Group #11858669 — subgroups

Subgroups — #11858669

Order 1152.

1320 conjugacy classes of subgroups; only the 765 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 765 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×C₃²×#131	C₂	1	1	yes	maximal, characteristic
2	#10596290	C₂	1	2	yes	maximal
3	#10592824	C₂	1	6	yes	maximal, complemented
4	C₂×#63646	C₂	1	6	yes	maximal, complemented
5	#83789	—	3	4	no	maximal
6	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
7	C₃²×#131	C₄	1	8	yes	—
8	C₂×C₃²×M₁₆	C₂²	1	3	yes	—
9	C₂²×C₃²×C₈	C₂²	1	3	yes	—
10	#64157	—	2	8	no	—
11	C₂×#3748	C₂²	1	12	yes	—
12	#63646	C₂²	1	4	yes	—
13	#63646	C₂²	1	12	yes	—
14	C₂×C₃×#131	D₃	1	4	yes	—
15	#5819	—	3	8	no	—
16	#5125	—	3	24	no	—
17	C₂×#819	—	3	24	no	—
18	C₃²×#41	C₂×C₄	1	4	yes	—
19	C₃²×#41	D₄	1	4	yes	—
20	C₂×C₃²×Q₈	Q₈	1	1	yes	characteristic
21	C₂×C₃²×D₄	Q₈	1	3	yes	—
22	C₂²×C₃²×C₄	C₂³	1	3	yes	—
23	C₃²×M₁₆	C₂×C₄	1	12	yes	—
24	C₂×C₃²×C₈	C₂×C₄	1	12	yes	—
25	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
26	C₂×C₃²×C₈	C₂³	1	3	yes	—
27	#3748	—	2	12	no	—
28	#3748	C₂³	1	8	yes	—
29	C₂×C₃⋊(C₃⋊C₈)	—	2	12	no	—
30	#2916	—	9	1	no	Sylow
31	C₂×C₃×#41	C₂×D₃	1	4	yes	—
32	C₃×#131	Dic₃	1	32	yes	—
33	C₂×C₃×M₁₆	C₂×D₃	1	12	yes	—
34	C₂²×C₃×C₈	C₂×D₃	1	12	yes	—
35	#948	—	6	32	no	—
36	C₂×#208	—	3	48	no	—
37	#819	—	3	48	no	—
38	#819	—	3	16	no	—
39	C₂³×C₃²	C₂×Q₈	1	3	yes	—
40	C₃²×Q₈	C₄⋊C₄	1	4	yes	—
41	C₃²×D₄	C₄⋊C₄	1	12	yes	—
42	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
43	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
44	C₂×C₃²×C₄	C₂×Q₈	1	3	yes	—
45	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
46	C₃²×C₈	C₂²×C₄	1	2	yes	—
47	C₃²×C₈	C₂²×C₄	1	6	yes	—
48	C₃⋊(C₃⋊C₈)	—	2	8	no	—
49	#568	—	9	2	no	—
50	C₂×#131	C₃⋊D₃	1	1	yes	characteristic
51	#430	—	9	6	no	—
52	C₂×#108	—	9	6	no	—
53	C₃×#41	D₁₂	1	16	yes	—
54	C₃×#41	C₂×Dic₃	1	16	yes	—
55	C₂×C₃×Q₈	Dic₆	1	4	yes	—
56	C₂×C₃×D₄	Dic₆	1	12	yes	—
57	C₂²×C₃×C₄	C₂²×D₃	1	12	yes	—
58	C₃×M₁₆	C₂×Dic₃	1	48	yes	—
59	C₂×C₃×C₈	C₂×Dic₃	1	48	yes	—
60	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
61	C₂×C₃×C₈	C₂²×D₃	1	12	yes	—
62	#208	—	3	32	no	—
63	#208	—	6	48	no	—
64	C₂×C₃⋊C₈	—	6	48	no	—
65	C₂²×C₃²	—	4	3	no	—
66	C₂²×C₃²	C₂×C₄⋊C₄	1	6	yes	—
