Group #11772132 — subgroups

Subgroups — #11772132

Order 1152.

129 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 129 conjugacy classes of subgroups — too many to draw. Only its 62 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	#10588362	C₂	1	1	yes	maximal, characteristic
2	C₉×#335	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#67476	—	3	1	no	maximal
5	#63431	—	2	1	no	—
6	C₉×C₄⋊C₈	—	2	1	no	—
7	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
8	#63378	—	2	1	no	—
9	#63378	C₄	1	2	yes	—
10	C₂×C₉⋊C₁₆	—	2	1	no	—
11	#4682	—	3	1	no	—
12	C₃×#335	D₃	1	1	yes	characteristic
13	C₄⋊(C₃⋊C₁₆)	—	3	1	no	—
14	C₂×Dic₁₈	—	4	1	no	—
15	C₂×C₈×C₉	—	4	1	no	—
16	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₉	D₄	1	1	yes	characteristic
18	C₄²×C₉	D₄	1	1	yes	characteristic
19	C₄⋊Dic₉	—	2	2	no	—
20	C₄⋊Dic₉	—	4	1	no	—
21	C₉⋊C₁₆	—	4	1	no	—
22	#1365	—	9	1	no	Sylow
23	#869	—	6	1	no	—
24	C₃×C₄⋊C₈	—	2	1	no	—
25	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
26	#818	—	3	2	no	—
27	#818	—	6	1	no	—
28	C₂×C₃⋊C₁₆	—	6	1	no	—
29	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₉	D₈	1	1	yes	characteristic
31	C₂×C₄×C₉	SD₁₆	1	1	yes	characteristic
32	C₂×Dic₉	—	4	2	no	—
33	Dic₁₈	—	8	2	no	—
34	C₈×C₉	—	2	1	no	—
35	C₈×C₉	—	8	1	no	—
36	C₈×C₉	SD₁₆	1	1	yes	characteristic
37	C₈×C₉	Q₁₆	1	1	yes	characteristic
38	#500	—	9	1	no	—
39	C₄⋊C₁₆	—	9	1	no	—
40	#335	D₉	1	1	yes	characteristic
41	C₂×Dic₆	—	12	1	no	—
42	C₂×C₃×C₈	—	4	1	no	—
43	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
44	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
45	C₃×C₄²	#67	1	1	yes	characteristic
46	C₄⋊Dic₃	—	6	2	no	—
47	C₄⋊Dic₃	—	12	1	no	—
48	C₃⋊C₁₆	—	12	1	no	—
49	C₂²×C₉	#102	1	1	yes	characteristic
50	C₄×C₉	—	2	1	no	—
51	C₄×C₉	#101	1	1	yes	characteristic
52	C₄×C₉	#103	1	1	yes	characteristic
53	C₄×C₉	SD₃₂	1	1	yes	characteristic
54	C₄×C₉	Q₃₂	1	1	yes	characteristic
55	Dic₉	—	8	2	no	—
56	C₄⋊Q₈	—	18	1	no	—
57	C₂×C₁₆	—	18	1	no	—
58	#107	—	9	2	no	—
59	#107	—	18	1	no	—
60	C₄⋊C₈	—	2	1	no	—
61	C₄×C₈	C₂×D₉	1	1	yes	characteristic
62	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
63	C₂×C₃×C₄	#213	1	1	yes	characteristic
64	C₂×C₃×C₄	#215	1	1	yes	characteristic
65	C₂×Dic₃	—	12	2	no	—
66	Dic₆	—	24	2	no	—
67	C₃×C₈	—	2	1	no	—
68	C₃×C₈	—	8	1	no	—
69	C₃×C₈	#204	1	1	yes	characteristic
70	C₃×C₈	Dic₁₂	1	1	yes	characteristic
71	C₂×C₉	#332	1	1	yes	characteristic
72	C₂×C₉	#358	1	1	yes	characteristic
73	C₂×C₉	#361	1	1	yes	characteristic
74	C₂×Q₈	—	36	1	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	C₄×D₉	1	1	yes	characteristic
77	C₂×C₈	D₃₆	1	1	yes	characteristic
78	C₄⋊C₄	—	18	2	no	—
79	C₄⋊C₄	—	36	1	no	—
80	C₄²	#611	1	1	yes	characteristic
81	C₁₆	—	36	1	no	—
82	C₂²×C₃	#809	1	1	yes	characteristic
83	C₃×C₄	—	2	1	no	—
84	C₃×C₄	#816	1	1	yes	characteristic
85	C₃×C₄	#824	1	1	yes	characteristic
86	C₃×C₄	#827	1	1	yes	characteristic
87	C₃×C₄	#829	1	1	yes	characteristic
88	Dic₃	—	24	2	no	—
89	C₉	#1365	1	1	yes	characteristic, complemented, Sylow
90	Q₈	—	72	2	no	—
91	C₂×C₄	—	36	2	no	—
92	C₂×C₄	(C₂×D₉)⋊C₄	1	1	yes	characteristic
93	C₂×C₄	#3673	1	1	yes	characteristic
94	C₂×C₄	#3675	1	1	yes	characteristic
95	C₈	—	2	1	no	—
96	C₈	—	8	1	no	—
97	C₈	Dic₃₆	1	1	yes	characteristic
98	C₈	#3664	1	1	yes	characteristic
99	C₂×C₃	#4482	1	1	yes	characteristic
100	C₂×C₃	#4492	1	1	yes	characteristic
101	C₂×C₃	#4495	1	1	yes	characteristic
102	C₂²	#63369	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	72	2	no	—
105	C₄	#63376	1	1	yes	characteristic
106	C₄	#63382	1	1	yes	characteristic
107	C₄	#63386	1	1	yes	characteristic
108	C₄	#63388	1	1	yes	characteristic
109	C₃	#67476	1	1	yes	characteristic
110	C₂	#10588159	1	1	yes	characteristic
111	C₂	#10588169	1	1	yes	characteristic
112	C₂	#10588172	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10588362

