Group #11783515 — subgroups

Subgroups — #11783515

Order 1152.

386 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 90 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	#10593733	C₂	1	1	yes	maximal, characteristic
2	C₄×#3787	C₂	1	1	yes	maximal, characteristic
3	C₃⋊D₃×#97	C₂	1	1	yes	maximal, characteristic
4	#10590181	C₂	1	4	yes	maximal
5	C₂×C₄×#157	C₂²	1	2	yes	—
6	C₂×#3787	C₂²	1	2	yes	—
7	C₂×C₈×C₃⋊D₃	C₂²	1	2	yes	—
8	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
9	#63781	C₄	1	4	yes	—
10	C₄×#622	C₄	1	4	yes	complemented
11	C₃²×#97	C₄	1	1	yes	characteristic, complemented
12	#63642	C₄	1	2	yes	complemented
13	#63630	C₄	1	1	yes	characteristic, complemented
14	D₃×#97	—	6	2	no	—
15	C₂²×#157	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₃⋊D₃	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
18	C₂×#622	C₂×C₄	1	4	yes	—
19	C₄×#157	—	2	4	no	—
20	#3787	—	2	4	no	—
21	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
22	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
23	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
24	C₄×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
25	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
26	C₈×C₃⋊D₃	—	2	4	no	—
27	#1746	—	9	1	no	maximal, Sylow
28	C₂×D₃×C₈	—	6	4	no	—
29	C₄²×D₃	—	6	2	no	—
30	C₃×#97	—	2	2	no	—
31	#815	—	6	4	no	—
32	#803	—	6	2	no	—
33	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×#157	—	2	4	no	—
35	C₂×#157	—	2	8	no	—
36	C₂×C₃²×C₄	C₄²	1	2	yes	—
37	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₃⋊Dic₃	C₄²	1	2	yes	—
39	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
40	C₄×C₃⋊D₃	—	2	4	no	—
41	C₄×C₃⋊D₃	#41	1	4	yes	—
42	#622	—	2	4	no	—
43	C₃²×C₈	—	2	2	no	—
44	C₃⋊(C₃⋊C₈)	—	2	2	no	—
45	C₂×#97	—	9	1	no	—
46	C₂×C₄×C₈	—	9	1	no	—
47	#376	—	9	1	no	—
48	#336	—	9	4	no	—
49	C₂×C₄×D₃	—	6	2	no	—
50	C₂×C₄×D₃	—	6	4	no	—
51	C₂×C₃×C₈	—	2	4	no	—
52	C₃×C₄²	—	2	2	no	—
53	C₄×Dic₃	—	6	2	no	—
