Group #11785978 — subgroups

Subgroups — #11785978

Order 1152.

648 conjugacy classes of subgroups; only the 305 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 305 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	C₃²×#376	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₃⋊(C₃⋊C₈))	C₂	1	2	yes	maximal
3	#10589390	C₂	1	4	yes	maximal
4	#69437	—	3	4	no	maximal
5	C₂×C₃²×C₄²	C₂²	1	2	yes	—
6	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
7	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	4	yes	—
8	C₃²×#95	C₄	1	4	yes	—
9	C₄⋊(C₃⋊(C₃⋊C₈))	—	2	4	no	—
10	C₃×#376	D₃	1	4	yes	—
11	C₂×C₄⋊(C₃⋊C₈)	—	3	8	no	—
12	#4524	—	3	16	no	—
13	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
14	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
15	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
16	C₃²×C₄²	—	2	4	no	—
17	C₃²×C₄²	D₄	1	2	yes	—
18	C₃²×C₄²	Q₈	1	2	yes	—
19	C₂×C₃⋊(C₃⋊C₈)	—	2	4	no	—
20	C₂×C₃⋊(C₃⋊C₈)	—	2	8	no	—
21	#1832	—	9	1	no	Sylow
22	C₂×C₃×C₄²	C₂×D₃	1	8	yes	—
23	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
24	C₂²×C₃⋊C₈	—	3	16	no	—
25	C₃×#95	Dic₃	1	16	yes	—
26	C₄⋊(C₃⋊C₈)	—	6	16	no	—
27	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₃²×C₄	—	2	4	no	—
29	C₂×C₃²×C₄	—	2	4	no	—
30	C₂×C₃²×C₄	—	2	8	no	—
31	C₂×C₃²×C₄	C₄⋊C₄	1	4	yes	—
32	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
33	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₃²×C₄	#41	1	4	yes	—
35	C₃⋊(C₃⋊C₈)	—	4	4	no	—
36	C₂×C₄⋊C₈	—	9	2	no	—
37	#376	C₃⋊D₃	1	1	yes	characteristic
38	#336	—	9	4	no	—
39	C₂²×C₃×C₄	C₂×Dic₃	1	16	yes	—
40	C₂²×C₃×C₄	C₂×Dic₃	1	8	yes	—
41	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
42	C₃×C₄²	—	2	16	no	—
43	C₃×C₄²	Dic₆	1	8	yes	—
44	C₃×C₄²	D₁₂	1	8	yes	—
45	C₂×C₃⋊C₈	—	6	16	no	—
46	C₂×C₃⋊C₈	—	6	32	no	—
47	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₃²	#117	1	2	yes	—
49	C₂²×C₃²	#131	1	4	yes	—
50	C₃²×C₄	—	2	4	no	—
51	C₃²×C₄	—	4	4	no	—
52	C₃²×C₄	#124	1	2	yes	—
53	C₃²×C₄	#125	1	2	yes	—
54	C₂²×C₈	—	9	4	no	—
55	C₂×C₄²	C₂×C₃⋊D₃	1	2	yes	—
56	C₂×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
57	C₄⋊C₈	—	18	4	no	—
58	#95	C₃⋊Dic₃	1	4	yes	—
59	C₂³×C₃	C₂²×Dic₃	1	4	yes	—
60	C₂×C₃×C₄	—	2	16	no	—
61	C₂×C₃×C₄	—	2	16	no	—
62	C₂×C₃×C₄	—	2	32	no	—
63	C₂×C₃×C₄	C₄⋊Dic₃	1	16	yes	—
64	C₂×C₃×C₄	C₂×Dic₆	1	4	yes	—
65	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
66	C₂×C₃×C₄	#235	1	16	yes	—
67	C₃⋊C₈	—	12	16	no	—
68	C₂×C₃²	#382	1	1	yes	characteristic
69	C₂×C₃²	#424	1	2	yes	—
70	C₂×C₃²	#433	1	4	yes	—
71	C₂²×C₄	C₂×C₃⋊Dic₃	1	4	yes	—
72	C₂²×C₄	C₂×C₃⋊Dic₃	1	2	yes	—
73	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
74	C₂×C₈	—	18	4	no	—
75	C₂×C₈	—	18	8	no	—
76	C₄²	—	2	4	no	—
77	C₄²	#634	1	2	yes	—
78	C₄²	C₄⋊(C₃⋊D₃)	1	2	yes	—
79	C₂²×C₃	C₂×C₄⋊Dic₃	1	4	yes	—
80	C₂²×C₃	#926	1	8	yes	—
81	C₂²×C₃	#948	1	16	yes	—
82	C₃×C₄	—	2	16	no	—
83	C₃×C₄	—	4	16	no	—
84	C₃×C₄	#870	1	8	yes	—
85	C₃×C₄	#875	1	8	yes	—
86	C₃²	#1832	1	1	yes	characteristic, complemented, Sylow
87	C₂³	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	C₄⋊(C₃⋊Dic₃)	1	4	yes	—
92	C₂×C₄	C₂×#634	1	1	yes	characteristic
93	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
94	C₂×C₄	#3828	1	4	yes	—
95	C₈	—	36	4	no	—
96	C₂×C₃	#4936	1	4	yes	—
97	C₂×C₃	#4999	1	8	yes	—
98	C₂×C₃	#5000	1	16	yes	—
99	C₂²	C₂×C₄⋊(C₃⋊Dic₃)	1	1	yes	characteristic
100	C₂²	#64135	1	2	yes	—
101	C₂²	#64157	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	4	4	no	—
104	C₄	#64079	1	2	yes	—
105	C₄	#64084	1	2	yes	—
106	C₃	#69437	1	4	yes	complemented
107	C₂	#10592635	1	1	yes	characteristic
108	C₂	#10592698	1	2	yes	—
109	C₂	#10592699	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#376

