Group #11766563 — subgroups

Subgroups — C₉×#1842 #11766563

Order 1152.

450 conjugacy classes of subgroups; only the 312 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 312 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	C₂×C₉×C₄⋊C₈	C₂	1	6	yes	maximal
2	C₄³×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃×#1842	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₉	C₂²	1	4	yes	—
5	C₂×C₄²×C₉	C₄	1	3	yes	—
6	C₂×C₄²×C₉	C₄	1	1	yes	characteristic
7	C₂×C₄²×C₉	C₂²	1	3	yes	—
8	C₉×C₄⋊C₈	—	2	12	no	—
9	C₂×C₃×C₄⋊C₈	C₂×C₃	1	6	yes	—
10	C₃×C₄³	C₂×C₃	1	1	yes	characteristic
11	C₂²×C₄×C₉	C₂×C₄	1	3	yes	—
12	C₂²×C₄×C₉	C₂×C₄	1	3	yes	—
13	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
14	C₂×C₈×C₉	—	2	12	no	—
15	C₄²×C₉	—	2	6	no	—
16	C₄²×C₉	C₈	1	4	yes	complemented
17	C₄²×C₉	D₄	1	6	yes	—
18	C₄²×C₉	Q₈	1	6	yes	—
19	#1842	C₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
21	C₂×C₃×C₄²	C₃×C₄	1	3	yes	—
22	C₂×C₃×C₄²	C₃×C₄	1	1	yes	characteristic
23	C₂×C₃×C₄²	C₂²×C₃	1	3	yes	—
24	C₃×C₄⋊C₈	—	2	12	no	—
25	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₉	—	2	6	no	—
27	C₂×C₄×C₉	C₄⋊C₄	1	6	yes	—
28	C₂×C₄×C₉	C₄⋊C₄	1	6	yes	—
29	C₂×C₄×C₉	C₂×C₈	1	6	yes	—
30	C₂×C₄×C₉	M₁₆	1	6	yes	—
31	C₂×C₄×C₉	C₂×D₄	1	3	yes	—
32	C₂×C₄×C₉	C₂×Q₈	1	3	yes	—
33	C₈×C₉	—	4	4	no	—
34	C₂×C₄⋊C₈	C₂×C₉	1	6	yes	—
35	C₄³	C₂×C₉	1	1	yes	characteristic
36	C₂²×C₃×C₄	C₂×C₃×C₄	1	3	yes	—
37	C₂²×C₃×C₄	C₂×C₃×C₄	1	3	yes	—
38	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
39	C₂×C₃×C₈	—	2	12	no	—
40	C₃×C₄²	—	2	6	no	—
41	C₃×C₄²	C₃×C₈	1	4	yes	—
42	C₃×C₄²	C₃×D₄	1	6	yes	—
43	C₃×C₄²	C₃×Q₈	1	6	yes	—
44	C₂²×C₉	C₂×C₄⋊C₄	1	3	yes	—
45	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
46	C₂²×C₉	C₂×M₁₆	1	3	yes	—
47	C₄×C₉	—	2	6	no	—
48	C₄×C₉	C₄⋊C₈	1	12	yes	complemented
49	C₄×C₉	#127	1	1	yes	characteristic
50	C₄×C₉	C₄⋊Q₈	1	3	yes	—
