Group #11899426 — subgroups

Subgroups — #11899426

Order 1152.

442 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 187 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×#64289	C₂	1	1	yes	maximal, characteristic
2	#10596487	C₂	1	8	yes	maximal, complemented
3	#10596481	C₂	1	6	yes	maximal, complemented
4	C₂×#3832	C₄	1	1	yes	characteristic
5	#64289	C₄	1	4	yes	—
6	#64289	C₂²	1	4	yes	—
7	C₂×#3788	C₄	1	3	yes	—
8	C₂×#3787	C₂²	1	3	yes	—
9	#64218	C₂²	1	4	yes	—
10	#64214	C₂²	1	12	yes	complemented
11	#64213	C₂²	1	12	yes	complemented
12	C₂×C₃²×Q₈	C₈	1	1	yes	characteristic
13	#3832	C₈	1	4	yes	—
14	#3832	C₂×C₄	1	4	yes	—
15	C₂×C₄⋊(C₃⋊D₃)	C₈	1	3	yes	—
16	C₂×C₄×C₃⋊D₃	C₂×C₄	1	3	yes	—
17	C₂×#622	C₂×C₄	1	3	yes	—
18	C₂×#622	C₂³	1	1	yes	characteristic
19	#3788	C₂×C₄	1	12	yes	—
20	#3787	C₂×C₄	1	6	yes	—
21	#3787	C₂³	1	6	yes	—
22	#3771	C₂³	1	8	yes	—
23	#3407	—	9	1	no	maximal, Sylow
24	C₂×#239	—	12	1	no	—
25	C₂²×C₃⋊D₃	C₂×C₈	1	3	yes	—
26	C₃²×Q₈	C₂×C₈	1	4	yes	—
27	C₂×C₃²×C₄	C₂×C₈	1	3	yes	—
28	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
29	C₄⋊(C₃⋊D₃)	C₂×C₈	1	12	yes	—
30	C₄×C₃⋊D₃	C₂×C₈	1	6	yes	—
31	C₄×C₃⋊D₃	C₂²×C₄	1	6	yes	—
32	#622	C₂²×C₄	1	1	yes	characteristic
33	#622	C₂²×C₄	1	6	yes	—
34	#622	C₂⁴	1	1	yes	characteristic
35	C₂×#131	—	9	1	no	—
36	#504	—	9	8	no	—
37	C₂×M₃₂	—	9	6	no	—
38	C₂×C₃×Q₈	—	4	1	no	—
39	#239	—	12	4	no	—
40	#239	—	12	4	no	—
41	C₂×D₁₂	—	12	3	no	—
42	C₂×C₄×D₃	—	12	3	no	—
43	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
44	C₂×C₃⋊D₃	—	4	3	no	—
45	C₂×C₃⋊D₃	C₂²×C₈	1	6	yes	—
46	C₃²×C₄	C₂²×C₈	1	6	yes	—
47	C₃⋊Dic₃	C₂²×C₈	1	1	yes	characteristic
48	C₃⋊Dic₃	C₂³×C₄	1	1	yes	characteristic
49	C₂×#41	—	9	1	no	—
50	#131	—	9	4	no	—
51	#131	—	9	4	no	—
52	C₂×M₁₆	—	9	3	no	—
53	C₂²×C₈	—	9	3	no	—
54	M₃₂	—	9	12	no	—
55	M₃₂	—	9	4	no	—
56	C₂×C₁₆	—	9	12	no	—
57	C₂²×D₃	—	12	3	no	—
58	C₃×Q₈	—	4	4	no	—
59	C₂×C₃×C₄	—	4	3	no	—
60	C₂×Dic₃	—	12	1	no	—
61	D₁₂	—	12	12	no	—
62	C₄×D₃	—	12	6	no	—
63	C₄×D₃	—	12	6	no	—
64	C₂×C₃²	—	2	1	no	—
65	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
66	C₃⋊D₃	—	2	6	no	—
67	#41	—	9	4	no	—
68	#41	—	9	4	no	—
69	C₂×Q₈	AGL(1,𝔽₉)	1	1	yes	characteristic
70	C₂×D₄	—	9	3	no	—
71	C₂²×C₄	—	9	3	no	—
72	M₁₆	—	9	12	no	—
73	C₂×C₈	—	9	6	no	—
74	C₂×C₈	—	9	1	no	—
75	C₂×C₈	—	9	3	no	—
76	C₂×C₈	—	9	6	no	—
77	C₁₆	—	9	8	no	—
78	C₂²×C₃	—	4	1	no	—
79	C₂×D₃	—	12	6	no	—
80	C₂×D₃	—	24	6	no	—
81	C₃×C₄	—	4	6	no	—
82	Dic₃	—	12	1	no	—
83	Dic₃	—	12	1	no	—
84	C₃²	#3407	1	1	yes	characteristic, complemented, Sylow
85	C₂³	—	9	3	no	—
86	Q₈	C₂×AGL(1,𝔽₉)	1	4	yes	—
87	D₄	—	9	12	no	—
88	C₂×C₄	—	9	1	no	—
89	C₂×C₄	—	9	6	no	—
90	C₂×C₄	—	9	6	no	—
91	C₂×C₄	C₂×AGL(1,𝔽₉)	1	3	yes	—
92	C₈	—	9	1	no	—
93	C₈	—	9	1	no	—
94	C₈	—	9	6	no	—
95	C₂×C₃	—	4	2	no	—
96	C₂×C₃	—	4	1	no	—
97	D₃	—	24	6	no	—
98	C₂²	—	9	6	no	—
99	C₂²	—	36	3	no	—
100	C₂²	C₂²×AGL(1,𝔽₉)	1	1	yes	characteristic
101	C₄	—	9	1	no	—
102	C₄	—	9	1	no	—
103	C₄	C₂²×AGL(1,𝔽₉)	1	6	yes	—
104	C₃	—	4	1	no	—
105	C₂	—	2	1	no	—
106	C₂	—	18	6	no	—
107	C₂	C₂³×AGL(1,𝔽₉)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#64289

