Group #37550057 — subgroups

Subgroups — #37550057

Order 23168.

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×#19153891	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₈₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#26042200	C₂	1	2	yes	maximal, complemented
4	C₄⋊#15668452	C₂	1	2	yes	maximal, complemented
5	#26041236	C₂	1	1	yes	maximal, characteristic
6	#19153891	—	2	2	no	—
7	D₁₈₁⋊C₁₆	—	2	2	no	—
8	C₂×#15668452	C₂²	1	2	yes	—
9	C₂×#15668452	C₂²	1	2	yes	—
10	C₂×#15668432	C₄	1	1	yes	characteristic
11	C₂×C₈×D₁₈₁	C₂²	1	1	yes	characteristic
12	#19153773	C₄	1	1	yes	characteristic
13	#19153726	C₄	1	1	yes	characteristic
14	C₄×#13089678	C₂²	1	1	yes	characteristic
15	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
16	#97×C₁₈₁	C₄	1	1	yes	characteristic
17	#15668452	—	2	2	no	—
18	#15668452	—	2	2	no	—
19	C₂×C₄×D₁₈₁	C₂×C₄	1	1	yes	characteristic
20	#15668432	—	2	2	no	—
21	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
22	C₂×#13089678	C₂³	1	1	yes	characteristic
23	C₈×D₁₈₁	D₄	1	2	yes	—
24	C₈×D₁₈₁	Q₈	1	2	yes	—
25	#15668428	C₈	1	2	yes	—
26	#15668426	C₈	1	2	yes	—
27	C₄×Dic₁₈₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₁₈₁	C₂×C₈	1	1	yes	characteristic
32	C₂×Dic₁₈₁	C₂×C₈	1	2	yes	—
33	C₂×Dic₁₈₁	C₂×C₈	1	1	yes	characteristic
34	C₄×D₁₈₁	C₄⋊C₄	1	2	yes	—
35	C₄×D₁₈₁	M₁₆	1	2	yes	—
36	#13089678	—	2	1	no	—
37	#13089678	C₂×D₄	1	1	yes	characteristic
38	#13089678	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₈₁	C₂×C₈	1	2	yes	—
40	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
41	C₈×C₁₈₁	—	2	1	no	—
42	C₈×C₁₈₁	C₄⋊C₄	1	2	yes	—
43	C₂²×C₁₈₁	C₂²×C₈	1	1	yes	characteristic
44	C₂×D₁₈₁	—	2	2	no	—
45	C₂×D₁₈₁	C₄⋊C₈	1	2	yes	—
46	C₄×C₁₈₁	—	2	2	no	—
47	C₄×C₁₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₁₈₁	C₂×M₁₆	1	1	yes	characteristic
49	Dic₁₈₁	—	2	2	no	—
50	Dic₁₈₁	C₄⋊C₈	1	2	yes	—
51	C₂×C₁₈₁	C₂×C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₁₈₁	#504	1	2	yes	—
53	D₁₈₁	—	2	2	no	—
54	C₁₈₁	#2151	1	1	yes	characteristic, complemented, Sylow
55	#2151	—	181	1	no	maximal, Sylow
56	C₂×M₃₂	—	181	1	no	—
57	C₂²×C₁₆	—	181	1	no	—
58	#405	—	181	1	no	—
59	C₄⋊C₁₆	—	181	2	no	—
60	C₄⋊C₁₆	—	181	2	no	—
61	C₂×M₁₆	—	181	1	no	—
62	C₂²×C₈	—	181	1	no	—
63	#117	—	181	1	no	—
64	M₃₂	—	362	2	no	—
65	C₂×C₁₆	—	362	2	no	—
66	C₂×C₁₆	—	181	2	no	—
67	C₂×C₁₆	—	181	2	no	—
68	#97	—	181	1	no	—
69	#97	#10624382	1	1	yes	characteristic
70	C₄×C₈	—	181	1	no	—
71	C₄×C₈	—	181	1	no	—
72	C₂²×C₄	—	181	1	no	—
73	M₁₆	—	362	2	no	—
74	C₂×C₈	—	181	1	no	—
75	C₂×C₈	—	181	1	no	—
76	C₂×C₈	—	181	2	no	—
77	C₂×C₈	—	181	2	no	—
78	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
79	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
80	C₄⋊C₄	—	181	2	no	—
81	C₂²⋊C₄	—	181	2	no	—
82	C₄²	—	181	1	no	—
83	C₄²	C₂×#10624382	1	1	yes	characteristic
84	C₁₆	—	362	2	no	—
85	C₁₆	—	362	2	no	—
86	C₂³	—	181	1	no	—
87	C₂×C₄	—	181	2	no	—
88	C₂×C₄	—	181	1	no	—
89	C₂×C₄	—	181	2	no	—
90	C₂×C₄	—	181	2	no	—
91	C₂×C₄	D₁₈₁⋊C₈	1	2	yes	—
92	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	362	1	no	—
95	C₈	—	181	1	no	—
96	C₈	—	181	1	no	—
97	C₈	C₄⋊#10624382	1	2	yes	—
98	C₂²	—	362	2	no	—
99	C₂²	—	181	2	no	—
100	C₂²	C₂×D₁₈₁⋊C₈	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	362	2	no	—
103	C₄	—	181	2	no	—
104	C₄	C₂×C₄⋊#10624382	1	1	yes	characteristic
105	C₄	D₁₈₁⋊M₁₆	1	1	yes	characteristic
106	C₂	—	362	2	no	—
107	C₂	D₁₈₁⋊(C₄⋊C₈)	1	1	yes	characteristic
108	C₂	#26042338	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19153891

