Group #11767101 — subgroups

Subgroups — C₉×#2380 #11767101

Order 1152.

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

normal subgroups only

This group has 972 conjugacy classes of subgroups — too many to draw. Only its 396 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×#127	C₂	1	1	yes	maximal, characteristic
2	C₉×#386	C₂	1	12	yes	maximal, complemented
3	C₉×#383	C₂	1	2	yes	maximal, complemented
4	C₃×#2380	C₃	1	1	yes	maximal, characteristic
5	C₂²×D₄×C₉	C₂²	1	6	yes	—
6	C₂³×C₄×C₉	C₂²	1	4	yes	—
7	C₉×#127	C₄	1	8	yes	complemented
8	C₂×C₉×C₂²⋊C₄	C₂²	1	12	yes	—
9	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
10	C₉×#95	C₂²	1	12	yes	—
11	C₂×C₃×#127	C₂×C₃	1	1	yes	characteristic
12	C₃×#386	C₂×C₃	1	12	yes	—
13	C₃×#383	C₂×C₃	1	2	yes	—
14	C₂⁴×C₉	C₂³	1	4	yes	—
15	C₂×D₄×C₉	—	4	6	no	—
16	C₂×D₄×C₉	—	4	6	no	—
17	C₂×D₄×C₉	C₂×C₄	1	24	yes	complemented
18	C₂²×C₄×C₉	—	4	12	no	—
19	C₂²×C₄×C₉	C₂³	1	8	yes	—
20	C₂²×C₄×C₉	C₂³	1	3	yes	—
21	C₉×C₂²⋊C₄	—	4	12	no	—
22	C₄²×C₉	C₂×C₄	1	4	yes	complemented
23	#2380	C₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃×D₄	C₂²×C₃	1	6	yes	—
25	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
26	C₃×#127	C₃×C₄	1	8	yes	—
27	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	12	yes	—
28	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
29	C₃×#95	C₂²×C₃	1	12	yes	—
30	C₂³×C₉	—	2	12	no	—
31	C₂³×C₉	—	2	12	no	—
32	C₂³×C₉	C₂²×C₄	1	8	yes	—
33	C₂³×C₉	C₂⁴	1	1	yes	characteristic
34	D₄×C₉	—	4	24	no	—
35	C₂×C₄×C₉	—	2	6	no	—
36	C₂×C₄×C₉	—	2	24	no	—
37	C₂×C₄×C₉	—	4	16	no	—
38	C₂×C₄×C₉	C₂²×C₄	1	6	yes	—
39	C₂×#127	C₂×C₉	1	1	yes	characteristic
40	#386	C₂×C₉	1	12	yes	complemented
41	#383	C₂×C₉	1	2	yes	complemented
42	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
43	C₂×C₃×D₄	—	4	6	no	—
44	C₂×C₃×D₄	—	4	6	no	—
45	C₂×C₃×D₄	C₂×C₃×C₄	1	24	yes	—
46	C₂²×C₃×C₄	—	4	12	no	—
47	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
48	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
49	C₃×C₂²⋊C₄	—	4	12	no	—
50	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
51	C₂²×C₉	—	2	24	no	—
52	C₂²×C₉	—	4	4	no	—
53	C₂²×C₉	—	4	12	no	—
54	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
55	C₂²×C₉	H(5,𝔽₂)	1	6	yes	—
56	C₄×C₉	—	2	6	no	—
57	C₄×C₉	—	4	8	no	—
58	C₂²×D₄	C₂²×C₉	1	6	yes	—
59	C₂³×C₄	C₂²×C₉	1	4	yes	—
60	#127	C₄×C₉	1	8	yes	complemented
61	C₂×C₂²⋊C₄	C₂²×C₉	1	12	yes	—
62	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
63	#95	C₂²×C₉	1	12	yes	—
64	C₂³×C₃	—	2	12	no	—
65	C₂³×C₃	—	2	12	no	—
66	C₂³×C₃	C₂²×C₃×C₄	1	8	yes	—
67	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
68	C₃×D₄	—	4	24	no	—
69	C₂×C₃×C₄	—	2	6	no	—
70	C₂×C₃×C₄	—	2	24	no	—
71	C₂×C₃×C₄	—	4	16	no	—
72	C₂×C₃×C₄	C₂²×C₃×C₄	1	6	yes	—
73	C₂×C₉	—	4	8	no	—
74	C₂×C₉	#518	1	3	yes	—
75	C₂×C₉	#560	1	4	yes	—
76	C₂⁴	C₂³×C₉	1	4	yes	—
77	C₂×D₄	—	4	6	no	—
78	C₂×D₄	—	4	6	no	—
79	C₂×D₄	C₂×C₄×C₉	1	24	yes	complemented
80	C₂²×C₄	—	4	12	no	—
81	C₂²×C₄	C₂³×C₉	1	8	yes	—
82	C₂²×C₄	C₂³×C₉	1	3	yes	—
83	C₂²⋊C₄	—	4	12	no	—
84	C₄²	C₂×C₄×C₉	1	4	yes	complemented
85	C₂²×C₃	—	2	24	no	—
86	C₂²×C₃	—	4	4	no	—
87	C₂²×C₃	—	4	12	no	—
88	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
89	C₂²×C₃	C₃×H(5,𝔽₂)	1	6	yes	—
90	C₃×C₄	—	2	6	no	—
91	C₃×C₄	—	4	8	no	—
92	C₉	#2380	1	1	yes	characteristic, direct product factor, Sylow
93	C₂³	—	2	12	no	—
94	C₂³	—	2	12	no	—
95	C₂³	C₂²×C₄×C₉	1	8	yes	—
96	C₂³	C₂⁴×C₉	1	1	yes	characteristic
97	D₄	—	4	24	no	—
98	C₂×C₄	—	2	6	no	—
99	C₂×C₄	—	2	24	no	—
100	C₂×C₄	—	4	16	no	—
101	C₂×C₄	C₂²×C₄×C₉	1	6	yes	—
102	C₂×C₃	—	4	8	no	—
103	C₂×C₃	C₃×#518	1	3	yes	—
104	C₂×C₃	C₃×#560	1	4	yes	—
105	C₂²	—	2	24	no	—
106	C₂²	—	4	4	no	—
107	C₂²	—	4	12	no	—
108	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
109	C₂²	C₉×H(5,𝔽₂)	1	6	yes	—
110	C₄	—	2	6	no	—
111	C₄	—	4	8	no	—
112	C₃	C₃×#2380	1	1	yes	characteristic
113	C₂	—	4	8	no	—
114	C₂	C₉×#518	1	3	yes	—
115	C₂	C₉×#560	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#127