54	C₄×Dic₃	—	6	4	no	—
55	C₂×C₃⋊C₈	—	6	4	no	—
56	D₃×C₈	—	6	16	no	—
57	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
58	C₂×C₃⋊D₃	#117	1	2	yes	—
59	C₂×C₃⋊D₃	#131	1	4	yes	—
60	#157	—	4	4	no	—
61	C₃²×C₄	—	2	2	no	—
62	C₃²×C₄	#117	1	2	yes	—
63	C₃⋊Dic₃	—	2	2	no	—
64	C₃⋊Dic₃	#117	1	2	yes	—
65	C₂²×C₈	—	9	2	no	—
66	C₂²×C₈	—	9	2	no	—
67	C₂×C₄²	—	9	1	no	—
68	C₂×C₄²	—	9	2	no	—
69	#97	—	9	2	no	—
70	#97	—	9	1	no	—
71	#97	#157	1	1	yes	characteristic, complemented
72	C₄×C₈	—	9	4	no	—
73	#95	—	9	4	no	—
74	C₂²×D₃	—	6	2	no	—
75	C₂×C₃×C₄	—	2	2	no	—
76	C₂×C₃×C₄	—	2	4	no	—
77	C₂×Dic₃	—	6	2	no	—
78	C₂×Dic₃	—	6	4	no	—
79	C₄×D₃	—	6	8	no	—
80	C₄×D₃	—	12	8	no	—
81	C₃×C₈	—	2	8	no	—
82	C₃⋊C₈	—	6	8	no	—
83	C₂×C₃²	#376	1	1	yes	characteristic
84	C₂×C₃²	#405	1	2	yes	—
85	C₃⋊D₃	#433	1	4	yes	—
86	C₂²×C₄	—	9	1	no	—
87	C₂²×C₄	—	9	2	no	—
88	C₂²×C₄	—	9	4	no	—
89	C₂×C₈	—	9	4	no	—
90	C₂×C₈	—	9	2	no	—
91	C₂×C₈	—	18	4	no	—
92	C₂×C₈	—	18	4	no	—
93	C₂×C₈	C₂×#157	1	2	yes	—
94	C₄²	—	9	1	no	—
95	C₄²	—	9	2	no	—
96	C₄²	—	18	4	no	—
97	C₄²	C₂×#157	1	1	yes	characteristic
98	C₂²×C₃	—	2	2	no	—
99	C₂×D₃	—	6	4	no	—
100	C₂×D₃	—	6	8	no	—
101	C₃×C₄	—	2	4	no	—
102	C₃×C₄	—	4	4	no	—
103	Dic₃	—	6	4	no	—
104	Dic₃	—	12	4	no	—
105	C₃²	#1746	1	1	yes	characteristic, complemented, Sylow
106	C₂³	—	9	1	no	—
107	C₂×C₄	—	9	1	no	—
108	C₂×C₄	—	9	4	no	—
109	C₂×C₄	—	9	2	no	—
110	C₂×C₄	—	18	4	no	—
111	C₂×C₄	—	18	4	no	—
112	C₂×C₄	—	18	8	no	—
113	C₂×C₄	C₄×#157	1	2	yes	—
114	C₂×C₄	C₂²×#157	1	1	yes	characteristic
115	C₈	—	2	2	no	—
116	C₈	—	18	4	no	—
117	C₈	—	18	2	no	—
118	C₂×C₃	—	2	2	no	—
119	C₂×C₃	—	2	4	no	—
120	D₃	—	6	8	no	—
121	C₂²	—	9	2	no	—
122	C₂²	—	9	4	no	—
123	C₂²	C₂×C₄×#157	1	1	yes	characteristic
124	C₄	—	2	2	no	—
125	C₄	—	9	2	no	—
126	C₄	—	18	2	no	—
127	C₄	—	36	4	no	—
128	C₄	#64286	1	2	yes	—
129	C₃	—	2	2	no	—
130	C₂	—	9	4	no	—
131	C₂	#10593733	1	1	yes	characteristic
132	C₂	#10593775	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#10593733