C₂

yes

maximal, characteristic

C₂×D₁₈₁⋊C₁₆

C₂

yes

maximal, characteristic

#26042200

C₂

yes

maximal, complemented

C₄⋊#15668452

C₂

yes

maximal, complemented

#26041236

C₂

yes

maximal, characteristic

#19153891

—

D₁₈₁⋊C₁₆

—

C₂×#15668452

C₂²

yes

—

C₂×#15668452

C₂²

yes

—

C₂×#15668432

C₄

yes

characteristic

C₂×C₈×D₁₈₁

C₂²

yes

characteristic

#19153773

C₄

yes

characteristic

#19153726

C₄

yes

characteristic

C₄×#13089678

C₂²

yes

characteristic

C₈×Dic₁₈₁

C₂²

yes

characteristic

#97×C₁₈₁

C₄

yes

characteristic

#15668452

—

#15668452

—

C₂×C₄×D₁₈₁

C₂×C₄

yes

characteristic

#15668432

—

C₂×#13089678

C₂×C₄

yes

characteristic

C₂×#13089678

C₂³

yes

characteristic

C₈×D₁₈₁

D₄

yes

—

C₈×D₁₈₁

Q₈

yes

—

#15668428

C₈

yes

—

#15668426

C₈

yes

—

C₄×Dic₁₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₈₁

C₂×C₄

yes

characteristic

C₄²×C₁₈₁

C₂×C₄

yes

characteristic

C₂²×D₁₈₁

C₂×C₈

yes

characteristic

C₂×Dic₁₈₁

C₂×C₈

yes

—

C₂×Dic₁₈₁

C₂×C₈

yes

characteristic

C₄×D₁₈₁

C₄⋊C₄

yes

—

C₄×D₁₈₁

M₁₆

yes

—

#13089678

—

#13089678

C₂×D₄

yes

characteristic

#13089678

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₈₁

C₂×C₈

yes

—

C₂×C₄×C₁₈₁

C₂²×C₄

yes

characteristic

C₈×C₁₈₁

—

C₈×C₁₈₁

C₄⋊C₄

yes

—

C₂²×C₁₈₁

C₂²×C₈

yes

characteristic

C₂×D₁₈₁

—

C₂×D₁₈₁

C₄⋊C₈

yes

—

C₄×C₁₈₁

—

C₄×C₁₈₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₈₁

C₂×M₁₆

yes

characteristic

Dic₁₈₁

—

Dic₁₈₁

C₄⋊C₈

yes

—

C₂×C₁₈₁

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₈₁

#504

yes

—

D₁₈₁

—

C₁₈₁

#2151

yes

characteristic, complemented, Sylow

#2151

—

181

maximal, Sylow

C₂×M₃₂

—

181

—

C₂²×C₁₆

—

181

—

#405

—

181

—

C₄⋊C₁₆

—

181

—

C₄⋊C₁₆

—

181

—

C₂×M₁₆

—

181

—

C₂²×C₈

—

181

—

#117

—

181

—

M₃₂

—

362

—

C₂×C₁₆

—

362

—

C₂×C₁₆

—

181

—

C₂×C₁₆

—

181

—

#97

—

181

—

#97

#10624382

yes

characteristic

C₄×C₈

—

181

—

C₄×C₈

—

181

—

C₂²×C₄

—

181

—

M₁₆

—

362

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

181

—

C₂²⋊C₄

—

181

—

C₄²

—

181

—

C₄²

C₂×#10624382

yes

characteristic

C₁₆

—

362

—

C₁₆

—

362

—

C₂³

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

D₁₈₁⋊C₈

yes

—

C₂×C₄

C₂²×#10624382

yes

characteristic

C₈

—

C₈

—

362

—

C₈

—

181

—

C₈

—

181

—

C₈

C₄⋊#10624382

yes

—

C₂²

—

362

—

C₂²

—

181

—

100

C₂²

C₂×D₁₈₁⋊C₈

yes

characteristic

101

C₄

—

102

C₄

—

362

—

103

C₄

—

181

—

104

C₄

C₂×C₄⋊#10624382

yes

characteristic

105

C₄

D₁₈₁⋊M₁₆

yes

characteristic

106

C₂

—

362

—

107

C₂

D₁₈₁⋊(C₄⋊C₈)

yes

characteristic

108

C₂

#26042338

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10624382
commutator, socle	C₂²×C₁₈₁	C₂²×C₈
Fitting	#97×C₁₈₁	C₄
prime radical	C₂²×D₁₈₁	C₂×C₈
cosocle	C₂×#13089678	C₂³
hypercenter	#97	#10624382
hypocenter	C₁₈₁	#2151
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#10624382

commutator, socle

C₂²×C₁₈₁

C₂²×C₈

Fitting

#97×C₁₈₁

C₄

prime radical

C₂²×D₁₈₁

C₂×C₈

C₂³

C₁₈₁

G ▷ C₂²×C₁₈₁ ▷ C₁₈₁

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
3. #26042200	C₂	semidirect
4. C₄⋊#15668452	C₂	semidirect
54. C₁₈₁	#2151	semidirect

H ≅ G/N

type

3. #26042200

C₂

semidirect

4. C₄⋊#15668452

C₂

semidirect

54. C₁₈₁

#2151

semidirect

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

subgroup	index
C₂×#19153891	2
C₂×D₁₈₁⋊C₁₆	2
#26042200	2
C₄⋊#15668452	2
#26041236	2
#2151	181

subgroup

index

C₂×D₁₈₁⋊C₁₆

181

Subgroups — #37550057

Conjugacy classes of subgroups

Complements

Maximal subgroups