51	C₂²×C₈	C₂²×C₉	1	4	yes	—
52	C₂×C₄²	C₄×C₉	1	3	yes	—
53	C₂×C₄²	C₄×C₉	1	1	yes	characteristic
54	C₂×C₄²	C₂²×C₉	1	3	yes	—
55	C₄⋊C₈	—	2	12	no	—
56	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄	—	2	6	no	—
58	C₂×C₃×C₄	C₃×C₄⋊C₄	1	6	yes	—
59	C₂×C₃×C₄	C₃×C₄⋊C₄	1	6	yes	—
60	C₂×C₃×C₄	C₂×C₃×C₈	1	6	yes	—
61	C₂×C₃×C₄	C₃×M₁₆	1	6	yes	—
62	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
63	C₂×C₃×C₄	C₂×C₃×Q₈	1	3	yes	—
64	C₃×C₈	—	4	4	no	—
65	C₂×C₉	#384	1	1	yes	characteristic
66	C₂×C₉	C₂×C₄⋊C₈	1	3	yes	—
67	C₂×C₉	#423	1	3	yes	—
68	C₂²×C₄	C₂×C₄×C₉	1	3	yes	—
69	C₂²×C₄	C₂×C₄×C₉	1	3	yes	—
70	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
71	C₂×C₈	—	2	12	no	—
72	C₄²	—	2	6	no	—
73	C₄²	C₈×C₉	1	4	yes	complemented
74	C₄²	D₄×C₉	1	6	yes	—
75	C₄²	Q₈×C₉	1	6	yes	—
76	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	3	yes	—
77	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
78	C₂²×C₃	C₂×C₃×M₁₆	1	3	yes	—
79	C₃×C₄	—	2	6	no	—
80	C₃×C₄	C₃×C₄⋊C₈	1	12	yes	—
81	C₃×C₄	C₃×#127	1	1	yes	characteristic
82	C₃×C₄	C₃×C₄⋊Q₈	1	3	yes	—
83	C₉	#1842	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
85	C₂×C₄	—	2	6	no	—
86	C₂×C₄	C₉×C₄⋊C₄	1	6	yes	—
87	C₂×C₄	C₉×C₄⋊C₄	1	6	yes	—
88	C₂×C₄	C₂×C₈×C₉	1	6	yes	—
89	C₂×C₄	C₉×M₁₆	1	6	yes	—
90	C₂×C₄	C₂×D₄×C₉	1	3	yes	—
91	C₂×C₄	C₂×Q₈×C₉	1	3	yes	—
92	C₈	—	4	4	no	—
93	C₂×C₃	C₃×#384	1	1	yes	characteristic
94	C₂×C₃	C₂×C₃×C₄⋊C₈	1	3	yes	—
95	C₂×C₃	C₃×#423	1	3	yes	—
96	C₂²	C₂×C₉×C₄⋊C₄	1	3	yes	—
97	C₂²	C₂²×C₈×C₉	1	1	yes	characteristic
98	C₂²	C₂×C₉×M₁₆	1	3	yes	—
99	C₄	—	2	6	no	—
100	C₄	C₉×C₄⋊C₈	1	12	yes	complemented
101	C₄	C₉×#127	1	1	yes	characteristic
102	C₄	C₉×C₄⋊Q₈	1	3	yes	—
103	C₃	C₃×#1842	1	1	yes	characteristic
104	C₂	C₉×#384	1	1	yes	characteristic
105	C₂	C₂×C₉×C₄⋊C₈	1	3	yes	—
106	C₂	C₉×#423	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×C₄⋊C₈

