Group #11771275 — subgroups

Subgroups — #11771275

Order 1152.

438 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 181 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	C₃²×#423	C₂	1	1	yes	maximal, characteristic
2	#10592623	C₂	1	2	yes	maximal
3	C₃⋊#1309	—	3	4	no	maximal
4	C₂×C₃²×M₁₆	C₄	1	2	yes	—
5	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
6	C₂×#3748	C₄	1	4	yes	—
7	C₃²×C₄⋊C₈	—	2	2	no	—
8	C₄⋊(C₃⋊(C₃⋊C₈))	—	2	2	no	—
9	C₄⋊(C₃⋊(C₃⋊C₈))	—	2	2	no	—
10	C₃×#423	D₃	1	4	yes	—
11	#4924	—	3	8	no	—
12	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
13	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
14	C₃²×M₁₆	—	4	2	no	—
15	C₂×C₃²×C₈	—	2	2	no	—
16	C₃²×C₄²	D₄	1	1	yes	characteristic
17	C₃²×C₄²	D₄	1	2	yes	—
18	C₃²×C₄²	Q₈	1	1	yes	characteristic
19	#3748	—	4	4	no	—
20	C₂×C₃⋊(C₃⋊C₈)	—	2	4	no	—
21	#1309	—	9	1	no	Sylow
22	C₂×C₃×M₁₆	Dic₃	1	8	yes	—
23	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
24	C₂×#208	—	3	16	no	—
25	C₃×C₄⋊C₈	—	2	8	no	—
26	C₄⋊(C₃⋊C₈)	—	6	8	no	—
27	C₄⋊(C₃⋊C₈)	—	6	8	no	—
28	C₂³×C₃²	C₄²	1	1	yes	characteristic
29	C₂×C₃²×C₄	—	2	2	no	—
30	C₂×C₃²×C₄	—	2	1	no	—
31	C₂×C₃²×C₄	—	2	2	no	—
32	C₂×C₃²×C₄	—	2	1	no	—
33	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
34	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
36	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
37	C₃²×C₈	—	4	2	no	—
38	C₃⋊(C₃⋊C₈)	—	4	4	no	—
39	#423	—	9	2	no	—
40	#423	C₃⋊D₃	1	1	yes	characteristic
41	C₂²×C₃×C₄	C₄×D₃	1	8	yes	—
42	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
43	C₃×M₁₆	—	4	8	no	—
44	C₂×C₃×C₈	—	2	8	no	—
45	C₃×C₄²	Dic₆	1	4	yes	—
46	C₃×C₄²	D₁₂	1	4	yes	—
47	C₃×C₄²	#67	1	8	yes	—
48	#208	—	12	16	no	—
49	C₂×C₃⋊C₈	—	6	16	no	—
50	C₂²×C₃²	—	2	1	no	—
51	C₂²×C₃²	—	2	2	no	—
52	C₂²×C₃²	#95	1	1	yes	characteristic
53	C₃²×C₄	—	2	1	no	—
54	C₃²×C₄	—	2	2	no	—
55	C₃²×C₄	#100	1	2	yes	—
56	C₃²×C₄	#100	1	1	yes	characteristic
57	C₃²×C₄	#101	1	2	yes	—
