Group #11771454 — subgroups

Subgroups — #11771454

Order 1152.

208 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 34 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	#10592818	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#3708	C₂	1	2	yes	maximal
3	C₂×C₃²×M₁₆	C₄	1	1	yes	characteristic
4	#64135	C₄	1	1	yes	characteristic
5	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
6	C₂×#3708	—	2	2	no	—
7	#63641	—	2	2	no	—
8	#5119	—	6	2	no	—
9	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
10	C₃²×M₁₆	—	4	1	no	—
11	C₂×C₃²×C₈	—	2	1	no	—
12	#3757	—	2	1	no	—
13	C₄⋊(C₃⋊Dic₃)	C₈	1	2	yes	—
14	C₄×C₃⋊Dic₃	—	2	1	no	—
15	C₂×C₃⋊(C₃⋊C₈)	—	4	1	no	—
16	C₂×C₃⋊(C₃⋊C₈)	D₄	1	2	yes	—
17	#3708	—	4	2	no	—
18	#1323	—	9	1	no	maximal, Sylow
19	C₂×C₃×M₁₆	—	2	2	no	—
20	#926	—	6	2	no	—
21	C₂²×C₃⋊C₈	—	6	2	no	—
22	Dic₃⋊C₈	—	6	8	no	—
23	C₂³×C₃²	M₁₆	1	1	yes	characteristic
24	C₂×C₃²×C₄	—	2	1	no	—
25	C₂×C₃²×C₄	—	2	1	no	—
26	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
28	C₂×C₃⋊Dic₃	—	2	2	no	—
29	C₃²×C₈	—	4	1	no	—
30	C₃⋊(C₃⋊C₈)	—	2	2	no	—
31	#424	—	9	1	no	—
32	C₂²⋊C₁₆	—	9	2	no	—
33	C₂²×C₃×C₄	—	2	2	no	—
34	C₃×M₁₆	—	4	4	no	—
35	C₂×C₃×C₈	—	2	4	no	—
36	#217	—	6	4	no	—
37	C₄⋊Dic₃	—	6	4	no	—
38	C₄×Dic₃	—	6	4	no	—
39	C₂×C₃⋊C₈	—	6	4	no	—
40	C₂×C₃⋊C₈	—	12	4	no	—
41	C₂²×C₃²	—	2	1	no	—
42	C₂²×C₃²	—	2	2	no	—
43	C₂²×C₃²	C₂²⋊C₈	1	1	yes	characteristic
44	C₃²×C₄	—	2	1	no	—
45	C₃²×C₄	#99	1	1	yes	characteristic
46	C₃²×C₄	#101	1	1	yes	characteristic
47	C₃⋊Dic₃	—	4	2	no	—
48	C₂×M₁₆	#157	1	1	yes	characteristic
49	C₂²×C₈	—	9	1	no	—
50	#117	—	9	1	no	—
51	C₂×C₁₆	—	18	2	no	—
52	C₄⋊C₈	—	18	2	no	—
53	C₂³×C₃	—	2	2	no	—
54	C₂×C₃×C₄	—	2	4	no	—
55	C₂×C₃×C₄	—	2	4	no	—
56	C₂×C₃×C₄	—	2	2	no	—
57	C₂×C₃×C₄	—	2	2	no	—
58	C₂×Dic₃	—	6	8	no	—
59	C₃×C₈	—	4	4	no	—
60	C₃⋊C₈	—	12	4	no	—
61	C₂×C₃²	—	4	1	no	—
62	C₂×C₃²	#324	1	1	yes	characteristic
63	C₂×C₃²	#350	1	2	yes	—
64	C₂²×C₄	C₂×#157	1	1	yes	characteristic
65	M₁₆	—	4	1	no	—
66	C₂×C₈	—	2	1	no	—
67	C₂×C₈	—	9	2	no	—
68	C₂×C₈	—	36	1	no	—
69	C₄⋊C₄	—	9	2	no	—
70	C₂²⋊C₄	—	18	1	no	—
71	C₄²	—	18	1	no	—
72	C₁₆	—	36	2	no	—
73	C₂²×C₃	—	2	4	no	—
74	C₂²×C₃	—	2	2	no	—
75	C₂²×C₃	—	4	4	no	—
76	C₃×C₄	—	2	4	no	—
77	C₃×C₄	—	2	2	no	—
78	C₃×C₄	—	2	2	no	—
79	Dic₃	—	12	8	no	—
80	C₃²	#1323	1	1	yes	characteristic, complemented, Sylow
81	C₂³	#3788	1	1	yes	characteristic
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	18	2	no	—
85	C₂×C₄	#3787	1	1	yes	characteristic
86	C₂×C₄	C₂²⋊#157	1	1	yes	characteristic
87	C₈	—	4	1	no	—
88	C₈	—	18	2	no	—
89	C₂×C₃	—	2	4	no	—
90	C₂×C₃	—	2	2	no	—
91	C₂×C₃	—	4	4	no	—
92	C₂²	—	2	2	no	—
93	C₂²	—	2	1	no	—
94	C₂²	#63778	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	36	2	no	—
97	C₄	#63780	1	1	yes	characteristic
98	C₄	#63786	1	1	yes	characteristic
99	C₃	—	2	2	no	—
100	C₂	—	4	1	no	—
101	C₂	#10590187	1	2	yes	—
102	C₂	#10590203	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10592818

