Group #17995387 — subgroups

Subgroups — #17995387

Order 4736.

184 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14557582	C₂	1	2	yes	maximal
2	C₂×#11924472	C₂	1	1	yes	maximal, characteristic
3	#14557488	C₂	1	1	yes	maximal, characteristic
4	#14557305	C₂	1	2	yes	maximal
5	C₂×#108×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596934	C₂²	1	2	yes	—
7	C₂×#10596934	C₂²	1	1	yes	characteristic
8	#11924495	C₂²	1	1	yes	characteristic
9	#11924472	—	2	1	no	—
10	#11924472	—	2	1	no	—
11	#11924472	—	2	4	no	—
12	#11924446	—	2	1	no	—
13	C₈×Dic₃₇	—	2	1	no	—
14	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
15	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
16	#108×C₃₇	C₄	1	4	yes	complemented
17	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
18	M₁₆×C₃₇	—	2	2	no	—
19	M₁₆×C₃₇	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₃₇	—	2	2	no	—
21	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
23	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
24	C₂×C₈×C₃₇	Q₈	1	2	yes	—
25	C₂²⋊Dic₃₇	Q₈	1	2	yes	—
26	C₄⋊Dic₃₇	—	2	1	no	—
27	C₄×Dic₃₇	—	2	1	no	—
28	#10596934	—	2	1	no	—
29	#10596934	—	2	2	no	—
30	#10596934	—	2	2	no	—
31	#10596934	D₄	1	2	yes	—
32	C₂×#64436	—	2	1	no	—
33	C₂×#64436	—	2	2	no	—
34	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₃₇	#41	1	1	yes	characteristic
40	C₂×C₄×C₃₇	#41	1	1	yes	characteristic
41	C₂×Dic₃₇	—	2	2	no	—
42	C₈×C₃₇	—	2	4	no	—
43	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
44	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
45	#64436	—	2	2	no	—
46	#64436	—	4	2	no	—
47	C₂²×C₃₇	—	4	1	no	—
48	C₂²×C₃₇	C₄×Q₈	1	1	yes	characteristic
49	C₂²×C₃₇	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
51	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
53	C₄×C₃₇	#121	1	1	yes	characteristic
54	C₄×C₃₇	#125	1	1	yes	characteristic
55	Dic₃₇	—	4	2	no	—
56	#1953	—	37	1	no	maximal, Sylow
57	C₂×C₃₇	—	2	1	no	—
58	C₂×C₃₇	—	2	1	no	—
59	C₂×C₃₇	—	2	1	no	—
60	C₂×C₃₇	#389	1	1	yes	characteristic
61	#430	—	37	2	no	—
62	C₂×#108	—	37	1	no	—
63	C₂×#108	D₃₇	1	1	yes	characteristic
64	#405	—	37	1	no	—
65	#344	—	37	2	no	—
66	C₃₇	#1953	1	1	yes	characteristic, complemented, Sylow
67	C₂×M₁₆	—	37	1	no	—
68	C₂×M₁₆	—	37	2	no	—
69	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
70	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
71	#117	—	37	1	no	—
72	#108	—	74	4	no	—
73	#108	—	74	1	no	—
74	#108	—	74	1	no	—
75	#108	Dic₃₇	1	4	yes	complemented
76	#97	—	74	1	no	—
77	C₄×C₈	—	74	1	no	—
78	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
79	M₁₆	—	2	2	no	—
80	M₁₆	—	37	2	no	—
81	M₁₆	—	74	1	no	—
82	M₁₆	—	74	2	no	—
83	M₁₆	—	74	2	no	—
84	M₁₆	C₂×Dic₃₇	1	4	yes	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	74	1	no	—
87	C₂×C₈	—	74	2	no	—
88	C₂×C₈	Dic₇₄	1	2	yes	—
89	C₂×C₈	D₁₄₈	1	1	yes	characteristic
90	C₂×C₈	D₁₄₈	1	1	yes	characteristic
91	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
92	C₄⋊C₄	—	74	1	no	—
93	C₂²⋊C₄	—	37	2	no	—
94	C₄²	—	74	1	no	—
95	C₂³	Q₈×D₃₇	1	1	yes	characteristic
96	C₂×C₄	—	74	2	no	—
97	C₂×C₄	C₂×Dic₇₄	1	1	yes	characteristic
98	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
99	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
100	C₂×C₄	#10596964	1	1	yes	characteristic
101	C₂×C₄	#10596966	1	1	yes	characteristic
102	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
103	C₈	—	2	4	no	—
104	C₈	—	74	2	no	—
105	C₈	—	148	2	no	—
106	C₈	C₄⋊Dic₃₇	1	2	yes	—
107	C₈	C₄⋊Dic₃₇	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	Q₈×Dic₃₇	1	1	yes	characteristic
110	C₂²	#11924516	1	1	yes	characteristic
111	C₂²	#11924535	1	1	yes	characteristic
112	C₄	—	148	2	no	—
113	C₄	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
114	C₄	D₄×Dic₃₇	1	1	yes	characteristic
115	C₄	#11924511	1	1	yes	characteristic
116	C₄	#11924527	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	#14557432	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14557582

