Group #18010513 — subgroups

Subgroups — #18010513

Order 4736.

260 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 114 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×C₄⋊#64438	C₂	1	2	yes	maximal
2	#14558399	C₂	1	4	yes	maximal
3	C₄²×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64438	C₂²	1	4	yes	—
5	C₄⋊#64438	—	2	4	no	—
6	C₂×C₄×Dic₃₇	C₄	1	2	yes	—
7	C₂×C₄×Dic₃₇	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
9	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₃₇	C₄	1	1	yes	characteristic
11	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
15	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
16	C₂×#64438	—	2	4	no	—
17	C₂×#64438	—	2	8	no	—
18	C₄²×C₃₇	—	2	2	no	—
19	C₄×Dic₃₇	—	2	4	no	—
20	C₄×Dic₃₇	—	2	4	no	—
21	C₄×Dic₃₇	C₈	1	4	yes	complemented
22	C₄×Dic₃₇	D₄	1	2	yes	—
23	C₄×Dic₃₇	Q₈	1	2	yes	—
24	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	—	2	2	no	—
26	C₂×C₄×C₃₇	—	2	2	no	—
27	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₃₇	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₃₇	M₁₆	1	4	yes	—
30	C₂×C₄×C₃₇	M₁₆	1	2	yes	—
31	C₂×Dic₃₇	—	2	2	no	—
32	C₂×Dic₃₇	—	2	2	no	—
33	C₂×Dic₃₇	—	2	2	no	—
34	C₂×Dic₃₇	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₃₇	C₂×C₈	1	4	yes	—
36	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₃₇	C₂×Q₈	1	1	yes	characteristic
38	C₂×Dic₃₇	#41	1	4	yes	—
39	#64438	—	4	4	no	—
40	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₃₇	#117	1	2	yes	—
42	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
43	C₂²×C₃₇	C₂×M₁₆	1	1	yes	characteristic
44	C₂²×C₃₇	C₂×M₁₆	1	2	yes	—
45	C₄×C₃₇	—	2	4	no	—
46	C₄×C₃₇	C₄⋊C₈	1	4	yes	—
47	Dic₃₇	—	2	2	no	—
48	Dic₃₇	—	2	4	no	—
49	Dic₃₇	#124	1	2	yes	—
50	Dic₃₇	#125	1	2	yes	—
51	#1831	—	37	1	no	maximal, Sylow
52	C₂×C₃₇	#382	1	1	yes	characteristic
53	C₂×C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic
54	C₂×C₃₇	#423	1	1	yes	characteristic
55	C₂×C₃₇	#431	1	2	yes	—
56	C₂×C₃₇	#432	1	2	yes	—
57	C₂×C₄⋊C₈	—	37	2	no	—
58	C₄³	—	37	1	no	—
59	#336	—	37	4	no	—
60	C₃₇	#1831	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₈	—	37	4	no	—
62	C₂×C₄²	—	37	1	no	—
63	C₂×C₄²	—	37	1	no	—
64	C₂×C₄²	—	37	2	no	—
65	C₂×C₄²	—	37	2	no	—
66	C₂×C₄²	#3866	1	1	yes	characteristic
67	C₄⋊C₈	—	74	4	no	—
68	C₂²×C₄	—	37	1	no	—
69	C₂²×C₄	—	37	1	no	—
70	C₂²×C₄	—	37	2	no	—
71	C₂²×C₄	C₂×#3866	1	2	yes	—
72	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
73	C₂×C₈	—	74	4	no	—
74	C₂×C₈	—	74	8	no	—
75	C₄²	—	2	2	no	—
76	C₄²	—	37	4	no	—
77	C₄²	—	37	2	no	—
78	C₄²	—	37	2	no	—
79	C₄²	—	74	4	no	—
80	C₄²	—	74	4	no	—
81	C₂³	C₂²×#3866	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	37	1	no	—
85	C₂×C₄	—	37	1	no	—
86	C₂×C₄	—	37	4	no	—
87	C₂×C₄	—	37	2	no	—
88	C₂×C₄	—	37	4	no	—
89	C₂×C₄	—	74	2	no	—
90	C₂×C₄	—	74	2	no	—
91	C₂×C₄	—	74	2	no	—
92	C₂×C₄	D₃₇⋊C₈	1	2	yes	—
93	C₂×C₄	#10596953	1	4	yes	—
94	C₂×C₄	C₄⋊#3866	1	2	yes	—
95	C₂×C₄	#10596957	1	2	yes	—
96	C₈	—	148	4	no	—
97	C₂²	C₂×C₄⋊#3866	1	1	yes	characteristic
98	C₂²	#11924615	1	2	yes	—
99	C₂²	C₂×D₃₇⋊C₈	1	1	yes	characteristic
100	C₂²	C₂×#10596957	1	1	yes	characteristic
101	C₂²	C₂×#10596953	1	2	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	37	2	no	—
104	C₄	—	37	2	no	—
105	C₄	—	74	2	no	—
106	C₄	—	74	4	no	—
107	C₄	#11924603	1	4	yes	—
108	C₂	#14558477	1	1	yes	characteristic
109	C₂	C₂×#11924603	1	1	yes	characteristic
110	C₂	#14558537	1	1	yes	characteristic
111	C₂	#14558552	1	2	yes	—
112	C₂	#14558554	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#64438

