Group #17994454 — subgroups

Subgroups — #17994454

Order 4736.

260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 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×#11924465	C₂	1	2	yes	maximal
2	C₂×#11924447	C₂	1	1	yes	maximal, characteristic
3	#14557379	C₂	1	1	yes	maximal, characteristic
4	#14557287	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64436	C₂²	1	2	yes	—
7	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
9	#11924465	C₄	1	8	yes	complemented
10	#11924447	—	2	2	no	—
11	#11924443	C₄	1	4	yes	—
12	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
13	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₃₇	—	2	2	no	—
15	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
18	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₃₇	—	2	2	no	—
20	C₂×C₈×C₃₇	—	2	2	no	—
21	C₂×C₈×C₃₇	C₂×C₄	1	4	yes	—
22	C₄²×C₃₇	D₄	1	2	yes	—
23	C₄²×C₃₇	Q₈	1	2	yes	—
24	C₄×Dic₃₇	—	2	2	no	—
25	C₄×Dic₃₇	C₂×C₄	1	4	yes	—
26	C₂×#64436	—	2	2	no	—
27	C₂×#64436	—	2	2	no	—
28	C₂×#64436	C₂×C₄	1	4	yes	—
29	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₃₇	—	2	4	no	—
31	C₂×C₄×C₃₇	C₄⋊C₄	1	4	yes	—
32	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
33	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₃₇	#41	1	2	yes	—
36	C₂×Dic₃₇	—	2	4	no	—
37	C₂×Dic₃₇	—	2	2	no	—
38	C₂×Dic₃₇	—	2	4	no	—
39	C₂×Dic₃₇	C₄²	1	4	yes	—
40	C₈×C₃₇	—	2	4	no	—
41	#64436	—	2	4	no	—
42	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
43	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₃₇	#117	1	1	yes	characteristic
45	C₂²×C₃₇	#131	1	4	yes	—
46	C₄×C₃₇	—	2	4	no	—
47	C₄×C₃₇	C₄×D₄	1	2	yes	—
48	C₄×C₃₇	C₄×Q₈	1	2	yes	—
49	Dic₃₇	—	2	4	no	—
50	Dic₃₇	—	4	2	no	—
51	#1768	—	37	1	no	maximal, Sylow
52	C₂×C₃₇	C₄×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₃₇	#405	1	2	yes	—
54	C₂×C₃₇	#424	1	2	yes	—
55	C₂×C₃₇	#433	1	2	yes	—
56	C₂×C₄⋊C₈	—	37	2	no	—
57	C₂×#97	—	37	1	no	—
58	C₂×C₄×C₈	D₃₇	1	1	yes	characteristic
59	#376	—	37	1	no	—
60	#336	—	37	2	no	—
61	C₃₇	#1768	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	37	2	no	—
63	C₂²×C₈	C₂×D₃₇	1	2	yes	—
64	C₂×C₄²	—	37	1	no	—
65	C₂×C₄²	—	37	1	no	—
66	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
67	C₄⋊C₈	—	37	8	no	—
68	#97	—	74	2	no	—
69	C₄×C₈	—	2	2	no	—
70	#95	—	37	4	no	—
71	C₂²×C₄	—	37	2	no	—
72	C₂²×C₄	—	37	2	no	—
73	C₂²×C₄	C₄×D₃₇	1	2	yes	—
74	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	37	4	no	—
78	C₂×C₈	—	74	2	no	—
79	C₂×C₈	—	74	2	no	—
80	C₂×C₈	C₄×D₃₇	1	4	yes	—
81	C₄²	—	37	4	no	—
82	C₄²	—	74	2	no	—
83	C₄²	Dic₇₄	1	2	yes	—
84	C₄²	C₂²⋊D₃₇	1	2	yes	—
85	C₂³	C₂×C₄×D₃₇	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	37	4	no	—
88	C₂×C₄	—	74	4	no	—
89	C₂×C₄	—	74	2	no	—
90	C₂×C₄	—	74	4	no	—
91	C₂×C₄	#10596936	1	4	yes	—
92	C₂×C₄	C₂×Dic₇₄	1	1	yes	characteristic
93	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
94	C₂×C₄	#10596962	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
96	C₈	—	2	4	no	—
97	C₈	—	74	4	no	—
98	C₂²	C₄²×D₃₇	1	1	yes	characteristic
99	C₂²	C₂×#10596936	1	1	yes	characteristic
100	C₂²	#11924493	1	1	yes	characteristic
101	C₂²	#11924542	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	74	4	no	—
104	C₄	—	148	2	no	—
105	C₄	C₄×C₂²⋊D₃₇	1	2	yes	—
106	C₄	C₄×Dic₇₄	1	2	yes	—
107	C₂	C₄×#10596936	1	1	yes	characteristic
108	C₂	#14557487	1	2	yes	—
109	C₂	#14557559	1	2	yes	—
110	C₂	#14557592	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924465