C₂

yes

maximal

C₂×#11924472

C₂

yes

maximal, characteristic

#14557488

C₂

yes

maximal, characteristic

#14557305

C₂

yes

maximal

C₂×#108×C₃₇

C₂

yes

maximal, characteristic

C₂×#10596934

C₂²

yes

—

C₂×#10596934

C₂²

yes

characteristic

#11924495

C₂²

yes

—

—

—

—

C₈×Dic₃₇

—

C₂×M₁₆×C₃₇

C₂²

yes

—

C₂²×C₈×C₃₇

C₂²

yes

characteristic

#108×C₃₇

C₄

yes

complemented

C₂²×C₄×C₃₇

C₂³

yes

characteristic

M₁₆×C₃₇

—

M₁₆×C₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

D₄

yes

characteristic

C₂×C₈×C₃₇

D₄

yes

characteristic

C₂×C₈×C₃₇

Q₈

yes

—

C₂²⋊Dic₃₇

Q₈

yes

—

C₄⋊Dic₃₇

—

C₄×Dic₃₇

—

—

—

—

D₄

yes

—

C₂×#64436

—

C₂×#64436

—

C₂³×C₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

C₂×C₄×C₃₇

yes

C₂×C₄×C₃₇

yes

C₂×Dic₃₇

—

C₈×C₃₇

—

C₈×C₃₇

C₄⋊C₄

yes

—

C₈×C₃₇

C₄⋊C₄

yes

—

#64436

—

#64436

—

C₂²×C₃₇

—

C₂²×C₃₇

C₄×Q₈

yes

characteristic

C₂²×C₃₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₃₇

C₄⋊Q₈

yes

characteristic

C₄×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₇

C₄×D₄

yes

C₄×C₃₇

yes

C₄×C₃₇

yes

Dic₃₇

—

#1953

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

—

C₂×C₃₇

—

C₂×C₃₇

yes

—

—

D₃₇

yes

characteristic

#405

—

#344

—

C₃₇

#1953

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₃₇

yes

—

C₂²×C₈

C₂×D₃₇

yes

—

—

—

—

Dic₃₇

yes

complemented

#97

—

C₄×C₈

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₃₇

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₇₄

yes

—

C₂×C₈

D₁₄₈

yes

characteristic

C₂×C₈

D₁₄₈

yes

characteristic

C₂×C₈

C₂×Dic₃₇

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

Q₈×D₃₇

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×Dic₇₄

yes

characteristic

C₂×C₄

C₂×D₁₄₈

yes

characteristic

C₂×C₄

D₄×D₃₇

yes

characteristic

100

C₂×C₄

#10596964

yes

characteristic

101

C₂×C₄

#10596966

yes

characteristic

102

C₂×C₄

C₂²×Dic₃₇

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

148

—

106

C₈

C₄⋊Dic₃₇

yes

—

107

C₈

C₄⋊Dic₃₇

yes

—

108

C₂²

—

109

C₂²

Q₈×Dic₃₇

yes

characteristic

110

C₂²

#11924516

yes

characteristic

111

C₂²

#11924535

yes

characteristic

112

C₄

—

148

—

113

C₄

C₂×C₄⋊Dic₃₇

yes

characteristic

114

C₄

D₄×Dic₃₇

yes

characteristic

115

C₄

#11924511

yes

characteristic

116

C₄

#11924527

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#14557432

yes

characteristic

	subgroup	G/H
center	C₄	#11924511
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₂×#108×C₃₇	C₂
socle	C₂×C₃₇	#389
prime radical	C₂³×C₃₇	C₂×Q₈
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×#108	D₃₇
hypocenter	C₃₇	#1953
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#11924511

commutator

C₂×C₄×C₃₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₇

Fitting

C₂×#108×C₃₇

C₂

socle

C₂×C₃₇

#389

prime radical

C₂³×C₃₇

C₂×Q₈

cosocle

C₂²×C₄×C₃₇

C₂³

D₃₇

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
16. #108×C₃₇	C₄	semidirect
66. C₃₇	#1953	semidirect
75. #108	Dic₃₇	semidirect

H ≅ G/N

type

16. #108×C₃₇

C₄

semidirect

66. C₃₇

#1953

semidirect

75. #108

Dic₃₇

semidirect

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

subgroup	index
#14557582	2
C₂×#11924472	2
#14557488	2
#14557305	2
C₂×#108×C₃₇	2
#1953	37

subgroup

index

C₂×#108×C₃₇

Subgroups — #17995387

Conjugacy classes of subgroups

Complements

Maximal subgroups