Group #11772074 — subgroups

Subgroups — #11772074

Order 1152.

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

normal subgroups only

This group has 147 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	#10588365	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	#67474	—	3	1	no	maximal
5	C₂×Dic₃₆	—	2	1	no	—
6	C₂×Dic₃₆	C₄	1	2	yes	—
7	#63431	—	2	1	no	—
8	C₉×C₄⋊C₈	—	2	1	no	—
9	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₉⋊C₁₆	—	2	1	no	—
11	#4699	—	3	1	no	—
12	C₃×#335	D₃	1	1	yes	characteristic
13	C₄⋊(C₃⋊C₁₆)	—	3	1	no	—
14	C₂×Dic₁₈	—	2	2	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	—	4	1	no	—
20	C₄⋊Dic₉	—	4	1	no	—
21	Dic₃₆	—	4	2	no	—
22	Dic₃₆	—	4	1	no	—
23	Dic₃₆	—	4	1	no	—
24	C₉⋊C₁₆	—	4	1	no	—
25	#1362	—	9	1	no	Sylow
26	C₂×Dic₁₂	—	3	2	no	—
27	C₂×Dic₁₂	—	6	1	no	—
28	#869	—	6	1	no	—
29	C₃×C₄⋊C₈	—	2	1	no	—
30	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
31	C₂×C₃⋊C₁₆	—	6	1	no	—
32	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₉	D₈	1	1	yes	characteristic
34	C₂×C₄×C₉	SD₁₆	1	1	yes	characteristic
35	C₂×Dic₉	—	4	2	no	—
36	Dic₁₈	—	4	2	no	—
37	Dic₁₈	—	4	2	no	—
38	C₈×C₉	—	2	1	no	—
39	C₈×C₉	—	8	1	no	—
40	C₈×C₉	D₈	1	1	yes	characteristic
41	C₈×C₉	SD₁₆	1	1	yes	characteristic
42	#494	—	9	1	no	—
43	C₄⋊C₁₆	—	9	1	no	—
44	#335	D₉	1	1	yes	characteristic
45	C₂×Dic₆	—	6	2	no	—
46	C₂×C₃×C₈	—	4	1	no	—
47	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
48	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
49	C₃×C₄²	#67	1	1	yes	characteristic
50	C₄⋊Dic₃	—	12	1	no	—
51	C₄⋊Dic₃	—	12	1	no	—
52	Dic₁₂	—	12	2	no	—
53	Dic₁₂	—	12	1	no	—
54	Dic₁₂	—	12	1	no	—
55	C₃⋊C₁₆	—	12	1	no	—
56	C₂²×C₉	#102	1	1	yes	characteristic
57	C₄×C₉	—	2	1	no	—
58	C₄×C₉	#100	1	1	yes	characteristic
59	C₄×C₉	#102	1	1	yes	characteristic
60	C₄×C₉	SD₃₂	1	1	yes	characteristic
61	C₄×C₉	Q₃₂	1	1	yes	characteristic
62	Dic₉	—	8	2	no	—
63	C₂×Q₁₆	—	9	2	no	—
64	C₂×Q₁₆	—	18	1	no	—
65	C₄⋊Q₈	—	18	1	no	—
66	C₂×C₁₆	—	18	1	no	—
67	C₄⋊C₈	—	2	1	no	—
68	C₄×C₈	C₂×D₉	1	1	yes	characteristic
69	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
70	C₂×C₃×C₄	#213	1	1	yes	characteristic
71	C₂×C₃×C₄	#215	1	1	yes	characteristic
72	C₂×Dic₃	—	12	2	no	—
73	Dic₆	—	12	2	no	—
74	Dic₆	—	12	2	no	—
75	C₃×C₈	—	2	1	no	—
76	C₃×C₈	—	8	1	no	—
77	C₃×C₈	#204	1	1	yes	characteristic
78	C₃×C₈	D₂₄	1	1	yes	characteristic
79	C₂×C₉	#331	1	1	yes	characteristic
80	C₂×C₉	#358	1	1	yes	characteristic
81	C₂×C₉	#362	1	1	yes	characteristic
82	C₂×Q₈	—	18	2	no	—
83	Q₁₆	—	36	2	no	—
84	Q₁₆	—	36	1	no	—
85	Q₁₆	—	36	1	no	—
86	C₂×C₈	—	4	1	no	—
87	C₂×C₈	C₄×D₉	1	1	yes	characteristic
88	C₂×C₈	D₃₆	1	1	yes	characteristic
89	C₄⋊C₄	—	36	1	no	—
90	C₄⋊C₄	—	36	1	no	—
91	C₄²	#611	1	1	yes	characteristic
92	C₁₆	—	36	1	no	—
93	C₂²×C₃	#809	1	1	yes	characteristic
94	C₃×C₄	—	2	1	no	—
95	C₃×C₄	#821	1	1	yes	characteristic
96	C₃×C₄	#823	1	1	yes	characteristic
97	C₃×C₄	#827	1	1	yes	characteristic
98	C₃×C₄	#829	1	1	yes	characteristic
99	Dic₃	—	24	2	no	—
100	C₉	#1362	1	1	yes	characteristic, complemented, Sylow
101	Q₈	—	36	2	no	—
102	Q₈	—	36	2	no	—
103	C₂×C₄	—	36	2	no	—
104	C₂×C₄	(C₂×D₉)⋊C₄	1	1	yes	characteristic
105	C₂×C₄	#3673	1	1	yes	characteristic
106	C₂×C₄	#3675	1	1	yes	characteristic
107	C₈	—	2	1	no	—
108	C₈	—	8	1	no	—
109	C₈	#3664	1	1	yes	characteristic
110	C₈	D₇₂	1	1	yes	characteristic
111	C₂×C₃	#4485	1	1	yes	characteristic
112	C₂×C₃	#4492	1	1	yes	characteristic
113	C₂×C₃	#4496	1	1	yes	characteristic
114	C₂²	#63369	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	72	2	no	—
117	C₄	#63380	1	1	yes	characteristic
118	C₄	#63383	1	1	yes	characteristic
119	C₄	#63386	1	1	yes	characteristic
120	C₄	#63388	1	1	yes	characteristic
121	C₃	#67474	1	1	yes	characteristic
122	C₂	#10588163	1	1	yes	characteristic
123	C₂	#10588169	1	1	yes	characteristic
124	C₂	#10588174	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10588365