67	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
68	C₃²×C₄	C₂×C₄⋊C₄	1	6	yes	—
69	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
70	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
71	C₂×#41	C₂×C₃⋊D₃	1	1	yes	characteristic
72	#131	—	18	8	no	—
73	#131	C₃⋊Dic₃	1	8	yes	—
74	C₂×M₁₆	—	9	12	no	—
75	C₂×M₁₆	C₂×C₃⋊D₃	1	3	yes	—
76	C₂²×C₈	C₂×C₃⋊D₃	1	3	yes	—
77	#108	—	9	4	no	—
78	#108	—	9	12	no	—
79	C₂³×C₃	C₂×Dic₆	1	12	yes	—
80	C₃×Q₈	C₄⋊Dic₃	1	16	yes	—
81	C₃×D₄	C₄⋊Dic₃	1	48	yes	—
82	C₂×C₃×C₄	C₂×Dic₆	1	12	yes	—
83	C₂×C₃×C₄	C₂×D₁₂	1	24	yes	—
84	C₂×C₃×C₄	C₂²×Dic₃	1	24	yes	—
85	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
86	C₃×C₈	C₂²×Dic₃	1	8	yes	—
87	C₃×C₈	C₂²×Dic₃	1	24	yes	—
88	C₃⋊C₈	—	6	32	no	—
89	C₂×C₃²	—	2	1	no	—
90	C₂×C₃²	—	2	6	no	—
91	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
92	#41	C₄⋊(C₃⋊D₃)	1	4	yes	—
93	#41	C₂×C₃⋊Dic₃	1	4	yes	—
94	C₂×Q₈	#634	1	1	yes	characteristic
95	C₂×D₄	#634	1	3	yes	—
96	C₂²×C₄	C₂²×C₃⋊D₃	1	3	yes	—
97	M₁₆	—	9	8	no	—
98	M₁₆	—	18	12	no	—
99	M₁₆	C₂×C₃⋊Dic₃	1	12	yes	—
100	C₂×C₈	—	18	12	no	—
101	C₂×C₈	C₂×C₃⋊Dic₃	1	12	yes	—
102	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
103	C₂×C₈	C₂²×C₃⋊D₃	1	3	yes	—
104	C₂²×C₃	—	4	12	no	—
105	C₂²×C₃	C₂×C₄⋊Dic₃	1	24	yes	—
106	C₂²×C₃	C₂²×Dic₆	1	4	yes	—
107	C₃×C₄	C₂×C₄⋊Dic₃	1	24	yes	—
108	C₃×C₄	C₂²×D₁₂	1	4	yes	—
109	C₃×C₄	C₂³×Dic₃	1	4	yes	—
110	C₃²	#2916	1	1	yes	characteristic, complemented, Sylow
111	C₂³	C₂×#634	1	3	yes	—
112	Q₈	C₄⋊(C₃⋊Dic₃)	1	4	yes	—
113	D₄	C₄⋊(C₃⋊Dic₃)	1	12	yes	—
114	C₂×C₄	C₂×#634	1	3	yes	—
115	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	6	yes	—
116	C₂×C₄	C₂²×C₃⋊Dic₃	1	6	yes	—
117	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
118	C₈	—	18	8	no	—
119	C₈	C₂²×C₃⋊Dic₃	1	2	yes	—
120	C₈	C₂²×C₃⋊Dic₃	1	6	yes	—
121	C₂×C₃	—	2	4	no	—
122	C₂×C₃	—	2	24	no	—
123	C₂×C₃	C₂²×C₄⋊Dic₃	1	4	yes	—
124	C₂²	—	4	3	no	—
125	C₂²	C₂×C₄⋊(C₃⋊Dic₃)	1	6	yes	—
126	C₂²	C₂²×#634	1	1	yes	characteristic
127	C₄	C₂×C₄⋊(C₃⋊Dic₃)	1	6	yes	—
128	C₄	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
129	C₄	C₂³×C₃⋊Dic₃	1	1	yes	characteristic
130	C₃	#83789	1	4	yes	complemented
131	C₂	—	2	1	no	—
132	C₂	—	2	6	no	—
133	C₂	C₂²×C₄⋊(C₃⋊Dic₃)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃²×#131

