Group #11785938 — subgroups

Subgroups — #11785938

Order 1152.

354 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 128 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×#519	C₂	1	1	yes	maximal, characteristic
2	C₂×#63394	C₂	1	2	yes	maximal
3	#10588209	C₂	1	4	yes	maximal
4	#71659	—	3	1	no	maximal
5	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
6	C₄×Q₈×C₉	—	2	4	no	—
7	C₉×#117	C₄	1	4	yes	—
8	C₉×#117	C₂²	1	2	yes	—
9	C₂×#3667	C₂²	1	4	yes	—
10	#63394	—	2	4	no	—
11	C₃×#519	D₃	1	1	yes	characteristic
12	C₂×#836	—	3	2	no	—
13	#4533	—	3	4	no	—
14	C₂×Q₈×C₉	—	2	4	no	—
15	C₂×Q₈×C₉	D₄	1	4	yes	—
16	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
18	C₉×C₄⋊C₄	—	2	4	no	—
19	C₉×C₄⋊C₄	—	2	2	no	—
20	C₉×C₂²⋊C₄	C₂×C₄	1	4	yes	—
21	C₄²×C₉	—	2	4	no	—
22	C₄²×C₉	—	2	2	no	—
23	#3667	—	2	4	no	—
24	#3667	—	2	4	no	—
25	C₂×C₉⋊C₈	—	2	4	no	—
26	#1830	—	9	1	no	Sylow
27	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
28	C₃×C₄×Q₈	—	2	4	no	—
29	C₃×#117	Dic₃	1	4	yes	—
30	C₃×#117	C₂×D₃	1	2	yes	—
31	C₂×#208	—	3	4	no	—
32	#836	—	6	4	no	—
33	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
34	Q₈×C₉	—	2	8	no	—
35	C₂×C₄×C₉	—	2	4	no	—
36	C₂×C₄×C₉	—	2	4	no	—
37	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
38	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₉	#41	1	4	yes	—
40	C₉⋊C₈	—	4	4	no	—
41	#519	D₉	1	1	yes	characteristic
42	C₂×#101	—	9	2	no	—
43	#344	—	9	4	no	—
44	C₂×C₃×Q₈	—	2	4	no	—
45	C₂×C₃×Q₈	#67	1	4	yes	—
46	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
47	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
48	C₃×C₄⋊C₄	—	2	4	no	—
49	C₃×C₄⋊C₄	—	2	2	no	—
50	C₃×C₂²⋊C₄	C₂×Dic₃	1	4	yes	—
51	C₃×C₄²	—	2	4	no	—
52	C₃×C₄²	—	2	2	no	—
53	#208	—	6	4	no	—
54	#208	—	6	4	no	—
55	C₂×C₃⋊C₈	—	6	4	no	—
56	C₂²×C₉	—	4	1	no	—
57	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₉	#117	1	2	yes	—
59	C₄×C₉	—	2	4	no	—
60	C₄×C₉	—	4	4	no	—
61	C₄×C₉	#123	1	4	yes	—
62	C₂²×Q₈	C₂×D₉	1	1	yes	characteristic
63	C₂×M₁₆	—	9	4	no	—
64	C₄×Q₈	—	2	4	no	—
65	#117	Dic₉	1	4	yes	—
66	#117	C₂×D₉	1	2	yes	—
67	#101	—	18	4	no	—
68	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
69	C₃×Q₈	—	2	8	no	—
70	C₂×C₃×C₄	—	2	4	no	—
71	C₂×C₃×C₄	—	2	4	no	—
72	C₂×C₃×C₄	#217	1	4	yes	—
73	C₂×C₃×C₄	#235	1	4	yes	—
74	C₂×C₃×C₄	C₂×#67	1	2	yes	—
75	C₃⋊C₈	—	12	4	no	—
76	C₂×C₉	—	2	1	no	—
77	C₂×C₉	—	2	2	no	—
78	C₂×C₉	#381	1	1	yes	characteristic
79	C₂×Q₈	—	2	4	no	—
80	C₂×Q₈	#611	1	4	yes	—
81	C₂²×C₄	C₂×Dic₉	1	2	yes	—
82	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
83	M₁₆	—	18	4	no	—
84	M₁₆	—	18	4	no	—
85	C₂×C₈	—	18	4	no	—
86	C₄⋊C₄	—	2	4	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₂²⋊C₄	C₂×Dic₉	1	4	yes	—
89	C₄²	—	2	4	no	—
90	C₄²	—	2	2	no	—
91	C₂²×C₃	—	4	1	no	—
92	C₂²×C₃	#926	1	2	yes	—
93	C₂²×C₃	C₂×#217	1	1	yes	characteristic
94	C₃×C₄	—	2	4	no	—
95	C₃×C₄	—	4	4	no	—
96	C₃×C₄	#929	1	4	yes	—
97	C₉	#1830	1	1	yes	characteristic, complemented, Sylow
98	C₂³	C₂²×Dic₉	1	1	yes	characteristic
99	Q₈	—	2	8	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	#3676	1	4	yes	—
103	C₂×C₄	#3697	1	4	yes	—
104	C₂×C₄	C₂×#611	1	2	yes	—
105	C₈	—	36	4	no	—
106	C₂×C₃	—	2	1	no	—
107	C₂×C₃	—	2	2	no	—
108	C₂×C₃	#5211	1	1	yes	characteristic
109	C₂²	—	4	1	no	—
110	C₂²	#63488	1	2	yes	—
111	C₂²	C₂×#3676	1	1	yes	characteristic
112	C₄	—	2	4	no	—
113	C₄	—	4	4	no	—
114	C₄	#63491	1	4	yes	—
115	C₃	#71659	1	1	yes	characteristic
116	C₂	—	2	1	no	—
117	C₂	—	2	2	no	—
118	C₂	#10588891	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#519

