Group #11772030 — subgroups

Subgroups — #11772030

Order 1152.

153 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 153 conjugacy classes of subgroups — too many to draw. Only its 54 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	C₉×#492	C₂	1	1	yes	maximal, characteristic
2	#10588140	C₂	1	2	yes	maximal, complemented
3	#67787	—	3	1	no	maximal
4	C₂×C₉×SD₁₆	—	2	2	no	—
5	C₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₉×#127	C₄	1	1	yes	characteristic
7	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
8	#63371	—	2	2	no	—
9	C₃×#492	D₃	1	1	yes	characteristic
10	#4463	—	3	2	no	—
11	C₂×Q₈×C₉	—	2	1	no	—
12	C₂×D₄×C₉	—	2	1	no	—
13	C₂×D₄×C₉	—	4	1	no	—
14	C₉×SD₁₆	—	4	2	no	—
15	C₉×SD₁₆	—	4	2	no	—
16	C₂×C₈×C₉	D₄	1	2	yes	—
17	C₉×C₄⋊C₄	—	4	1	no	—
18	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
19	C₉⋊C₁₆	—	4	2	no	—
20	#1359	—	9	1	no	Sylow
21	C₂×C₃×SD₁₆	—	2	2	no	—
22	C₃×C₄⋊Q₈	Dic₃	1	1	yes	characteristic
23	C₃×#127	Dic₃	1	1	yes	characteristic
24	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
25	#812	—	6	2	no	—
26	C₂³×C₉	—	4	1	no	—
27	Q₈×C₉	—	4	2	no	—
28	D₄×C₉	—	4	2	no	—
29	D₄×C₉	—	8	2	no	—
30	C₂×C₄×C₉	—	2	1	no	—
31	C₂×C₄×C₉	—	4	1	no	—
32	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₈×C₉	D₈	1	2	yes	—
34	C₈×C₉	SD₁₆	1	2	yes	—
35	#492	D₉	1	1	yes	characteristic
36	#364	—	9	2	no	—
37	C₂×C₃×Q₈	—	2	1	no	—
38	C₂×C₃×D₄	—	2	1	no	—
39	C₂×C₃×D₄	—	4	1	no	—
40	C₃×SD₁₆	—	4	2	no	—
41	C₃×SD₁₆	—	4	2	no	—
42	C₂×C₃×C₈	#67	1	2	yes	—
43	C₃×C₄⋊C₄	—	4	1	no	—
44	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
45	C₃⋊C₁₆	—	12	2	no	—
46	C₂²×C₉	—	8	2	no	—
47	C₂²×C₉	—	8	1	no	—
48	C₂²×C₉	#100	1	1	yes	characteristic
49	C₄×C₉	—	2	2	no	—
50	C₄×C₉	—	8	1	no	—
51	C₄×C₉	#102	1	2	yes	—
52	C₂×SD₁₆	—	2	2	no	—
53	C₄⋊Q₈	Dic₉	1	1	yes	characteristic
54	#127	Dic₉	1	1	yes	characteristic
55	M₃₂	—	18	2	no	—
56	C₄×C₈	C₂×D₉	1	1	yes	characteristic
57	C₂³×C₃	—	4	1	no	—
58	C₃×Q₈	—	4	2	no	—
59	C₃×D₄	—	4	2	no	—
60	C₃×D₄	—	8	2	no	—
61	C₂×C₃×C₄	—	2	1	no	—
62	C₂×C₃×C₄	—	4	1	no	—
63	C₂×C₃×C₄	#217	1	1	yes	characteristic
64	C₃×C₈	#213	1	2	yes	—
65	C₃×C₈	#214	1	2	yes	—
66	C₂×C₉	—	2	1	no	—
67	C₂×C₉	—	16	1	no	—
68	C₂×C₉	#331	1	1	yes	characteristic
69	C₂×Q₈	—	2	1	no	—
70	C₂×D₄	—	2	1	no	—
71	C₂×D₄	—	4	1	no	—
72	SD₁₆	—	4	2	no	—
73	SD₁₆	—	4	2	no	—
74	C₂×C₈	#611	1	2	yes	—
75	C₄⋊C₄	—	4	1	no	—
76	C₄²	C₂×Dic₉	1	1	yes	characteristic
77	C₁₆	—	36	2	no	—
78	C₂²×C₃	—	8	2	no	—
79	C₂²×C₃	—	8	1	no	—
80	C₂²×C₃	#833	1	1	yes	characteristic
81	C₃×C₄	—	2	2	no	—
82	C₃×C₄	—	8	1	no	—
83	C₃×C₄	#832	1	2	yes	—
84	C₉	#1359	1	1	yes	characteristic, complemented, Sylow
85	C₂³	—	4	1	no	—
86	Q₈	—	4	2	no	—
87	D₄	—	4	2	no	—
88	D₄	—	8	2	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	#3676	1	1	yes	characteristic
92	C₈	#3672	1	2	yes	—
93	C₈	#3673	1	2	yes	—
94	C₂×C₃	—	2	1	no	—
95	C₂×C₃	—	16	1	no	—
96	C₂×C₃	#4544	1	1	yes	characteristic
97	C₂²	—	8	2	no	—
98	C₂²	—	8	1	no	—
99	C₂²	#63391	1	1	yes	characteristic
100	C₄	—	2	2	no	—
101	C₄	—	8	1	no	—
102	C₄	#63392	1	2	yes	—
103	C₃	#67787	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	16	1	no	—
106	C₂	#10588221	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#492