C₂

yes

maximal, characteristic

C₂²⋊#3708

C₂

yes

maximal

C₂×C₃²×M₁₆

C₄

yes

characteristic

#64135

C₄

yes

characteristic

C₂²×C₃⋊(C₃⋊C₈)

C₂²

yes

—

—

—

C₂²×C₃²×C₄

C₂×C₄

yes

characteristic

C₃²×M₁₆

—

C₂×C₃²×C₈

—

#3757

—

C₄⋊(C₃⋊Dic₃)

C₈

yes

—

C₄×C₃⋊Dic₃

—

C₂×C₃⋊(C₃⋊C₈)

—

C₂×C₃⋊(C₃⋊C₈)

D₄

yes

—

#3708

—

#1323

—

maximal, Sylow

C₂×C₃×M₁₆

—

#926

—

C₂²×C₃⋊C₈

—

Dic₃⋊C₈

—

C₂³×C₃²

M₁₆

yes

characteristic

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂²⋊C₄

yes

characteristic

C₂×C₃²×C₄

C₂×C₈

yes

characteristic

C₂×C₃⋊Dic₃

—

C₃²×C₈

—

C₃⋊(C₃⋊C₈)

—

#424

—

C₂²⋊C₁₆

—

C₂²×C₃×C₄

—

C₃×M₁₆

—

C₂×C₃×C₈

—

#217

—

C₄⋊Dic₃

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

C₂²⋊C₈

yes

characteristic

C₃²×C₄

—

C₃²×C₄

yes

C₃²×C₄

yes

C₃⋊Dic₃

—

C₂×M₁₆

#157

yes

characteristic

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂³×C₃

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

—

C₂×C₃²

#324

yes

characteristic

C₂×C₃²

#350

yes

—

C₂²×C₄

C₂×#157

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

—

Dic₃

—

C₃²

#1323

yes

characteristic, complemented, Sylow

C₂³

#3788

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#3787

yes

characteristic

C₂×C₄

C₂²⋊#157

yes

characteristic

C₈

—

C₈

—

C₂×C₃

—

C₂×C₃

—

C₂×C₃

—

C₂²

—

C₂²

—

C₂²

#63778

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₃

—

100

C₂

—

101

C₂

#10590187

yes

—

102

C₂

#10590203

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#157
commutator	C₂×C₃²×C₄	C₂×C₈
Frattini	C₂²×C₄	C₂×#157
Fitting	C₂×C₃²×M₁₆	C₄
socle	C₂²×C₃²	C₂²⋊C₈
prime radical	C₂³×C₃²	M₁₆
cosocle	C₂²×C₃⋊(C₃⋊C₈)	C₂²
hypercenter	C₂×M₁₆	#157
hypocenter	C₃²	#1323
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₂×C₄

C₂²⋊#157

commutator

C₂×C₃²×C₄

C₂×C₈

Frattini

C₂²×C₄

C₂×#157

Fitting

C₂×C₃²×M₁₆

C₄

socle

C₂²×C₃²

C₂²⋊C₈

prime radical

C₂³×C₃²

M₁₆

cosocle

C₂²×C₃⋊(C₃⋊C₈)

C₂²

C₂×M₁₆

C₃²

G ▷ C₂×C₃²×C₄ ▷ C₂²×C₃² ▷ C₃²

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
80. C₃²	#1323	semidirect

H ≅ G/N

type

80. C₃²

#1323

semidirect

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

subgroup	index
#10592818	2
C₂²⋊#3708	2
#1323	9

subgroup

index

#10592818

C₂²⋊#3708

#1323

Subgroups — #11771454

Conjugacy classes of subgroups

Complements

Maximal subgroups