C₂

yes

maximal

#14558399

C₂

yes

maximal

C₄²×Dic₃₇

C₂

yes

maximal, characteristic

C₂²×#64438

C₂²

yes

—

C₄⋊#64438

—

C₂×C₄×Dic₃₇

C₄

yes

—

C₂×C₄×Dic₃₇

C₄

yes

characteristic

C₂×C₄×Dic₃₇

C₂²

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

C₂×C₄²×C₃₇

C₄

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

—

C₂²×C₄×C₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂²×Dic₃₇

C₂³

yes

characteristic

C₂×#64438

—

C₂×#64438

—

C₄²×C₃₇

—

C₄×Dic₃₇

—

C₄×Dic₃₇

—

C₄×Dic₃₇

C₈

yes

complemented

C₄×Dic₃₇

D₄

yes

—

C₄×Dic₃₇

Q₈

yes

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₄⋊C₄

yes

—

C₂×C₄×C₃₇

C₂×C₈

yes

—

C₂×C₄×C₃₇

M₁₆

yes

—

C₂×C₄×C₃₇

M₁₆

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

C₄⋊C₄

yes

—

C₂×Dic₃₇

C₂×C₈

yes

—

C₂×Dic₃₇

C₂×D₄

yes

characteristic

C₂×Dic₃₇

C₂×Q₈

yes

characteristic

C₂×Dic₃₇

#41

yes

—

#64438

—

C₂²×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃₇

#117

yes

—

C₂²×C₃₇

C₂²×C₈

yes

characteristic

C₂²×C₃₇

C₂×M₁₆

yes

characteristic

C₂²×C₃₇

C₂×M₁₆

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₄⋊C₈

yes

—

Dic₃₇

—

Dic₃₇

—

Dic₃₇

#124

yes

—

Dic₃₇

#125

yes

—

—

C₂×C₃₇

yes

C₂×C₃₇

C₂×C₄⋊C₈

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

—

C₂×C₃₇

#432

yes

—

C₂×C₄⋊C₈

—

C₄³

—

#336

—

C₃₇

#1831

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

#3866

yes

characteristic

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#3866

yes

—

C₂²×C₄

C₂×#3866

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²×#3866

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₃₇⋊C₈

yes

—

C₂×C₄

#10596953

yes

—

C₂×C₄

C₄⋊#3866

yes

—

C₂×C₄

#10596957

yes

—

C₈

—

148

—

C₂²

C₂×C₄⋊#3866

yes

characteristic

C₂²

#11924615

yes

—

C₂²

C₂×D₃₇⋊C₈

yes

characteristic

100

C₂²

C₂×#10596957

yes

characteristic

101

C₂²

C₂×#10596953

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

#11924603

yes

—

108

C₂

#14558477

yes

characteristic

109

C₂

C₂×#11924603

yes

characteristic

110

C₂

#14558537

yes

characteristic

111

C₂

#14558552

yes

—

112

C₂

#14558554

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#3866
commutator	C₂²×C₃₇	C₂²×C₈
Fitting	C₂×C₄²×C₃₇	C₄
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂²×Dic₃₇	C₂³
hypercenter	C₂×C₄²	#3866
hypocenter	C₃₇	#1831
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

subgroup

G/H

center, Frattini

C₂³

C₂²×#3866

commutator

C₂²×C₃₇

C₂²×C₈

Fitting

C₂×C₄²×C₃₇

C₄

socle, prime radical

C₂³×C₃₇

C₂²×C₄

cosocle

C₂²×Dic₃₇

C₂³

C₂×C₄²

C₃₇

G ▷ C₂²×C₃₇ ▷ C₃₇

C₁ ◁ C₂³ ◁ C₂×C₄²

N	H ≅ G/N	type
21. C₄×Dic₃₇	C₈	semidirect
60. C₃₇	#1831	semidirect

H ≅ G/N

type

21. C₄×Dic₃₇

C₈

semidirect

60. C₃₇

#1831

semidirect

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

subgroup	index
C₂×C₄⋊#64438	2
#14558399	2
C₄²×Dic₃₇	2
#1831	37

subgroup

index

C₂×C₄⋊#64438

#14558399

C₄²×Dic₃₇

#1831

Subgroups — #18010513

Conjugacy classes of subgroups

Complements

Maximal subgroups