Group #11795362 — subgroups

Subgroups — #11795362

Order 1152.

666 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 175 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	#10592825	C₂	1	3	yes	maximal
2	#10592824	C₂	1	3	yes	maximal, complemented
3	C₃²×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	#68721	—	3	4	no	maximal
5	C₂²×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₂×C₃²×M₁₆	C₂²	1	3	yes	—
7	C₂×#3748	C₂²	1	3	yes	—
8	#63647	—	2	6	no	—
9	#63646	—	2	6	no	—
10	#5126	—	3	12	no	—
11	#5125	—	3	12	no	—
12	C₃×#338	D₃	1	4	yes	complemented
13	C₂³×C₃⋊D₃	Q₈	1	1	yes	characteristic
14	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
15	C₂²×C₃⋊Dic₃	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₃⋊D₃	—	2	3	no	—
17	C₂×C₄×C₃⋊D₃	—	2	3	no	—
18	C₃²×M₁₆	—	2	6	no	—
19	C₂×C₃²×C₈	D₄	1	6	yes	—
20	#3748	—	2	6	no	—
21	C₂×C₃⋊(C₃⋊C₈)	—	2	3	no	—
22	#2091	—	9	1	no	Sylow
23	C₂²×C₄×D₃	—	3	4	no	—
24	C₂×C₃×M₁₆	C₂×D₃	1	12	yes	—
25	C₂×#208	—	3	12	no	—
26	(C₂×D₃)⋊C₈	—	6	24	no	—
27	#819	—	6	24	no	—
28	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₃⋊D₃	—	2	3	no	—
30	C₂²×C₃⋊D₃	—	4	2	no	—
31	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
32	C₂×C₃²×C₄	#41	1	3	yes	—
33	C₂×C₃⋊Dic₃	—	2	3	no	—
34	C₄×C₃⋊D₃	—	4	3	no	—
35	C₄×C₃⋊D₃	—	4	1	no	—
36	C₃²×C₈	—	2	6	no	—
37	C₃⋊(C₃⋊C₈)	—	4	3	no	—
38	#430	—	9	3	no	—
39	#407	—	9	3	no	—
40	#338	C₃⋊D₃	1	1	yes	characteristic, complemented
41	C₂³×D₃	—	3	4	no	—
42	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
43	C₂²×Dic₃	—	3	4	no	—
44	C₂×C₄×D₃	—	6	12	no	—
45	C₂×C₄×D₃	—	6	12	no	—
46	C₃×M₁₆	—	2	24	no	—
47	C₂×C₃×C₈	D₁₂	1	24	yes	—
48	#208	—	6	24	no	—
49	C₂×C₃⋊C₈	—	6	12	no	—
50	C₂²×C₃²	—	4	1	no	—
51	C₂²×C₃²	C₂²⋊Q₈	1	3	yes	—
52	C₂×C₃⋊D₃	—	2	6	no	—
53	C₂×C₃⋊D₃	—	4	3	no	—
54	C₂×C₃⋊D₃	—	4	1	no	—
55	C₃²×C₄	#123	1	3	yes	—
56	C₃²×C₄	#127	1	1	yes	characteristic
57	C₃⋊Dic₃	—	4	1	no	—
58	C₂³×C₄	—	9	1	no	—
59	C₂×M₁₆	—	9	3	no	—
60	C₂×M₁₆	C₂×C₃⋊D₃	1	3	yes	—
61	#108	—	18	6	no	—
62	C₂²⋊C₈	—	18	6	no	—
63	C₂³×C₃	D₃×Q₈	1	4	yes	—
64	C₂²×D₃	—	6	12	no	—
65	C₂²×D₃	—	12	8	no	—
66	C₂×C₃×C₄	C₂×D₁₂	1	12	yes	—
67	C₂×C₃×C₄	#237	1	12	yes	—
68	C₂×Dic₃	—	6	12	no	—
69	C₄×D₃	—	12	4	no	—
70	C₄×D₃	—	12	12	no	—
71	C₃×C₈	—	2	24	no	—
72	C₃⋊C₈	—	12	12	no	—
73	C₂×C₃²	—	2	3	no	—
74	C₂×C₃²	#399	1	1	yes	characteristic
75	C₃⋊D₃	—	4	2	no	—
76	C₂⁴	—	9	1	no	—
77	C₂²×C₄	—	9	1	no	—
78	C₂²×C₄	—	18	3	no	—
79	C₂²×C₄	—	18	3	no	—
80	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
81	M₁₆	—	2	6	no	—
82	M₁₆	—	18	6	no	—
83	C₂×C₈	—	18	3	no	—
84	C₂×C₈	C₄⋊(C₃⋊D₃)	1	6	yes	—
85	C₂²×C₃	—	4	4	no	—
86	C₂²×C₃	#897	1	12	yes	—
87	C₂×D₃	—	6	24	no	—
88	C₂×D₃	—	12	12	no	—
89	C₂×D₃	—	12	4	no	—
90	C₃×C₄	#874	1	4	yes	—
91	C₃×C₄	#886	1	12	yes	—
92	Dic₃	—	12	4	no	—
93	C₃²	#2091	1	1	yes	characteristic, complemented, Sylow
94	C₂³	—	18	3	no	—
95	C₂³	—	36	2	no	—
96	C₂³	Q₈×C₃⋊D₃	1	1	yes	characteristic
97	C₂×C₄	—	18	3	no	—
98	C₂×C₄	—	36	1	no	—
99	C₂×C₄	—	36	3	no	—
100	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	3	yes	—
101	C₂×C₄	#3830	1	3	yes	—
102	C₈	—	2	6	no	—
103	C₈	—	36	3	no	—
104	C₂×C₃	—	2	12	no	—
105	C₂×C₃	#4677	1	4	yes	—
106	D₃	—	12	8	no	—
107	C₂²	—	4	1	no	—
108	C₂²	—	18	6	no	—
109	C₂²	—	36	3	no	—
110	C₂²	—	36	1	no	—
111	C₂²	#64106	1	3	yes	—
112	C₄	—	36	1	no	—
113	C₄	#64083	1	1	yes	characteristic
114	C₄	#64095	1	3	yes	—
115	C₃	#68721	1	4	yes	complemented
116	C₂	—	2	3	no	—
117	C₂	—	36	2	no	—
118	C₂	#10592376	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10592825