C₂

yes

maximal, characteristic

C₉×#335

C₂

yes

maximal, characteristic

C₄⋊(C₉⋊C₁₆)

C₂

yes

maximal, characteristic

#67476

—

maximal

#63431

—

C₉×C₄⋊C₈

—

C₄×C₈×C₉

C₂²

yes

characteristic

#63378

—

#63378

C₄

yes

—

C₂×C₉⋊C₁₆

—

#4682

—

C₃×#335

D₃

yes

characteristic

C₄⋊(C₃⋊C₁₆)

—

C₂×Dic₁₈

—

C₂×C₈×C₉

—

C₂×C₈×C₉

C₂×C₄

yes

characteristic

C₂×C₈×C₉

D₄

yes

characteristic

C₄²×C₉

D₄

yes

characteristic

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₉⋊C₁₆

—

#1365

—

Sylow

#869

—

C₃×C₄⋊C₈

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#818

—

#818

—

C₂×C₃⋊C₁₆

—

C₂×C₄×C₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₉

D₈

yes

characteristic

C₂×C₄×C₉

SD₁₆

yes

characteristic

C₂×Dic₉

—

Dic₁₈

—

C₈×C₉

—

C₈×C₉

—

C₈×C₉

SD₁₆

yes

characteristic

C₈×C₉

Q₁₆

yes

characteristic

#500

—

C₄⋊C₁₆

—

#335

D₉

yes

characteristic

C₂×Dic₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₄×D₃

yes

characteristic

C₂×C₃×C₈

D₁₂

yes

characteristic

C₃×C₄²

#67

yes

characteristic

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₃⋊C₁₆

—

C₂²×C₉

#102

yes

characteristic

C₄×C₉

—

C₄×C₉

yes

C₄×C₉

yes

C₄×C₉

SD₃₂

yes

characteristic

C₄×C₉

Q₃₂

yes

characteristic

Dic₉

—

C₄⋊Q₈

—

C₂×C₁₆

—

#107

—

#107

—

C₄⋊C₈

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

C₂×C₃×C₄

yes

C₂×C₃×C₄

yes

C₂×Dic₃

—

Dic₆

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

#204

yes

characteristic

C₃×C₈

Dic₁₂

yes

C₂×C₉

yes

C₂×C₉

yes

C₂×C₉

yes

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

C₄×D₉

yes

characteristic

C₂×C₈

D₃₆

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

#611

yes

characteristic

C₁₆

—

C₂²×C₃

#809

yes

characteristic

C₃×C₄

—

C₃×C₄

yes

C₃×C₄

yes

C₃×C₄

yes

C₃×C₄

yes

Dic₃

—

C₉

#1365

yes

characteristic, complemented, Sylow

Q₈

—

C₂×C₄

—

C₂×C₄

(C₂×D₉)⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

Dic₃₆

yes

C₈

yes

C₂×C₃

yes

100

C₂×C₃

#4492

yes

characteristic

101

C₂×C₃

#4495

yes

characteristic

102

C₂²

#63369

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

#63376

yes

characteristic

106

C₄

#63382

yes

characteristic

107

C₄

#63386

yes

characteristic

108

C₄

#63388

yes

characteristic

109

C₃

#67476

yes

characteristic

110

C₂

#10588159

yes

characteristic

111

C₂

#10588169

yes

characteristic

112

C₂

#10588172

yes

characteristic

	subgroup	G/H
center	C₂²	#63369
commutator	C₂×C₈×C₉	C₂×C₄
Frattini	C₃×C₄×C₈	C₂×D₃
Fitting	C₉×#335	C₂
socle, prime radical	C₂²×C₃	#809
cosocle	C₄×C₈×C₉	C₂²
hypercenter	#335	D₉
hypocenter	C₉	#1365
LCS	G ▷ C₂×C₈×C₉ ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

subgroup

G/H

center

C₂²

#63369

commutator

C₂×C₈×C₉

C₂×C₄

Frattini

C₃×C₄×C₈

C₂×D₃

C₂

C₂²×C₃

C₄×C₈×C₉

C₂²

D₉

C₉

G ▷ C₂×C₈×C₉ ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

N	H ≅ G/N	type
89. C₉	#1365	semidirect

H ≅ G/N

type

89. C₉

#1365

semidirect

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

subgroup	index
#10588362	2
C₉×#335	2
C₄⋊(C₉⋊C₁₆)	2
#67476	3

subgroup

index

#10588362

C₉×#335

C₄⋊(C₉⋊C₁₆)

#67476

Subgroups — #11772132

Conjugacy classes of subgroups

Complements

Maximal subgroups