Group #18010413 — subgroups

Subgroups — C₄×#11924606 #18010413

Order 4736.

228 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 98 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×#11924606	C₂	1	2	yes	maximal
2	C₄×#10596953	C₂	1	2	yes	maximal
3	#14558409	C₂	1	2	yes	maximal
4	C₄×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10596953	C₂²	1	4	yes	—
6	#11924606	C₄	1	8	yes	direct product factor
7	#11924591	—	2	2	no	—
8	C₄×#64438	—	2	2	no	—
9	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
11	C₄²×D₃₇	C₂²	1	1	yes	characteristic
12	C₄×#64436	C₄	1	1	yes	characteristic
13	C₈×Dic₃₇	C₄	1	1	yes	characteristic
14	C₈×Dic₃₇	C₄	1	1	yes	characteristic
15	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
16	C₂×C₄×D₃₇	Q₈	1	1	yes	characteristic
17	C₂×C₄×D₃₇	Q₈	1	1	yes	characteristic
18	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
19	C₂×#64438	—	2	4	no	—
20	#10596953	—	2	4	no	—
21	#10596953	C₂×C₄	1	8	yes	—
22	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₃₇	D₄	1	1	yes	characteristic
27	C₄×Dic₃₇	D₄	1	1	yes	characteristic
28	C₂×#64436	C₂×C₄	1	1	yes	characteristic
29	C₂×#64436	C₂×C₄	1	1	yes	characteristic
30	C₈×D₃₇	—	2	2	no	—
31	C₈×D₃₇	C₂×C₄	1	4	yes	—
32	C₂²×D₃₇	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
39	C₄×D₃₇	—	2	2	no	—
40	C₄×D₃₇	—	2	2	no	—
41	C₄×D₃₇	C₂²×C₄	1	2	yes	—
42	C₄×D₃₇	#41	1	2	yes	—
43	#64438	—	2	8	no	—
44	C₈×C₃₇	—	2	1	no	—
45	C₈×C₃₇	C₄²	1	2	yes	—
46	#64436	—	2	1	no	—
47	#64436	C₄²	1	2	yes	—
48	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×D₃₇	—	2	1	no	—
50	C₂×D₃₇	—	2	1	no	—
51	C₂×D₃₇	C₄×Q₈	1	2	yes	—
52	C₄×C₃₇	—	2	1	no	—
53	C₄×C₃₇	#108	1	2	yes	complemented
54	C₄×C₃₇	C₂×C₄²	1	1	yes	characteristic
55	C₄×C₃₇	#117	1	1	yes	characteristic
56	Dic₃₇	—	2	1	no	—
57	Dic₃₇	#108	1	2	yes	complemented
58	Dic₃₇	C₄×D₄	1	2	yes	—
59	C₄×#108	—	37	1	no	maximal, Sylow
60	C₂×C₃₇	C₄×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₃₇	C₂×#108	1	1	yes	characteristic
62	C₂×C₃₇	C₂×#108	1	1	yes	characteristic
63	D₃₇	—	2	2	no	—
64	C₂×#108	—	37	2	no	—
65	C₄×M₁₆	—	37	2	no	—
66	C₂×C₄×C₈	—	37	1	no	—
67	#341	—	37	2	no	—
68	C₃₇	C₄×#108	1	1	yes	characteristic, complemented, Sylow
69	C₂×M₁₆	—	37	4	no	—
70	C₂²×C₈	—	37	1	no	—
71	C₂²×C₈	—	37	1	no	—
72	C₂×C₄²	—	37	1	no	—
73	#108	—	37	8	no	—
74	#97	—	74	2	no	—
75	C₄×C₈	—	37	1	no	—
76	C₄×C₈	—	37	1	no	—
77	C₄×C₈	—	37	1	no	—
78	C₄×C₈	—	74	2	no	—
79	C₄×C₈	#3866	1	1	yes	characteristic
80	C₂²×C₄	—	37	1	no	—
81	C₂²×C₄	—	37	1	no	—
82	C₂²×C₄	—	37	1	no	—
83	M₁₆	—	37	8	no	—
84	M₁₆	—	74	4	no	—
85	C₂×C₈	—	37	1	no	—
86	C₂×C₈	—	37	4	no	—
87	C₂×C₈	—	37	1	no	—
88	C₂×C₈	—	74	2	no	—
89	C₂×C₈	—	74	4	no	—
90	C₂×C₈	C₂×#3866	1	1	yes	characteristic
91	C₂×C₈	C₂×#3866	1	1	yes	characteristic
92	C₄²	—	37	1	no	—
93	C₄²	—	37	1	no	—
94	C₄²	—	37	1	no	—
95	C₄²	C₂×#3866	1	1	yes	characteristic
96	C₂³	—	37	1	no	—
97	C₂×C₄	—	37	1	no	—
98	C₂×C₄	—	37	1	no	—
99	C₂×C₄	—	37	2	no	—
100	C₂×C₄	—	37	2	no	—
101	C₂×C₄	—	37	1	no	—
102	C₂×C₄	—	74	2	no	—
103	C₂×C₄	—	74	2	no	—
104	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
105	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
106	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
107	C₈	—	2	1	no	—
108	C₈	—	37	2	no	—
109	C₈	—	74	8	no	—
110	C₈	—	74	1	no	—
111	C₈	C₄×#3866	1	2	yes	—
112	C₂²	—	37	2	no	—
113	C₂²	—	74	1	no	—
114	C₂²	—	74	1	no	—
115	C₂²	C₂×C₄⋊#3866	1	1	yes	characteristic
116	C₄	—	2	1	no	—
117	C₄	—	37	2	no	—
118	C₄	—	37	2	no	—
119	C₄	—	74	1	no	—
120	C₄	#11924606	1	2	yes	direct product factor
121	C₄	C₂×C₄×#3866	1	1	yes	characteristic
122	C₄	#11924615	1	1	yes	characteristic
123	C₂	—	74	2	no	—
124	C₂	C₄×C₄⋊#3866	1	1	yes	characteristic
125	C₂	C₂×#11924606	1	1	yes	characteristic
126	C₂	D₃₇⋊#108	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924606

