Group #11773671 — subgroups

Subgroups — C₃×#68049 #11773671

Order 1152.

393 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 393 conjugacy classes of subgroups — too many to draw. Only its 178 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	C₃×#4685	C₂	1	3	yes	maximal
2	C₃²×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4454	C₂	1	3	yes	maximal, complemented
4	C₃×#1454	—	3	1	no	maximal
5	#68049	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
7	C₃²×C₄×C₈	C₂²	1	3	yes	—
8	C₃×(C₂×D₃)⋊C₈	C₄	1	6	yes	—
9	C₃×Dic₃⋊C₈	C₄	1	6	yes	—
10	C₃×C₄×C₃⋊C₈	C₂²	1	3	yes	—
11	C₃×#431	—	3	3	no	—
12	#4685	C₂×C₃	1	3	yes	—
13	C₃×#322	—	3	3	no	—
14	C₃×C₈²	—	2	1	no	—
15	C₃×C₈²	D₃	1	1	yes	characteristic, complemented
16	C₃×C₈²	C₂×C₃	1	1	yes	characteristic, complemented
17	#4454	C₂×C₃	1	3	yes	complemented
18	C₂×C₃×C₄×D₃	C₂×C₄	1	3	yes	—
19	C₂×C₃²×C₈	C₂×C₄	1	6	yes	—
20	C₃²×C₄²	C₂³	1	1	yes	characteristic
21	C₃×C₄×Dic₃	C₂×C₄	1	3	yes	—
22	C₂×C₃×C₃⋊C₈	C₂×C₄	1	6	yes	—
23	#1454	—	3	1	no	Sylow
24	C₂×C₃×C₄²	—	3	1	no	—
25	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
26	C₃×C₄⋊C₈	—	3	6	no	—
27	C₃×C₂²⋊C₈	—	3	6	no	—
28	C₃×C₄×C₈	—	2	3	no	—
29	C₃×C₄×C₈	—	3	3	no	—
30	C₃×C₄×C₈	C₂×D₃	1	3	yes	—
31	C₃×C₄×C₈	C₂²×C₃	1	3	yes	—
32	(C₂×D₃)⋊C₈	C₃×C₄	1	6	yes	—
33	Dic₃⋊C₈	C₃×C₄	1	6	yes	—
34	C₄×C₃⋊C₈	C₂²×C₃	1	3	yes	—
35	C₂²×C₃×D₃	C₄²	1	1	yes	characteristic
36	C₂×C₃²×C₄	C₂²×C₄	1	3	yes	—
37	C₂×C₃×Dic₃	C₄²	1	3	yes	—
38	C₃×C₄×D₃	—	2	6	no	—
39	C₃²×C₈	—	2	6	no	—
40	C₃×C₃⋊C₈	—	2	6	no	—
41	#431	—	3	3	no	—
42	#322	—	3	3	no	—
43	C₈²	C₃×D₃	1	1	yes	characteristic, complemented
44	C₂²×C₃×C₄	—	3	3	no	—
45	C₂×C₄×D₃	C₂×C₃×C₄	1	3	yes	—
46	C₂×C₃×C₈	—	2	6	no	—
47	C₂×C₃×C₈	—	3	6	no	—
48	C₂×C₃×C₈	C₄×D₃	1	6	yes	—
49	C₂×C₃×C₈	C₂×C₃×C₄	1	6	yes	—
50	C₃×C₄²	—	2	1	no	—
51	C₃×C₄²	—	3	3	no	—
52	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
