Group #11768881 — subgroups

Subgroups — C₃²×#1832 #11768881

Order 1152.

648 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 360 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×C₃²×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₃²×#376	C₂	1	1	yes	maximal, characteristic
3	C₃²×#336	C₂	1	4	yes	maximal
4	C₃×#1832	C₃	1	4	yes	maximal, direct product factor
5	C₂²×C₃²×C₈	C₂²	1	4	yes	—
6	C₂×C₃²×C₄²	C₂²	1	2	yes	—
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₃²×C₄⋊C₈	—	2	4	no	—
9	C₃²×#95	C₄	1	4	yes	—
10	C₂×C₃×C₄⋊C₈	C₂×C₃	1	8	yes	—
11	C₃×#376	C₂×C₃	1	4	yes	—
12	C₃×#336	C₂×C₃	1	16	yes	—
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	C₂×C₃²×C₈	—	2	4	no	—
17	C₂×C₃²×C₈	—	2	8	no	—
18	C₃²×C₄²	—	2	4	no	—
19	C₃²×C₄²	D₄	1	2	yes	—
20	C₃²×C₄²	Q₈	1	2	yes	—
21	#1832	C₃²	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₃×C₈	C₂²×C₃	1	16	yes	—
23	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	—
24	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
25	C₃×C₄⋊C₈	—	2	16	no	—
26	C₃×#95	C₃×C₄	1	16	yes	—
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	C₃²×C₈	—	4	4	no	—
36	C₂×C₄⋊C₈	C₂×C₃²	1	2	yes	—
37	#376	C₂×C₃²	1	1	yes	characteristic
38	#336	C₂×C₃²	1	4	yes	—
39	C₂²×C₃×C₄	C₂×C₃×C₄	1	16	yes	—
40	C₂²×C₃×C₄	C₂×C₃×C₄	1	8	yes	—
41	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
42	C₂×C₃×C₈	—	2	16	no	—
43	C₂×C₃×C₈	—	2	32	no	—
44	C₃×C₄²	—	2	16	no	—
45	C₃×C₄²	C₃×D₄	1	8	yes	—
46	C₃×C₄²	C₃×Q₈	1	8	yes	—
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	C₂²×C₃²	1	4	yes	—
55	C₂×C₄²	C₂²×C₃²	1	2	yes	—
56	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
57	C₄⋊C₈	—	2	4	no	—
58	#95	C₃²×C₄	1	4	yes	—
59	C₂³×C₃	C₂²×C₃×C₄	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	C₃×C₄⋊C₄	1	16	yes	—
64	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
65	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
66	C₂×C₃×C₄	C₃×#41	1	16	yes	—
67	C₃×C₈	—	4	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×C₃²×C₄	1	4	yes	—
72	C₂²×C₄	C₂×C₃²×C₄	1	2	yes	—
73	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
74	C₂×C₈	—	2	4	no	—
75	C₂×C₈	—	2	8	no	—
76	C₄²	—	2	4	no	—
77	C₄²	C₃²×D₄	1	2	yes	—
78	C₄²	C₃²×Q₈	1	2	yes	—
79	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
80	C₂²×C₃	C₃×#117	1	8	yes	—
81	C₂²×C₃	C₃×#131	1	16	yes	—
82	C₃×C₄	—	2	16	no	—
83	C₃×C₄	—	4	16	no	—
84	C₃×C₄	C₃×#124	1	8	yes	—
85	C₃×C₄	C₃×#125	1	8	yes	—
86	C₃²	#1832	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³	C₂²×C₃²×C₄	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	C₃²×C₄⋊C₄	1	4	yes	—
92	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
93	C₂×C₄	C₂×C₃²×Q₈	1	1	yes	characteristic
94	C₂×C₄	C₃²×#41	1	4	yes	—
95	C₈	—	4	4	no	—
96	C₂×C₃	C₃×#382	1	4	yes	—
97	C₂×C₃	C₃×#424	1	8	yes	—
98	C₂×C₃	C₃×#433	1	16	yes	—
99	C₂²	C₂×C₃²×C₄⋊C₄	1	1	yes	characteristic
100	C₂²	C₃²×#117	1	2	yes	—
101	C₂²	C₃²×#131	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	4	4	no	—
104	C₄	C₃²×#124	1	2	yes	—
105	C₄	C₃²×#125	1	2	yes	—
106	C₃	C₃×#1832	1	4	yes	direct product factor
107	C₂	C₃²×#382	1	1	yes	characteristic
108	C₂	C₃²×#424	1	2	yes	—
109	C₂	C₃²×#433	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃²×C₄⋊C₈

