Group #18010315 — subgroups

Subgroups — #18010315

Order 4736.

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

normal subgroups only

This group has 240 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×#11924591	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#64438	C₂	1	1	yes	maximal, characteristic
3	#14558399	C₂	1	4	yes	maximal
4	#14557378	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64438	C₂²	1	2	yes	—
6	C₂²×#64438	C₂²	1	2	yes	—
7	#11924591	C₄	1	4	yes	complemented
8	C₄×#64438	C₄	1	4	yes	complemented
9	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
10	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
11	#11924443	C₄	1	1	yes	characteristic
12	#11924443	C₄	1	2	yes	—
13	#95×C₃₇	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
17	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
19	C₂×#64438	—	2	4	no	—
20	C₂×#64438	—	2	4	no	—
21	C₂×#64438	C₂×C₄	1	4	yes	—
22	C₂×#64438	C₂×C₄	1	4	yes	—
23	C₄×Dic₃₇	—	2	4	no	—
24	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
25	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
26	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇	—	2	2	no	—
28	C₂×C₄×C₃₇	—	2	2	no	—
29	C₂×C₄×C₃₇	—	2	2	no	—
30	C₂×C₄×C₃₇	—	2	2	no	—
31	C₂×C₄×C₃₇	C₄²	1	2	yes	—
32	C₂×Dic₃₇	—	2	1	no	—
33	C₂×Dic₃₇	—	2	1	no	—
34	C₂×Dic₃₇	—	2	2	no	—
35	C₂×Dic₃₇	—	2	2	no	—
36	C₂×Dic₃₇	—	2	2	no	—
37	C₂×Dic₃₇	C₄²	1	2	yes	—
38	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₃₇	#41	1	4	yes	—
41	#64438	—	2	4	no	—
42	#64438	—	2	4	no	—
43	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₃₇	#117	1	2	yes	—
45	C₂²×C₃₇	#131	1	2	yes	—
46	C₂²×C₃₇	#131	1	1	yes	characteristic
47	C₂²×C₃₇	#131	1	1	yes	characteristic
48	C₄×C₃₇	—	2	2	no	—
49	C₄×C₃₇	—	4	2	no	—
50	Dic₃₇	—	2	2	no	—
51	Dic₃₇	—	4	2	no	—
52	Dic₃₇	#117	1	2	yes	—
53	Dic₃₇	#117	1	2	yes	—
54	#1746	—	37	1	no	maximal, Sylow
55	C₂×C₃₇	#376	1	1	yes	characteristic
56	C₂×C₃₇	#405	1	1	yes	characteristic
57	C₂×C₃₇	#405	1	1	yes	characteristic
58	C₂×C₃₇	#433	1	2	yes	—
59	C₂×C₃₇	#433	1	2	yes	—
60	C₂×#97	—	37	1	no	—
61	C₂×C₄×C₈	—	37	1	no	—
62	#376	—	37	1	no	—
63	#336	—	37	4	no	—
64	C₃₇	#1746	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₈	—	37	2	no	—
66	C₂²×C₈	—	37	2	no	—
67	C₂×C₄²	—	37	1	no	—
68	C₂×C₄²	—	37	2	no	—
69	#97	—	37	4	no	—
70	C₄×C₈	—	37	4	no	—
71	#95	—	37	2	no	—
72	#95	—	37	1	no	—
73	#95	#3866	1	1	yes	characteristic
74	C₂²×C₄	—	37	1	no	—
75	C₂²×C₄	—	37	1	no	—
76	C₂²×C₄	—	37	2	no	—
77	C₂²×C₄	C₂×#3866	1	2	yes	—
78	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
79	C₂×C₈	—	37	4	no	—
80	C₂×C₈	—	37	4	no	—
81	C₂×C₈	—	74	4	no	—
82	C₂×C₈	—	74	4	no	—
83	C₄²	—	37	2	no	—
84	C₄²	—	37	2	no	—
85	C₄²	—	74	4	no	—
86	C₂³	C₂²×#3866	1	1	yes	characteristic
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	37	1	no	—
92	C₂×C₄	—	37	1	no	—
93	C₂×C₄	—	37	4	no	—
94	C₂×C₄	—	37	2	no	—
95	C₂×C₄	—	74	1	no	—
96	C₂×C₄	—	74	1	no	—
97	C₂×C₄	—	74	2	no	—
98	C₂×C₄	—	74	2	no	—
99	C₂×C₄	—	74	2	no	—
100	C₂×C₄	C₄×#3866	1	2	yes	—
101	C₈	—	74	4	no	—
102	C₈	—	74	4	no	—
103	C₂²	C₂×C₄×#3866	1	1	yes	characteristic
104	C₂²	#11924615	1	2	yes	—
105	C₂²	#11924623	1	2	yes	—
106	C₂²	#11924623	1	1	yes	characteristic
107	C₂²	#11924624	1	1	yes	characteristic
108	C₄	—	2	2	no	—
109	C₄	—	4	2	no	—
110	C₄	—	37	2	no	—
111	C₄	—	37	2	no	—
112	C₄	—	74	2	no	—
113	C₄	—	148	2	no	—
114	C₂	#14558469	1	1	yes	characteristic
115	C₂	#14558497	1	1	yes	characteristic
116	C₂	#14558498	1	1	yes	characteristic
117	C₂	#14558557	1	2	yes	—
118	C₂	#14558558	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924591

