Group #37533856 — subgroups

Subgroups — #37533856

Order 23168.

224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19153727	C₂	1	1	yes	maximal, characteristic
2	#26041145	C₂	1	1	yes	maximal, characteristic
3	#26041041	C₂	1	4	yes	maximal
4	#384×C₁₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#13089678	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₁₈₁	C₂²	1	2	yes	—
7	#19153727	C₄	1	4	yes	complemented
8	#19153723	—	2	2	no	—
9	C₂×C₄⋊C₄×C₁₈₁	—	2	2	no	—
10	C₂×C₄⋊C₄×C₁₈₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₈₁	C₂²	1	1	yes	characteristic
12	C₂²×Dic₁₈₁	—	2	2	no	—
13	C₂×#13089678	—	2	2	no	—
14	C₂×#13089678	—	2	2	no	—
15	C₂×#13089678	C₂×C₄	1	4	yes	—
16	C₄⋊Dic₁₈₁	—	2	4	no	—
17	C₂²×C₄×C₁₈₁	—	2	2	no	—
18	C₂²×C₄×C₁₈₁	D₄	1	2	yes	—
19	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₁₈₁	—	2	4	no	—
21	C₄⋊C₄×C₁₈₁	—	4	4	no	—
22	C₄²×C₁₈₁	C₂×C₄	1	2	yes	—
23	C₄²×C₁₈₁	Q₈	1	2	yes	—
24	C₂×Dic₁₈₁	—	4	2	no	—
25	C₂×Dic₁₈₁	—	4	2	no	—
26	C₂×Dic₁₈₁	—	4	2	no	—
27	#13089678	—	2	4	no	—
28	C₂³×C₁₈₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₁₈₁	—	2	2	no	—
30	C₂×C₄×C₁₈₁	—	2	2	no	—
31	C₂×C₄×C₁₈₁	—	4	2	no	—
32	C₂×C₄×C₁₈₁	—	4	4	no	—
33	C₂×C₄×C₁₈₁	C₄⋊C₄	1	4	yes	—
34	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₈₁	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₁₈₁	#41	1	2	yes	—
37	C₂×C₄×C₁₈₁	#41	1	2	yes	—
38	C₂²×C₁₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₁₈₁	#124	1	1	yes	characteristic
40	C₂²×C₁₈₁	#124	1	1	yes	characteristic
41	C₂²×C₁₈₁	AGL(1,ℤ/8)	1	2	yes	—
42	C₂²×C₁₈₁	#137	1	2	yes	—
43	C₄×C₁₈₁	—	2	4	no	—
44	C₄×C₁₈₁	—	8	2	no	—
45	C₄×C₁₈₁	#117	1	2	yes	—
46	C₄×C₁₈₁	#125	1	2	yes	—
47	Dic₁₈₁	—	8	2	no	—
48	C₂×C₁₈₁	#382	1	1	yes	characteristic
49	C₂×C₁₈₁	#428	1	2	yes	—
50	C₂×C₁₈₁	#489	1	2	yes	—
51	C₂×C₁₈₁	#490	1	1	yes	characteristic
52	C₂×C₁₈₁	#491	1	1	yes	characteristic
53	C₁₈₁	#1836	1	1	yes	characteristic, complemented, Sylow
54	#1836	—	181	1	no	maximal, Sylow
55	C₂×#97	—	181	1	no	—
56	#384	D₁₈₁	1	1	yes	characteristic
57	#382	—	181	1	no	—
58	#340	—	181	4	no	—
59	C₂²×C₈	—	181	2	no	—
60	C₂×C₄⋊C₄	—	2	2	no	—
61	C₂×C₄⋊C₄	—	181	2	no	—
62	C₂×C₄⋊C₄	C₂×D₁₈₁	1	2	yes	—
63	C₂×C₄²	C₂×D₁₈₁	1	1	yes	characteristic
64	#97	—	181	4	no	—
65	#95	—	362	2	no	—
66	C₂²×C₄	—	2	2	no	—
67	C₂²×C₄	—	362	2	no	—
68	C₂²×C₄	C₂²⋊D₁₈₁	1	2	yes	—
69	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
70	C₂×C₈	—	362	2	no	—
71	C₂×C₈	—	362	2	no	—
72	C₂×C₈	—	181	4	no	—
73	C₄⋊C₄	—	2	4	no	—
74	C₄⋊C₄	—	4	4	no	—
75	C₄⋊C₄	—	362	4	no	—
76	C₄²	C₄×D₁₈₁	1	2	yes	—
77	C₄²	Dic₃₆₂	1	2	yes	—
78	C₂³	C₂×C₂²⋊D₁₈₁	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	4	4	no	—
83	C₂×C₄	—	724	2	no	—
84	C₂×C₄	—	724	2	no	—
85	C₂×C₄	—	724	2	no	—
86	C₂×C₄	#15668428	1	4	yes	—
87	C₂×C₄	C₂×C₄×D₁₈₁	1	1	yes	characteristic
88	C₂×C₄	C₂×Dic₃₆₂	1	1	yes	characteristic
89	C₂×C₄	#15668448	1	2	yes	—
90	C₂×C₄	#15668450	1	2	yes	—
91	C₈	—	362	4	no	—
92	C₂²	C₂×#15668428	1	1	yes	characteristic
93	C₂²	#19153803	1	1	yes	characteristic
94	C₂²	#19153805	1	1	yes	characteristic
95	C₂²	#19153842	1	2	yes	—
96	C₂²	#19153847	1	2	yes	—
97	C₄	—	2	4	no	—
98	C₄	—	8	2	no	—
99	C₄	—	1448	2	no	—
100	C₄	#19153774	1	2	yes	—
101	C₄	#19153807	1	2	yes	—
102	C₂	#26041144	1	1	yes	characteristic
103	C₂	#26041319	1	2	yes	—
104	C₂	#26041641	1	2	yes	—
105	C₂	#26041643	1	1	yes	characteristic
106	C₂	#26041647	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19153727