C₂

yes

maximal

C₄³×C₉

C₂

yes

maximal, characteristic

C₃×#1842

C₃

yes

maximal, characteristic

C₂²×C₈×C₉

C₂²

yes

—

C₂×C₄²×C₉

C₄

yes

—

C₂×C₄²×C₉

C₄

yes

characteristic

C₂×C₄²×C₉

C₂²

yes

—

C₉×C₄⋊C₈

—

C₂×C₃×C₄⋊C₈

C₂×C₃

yes

—

C₃×C₄³

C₂×C₃

yes

characteristic

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂×C₈×C₉

—

C₄²×C₉

—

C₄²×C₉

C₈

yes

complemented

C₄²×C₉

D₄

yes

—

C₄²×C₉

Q₈

yes

—

#1842

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×C₈

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₃×C₄

yes

—

C₂×C₃×C₄²

C₃×C₄

yes

characteristic

C₂×C₃×C₄²

C₂²×C₃

yes

—

C₃×C₄⋊C₈

—

C₂³×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂×C₈

yes

—

C₂×C₄×C₉

M₁₆

yes

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×Q₈

yes

—

C₈×C₉

—

C₂×C₄⋊C₈

C₂×C₉

yes

—

C₄³

C₂×C₉

yes

characteristic

C₂²×C₃×C₄

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₂×C₃×C₈

—

C₃×C₄²

—

C₃×C₄²

C₃×C₈

yes

—

C₃×C₄²

C₃×D₄

yes

—

C₃×C₄²

C₃×Q₈

yes

—

C₂²×C₉

C₂×C₄⋊C₄

yes

—

C₂²×C₉

C₂²×C₈

yes

characteristic

C₂²×C₉

C₂×M₁₆

yes

—

C₄×C₉

—

C₄×C₉

C₄⋊C₈

yes

complemented

C₄×C₉

#127

yes

characteristic

C₄×C₉

C₄⋊Q₈

yes

—

C₂²×C₈

C₂²×C₉

yes

—

C₂×C₄²

C₄×C₉

yes

—

C₂×C₄²

C₄×C₉

yes

characteristic

C₂×C₄²

C₂²×C₉

yes

—

C₄⋊C₈

—

C₂³×C₃

C₂²×C₃×C₄

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₃×C₄⋊C₄

yes

—

C₂×C₃×C₄

C₃×C₄⋊C₄

yes

—

C₂×C₃×C₄

C₂×C₃×C₈

yes

—

C₂×C₃×C₄

C₃×M₁₆

yes

—

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

C₂×C₃×C₄

C₂×C₃×Q₈

yes

—

C₃×C₈

—

C₂×C₉

#384

yes

characteristic

C₂×C₉

C₂×C₄⋊C₈

yes

—

C₂×C₉

#423

yes

—

C₂²×C₄

C₂×C₄×C₉

yes

—

C₂²×C₄

C₂×C₄×C₉

yes

—

C₂²×C₄

C₂³×C₉

yes

characteristic

C₂×C₈

—

C₄²

—

C₄²

C₈×C₉

yes

complemented

C₄²

D₄×C₉

yes

—

C₄²

Q₈×C₉

yes

—

C₂²×C₃

C₂×C₃×C₄⋊C₄

yes

—

C₂²×C₃

C₂²×C₃×C₈

yes

characteristic

C₂²×C₃

C₂×C₃×M₁₆

yes

—

C₃×C₄

—

C₃×C₄

C₃×C₄⋊C₈

yes

—

C₃×C₄

C₃×#127

yes

characteristic

C₃×C₄

C₃×C₄⋊Q₈

yes

—

C₉

#1842

yes

characteristic, direct product factor, Sylow

C₂³

C₂²×C₄×C₉

yes

characteristic

C₂×C₄

—

C₂×C₄

C₉×C₄⋊C₄

yes

—

C₂×C₄

C₉×C₄⋊C₄

yes

—

C₂×C₄

C₂×C₈×C₉

yes

—

C₂×C₄

C₉×M₁₆

yes

—

C₂×C₄

C₂×D₄×C₉

yes

—

C₂×C₄

C₂×Q₈×C₉

yes

—

C₈

—

C₂×C₃

C₃×#384

yes

characteristic

C₂×C₃

C₂×C₃×C₄⋊C₈

yes

—

C₂×C₃

C₃×#423

yes

—

C₂²

C₂×C₉×C₄⋊C₄

yes

—

C₂²

C₂²×C₈×C₉

yes

characteristic

C₂²

C₂×C₉×M₁₆

yes

—

C₄

—

100

C₄

C₉×C₄⋊C₈

yes

complemented

101

C₄

C₉×#127

yes

characteristic

102

C₄

C₉×C₄⋊Q₈

yes

—

103

C₃

C₃×#1842

yes

characteristic

104

C₂

C₉×#384

yes

characteristic

105

C₂

C₂×C₉×C₄⋊C₈

yes

—

106

C₂

C₉×#423

yes

—

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂²	C₂²×C₈×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂²×C₃×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

subgroup

G/H

center

C₂²×C₄×C₉

C₂³

commutator

C₂²

C₂²×C₈×C₉

Frattini, cosocle

C₂²×C₃×C₄

C₂³×C₃

socle, prime radical

C₂³×C₃

C₂²×C₃×C₄

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
16. C₄²×C₉	C₈	semidirect
19. #1842	C₉	direct (N × H)
48. C₄×C₉	C₄⋊C₈	semidirect
73. C₄²	C₈×C₉	semidirect
83. C₉	#1842	direct (N × H)
100. C₄	C₉×C₄⋊C₈	semidirect

H ≅ G/N

type

16. C₄²×C₉

C₈

semidirect

19. #1842

C₉

direct (N × H)

48. C₄×C₉

C₄⋊C₈

semidirect

73. C₄²

C₈×C₉

semidirect

83. C₉

#1842

direct (N × H)

100. C₄

C₉×C₄⋊C₈

semidirect

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

subgroup	index
C₂×C₉×C₄⋊C₈	2
C₄³×C₉	2
C₃×#1842	3

subgroup

index

C₂×C₉×C₄⋊C₈

C₄³×C₉

C₃×#1842

Subgroups — C₉×#1842 #11766563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#1842 #11766563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1842 #11766563