58	C₃²×C₄	#101	1	1	yes	characteristic
59	C₂×M₁₆	—	9	4	no	—
60	C₂×M₁₆	C₃⋊Dic₃	1	2	yes	—
61	C₂×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
62	C₄⋊C₈	—	2	2	no	—
63	C₄⋊C₈	—	18	2	no	—
64	C₄⋊C₈	—	18	2	no	—
65	C₂³×C₃	C₄×Dic₃	1	4	yes	—
66	C₂×C₃×C₄	—	2	8	no	—
67	C₂×C₃×C₄	—	2	8	no	—
68	C₂×C₃×C₄	—	2	4	no	—
69	C₂×C₃×C₄	—	2	4	no	—
70	C₂×C₃×C₄	Dic₃⋊C₄	1	8	yes	—
71	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
72	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	8	yes	—
73	C₂×C₃×C₄	#217	1	4	yes	—
74	C₃×C₈	—	4	8	no	—
75	C₃⋊C₈	—	12	16	no	—
76	C₂×C₃²	—	4	1	no	—
77	C₂×C₃²	#343	1	1	yes	characteristic
78	C₂×C₃²	#343	1	2	yes	—
79	C₂²×C₄	C₄×C₃⋊D₃	1	2	yes	—
80	C₂²×C₄	C₂×C₃⋊Dic₃	1	1	yes	characteristic
81	M₁₆	—	4	2	no	—
82	M₁₆	—	36	4	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	18	4	no	—
85	C₄²	#634	1	1	yes	characteristic
86	C₄²	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
87	C₄²	#638	1	2	yes	—
88	C₂²×C₃	—	2	4	no	—
89	C₂²×C₃	—	2	8	no	—
90	C₂²×C₃	C₃⋊#95	1	4	yes	—
91	C₃×C₄	—	2	4	no	—
92	C₃×C₄	—	2	8	no	—
93	C₃×C₄	#823	1	8	yes	—
94	C₃×C₄	#824	1	8	yes	—
95	C₃×C₄	#833	1	4	yes	—
96	C₃×C₄	#836	1	4	yes	—
97	C₃²	#1309	1	1	yes	characteristic, complemented, Sylow
98	C₂³	C₄×C₃⋊Dic₃	1	1	yes	characteristic
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	#3750	1	2	yes	—
104	C₂×C₄	C₄⋊(C₃⋊Dic₃)	1	1	yes	characteristic
105	C₂×C₄	#3752	1	2	yes	—
106	C₂×C₄	#3757	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	36	4	no	—
109	C₂×C₃	—	4	4	no	—
110	C₂×C₃	#4530	1	4	yes	—
111	C₂×C₃	#4554	1	8	yes	—
112	C₂²	—	2	1	no	—
113	C₂²	—	2	2	no	—
114	C₂²	#63658	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	2	2	no	—
117	C₄	#63650	1	2	yes	—
118	C₄	#63651	1	2	yes	—
119	C₄	#63660	1	1	yes	characteristic
120	C₄	#63663	1	1	yes	characteristic
121	C₃	C₃⋊#1309	1	4	yes	complemented
122	C₂	—	4	1	no	—
123	C₂	#10589396	1	1	yes	characteristic
124	C₂	#10589420	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#423

