Group #18010538 — subgroups

Subgroups — #18010538

Order 4736.

212 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 86 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	1	yes	maximal, characteristic
4	#14558537	C₂	1	1	yes	maximal, characteristic
5	#97×D₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596953	C₂²	1	2	yes	—
7	C₂×#10596953	C₂²	1	1	yes	characteristic
8	C₂×#10596953	C₂²	1	1	yes	characteristic
9	#11924607	—	2	4	no	—
10	#11924606	—	2	4	no	—
11	#11924603	—	2	2	no	—
12	C₄⋊#64438	—	2	2	no	—
13	C₂×C₈×D₃₇	C₂²	1	2	yes	—
14	C₄²×D₃₇	C₂²	1	1	yes	characteristic
15	#11924447	C₄	1	1	yes	characteristic
16	#11924446	C₄	1	2	yes	—
17	#97×C₃₇	C₄	1	1	yes	characteristic
18	C₂×C₄×D₃₇	Q₈	1	2	yes	—
19	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
20	C₂×#64438	—	2	2	no	—
21	C₂×#64438	—	2	1	no	—
22	C₂×#64438	—	2	1	no	—
23	#10596953	—	2	2	no	—
24	#10596953	—	2	2	no	—
25	#10596953	—	2	2	no	—
26	#10596953	—	2	2	no	—
27	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
28	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₃₇	D₄	1	2	yes	—
31	C₂×#64436	C₂×C₄	1	2	yes	—
32	C₈×D₃₇	D₄	1	4	yes	—
33	C₈×D₃₇	Q₈	1	4	yes	—
34	C₂²×D₃₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₃₇	C₄⋊C₄	1	2	yes	—
38	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
39	C₄×D₃₇	—	4	2	no	—
40	C₄×D₃₇	C₂×D₄	1	2	yes	—
41	C₄×D₃₇	C₂×Q₈	1	2	yes	—
42	#64438	—	4	1	no	—
43	#64438	—	4	2	no	—
44	#64438	—	4	1	no	—
45	C₈×C₃₇	C₄⋊C₄	1	4	yes	—
46	#64436	C₄⋊C₄	1	4	yes	—
47	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×D₃₇	—	2	2	no	—
49	C₂×D₃₇	C₄⋊Q₈	1	2	yes	—
50	C₄×C₃₇	—	2	2	no	—
51	C₄×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
52	Dic₃₇	—	2	2	no	—
53	Dic₃₇	#127	1	1	yes	characteristic
54	Dic₃₇	C₄⋊Q₈	1	1	yes	characteristic
55	#1849	—	37	1	no	maximal, Sylow
56	C₂×C₃₇	#384	1	1	yes	characteristic
57	C₂×C₃₇	#430	1	2	yes	—
58	D₃₇	—	2	2	no	—
59	C₂×#108	—	37	2	no	—
60	C₂×#108	—	37	2	no	—
61	#423	—	37	1	no	—
62	#423	—	37	1	no	—
63	C₂×#97	—	37	1	no	—
64	C₃₇	#1849	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₁₆	—	37	2	no	—
66	C₂×M₁₆	—	37	1	no	—
67	C₂×M₁₆	—	37	1	no	—
68	C₂²×C₈	—	37	2	no	—
69	C₂×C₄²	—	37	1	no	—
70	#108	—	74	4	no	—
71	#108	—	74	4	no	—
72	C₄⋊C₈	—	74	2	no	—
73	C₄⋊C₈	—	74	2	no	—
74	#97	—	37	2	no	—
75	#97	—	37	1	no	—
76	#97	#3866	1	1	yes	characteristic
77	C₂²×C₄	—	37	1	no	—
78	C₂²×C₄	—	37	2	no	—
79	M₁₆	—	74	2	no	—
80	M₁₆	—	74	2	no	—
81	M₁₆	—	74	2	no	—
82	M₁₆	—	74	2	no	—
83	C₂×C₈	—	37	2	no	—
84	C₂×C₈	—	37	4	no	—
85	C₂×C₈	—	37	4	no	—
86	C₂×C₈	—	74	2	no	—
87	C₂×C₈	—	74	1	no	—
88	C₂×C₈	—	74	1	no	—
89	C₂×C₈	C₂×#3866	1	2	yes	—
90	C₄²	—	37	2	no	—
91	C₄²	—	37	1	no	—
92	C₄²	C₂×#3866	1	1	yes	characteristic
93	C₂³	—	37	1	no	—
94	C₂×C₄	—	37	1	no	—
95	C₂×C₄	—	37	2	no	—
96	C₂×C₄	—	37	2	no	—
97	C₂×C₄	—	37	2	no	—
98	C₂×C₄	—	148	2	no	—
99	C₂×C₄	C₄⋊#3866	1	2	yes	—
100	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
101	C₈	—	37	4	no	—
102	C₈	—	148	2	no	—
103	C₈	—	148	1	no	—
104	C₈	—	148	1	no	—
105	C₈	C₄⋊#3866	1	4	yes	—
106	C₂²	—	37	2	no	—
107	C₂²	—	74	2	no	—
108	C₂²	C₂×C₄⋊#3866	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	37	1	no	—
111	C₄	—	37	1	no	—
112	C₄	—	74	2	no	—
113	C₄	C₂×C₄⋊#3866	1	2	yes	—
114	C₂	—	74	2	no	—
115	C₂	#14558479	1	1	yes	characteristic
116	C₂	#14558548	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, characteristic

