Group #11772452 — subgroups

Subgroups — #11772452

Order 1152.

186 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 100 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×C₉×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#63372	C₂	1	2	yes	maximal
3	#67820	—	3	1	no	maximal
4	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
5	C₂×#3667	—	2	2	no	—
6	C₉×M₃₂	—	2	2	no	—
7	C₂×C₉×C₁₆	C₄	1	2	yes	—
8	#63372	—	2	2	no	—
9	#63372	C₄	1	4	yes	—
10	C₂×C₃×M₃₂	D₃	1	1	yes	characteristic
11	C₂×#819	—	3	2	no	—
12	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₉	D₄	1	2	yes	—
16	C₂×C₈×C₉	Q₈	1	1	yes	characteristic
17	#3667	—	2	4	no	—
18	#3667	—	4	2	no	—
19	C₂×C₉⋊C₈	—	4	2	no	—
20	C₉×C₁₆	—	2	2	no	—
21	#1385	—	9	1	no	Sylow
22	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
23	C₂×#208	—	6	2	no	—
24	C₃×M₃₂	—	2	2	no	—
25	C₂×C₃×C₁₆	Dic₃	1	2	yes	—
26	#819	—	3	4	no	—
27	#819	—	6	2	no	—
28	C₂³×C₉	Q₁₆	1	1	yes	characteristic
29	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
30	C₂×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₉	D₈	1	1	yes	characteristic
32	C₂×C₄×C₉	SD₁₆	1	2	yes	—
33	C₈×C₉	C₄²	1	1	yes	characteristic
34	C₈×C₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₈×C₉	C₄⋊C₄	1	2	yes	—
36	C₉⋊C₈	—	4	4	no	—
37	C₂×M₃₂	D₉	1	1	yes	characteristic
38	C₂×#108	—	9	2	no	—
39	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
40	C₂×C₃×C₈	Dic₆	1	1	yes	characteristic
41	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
42	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
43	C₂×C₃×C₈	#67	1	2	yes	—
44	#208	—	6	4	no	—
45	#208	—	12	2	no	—
46	C₂×C₃⋊C₈	—	12	2	no	—
47	C₃×C₁₆	—	2	2	no	—
48	C₂²×C₉	—	4	1	no	—
49	C₂²×C₉	#103	1	2	yes	—
50	C₂²×C₉	#107	1	1	yes	characteristic
51	C₄×C₉	#95	1	1	yes	characteristic
52	C₄×C₉	#102	1	2	yes	—
53	C₄×C₉	#106	1	1	yes	characteristic
54	C₂×M₁₆	—	18	2	no	—
55	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
56	M₃₂	—	2	2	no	—
57	C₂×C₁₆	Dic₉	1	2	yes	—
58	#108	—	9	4	no	—
59	#108	—	18	2	no	—
60	C₂³×C₃	Dic₁₂	1	1	yes	characteristic
61	C₂×C₃×C₄	#204	1	2	yes	—
62	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
63	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
64	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
65	C₃×C₈	C₄×Dic₃	1	1	yes	characteristic
66	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
67	C₃×C₈	#217	1	1	yes	characteristic
68	C₃⋊C₈	—	12	4	no	—
69	C₂×C₉	—	2	2	no	—
70	C₂×C₉	—	2	1	no	—
71	C₂×C₉	#340	1	1	yes	characteristic
72	C₂²×C₄	D₃₆	1	1	yes	characteristic
73	M₁₆	—	18	4	no	—
74	M₁₆	—	36	2	no	—
75	C₂×C₈	—	36	2	no	—
76	C₂×C₈	Dic₁₈	1	1	yes	characteristic
77	C₂×C₈	C₄×D₉	1	2	yes	—
78	C₂×C₈	C₂×Dic₉	1	1	yes	characteristic
79	C₂×C₈	#611	1	2	yes	—
80	C₁₆	—	2	2	no	—
81	C₂²×C₃	—	4	1	no	—
82	C₂²×C₃	#816	1	2	yes	—
83	C₂²×C₃	#818	1	1	yes	characteristic
84	C₃×C₄	#817	1	1	yes	characteristic
85	C₃×C₄	#821	1	2	yes	—
86	C₃×C₄	C₃⋊#95	1	1	yes	characteristic
87	C₉	#1385	1	1	yes	characteristic, complemented, Sylow
88	C₂³	Dic₃₆	1	1	yes	characteristic
89	C₂×C₄	#3664	1	2	yes	—
90	C₂×C₄	D₇₂	1	1	yes	characteristic
91	C₂×C₄	C₄⋊Dic₉	1	1	yes	characteristic
92	C₂×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
93	C₈	—	36	4	no	—
94	C₈	C₄×Dic₉	1	1	yes	characteristic
95	C₈	Dic₉⋊C₄	1	2	yes	—
96	C₈	#3676	1	1	yes	characteristic
97	C₂×C₃	—	2	2	no	—
98	C₂×C₃	—	2	1	no	—
99	C₂×C₃	#4551	1	1	yes	characteristic
100	C₂²	—	4	1	no	—
101	C₂²	#63376	1	2	yes	—
102	C₂²	#63378	1	1	yes	characteristic
103	C₄	#63377	1	1	yes	characteristic
104	C₄	#63380	1	2	yes	—
105	C₄	C₉⋊#95	1	1	yes	characteristic
106	C₃	#67820	1	1	yes	characteristic
107	C₂	—	2	2	no	—
108	C₂	—	2	1	no	—
109	C₂	#10588229	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×M₃₂

