Group #11800083 — subgroups

Subgroups — #11800083

Order 1152.

170 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 40 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	#10593536	C₂	1	1	yes	maximal, characteristic
2	#10593295	C₂	1	1	yes	maximal, characteristic
3	#10593254	C₂	1	1	yes	maximal, characteristic
4	#10593161	C₂	1	4	yes	maximal
5	C₄⋊PSU(3,𝔽₂)	—	2	1	no	—
6	#64228	C₂²	1	2	yes	—
7	#64222	—	2	1	no	—
8	#64213	C₂²	1	2	yes	—
9	#63802	—	2	1	no	—
10	#63769	—	2	1	no	—
11	C₈×#157	C₂²	1	1	yes	characteristic
12	#63746	C₂²	1	2	yes	—
13	C₂×PSU(3,𝔽₂)	—	4	1	no	—
14	#3797	—	2	2	no	—
15	C₄⋊#157	—	2	2	no	—
16	C₄×#157	D₄	1	1	yes	characteristic
17	#3787	C₂³	1	1	yes	characteristic
18	#3777	—	4	1	no	—
19	#3776	—	2	4	no	—
20	#3773	—	4	1	no	—
21	#3773	—	4	1	no	—
22	#3771	—	2	2	no	—
23	C₈×C₃⋊D₃	D₄	1	1	yes	characteristic
24	C₃×Dic₁₂	—	4	1	no	—
25	#3718	—	4	1	no	—
26	#2241	—	9	1	no	maximal, Sylow
27	D₃×Q₁₆	—	12	1	no	—
28	C₂×#157	—	4	2	no	—
29	C₂×#157	D₈	1	1	yes	characteristic
30	C₂×#157	D₈	1	1	yes	characteristic
31	PSU(3,𝔽₂)	—	8	2	no	—
32	C₄×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
33	C₃×Dic₆	—	4	2	no	—
34	#627	—	4	2	no	—
35	#624	—	4	2	no	—
36	#622	#41	1	2	yes	—
37	C₃²×C₈	SD₁₆	1	1	yes	characteristic
38	C₃⋊(C₃⋊C₈)	SD₁₆	1	1	yes	characteristic
39	#500	—	9	1	no	—
40	#494	—	9	1	no	—
41	#358	—	9	4	no	—
42	C₄×C₁₆	—	9	1	no	—
43	D₃×Q₈	—	12	2	no	—
44	C₃×Q₁₆	—	12	1	no	—
45	#216	—	12	2	no	—
46	Dic₁₂	—	4	1	no	—
47	D₃×C₈	—	12	1	no	—
48	C₂×C₃⋊D₃	C₂×D₈	1	1	yes	characteristic
49	#157	—	8	2	no	—
50	#157	SD₃₂	1	2	yes	—
51	#157	Q₃₂	1	2	yes	—
52	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
53	C₃⋊Dic₃	#124	1	1	yes	characteristic
54	C₃×Dic₃	—	8	2	no	—
55	C₂×Q₁₆	—	9	2	no	—
56	C₂×Q₁₆	—	18	1	no	—
57	C₄⋊Q₈	—	18	1	no	—
58	C₄⋊Q₈	—	18	1	no	—
59	C₂×C₁₆	—	9	2	no	—
60	#107	—	9	2	no	—
61	#107	—	18	1	no	—
62	C₄×C₈	—	9	1	no	—
63	C₃×Q₈	—	12	2	no	—
64	C₄×D₃	—	12	1	no	—
65	C₄×D₃	—	24	2	no	—
66	Dic₆	—	4	2	no	—
67	Dic₆	—	24	2	no	—
68	C₃×C₈	—	4	1	no	—
69	C₃⋊C₈	—	12	1	no	—
70	C₂×C₃²	#486	1	1	yes	characteristic
71	C₃⋊D₃	C₂×SD₃₂	1	1	yes	characteristic
72	C₃⋊D₃	C₂×Q₃₂	1	1	yes	characteristic
73	C₂×Q₈	—	18	2	no	—
74	C₂×Q₈	—	36	1	no	—
75	Q₁₆	—	12	1	no	—
76	Q₁₆	—	18	4	no	—
77	Q₁₆	—	36	1	no	—
78	C₂×C₈	—	9	1	no	—
79	C₂×C₈	—	9	1	no	—
80	C₄⋊C₄	—	18	2	no	—
81	C₄⋊C₄	—	36	1	no	—
82	C₄⋊C₄	—	36	1	no	—
83	C₄⋊C₄	—	36	1	no	—
84	C₄²	—	9	1	no	—
85	C₁₆	—	18	2	no	—
86	C₂×D₃	—	12	1	no	—
87	C₃×C₄	—	4	1	no	—
88	C₃×C₄	—	24	2	no	—
89	Dic₃	—	8	2	no	—
90	Dic₃	—	12	1	no	—
91	C₃²	#2241	1	1	yes	characteristic, complemented, Sylow
92	Q₈	—	12	2	no	—
93	Q₈	—	36	2	no	—
94	Q₈	—	72	2	no	—
95	C₂×C₄	—	9	1	no	—
96	C₂×C₄	—	9	1	no	—
97	C₂×C₄	—	9	1	no	—
98	C₂×C₄	—	36	2	no	—
99	C₂×C₄	—	36	2	no	—
100	C₈	—	9	2	no	—
101	C₈	—	9	1	no	—
102	C₈	AΓL(1,𝔽₉)	1	1	yes	characteristic
103	C₂×C₃	—	4	1	no	—
104	D₃	—	12	1	no	—
105	D₃	—	12	1	no	—
106	C₂²	—	9	1	no	—
107	C₄	—	9	2	no	—
108	C₄	—	9	2	no	—
109	C₄	—	9	1	no	—
110	C₄	—	24	2	no	—
111	C₄	—	72	2	no	—
112	C₄	C₂×AΓL(1,𝔽₉)	1	1	yes	characteristic
113	C₃	—	4	1	no	—
114	C₂	—	9	1	no	—
115	C₂	—	9	1	no	—
116	C₂	#10596402	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10593536

