Group #23765685 — subgroups

Subgroups — #23765685

Order 10112.

120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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	#19098967	C₂	1	1	yes	maximal, characteristic
2	#19098964	C₂	1	1	yes	maximal, characteristic
3	#19098390	C₂	1	1	yes	maximal, characteristic
4	#19098389	C₂	1	1	yes	maximal, characteristic
5	#19098388	C₂	1	1	yes	maximal, characteristic
6	#19098338	C₂	1	1	yes	maximal, characteristic
7	#367×C₇₉	C₂	1	1	yes	maximal, characteristic
8	#14579160	—	2	1	no	—
9	#14579152	—	2	1	no	—
10	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
11	#14579095	C₂²	1	1	yes	characteristic
12	#14579095	C₂²	1	1	yes	characteristic
13	#14579094	—	2	1	no	—
14	#14579092	—	2	1	no	—
15	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	#107×C₇₉	C₂²	1	1	yes	characteristic
18	#107×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₅₈	—	4	1	no	—
20	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
21	C₄⋊Dic₇₉	—	2	1	no	—
22	C₄⋊Dic₇₉	—	2	1	no	—
23	C₄⋊Dic₇₉	—	4	1	no	—
24	Dic₇₉⋊C₄	—	4	1	no	—
25	Dic₇₉⋊C₄	—	4	1	no	—
26	C₄×Dic₇₉	D₄	1	1	yes	characteristic
27	C₇₉⋊C₁₆	Q₈	1	2	yes	complemented
28	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
29	C₄⋊C₄×C₇₉	—	2	1	no	—
30	C₄⋊C₄×C₇₉	—	2	1	no	—
31	C₁₆×C₇₉	Q₈	1	2	yes	complemented
32	C₂×C₄×C₇₉	—	4	1	no	—
33	C₂×C₄×C₇₉	—	4	1	no	—
34	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₉	—	4	1	no	—
36	C₂×Dic₇₉	—	4	1	no	—
37	C₂×Dic₇₉	D₈	1	1	yes	characteristic
38	C₂×Dic₇₉	D₈	1	1	yes	characteristic
39	Dic₁₅₈	—	8	2	no	—
40	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
41	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
42	C₇₉⋊C₈	Q₁₆	1	2	yes	—
43	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
44	C₄×C₇₉	—	8	1	no	—
45	C₄×C₇₉	—	8	1	no	—
46	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
47	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
48	Dic₇₉	—	2	1	no	—
49	Dic₇₉	—	2	1	no	—
50	Dic₇₉	—	8	1	no	—
51	Dic₇₉	—	8	1	no	—
52	C₂×C₇₉	#500	1	1	yes	characteristic
53	C₂×C₇₉	#509	1	1	yes	characteristic
54	C₂×C₇₉	#510	1	1	yes	characteristic
55	#2255	—	79	1	no	maximal, Sylow
56	C₇₉	#2255	1	1	yes	characteristic, complemented, Sylow
57	#500	—	79	1	no	—
58	#499	—	79	1	no	—
59	#367	—	79	1	no	—
60	#367	D₇₉	1	1	yes	characteristic
61	#366	—	79	1	no	—
62	#366	—	79	1	no	—
63	#346	—	79	1	no	—
64	C₄⋊Q₈	—	158	1	no	—
65	#125	—	158	1	no	—
66	C₂×C₁₆	—	79	1	no	—
67	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
68	#107	—	79	1	no	—
69	#107	—	79	1	no	—
70	#107	—	158	1	no	—
71	#107	C₂×D₇₉	1	1	yes	characteristic
72	#107	C₂×D₇₉	1	1	yes	characteristic
73	#106	—	158	1	no	—
74	C₄×C₈	—	79	1	no	—
75	C₂×Q₈	—	316	1	no	—
76	C₂×C₈	—	79	1	no	—
77	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
78	C₄⋊C₄	—	2	1	no	—
79	C₄⋊C₄	—	2	1	no	—
80	C₄⋊C₄	—	316	1	no	—
81	C₄⋊C₄	—	316	1	no	—
82	C₄⋊C₄	—	316	1	no	—
83	C₄⋊C₄	—	158	1	no	—
84	C₄⋊C₄	—	158	1	no	—
85	C₄²	—	79	1	no	—
86	C₁₆	—	79	2	no	—
87	C₁₆	Dic₁₅₈	1	2	yes	complemented
88	Q₈	—	632	2	no	—
89	C₂×C₄	—	4	1	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	—	316	1	no	—
92	C₂×C₄	—	316	1	no	—
93	C₂×C₄	—	79	1	no	—
94	C₂×C₄	—	79	1	no	—
95	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
96	C₈	—	79	2	no	—
97	C₈	Q₈×D₇₉	1	1	yes	characteristic
98	C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
99	C₂²	D₈×D₇₉	1	1	yes	characteristic
100	C₄	—	8	1	no	—
101	C₄	—	8	1	no	—
102	C₄	—	632	1	no	—
103	C₄	—	632	1	no	—
104	C₄	—	158	1	no	—
105	C₄	—	158	1	no	—
106	C₄	#14579160	1	1	yes	characteristic
107	C₄	Q₁₆×D₇₉	1	1	yes	characteristic
108	C₂	#19098967	1	1	yes	characteristic
109	C₂	#19099000	1	1	yes	characteristic
110	C₂	#19099002	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098967

