Group #17995377 — subgroups

Subgroups — #17995377

Order 4736.

196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14557575	C₂	1	2	yes	maximal
2	C₂×#11924468	C₂	1	1	yes	maximal, characteristic
3	#14557488	C₂	1	1	yes	maximal, characteristic
4	#14557301	C₂	1	2	yes	maximal
5	C₂×#108×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596934	C₂²	1	1	yes	characteristic
7	#11924495	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₃₇	C₂²	1	2	yes	—
9	#11924470	—	2	2	no	—
10	#11924468	—	2	1	no	—
11	#11924468	—	2	1	no	—
12	#11924468	—	2	2	no	—
13	#11924446	—	2	1	no	—
14	C₈×Dic₃₇	—	2	1	no	—
15	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
16	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
17	#108×C₃₇	C₄	1	4	yes	complemented
18	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
19	C₂²×Dic₃₇	—	2	2	no	—
20	M₁₆×C₃₇	—	2	2	no	—
21	M₁₆×C₃₇	C₂×C₄	1	4	yes	—
22	C₂×C₈×C₃₇	—	2	2	no	—
23	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
25	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
26	C₂×C₈×C₃₇	Q₈	1	2	yes	—
27	C₂²⋊Dic₃₇	—	2	1	no	—
28	C₄⋊Dic₃₇	—	2	2	no	—
29	C₄⋊Dic₃₇	—	2	2	no	—
30	C₄⋊Dic₃₇	D₄	1	2	yes	—
31	C₄×Dic₃₇	—	2	1	no	—
32	#10596934	—	2	1	no	—
33	#10596934	Q₈	1	2	yes	—
34	C₂×#64436	—	2	1	no	—
35	C₂³×C₃₇	#41	1	1	yes	characteristic
36	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₃₇	#41	1	1	yes	characteristic
42	C₂×Dic₃₇	—	2	2	no	—
43	C₂×Dic₃₇	—	4	2	no	—
44	C₂×Dic₃₇	—	8	2	no	—
45	C₈×C₃₇	—	2	4	no	—
46	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
47	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
48	#64436	—	2	2	no	—
49	C₂²×C₃₇	—	2	2	no	—
50	C₂²×C₃₇	C₄×Q₈	1	1	yes	characteristic
51	C₂²×C₃₇	#121	1	1	yes	characteristic
52	C₂²×C₃₇	#125	1	1	yes	characteristic
53	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
55	C₄×C₃₇	C₂²⋊Q₈	1	1	yes	characteristic
56	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
57	Dic₃₇	—	4	2	no	—
58	Dic₃₇	—	8	2	no	—
59	#1951	—	37	1	no	maximal, Sylow
60	C₂×C₃₇	—	2	1	no	—
61	C₂×C₃₇	—	2	1	no	—
62	C₂×C₃₇	#389	1	1	yes	characteristic
63	C₂×C₃₇	#471	1	2	yes	—
64	C₂×#108	D₃₇	1	1	yes	characteristic
65	#428	—	37	2	no	—
66	C₂×#106	—	37	1	no	—
67	#405	—	37	1	no	—
68	#343	—	37	2	no	—
69	C₃₇	#1951	1	1	yes	characteristic, complemented, Sylow
70	C₂×M₁₆	—	37	1	no	—
71	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
72	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
73	#117	—	37	1	no	—
74	C₂×C₄⋊C₄	—	37	2	no	—
75	#108	Dic₃₇	1	4	yes	complemented
76	#107	—	74	2	no	—
77	#106	—	74	2	no	—
78	#106	—	74	1	no	—
79	#106	—	74	1	no	—
80	#97	—	74	1	no	—
81	C₄×C₈	—	74	1	no	—
82	C₂²×C₄	—	74	2	no	—
83	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
84	M₁₆	—	2	2	no	—
85	M₁₆	—	37	2	no	—
86	M₁₆	—	74	1	no	—
87	M₁₆	C₂×Dic₃₇	1	4	yes	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	74	1	no	—
90	C₂×C₈	Dic₇₄	1	2	yes	—
91	C₂×C₈	D₁₄₈	1	1	yes	characteristic
92	C₂×C₈	D₁₄₈	1	1	yes	characteristic
93	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
94	C₄⋊C₄	—	37	2	no	—
95	C₄⋊C₄	—	74	2	no	—
96	C₄⋊C₄	—	74	2	no	—
97	C₂²⋊C₄	—	74	1	no	—
98	C₄²	—	74	1	no	—
99	C₂³	#10596966	1	1	yes	characteristic
100	C₂×C₄	—	296	2	no	—
101	C₂×C₄	—	74	2	no	—
102	C₂×C₄	—	148	2	no	—
103	C₂×C₄	C₂×Dic₇₄	1	1	yes	characteristic
104	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
105	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
106	C₂×C₄	#10596964	1	1	yes	characteristic
107	C₂×C₄	Q₈×D₃₇	1	1	yes	characteristic
108	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
109	C₈	—	2	4	no	—
110	C₈	—	74	2	no	—
111	C₈	C₄⋊Dic₃₇	1	2	yes	—
112	C₈	C₄⋊Dic₃₇	1	2	yes	—
113	C₂²	—	2	2	no	—
114	C₂²	Q₈×Dic₃₇	1	1	yes	characteristic
115	C₂²	#11924511	1	1	yes	characteristic
116	C₂²	#11924527	1	1	yes	characteristic
117	C₄	—	296	2	no	—
118	C₄	—	148	2	no	—
119	C₄	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
120	C₄	D₄×Dic₃₇	1	1	yes	characteristic
121	C₄	#11924516	1	1	yes	characteristic
122	C₄	#11924535	1	1	yes	characteristic
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	#14557432	1	1	yes	characteristic
126	C₂	#14557797	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14557575

