Group #17994714 — subgroups

Subgroups — #17994714

Order 4736.

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

normal subgroups only

This group has 216 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	C₂×#11924465	C₂	1	2	yes	maximal
2	#14557379	C₂	1	1	yes	maximal, characteristic
3	#14557288	C₂	1	1	yes	maximal, characteristic
4	#14557287	C₂	1	2	yes	maximal
5	C₃₇×#336	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	—	2	4	no	—
10	#11924443	C₄	1	2	yes	—
11	#11924443	C₄	1	2	yes	—
12	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
13	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
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	—	2	2	no	—
22	C₄²×C₃₇	—	2	2	no	—
23	C₄×Dic₃₇	—	2	2	no	—
24	C₄×Dic₃₇	D₄	1	2	yes	—
25	C₄×Dic₃₇	Q₈	1	2	yes	—
26	C₂×#64436	—	2	2	no	—
27	C₂×#64436	—	2	2	no	—
28	C₂×#64436	—	2	2	no	—
29	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₃₇	—	2	2	no	—
31	C₂×C₄×C₃₇	—	2	2	no	—
32	C₂×C₄×C₃₇	—	2	2	no	—
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×C₄×C₃₇	#41	1	2	yes	—
37	C₂×Dic₃₇	—	2	2	no	—
38	C₂×Dic₃₇	—	2	2	no	—
39	C₂×Dic₃₇	—	2	1	no	—
40	C₂×Dic₃₇	—	2	1	no	—
41	C₂×Dic₃₇	—	2	2	no	—
42	C₂×Dic₃₇	—	2	2	no	—
43	C₂×Dic₃₇	C₄⋊C₄	1	4	yes	—
44	C₈×C₃₇	—	4	2	no	—
45	#64436	—	4	2	no	—
46	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₃₇	#117	1	1	yes	characteristic
48	C₂²×C₃₇	#117	1	1	yes	characteristic
49	C₂²×C₃₇	#131	1	2	yes	—
50	C₂²×C₃₇	#131	1	2	yes	—
51	C₄×C₃₇	—	4	2	no	—
52	C₄×C₃₇	#124	1	2	yes	—
53	C₄×C₃₇	#125	1	2	yes	—
54	Dic₃₇	—	2	4	no	—
55	Dic₃₇	—	4	1	no	—
56	Dic₃₇	—	4	1	no	—
57	#1832	—	37	1	no	maximal, Sylow
58	C₂×C₃₇	#382	1	1	yes	characteristic
59	C₂×C₃₇	#424	1	2	yes	—
60	C₂×C₃₇	#433	1	2	yes	—
61	C₂×C₃₇	#433	1	1	yes	characteristic
62	C₂×C₃₇	#433	1	1	yes	characteristic
63	C₂×C₄⋊C₈	—	37	2	no	—
64	#376	—	37	1	no	—
65	#336	—	37	2	no	—
66	#336	—	37	1	no	—
67	#336	D₃₇	1	1	yes	characteristic
68	C₃₇	#1832	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	37	2	no	—
70	C₂²×C₈	C₂×D₃₇	1	2	yes	—
71	C₂×C₄²	—	37	1	no	—
72	C₂×C₄²	—	37	1	no	—
73	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
74	C₄⋊C₈	—	74	4	no	—
75	#95	—	37	2	no	—
76	#95	—	37	2	no	—
77	C₂²×C₄	—	37	2	no	—
78	C₂²×C₄	—	37	1	no	—
79	C₂²×C₄	—	37	1	no	—
80	C₂²×C₄	C₄×D₃₇	1	2	yes	—
81	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	74	2	no	—
86	C₂×C₈	—	74	2	no	—
87	C₂×C₈	—	74	2	no	—
88	C₄²	—	2	2	no	—
89	C₄²	—	37	2	no	—
90	C₄²	—	37	2	no	—
91	C₄²	—	74	2	no	—
92	C₂³	C₂×C₄×D₃₇	1	1	yes	characteristic
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	37	4	no	—
97	C₂×C₄	—	74	2	no	—
98	C₂×C₄	—	74	2	no	—
99	C₂×C₄	—	74	1	no	—
100	C₂×C₄	—	74	1	no	—
101	C₂×C₄	—	74	2	no	—
102	C₂×C₄	—	74	2	no	—
103	C₂×C₄	#10596962	1	2	yes	—
104	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
105	C₂×C₄	#10596964	1	2	yes	—
106	C₂×C₄	Q₈×D₃₇	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	148	2	no	—
109	C₂²	C₄⋊C₄×D₃₇	1	1	yes	characteristic
110	C₂²	#11924492	1	1	yes	characteristic
111	C₂²	#11924493	1	1	yes	characteristic
112	C₂²	#11924542	1	2	yes	—
113	C₂²	#11924544	1	2	yes	—
114	C₄	—	4	2	no	—
115	C₄	—	74	4	no	—
116	C₄	—	148	1	no	—
117	C₄	—	148	1	no	—
118	C₄	#11924522	1	2	yes	—
119	C₄	#11924526	1	2	yes	—
120	C₂	#14557397	1	1	yes	characteristic
121	C₂	#14557558	1	2	yes	—
122	C₂	#14557591	1	2	yes	—
123	C₂	#14557592	1	1	yes	characteristic
124	C₂	#14557595	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924465

