Group #23765281 — subgroups

Subgroups — #23765281

Order 10112.

146 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 61 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	#19098680	C₂	1	2	yes	maximal, complemented
2	#19098393	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098370	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#508×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#14579168	—	2	2	no	—
7	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
8	#14579097	C₂²	1	2	yes	—
9	#14579088	—	2	2	no	—
10	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
11	#135×C₇₉	C₂²	1	2	yes	—
12	Q₃₂×C₇₉	C₄	1	1	yes	characteristic, complemented
13	SD₃₂×C₇₉	C₄	1	2	yes	complemented
14	D₁₆×C₇₉	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
16	#11929608	—	2	2	no	—
17	#11929608	—	4	2	no	—
18	C₂×C₇₉⋊C₈	—	4	2	no	—
19	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
20	C₄×Dic₇₉	D₄	1	1	yes	characteristic
21	C₇₉⋊C₁₆	—	2	1	no	—
22	#41×C₇₉	—	2	2	no	—
23	Q₁₆×C₇₉	C₂×C₄	1	2	yes	—
24	SD₁₆×C₇₉	—	2	2	no	—
25	D₈×C₇₉	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
27	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
29	Q₈×C₇₉	—	2	2	no	—
30	D₄×C₇₉	—	2	2	no	—
31	D₄×C₇₉	—	4	2	no	—
32	C₂×C₄×C₇₉	—	4	2	no	—
33	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₇₉	—	2	1	no	—
35	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
36	C₈×C₇₉	#41	1	1	yes	characteristic
37	C₇₉⋊C₈	—	4	2	no	—
38	C₇₉⋊C₈	D₈	1	1	yes	characteristic
39	C₇₉⋊C₈	D₈	1	1	yes	characteristic
40	C₂²×C₇₉	—	4	2	no	—
41	C₂²×C₇₉	#135	1	1	yes	characteristic
42	C₄×C₇₉	—	4	2	no	—
43	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
44	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
45	Dic₇₉	—	2	2	no	—
46	C₂×C₇₉	—	2	1	no	—
47	C₂×C₇₉	—	8	2	no	—
48	C₂×C₇₉	C₄×D₈	1	1	yes	characteristic
49	#2178	—	79	1	no	maximal, Sylow
50	C₇₉	#2178	1	1	yes	characteristic, complemented, Sylow
51	#508	D₇₉	1	1	yes	characteristic
52	#443	—	79	2	no	—
53	#368	—	79	1	no	—
54	#359	—	79	2	no	—
55	C₄×C₁₆	—	79	1	no	—
56	#135	C₂×D₇₉	1	2	yes	—
57	#131	—	158	2	no	—
58	Q₃₂	Dic₇₉	1	1	yes	characteristic, complemented
59	SD₃₂	Dic₇₉	1	2	yes	complemented
60	D₁₆	Dic₇₉	1	1	yes	characteristic, complemented
61	C₂×C₁₆	—	79	1	no	—
62	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
63	#108	—	79	2	no	—
64	#104	—	158	2	no	—
65	C₄×C₈	—	79	1	no	—
66	#41	—	2	2	no	—
67	Q₁₆	C₂×Dic₇₉	1	2	yes	—
68	SD₁₆	—	2	2	no	—
69	D₈	C₂×Dic₇₉	1	2	yes	—
70	M₁₆	—	316	2	no	—
71	M₁₆	—	158	2	no	—
72	C₂×C₈	—	316	2	no	—
73	C₂×C₈	—	79	1	no	—
74	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
75	C₄²	—	79	1	no	—
76	C₁₆	—	158	1	no	—
77	C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
78	C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
79	Q₈	—	2	2	no	—
80	D₄	—	2	2	no	—
81	D₄	—	4	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	158	1	no	—
84	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
85	C₈	—	316	2	no	—
86	C₈	—	79	1	no	—
87	C₈	—	79	1	no	—
88	C₈	C₂²×Dic₇₉	1	1	yes	characteristic
89	C₈	#11929623	1	1	yes	characteristic
90	C₂²	—	4	2	no	—
91	C₂²	#14579180	1	1	yes	characteristic
92	C₄	—	4	2	no	—
93	C₄	—	158	2	no	—
94	C₄	D₄×Dic₇₉	1	1	yes	characteristic
95	C₄	D₈×D₇₉	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	8	2	no	—
98	C₂	D₈×Dic₇₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098680

