Group #18010536 — subgroups

Subgroups — #18010536

Order 4736.

220 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 90 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×#11924607	C₂	1	2	yes	maximal
2	C₂×#11924606	C₂	1	2	yes	maximal
3	#14558538	C₂	1	2	yes	maximal
4	C₄×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10596953	C₂²	1	4	yes	—
6	#11924607	—	2	4	no	—
7	#11924606	—	2	4	no	—
8	#11924603	—	2	4	no	—
9	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
11	C₄²×D₃₇	C₂²	1	1	yes	characteristic
12	C₄×#64436	C₄	1	1	yes	characteristic
13	C₈×Dic₃₇	C₄	1	1	yes	characteristic
14	C₈×Dic₃₇	C₄	1	1	yes	characteristic
15	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
16	C₂×C₄×D₃₇	Q₈	1	2	yes	—
17	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
18	C₂×#64438	—	2	4	no	—
19	#10596953	—	2	4	no	—
20	#10596953	—	2	4	no	—
21	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₃₇	D₄	1	2	yes	—
26	C₂×#64436	C₂×C₄	1	1	yes	characteristic
27	C₂×#64436	C₂×C₄	1	1	yes	characteristic
28	C₈×D₃₇	D₄	1	2	yes	—
29	C₈×D₃₇	D₄	1	2	yes	—
30	C₈×D₃₇	Q₈	1	2	yes	—
31	C₈×D₃₇	Q₈	1	2	yes	—
32	C₂²×D₃₇	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₃₇	C₄⋊C₄	1	2	yes	—
36	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
37	C₄×D₃₇	—	2	4	no	—
38	C₄×D₃₇	C₂×D₄	1	1	yes	characteristic
39	C₄×D₃₇	C₂×D₄	1	1	yes	characteristic
40	C₄×D₃₇	C₂×Q₈	1	1	yes	characteristic
41	C₄×D₃₇	C₂×Q₈	1	1	yes	characteristic
42	#64438	—	4	4	no	—
43	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
44	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
45	#64436	C₄⋊C₄	1	2	yes	—
46	#64436	C₄⋊C₄	1	2	yes	—
47	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×D₃₇	—	2	2	no	—
49	C₂×D₃₇	C₄⋊Q₈	1	1	yes	characteristic
50	C₂×D₃₇	C₄⋊Q₈	1	1	yes	characteristic
51	C₄×C₃₇	—	2	2	no	—
52	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
54	Dic₃₇	#108	1	4	yes	complemented
55	Dic₃₇	#127	1	1	yes	characteristic
56	Dic₃₇	C₄⋊Q₈	1	1	yes	characteristic
57	#1848	—	37	1	no	maximal, Sylow
58	C₂×C₃₇	#384	1	1	yes	characteristic
59	C₂×C₃₇	C₂×#108	1	2	yes	—
60	D₃₇	—	2	1	no	—
61	D₃₇	—	2	1	no	—
62	C₂×#108	—	37	2	no	—
63	C₂×#108	—	37	2	no	—
64	#423	—	37	2	no	—
65	C₂×C₄×C₈	—	37	1	no	—
66	C₃₇	#1848	1	1	yes	characteristic, complemented, Sylow
67	C₂×M₁₆	—	37	4	no	—
68	C₂²×C₈	—	37	1	no	—
69	C₂²×C₈	—	37	1	no	—
70	C₂×C₄²	—	37	1	no	—
71	#108	—	74	4	no	—
72	#108	—	74	4	no	—
73	C₄⋊C₈	—	74	4	no	—
74	C₄×C₈	—	37	1	no	—
75	C₄×C₈	—	37	1	no	—
76	C₄×C₈	—	37	1	no	—
77	C₄×C₈	#3866	1	1	yes	characteristic
78	C₂²×C₄	—	37	1	no	—
79	C₂²×C₄	—	37	2	no	—
80	M₁₆	—	74	4	no	—
81	M₁₆	—	74	4	no	—
82	C₂×C₈	—	37	1	no	—
83	C₂×C₈	—	37	1	no	—
84	C₂×C₈	—	37	2	no	—
85	C₂×C₈	—	37	2	no	—
86	C₂×C₈	—	37	2	no	—
87	C₂×C₈	—	37	2	no	—
88	C₂×C₈	—	74	4	no	—
89	C₂×C₈	C₂×#3866	1	1	yes	characteristic
90	C₂×C₈	C₂×#3866	1	1	yes	characteristic
91	C₄²	—	37	2	no	—
92	C₄²	—	37	1	no	—
93	C₄²	C₂×#3866	1	1	yes	characteristic
94	C₂³	—	37	1	no	—
95	C₂×C₄	—	37	1	no	—
96	C₂×C₄	—	37	2	no	—
97	C₂×C₄	—	37	1	no	—
98	C₂×C₄	—	37	1	no	—
99	C₂×C₄	—	37	1	no	—
100	C₂×C₄	—	37	1	no	—
101	C₂×C₄	—	74	4	no	—
102	C₂×C₄	C₄⋊#3866	1	2	yes	—
103	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
104	C₈	—	37	2	no	—
105	C₈	—	37	2	no	—
106	C₈	—	148	4	no	—
107	C₈	C₄⋊#3866	1	2	yes	—
108	C₈	C₄⋊#3866	1	2	yes	—
109	C₂²	—	37	1	no	—
110	C₂²	—	37	1	no	—
111	C₂²	—	74	2	no	—
112	C₂²	C₂×C₄⋊#3866	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	37	1	no	—
115	C₄	—	37	1	no	—
116	C₄	—	37	4	no	—
117	C₄	C₂×C₄⋊#3866	1	1	yes	characteristic
118	C₄	C₂×C₄⋊#3866	1	1	yes	characteristic
119	C₂	—	74	1	no	—
120	C₂	—	74	1	no	—
121	C₂	#14558479	1	1	yes	characteristic
122	C₂	D₃₇⋊#108	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924607