C₂

yes

maximal

C₂×#11924468

C₂

yes

maximal, characteristic

#14557488

C₂

yes

maximal, characteristic

#14557301

C₂

yes

maximal

C₂×#108×C₃₇

C₂

yes

maximal, characteristic

C₂×#10596934

C₂²

yes

characteristic

#11924495

C₂²

yes

characteristic

C₂×C₄⋊Dic₃₇

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

C₂²×Dic₃₇

—

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

—

C₄⋊Dic₃₇

—

C₄⋊Dic₃₇

—

C₄⋊Dic₃₇

D₄

yes

—

C₄×Dic₃₇

—

#10596934

—

#10596934

Q₈

yes

—

C₂×#64436

—

C₂³×C₃₇

#41

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

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

#41

yes

characteristic

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₈×C₃₇

—

C₈×C₃₇

C₄⋊C₄

yes

—

C₈×C₃₇

C₄⋊C₄

yes

—

#64436

—

C₂²×C₃₇

—

C₂²×C₃₇

C₄×Q₈

yes

C₂²×C₃₇

yes

C₂²×C₃₇

yes

C₄×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₇

C₄×D₄

yes

characteristic

C₄×C₃₇

C₂²⋊Q₈

yes

characteristic

C₄×C₃₇

C₄⋊Q₈

yes

characteristic

Dic₃₇

—

Dic₃₇

—

#1951

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

—

C₂×C₃₇

#389

yes

characteristic

C₂×C₃₇

#471

yes

—

C₂×#108

D₃₇

yes

—

—

—

—

C₃₇

#1951

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₃₇

yes

—

C₂²×C₈

C₂×D₃₇

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#108

Dic₃₇

yes

—

—

—

—

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₃₇

yes

—

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

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#10596966

yes

characteristic

100

C₂×C₄

—

296

—

101

C₂×C₄

—

102

C₂×C₄

—

148

—

103

C₂×C₄

C₂×Dic₇₄

yes

characteristic

104

C₂×C₄

C₂×D₁₄₈

yes

characteristic

105

C₂×C₄

D₄×D₃₇

yes

characteristic

106

C₂×C₄

#10596964

yes

characteristic

107

C₂×C₄

Q₈×D₃₇

yes

characteristic

108

C₂×C₄

C₂²×Dic₃₇

yes

characteristic

109

C₈

—

110

C₈

—

111

C₈

C₄⋊Dic₃₇

yes

—

112

C₈

C₄⋊Dic₃₇

yes

—

113

C₂²

—

114

C₂²

Q₈×Dic₃₇

yes

characteristic

115

C₂²

#11924511

yes

characteristic

116

C₂²

#11924527

yes

characteristic

117

C₄

—

296

—

118

C₄

—

148

—

119

C₄

C₂×C₄⋊Dic₃₇

yes

characteristic

120

C₄

D₄×Dic₃₇

yes

characteristic

121

C₄

#11924516

yes

characteristic

122

C₄

#11924535

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

#14557432

yes

characteristic

126

C₂

#14557797

yes

—

	subgroup	G/H
center	C₂²	#11924511
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₂×#108×C₃₇	C₂
socle	C₂²×C₃₇	#121
prime radical	C₂³×C₃₇	#41
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×#108	D₃₇
hypocenter	C₃₇	#1951
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂²

#11924511

commutator

C₂×C₄×C₃₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₇

Fitting

C₂×#108×C₃₇

C₂

C₂²×C₃₇

C₂³×C₃₇

C₂²×C₄×C₃₇

C₂³

D₃₇

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
17. #108×C₃₇	C₄	semidirect
69. C₃₇	#1951	semidirect
75. #108	Dic₃₇	semidirect

H ≅ G/N

type

17. #108×C₃₇

C₄

semidirect

69. C₃₇

#1951

semidirect

75. #108

Dic₃₇

semidirect

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

subgroup	index
#14557575	2
C₂×#11924468	2
#14557488	2
#14557301	2
C₂×#108×C₃₇	2
#1951	37

subgroup

index

C₂×#108×C₃₇

Subgroups — #17995377

Conjugacy classes of subgroups

Complements

Maximal subgroups