C₂

yes

maximal, characteristic

C₂×#63372

C₂

yes

maximal

#67820

—

maximal

C₂²×C₈×C₉

C₂²

yes

characteristic

C₂×#3667

—

C₉×M₃₂

—

C₂×C₉×C₁₆

C₄

yes

—

#63372

—

#63372

C₄

yes

—

C₂×C₃×M₃₂

D₃

yes

characteristic

C₂×#819

—

C₂²×C₄×C₉

D₄

yes

characteristic

C₂×C₈×C₉

C₂×C₄

yes

characteristic

C₂×C₈×C₉

C₂×C₄

yes

—

C₂×C₈×C₉

D₄

yes

—

C₂×C₈×C₉

Q₈

yes

characteristic

#3667

—

#3667

—

C₂×C₉⋊C₈

—

C₉×C₁₆

—

#1385

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

C₂×#208

—

C₃×M₃₂

—

C₂×C₃×C₁₆

Dic₃

yes

—

#819

—

#819

—

C₂³×C₉

Q₁₆

yes

characteristic

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₉

D₈

yes

characteristic

C₂×C₄×C₉

SD₁₆

yes

—

C₈×C₉

C₄²

yes

characteristic

C₈×C₉

C₂²⋊C₄

yes

characteristic

C₈×C₉

C₄⋊C₄

yes

—

C₉⋊C₈

—

C₂×M₃₂

D₉

yes

characteristic

C₂×#108

—

C₂²×C₃×C₄

D₁₂

yes

characteristic

C₂×C₃×C₈

Dic₆

yes

characteristic

C₂×C₃×C₈

C₄×D₃

yes

—

C₂×C₃×C₈

C₂×Dic₃

yes

characteristic

C₂×C₃×C₈

#67

yes

—

#208

—

#208

—

C₂×C₃⋊C₈

—

C₃×C₁₆

—

C₂²×C₉

—

C₂²×C₉

#103

yes

—

C₂²×C₉

yes

C₄×C₉

yes

C₄×C₉

yes

—

C₄×C₉

#106

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₂×D₉

yes

characteristic

M₃₂

—

C₂×C₁₆

Dic₉

yes

—

#108

—

#108

—

C₂³×C₃

Dic₁₂

yes

characteristic

C₂×C₃×C₄

#204

yes

—

C₂×C₃×C₄

D₂₄

yes

characteristic

C₂×C₃×C₄

C₄⋊Dic₃

yes

characteristic

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

C₃×C₈

C₄×Dic₃

yes

characteristic

C₃×C₈

Dic₃⋊C₄

yes

—

C₃×C₈

#217

yes

characteristic

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#340

yes

characteristic

C₂²×C₄

D₃₆

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₁₈

yes

characteristic

C₂×C₈

C₄×D₉

yes

—

C₂×C₈

C₂×Dic₉

yes

characteristic

C₂×C₈

#611

yes

—

C₁₆

—

C₂²×C₃

—

C₂²×C₃

#816

yes

—

C₂²×C₃

yes

C₃×C₄

yes

C₃×C₄

yes

—

C₃×C₄

C₃⋊#95

yes

characteristic

C₉

#1385

yes

characteristic, complemented, Sylow

C₂³

Dic₃₆

yes

characteristic

C₂×C₄

#3664

yes

—

C₂×C₄

D₇₂

yes

characteristic

C₂×C₄

C₄⋊Dic₉

yes

characteristic

C₂×C₄

(C₂×D₉)⋊C₄

yes

—

C₈

—

C₈

C₄×Dic₉

yes

characteristic

C₈

Dic₉⋊C₄

yes

—

C₈

#3676

yes

characteristic

C₂×C₃

—

C₂×C₃

—

C₂×C₃

#4551

yes

characteristic

100

C₂²

—

101

C₂²

#63376

yes

—

102

C₂²

#63378

yes

characteristic

103

C₄

#63377

yes

characteristic

104

C₄

#63380

yes

—

105

C₄

C₉⋊#95

yes

characteristic

106

C₃

#67820

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

#10588229

yes

characteristic

	subgroup	G/H
center	C₄	#63377
commutator	C₈×C₉	C₄²
Frattini	C₂²×C₃×C₈	C₂×D₃
Fitting	C₂×C₉×M₃₂	C₂
socle	C₂×C₃	#4551
prime radical	C₂³×C₃	Dic₁₂
cosocle	C₂²×C₈×C₉	C₂²
hypercenter	C₂×M₃₂	D₉
hypocenter	C₉	#1385
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₄

#63377

commutator

C₈×C₉

C₄²

Frattini

C₂²×C₃×C₈

C₂×D₃

Fitting

C₂×C₉×M₃₂

C₂

socle

C₂×C₃

#4551

prime radical

C₂³×C₃

Dic₁₂

cosocle

C₂²×C₈×C₉

C₂²

hypercenter

C₂×M₃₂

D₉

hypocenter

C₉

#1385

LCS

G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
87. C₉	#1385	semidirect

H ≅ G/N

type

87. C₉

#1385

semidirect

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

subgroup	index
C₂×C₉×M₃₂	2
C₂×#63372	2
#67820	3

subgroup

index

C₂×C₉×M₃₂

C₂×#63372

#67820

Subgroups — #11772452

Conjugacy classes of subgroups

Complements

Maximal subgroups