53	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
54	C₄×Dic₃	C₂×C₃×C₄	1	3	yes	—
55	C₂×C₃⋊C₈	C₂×C₃×C₄	1	6	yes	—
56	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₃×D₃	—	2	3	no	—
58	C₃²×C₄	#131	1	6	yes	—
59	C₃×Dic₃	—	2	3	no	—
60	C₂×C₄²	—	3	1	no	—
61	C₄⋊C₈	—	3	6	no	—
62	C₂²⋊C₈	—	3	6	no	—
63	C₄×C₈	—	3	3	no	—
64	C₄×C₈	C₂×C₃×D₃	1	3	yes	—
65	C₂³×C₃	—	3	1	no	—
66	C₂²×D₃	C₃×C₄²	1	1	yes	characteristic
67	C₂×C₃×C₄	—	2	3	no	—
68	C₂×C₃×C₄	—	3	3	no	—
69	C₂×C₃×C₄	—	6	6	no	—
70	C₂×C₃×C₄	C₂×C₄×D₃	1	3	yes	—
71	C₂×C₃×C₄	C₂²×C₃×C₄	1	3	yes	—
72	C₂×Dic₃	C₃×C₄²	1	3	yes	—
73	C₄×D₃	—	2	6	no	—
74	C₃×C₈	—	2	12	no	—
75	C₃×C₈	—	2	6	no	—
76	C₃×C₈	—	2	6	no	—
77	C₃×C₈	—	6	6	no	—
78	C₃⋊C₈	—	2	6	no	—
79	C₂×C₃²	#405	1	3	yes	—
80	C₃×D₃	—	4	1	no	—
81	C₂²×C₄	—	3	3	no	—
82	C₂×C₈	—	3	6	no	—
83	C₂×C₈	C₃×C₄×D₃	1	6	yes	—
84	C₄²	—	3	3	no	—
85	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
86	C₂²×C₃	—	2	1	no	—
87	C₂²×C₃	—	6	3	no	—
88	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
89	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
90	C₂×D₃	—	2	3	no	—
91	C₃×C₄	—	2	6	no	—
92	C₃×C₄	—	6	3	no	—
93	C₃×C₄	#901	1	6	yes	—
94	C₃×C₄	C₃×#131	1	6	yes	—
95	Dic₃	—	2	3	no	—
96	C₃²	#1454	1	1	yes	characteristic, complemented, Sylow
97	C₂³	—	3	1	no	—
98	C₂×C₄	—	3	3	no	—
99	C₂×C₄	—	6	6	no	—
100	C₂×C₄	C₂×C₃×C₄×D₃	1	3	yes	—
101	C₈	—	2	6	no	—
102	C₈	—	6	6	no	—
103	C₂×C₃	—	2	3	no	—
104	C₂×C₃	—	12	1	no	—
105	C₂×C₃	#4689	1	3	yes	—
106	C₂×C₃	C₃×#405	1	3	yes	—
107	D₃	—	4	1	no	—
108	C₂²	—	6	3	no	—
109	C₂²	C₃×C₄²×D₃	1	1	yes	characteristic
110	C₄	—	6	3	no	—
111	C₄	C₃×#901	1	6	yes	—
112	C₃	—	2	1	no	—
113	C₃	#68049	1	1	yes	characteristic, direct product factor
114	C₃	C₃×#1454	1	1	yes	characteristic, complemented
115	C₂	—	12	1	no	—
116	C₂	C₃×#4689	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#4685

