Group #17995561 — subgroups

Subgroups — #17995561

Order 4736.

252 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11924528	C₂	1	1	yes	maximal, characteristic
2	#14557399	C₂	1	1	yes	maximal, characteristic
3	#14557296	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
5	#11924528	—	2	2	no	—
6	#11924528	C₄	1	4	yes	complemented
7	C₂×C₄⋊Dic₃₇	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₃₇	C₂²	1	2	yes	—
9	C₂×#10596936	—	2	2	no	—
10	#11924443	—	2	2	no	—
11	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
12	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₃₇	—	2	2	no	—
14	C₂²×C₄×C₃₇	D₄	1	2	yes	—
15	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₃₇	—	2	2	no	—
17	C₂²×Dic₃₇	—	2	2	no	—
18	C₂×C₈×C₃₇	—	2	2	no	—
19	C₂×C₈×C₃₇	—	2	2	no	—
20	C₂×C₈×C₃₇	Q₈	1	4	yes	—
21	C₄²×C₃₇	C₂×C₄	1	2	yes	—
22	C₄²×C₃₇	D₄	1	2	yes	—
23	C₄⋊Dic₃₇	—	2	2	no	—
24	C₄⋊Dic₃₇	—	2	4	no	—
25	C₄⋊Dic₃₇	C₂×C₄	1	4	yes	—
26	#10596936	—	2	8	no	—
27	C₂³×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₇	—	2	4	no	—
29	C₂×C₄×C₃₇	C₂²⋊C₄	1	4	yes	—
30	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₃₇	C₂×Q₈	1	2	yes	—
33	C₂×C₄×C₃₇	#41	1	2	yes	—
34	C₂×Dic₃₇	—	2	4	no	—
35	C₂×Dic₃₇	—	4	4	no	—
36	C₂×Dic₃₇	—	4	2	no	—
37	C₂×Dic₃₇	—	4	4	no	—
38	C₈×C₃₇	—	2	4	no	—
39	C₂²×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₃₇	#124	1	1	yes	characteristic
41	C₂²×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₃₇	#135	1	4	yes	—
43	C₄×C₃₇	—	2	4	no	—
44	C₄×C₃₇	C₄×Q₈	1	2	yes	—
45	C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
46	Dic₃₇	—	4	4	no	—
47	Dic₃₇	—	8	2	no	—
48	#1991	—	37	1	no	maximal, Sylow
49	C₂×C₃₇	#391	1	1	yes	characteristic
50	C₂×C₃₇	#416	1	2	yes	—
51	C₂×C₃₇	#488	1	2	yes	—
52	C₂×C₃₇	#499	1	2	yes	—
53	C₂×#125	—	37	1	no	—
54	C₂×C₄×C₈	D₃₇	1	1	yes	characteristic
55	#382	—	37	1	no	—
56	#340	—	37	4	no	—
57	C₃₇	#1991	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₈	C₂×D₃₇	1	2	yes	—
59	#125	—	37	4	no	—
60	#125	—	74	2	no	—
61	C₂×C₄⋊C₄	—	37	2	no	—
62	C₂×C₄⋊C₄	—	37	2	no	—
63	C₂×C₄⋊C₄	—	74	2	no	—
64	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
65	C₄×C₈	—	2	2	no	—
66	#95	—	74	2	no	—
67	C₂²×C₄	—	74	2	no	—
68	C₂²×C₄	—	74	2	no	—
69	C₂²×C₄	D₁₄₈	1	2	yes	—
70	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	Dic₇₄	1	4	yes	—
74	C₄⋊C₄	—	37	4	no	—
75	C₄⋊C₄	—	74	8	no	—
76	C₄⋊C₄	—	74	2	no	—
77	C₄⋊C₄	—	74	4	no	—
78	C₄²	C₄×D₃₇	1	2	yes	—
79	C₄²	C₂²⋊D₃₇	1	2	yes	—
80	C₂³	C₂×D₁₄₈	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	74	4	no	—
83	C₂×C₄	—	148	2	no	—
84	C₂×C₄	—	148	4	no	—
85	C₂×C₄	—	148	4	no	—
86	C₂×C₄	#10596938	1	4	yes	—
87	C₂×C₄	C₂×Dic₇₄	1	2	yes	—
88	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
89	C₂×C₄	#10596962	1	2	yes	—
90	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
91	C₈	—	2	4	no	—
92	C₂²	C₂×#10596938	1	1	yes	characteristic
93	C₂²	#11924524	1	1	yes	characteristic
94	C₂²	#11924536	1	1	yes	characteristic
95	C₂²	#11924558	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	296	2	no	—
98	C₄	—	148	4	no	—
99	C₄	C₄×Dic₇₄	1	2	yes	—
100	C₄	#11924515	1	2	yes	—
101	C₂	#14557439	1	1	yes	characteristic
102	C₂	#14557530	1	2	yes	—
103	C₂	#14557888	1	2	yes	—
104	C₂	#14557935	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924528

