Group #11800177 — subgroups

Subgroups — #11800177

Order 1152.

396 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 137 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	#10592398	C₂	1	1	yes	maximal, characteristic
2	#10592382	C₂	1	1	yes	maximal, characteristic
3	C₃²×#346	C₂	1	1	yes	maximal, characteristic
4	#10589369	C₂	1	4	yes	maximal
5	#69083	—	3	4	no	maximal
6	C₂×#3746	—	2	1	no	—
7	C₂×#3746	C₂²	1	2	yes	—
8	#64079	—	2	1	no	—
9	#64078	—	2	1	no	—
10	C₂×C₃²×C₁₆	C₂²	1	2	yes	—
11	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
12	#63645	C₂²	1	2	yes	—
13	#63644	—	2	1	no	—
14	#4699	—	3	4	no	—
15	#4683	—	3	4	no	—
16	C₃×#346	D₃	1	4	yes	—
17	#4503	—	3	16	no	—
18	C₂×#634	—	2	2	no	—
19	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
20	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
21	C₃²×C₄²	D₄	1	1	yes	characteristic
22	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
23	C₄⋊(C₃⋊Dic₃)	—	4	2	no	—
24	#3750	—	4	2	no	—
25	#3746	—	2	4	no	—
26	#3746	—	4	2	no	—
27	C₃²×C₁₆	—	2	2	no	—
28	#2245	—	9	1	no	Sylow
29	C₂×Dic₁₂	—	3	8	no	—
30	C₂×Dic₁₂	—	6	4	no	—
31	#870	—	6	4	no	—
32	#869	—	6	4	no	—
33	C₂×C₃×C₁₆	C₂×D₃	1	8	yes	—
34	C₃×C₄×C₈	C₂×D₃	1	4	yes	—
35	#818	—	3	8	no	—
36	#817	—	6	4	no	—
37	C₂×C₃²×C₄	D₈	1	2	yes	—
38	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
39	C₂×C₃⋊Dic₃	—	4	2	no	—
40	C₂×C₃⋊Dic₃	—	4	2	no	—
41	#634	—	4	2	no	—
42	#634	—	4	2	no	—
43	C₃²×C₈	SD₁₆	1	2	yes	—
44	C₃²×C₈	#41	1	2	yes	—
45	#499	—	9	1	no	—
46	#494	—	9	1	no	—
47	#358	—	9	4	no	—
48	#346	C₃⋊D₃	1	1	yes	characteristic
49	C₂×Dic₆	—	6	8	no	—
50	C₂×C₃×C₈	D₁₂	1	4	yes	—
51	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
52	C₃×C₄²	D₁₂	1	4	yes	—
53	C₄⋊Dic₃	—	6	8	no	—
54	C₄⋊Dic₃	—	12	8	no	—
55	Dic₃⋊C₄	—	12	8	no	—
56	Dic₁₂	—	6	16	no	—
57	Dic₁₂	—	12	8	no	—
58	C₃×C₁₆	—	2	8	no	—
59	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
60	C₃²×C₄	—	2	2	no	—
61	C₃²×C₄	#124	1	1	yes	characteristic
62	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
63	C₃⋊Dic₃	—	8	2	no	—
64	C₃⋊Dic₃	—	8	2	no	—
65	C₂×Q₁₆	—	9	2	no	—
66	C₂×Q₁₆	—	18	1	no	—
67	C₄⋊Q₈	—	18	1	no	—
68	#125	—	18	1	no	—
69	C₂×C₁₆	C₂×C₃⋊D₃	1	2	yes	—
70	#107	—	9	2	no	—
71	#106	—	18	1	no	—
72	C₄×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
73	C₂×C₃×C₄	D₂₄	1	8	yes	—
74	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
75	C₂×Dic₃	—	12	8	no	—
76	C₂×Dic₃	—	12	8	no	—
77	Dic₆	—	12	8	no	—
78	Dic₆	—	12	8	no	—
79	C₃×C₈	#204	1	8	yes	—
80	C₃×C₈	#235	1	8	yes	—
81	C₂×C₃²	#486	1	1	yes	characteristic
82	C₂×C₃²	#510	1	2	yes	—
83	C₂×Q₈	—	18	2	no	—
84	Q₁₆	—	18	4	no	—
85	Q₁₆	—	36	2	no	—
86	C₂×C₈	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
87	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
88	C₄⋊C₄	—	18	2	no	—
89	C₄⋊C₄	—	36	2	no	—
90	C₄⋊C₄	—	36	2	no	—
91	C₄²	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
92	C₁₆	—	2	2	no	—
93	C₂²×C₃	C₂×D₂₄	1	4	yes	—
94	C₃×C₄	—	2	8	no	—
95	C₃×C₄	#875	1	4	yes	—
96	C₃×C₄	C₂×#204	1	4	yes	—
97	Dic₃	—	24	8	no	—
98	Dic₃	—	24	8	no	—
99	C₃²	#2245	1	1	yes	characteristic, complemented, Sylow
100	Q₈	—	36	2	no	—
101	Q₈	—	36	2	no	—
102	C₂×C₄	—	36	2	no	—
103	C₂×C₄	—	36	2	no	—
104	C₂×C₄	#3745	1	2	yes	—
105	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
106	C₈	#3744	1	2	yes	—
107	C₈	#3828	1	2	yes	—
108	C₂×C₃	#4694	1	4	yes	—
109	C₂×C₃	#4909	1	8	yes	—
110	C₂²	C₂×#3745	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	72	2	no	—
113	C₄	—	72	2	no	—
114	C₄	#64084	1	1	yes	characteristic
115	C₄	C₂×#3744	1	1	yes	characteristic
116	C₃	#69083	1	4	yes	complemented
117	C₂	#10592393	1	1	yes	characteristic
118	C₂	#10592608	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#10592398

