Group #10593743 — subgroups

Subgroups — #10593743

Order 576.

190 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 52 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×#3792	C₂	1	1	yes	maximal, characteristic
2	C₂²×#622	C₂	1	1	yes	maximal, characteristic
3	#64086	C₂	1	1	yes	maximal, characteristic
4	#63779	C₂	1	2	yes	maximal, complemented
5	C₄⋊#622	C₂	1	2	yes	maximal, complemented
6	C₂²×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
7	#3792	—	2	2	no	—
8	C₂×#622	—	2	2	no	—
9	C₂×#622	C₂²	1	1	yes	characteristic
10	C₂×#622	C₂²	1	2	yes	—
11	C₂×#622	C₂²	1	1	yes	characteristic
12	C₃²×C₂²⋊C₄	C₄	1	1	yes	characteristic
13	#3757	C₄	1	1	yes	characteristic
14	#3750	C₄	1	2	yes	—
15	C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
16	#877	—	6	2	no	—
17	C₂³×C₃²	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃²×C₄	C₂×C₄	1	2	yes	—
19	C₂×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
20	C₂×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₃⋊Dic₃	D₄	1	2	yes	—
22	C₂×C₃⋊Dic₃	Q₈	1	2	yes	—
23	C₂×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
24	#622	—	2	2	no	—
25	#622	—	2	1	no	—
26	#622	—	2	1	no	—
27	#424	—	9	1	no	maximal, Sylow
28	C₂²×Dic₃	—	6	2	no	—
29	C₃×C₂²⋊C₄	—	2	2	no	—
30	#217	—	6	2	no	—
31	Dic₃⋊C₄	—	6	4	no	—
32	C₄×Dic₃	—	6	4	no	—
33	C₂²×C₃²	—	2	2	no	—
34	C₂²×C₃²	C₄⋊C₄	1	2	yes	—
35	C₂²×C₃²	C₂²×C₄	1	1	yes	characteristic
36	C₃²×C₄	—	2	2	no	—
37	C₃⋊Dic₃	—	2	2	no	—
38	C₃⋊Dic₃	C₄⋊C₄	1	2	yes	—
39	C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
40	C₃⋊Dic₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×M₁₆	—	9	1	no	—
42	C₂²×C₈	—	9	1	no	—
43	#117	—	9	1	no	—
44	C₄⋊C₈	—	9	2	no	—
45	C₄⋊C₈	—	9	2	no	—
46	C₂³×C₃	—	2	2	no	—
47	C₂×C₃×C₄	—	2	4	no	—
48	C₂×Dic₃	—	6	2	no	—
49	C₂×Dic₃	—	6	4	no	—
50	C₂×Dic₃	—	6	4	no	—
51	C₂×Dic₃	—	6	2	no	—
52	C₂×Dic₃	—	6	4	no	—
53	C₂×C₃²	—	2	2	no	—
54	C₂×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₃²	#131	1	2	yes	—
56	C₂²×C₄	—	9	1	no	—
57	M₁₆	—	18	2	no	—
58	C₂×C₈	—	9	2	no	—
59	C₂×C₈	—	9	1	no	—
60	C₂×C₈	—	9	1	no	—
61	C₂×C₈	—	18	2	no	—
62	C₄⋊C₄	—	9	2	no	—
63	C₂²⋊C₄	—	9	1	no	—
64	C₂²⋊C₄	#157	1	1	yes	characteristic
65	C₄²	—	9	2	no	—
66	C₂²×C₃	—	2	2	no	—
67	C₂²×C₃	—	2	4	no	—
68	C₂²×C₃	—	4	4	no	—
69	C₃×C₄	—	4	4	no	—
70	Dic₃	—	6	4	no	—
71	Dic₃	—	6	2	no	—
72	Dic₃	—	6	2	no	—
73	Dic₃	—	12	4	no	—
74	C₃²	#424	1	1	yes	characteristic, complemented, Sylow
75	C₂³	C₂×#157	1	1	yes	characteristic
76	C₂×C₄	—	9	1	no	—
77	C₂×C₄	—	9	1	no	—
78	C₂×C₄	—	9	2	no	—
79	C₂×C₄	—	9	2	no	—
80	C₂×C₄	—	9	2	no	—
81	C₂×C₄	C₂×#157	1	2	yes	—
82	C₈	—	18	2	no	—
83	C₈	—	18	1	no	—
84	C₈	—	18	1	no	—
85	C₂×C₃	—	2	2	no	—
86	C₂×C₃	—	2	4	no	—
87	C₂×C₃	—	4	4	no	—
88	C₂²	—	2	2	no	—
89	C₂²	C₄⋊#157	1	2	yes	—
90	C₂²	C₂²×#157	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	9	1	no	—
93	C₄	—	9	1	no	—
94	C₄	—	9	2	no	—
95	C₄	—	18	2	no	—
96	C₃	—	2	2	no	—
97	C₂	—	2	2	no	—
98	C₂	C₂×C₄⋊#157	1	1	yes	characteristic
99	C₂	#64287	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#3792