C₂

yes

maximal, characteristic

#10592623

C₂

yes

maximal

C₃⋊#1309

—

maximal

C₂×C₃²×M₁₆

C₄

yes

—

C₂×C₃²×C₄²

C₂²

yes

characteristic

C₂×#3748

C₄

yes

—

C₃²×C₄⋊C₈

—

C₄⋊(C₃⋊(C₃⋊C₈))

—

C₄⋊(C₃⋊(C₃⋊C₈))

—

C₃×#423

D₃

yes

—

#4924

—

C₂²×C₃²×C₄

C₂×C₄

yes

—

C₂²×C₃²×C₄

C₂×C₄

yes

characteristic

C₃²×M₁₆

—

C₂×C₃²×C₈

—

C₃²×C₄²

D₄

yes

characteristic

C₃²×C₄²

D₄

yes

—

C₃²×C₄²

Q₈

yes

characteristic

#3748

—

C₂×C₃⋊(C₃⋊C₈)

—

#1309

—

Sylow

C₂×C₃×M₁₆

Dic₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

—

C₂×#208

—

C₃×C₄⋊C₈

—

C₄⋊(C₃⋊C₈)

—

C₄⋊(C₃⋊C₈)

—

C₂³×C₃²

C₄²

yes

characteristic

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂²⋊C₄

yes

—

C₂×C₃²×C₄

C₂²⋊C₄

yes

characteristic

C₂×C₃²×C₄

C₄⋊C₄

yes

—

C₂×C₃²×C₄

C₄⋊C₄

yes

characteristic

C₃²×C₈

—

C₃⋊(C₃⋊C₈)

—

#423

—

#423

C₃⋊D₃

yes

characteristic

C₂²×C₃×C₄

C₄×D₃

yes

—

C₂²×C₃×C₄

C₂×Dic₃

yes

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₄²

Dic₆

yes

—

C₃×C₄²

D₁₂

yes

—

C₃×C₄²

#67

yes

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

#95

yes

characteristic

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

#100

yes

—

C₃²×C₄

#100

yes

characteristic

C₃²×C₄

#101

yes

—

C₃²×C₄

#101

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₃⋊Dic₃

yes

—

C₂×C₄²

C₂×C₃⋊D₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂³×C₃

C₄×Dic₃

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

Dic₃⋊C₄

yes

—

C₂×C₃×C₄

C₄⋊Dic₃

yes

—

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

C₂×C₃×C₄

#217

yes

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

—

C₂×C₃²

#343

yes

characteristic

C₂×C₃²

#343

yes

—

C₂²×C₄

C₄×C₃⋊D₃

yes

—

C₂²×C₄

C₂×C₃⋊Dic₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄²

#634

yes

characteristic

C₄²

C₄⋊(C₃⋊D₃)

yes

characteristic

C₄²

#638

yes

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

C₃⋊#95

yes

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

#823

yes

—

C₃×C₄

#824

yes

—

C₃×C₄

#833

yes

—

C₃×C₄

#836

yes

—

C₃²

#1309

yes

characteristic, complemented, Sylow

C₂³

C₄×C₃⋊Dic₃

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#3750

yes

—

104

C₂×C₄

C₄⋊(C₃⋊Dic₃)

yes

characteristic

105

C₂×C₄

#3752

yes

—

106

C₂×C₄

#3757

yes

characteristic

107

C₈

—

108

C₈

—

109

C₂×C₃

—

110

C₂×C₃

#4530

yes

—

111

C₂×C₃

#4554

yes

—

112

C₂²

—

113

C₂²

—

114

C₂²

#63658

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

#63650

yes

—

118

C₄

#63651

yes

—

119

C₄

#63660

yes

characteristic

120

C₄

#63663

yes

characteristic

121

C₃

C₃⋊#1309

yes

complemented

122

C₂

—

123

C₂

#10589396

yes

characteristic

124

C₂

#10589420

yes

—

	subgroup	G/H
center	C₂²	#63658
commutator, prime radical	C₂³×C₃²	C₄²
Frattini	C₂×C₄²	C₂×C₃⋊D₃
Fitting	C₃²×#423	C₂
socle	C₂²×C₃²	#95
cosocle	C₂×C₃²×C₄²	C₂²
hypercenter	#423	C₃⋊D₃
hypocenter	C₃²	#1309
LCS	G ▷ C₂³×C₃² ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

#63658

commutator, prime radical

C₂³×C₃²

C₄²

Frattini

C₂×C₄²

C₂×C₃⋊D₃

Fitting

C₃²×#423

C₂

socle

C₂²×C₃²

#95

cosocle

C₂×C₃²×C₄²

C₂²

C₃⋊D₃

C₃²

G ▷ C₂³×C₃² ▷ C₂²×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
97. C₃²	#1309	semidirect
121. C₃	C₃⋊#1309	semidirect

H ≅ G/N

type

97. C₃²

#1309

semidirect

121. C₃

C₃⋊#1309

semidirect

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

subgroup	index
C₃²×#423	2
#10592623	2
C₃⋊#1309	3

subgroup

index

C₃²×#423

#10592623

C₃⋊#1309

Subgroups — #11771275

Conjugacy classes of subgroups

Complements

Maximal subgroups