C₂

yes

maximal, characteristic

C₂×C₄×#64438

C₂

yes

maximal, characteristic

#14558399

C₂

yes

maximal

#14557378

C₂

yes

maximal, characteristic

C₂²×#64438

C₂²

yes

—

C₂²×#64438

C₂²

yes

—

#11924591

C₄

yes

complemented

C₄×#64438

C₄

yes

complemented

C₂×C₄×Dic₃₇

C₂²

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

#11924443

C₄

yes

characteristic

#11924443

C₄

yes

—

#95×C₃₇

C₄

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

—

C₂²×C₄×C₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂²×Dic₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂³

yes

—

—

C₂×C₄

yes

—

C₂×#64438

C₂×C₄

yes

—

C₄×Dic₃₇

—

C₄×Dic₃₇

C₂×C₄

yes

—

C₄×Dic₃₇

C₂×C₄

yes

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₄²

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

C₄²

yes

—

C₂×Dic₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

#41

yes

—

#64438

—

#64438

—

C₂²×C₃₇

C₂×C₄²

yes

characteristic

C₂²×C₃₇

#117

yes

—

C₂²×C₃₇

#131

yes

—

C₂²×C₃₇

yes

C₂²×C₃₇

yes

C₄×C₃₇

—

C₄×C₃₇

—

Dic₃₇

—

Dic₃₇

—

Dic₃₇

#117

yes

—

Dic₃₇

#117

yes

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

—

C₂×C₃₇

#433

yes

—

C₂×#97

—

C₂×C₄×C₈

—

#376

—

#336

—

C₃₇

#1746

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

#97

—

C₄×C₈

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#3866

yes

—

C₂²×C₄

C₂×#3866

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

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

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₄×#3866

yes

—

101

C₈

—

102

C₈

—

103

C₂²

C₂×C₄×#3866

yes

characteristic

104

C₂²

#11924615

yes

—

105

C₂²

#11924623

yes

—

106

C₂²

#11924623

yes

characteristic

107

C₂²

#11924624

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

148

—

114

C₂

#14558469

yes

characteristic

115

C₂

#14558497

yes

characteristic

116

C₂

#14558498

yes

characteristic

117

C₂

#14558557

yes

—

118

C₂

#14558558

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#3866
commutator	C₂²×C₃₇	C₂×C₄²
Fitting	#95×C₃₇	C₄
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂²×Dic₃₇	C₂³
hypercenter	#95	#3866
hypocenter	C₃₇	#1746
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#3866

commutator

C₂²×C₃₇

C₂×C₄²

Fitting

#95×C₃₇

C₄

socle, prime radical

C₂³×C₃₇

C₂²×C₄

cosocle

C₂²×Dic₃₇

C₂³

C₃₇

G ▷ C₂²×C₃₇ ▷ C₃₇

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
7. #11924591	C₄	semidirect
8. C₄×#64438	C₄	semidirect
64. C₃₇	#1746	semidirect

H ≅ G/N

type

7. #11924591

C₄

semidirect

8. C₄×#64438

C₄

semidirect

64. C₃₇

#1746

semidirect

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

subgroup	index
C₂×#11924591	2
C₂×C₄×#64438	2
#14558399	2
#14557378	2
#1746	37

subgroup

index

C₂×C₄×#64438

Subgroups — #18010315

Conjugacy classes of subgroups

Complements

Maximal subgroups