C₂

yes

maximal, characteristic

#10593295

C₂

yes

maximal, characteristic

#10593254

C₂

yes

maximal, characteristic

#10593161

C₂

yes

maximal

C₄⋊PSU(3,𝔽₂)

—

#64228

C₂²

yes

—

#64222

—

#64213

C₂²

yes

—

#63802

—

#63769

—

C₈×#157

C₂²

yes

characteristic

#63746

C₂²

yes

—

—

—

—

D₄

yes

characteristic

#3787

C₂³

yes

—

—

—

—

—

C₈×C₃⋊D₃

D₄

yes

characteristic

C₃×Dic₁₂

—

#3718

—

#2241

—

maximal, Sylow

D₃×Q₁₆

—

C₂×#157

—

C₂×#157

D₈

yes

characteristic

C₂×#157

D₈

yes

characteristic

PSU(3,𝔽₂)

—

C₄×C₃⋊D₃

C₂×D₄

yes

characteristic

C₃×Dic₆

—

—

—

yes

—

C₃²×C₈

SD₁₆

yes

characteristic

C₃⋊(C₃⋊C₈)

SD₁₆

yes

—

—

—

C₄×C₁₆

—

D₃×Q₈

—

C₃×Q₁₆

—

#216

—

Dic₁₂

—

D₃×C₈

—

C₂×C₃⋊D₃

C₂×D₈

yes

characteristic

#157

—

#157

SD₃₂

yes

—

#157

Q₃₂

yes

—

C₃²×C₄

C₂×SD₁₆

yes

characteristic

C₃⋊Dic₃

#124

yes

characteristic

C₃×Dic₃

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₁₆

—

#107

—

#107

—

C₄×C₈

—

C₃×Q₈

—

C₄×D₃

—

C₄×D₃

—

Dic₆

—

Dic₆

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

#486

yes

characteristic

C₃⋊D₃

C₂×SD₃₂

yes

characteristic

C₃⋊D₃

C₂×Q₃₂

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₁₆

—

C₂×D₃

—

C₃×C₄

—

C₃×C₄

—

Dic₃

—

Dic₃

—

C₃²

#2241

yes

characteristic, complemented, Sylow

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₈

—

101

C₈

—

102

C₈

AΓL(1,𝔽₉)

yes

characteristic

103

C₂×C₃

—

104

D₃

—

105

D₃

—

106

C₂²

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

C₂×AΓL(1,𝔽₉)

yes

characteristic

113

C₃

—

114

C₂

—

115

C₂

—

116

C₂

#10596402

yes

characteristic

	subgroup	G/H
center	C₂	#10596402
commutator, cosocle	#3787	C₂³
Frattini	C₄	C₂×AΓL(1,𝔽₉)
Fitting	C₃²×C₈	SD₁₆
socle	C₂×C₃²	#486
prime radical	C₂×C₃⋊D₃	C₂×D₈
hypercenter	C₈	AΓL(1,𝔽₉)
hypocenter	C₃²	#2241
LCS	G ▷ #3787 ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

subgroup

G/H

C₂

C₂³

C₄

C₃²×C₈

SD₁₆

socle

C₂×C₃²

#486

prime radical

C₂×C₃⋊D₃

C₂×D₈

C₈

C₃²

G ▷ #3787 ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈

N	H ≅ G/N	type
91. C₃²	#2241	semidirect

H ≅ G/N

type

91. C₃²

#2241

semidirect

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

subgroup	index
#10593536	2
#10593295	2
#10593254	2
#10593161	2
#2241	9

subgroup

index

Subgroups — #11800083

Conjugacy classes of subgroups

Complements

Maximal subgroups