Group #17995342 — subgroups

Subgroups — #17995342

Order 4736.

208 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14557571	C₂	1	1	yes	maximal, characteristic
2	#14557561	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	#14557294	C₂	1	2	yes	maximal
5	C₂×#108×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64436	C₂²	1	1	yes	characteristic
7	#11924495	C₂²	1	2	yes	—
8	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
9	#11924470	C₄	1	2	yes	complemented
10	#11924468	C₄	1	2	yes	complemented
11	#11924465	—	2	4	no	—
12	C₈×Dic₃₇	—	2	2	no	—
13	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	#108×C₃₇	—	2	2	no	—
16	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₃₇	—	2	1	no	—
18	M₁₆×C₃₇	—	2	2	no	—
19	M₁₆×C₃₇	—	2	2	no	—
20	C₂×C₈×C₃₇	—	2	2	no	—
21	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₃₇	D₄	1	2	yes	—
24	C₂×C₈×C₃₇	Q₈	1	2	yes	—
25	C₂²⋊Dic₃₇	—	2	2	no	—
26	C₄⋊Dic₃₇	C₂×C₄	1	4	yes	—
27	C₄×Dic₃₇	—	2	1	no	—
28	C₄×Dic₃₇	—	2	2	no	—
29	C₄×Dic₃₇	Q₈	1	2	yes	—
30	C₂×#64436	—	2	1	no	—
31	C₂×#64436	—	2	1	no	—
32	C₂×#64436	D₄	1	2	yes	—
33	C₂³×C₃₇	#41	1	1	yes	characteristic
34	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₃₇	C₂×Q₈	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×Dic₃₇	—	2	4	no	—
41	C₂×Dic₃₇	—	2	2	no	—
42	C₂×Dic₃₇	—	2	4	no	—
43	C₈×C₃₇	—	4	2	no	—
44	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
45	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
46	#64436	—	2	2	no	—
47	C₂²×C₃₇	—	2	2	no	—
48	C₂²×C₃₇	C₄×D₄	1	1	yes	characteristic
49	C₂²×C₃₇	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₃₇	#125	1	1	yes	characteristic
51	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₃₇	C₄×Q₈	1	1	yes	characteristic
53	C₄×C₃₇	#121	1	1	yes	characteristic
54	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
55	Dic₃₇	—	2	4	no	—
56	Dic₃₇	—	4	4	no	—
57	#1945	—	37	1	no	maximal, Sylow
58	C₂×C₃₇	—	2	1	no	—
59	C₂×C₃₇	—	2	1	no	—
60	C₂×C₃₇	#389	1	1	yes	characteristic
61	C₂×C₃₇	#443	1	2	yes	—
62	C₂×#108	D₃₇	1	1	yes	characteristic
63	#427	—	37	1	no	—
64	#424	—	37	2	no	—
65	C₂×C₄×C₈	—	37	1	no	—
66	#339	—	37	2	no	—
67	C₃₇	#1945	1	1	yes	characteristic, complemented, Sylow
68	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
69	C₂²×C₈	—	37	1	no	—
70	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
71	#117	—	37	2	no	—
72	C₂×C₄²	—	37	1	no	—
73	#108	—	2	2	no	—
74	#107	—	37	2	no	—
75	#106	—	37	2	no	—
76	C₄⋊C₈	—	74	4	no	—
77	C₄×C₈	—	74	2	no	—
78	C₂²×C₄	—	74	1	no	—
79	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
80	M₁₆	—	2	2	no	—
81	M₁₆	—	2	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	37	2	no	—
84	C₂×C₈	—	74	1	no	—
85	C₂×C₈	—	74	1	no	—
86	C₂×C₈	Dic₇₄	1	2	yes	—
87	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
88	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
89	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
90	C₄⋊C₄	—	37	4	no	—
91	C₂²⋊C₄	—	74	2	no	—
92	C₄²	—	37	2	no	—
93	C₄²	—	74	2	no	—
94	C₄²	—	74	1	no	—
95	C₂³	#10596966	1	1	yes	characteristic
96	C₂×C₄	—	74	4	no	—
97	C₂×C₄	—	74	2	no	—
98	C₂×C₄	—	74	4	no	—
99	C₂×C₄	C₂×Dic₇₄	1	1	yes	characteristic
100	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
101	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
102	C₂×C₄	#10596964	1	1	yes	characteristic
103	C₂×C₄	Q₈×D₃₇	1	1	yes	characteristic
104	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
105	C₈	—	4	2	no	—
106	C₈	—	74	2	no	—
107	C₈	#10596936	1	2	yes	—
108	C₈	#10596936	1	2	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	#11924498	1	1	yes	characteristic
111	C₂²	#11924512	1	1	yes	characteristic
112	C₂²	#11924527	1	1	yes	characteristic
113	C₄	—	74	4	no	—
114	C₄	—	148	4	no	—
115	C₄	C₂×#10596936	1	1	yes	characteristic
116	C₄	#11924501	1	1	yes	characteristic
117	C₄	#11924507	1	1	yes	characteristic
118	C₄	#11924535	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	2	1	no	—
121	C₂	#14557429	1	1	yes	characteristic
122	C₂	#14557649	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14557571