C₂

yes

maximal

#14557379

C₂

yes

maximal, characteristic

#14557288

C₂

yes

maximal, characteristic

#14557287

C₂

yes

maximal

C₃₇×#336

C₂

yes

maximal, characteristic

C₂²×#64436

C₂²

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

#11924465

—

#11924443

C₄

yes

—

#11924443

C₄

yes

—

C₂²×C₈×C₃₇

C₂²

yes

—

C₂×C₄²×C₃₇

C₂²

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

—

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₄²×C₃₇

—

C₄×Dic₃₇

—

C₄×Dic₃₇

D₄

yes

—

C₄×Dic₃₇

Q₈

yes

—

C₂×#64436

—

C₂×#64436

—

C₂×#64436

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

#41

yes

—

C₂×C₄×C₃₇

#41

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

C₄⋊C₄

yes

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

C₂×C₄⋊C₄

yes

C₂²×C₃₇

yes

C₂²×C₃₇

yes

C₂²×C₃₇

yes

—

C₂²×C₃₇

#131

yes

—

C₄×C₃₇

—

C₄×C₃₇

#124

yes

—

C₄×C₃₇

#125

yes

—

Dic₃₇

—

Dic₃₇

—

Dic₃₇

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

—

C₂×C₃₇

#433

yes

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₄⋊C₈

—

—

—

—

D₃₇

yes

characteristic

C₃₇

#1832

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₃₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₃₇

yes

characteristic

C₄⋊C₈

—

#95

—

#95

—

C₂²×C₄

—

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

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂×C₄×D₃₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#10596962

yes

—

104

C₂×C₄

D₄×D₃₇

yes

characteristic

105

C₂×C₄

#10596964

yes

—

106

C₂×C₄

Q₈×D₃₇

yes

characteristic

107

C₈

—

108

C₈

—

148

—

109

C₂²

C₄⋊C₄×D₃₇

yes

characteristic

110

C₂²

#11924492

yes

characteristic

111

C₂²

#11924493

yes

characteristic

112

C₂²

#11924542

yes

—

113

C₂²

#11924544

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

148

—

117

C₄

—

148

—

118

C₄

#11924522

yes

—

119

C₄

#11924526

yes

—

120

C₂

#14557397

yes

characteristic

121

C₂

#14557558

yes

—

122

C₂

#14557591

yes

—

123

C₂

#14557592

yes

characteristic

124

C₂

#14557595

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₇
commutator, socle, prime radical	C₂³×C₃₇	C₂²×C₄
Fitting	C₃₇×#336	C₂
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#336	D₃₇
hypocenter	C₃₇	#1832
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₃₇

commutator, socle, prime radical

C₂³×C₃₇

C₂²×C₄

Fitting

C₃₇×#336

C₂

cosocle

C₂²×C₄×C₃₇

C₂³

D₃₇

C₃₇

G ▷ C₂³×C₃₇ ▷ C₃₇

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
68. C₃₇	#1832	semidirect

H ≅ G/N

type

68. C₃₇

#1832

semidirect

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

subgroup	index
C₂×#11924465	2
#14557379	2
#14557288	2
#14557287	2
C₃₇×#336	2
#1832	37

subgroup

index

C₃₇×#336

Subgroups — #17994714

Conjugacy classes of subgroups

Complements

Maximal subgroups