Group #37548925 — subgroups

Subgroups — #37548925

Order 23168.

212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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	#26042297	C₂	1	2	yes	maximal
2	#26042120	C₂	1	2	yes	maximal, complemented
3	C₈×#13089685	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₁₈₁	C₂	1	1	yes	maximal, characteristic
5	#19153883	C₄	1	4	yes	—
6	#19153873	C₄	1	4	yes	—
7	C₄×#13089685	C₂²	1	4	yes	—
8	C₂×C₈×D₁₈₁	C₄	1	1	yes	characteristic
9	C₂×C₈×D₁₈₁	C₄	1	1	yes	characteristic
10	C₄²×D₁₈₁	C₂²	1	1	yes	characteristic
11	C₄×#13089678	C₄	1	1	yes	characteristic
12	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₁₈₁	C₄	1	1	yes	characteristic
15	C₂×#13089685	C₂×C₄	1	8	yes	—
16	C₂×C₄×D₁₈₁	C₂×C₄	1	2	yes	—
17	C₂×C₄×D₁₈₁	C₂×C₄	1	1	yes	characteristic
18	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
19	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
20	C₈×D₁₈₁	C₈	1	4	yes	complemented
21	C₈×D₁₈₁	C₈	1	4	yes	complemented
22	C₄×Dic₁₈₁	C₂×C₄	1	2	yes	—
23	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
27	#13089685	—	2	8	no	—
28	C₂²×D₁₈₁	C₄²	1	1	yes	characteristic
29	C₂×Dic₁₈₁	C₄²	1	1	yes	characteristic
30	C₂×Dic₁₈₁	C₂²×C₄	1	2	yes	—
31	C₄×D₁₈₁	—	2	4	no	—
32	C₄×D₁₈₁	C₂×C₈	1	2	yes	—
33	C₄×D₁₈₁	C₂×C₈	1	2	yes	—
34	#13089678	C₂×C₈	1	2	yes	—
35	#13089678	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₁₈₁	C₄²	1	2	yes	—
37	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₁₈₁	C₂×C₈	1	2	yes	—
39	C₈×C₁₈₁	C₂×C₈	1	2	yes	—
40	C₂²×C₁₈₁	C₂×C₄²	1	1	yes	characteristic
41	C₂×D₁₈₁	—	2	2	no	—
42	C₂×D₁₈₁	C₄×C₈	1	2	yes	—
43	C₄×C₁₈₁	—	2	2	no	—
44	C₄×C₁₈₁	C₂²×C₈	1	1	yes	characteristic
45	C₄×C₁₈₁	C₂²×C₈	1	1	yes	characteristic
46	Dic₁₈₁	C₄×C₈	1	2	yes	—
47	Dic₁₈₁	#131	1	4	yes	—
48	C₂×C₁₈₁	C₂×C₄×C₈	1	1	yes	characteristic
49	C₂×C₁₈₁	#405	1	2	yes	—
50	D₁₈₁	—	2	2	no	—
51	C₁₈₁	#1450	1	1	yes	characteristic, complemented, Sylow
52	#1450	—	181	1	no	maximal, Sylow
53	#431	—	181	2	no	—
54	C₂×C₄×C₈	—	181	1	no	—
55	#322	—	181	2	no	—
56	C₈²	—	181	2	no	—
57	C₂²×C₈	—	181	1	no	—
58	C₂²×C₈	—	181	1	no	—
59	C₂×C₄²	—	181	1	no	—
60	C₄⋊C₈	—	181	4	no	—
61	C₂²⋊C₈	—	181	4	no	—
62	C₄×C₈	—	181	4	no	—
63	C₄×C₈	—	181	1	no	—
64	C₄×C₈	—	181	1	no	—
65	C₄×C₈	—	181	1	no	—
66	C₄×C₈	#10624382	1	1	yes	characteristic
67	C₂²×C₄	—	181	2	no	—
68	C₂²×C₄	—	181	1	no	—
69	C₂×C₈	—	181	8	no	—
70	C₂×C₈	—	181	1	no	—
71	C₂×C₈	—	181	1	no	—
72	C₂×C₈	—	181	4	no	—
73	C₂×C₈	—	181	4	no	—
74	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
75	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
76	C₄²	—	181	2	no	—
77	C₄²	—	181	1	no	—
78	C₄²	C₂×#10624382	1	1	yes	characteristic
79	C₂³	—	181	1	no	—
80	C₂×C₄	—	362	4	no	—
81	C₂×C₄	—	181	2	no	—
82	C₂×C₄	—	181	1	no	—
83	C₂×C₄	—	181	2	no	—
84	C₂×C₄	—	181	2	no	—
85	C₂×C₄	C₄×#10624382	1	2	yes	—
86	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
87	C₈	—	362	8	no	—
88	C₈	—	181	2	no	—
89	C₈	—	181	2	no	—
90	C₈	D₁₈₁⋊C₈	1	2	yes	—
91	C₈	D₁₈₁⋊C₈	1	2	yes	—
92	C₂²	—	362	2	no	—
93	C₂²	—	181	2	no	—
94	C₂²	C₂×C₄×#10624382	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	181	2	no	—
97	C₄	—	181	4	no	—
98	C₄	C₂×D₁₈₁⋊C₈	1	1	yes	characteristic
99	C₄	C₂×D₁₈₁⋊C₈	1	1	yes	characteristic
100	C₂	—	362	2	no	—
101	C₂	C₄×D₁₈₁⋊C₈	1	1	yes	characteristic
102	C₂	#26042242	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26042297

