Group #23765571 — subgroups

Subgroups — #23765571

Order 10112.

126 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 49 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	#19098961	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098387	C₂	1	2	yes	maximal, complemented
3	#19098384	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098373	C₂	1	2	yes	maximal
5	#443×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#14579161	—	2	1	no	—
7	#14579101	C₂²	1	2	yes	—
8	#14579093	—	2	1	no	—
9	#14579093	C₂²	1	2	yes	—
10	#135×C₇₉	C₂²	1	1	yes	characteristic
11	#131×C₇₉	—	2	1	no	—
12	#108×C₇₉	C₂²	1	1	yes	characteristic
13	#104×C₇₉	—	2	1	no	—
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	4	1	no	—
16	C₄⋊Dic₇₉	—	2	2	no	—
17	C₄⋊Dic₇₉	—	4	1	no	—
18	C₇₉⋊C₁₆	—	2	2	no	—
19	#41×C₇₉	—	2	1	no	—
20	Q₁₆×C₇₉	Q₈	1	1	yes	characteristic, complemented
21	SD₁₆×C₇₉	—	2	1	no	—
22	D₈×C₇₉	Q₈	1	1	yes	characteristic, complemented
23	M₁₆×C₇₉	—	2	1	no	—
24	M₁₆×C₇₉	—	4	1	no	—
25	C₂×C₈×C₇₉	—	4	1	no	—
26	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
28	C₄²×C₇₉	D₄	1	1	yes	characteristic
29	Q₈×C₇₉	—	2	1	no	—
30	D₄×C₇₉	—	2	1	no	—
31	D₄×C₇₉	—	4	1	no	—
32	C₂×C₄×C₇₉	—	2	1	no	—
33	C₂×C₄×C₇₉	—	4	1	no	—
34	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₉	—	4	2	no	—
36	Dic₁₅₈	—	8	2	no	—
37	C₈×C₇₉	—	4	1	no	—
38	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
39	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
40	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
41	C₈×C₇₉	#41	1	1	yes	characteristic
42	C₂²×C₇₉	—	4	1	no	—
43	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
44	C₄×C₇₉	—	2	2	no	—
45	C₄×C₇₉	—	4	1	no	—
46	C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
47	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
48	Dic₇₉	—	8	2	no	—
49	C₂×C₇₉	—	2	1	no	—
50	C₂×C₇₉	—	8	1	no	—
51	C₂×C₇₉	#476	1	1	yes	characteristic
52	#2230	—	79	1	no	maximal, Sylow
53	C₇₉	#2230	1	1	yes	characteristic, complemented, Sylow
54	#498	—	79	1	no	—
55	#443	D₇₉	1	1	yes	characteristic
56	#365	—	79	2	no	—
57	#364	—	79	1	no	—
58	#360	—	79	2	no	—
59	#135	C₂×D₇₉	1	1	yes	characteristic
60	#131	—	2	1	no	—
61	C₄⋊Q₈	—	158	1	no	—
62	M₃₂	—	79	2	no	—
63	#108	C₂×D₇₉	1	1	yes	characteristic
64	#106	—	79	2	no	—
65	#106	—	158	1	no	—
66	#104	—	2	1	no	—
67	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
68	#41	—	2	1	no	—
69	C₂×Q₈	—	316	1	no	—
70	Q₁₆	Dic₁₅₈	1	1	yes	characteristic, complemented
71	SD₁₆	—	2	1	no	—
72	D₈	Dic₁₅₈	1	1	yes	characteristic, complemented
73	M₁₆	—	2	1	no	—
74	M₁₆	—	4	1	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
77	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
78	C₄⋊C₄	—	316	1	no	—
79	C₄⋊C₄	—	158	2	no	—
80	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
81	C₁₆	—	158	2	no	—
82	Q₈	—	2	1	no	—
83	Q₈	—	632	2	no	—
84	D₄	—	2	1	no	—
85	D₄	—	4	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	316	2	no	—
89	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
90	C₈	—	4	1	no	—
91	C₈	#11929612	1	1	yes	characteristic
92	C₈	#11929612	1	1	yes	characteristic
93	C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
94	C₈	#11929624	1	1	yes	characteristic
95	C₂²	—	4	1	no	—
96	C₂²	#14579186	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	4	1	no	—
99	C₄	—	632	2	no	—
100	C₄	#14579140	1	1	yes	characteristic
101	C₄	C₂×#11929612	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	8	1	no	—
104	C₂	#19098853	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098961