C₂

yes

maximal, characteristic

#10596290

C₂

yes

maximal

#10592824

C₂

yes

maximal, complemented

C₂×#63646

C₂

yes

maximal, complemented

#83789

—

maximal

C₂×C₃²×#41

C₂²

yes

characteristic

C₃²×#131

C₄

yes

—

C₂×C₃²×M₁₆

C₂²

yes

—

C₂²×C₃²×C₈

C₂²

yes

—

#64157

—

C₂×#3748

C₂²

yes

—

#63646

C₂²

yes

—

#63646

C₂²

yes

—

C₂×C₃×#131

D₃

yes

—

#5819

—

#5125

—

C₂×#819

—

C₃²×#41

C₂×C₄

yes

—

C₃²×#41

D₄

yes

—

C₂×C₃²×Q₈

Q₈

yes

characteristic

C₂×C₃²×D₄

Q₈

yes

—

C₂²×C₃²×C₄

C₂³

yes

—

C₃²×M₁₆

C₂×C₄

yes

—

C₂×C₃²×C₈

C₂×C₄

yes

—

C₂×C₃²×C₈

C₂³

yes

characteristic

C₂×C₃²×C₈

C₂³

yes

—

#3748

—

#3748

C₂³

yes

—

C₂×C₃⋊(C₃⋊C₈)

—

#2916

—

Sylow

C₂×C₃×#41

C₂×D₃

yes

—

C₃×#131

Dic₃

yes

—

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂²×C₃×C₈

C₂×D₃

yes

—

—

—

—

—

C₂³×C₃²

C₂×Q₈

yes

—

C₃²×Q₈

C₄⋊C₄

yes

—

C₃²×D₄

C₄⋊C₄

yes

—

C₂×C₃²×C₄

C₂²×C₄

yes

—

C₂×C₃²×C₄

C₂×D₄

yes

—

C₂×C₃²×C₄

C₂×Q₈

yes

—

C₂×C₃²×C₄

C₂⁴

yes

characteristic

C₃²×C₈

C₂²×C₄

yes

—

C₃²×C₈

C₂²×C₄

yes

—

C₃⋊(C₃⋊C₈)

—

#568

—

C₂×#131

C₃⋊D₃

yes

characteristic

#430

—

C₂×#108

—

C₃×#41

D₁₂

yes

—

C₃×#41

C₂×Dic₃

yes

—

C₂×C₃×Q₈

Dic₆

yes

—

C₂×C₃×D₄

Dic₆

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₃×M₁₆

C₂×Dic₃

yes

—

C₂×C₃×C₈

C₂×Dic₃

yes

—

C₂×C₃×C₈

C₂²×D₃

yes

—

C₂×C₃×C₈

C₂²×D₃

yes

—

#208

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

C₂×C₄⋊C₄

yes

—

C₂²×C₃²

C₂²×Q₈

yes

characteristic

C₃²×C₄

C₂×C₄⋊C₄

yes

—

C₃²×C₄

C₂³×C₄

yes

characteristic

C₃²×C₄

C₂²×D₄

yes

characteristic

C₂×#41

C₂×C₃⋊D₃

yes

characteristic

#131

—

#131

C₃⋊Dic₃

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×C₃⋊D₃

yes

—

C₂²×C₈

C₂×C₃⋊D₃

yes

—

#108

—

#108

—

C₂³×C₃

C₂×Dic₆

yes

—

C₃×Q₈

C₄⋊Dic₃

yes

—

C₃×D₄

C₄⋊Dic₃

yes

—

C₂×C₃×C₄

C₂×Dic₆

yes

—

C₂×C₃×C₄

C₂×D₁₂

yes

—

C₂×C₃×C₄

C₂²×Dic₃

yes

—

C₂×C₃×C₄

C₂³×D₃

yes

—

C₃×C₈

C₂²×Dic₃

yes

—

C₃×C₈

C₂²×Dic₃

yes

—

C₃⋊C₈

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

C₂²×C₄⋊C₄

yes

characteristic

#41

C₄⋊(C₃⋊D₃)