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₃⋊(C₃⋊C₈))

C₂

yes

maximal

#10589390

C₂

yes

maximal

#69437

—

maximal

C₂×C₃²×C₄²

C₂²

yes

—

C₂×C₃²×C₄²

C₂²

yes

characteristic

C₂²×C₃⋊(C₃⋊C₈)

C₂²

yes

—

C₃²×#95

C₄

yes

—

C₄⋊(C₃⋊(C₃⋊C₈))

—

C₃×#376

D₃

yes

—

C₂×C₄⋊(C₃⋊C₈)

—

#4524

—

C₂²×C₃²×C₄

C₂×C₄

yes

—

C₂²×C₃²×C₄

C₂×C₄

yes

—

C₂²×C₃²×C₄

C₂³

yes

characteristic

C₃²×C₄²

—

C₃²×C₄²

D₄

yes

—

C₃²×C₄²

Q₈

yes

—

C₂×C₃⋊(C₃⋊C₈)

—

C₂×C₃⋊(C₃⋊C₈)

—

#1832

—

Sylow

C₂×C₃×C₄²

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

—

C₂²×C₃⋊C₈

—

C₃×#95

Dic₃

yes

—

C₄⋊(C₃⋊C₈)

—

C₂³×C₃²

C₂²×C₄

yes

characteristic

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₄⋊C₄

yes

—

C₂×C₃²×C₄

C₂×D₄

yes

characteristic

C₂×C₃²×C₄

C₂×Q₈

yes

characteristic

C₂×C₃²×C₄

#41

yes

—

C₃⋊(C₃⋊C₈)

—

C₂×C₄⋊C₈

—

#376

C₃⋊D₃

yes

characteristic

#336

—

C₂²×C₃×C₄

C₂×Dic₃

yes

—

C₂²×C₃×C₄

C₂×Dic₃

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₃×C₄²

—

C₃×C₄²

Dic₆

yes

—

C₃×C₄²

D₁₂

yes

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₃²

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃²

#117

yes

—

C₂²×C₃²

#131

yes

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

#124

yes

—

C₃²×C₄

#125

yes

—

C₂²×C₈

—

C₂×C₄²

C₂×C₃⋊D₃

yes

—

C₂×C₄²

C₂×C₃⋊D₃

yes

characteristic

C₄⋊C₈

—

#95

C₃⋊Dic₃

yes

—

C₂³×C₃

C₂²×Dic₃

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₄⋊Dic₃

yes

—

C₂×C₃×C₄

C₂×Dic₆

yes

—

C₂×C₃×C₄

C₂×D₁₂

yes

—

C₂×C₃×C₄

#235

yes

—

C₃⋊C₈

—

C₂×C₃²

#382

yes

characteristic

C₂×C₃²

#424

yes

—

C₂×C₃²

#433

yes

—

C₂²×C₄

C₂×C₃⋊Dic₃

yes

—

C₂²×C₄

C₂×C₃⋊Dic₃

yes

—

C₂²×C₄

C₂²×C₃⋊D₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

#634

yes

—

C₄²

C₄⋊(C₃⋊D₃)

yes

—

C₂²×C₃

C₂×C₄⋊Dic₃

yes

—

C₂²×C₃

#926

yes

—

C₂²×C₃

#948

yes

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

#870

yes

—

C₃×C₄

#875

yes

—

C₃²

#1832

yes

characteristic, complemented, Sylow

C₂³

C₂²×C₃⋊Dic₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊(C₃⋊Dic₃)

yes

—

C₂×C₄

C₂×#634

yes

characteristic

C₂×C₄

C₂×C₄⋊(C₃⋊D₃)

yes

characteristic

C₂×C₄

#3828

yes

—

C₈

—

C₂×C₃

#4936

yes

—

C₂×C₃

#4999

yes

—

C₂×C₃

#5000

yes

—

C₂²

C₂×C₄⋊(C₃⋊Dic₃)

yes

characteristic

100

C₂²

#64135

yes

—

101

C₂²

#64157

yes

—

102

C₄

—

103

C₄

—

104

C₄

#64079

yes

—

105

C₄

#64084

yes

—

106

C₃

#69437

yes

complemented

107

C₂

#10592635

yes

characteristic

108

C₂

#10592698

yes

—

109

C₂

#10592699

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×C₃⋊D₃
commutator, socle, prime radical	C₂³×C₃²	C₂²×C₄
Fitting	C₃²×#376	C₂
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	#376	C₃⋊D₃
hypocenter	C₃²	#1832
LCS	G ▷ C₂³×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×C₃⋊D₃

commutator, socle, prime radical

C₂³×C₃²

C₂²×C₄

Fitting

C₃²×#376

C₂

cosocle

C₂²×C₃²×C₄

C₂³

C₃⋊D₃

C₃²

G ▷ C₂³×C₃² ▷ C₃²

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
86. C₃²	#1832	semidirect
106. C₃	#69437	semidirect

H ≅ G/N

type

86. C₃²

#1832

semidirect

106. C₃

#69437

semidirect

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

subgroup	index
C₃²×#376	2
C₂×C₄⋊(C₃⋊(C₃⋊C₈))	2
#10589390	2
#69437	3

subgroup

index

C₃²×#376

C₂×C₄⋊(C₃⋊(C₃⋊C₈))

#10589390

#69437

Subgroups — #11785978

Conjugacy classes of subgroups

Complements

Maximal subgroups