C₂

yes

maximal, complemented

#19098393

C₂

yes

maximal, characteristic, complemented

#19098370

C₂

yes

maximal, complemented

C₁₆×Dic₇₉

C₂

yes

maximal, characteristic, complemented

#508×C₇₉

C₂

yes

maximal, characteristic

#14579168

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579097

C₂²

yes

—

#14579088

—

C₈×Dic₇₉

C₂²

yes

characteristic

#135×C₇₉

C₂²

yes

—

Q₃₂×C₇₉

C₄

yes

characteristic, complemented

SD₃₂×C₇₉

C₄

yes

complemented

D₁₆×C₇₉

C₄

yes

characteristic, complemented

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

#41×C₇₉

—

Q₁₆×C₇₉

C₂×C₄

yes

—

SD₁₆×C₇₉

—

D₈×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

C₂×C₄

yes

characteristic

C₁₆×C₇₉

C₂×C₄

yes

characteristic

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₇₉⋊C₈

D₈

yes

characteristic

C₇₉⋊C₈

D₈

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

#135

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₄×D₈

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#508

D₇₉

yes

—

—

—

C₄×C₁₆

—

#135

C₂×D₇₉

yes

—

#131

—

158

—

Q₃₂

Dic₇₉

yes

characteristic, complemented

SD₃₂

Dic₇₉

yes

complemented

D₁₆

Dic₇₉

yes

characteristic, complemented

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#108

—

#104

—

158

—

C₄×C₈

—

#41

—

Q₁₆

C₂×Dic₇₉

yes

—

SD₁₆

—

D₈

C₂×Dic₇₉

yes

—

M₁₆

—

316

—

M₁₆

—

158

—

C₂×C₈

—

316

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄²

—

C₁₆

—

158

—

C₁₆

C₂×Dic₇₉

yes

characteristic

C₁₆

C₂×Dic₇₉

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

D₄×D₇₉

yes

characteristic

C₈

—

316

—

C₈

—

C₈

—

C₈

C₂²×Dic₇₉

yes

characteristic

C₈

#11929623

yes

characteristic

C₂²

—

C₂²

#14579180

yes

characteristic

C₄

—

C₄

—

158

—

C₄

D₄×Dic₇₉

yes

characteristic

C₄

D₈×D₇₉

yes

characteristic

C₂

—

C₂

—

C₂

D₈×Dic₇₉

yes

characteristic

	subgroup	G/H
center	C₄	D₈×D₇₉
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting, prime radical	#508×C₇₉	C₂
socle	C₂×C₇₉	C₄×D₈
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	#508	D₇₉
hypocenter	C₇₉	#2178
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

subgroup

G/H

center

C₄

D₈×D₇₉

commutator

C₈×C₇₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₉

Fitting, prime radical

#508×C₇₉

C₂

socle

C₂×C₇₉

C₄×D₈

cosocle

C₂×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

N	H ≅ G/N	type
1. #19098680	C₂	semidirect
2. #19098393	C₂	semidirect
3. #19098370	C₂	semidirect
4. C₁₆×Dic₇₉	C₂	semidirect
12. Q₃₂×C₇₉	C₄	semidirect
13. SD₃₂×C₇₉	C₄	semidirect
14. D₁₆×C₇₉	C₄	semidirect
50. C₇₉	#2178	semidirect
58. Q₃₂	Dic₇₉	semidirect
59. SD₃₂	Dic₇₉	semidirect
60. D₁₆	Dic₇₉	semidirect

H ≅ G/N

type

1. #19098680

C₂

semidirect

2. #19098393

C₂

semidirect

3. #19098370

C₂

semidirect

4. C₁₆×Dic₇₉

C₂

semidirect

12. Q₃₂×C₇₉

C₄

semidirect

13. SD₃₂×C₇₉

C₄

semidirect

14. D₁₆×C₇₉

C₄

semidirect

50. C₇₉

#2178

semidirect

58. Q₃₂

Dic₇₉

semidirect

59. SD₃₂

Dic₇₉

semidirect

60. D₁₆

Dic₇₉

semidirect

Subgroups — #23765281

Conjugacy classes of subgroups

Complements