C₂

yes

maximal, characteristic

C₂×#63394

C₂

yes

maximal

#10588209

C₂

yes

maximal

#71659

—

maximal

C₂²×Q₈×C₉

C₂²

yes

characteristic

C₄×Q₈×C₉

—

C₉×#117

C₄

yes

—

C₉×#117

C₂²

yes

—

C₂×#3667

C₂²

yes

—

#63394

—

C₃×#519

D₃

yes

characteristic

C₂×#836

—

#4533

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₉×C₂²⋊C₄

C₂×C₄

yes

—

C₄²×C₉

—

C₄²×C₉

—

#3667

—

#3667

—

C₂×C₉⋊C₈

—

#1830

—

Sylow

C₂²×C₃×Q₈

C₂×D₃

yes

characteristic

C₃×C₄×Q₈

—

C₃×#117

Dic₃

yes

—

C₃×#117

C₂×D₃

yes

—

C₂×#208

—

#836

—

C₂³×C₉

C₂²×C₄

yes

characteristic

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

#41

yes

—

C₉⋊C₈

—

#519

D₉

yes

characteristic

C₂×#101

—

#344

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

#67

yes

—

C₂²×C₃×C₄

C₂×Dic₃

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

C₂×Dic₃

yes

—

C₃×C₄²

—

C₃×C₄²

—

#208

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₉

#117

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#123

yes

—

C₂²×Q₈

C₂×D₉

yes

characteristic

C₂×M₁₆

—

C₄×Q₈

—

#117

Dic₉

yes

—

#117

C₂×D₉

yes

—

#101

—

C₂³×C₃

C₂²×Dic₃

yes

characteristic

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

#217

yes

—

C₂×C₃×C₄

#235

yes

—

C₂×C₃×C₄

C₂×#67

yes

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#381

yes

characteristic

C₂×Q₈

—

C₂×Q₈

#611

yes

—

C₂²×C₄

C₂×Dic₉

yes

—

C₂²×C₄

C₂²×D₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

C₂×Dic₉

yes

—

C₄²

—

C₄²

—

C₂²×C₃

—

C₂²×C₃

#926

yes

—

C₂²×C₃

C₂×#217

yes

characteristic

C₃×C₄

—

C₃×C₄

—

C₃×C₄

#929

yes

—

C₉

#1830

yes

characteristic, complemented, Sylow

C₂³

C₂²×Dic₉

yes

characteristic

Q₈

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

#3676

yes

—

103

C₂×C₄

#3697

yes

—

104

C₂×C₄

C₂×#611

yes

—

105

C₈

—

106

C₂×C₃

—

107

C₂×C₃

—

108

C₂×C₃

#5211

yes

characteristic

109

C₂²

—

110

C₂²

#63488

yes

—

111

C₂²

C₂×#3676

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

#63491

yes

—

115

C₃

#71659

yes

characteristic

116

C₂

—

117

C₂

—

118

C₂

#10588891

yes

characteristic

	subgroup	G/H
center	C₂	#10588891
commutator	C₂³×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#519	C₂
socle	C₂×C₃	#5211
prime radical	C₂³×C₃	C₂²×Dic₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#519	D₉
hypocenter	C₉	#1830
LCS	G ▷ C₂³×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #519

subgroup

G/H

center

C₂

#10588891

commutator

C₂³×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

C₂

C₂×C₃

C₂³×C₃

C₂²×Dic₃

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂³×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #519

N	H ≅ G/N	type
97. C₉	#1830	semidirect

H ≅ G/N

type

97. C₉

#1830

semidirect

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

subgroup	index
C₉×#519	2
C₂×#63394	2
#10588209	2
#71659	3

subgroup

index

Subgroups — #11785938

Conjugacy classes of subgroups

Complements

Maximal subgroups