C₂

yes

maximal, characteristic

C₉×#335

C₂

yes

maximal, characteristic

C₄⋊(C₉⋊C₁₆)

C₂

yes

maximal, characteristic

#67474

—

maximal

C₂×Dic₃₆

—

C₂×Dic₃₆

C₄

yes

—

#63431

—

C₉×C₄⋊C₈

—

C₄×C₈×C₉

C₂²

yes

characteristic

C₂×C₉⋊C₁₆

—

#4699

—

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

—

Dic₃₆

—

Dic₃₆

—

Dic₃₆

—

C₉⋊C₁₆

—

#1362

—

Sylow

C₂×Dic₁₂

—

C₂×Dic₁₂

—

#869

—

C₃×C₄⋊C₈

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

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

—

Dic₁₈

—

C₈×C₉

—

C₈×C₉

—

C₈×C₉

D₈

yes

characteristic

C₈×C₉

SD₁₆

yes

characteristic

#494

—

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

—

Dic₁₂

—

Dic₁₂

—

Dic₁₂

—

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

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₂×C₁₆

—

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

—

Dic₆

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

#204

yes

characteristic

C₃×C₈

D₂₄

yes

C₂×C₉

yes

C₂×C₉

yes

C₂×C₉

yes

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

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

—

100

C₉

#1362

yes

characteristic, complemented, Sylow

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

(C₂×D₉)⋊C₄

yes

characteristic

105

C₂×C₄

#3673

yes

characteristic

106

C₂×C₄

#3675

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

#3664

yes

characteristic

110

C₈

D₇₂

yes

characteristic

111

C₂×C₃

#4485

yes

characteristic

112

C₂×C₃

#4492

yes

characteristic

113

C₂×C₃

#4496

yes

characteristic

114

C₂²

#63369

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

#63380

yes

characteristic

118

C₄

#63383

yes

characteristic

119

C₄

#63386

yes

characteristic

120

C₄

#63388

yes

characteristic

121

C₃

#67474

yes

characteristic

122

C₂

#10588163

yes

characteristic

123

C₂

#10588169

yes

characteristic

124

C₂

#10588174

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	#1362
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
100. C₉	#1362	semidirect

H ≅ G/N

type

100. C₉

#1362

semidirect

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

subgroup	index
#10588365	2
C₉×#335	2
C₄⋊(C₉⋊C₁₆)	2
#67474	3

subgroup

index

#10588365

C₉×#335

C₄⋊(C₉⋊C₁₆)

#67474

Subgroups — #11772074

Conjugacy classes of subgroups

Complements

Maximal subgroups