Group #37549645 — subgroups

Subgroups — #37549645

Order 23168.

188 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 74 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	#26042283	C₂	1	2	yes	maximal
2	#26042155	C₂	1	4	yes	maximal
3	C₄×C₈×D₁₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668459	C₂²	1	4	yes	—
5	C₄⋊#13089685	—	2	2	no	—
6	C₄⋊#13089685	—	2	2	no	—
7	C₂×C₈×D₁₈₁	C₂²	1	2	yes	—
8	C₄²×D₁₈₁	C₂²	1	1	yes	characteristic
9	C₄×#13089678	C₄	1	1	yes	characteristic
10	C₈×Dic₁₈₁	C₄	1	2	yes	—
11	C₄×C₈×C₁₈₁	C₄	1	1	yes	characteristic
12	#15668459	—	2	8	no	—
13	C₂×#13089685	—	2	4	no	—
14	C₂×C₄×D₁₈₁	Q₈	1	1	yes	characteristic
15	C₂×C₄×D₁₈₁	Q₈	1	1	yes	characteristic
16	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
17	C₂×#13089678	C₂×C₄	1	2	yes	—
18	C₈×D₁₈₁	—	2	4	no	—
19	C₄×Dic₁₈₁	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₁₈₁	D₄	1	1	yes	characteristic
21	C₄×Dic₁₈₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₈₁	C₂×C₄	1	2	yes	—
23	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
24	#13089685	—	4	4	no	—
25	C₂²×D₁₈₁	C₂×Q₈	1	1	yes	characteristic
26	C₂×Dic₁₈₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₈₁	C₄⋊C₄	1	1	yes	characteristic
28	C₂×Dic₁₈₁	C₂×D₄	1	1	yes	characteristic
29	C₄×D₁₈₁	—	2	2	no	—
30	C₄×D₁₈₁	—	2	2	no	—
31	C₄×D₁₈₁	#41	1	4	yes	—
32	#13089678	—	2	2	no	—
33	C₂×C₄×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
36	C₈×C₁₈₁	—	2	2	no	—
37	C₂²×C₁₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×D₁₈₁	—	2	1	no	—
39	C₂×D₁₈₁	—	2	1	no	—
40	C₂×D₁₈₁	#125	1	2	yes	—
41	C₄×C₁₈₁	#108	1	2	yes	—
42	C₄×C₁₈₁	#108	1	2	yes	—
43	C₄×C₁₈₁	#117	1	2	yes	—
44	Dic₁₈₁	—	2	1	no	—
45	Dic₁₈₁	—	2	1	no	—
46	Dic₁₈₁	#124	1	2	yes	—
47	C₂×C₁₈₁	#382	1	1	yes	characteristic
48	C₂×C₁₈₁	C₂×#108	1	1	yes	characteristic
49	C₂×C₁₈₁	C₂×#108	1	1	yes	characteristic
50	D₁₈₁	—	2	2	no	—
51	C₁₈₁	#1837	1	1	yes	characteristic, complemented, Sylow
52	#1837	—	181	1	no	maximal, Sylow
53	#423	—	181	2	no	—
54	C₂×C₄×C₈	—	181	1	no	—
55	#341	—	181	4	no	—
56	C₂×M₁₆	—	181	4	no	—
57	C₂²×C₈	—	181	2	no	—
58	C₂×C₄²	—	181	1	no	—
59	C₄⋊C₈	—	362	2	no	—
60	C₄⋊C₈	—	362	2	no	—
61	C₄×C₈	—	181	2	no	—
62	C₄×C₈	—	181	1	no	—
63	C₄×C₈	#10624382	1	1	yes	characteristic
64	C₂²×C₄	—	181	1	no	—
65	C₂²×C₄	—	181	1	no	—
66	C₂²×C₄	—	181	1	no	—
67	M₁₆	—	362	8	no	—
68	C₂×C₈	—	362	4	no	—
69	C₂×C₈	—	362	4	no	—
70	C₂×C₈	—	181	2	no	—
71	C₂×C₈	C₂×#10624382	1	2	yes	—
72	C₄²	—	181	1	no	—
73	C₄²	—	181	1	no	—
74	C₄²	—	181	1	no	—
75	C₄²	C₂×#10624382	1	1	yes	characteristic
76	C₂³	—	181	1	no	—
77	C₂×C₄	—	362	2	no	—
78	C₂×C₄	—	362	2	no	—
79	C₂×C₄	—	181	1	no	—
80	C₂×C₄	—	181	1	no	—
81	C₂×C₄	—	181	1	no	—
82	C₂×C₄	—	181	4	no	—
83	C₂×C₄	C₄⋊#10624382	1	1	yes	characteristic
84	C₂×C₄	C₄⋊#10624382	1	1	yes	characteristic
85	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	362	2	no	—
88	C₈	—	724	4	no	—
89	C₂²	—	362	1	no	—
90	C₂²	—	362	1	no	—
91	C₂²	—	181	2	no	—
92	C₂²	C₂×C₄⋊#10624382	1	1	yes	characteristic
93	C₄	—	362	1	no	—
94	C₄	—	362	1	no	—
95	C₄	—	181	2	no	—
96	C₄	#19153886	1	2	yes	—
97	C₄	#19153887	1	2	yes	—
98	C₄	#19153895	1	2	yes	—
99	C₂	—	362	2	no	—
100	C₂	#26042223	1	1	yes	characteristic
101	C₂	C₂×#19153886	1	1	yes	characteristic
102	C₂	C₂×#19153887	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26042283