C₂

yes

maximal, characteristic

#14557561

C₂

yes

maximal

C₂×C₈×Dic₃₇

C₂

yes

maximal, characteristic

#14557294

C₂

yes

maximal

C₂×#108×C₃₇

C₂

yes

maximal, characteristic

C₂²×#64436

C₂²

yes

characteristic

#11924495

C₂²

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

#11924470

C₄

yes

complemented

#11924468

C₄

yes

complemented

#11924465

—

C₈×Dic₃₇

—

C₂×M₁₆×C₃₇

C₂²

yes

—

C₂²×C₈×C₃₇

C₂²

yes

characteristic

#108×C₃₇

—

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂²×Dic₃₇

—

M₁₆×C₃₇

—

M₁₆×C₃₇

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

D₄

yes

—

C₂×C₈×C₃₇

Q₈

yes

—

C₂²⋊Dic₃₇

—

C₄⋊Dic₃₇

C₂×C₄

yes

—

C₄×Dic₃₇

—

C₄×Dic₃₇

—

C₄×Dic₃₇

Q₈

yes

—

C₂×#64436

—

C₂×#64436

—

C₂×#64436

D₄

yes

—

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×D₄

yes

characteristic

C₂²×C₃₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₃₇

#125

yes

characteristic

C₄×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₇

C₄×Q₈

yes

characteristic

C₄×C₃₇

#121

yes

characteristic

C₄×C₃₇

C₄⋊Q₈

yes

characteristic

Dic₃₇

—

Dic₃₇

—

#1945

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

—

C₂×C₃₇

#389

yes

characteristic

C₂×C₃₇

#443

yes

—

C₂×#108

D₃₇

yes

characteristic

#427

—

#424

—

C₂×C₄×C₈

—

#339

—

C₃₇

#1945

yes

characteristic, complemented, Sylow

C₂×M₁₆

C₂×D₃₇

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₃₇

yes

characteristic

#117

—

C₂×C₄²

—

#108

—

#107

—

#106

—

C₄⋊C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₇₄

yes

—

C₂×C₈

C₄×D₃₇

yes

characteristic

C₂×C₈

C₄×D₃₇

yes

characteristic

C₂×C₈

C₂²⋊D₃₇

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₂³

#10596966

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₇₄

yes

characteristic

100

C₂×C₄

C₂×C₄×D₃₇

yes

characteristic

101

C₂×C₄

D₄×D₃₇

yes

characteristic

102

C₂×C₄

#10596964

yes

characteristic

103

C₂×C₄

Q₈×D₃₇

yes

characteristic

104

C₂×C₄

C₂×C₂²⋊D₃₇

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

#10596936

yes

—

108

C₈

#10596936

yes

—

109

C₂²

—

110

C₂²

#11924498

yes

characteristic

111

C₂²

#11924512

yes

characteristic

112

C₂²

#11924527

yes

characteristic

113

C₄

—

114

C₄

—

148

—

115

C₄

C₂×#10596936

yes

characteristic

116

C₄

#11924501

yes

characteristic

117

C₄

#11924507

yes

characteristic

118

C₄

#11924535

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#14557429

yes

characteristic

122

C₂

#14557649

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₃₇
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₂×#108×C₃₇	C₂
socle	C₂²×C₃₇	C₄×D₄
prime radical	C₂³×C₃₇	#41
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×#108	D₃₇
hypocenter	C₃₇	#1945
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₃₇

commutator

C₂×C₄×C₃₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₇

Fitting

C₂×#108×C₃₇

C₂

socle

C₂²×C₃₇

C₄×D₄

prime radical

C₂³×C₃₇

#41

cosocle

C₂²×C₄×C₃₇

C₂³

D₃₇

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
9. #11924470	C₄	semidirect
10. #11924468	C₄	semidirect
67. C₃₇	#1945	semidirect

H ≅ G/N

type

9. #11924470

C₄

semidirect

10. #11924468

C₄

semidirect

67. C₃₇

#1945

semidirect

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

subgroup	index
#14557571	2
#14557561	2
C₂×C₈×Dic₃₇	2
#14557294	2
C₂×#108×C₃₇	2
#1945	37

subgroup

index

C₂×C₈×Dic₃₇

C₂×#108×C₃₇

Subgroups — #17995342

Conjugacy classes of subgroups

Complements

Maximal subgroups