C₂

yes

maximal, characteristic

C₂²×#622

C₂

yes

maximal, characteristic

#64086

C₂

yes

maximal, characteristic

#63779

C₂

yes

maximal, complemented

C₄⋊#622

C₂

yes

maximal, complemented

C₂²×C₃⋊Dic₃

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#622

C₂²

yes

—

C₂×#622

C₂²

yes

characteristic

C₃²×C₂²⋊C₄

C₄

yes

characteristic

#3757

C₄

yes

characteristic

#3750

C₄

yes

—

C₄×C₃⋊Dic₃

C₂²

yes

—

#877

—

C₂³×C₃²

C₂×C₄

yes

characteristic

C₂×C₃²×C₄

C₂×C₄

yes

—

C₂×C₃⋊Dic₃

C₂×C₄

yes

—

C₂×C₃⋊Dic₃

C₂×C₄

yes

characteristic

C₂×C₃⋊Dic₃

D₄

yes

—

C₂×C₃⋊Dic₃

Q₈

yes

—

C₂×C₃⋊Dic₃

C₂³

yes

—

—

—

—

C₂²×Dic₃

—

C₃×C₂²⋊C₄

—

#217

—

Dic₃⋊C₄

—

C₄×Dic₃

—

C₂²×C₃²

—

C₂²×C₃²

C₄⋊C₄

yes

—

C₂²×C₃²

C₂²×C₄

yes

characteristic

C₃²×C₄

—

C₃⋊Dic₃

—

C₃⋊Dic₃

C₄⋊C₄

yes

—

C₃⋊Dic₃

C₂×D₄

yes

characteristic

C₃⋊Dic₃

C₂×Q₈

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂³×C₃

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×C₃²

—

C₂×C₃²

C₂×C₄⋊C₄

yes

characteristic

C₂×C₃²

#131

yes

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

#157

yes

characteristic

C₄²

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₃×C₄

—

Dic₃

—

Dic₃

—

Dic₃

—

Dic₃

—

C₃²

#424

yes

characteristic, complemented, Sylow

C₂³

C₂×#157

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#157

yes

—

C₈

—

C₈

—

C₈

—

C₂×C₃

—

C₂×C₃

—

C₂×C₃

—

C₂²

—

C₂²

C₄⋊#157

yes

—

C₂²

C₂²×#157

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₃

—

C₂

—

C₂

C₂×C₄⋊#157

yes

characteristic

C₂

#64287

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#157
commutator, socle	C₂²×C₃²	C₂²×C₄
Fitting	C₃²×C₂²⋊C₄	C₄
prime radical	C₂³×C₃²	C₂×C₄
cosocle	C₂×C₃⋊Dic₃	C₂³
hypercenter	C₂²⋊C₄	#157
hypocenter	C₃²	#424
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂²

C₂²×#157

commutator, socle

C₂²×C₃²

C₂²×C₄

Fitting

C₃²×C₂²⋊C₄

C₄

prime radical

C₂³×C₃²

C₂×C₄

cosocle

C₂×C₃⋊Dic₃

C₂³

C₂²⋊C₄

C₃²

G ▷ C₂²×C₃² ▷ C₃²

C₁ ◁ C₂² ◁ C₂²⋊C₄

N	H ≅ G/N	type
4. #63779	C₂	semidirect
5. C₄⋊#622	C₂	semidirect
74. C₃²	#424	semidirect

H ≅ G/N

type

4. #63779

C₂

semidirect

5. C₄⋊#622

C₂

semidirect

74. C₃²

#424

semidirect

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

subgroup	index
C₂×#3792	2
C₂²×#622	2
#64086	2
#63779	2
C₄⋊#622	2
#424	9

subgroup

index

C₂²×#622

Subgroups — #10593743

Conjugacy classes of subgroups

Complements

Maximal subgroups