#14558537

C₂

yes

maximal, characteristic

#97×D₃₇

C₂

yes

maximal, characteristic

C₂×#10596953

C₂²

yes

—

C₂×#10596953

C₂²

yes

characteristic

C₂×#10596953

C₂²

yes

—

—

—

—

C₂×C₈×D₃₇

C₂²

yes

—

C₄²×D₃₇

C₂²

yes

characteristic

#11924447

C₄

yes

characteristic

#11924446

C₄

yes

—

#97×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

Q₈

yes

—

C₂×C₄×D₃₇

C₂³

yes

—

—

—

—

—

—

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

D₄

yes

—

C₂×#64436

C₂×C₄

yes

—

C₈×D₃₇

D₄

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

—

C₄×D₃₇

C₂×Q₈

yes

—

#64438

—

#64438

—

#64438

—

C₈×C₃₇

C₄⋊C₄

yes

—

#64436

C₄⋊C₄

yes

—

C₂²×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

C₄⋊Q₈

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₂×C₄⋊C₄

yes

—

Dic₃₇

—

Dic₃₇

#127

yes

characteristic

Dic₃₇

C₄⋊Q₈

yes

—

C₂×C₃₇

yes

C₂×C₃₇

yes

—

D₃₇

—

—

—

—

—

C₂×#97

—

C₃₇

#1849

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#3866

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

148

—

C₂×C₄

C₄⋊#3866

yes

—

100

C₂×C₄

C₂²×#3866

yes

characteristic

101

C₈

—

102

C₈

—

148

—

103

C₈

—

148

—

104

C₈

—

148

—

105

C₈

C₄⋊#3866

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₂×C₄⋊#3866

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

C₂×C₄⋊#3866

yes

—

114

C₂

—

115

C₂

#14558479

yes

characteristic

116

C₂

#14558548

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#3866
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#3866
Fitting	#97×C₃₇	C₄
socle	C₂²×C₃₇	C₂×C₄⋊C₄
prime radical	C₂²×D₃₇	C₂×Q₈
cosocle	C₂×C₄×D₃₇	C₂³
hypercenter	#97	#3866
hypocenter	C₃₇	#1849
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#3866

commutator

C₂×C₄×C₃₇

C₂²×C₄

Frattini

C₂×C₄

C₂²×#3866

Fitting

#97×C₃₇

C₄

socle

C₂²×C₃₇

C₂×C₄⋊C₄

prime radical

C₂²×D₃₇

C₂×Q₈

cosocle

C₂×C₄×D₃₇

C₂³

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
64. C₃₇	#1849	semidirect

H ≅ G/N

type

64. C₃₇

#1849

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
#14558537	2
#97×D₃₇	2
#1849	37

subgroup

index

#97×D₃₇

Subgroups — #18010538

Conjugacy classes of subgroups

Complements

Maximal subgroups