C₂

yes

maximal

C₂×#11924447

C₂

yes

maximal, characteristic

#14557379

C₂

yes

maximal, characteristic

#14557287

C₂

yes

maximal

C₂×C₄×C₈×C₃₇

C₂

yes

maximal, characteristic

C₂²×#64436

C₂²

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

#11924465

C₄

yes

complemented

#11924447

—

#11924443

C₄

yes

—

C₂²×C₈×C₃₇

C₂²

yes

—

C₂×C₄²×C₃₇

C₂²

yes

characteristic

C₄×C₈×C₃₇

—

C₂²×C₄×C₃₇

C₂×C₄

yes

—

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₄²×C₃₇

D₄

yes

—

C₄²×C₃₇

Q₈

yes

—

C₄×Dic₃₇

—

C₄×Dic₃₇

C₂×C₄

yes

—

C₂×#64436

—

C₂×#64436

—

C₂×#64436

C₂×C₄

yes

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₄⋊C₄

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

#41

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

C₄²

yes

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

C₂×C₄²

yes

characteristic

C₂²×C₃₇

C₂×C₄⋊C₄

yes

C₂²×C₃₇

yes

C₂²×C₃₇

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₄×D₄

yes

—

C₄×C₃₇

C₄×Q₈

yes

—

Dic₃₇

—

Dic₃₇

—

#1768

—

maximal, Sylow

C₂×C₃₇

C₄×C₄⋊C₄

yes

characteristic

C₂×C₃₇

#405

yes

—

C₂×C₃₇

#424

yes

—

C₂×C₃₇

#433

yes

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×C₄×C₈

D₃₇

yes

characteristic

#376

—

#336

—

C₃₇

#1768

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₃₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₃₇

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₃₇

yes

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₃₇

yes

—

C₄²

—

C₄²

—

C₄²

Dic₇₄

yes

—

C₄²

C₂²⋊D₃₇

yes

—

C₂³

C₂×C₄×D₃₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10596936

yes

—

C₂×C₄

C₂×Dic₇₄

yes

characteristic

C₂×C₄

C₂×C₄×D₃₇

yes

—

C₂×C₄

#10596962

yes

—

C₂×C₄

C₂×C₂²⋊D₃₇

yes

characteristic

C₈

—

C₈

—

C₂²

C₄²×D₃₇

yes

characteristic

C₂²

C₂×#10596936

yes

characteristic

100

C₂²

#11924493

yes

characteristic

101

C₂²

#11924542

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

148

—

105

C₄

C₄×C₂²⋊D₃₇

yes

—

106

C₄

C₄×Dic₇₄

yes

—

107

C₂

C₄×#10596936

yes

characteristic

108

C₂

#14557487

yes

—

109

C₂

#14557559

yes

—

110

C₂

#14557592

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₇
commutator	C₂²×C₃₇	C₂×C₄²
Fitting	C₂×C₄×C₈×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×C₄×C₈	D₃₇
hypocenter	C₃₇	#1768
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₃₇

commutator

C₂²×C₃₇

C₂×C₄²

Fitting

C₂×C₄×C₈×C₃₇

C₂

socle, prime radical

C₂³×C₃₇

C₂²×C₄

cosocle

C₂²×C₄×C₃₇

C₂³

hypercenter

C₂×C₄×C₈

D₃₇

C₃₇

G ▷ C₂²×C₃₇ ▷ C₃₇

C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. #11924465	C₄	semidirect
61. C₃₇	#1768	semidirect

H ≅ G/N

type

9. #11924465

C₄

semidirect

61. C₃₇

#1768

semidirect

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

subgroup	index
C₂×#11924465	2
C₂×#11924447	2
#14557379	2
#14557287	2
C₂×C₄×C₈×C₃₇	2
#1768	37

subgroup

index

C₂×C₄×C₈×C₃₇

Subgroups — #17994454

Conjugacy classes of subgroups

Complements

Maximal subgroups