C₂

yes

maximal, characteristic

#10596487

C₂

yes

maximal, complemented

#10596481

C₂

yes

maximal, complemented

C₂×#3832

C₄

yes

characteristic

#64289

C₄

yes

—

#64289

C₂²

yes

—

C₂×#3788

C₄

yes

—

C₂×#3787

C₂²

yes

—

#64218

C₂²

yes

—

#64214

C₂²

yes

complemented

#64213

C₂²

yes

complemented

C₂×C₃²×Q₈

C₈

yes

characteristic

#3832

C₈

yes

—

#3832

C₂×C₄

yes

—

C₂×C₄⋊(C₃⋊D₃)

C₈

yes

—

C₂×C₄×C₃⋊D₃

C₂×C₄

yes

—

C₂×#622

C₂×C₄

yes

—

C₂×#622

C₂³

yes

characteristic

#3788

C₂×C₄

yes

—

#3787

C₂×C₄

yes

—

#3787

C₂³

yes

—

#3771

C₂³

yes

—

#3407

—

maximal, Sylow

C₂×#239

—

C₂²×C₃⋊D₃

C₂×C₈

yes

—

C₃²×Q₈

C₂×C₈

yes

—

C₂×C₃²×C₄

C₂×C₈

yes

—

C₂×C₃⋊Dic₃

C₂²×C₄

yes

characteristic

C₄⋊(C₃⋊D₃)

C₂×C₈

yes

—

C₄×C₃⋊D₃

C₂×C₈

yes

—

C₄×C₃⋊D₃

C₂²×C₄

yes

—

#622

C₂²×C₄

yes

characteristic

#622

C₂²×C₄

yes

—

#622

C₂⁴

yes

characteristic

C₂×#131

—

#504

—

C₂×M₃₂

—

C₂×C₃×Q₈

—

#239

—

#239

—

C₂×D₁₂

—

C₂×C₄×D₃

—

C₂²×C₃²

C₂²×C₈

yes

characteristic

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

C₂²×C₈

yes

—

C₃²×C₄

C₂²×C₈

yes

—

C₃⋊Dic₃

C₂²×C₈

yes

characteristic

C₃⋊Dic₃

C₂³×C₄

yes

characteristic

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂²×D₃

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×Dic₃

—

D₁₂

—

C₄×D₃

—

C₄×D₃

—

C₂×C₃²

—

C₂×C₃²

C₂³×C₈

yes

characteristic

C₃⋊D₃

—

#41

—

#41

—

C₂×Q₈

AGL(1,𝔽₉)

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₁₆

—

C₂²×C₃

—

C₂×D₃

—

C₂×D₃

—

C₃×C₄

—

Dic₃

—

Dic₃

—

C₃²

#3407

yes

characteristic, complemented, Sylow

C₂³

—

Q₈

C₂×AGL(1,𝔽₉)

yes

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×AGL(1,𝔽₉)

yes

—

C₈

—

C₈

—

C₈

—

C₂×C₃

—

C₂×C₃

—

D₃

—

C₂²

—

C₂²

—

100

C₂²

C₂²×AGL(1,𝔽₉)

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

C₂²×AGL(1,𝔽₉)

yes

—

104

C₃

—

105

C₂

—

106

C₂

—

107

C₂

C₂³×AGL(1,𝔽₉)

yes

characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×AGL(1,𝔽₉)
commutator, socle	C₂×C₃²	C₂³×C₈
Fitting	C₂×C₃²×Q₈	C₈
prime radical	C₂×#3832	C₄
cosocle	#622	C₂⁴
hypercenter	C₂×Q₈	AGL(1,𝔽₉)
hypocenter	C₃²	#3407
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₂×Q₈

subgroup

G/H

center, Frattini

C₂

C₂³×AGL(1,𝔽₉)

commutator, socle

C₂×C₃²

C₂³×C₈

Fitting

C₂×C₃²×Q₈

C₈

C₄

C₂⁴

C₂×Q₈

C₃²

G ▷ C₂×C₃² ▷ C₃²

C₁ ◁ C₂ ◁ C₂×Q₈

N	H ≅ G/N	type
2. #10596487	C₂	semidirect
3. #10596481	C₂	semidirect
10. #64214	C₂²	semidirect
11. #64213	C₂²	semidirect
84. C₃²	#3407	semidirect

H ≅ G/N

type

2. #10596487

C₂

semidirect

3. #10596481

C₂

semidirect

10. #64214

C₂²

semidirect

11. #64213

C₂²

semidirect

84. C₃²

#3407

semidirect

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

subgroup	index
C₂×#64289	2
#10596487	2
#10596481	2
#3407	9

subgroup

index

Subgroups — #11899426

Conjugacy classes of subgroups

Complements

Maximal subgroups