C₂

yes

maximal

C₂×#11924606

C₂

yes

maximal

#14558538

C₂

yes

maximal

C₄×C₈×D₃₇

C₂

yes

maximal, characteristic

C₂×#10596953

C₂²

yes

—

#11924607

—

#11924606

—

#11924603

—

C₂×C₈×D₃₇

C₂²

yes

characteristic

C₂×C₈×D₃₇

C₂²

yes

characteristic

C₄²×D₃₇

C₂²

yes

characteristic

C₄×#64436

C₄

yes

characteristic

C₈×Dic₃₇

C₄

yes

characteristic

C₈×Dic₃₇

C₄

yes

characteristic

C₄×C₈×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

Q₈

yes

—

C₂×C₄×D₃₇

C₂³

yes

—

—

—

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

D₄

yes

—

C₂×#64436

C₂×C₄

yes

characteristic

C₂×#64436

C₂×C₄

yes

characteristic

C₈×D₃₇

D₄

yes

—

C₈×D₃₇

D₄

yes

—

C₈×D₃₇

Q₈

yes

—

C₈×D₃₇

Q₈

yes

—

C₂²×D₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

C₄⋊C₄

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₄⋊C₄

yes

—

C₂×Dic₃₇

C₂×D₄

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

C₂×D₄

yes

characteristic

C₄×D₃₇

C₂×D₄

yes

characteristic

C₄×D₃₇

C₂×Q₈

yes

characteristic

C₄×D₃₇

C₂×Q₈

yes

characteristic

#64438

—

C₈×C₃₇

C₄⋊C₄

yes

—

C₈×C₃₇

C₄⋊C₄

yes

—

#64436

C₄⋊C₄

yes

—

#64436

C₄⋊C₄

yes

—

C₂²×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

C₄⋊Q₈

yes

characteristic

C₂×D₃₇

C₄⋊Q₈

yes

characteristic

C₄×C₃₇

—

C₄×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₇

C₂×C₄⋊C₄

yes

Dic₃₇

yes

Dic₃₇

yes

Dic₃₇

C₄⋊Q₈

yes

—

C₂×C₃₇

yes

C₂×C₃₇

yes

—

D₃₇

—

D₃₇

—

C₂×#108

—

C₂×#108

—

#423

—

C₂×C₄×C₈

—

C₃₇

#1848

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#3866

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₄⋊#3866

yes

—

103

C₂×C₄

C₂²×#3866

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

148

—

107

C₈

C₄⋊#3866

yes

—

108

C₈

C₄⋊#3866

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂×C₄⋊#3866

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×C₄⋊#3866

yes

characteristic

118

C₄

C₂×C₄⋊#3866

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#14558479

yes

characteristic

122

C₂

D₃₇⋊#108

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#3866
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#3866
Fitting	C₄×C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₂×C₄⋊C₄
prime radical	C₂²×D₃₇	C₂×Q₈
cosocle	C₂×C₄×D₃₇	C₂³
hypercenter	C₄×C₈	#3866
hypocenter	C₃₇	#1848
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#3866

commutator

C₂×C₄×C₃₇

C₂²×C₄

Frattini

C₂×C₄

C₂²×#3866

Fitting

C₄×C₈×C₃₇

C₄

socle

C₂²×C₃₇

C₂×C₄⋊C₄

prime radical

C₂²×D₃₇

C₂×Q₈

cosocle

C₂×C₄×D₃₇

C₂³

C₄×C₈

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
54. Dic₃₇	#108	semidirect
66. C₃₇	#1848	semidirect

H ≅ G/N

type

54. Dic₃₇

#108

semidirect

66. C₃₇

#1848

semidirect

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

subgroup	index
C₂×#11924607	2
C₂×#11924606	2
#14558538	2
C₄×C₈×D₃₇	2
#1848	37

subgroup

index

C₄×C₈×D₃₇

Subgroups — #18010536

Conjugacy classes of subgroups

Complements

Maximal subgroups