C₂

yes

maximal, characteristic

C₄×#3787

C₂

yes

maximal, characteristic

C₃⋊D₃×#97

C₂

yes

maximal, characteristic

#10590181

C₂

yes

maximal

C₂×C₄×#157

C₂²

yes

—

C₂×#3787

C₂²

yes

—

C₂×C₈×C₃⋊D₃

C₂²

yes

—

C₄²×C₃⋊D₃

C₂²

yes

characteristic

#63781

C₄

yes

—

C₄×#622

C₄

yes

complemented

C₃²×#97

C₄

yes

characteristic, complemented

#63642

C₄

yes

complemented

#63630

C₄

yes

characteristic, complemented

D₃×#97

—

C₂²×#157

C₂×C₄

yes

—

C₂×C₄×C₃⋊D₃

C₂×C₄

yes

—

C₂×C₄×C₃⋊D₃

C₂³

yes

characteristic

C₂×#622

C₂×C₄

yes

—

C₄×#157

—

#3787

—

C₂×C₃²×C₈

C₂×C₄

yes

—

C₃²×C₄²

C₂×C₄

yes

characteristic

C₄×C₃⋊Dic₃

C₂×C₄

yes

characteristic

C₄×C₃⋊Dic₃

C₂×C₄

yes

—

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

—

C₈×C₃⋊D₃

—

#1746

—

maximal, Sylow

C₂×D₃×C₈

—

C₄²×D₃

—

C₃×#97

—

#815

—

#803

—

C₂²×C₃⋊D₃

C₂²×C₄

yes

characteristic

C₂×#157

—

C₂×#157

—

C₂×C₃²×C₄

C₄²

yes

—

C₂×C₃²×C₄

C₂²×C₄

yes

characteristic

C₂×C₃⋊Dic₃

C₄²

yes

—

C₂×C₃⋊Dic₃

C₂²×C₄

yes

characteristic

C₄×C₃⋊D₃

—

C₄×C₃⋊D₃

#41

yes

—

#622

—

C₃²×C₈

—

C₃⋊(C₃⋊C₈)

—

C₂×#97

—

C₂×C₄×C₈

—

#376

—

#336

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₂×C₃×C₈

—

C₃×C₄²

—

C₄×Dic₃

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

D₃×C₈

—

C₂²×C₃²

C₂×C₄²

yes

characteristic

C₂×C₃⋊D₃

#117

yes

—

C₂×C₃⋊D₃

#131

yes

—

#157

—

C₃²×C₄

—

C₃²×C₄

#117

yes

—

C₃⋊Dic₃

—

C₃⋊Dic₃

#117

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

C₄×C₈

—

#95

—

C₂²×D₃

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

#376

yes

characteristic

C₂×C₃²

#405

yes

—

C₃⋊D₃

#433

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#157

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#157

yes

characteristic

C₂²×C₃

—

C₂×D₃

—

100

C₂×D₃

—

101

C₃×C₄

—

102

C₃×C₄

—

103

Dic₃

—

104

Dic₃

—

105

C₃²

#1746

yes

characteristic, complemented, Sylow

106

C₂³

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₄×#157

yes

—

114

C₂×C₄

C₂²×#157

yes

characteristic

115

C₈

—

116

C₈

—

117

C₈

—

118

C₂×C₃

—

119

C₂×C₃

—

120

D₃

—

121

C₂²

—

122

C₂²

—

123

C₂²

C₂×C₄×#157

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

#64286

yes

—

129

C₃

—

130

C₂

—

131

C₂

#10593733

yes

characteristic

132

C₂

#10593775

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#157
commutator, socle	C₂²×C₃²	C₂×C₄²
Fitting	C₃²×#97	C₄
prime radical	C₂²×C₃⋊D₃	C₂²×C₄
cosocle	C₂×C₄×C₃⋊D₃	C₂³
hypercenter	#97	#157
hypocenter	C₃²	#1746
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#157

commutator, socle

C₂²×C₃²

C₂×C₄²

Fitting

C₃²×#97

C₄

prime radical

C₂²×C₃⋊D₃

C₂²×C₄

cosocle

C₂×C₄×C₃⋊D₃

C₂³

C₃²

G ▷ C₂²×C₃² ▷ C₃²

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
10. C₄×#622	C₄	semidirect
11. C₃²×#97	C₄	semidirect
12. #63642	C₄	semidirect
13. #63630	C₄	semidirect
71. #97	#157	semidirect
105. C₃²	#1746	semidirect

H ≅ G/N

type

10. C₄×#622

C₄

semidirect

11. C₃²×#97

C₄

semidirect

12. #63642

C₄

semidirect

13. #63630

C₄

semidirect

71. #97

#157

semidirect

105. C₃²

#1746

semidirect

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

subgroup	index
#10593733	2
C₄×#3787	2
C₃⋊D₃×#97	2
#10590181	2
#1746	9

subgroup

index

C₃⋊D₃×#97

Subgroups — #11783515

Conjugacy classes of subgroups

Complements

Maximal subgroups