Group #18009801 — subgroups

Subgroups — #18009801

Order 4736.

212 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 104 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	#14558550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#64438	C₂	1	1	yes	maximal, characteristic
3	#64438⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₈×#64438	C₂	1	2	yes	maximal, complemented
5	#14557583	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64438	C₄	1	2	yes	—
7	#11924603	C₄	1	2	yes	—
8	C₂²⋊#64438	C₄	1	2	yes	—
9	C₄×#64438	C₄	1	2	yes	—
10	C₄×#64438	C₂²	1	1	yes	characteristic
11	C₄×#64438	C₂²	1	1	yes	characteristic
12	C₄×#64438	C₂²	1	2	yes	—
13	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
14	#11924465	C₄	1	2	yes	—
15	C₂²⋊#64436	C₄	1	1	yes	characteristic
16	C₈×Dic₃₇	C₂²	1	2	yes	—
17	C₂²⋊C₈×C₃₇	C₄	1	1	yes	characteristic
18	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
21	C₂×#64438	C₈	1	8	yes	complemented
22	C₂×#64438	C₂×C₄	1	4	yes	—
23	C₂×#64438	C₂×C₄	1	2	yes	—
24	C₂×#64438	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
26	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
30	C₂×#64436	C₂×C₄	1	2	yes	—
31	C₂³×C₃₇	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₃₇	—	2	2	no	—
33	C₂×C₄×C₃₇	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₃₇	—	2	2	no	—
36	C₂×Dic₃₇	C₄²	1	1	yes	characteristic
37	C₂×Dic₃₇	C₄²	1	1	yes	characteristic
38	C₂×Dic₃₇	C₂×C₈	1	4	yes	—
39	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
41	#64438	—	2	4	no	—
42	#64438	C₂×C₈	1	4	yes	—
43	#64438	C₂×C₈	1	4	yes	—
44	C₈×C₃₇	—	2	2	no	—
45	#64436	—	2	2	no	—
46	C₂²×C₃₇	—	2	1	no	—
47	C₂²×C₃₇	—	2	1	no	—
48	C₂²×C₃₇	C₄×C₈	1	2	yes	—
49	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
50	C₄×C₃₇	—	2	1	no	—
51	C₄×C₃₇	#131	1	2	yes	—
52	Dic₃₇	—	2	1	no	—
53	Dic₃₇	C₄×C₈	1	2	yes	—
54	Dic₃₇	C₂²×C₈	1	2	yes	—
55	Dic₃₇	#131	1	2	yes	—
56	#1450	—	37	1	no	maximal, Sylow
57	C₂×C₃₇	—	2	2	no	—
58	C₂×C₃₇	C₂×C₄×C₈	1	1	yes	characteristic
59	C₂×C₃₇	#405	1	1	yes	characteristic
60	C₂×C₃₇	#405	1	1	yes	characteristic
61	#431	—	37	1	no	—
62	#431	—	37	1	no	—
63	C₂×C₄×C₈	—	37	1	no	—
64	#322	—	37	2	no	—
65	C₈²	—	37	2	no	—
66	C₃₇	#1450	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₈	—	37	2	no	—
68	C₂×C₄²	—	37	1	no	—
69	C₄⋊C₈	—	37	2	no	—
70	C₄⋊C₈	—	37	2	no	—
71	C₂²⋊C₈	—	37	2	no	—
72	C₂²⋊C₈	—	37	1	no	—
73	C₂²⋊C₈	#3866	1	1	yes	characteristic
74	C₄×C₈	—	37	1	no	—
75	C₄×C₈	—	37	2	no	—
76	C₄×C₈	—	37	1	no	—
77	C₄×C₈	—	37	2	no	—
78	C₄×C₈	—	37	2	no	—
79	C₂²×C₄	—	37	1	no	—
80	C₂²×C₄	—	37	1	no	—
81	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
82	C₂×C₈	—	37	8	no	—
83	C₂×C₈	—	37	2	no	—
84	C₂×C₈	—	37	2	no	—
85	C₂×C₈	—	37	4	no	—
86	C₂×C₈	—	37	2	no	—
87	C₂×C₈	C₂×#3866	1	2	yes	—
88	C₄²	—	37	1	no	—
89	C₄²	—	37	1	no	—
90	C₄²	—	37	1	no	—
91	C₄²	—	37	1	no	—
92	C₂³	C₄×#3866	1	1	yes	characteristic
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	37	4	no	—
95	C₂×C₄	—	37	1	no	—
96	C₂×C₄	—	37	1	no	—
97	C₂×C₄	—	37	1	no	—
98	C₂×C₄	—	37	1	no	—
99	C₂×C₄	—	74	2	no	—
100	C₂×C₄	C₄×#3866	1	1	yes	characteristic
101	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
102	C₈	—	2	2	no	—
103	C₈	—	37	4	no	—
104	C₈	—	37	4	no	—
105	C₈	—	74	4	no	—
106	C₈	—	74	2	no	—
107	C₂²	—	2	1	no	—
108	C₂²	—	2	1	no	—
109	C₂²	C₈×#3866	1	2	yes	—
110	C₂²	C₂×C₄×#3866	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	37	2	no	—
113	C₄	—	37	2	no	—
114	C₄	—	37	2	no	—
115	C₄	—	74	1	no	—
116	C₄	#11924623	1	2	yes	—
117	C₂	—	2	2	no	—
118	C₂	C₂×C₈×#3866	1	1	yes	characteristic
119	C₂	#14558497	1	1	yes	characteristic
120	C₂	#14558499	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14558550