C₂

yes

maximal, characteristic

#19098964

C₂

yes

maximal, characteristic

#19098390

C₂

yes

maximal, characteristic

#19098389

C₂

yes

maximal, characteristic

#19098388

C₂

yes

maximal, characteristic

#19098338

C₂

yes

maximal, characteristic

#367×C₇₉

C₂

yes

maximal, characteristic

#14579160

—

#14579152

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

characteristic

#14579095

C₂²

yes

characteristic

#14579094

—

#14579092

—

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

Q₈

yes

complemented

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

Q₈

yes

complemented

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₂×Dic₇₉

D₈

yes

characteristic

Dic₁₅₈

—

C₈×C₇₉

C₂×Q₈

yes

characteristic

C₈×C₇₉

C₂×Q₈

yes

characteristic

C₇₉⋊C₈

Q₁₆

yes

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄⋊Q₈

yes

characteristic

C₄×C₇₉

C₂×Q₁₆

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

—

—

—

C₄⋊Q₈

—

158

—

#125

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

—

—

—

158

—

#107

C₂×D₇₉

yes

characteristic

#107

C₂×D₇₉

yes

characteristic

#106

—

158

—

C₄×C₈

—

C₂×Q₈

—

316

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

C₁₆

—

C₁₆

Dic₁₅₈

yes

complemented

Q₈

—

632

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₇₉

yes

characteristic

C₈

—

C₈

Q₈×D₇₉

yes

characteristic

C₈

C₂×Dic₁₅₈

yes

characteristic

C₂²

D₈×D₇₉

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

632

—

103

C₄

—

632

—

104

C₄

—

158

—

105

C₄

—

158

—

106

C₄

#14579160

yes

characteristic

107

C₄

Q₁₆×D₇₉

yes

characteristic

108

C₂

#19098967

yes

characteristic

109

C₂

#19099000

yes

characteristic

110

C₂

#19099002

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#367×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₈
hypercenter	#367	D₇₉
hypocenter	C₇₉	#2255
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#367×C₇₉

C₂

socle, prime radical

C₂²×C₇₉

C₂×D₈

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

N	H ≅ G/N	type
27. C₇₉⋊C₁₆	Q₈	semidirect
31. C₁₆×C₇₉	Q₈	semidirect
56. C₇₉	#2255	semidirect
87. C₁₆	Dic₁₅₈	semidirect

H ≅ G/N

type

27. C₇₉⋊C₁₆

Q₈

semidirect

31. C₁₆×C₇₉

Q₈

semidirect

56. C₇₉

#2255

semidirect

87. C₁₆

Dic₁₅₈

semidirect

Subgroups — #23765685

Conjugacy classes of subgroups

Complements