C₂

yes

maximal, characteristic, complemented

#19098387

C₂

yes

maximal, complemented

#19098384

C₂

yes

maximal, characteristic, complemented

#19098373

C₂

yes

maximal

#443×C₇₉

C₂

yes

maximal, characteristic

#14579161

—

#14579101

C₂²

yes

—

#14579093

—

#14579093

C₂²

yes

—

#135×C₇₉

C₂²

yes

characteristic

#131×C₇₉

—

#108×C₇₉

C₂²

yes

characteristic

#104×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₇₉⋊C₁₆

—

#41×C₇₉

—

Q₁₆×C₇₉

Q₈

yes

characteristic, complemented

SD₁₆×C₇₉

—

D₈×C₇₉

Q₈

yes

characteristic, complemented

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

SD₁₆

yes

characteristic

C₈×C₇₉

SD₁₆

yes

characteristic

C₈×C₇₉

C₂×Q₈

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₄×C₇₉

C₂×SD₁₆

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#498

—

#443

D₇₉

yes

—

—

—

C₂×D₇₉

yes

characteristic

#131

—

C₄⋊Q₈

—

158

—

M₃₂

—

#108

C₂×D₇₉

yes

characteristic

#106

—

#106

—

158

—

#104

—

C₄×C₈

C₂×D₇₉

yes

characteristic

#41

—

C₂×Q₈

—

316

—

Q₁₆

Dic₁₅₈

yes

characteristic, complemented

SD₁₆

—

D₈

Dic₁₅₈

yes

characteristic, complemented

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄²

C₂²⋊D₇₉

yes

characteristic

C₁₆

—

158

—

Q₈

—

Q₈

—

632

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₈

—

C₈

yes

C₈

yes

C₈

C₂×Dic₁₅₈

yes

characteristic

C₈

#11929624

yes

characteristic

C₂²

—

C₂²

#14579186

yes

characteristic

C₄

—

C₄

—

C₄

—

632

—

100

C₄

#14579140

yes

characteristic

101

C₄

C₂×#11929612

yes

characteristic

102

C₂

—

103

C₂

—

104

C₂

#19098853

yes

characteristic

	subgroup	G/H
center	C₂	#19098853
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#443×C₇₉	C₂
socle	C₂×C₇₉	#476
prime radical	#135×C₇₉	C₂²
hypercenter	#443	D₇₉
hypocenter	C₇₉	#2230
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

subgroup

G/H

center

C₂

#19098853

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#443×C₇₉

C₂

socle

C₂×C₇₉

#476

prime radical

#135×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

N	H ≅ G/N	type
1. #19098961	C₂	semidirect
2. #19098387	C₂	semidirect
3. #19098384	C₂	semidirect
20. Q₁₆×C₇₉	Q₈	semidirect
22. D₈×C₇₉	Q₈	semidirect
53. C₇₉	#2230	semidirect
70. Q₁₆	Dic₁₅₈	semidirect
72. D₈	Dic₁₅₈	semidirect

H ≅ G/N

type

1. #19098961

C₂

semidirect

2. #19098387

C₂

semidirect

3. #19098384

C₂

semidirect

20. Q₁₆×C₇₉

Q₈

semidirect

22. D₈×C₇₉

Q₈

semidirect

53. C₇₉

#2230

semidirect

70. Q₁₆

Dic₁₅₈

semidirect

72. D₈

Dic₁₅₈

semidirect

Subgroups — #23765571

Conjugacy classes of subgroups

Complements