C₂

yes

maximal

C₃²×C₈²

C₂

yes

maximal, characteristic, complemented

C₃×#4454

C₂

yes

maximal, complemented

C₃×#1454

—

maximal

#68049

C₃

yes

maximal, characteristic, direct product factor

C₃×C₄²×D₃

C₂²

yes

characteristic

C₃²×C₄×C₈

C₂²

yes

—

C₃×(C₂×D₃)⋊C₈

C₄

yes

—

C₃×Dic₃⋊C₈

C₄

yes

—

C₃×C₄×C₃⋊C₈

C₂²

yes

—

C₃×#431

—

#4685

C₂×C₃

yes

—

C₃×#322

—

C₃×C₈²

—

C₃×C₈²

D₃

yes

characteristic, complemented

C₃×C₈²

C₂×C₃

yes

characteristic, complemented

#4454

C₂×C₃

yes

complemented

C₂×C₃×C₄×D₃

C₂×C₄

yes

—

C₂×C₃²×C₈

C₂×C₄

yes

—

C₃²×C₄²

C₂³

yes

characteristic

C₃×C₄×Dic₃

C₂×C₄

yes

—

C₂×C₃×C₃⋊C₈

C₂×C₄

yes

—

#1454

—

Sylow

C₂×C₃×C₄²

—

C₄²×D₃

C₂²×C₃

yes

characteristic

C₃×C₄⋊C₈

—

C₃×C₂²⋊C₈

—

C₃×C₄×C₈

—

C₃×C₄×C₈

—

C₃×C₄×C₈

C₂×D₃

yes

—

C₃×C₄×C₈

C₂²×C₃

yes

—

(C₂×D₃)⋊C₈

C₃×C₄

yes

—

Dic₃⋊C₈

C₃×C₄

yes

—

C₄×C₃⋊C₈

C₂²×C₃

yes

—

C₂²×C₃×D₃

C₄²

yes

characteristic

C₂×C₃²×C₄

C₂²×C₄

yes

—

C₂×C₃×Dic₃

C₄²

yes

—

C₃×C₄×D₃

—

C₃²×C₈

—

C₃×C₃⋊C₈

—

#431

—

#322

—

C₈²

C₃×D₃

yes

characteristic, complemented

C₂²×C₃×C₄

—

C₂×C₄×D₃

C₂×C₃×C₄

yes

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₄×D₃

yes

—

C₂×C₃×C₈

C₂×C₃×C₄

yes

—

C₃×C₄²

—

C₃×C₄²

—

C₃×C₄²

C₂²×D₃

yes

characteristic

C₃×C₄²

C₂³×C₃

yes

characteristic

C₄×Dic₃

C₂×C₃×C₄

yes

—

C₂×C₃⋊C₈

C₂×C₃×C₄

yes

—

C₂²×C₃²

C₂×C₄²

yes

characteristic

C₂×C₃×D₃

—

C₃²×C₄

#131

yes

—

C₃×Dic₃

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

C₂×C₃×D₃

yes

—

C₂³×C₃

—

C₂²×D₃

C₃×C₄²

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂×C₄×D₃

yes

—

C₂×C₃×C₄

C₂²×C₃×C₄

yes

—

C₂×Dic₃

C₃×C₄²

yes

—

C₄×D₃

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

#405

yes

—

C₃×D₃

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

C₃×C₄×D₃

yes

—

C₄²

—

C₄²

C₂²×C₃×D₃

yes

characteristic

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

C₄²×D₃

yes

characteristic

C₂²×C₃

C₂×C₃×C₄²

yes

characteristic

C₂×D₃

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

#901

yes

—

C₃×C₄

C₃×#131

yes

—

Dic₃

—

C₃²

#1454

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂×C₃×C₄×D₃

yes

—

101

C₈

—

102

C₈

—

103

C₂×C₃

—

104

C₂×C₃

—

105

C₂×C₃

#4689

yes

—

106

C₂×C₃

C₃×#405

yes

—

107

D₃

—

108

C₂²

—

109

C₂²

C₃×C₄²×D₃

yes

characteristic

110

C₄

—

111

C₄

C₃×#901

yes

—

112

C₃

—

113

C₃

#68049

yes

characteristic, direct product factor

114

C₃

C₃×#1454

yes

characteristic, complemented

115

C₂

—

116

C₂

C₃×#4689

yes

—

	subgroup	G/H
center	C₃×C₄²	C₂²×D₃
commutator	C₂²×C₃	C₂×C₃×C₄²
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×C₈²	C₂
socle	C₂²×C₃²	C₂×C₄²
prime radical	C₂²×C₃×D₃	C₄²
cosocle	C₃×C₄²	C₂³×C₃
hypercenter	C₃×C₈²	D₃
hypocenter	C₃	C₃×#1454
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄² ◁ C₃×C₈²

subgroup

G/H

center

C₃×C₄²

C₂²×D₃

commutator

C₂²×C₃

C₂×C₃×C₄²

Frattini

C₄²

C₂²×C₃×D₃

Fitting

C₃²×C₈²

C₂

socle

C₂²×C₃²

C₂×C₄²

prime radical

C₂²×C₃×D₃

C₄²

cosocle

C₃×C₄²

C₂³×C₃

hypercenter

C₃×C₈²

D₃

C₃

G ▷ C₂²×C₃ ▷ C₃

C₁ ◁ C₃×C₄² ◁ C₃×C₈²

N	H ≅ G/N	type
2. C₃²×C₈²	C₂	semidirect
3. C₃×#4454	C₂	semidirect
5. #68049	C₃	direct (N × H)
15. C₃×C₈²	D₃	semidirect
16. C₃×C₈²	C₂×C₃	semidirect
17. #4454	C₂×C₃	semidirect
43. C₈²	C₃×D₃	semidirect
96. C₃²	#1454	semidirect
113. C₃	#68049	direct (N × H)
114. C₃	C₃×#1454	semidirect

H ≅ G/N

type

2. C₃²×C₈²

C₂

semidirect

3. C₃×#4454

C₂

semidirect

5. #68049

C₃

direct (N × H)

15. C₃×C₈²

D₃

semidirect

16. C₃×C₈²

C₂×C₃

semidirect

17. #4454

C₂×C₃

semidirect

43. C₈²

C₃×D₃

semidirect

96. C₃²

#1454

semidirect

113. C₃

#68049

direct (N × H)

114. C₃

C₃×#1454

semidirect

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

subgroup	index
C₃×#4685	2
C₃²×C₈²	2
C₃×#4454	2
C₃×#1454	3
#68049	3

subgroup

index

C₃²×C₈²

Subgroups — C₃×#68049 #11773671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#68049 #11773671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#68049 #11773671