C₂

yes

maximal, characteristic

C₉×#386

C₂

yes

maximal, complemented

C₉×#383

C₂

yes

maximal, complemented

C₃×#2380

C₃

yes

maximal, characteristic

C₂²×D₄×C₉

C₂²

yes

—

C₂³×C₄×C₉

C₂²

yes

—

C₉×#127

C₄

yes

complemented

C₂×C₉×C₂²⋊C₄

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₉×#95

C₂²

yes

—

C₂×C₃×#127

C₂×C₃

yes

characteristic

C₃×#386

C₂×C₃

yes

—

C₃×#383

C₂×C₃

yes

—

C₂⁴×C₉

C₂³

yes

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

C₂×C₄

yes

complemented

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×C₄×C₉

C₂³

yes

—

C₉×C₂²⋊C₄

—

C₄²×C₉

C₂×C₄

yes

complemented

#2380

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×D₄

C₂²×C₃

yes

—

C₂³×C₃×C₄

C₂²×C₃

yes

—

C₃×#127

C₃×C₄

yes

—

C₂×C₃×C₂²⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

characteristic

C₃×#95

C₂²×C₃

yes

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₂²×C₄

yes

—

C₂³×C₉

C₂⁴

yes

characteristic

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²×C₄

yes

—

C₂×#127

C₂×C₉

yes

characteristic

#386

C₂×C₉

yes

complemented

#383

C₂×C₉

yes

complemented

C₂⁴×C₃

C₂³×C₃

yes

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₃×C₂²⋊C₄

—

C₃×C₄²

C₂×C₃×C₄

yes

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂³×C₄

yes

characteristic

C₂²×C₉

H(5,𝔽₂)