yes

—

#41

C₂×C₃⋊Dic₃

yes

—

C₂×Q₈

#634

yes

characteristic

C₂×D₄

#634

yes

—

C₂²×C₄

C₂²×C₃⋊D₃

yes

—

M₁₆

—

M₁₆

—

M₁₆

C₂×C₃⋊Dic₃

yes

—

100

C₂×C₈

—

101

C₂×C₈

C₂×C₃⋊Dic₃

yes

—

102

C₂×C₈

C₂²×C₃⋊D₃

yes

characteristic

103

C₂×C₈

C₂²×C₃⋊D₃

yes

—

104

C₂²×C₃

—

105

C₂²×C₃

C₂×C₄⋊Dic₃

yes

—

106

C₂²×C₃

C₂²×Dic₆

yes

—

107

C₃×C₄

C₂×C₄⋊Dic₃

yes

—

108

C₃×C₄

C₂²×D₁₂

yes

—

109

C₃×C₄

C₂³×Dic₃

yes

—

110

C₃²

#2916

yes

characteristic, complemented, Sylow

111

C₂³

C₂×#634

yes

—

112

Q₈

C₄⋊(C₃⋊Dic₃)

yes

—

113

D₄

C₄⋊(C₃⋊Dic₃)

yes

—

114

C₂×C₄

C₂×#634

yes

—

115

C₂×C₄

C₂×C₄⋊(C₃⋊D₃)

yes

—

116

C₂×C₄

C₂²×C₃⋊Dic₃

yes

—

117

C₂×C₄

C₂³×C₃⋊D₃

yes

characteristic

118

C₈

—

119

C₈

C₂²×C₃⋊Dic₃

yes

—

120

C₈

C₂²×C₃⋊Dic₃

yes

—

121

C₂×C₃

—

122

C₂×C₃

—

123

C₂×C₃

C₂²×C₄⋊Dic₃

yes

—

124

C₂²

—

125

C₂²

C₂×C₄⋊(C₃⋊Dic₃)

yes

—

126

C₂²

C₂²×#634

yes

characteristic

127

C₄

C₂×C₄⋊(C₃⋊Dic₃)

yes

—

128

C₄

C₂²×C₄⋊(C₃⋊D₃)

yes

characteristic

129

C₄

C₂³×C₃⋊Dic₃

yes

characteristic

130

C₃

#83789

yes

complemented

131

C₂

—

132

C₂

—

133

C₂

C₂²×C₄⋊(C₃⋊Dic₃)

yes

characteristic

	subgroup	G/H
center	C₄	C₂²×C₄⋊(C₃⋊D₃)
commutator	C₃²×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂³×C₃⋊D₃
Fitting	C₂×C₃²×#131	C₂
socle	C₂×C₃²	C₂²×C₄⋊C₄
prime radical	C₂×C₃²×#41	C₂²
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂×#131	C₃⋊D₃
hypocenter	C₃²	#2916
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ C₂×#131

subgroup

G/H

center

C₄

C₂²×C₄⋊(C₃⋊D₃)

commutator

C₃²×C₄

C₂³×C₄

Frattini

C₂×C₄

C₂³×C₃⋊D₃

Fitting

C₂×C₃²×#131

C₂

socle

C₂×C₃²

C₂²×C₄⋊C₄

prime radical

C₂×C₃²×#41

C₂²

cosocle

C₂×C₃²×C₄

C₂⁴

C₃⋊D₃

C₃²

G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₄ ◁ C₂×#41 ◁ C₂×#131

N	H ≅ G/N	type
3. #10592824	C₂	semidirect
4. C₂×#63646	C₂	semidirect
110. C₃²	#2916	semidirect
130. C₃	#83789	semidirect

H ≅ G/N

type

3. #10592824

C₂

semidirect

4. C₂×#63646

C₂

semidirect

110. C₃²

#2916

semidirect

130. C₃

#83789

semidirect

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

subgroup	index
C₂×C₃²×#131	2
#10596290	2
#10592824	2
C₂×#63646	2
#83789	3

subgroup

index

C₂×C₃²×#131

Subgroups — #11858669

Conjugacy classes of subgroups

Complements

Maximal subgroups