C₂

yes

maximal, characteristic

#10588140

C₂

yes

maximal, complemented

#67787

—

maximal

C₂×C₉×SD₁₆

—

C₉×C₄⋊Q₈

C₄

yes

characteristic

C₉×#127

C₄

yes

characteristic

C₄×C₈×C₉

C₂²

yes

characteristic

#63371

—

C₃×#492

D₃

yes

characteristic

#4463

—

C₂×Q₈×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₉×SD₁₆

—

C₉×SD₁₆

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₄²×C₉

C₂×C₄

yes

characteristic

C₉⋊C₁₆

—

#1359

—

Sylow

C₂×C₃×SD₁₆

—

C₃×C₄⋊Q₈

Dic₃

yes

characteristic

C₃×#127

Dic₃

yes

characteristic

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#812

—

C₂³×C₉

—

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

characteristic

C₈×C₉

D₈

yes

—

C₈×C₉

SD₁₆

yes

—

#492

D₉

yes

characteristic

#364

—

C₂×C₃×Q₈

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₃×SD₁₆

—

C₃×SD₁₆

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂×Dic₃

yes

characteristic

C₃⋊C₁₆

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#100

yes

characteristic

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#102

yes

—

C₂×SD₁₆

—

C₄⋊Q₈

Dic₉

yes

characteristic

#127

Dic₉

yes

characteristic

M₃₂

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂³×C₃

—

C₃×Q₈

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

#217

yes

characteristic

C₃×C₈

#213

yes

—

C₃×C₈

#214

yes

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#331

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

SD₁₆

—

C₂×C₈

#611

yes

—

C₄⋊C₄

—

C₄²

C₂×Dic₉

yes

characteristic

C₁₆

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

#833

yes

characteristic

C₃×C₄

—

C₃×C₄

—

C₃×C₄

#832

yes

—

C₉

#1359

yes

characteristic, complemented, Sylow

C₂³

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#3676

yes

characteristic

C₈

#3672

yes

—

C₈

#3673

yes

—

C₂×C₃

—

C₂×C₃

—

C₂×C₃

#4544

yes

characteristic

C₂²

—

C₂²

—

C₂²

#63391

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

#63392

yes

—

103

C₃

#67787

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

#10588221

yes

characteristic

	subgroup	G/H
center	C₂	#10588221
commutator	C₄²×C₉	C₂×C₄
Frattini	C₃×C₄×C₈	C₂×D₃
Fitting	C₉×#492	C₂
socle	C₂×C₃	#4544
prime radical	C₃×#127	Dic₃
cosocle	C₄×C₈×C₉	C₂²
hypercenter	#492	D₉
hypocenter	C₉	#1359
LCS	G ▷ C₄²×C₉ ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #492

subgroup

G/H

center

C₂

#10588221

commutator

C₄²×C₉

C₂×C₄

Frattini

C₃×C₄×C₈

C₂×D₃

C₂

C₂×C₃

Dic₃

C₄×C₈×C₉

C₂²

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #492

N	H ≅ G/N	type
2. #10588140	C₂	semidirect
84. C₉	#1359	semidirect

H ≅ G/N

type

2. #10588140

C₂

semidirect

84. C₉

#1359

semidirect

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

subgroup	index
C₉×#492	2
#10588140	2
#67787	3

subgroup

index

C₉×#492

#10588140

#67787

Subgroups — #11772030

Conjugacy classes of subgroups

Complements

Maximal subgroups