C₂

yes

maximal, characteristic

#14557399

C₂

yes

maximal, characteristic

#14557296

C₂

yes

maximal

C₂×C₄×C₈×C₃₇

C₂

yes

maximal, characteristic

#11924528

—

#11924528

C₄

yes

complemented

C₂×C₄⋊Dic₃₇

C₂²

yes

—

C₂×C₄⋊Dic₃₇

C₂²

yes

—

C₂×#10596936

—

#11924443

—

C₂²×C₈×C₃₇

C₂²

yes

—

C₂×C₄²×C₃₇

C₂²

yes

characteristic

C₄×C₈×C₃₇

—

C₂²×C₄×C₃₇

D₄

yes

—

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂²×Dic₃₇

—

C₂²×Dic₃₇

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

Q₈

yes

—

C₄²×C₃₇

C₂×C₄

yes

—

C₄²×C₃₇

D₄

yes

—

C₄⋊Dic₃₇

—

C₄⋊Dic₃₇

—

C₄⋊Dic₃₇

C₂×C₄

yes

—

#10596936

—

C₂³×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₂²⋊C₄

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

—

C₂×C₄×C₃₇

#41

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₈×C₃₇

—

C₂²×C₃₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₃₇

#124

yes

characteristic

C₂²×C₃₇

C₄⋊Q₈

yes

characteristic

C₂²×C₃₇

#135

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₄×Q₈

yes

—

C₄×C₃₇

C₂²⋊Q₈

yes

—

Dic₃₇

—

Dic₃₇

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

—

C₂×C₃₇

#488

yes

—

C₂×C₃₇

#499

yes

—

C₂×#125

—

C₂×C₄×C₈

D₃₇

yes

characteristic

#382

—

#340

—

C₃₇

#1991

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₃₇

yes

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₃₇

yes

characteristic

C₄×C₈

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₄₈

yes

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₇₄

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₄×D₃₇

yes

—

C₄²

C₂²⋊D₃₇

yes

—

C₂³

C₂×D₁₄₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

148

—

C₂×C₄

—

148

—

C₂×C₄

—

148

—

C₂×C₄

#10596938

yes

—

C₂×C₄

C₂×Dic₇₄

yes

—

C₂×C₄

C₂×C₄×D₃₇

yes

characteristic

C₂×C₄

#10596962

yes

—

C₂×C₄

C₂×C₂²⋊D₃₇

yes

characteristic

C₈

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₄

—

C₄

—

296

—

C₄

—

148

—

C₄

C₄×Dic₇₄

yes

—

100

C₄

#11924515

yes

—

101

C₂

#14557439

yes

characteristic

102

C₂

#14557530

yes

—

103

C₂

#14557888

yes

—

104

C₂

#14557935

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₄₈
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₂×C₄×C₈×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	C₂×D₄
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×C₄×C₈	D₃₇
hypocenter	C₃₇	#1991
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₁₄₈

commutator

C₂×C₄×C₃₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₇

Fitting

C₂×C₄×C₈×C₃₇

C₂

socle, prime radical

C₂³×C₃₇

C₂×D₄

cosocle

C₂²×C₄×C₃₇

C₂³

hypercenter

C₂×C₄×C₈

D₃₇

hypocenter

C₃₇

#1991

LCS

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
6. #11924528	C₄	semidirect
57. C₃₇	#1991	semidirect

H ≅ G/N

type

6. #11924528

C₄

semidirect

57. C₃₇

#1991

semidirect

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

subgroup	index
C₂×#11924528	2
#14557399	2
#14557296	2
C₂×C₄×C₈×C₃₇	2
#1991	37

subgroup

index

C₂×C₄×C₈×C₃₇

Subgroups — #17995561

Conjugacy classes of subgroups

Complements

Maximal subgroups