C₂

yes

maximal

#26042155

C₂

yes

maximal

C₄×C₈×D₁₈₁

C₂

yes

maximal, characteristic

C₂×#15668459

C₂²

yes

—

C₄⋊#13089685

—

C₄⋊#13089685

—

C₂×C₈×D₁₈₁

C₂²

yes

—

C₄²×D₁₈₁

C₂²

yes

characteristic

C₄×#13089678

C₄

yes

characteristic

C₈×Dic₁₈₁

C₄

yes

—

C₄×C₈×C₁₈₁

C₄

yes

characteristic

#15668459

—

C₂×#13089685

—

C₂×C₄×D₁₈₁

Q₈

yes

characteristic

C₂×C₄×D₁₈₁

Q₈

yes

characteristic

C₂×C₄×D₁₈₁

C₂³

yes

characteristic

C₂×#13089678

C₂×C₄

yes

—

C₈×D₁₈₁

—

C₄×Dic₁₈₁

C₂×C₄

yes

characteristic

C₄×Dic₁₈₁

D₄

yes

characteristic

C₄×Dic₁₈₁

D₄

yes

characteristic

C₂×C₈×C₁₈₁

C₂×C₄

yes

—

C₄²×C₁₈₁

C₂×C₄

yes

characteristic

#13089685

—

C₂²×D₁₈₁

C₂×Q₈

yes

characteristic

C₂×Dic₁₈₁

C₄⋊C₄

yes

characteristic

C₂×Dic₁₈₁

C₄⋊C₄

yes

characteristic

C₂×Dic₁₈₁

C₂×D₄

yes

characteristic

C₄×D₁₈₁

—

C₄×D₁₈₁

—

C₄×D₁₈₁

#41

yes

—

#13089678

—

C₂×C₄×C₁₈₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₈₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₈₁

C₂²×C₄

yes

characteristic

C₈×C₁₈₁

—

C₂²×C₁₈₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₈₁

—

C₂×D₁₈₁

—

C₂×D₁₈₁

#125

yes

—

C₄×C₁₈₁

#108

yes

—

C₄×C₁₈₁

#108

yes

—

C₄×C₁₈₁

#117

yes

—

Dic₁₈₁

—

Dic₁₈₁

—

Dic₁₈₁

#124

yes

—

C₂×C₁₈₁

yes

C₂×C₁₈₁

yes

C₂×C₁₈₁

yes

D₁₈₁

—

C₁₈₁

#1837

yes

characteristic, complemented, Sylow

#1837

—

181

maximal, Sylow

#423

—

181

—

C₂×C₄×C₈

—

181

—

#341

—

181

—

C₂×M₁₆

—

181

—

C₂²×C₈

—

181

—

C₂×C₄²

—

181

—

C₄⋊C₈

—

362

—

C₄⋊C₈

—

362

—

C₄×C₈

—

181

—

C₄×C₈

—

181

—

C₄×C₈

#10624382

yes

characteristic

C₂²×C₄

—

181

—

C₂²×C₄

—

181

—

C₂²×C₄

—

181

—

M₁₆

—

362

—

C₂×C₈

—

362

—

C₂×C₈

—

362

—

C₂×C₈

—

181

—

C₂×C₈

C₂×#10624382

yes

—

C₄²

—

181

—

C₄²

—

181

—

C₄²

—

181

—

C₄²

C₂×#10624382

yes

characteristic

C₂³

—

181

—

C₂×C₄

—

362

—

C₂×C₄

—

362

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

362

—

C₈

—

724

—

C₂²

—

362

—

C₂²

—

362

—

C₂²

—

181

—

C₂²

C₂×C₄⋊#10624382

yes

characteristic

C₄

—

362

—

C₄

—

362

—

C₄

—

181

—

C₄

#19153886

yes

—

C₄

#19153887

yes

—

C₄

#19153895

yes

—

C₂

—

362

—

100

C₂

#26042223

yes

characteristic

101

C₂

C₂×#19153886

yes

characteristic

102

C₂

C₂×#19153887

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#10624382
commutator	C₂×C₄×C₁₈₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#10624382
Fitting	C₄×C₈×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂×C₄⋊C₄
prime radical	C₂²×D₁₈₁	C₂×Q₈
cosocle	C₂×C₄×D₁₈₁	C₂³
hypercenter	C₄×C₈	#10624382
hypocenter	C₁₈₁	#1837
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#10624382

commutator

C₂×C₄×C₁₈₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#10624382

Fitting

C₄×C₈×C₁₈₁

C₄

socle

C₂²×C₁₈₁

C₂×C₄⋊C₄

prime radical

C₂²×D₁₈₁

C₂×Q₈

cosocle

C₂×C₄×D₁₈₁

C₂³

C₄×C₈

C₁₈₁

G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
51. C₁₈₁	#1837	semidirect

H ≅ G/N

type

51. C₁₈₁

#1837

semidirect

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

subgroup	index
#26042283	2
#26042155	2
C₄×C₈×D₁₈₁	2
#1837	181

subgroup

index

#26042283

#26042155

C₄×C₈×D₁₈₁

#1837

181

Subgroups — #37549645

Conjugacy classes of subgroups

Complements

Maximal subgroups