C₂

yes

maximal

#26042120

C₂

yes

maximal, complemented

C₈×#13089685

C₂

yes

maximal, complemented

C₄×C₈×D₁₈₁

C₂

yes

maximal, characteristic

#19153883

C₄

yes

—

#19153873

C₄

yes

—

C₄×#13089685

C₂²

yes

—

C₂×C₈×D₁₈₁

C₄

yes

characteristic

C₂×C₈×D₁₈₁

C₄

yes

characteristic

C₄²×D₁₈₁

C₂²

yes

characteristic

C₄×#13089678

C₄

yes

characteristic

C₈×Dic₁₈₁

C₂²

yes

characteristic

C₈×Dic₁₈₁

C₂²

yes

characteristic

C₄×C₈×C₁₈₁

C₄

yes

characteristic

C₂×#13089685

C₂×C₄

yes

—

C₂×C₄×D₁₈₁

C₂×C₄

yes

—

C₂×C₄×D₁₈₁

C₂×C₄

yes

characteristic

C₂×#13089678

C₂×C₄

yes

characteristic

C₂×#13089678

C₂×C₄

yes

characteristic

C₈×D₁₈₁

C₈

yes

complemented

C₈×D₁₈₁

C₈

yes

complemented

C₄×Dic₁₈₁

C₂×C₄

yes

—

C₄×Dic₁₈₁

C₂³

yes

characteristic

C₂×C₈×C₁₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₈₁

C₂×C₄

yes

characteristic

C₄²×C₁₈₁

C₂×C₄

yes

characteristic

#13089685

—

C₂²×D₁₈₁

C₄²

yes

characteristic

C₂×Dic₁₈₁

C₄²

yes

characteristic

C₂×Dic₁₈₁

C₂²×C₄

yes

—

C₄×D₁₈₁

—

C₄×D₁₈₁

C₂×C₈

yes

—

C₄×D₁₈₁

C₂×C₈

yes

—

#13089678

C₂×C₈

yes

—

#13089678

C₂×C₈

yes

—

C₂×C₄×C₁₈₁

C₄²

yes

—

C₂×C₄×C₁₈₁

C₂²×C₄

yes

characteristic

C₈×C₁₈₁

C₂×C₈

yes

—

C₈×C₁₈₁

C₂×C₈

yes

—

C₂²×C₁₈₁

C₂×C₄²

yes

characteristic

C₂×D₁₈₁

—

C₂×D₁₈₁

C₄×C₈

yes

—

C₄×C₁₈₁

—

C₄×C₁₈₁

C₂²×C₈

yes

characteristic

C₄×C₁₈₁

C₂²×C₈

yes

characteristic

Dic₁₈₁

C₄×C₈

yes

—

Dic₁₈₁

#131

yes

—

C₂×C₁₈₁

C₂×C₄×C₈

yes

characteristic

C₂×C₁₈₁

#405

yes

—

D₁₈₁

—

C₁₈₁

#1450

yes

characteristic, complemented, Sylow

#1450

—

181

maximal, Sylow

#431

—

181

—

C₂×C₄×C₈

—

181

—

#322

—

181

—

C₈²

—

181

—

C₂²×C₈

—

181

—

C₂²×C₈

—

181

—

C₂×C₄²

—

181

—

C₄⋊C₈

—

181

—

C₂²⋊C₈

—

181

—

C₄×C₈

—

181

—

C₄×C₈

—

181

—

C₄×C₈

—

181

—

C₄×C₈

—

181

—

C₄×C₈