C₂

yes

maximal, characteristic

C₂×C₄×#64438

C₂

yes

maximal, characteristic

#64438⋊C₈

C₂

yes

maximal, complemented

C₈×#64438

C₂

yes

maximal, complemented

#14557583

C₂

yes

maximal, characteristic

C₂²×#64438

C₄

yes

—

#11924603

C₄

yes

—

C₂²⋊#64438

C₄

yes

—

C₄×#64438

C₄

yes

—

C₄×#64438

C₂²

yes

characteristic

C₄×#64438

C₂²

yes

characteristic

C₄×#64438

C₂²

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

#11924465

C₄

yes

—

C₂²⋊#64436

C₄

yes

characteristic

C₈×Dic₃₇

C₂²

yes

—

C₂²⋊C₈×C₃₇

C₄

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

characteristic

C₂×#64438

C₈

yes

complemented

C₂×#64438

C₂×C₄

yes

—

C₂×#64438

C₂×C₄

yes

—

C₂×#64438

C₂×C₄

yes

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂³

yes

characteristic

C₂×#64436

C₂×C₄

yes

—

C₂³×C₃₇

C₄²

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₄²

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

—

C₂×Dic₃₇

C₄²

yes

characteristic

C₂×Dic₃₇

C₄²

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

—

C₂×Dic₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₂²×C₄

yes

characteristic

#64438

—

#64438

C₂×C₈

yes

—

#64438

C₂×C₈

yes

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

C₄×C₈

yes

—

C₂²×C₃₇

C₂×C₄²

yes

characteristic

C₄×C₃₇

—

C₄×C₃₇

#131

yes

—

Dic₃₇

—

Dic₃₇

C₄×C₈

yes

—

Dic₃₇

C₂²×C₈

yes

—

Dic₃₇

#131

yes

—

#1450

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

C₂×C₄×C₈

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

—

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₃₇

#1450

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

#3866

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#3866

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#3866

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#3866

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₄×#3866

yes

characteristic

101

C₂×C₄

C₂²×#3866

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₈×#3866

yes

—

110

C₂²

C₂×C₄×#3866

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

#11924623

yes

—

117

C₂

—

118

C₂

C₂×C₈×#3866

yes

characteristic

119

C₂

#14558497

yes

characteristic

120

C₂

#14558499

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3866
commutator	C₂×C₃₇	C₂×C₄×C₈
Fitting	C₂²⋊C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₂×C₄²
prime radical	C₂³×C₃₇	C₄²
cosocle	C₄×Dic₃₇	C₂³
hypercenter	C₂²⋊C₈	#3866
hypocenter	C₃₇	#1450
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#3866

commutator

C₂×C₃₇

C₂×C₄×C₈

Fitting

C₂²⋊C₈×C₃₇

C₄

socle

C₂²×C₃₇

C₂×C₄²

prime radical

C₂³×C₃₇

C₄²

cosocle

C₄×Dic₃₇

C₂³

C₂²⋊C₈

C₃₇

G ▷ C₂×C₃₇ ▷ C₃₇

C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
3. #64438⋊C₈	C₂	semidirect
4. C₈×#64438	C₂	semidirect
21. C₂×#64438	C₈	semidirect
66. C₃₇	#1450	semidirect

H ≅ G/N

type

3. #64438⋊C₈

C₂

semidirect

4. C₈×#64438

C₂

semidirect

21. C₂×#64438

C₈

semidirect

66. C₃₇

#1450

semidirect

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

subgroup	index
#14558550	2
C₂×C₄×#64438	2
#64438⋊C₈	2
C₈×#64438	2
#14557583	2
#1450	37

subgroup

index

C₂×C₄×#64438

Subgroups — #18009801

Conjugacy classes of subgroups

Complements

Maximal subgroups