C₂

yes

maximal

C₄×#10596953

C₂

yes

maximal

#14558409

C₂

yes

maximal

C₄×C₈×D₃₇

C₂

yes

maximal, characteristic

C₂×#10596953

C₂²

yes

—

#11924606

C₄

yes

direct product factor

#11924591

—

C₄×#64438

—

C₂×C₈×D₃₇

C₂²

yes

characteristic

C₂×C₈×D₃₇

C₂²

yes

characteristic

C₄²×D₃₇

C₂²

yes

characteristic

C₄×#64436

C₄

yes

characteristic

C₈×Dic₃₇

C₄

yes

characteristic

C₈×Dic₃₇

C₄

yes

characteristic

C₄×C₈×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

Q₈

yes

characteristic

C₂×C₄×D₃₇

Q₈

yes

characteristic

C₂×C₄×D₃₇

C₂³

yes

—

—

C₂×C₄

yes

—

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

D₄

yes

characteristic

C₄×Dic₃₇

D₄

yes

characteristic

C₂×#64436

C₂×C₄

yes

characteristic

C₂×#64436

C₂×C₄

yes

characteristic

C₈×D₃₇

—

C₈×D₃₇

C₂×C₄

yes

—

C₂²×D₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₃₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₄⋊C₄

yes

characteristic

C₂×Dic₃₇

C₄⋊C₄

yes

characteristic

C₂×Dic₃₇

C₂×D₄

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

—

C₄×D₃₇

C₂²×C₄

yes

—

C₄×D₃₇

#41

yes

—

#64438

—

C₈×C₃₇

—

C₈×C₃₇

C₄²

yes

—

#64436

—

#64436

C₄²

yes

—

C₂²×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

—

C₂×D₃₇

C₄×Q₈

yes

—

C₄×C₃₇

—

C₄×C₃₇

#108

yes

complemented

C₄×C₃₇

C₂×C₄²

yes

characteristic

C₄×C₃₇

#117

yes

characteristic

Dic₃₇

—

Dic₃₇

#108

yes

complemented

Dic₃₇

C₄×D₄

yes

—

C₄×#108

—

maximal, Sylow

C₂×C₃₇

C₄×C₄⋊C₄

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

D₃₇

—

C₂×#108

—

C₄×M₁₆

—

C₂×C₄×C₈

—

#341

—

C₃₇

C₄×#108

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#3866

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₄⋊#3866

yes

characteristic

105

C₂×C₄

C₄⋊#3866

yes

characteristic

106

C₂×C₄

C₂²×#3866

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

C₄×#3866

yes

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂×C₄⋊#3866

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

#11924606

yes

direct product factor

121

C₄

C₂×C₄×#3866

yes

characteristic

122

C₄

#11924615

yes

characteristic

123

C₂

—

124

C₂

C₄×C₄⋊#3866

yes

characteristic

125

C₂

C₂×#11924606

yes

characteristic

126

C₂

D₃₇⋊#108

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#3866
commutator	C₄×C₃₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×#3866
Fitting	C₄×C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₂×C₄⋊C₄
prime radical	C₂²×D₃₇	C₂×Q₈
cosocle	C₂×C₄×D₃₇	C₂³
hypercenter	C₄×C₈	#3866
hypocenter	C₃₇	C₄×#108
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂×C₄

C₄⋊#3866

commutator

C₄×C₃₇

C₂×C₄²

Frattini

C₂×C₄

C₂²×#3866

Fitting

C₄×C₈×C₃₇

C₄

socle

C₂²×C₃₇

C₂×C₄⋊C₄

prime radical

C₂²×D₃₇

C₂×Q₈

cosocle

C₂×C₄×D₃₇

C₂³

C₄×C₈

C₃₇

G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
6. #11924606	C₄	direct (N × H)
53. C₄×C₃₇	#108	semidirect
57. Dic₃₇	#108	semidirect
68. C₃₇	C₄×#108	semidirect
120. C₄	#11924606	direct (N × H)

H ≅ G/N

type

6. #11924606

C₄

direct (N × H)

53. C₄×C₃₇

#108

semidirect

57. Dic₃₇

#108

semidirect

68. C₃₇

C₄×#108

semidirect

120. C₄

#11924606

direct (N × H)

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

subgroup	index
C₂×#11924606	2
C₄×#10596953	2
#14558409	2
C₄×C₈×D₃₇	2
C₄×#108	37

subgroup

index

C₄×C₈×D₃₇

Subgroups — C₄×#11924606 #18010413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×#11924606 #18010413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11924606 #18010413