#10624382

yes

characteristic

C₂²×C₄

—

181

—

C₂²×C₄

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

181

—

C₄²

—

181

—

C₄²

C₂×#10624382

yes

characteristic

C₂³

—

181

—

C₂×C₄

—

362

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

C₄×#10624382

yes

—

C₂×C₄

C₂²×#10624382

yes

characteristic

C₈

—

362

—

C₈

—

181

—

C₈

—

181

—

C₈

D₁₈₁⋊C₈

yes

—

C₈

D₁₈₁⋊C₈

yes

—

C₂²

—

362

—

C₂²

—

181

—

C₂²

C₂×C₄×#10624382

yes

characteristic

C₄

—

C₄

—

181

—

C₄

—

181

—

C₄

C₂×D₁₈₁⋊C₈

yes

characteristic

C₄

C₂×D₁₈₁⋊C₈

yes

characteristic

100

C₂

—

362

—

101

C₂

C₄×D₁₈₁⋊C₈

yes

characteristic

102

C₂

#26042242

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×#10624382
commutator	C₂×C₁₈₁	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#10624382
Fitting	C₄×C₈×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂×C₄²
prime radical	C₂²×D₁₈₁	C₄²
cosocle	C₄×Dic₁₈₁	C₂³
hypercenter	C₄×C₈	#10624382
hypocenter	C₁₈₁	#1450
LCS	G ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#10624382

commutator

C₂×C₁₈₁

C₂×C₄×C₈

Frattini

C₂×C₄

C₂²×#10624382

Fitting

C₄×C₈×C₁₈₁

C₄

socle

C₂²×C₁₈₁

C₂×C₄²

prime radical

C₂²×D₁₈₁

C₄²

cosocle

C₄×Dic₁₈₁

C₂³

C₄×C₈

C₁₈₁

G ▷ C₂×C₁₈₁ ▷ C₁₈₁

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #26042120	C₂	semidirect
3. C₈×#13089685	C₂	semidirect
20. C₈×D₁₈₁	C₈	semidirect
21. C₈×D₁₈₁	C₈	semidirect
51. C₁₈₁	#1450	semidirect

H ≅ G/N

type

2. #26042120

C₂

semidirect

3. C₈×#13089685

C₂

semidirect

20. C₈×D₁₈₁

C₈

semidirect

21. C₈×D₁₈₁

C₈

semidirect

51. C₁₈₁

#1450

semidirect

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

subgroup	index
#26042297	2
#26042120	2
C₈×#13089685	2
C₄×C₈×D₁₈₁	2
#1450	181

subgroup

index

C₄×C₈×D₁₈₁

181

Subgroups — #37548925

Conjugacy classes of subgroups

Complements

Maximal subgroups