C₂

yes

maximal, characteristic

#26041145

C₂

yes

maximal, characteristic

#26041041

C₂

yes

maximal

#384×C₁₈₁

C₂

yes

maximal, characteristic

C₂²×#13089678

C₂²

yes

—

C₂×C₄⋊Dic₁₈₁

C₂²

yes

—

#19153727

C₄

yes

complemented

#19153723

—

C₂×C₄⋊C₄×C₁₈₁

—

C₂×C₄⋊C₄×C₁₈₁

C₂²

yes

—

C₂×C₄²×C₁₈₁

C₂²

yes

characteristic

C₂²×Dic₁₈₁

—

C₂×#13089678

—

C₂×#13089678

—

C₂×#13089678

C₂×C₄

yes

—

C₄⋊Dic₁₈₁

—

C₂²×C₄×C₁₈₁

—

C₂²×C₄×C₁₈₁

D₄

yes

—

C₂²×C₄×C₁₈₁

C₂³

yes

characteristic

C₄⋊C₄×C₁₈₁

—

C₄⋊C₄×C₁₈₁

—

C₄²×C₁₈₁

C₂×C₄

yes

—

C₄²×C₁₈₁

Q₈

yes

—

C₂×Dic₁₈₁

—

C₂×Dic₁₈₁

—

C₂×Dic₁₈₁

—

#13089678

—

C₂³×C₁₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₈₁

—

C₂×C₄×C₁₈₁

—

C₂×C₄×C₁₈₁

—

C₂×C₄×C₁₈₁

—

C₂×C₄×C₁₈₁

C₄⋊C₄

yes

—

C₂×C₄×C₁₈₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₈₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₈₁

#41

yes

—

C₂×C₄×C₁₈₁

#41

yes

—

C₂²×C₁₈₁

C₂×C₄⋊C₄

yes

C₂²×C₁₈₁

yes

C₂²×C₁₈₁

yes

C₂²×C₁₈₁

yes

—

C₂²×C₁₈₁

#137

yes

—

C₄×C₁₈₁

—

C₄×C₁₈₁

—

C₄×C₁₈₁

#117

yes

—

C₄×C₁₈₁

#125

yes

—

Dic₁₈₁

—

C₂×C₁₈₁

#382

yes

characteristic

C₂×C₁₈₁

#428

yes

—

C₂×C₁₈₁

#489

yes

—

C₂×C₁₈₁

yes

C₂×C₁₈₁

yes

C₁₈₁

yes

characteristic, complemented, Sylow

#1836

—

181

maximal, Sylow

C₂×#97

—

181

—

#384

D₁₈₁

yes

characteristic

#382

—

181

—

#340

—

181

—

C₂²×C₈

—

181

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

181

—

C₂×C₄⋊C₄

C₂×D₁₈₁

yes

—

C₂×C₄²

C₂×D₁₈₁

yes

characteristic

#97

—

181

—

#95

—

362

—

C₂²×C₄

—

C₂²×C₄

—

362

—

C₂²×C₄

C₂²⋊D₁₈₁

yes

—

C₂²×C₄

C₂²×D₁₈₁

yes

characteristic

C₂×C₈

—

362

—

C₂×C₈

—

362

—

C₂×C₈

—

181

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

362

—

C₄²

C₄×D₁₈₁

yes

—

C₄²

Dic₃₆₂

yes

—

C₂³

C₂×C₂²⋊D₁₈₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

724

—

C₂×C₄

—

724

—

C₂×C₄

—

724

—

C₂×C₄

#15668428

yes

—

C₂×C₄

C₂×C₄×D₁₈₁

yes

characteristic

C₂×C₄

C₂×Dic₃₆₂

yes

characteristic

C₂×C₄

#15668448

yes

—

C₂×C₄

#15668450

yes

—

C₈

—

362

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#19153847

yes

—

C₄

—

C₄

—

C₄

—

1448

—

100

C₄

#19153774

yes

—

101

C₄

#19153807

yes

—

102

C₂

#26041144

yes

characteristic

103

C₂

#26041319

yes

—

104

C₂

#26041641

yes

—

105

C₂

#26041643

yes

characteristic

106

C₂

#26041647

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₈₁
commutator	C₂×C₄×C₁₈₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₈₁
Fitting	#384×C₁₈₁	C₂
socle, prime radical	C₂³×C₁₈₁	C₂×D₄
cosocle	C₂²×C₄×C₁₈₁	C₂³
hypercenter	#384	D₁₈₁
hypocenter	C₁₈₁	#1836
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₈₁

commutator

C₂×C₄×C₁₈₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₈₁

Fitting

#384×C₁₈₁

C₂

socle, prime radical

C₂³×C₁₈₁

C₂×D₄

cosocle

C₂²×C₄×C₁₈₁

C₂³

D₁₈₁

C₁₈₁

G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
7. #19153727	C₄	semidirect
53. C₁₈₁	#1836	semidirect

H ≅ G/N

type

7. #19153727

C₄

semidirect

53. C₁₈₁

#1836

semidirect

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

subgroup	index
C₂×#19153727	2
#26041145	2
#26041041	2
#384×C₁₈₁	2
#1836	181

subgroup

index

#384×C₁₈₁

181

Subgroups — #37533856

Conjugacy classes of subgroups

Complements

Maximal subgroups