C₂×C₈	—	37	1	no	—
75	C₂×C₈	—	37	2	no	—
76	C₂×C₈	—	37	2	no	—
77	C₂×C₈	—	37	1	no	—
78	C₂×C₈	C₂×#3866	1	1	yes	characteristic
79	C₂×C₈	C₂×#3866	1	1	yes	characteristic
80	C₄⋊C₄	—	37	2	no	—
81	C₂²⋊C₄	—	37	2	no	—
82	C₄²	—	37	1	no	—
83	C₄²	C₂×#3866	1	1	yes	characteristic
84	C₁₆	—	74	2	no	—
85	C₁₆	—	74	2	no	—
86	C₂³	—	37	1	no	—
87	C₂×C₄	—	37	1	no	—
88	C₂×C₄	—	37	2	no	—
89	C₂×C₄	—	37	2	no	—
90	C₂×C₄	—	37	2	no	—
91	C₂×C₄	D₃₇⋊C₈	1	2	yes	—
92	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	37	1	no	—
95	C₈	—	37	1	no	—
96	C₈	—	74	1	no	—
97	C₈	C₄⋊#3866	1	2	yes	—
98	C₂²	—	37	2	no	—
99	C₂²	—	74	2	no	—
100	C₂²	C₂×D₃₇⋊C₈	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	37	2	no	—
103	C₄	—	74	2	no	—
104	C₄	C₂×C₄⋊#3866	1	1	yes	characteristic
105	C₄	D₃₇⋊M₁₆	1	1	yes	characteristic
106	C₂	—	74	2	no	—
107	C₂	D₃₇⋊(C₄⋊C₈)	1	1	yes	characteristic
108	C₂	#14558592	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924611

C₂

yes

maximal, characteristic

C₂×D₃₇⋊C₁₆

C₂

yes

maximal, characteristic

#14558454

C₂

yes

maximal, complemented

C₄⋊#10596927

C₂

yes

maximal, complemented

#14557490

C₂

yes

maximal, characteristic

#11924611

—

D₃₇⋊C₁₆

—

C₂×#10596927

C₂²

yes

—

C₂×#10596927

C₂²

yes

—

C₂×#10596929

C₄

yes

characteristic

C₂×C₈×D₃₇

C₂²

yes

characteristic

#11924493

C₄

yes

characteristic

#11924446

C₄

yes

characteristic

C₄×#64436

C₂²

yes

characteristic

C₈×Dic₃₇

C₂²

yes

characteristic

#97×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₄²×C₃₇

C₂×C₄

yes

characteristic

#10596938

C₈

yes

—

#10596936

C₈

yes

—

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₂×#64436

C₂×C₄

yes

characteristic

C₂×#64436

C₂³

yes

characteristic

#10596929

—

C₈×D₃₇

D₄

yes

—

C₈×D₃₇

Q₈

yes

—

#10596927

—

#10596927

—

C₂²×D₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₂×C₈

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

—

C₂×Dic₃₇

C₂×C₈

yes

characteristic

C₄×D₃₇

C₄⋊C₄

yes

—

C₄×D₃₇

M₁₆

yes

—

C₈×C₃₇

—

C₈×C₃₇

C₄⋊C₄

yes

—

#64436

—

#64436

C₂×D₄

yes

characteristic

#64436

C₂×Q₈

yes

characteristic

C₂²×C₃₇

C₂²×C₈

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

C₄⋊C₈

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₇

C₂×M₁₆

yes

characteristic

Dic₃₇

—

Dic₃₇

C₄⋊C₈

yes

—

#2151

—

maximal, Sylow

C₂×C₃₇

C₂×C₄⋊C₈

yes

characteristic

C₂×C₃₇

#504

yes

—

D₃₇

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₃₇

#2151

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₃₇⋊C₈

yes

—

C₂×C₄

C₂²×#3866

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

C₄⋊#3866

yes

—

C₂²

—

C₂²

—

100

C₂²

C₂×D₃₇⋊C₈

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

C₂×C₄⋊#3866

yes

characteristic

105

C₄

D₃₇⋊M₁₆

yes

characteristic

106

C₂

—

107

C₂

D₃₇⋊(C₄⋊C₈)

yes

characteristic

108

C₂

#14558592

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3866
commutator, socle	C₂²×C₃₇	C₂²×C₈
Fitting	#97×C₃₇	C₄
prime radical	C₂²×D₃₇	C₂×C₈
cosocle	C₂×#64436	C₂³
hypercenter	#97	#3866
hypocenter	C₃₇	#2151
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#3866

commutator, socle

C₂²×C₃₇

C₂²×C₈

Fitting

#97×C₃₇

C₄

prime radical

C₂²×D₃₇

C₂×C₈

C₂³

C₃₇

G ▷ C₂²×C₃₇ ▷ C₃₇

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
3. #14558454	C₂	semidirect
4. C₄⋊#10596927	C₂	semidirect
60. C₃₇	#2151	semidirect

H ≅ G/N

type

3. #14558454

C₂

semidirect

4. C₄⋊#10596927

C₂

semidirect

60. C₃₇

#2151

semidirect

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

subgroup	index
C₂×#11924611	2
C₂×D₃₇⋊C₁₆	2
#14558454	2
C₄⋊#10596927	2
#14557490	2
#2151	37

subgroup

index

C₂×D₃₇⋊C₁₆

Subgroups — #18010932

Conjugacy classes of subgroups

Complements

Maximal subgroups