C₂

yes

maximal, characteristic

#10592382

C₂

yes

maximal, characteristic

C₃²×#346

C₂

yes

maximal, characteristic

#10589369

C₂

yes

—

—

C₂²

yes

—

#64079

—

#64078

—

C₂×C₃²×C₁₆

C₂²

yes

—

C₃²×C₄×C₈

C₂²

yes

characteristic

#63645

C₂²

yes

—

—

—

—

D₃

yes

—

#4503

—

C₂×#634

—

C₂×C₃²×C₈

D₄

yes

characteristic

C₂×C₃²×C₈

C₂³

yes

characteristic

C₃²×C₄²

D₄

yes

characteristic

C₄⋊(C₃⋊Dic₃)

—

C₄⋊(C₃⋊Dic₃)

—

#3750

—

#3746

—

#3746

—

C₃²×C₁₆

—

#2245

—

Sylow

C₂×Dic₁₂

—

C₂×Dic₁₂

—

#870

—

#869

—

C₂×C₃×C₁₆

C₂×D₃

yes

—

C₃×C₄×C₈

C₂×D₃

yes

—

#818

—

#817

—

C₂×C₃²×C₄

D₈

yes

—

C₂×C₃²×C₄

C₂×D₄

yes

characteristic

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

—

#634

—

#634

—

C₃²×C₈

SD₁₆

yes

—

C₃²×C₈

#41

yes

—

—

—

—

C₃⋊D₃

yes

characteristic

C₂×Dic₆

—

C₂×C₃×C₈

D₁₂

yes

—

C₂×C₃×C₈

C₂²×D₃

yes

—

C₃×C₄²

D₁₂

yes

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

Dic₃⋊C₄

—

Dic₁₂

—

Dic₁₂

—

C₃×C₁₆

—

C₂²×C₃²

C₂×D₈

yes

characteristic

C₃²×C₄

—

C₃²×C₄

#124

yes

characteristic

C₃²×C₄

C₂×SD₁₆

yes

characteristic

C₃⋊Dic₃

—

C₃⋊Dic₃

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

#125

—

C₂×C₁₆

C₂×C₃⋊D₃

yes

—

#107

—

#106

—

C₄×C₈

C₂×C₃⋊D₃

yes

characteristic

C₂×C₃×C₄

D₂₄

yes

—

C₂×C₃×C₄

C₂×D₁₂

yes

—

C₂×Dic₃

—

C₂×Dic₃

—

Dic₆

—

Dic₆

—

C₃×C₈

#204

yes

—

C₃×C₈

#235

yes

—

C₂×C₃²

#486

yes

characteristic

C₂×C₃²

#510

yes

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

C₄⋊(C₃⋊D₃)

yes

characteristic

C₂×C₈

C₂²×C₃⋊D₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₄⋊(C₃⋊D₃)

yes

characteristic

C₁₆

—

C₂²×C₃

C₂×D₂₄

yes

—

C₃×C₄

—

C₃×C₄

#875

yes

—

C₃×C₄

C₂×#204

yes

—

Dic₃

—

Dic₃

—

C₃²

#2245

yes

characteristic, complemented, Sylow

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

#3745

yes

—

105

C₂×C₄

C₂×C₄⋊(C₃⋊D₃)

yes

characteristic

106

C₈

#3744

yes

—

107

C₈

#3828

yes

—

108

C₂×C₃

#4694

yes

—

109

C₂×C₃

#4909

yes

—

110

C₂²

C₂×#3745

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

#64084

yes

characteristic

115

C₄

C₂×#3744

yes

characteristic

116

C₃

#69083

yes

complemented

117

C₂

#10592393

yes

characteristic

118

C₂

#10592608

yes

—

	subgroup	G/H
center	C₂²	C₂×#3745
commutator, cosocle	C₂×C₃²×C₈	C₂³
Frattini	C₂×C₈	C₂²×C₃⋊D₃
Fitting	C₃²×#346	C₂
socle, prime radical	C₂²×C₃²	C₂×D₈
hypercenter	#346	C₃⋊D₃
hypocenter	C₃²	#2245
LCS	G ▷ C₂×C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

subgroup

G/H

center

C₂²

C₂×#3745

commutator, cosocle

C₂×C₃²×C₈

C₂³

Frattini

C₂×C₈

C₂²×C₃⋊D₃

Fitting

C₃²×#346

C₂

socle, prime radical

C₂²×C₃²

C₂×D₈

C₃⋊D₃

C₃²

G ▷ C₂×C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

N	H ≅ G/N	type
99. C₃²	#2245	semidirect
116. C₃	#69083	semidirect

H ≅ G/N

type

99. C₃²

#2245

semidirect

116. C₃

#69083

semidirect

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

subgroup	index
#10592398	2
#10592382	2
C₃²×#346	2
#10589369	2
#69083	3

subgroup

index

C₃²×#346

Subgroups — #11800177

Conjugacy classes of subgroups

Complements

Maximal subgroups