yes

—

C₄×C₉

—

C₄×C₉

—

C₂²×D₄

C₂²×C₉

yes

—

C₂³×C₄

C₂²×C₉

yes

—

#127

C₄×C₉

yes

complemented

C₂×C₂²⋊C₄

C₂²×C₉

yes

—

C₂×C₄²

C₂²×C₉

yes

characteristic

#95

C₂²×C₉

yes

—

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

C₂²×C₃×C₄

yes

—

C₂³×C₃

C₂⁴×C₃

yes

characteristic

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²×C₃×C₄

yes

—

C₂×C₉

—

C₂×C₉

#518

yes

—

C₂×C₉

#560

yes

—

C₂⁴

C₂³×C₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×C₄×C₉

yes

complemented

C₂²×C₄

—

C₂²×C₄

C₂³×C₉

yes

—

C₂²×C₄

C₂³×C₉

yes

—

C₂²⋊C₄

—

C₄²

C₂×C₄×C₉

yes

complemented

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

C₂³×C₃×C₄

yes

characteristic

C₂²×C₃

C₃×H(5,𝔽₂)

yes

—

C₃×C₄

—

C₃×C₄

—

C₉

#2380

yes

characteristic, direct product factor, Sylow

C₂³

—

C₂³

—

C₂³

C₂²×C₄×C₉

yes

—

C₂³

C₂⁴×C₉

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₂²×C₄×C₉

yes

—

102

C₂×C₃

—

103

C₂×C₃

C₃×#518

yes

—

104

C₂×C₃

C₃×#560

yes

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₂³×C₄×C₉

yes

characteristic

109

C₂²

C₉×H(5,𝔽₂)

yes

—

110

C₄

—

111

C₄

—

112

C₃

C₃×#2380

yes

characteristic

113

C₂

—

114

C₂

C₉×#518

yes

—

115

C₂

C₉×#560

yes

—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#127	C₂×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

subgroup

G/H

center

C₂³×C₉

C₂⁴

commutator

C₂²

C₂³×C₄×C₉

Frattini, socle, cosocle

C₂³×C₃

C₂⁴×C₃

prime radical

C₂×C₃×#127

C₂×C₃

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₉ ◁ G

N	H ≅ G/N	type
2. C₉×#386	C₂	semidirect
3. C₉×#383	C₂	semidirect
7. C₉×#127	C₄	semidirect
17. C₂×D₄×C₉	C₂×C₄	semidirect
22. C₄²×C₉	C₂×C₄	semidirect
23. #2380	C₉	direct (N × H)
40. #386	C₂×C₉	semidirect
41. #383	C₂×C₉	semidirect
60. #127	C₄×C₉	semidirect
79. C₂×D₄	C₂×C₄×C₉	semidirect
84. C₄²	C₂×C₄×C₉	semidirect
92. C₉	#2380	direct (N × H)

H ≅ G/N

type

2. C₉×#386

C₂

semidirect

3. C₉×#383

C₂

semidirect

7. C₉×#127

C₄

semidirect

17. C₂×D₄×C₉

C₂×C₄

semidirect

22. C₄²×C₉

C₂×C₄

semidirect

23. #2380

C₉

direct (N × H)

40. #386

C₂×C₉

semidirect

41. #383

C₂×C₉

semidirect

60. #127

C₄×C₉

semidirect

79. C₂×D₄

C₂×C₄×C₉

semidirect

84. C₄²

C₂×C₄×C₉

semidirect

92. C₉

#2380

direct (N × H)

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

subgroup	index
C₂×C₉×#127	2
C₉×#386	2
C₉×#383	2
C₃×#2380	3

subgroup

index

C₂×C₉×#127

C₉×#386

C₉×#383

C₃×#2380

Subgroups — C₉×#2380 #11767101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2380 #11767101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2380 #11767101