C₂

yes

maximal

C₃²×#376

C₂

yes

maximal, characteristic

C₃²×#336

C₂

yes

maximal

C₃×#1832

C₃

yes

maximal, direct product factor

C₂²×C₃²×C₈

C₂²

yes

—

C₂×C₃²×C₄²

C₂²

yes

—

C₂×C₃²×C₄²

C₂²

yes

characteristic

C₃²×C₄⋊C₈

—

C₃²×#95

C₄

yes

—

C₂×C₃×C₄⋊C₈

C₂×C₃

yes

—

C₃×#376

C₂×C₃

yes

—

C₃×#336

C₂×C₃

yes

—

C₂²×C₃²×C₄

C₂×C₄

yes

—

C₂²×C₃²×C₄

C₂×C₄

yes

—

C₂²×C₃²×C₄

C₂³

yes

characteristic

C₂×C₃²×C₈

—

C₂×C₃²×C₈

—

C₃²×C₄²

—

C₃²×C₄²

D₄

yes

—

C₃²×C₄²

Q₈

yes

—

#1832

C₃²

yes

characteristic, direct product factor, Sylow

C₂²×C₃×C₈

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

—

C₃×C₄⋊C₈

—

C₃×#95

C₃×C₄

yes

—

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

—

C₃²×C₈

—

C₂×C₄⋊C₈

C₂×C₃²

yes

—

#376

C₂×C₃²

yes

characteristic

#336

C₂×C₃²

yes

—

C₂²×C₃×C₄

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₃×C₄²

—

C₃×C₄²

C₃×D₄

yes

—

C₃×C₄²

C₃×Q₈

yes

—

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

C₂²×C₃²

yes

—

C₂×C₄²

C₂²×C₃²

yes

—

C₂×C₄²

C₂²×C₃²

yes

characteristic

C₄⋊C₈

—

#95

C₃²×C₄

yes

—

C₂³×C₃

C₂²×C₃×C₄

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₃×C₄⋊C₄

yes

—

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

C₂×C₃×C₄

C₂×C₃×Q₈

yes

—

C₂×C₃×C₄

C₃×#41

yes

—

C₃×C₈

—

C₂×C₃²

#382

yes

characteristic

C₂×C₃²

#424

yes

—

C₂×C₃²

#433

yes

—

C₂²×C₄

C₂×C₃²×C₄

yes

—

C₂²×C₄

C₂×C₃²×C₄

yes

—

C₂²×C₄

C₂³×C₃²

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

C₃²×D₄

yes

—

C₄²

C₃²×Q₈

yes

—

C₂²×C₃

C₂×C₃×C₄⋊C₄

yes

—

C₂²×C₃

C₃×#117

yes

—

C₂²×C₃

C₃×#131

yes

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

C₃×#124

yes

—

C₃×C₄

C₃×#125

yes

—

C₃²

#1832

yes

characteristic, direct product factor, Sylow

C₂³

C₂²×C₃²×C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₃²×C₄⋊C₄

yes

—

C₂×C₄

C₂×C₃²×D₄

yes

characteristic

C₂×C₄

C₂×C₃²×Q₈

yes

characteristic

C₂×C₄

C₃²×#41

yes

—

C₈

—

C₂×C₃

C₃×#382

yes

—

C₂×C₃

C₃×#424

yes

—

C₂×C₃

C₃×#433

yes

—

C₂²

C₂×C₃²×C₄⋊C₄

yes

characteristic

100

C₂²

C₃²×#117

yes

—

101

C₂²

C₃²×#131

yes

—

102

C₄

—

103

C₄

—

104

C₄

C₃²×#124

yes

—

105

C₄

C₃²×#125

yes

—

106

C₃

C₃×#1832

yes

direct product factor

107

C₂

C₃²×#382

yes

characteristic

108

C₂

C₃²×#424

yes

—

109

C₂

C₃²×#433

yes

—

	subgroup	G/H
center	C₂²×C₃²×C₄	C₂³
commutator	C₂³	C₂²×C₃²×C₄
Frattini, cosocle	C₂²×C₄	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₃²×C₄ ◁ G

subgroup

G/H

center

C₂²×C₃²×C₄

C₂³

commutator

C₂³

C₂²×C₃²×C₄

Frattini, cosocle

C₂²×C₄

C₂³×C₃²

socle, prime radical

C₂³×C₃²

C₂²×C₄

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂²×C₃²×C₄ ◁ G

N	H ≅ G/N	type
4. C₃×#1832	C₃	direct (N × H)
21. #1832	C₃²	direct (N × H)
86. C₃²	#1832	direct (N × H)
106. C₃	C₃×#1832	direct (N × H)

H ≅ G/N

type

4. C₃×#1832

C₃

direct (N × H)

21. #1832

C₃²

direct (N × H)

86. C₃²

#1832

direct (N × H)

106. C₃

C₃×#1832

direct (N × H)

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

subgroup	index
C₂×C₃²×C₄⋊C₈	2
C₃²×#376	2
C₃²×#336	2
C₃×#1832	3

subgroup

index

C₂×C₃²×C₄⋊C₈

C₃²×#376

C₃²×#336

C₃×#1832

Subgroups — C₃²×#1832 #11768881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C32×#1832 #11768881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1832 #11768881