C₂

yes

maximal

#10592824

C₂

yes

maximal, complemented

C₃²×#338

C₂

yes

maximal, characteristic, complemented

#68721

—

maximal

C₂²×C₄×C₃⋊D₃

C₂²

yes

characteristic

C₂×C₃²×M₁₆

C₂²

yes

—

C₂×#3748

C₂²

yes

—

—

—

—

—

D₃

yes

complemented

C₂³×C₃⋊D₃

Q₈

yes

characteristic

C₂²×C₃²×C₄

C₂³

yes

characteristic

C₂²×C₃⋊Dic₃

Q₈

yes

characteristic

C₂×C₄×C₃⋊D₃

—

C₂×C₄×C₃⋊D₃

—

C₃²×M₁₆

—

C₂×C₃²×C₈

D₄

yes

—

#3748

—

C₂×C₃⋊(C₃⋊C₈)

—

#2091

—

Sylow

C₂²×C₄×D₃

—

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂×#208

—

(C₂×D₃)⋊C₈

—

#819

—

C₂³×C₃²

C₂×Q₈

yes

characteristic

C₂²×C₃⋊D₃

—

C₂²×C₃⋊D₃

—

C₂×C₃²×C₄

C₂×D₄

yes

—

C₂×C₃²×C₄

#41

yes

—

C₂×C₃⋊Dic₃

—

C₄×C₃⋊D₃

—

C₄×C₃⋊D₃

—

C₃²×C₈

—

C₃⋊(C₃⋊C₈)

—

#430

—

#407

—

#338

C₃⋊D₃

yes

characteristic, complemented

C₂³×D₃

—

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₂²×Dic₃

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₃×M₁₆

—

C₂×C₃×C₈

D₁₂

yes

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

C₂²⋊Q₈

yes

—

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

—

C₃²×C₄

#123

yes

—

C₃²×C₄

#127

yes

characteristic

C₃⋊Dic₃

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×C₃⋊D₃

yes

—

#108

—

C₂²⋊C₈

—

C₂³×C₃

D₃×Q₈

yes

—

C₂²×D₃

—

C₂²×D₃

—

C₂×C₃×C₄

C₂×D₁₂

yes

—

C₂×C₃×C₄

#237

yes

—

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

—

C₂×C₃²

#399

yes

characteristic

C₃⋊D₃

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×C₃⋊D₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₄⋊(C₃⋊D₃)

yes

—

C₂²×C₃

—

C₂²×C₃

#897

yes

—

C₂×D₃

—

C₂×D₃

—

C₂×D₃

—

C₃×C₄

#874

yes

—

C₃×C₄

#886

yes

—

Dic₃

—

C₃²

#2091

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

Q₈×C₃⋊D₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂×C₄⋊(C₃⋊D₃)

yes

—

101

C₂×C₄

#3830

yes

—

102

C₈

—

103

C₈

—

104

C₂×C₃

—

105

C₂×C₃

#4677

yes

—

106

D₃

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

#64106

yes

—

112

C₄

—

113

C₄

#64083

yes

characteristic

114

C₄

#64095

yes

—

115

C₃

#68721

yes

complemented

116

C₂

—

117

C₂

—

118

C₂

#10592376

yes

characteristic

	subgroup	G/H
center	C₄	#64083
commutator, cosocle	C₂²×C₃²×C₄	C₂³
Frattini	C₂²×C₄	C₂²×C₃⋊D₃
Fitting	C₃²×#338	C₂
socle	C₂×C₃²	#399
prime radical	C₂³×C₃⋊D₃	Q₈
hypercenter	#338	C₃⋊D₃
hypocenter	C₃²	#2091
LCS	G ▷ C₂²×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

subgroup

G/H

center

C₄

#64083

commutator, cosocle

C₂²×C₃²×C₄

C₂³

Frattini

C₂²×C₄

C₂²×C₃⋊D₃

Fitting

C₃²×#338

C₂

socle

C₂×C₃²

#399

prime radical

C₂³×C₃⋊D₃

Q₈

C₃⋊D₃

C₃²

G ▷ C₂²×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

N	H ≅ G/N	type
2. #10592824	C₂	semidirect
3. C₃²×#338	C₂	semidirect
12. C₃×#338	D₃	semidirect
40. #338	C₃⋊D₃	semidirect
93. C₃²	#2091	semidirect
115. C₃	#68721	semidirect

H ≅ G/N

type

2. #10592824

C₂

semidirect

3. C₃²×#338

C₂

semidirect

12. C₃×#338

D₃

semidirect

40. #338

C₃⋊D₃

semidirect

93. C₃²

#2091

semidirect

115. C₃

#68721

semidirect

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

subgroup	index
#10592825	2
#10592824	2
C₃²×#338	2
#68721	3

subgroup

index

#10592825

#10592824

C₃²×#338

#68721

Subgroups — #11795362

Conjugacy classes of subgroups

Complements

Maximal subgroups