Group #23765540 — subgroups

Subgroups — #23765540

Order 10112.

130 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 51 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	Q₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic
3	#19098391	C₂	1	1	yes	maximal, characteristic
4	#19098390	C₂	1	1	yes	maximal, characteristic
5	Dic₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	#19098367	C₂	1	1	yes	maximal, characteristic
7	#358×C₇₉	C₂	1	1	yes	maximal, characteristic
8	#14579160	—	2	1	no	—
9	Q₈×Dic₇₉	—	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	#14579085	—	2	1	no	—
15	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×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	C₄×Dic₇₉	—	4	1	no	—
26	C₄×Dic₇₉	D₄	1	1	yes	characteristic
27	C₇₉⋊C₁₆	—	2	1	no	—
28	C₂×Q₈×C₇₉	—	2	1	no	—
29	Q₁₆×C₇₉	—	2	1	no	—
30	Q₁₆×C₇₉	Q₈	1	2	yes	complemented
31	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
32	C₄⋊C₄×C₇₉	—	2	1	no	—
33	C₁₆×C₇₉	—	2	1	no	—
34	Q₈×C₇₉	—	2	2	no	—
35	Q₈×C₇₉	—	4	1	no	—
36	C₂×C₄×C₇₉	—	4	1	no	—
37	C₂×C₄×C₇₉	—	4	1	no	—
38	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₇₉	—	4	1	no	—
40	C₂×Dic₇₉	—	4	1	no	—
41	C₂×Dic₇₉	D₈	1	1	yes	characteristic
42	C₂×Dic₇₉	D₈	1	1	yes	characteristic
43	Dic₁₅₈	—	8	2	no	—
44	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₇₉	#41	1	1	yes	characteristic
46	C₇₉⋊C₈	—	2	1	no	—
47	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
48	C₄×C₇₉	—	4	2	no	—
49	C₄×C₇₉	—	8	1	no	—
50	C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
51	C₄×C₇₉	#137	1	1	yes	characteristic
52	Dic₇₉	—	2	1	no	—
53	Dic₇₉	—	8	1	no	—
54	Dic₇₉	—	8	1	no	—
55	Dic₇₉	SD₃₂	1	2	yes	—
56	C₂×C₇₉	#474	1	1	yes	characteristic
57	C₂×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
58	C₂×C₇₉	#510	1	1	yes	characteristic
59	#2225	—	79	1	no	maximal, Sylow
60	C₇₉	#2225	1	1	yes	characteristic, complemented, Sylow
61	#500	—	79	1	no	—
62	C₄×Q₁₆	—	79	1	no	—
63	#367	—	79	1	no	—
64	#367	—	79	1	no	—
65	C₄⋊C₁₆	—	79	1	no	—
66	#358	—	79	1	no	—
67	#358	D₇₉	1	1	yes	characteristic
68	C₂×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
69	C₄⋊Q₈	—	158	1	no	—
70	C₄×Q₈	—	158	1	no	—
71	C₂×C₁₆	—	79	1	no	—
72	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
73	#107	—	79	1	no	—
74	#107	—	79	1	no	—
75	#107	—	158	1	no	—
76	#107	C₂×D₇₉	1	1	yes	characteristic
77	#103	—	158	1	no	—
78	C₄×C₈	—	79	1	no	—
79	C₂×Q₈	—	2	1	no	—
80	C₂×Q₈	—	316	1	no	—
81	Q₁₆	—	2	1	no	—
82	Q₁₆	Dic₁₅₈	1	2	yes	complemented
83	C₂×C₈	—	79	1	no	—
84	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
85	C₄⋊C₄	—	2	1	no	—
86	C₄⋊C₄	—	316	1	no	—
87	C₄⋊C₄	—	316	1	no	—
88	C₄⋊C₄	—	158	1	no	—
89	C₄⋊C₄	—	158	1	no	—
90	C₄²	—	316	1	no	—
91	C₄²	—	79	1	no	—
92	C₁₆	—	2	1	no	—
93	C₁₆	—	158	1	no	—
94	Q₈	—	2	2	no	—
95	Q₈	—	4	1	no	—
96	Q₈	—	632	2	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	316	1	no	—
100	C₂×C₄	—	316	1	no	—
101	C₂×C₄	—	79	1	no	—
102	C₂×C₄	—	79	1	no	—
103	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
104	C₈	—	158	1	no	—
105	C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
106	C₈	#11929623	1	1	yes	characteristic
107	C₂²	D₈×D₇₉	1	1	yes	characteristic
108	C₄	—	4	2	no	—
109	C₄	—	8	1	no	—
110	C₄	—	79	2	no	—
111	C₄	—	632	1	no	—
112	C₄	—	632	1	no	—
113	C₄	—	158	1	no	—
114	C₄	#14579138	1	1	yes	characteristic
115	C₄	#14579190	1	1	yes	characteristic
116	C₂	#19098841	1	1	yes	characteristic
117	C₂	SD₃₂×D₇₉	1	1	yes	characteristic
118	C₂	#19099005	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098967

C₂

yes

maximal, characteristic

Q₁₆×Dic₇₉

C₂

yes

maximal, characteristic

#19098391

C₂

yes

maximal, characteristic

#19098390

C₂

yes

maximal, characteristic

Dic₇₉⋊C₁₆

C₂

yes

maximal, characteristic

#19098367

C₂

yes

maximal, characteristic

#358×C₇₉

C₂

yes

maximal, characteristic

#14579160

—

Q₈×Dic₇₉

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

characteristic

#14579095

C₂²

yes

characteristic

#14579094

—

#14579085

—

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×Q₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×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

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

C₂×Q₈×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

Q₈

yes

complemented

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

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

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₄×C₇₉

#137

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

SD₃₂

yes

—

C₂×C₇₉

#474

yes

characteristic

C₂×C₇₉

C₂×SD₃₂

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#500

—

C₄×Q₁₆

—

#367

—

#367

—

C₄⋊C₁₆

—

#358

—

#358

D₇₉

yes

characteristic

C₂×Q₁₆

C₂×D₇₉

yes

characteristic

C₄⋊Q₈

—

158

—

C₄×Q₈

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

—

—

—

158

—

#107

C₂×D₇₉

yes

characteristic

#103

—

158

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

316

—

Q₁₆

—

Q₁₆

Dic₁₅₈

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

316

—

C₄²

—

C₁₆

—

C₁₆

—

158

—

Q₈

—

Q₈

—

Q₈

—

632

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

100

C₂×C₄

—

316

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

D₄×D₇₉

yes

characteristic

104

C₈

—

158

—

105

C₈

C₂×Dic₁₅₈

yes

characteristic

106

C₈

#11929623

yes

characteristic

107

C₂²

D₈×D₇₉

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

632

—

112

C₄

—

632

—

113

C₄

—

158

—

114

C₄

#14579138

yes

characteristic

115

C₄

#14579190

yes

characteristic

116

C₂

#19098841

yes

characteristic

117

C₂

SD₃₂×D₇₉

yes

characteristic

118

C₂

#19099005

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#358×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₈
hypercenter	#358	D₇₉
hypocenter	C₇₉	#2225
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#358×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 ◁ #358

N	H ≅ G/N	type
30. Q₁₆×C₇₉	Q₈	semidirect
60. C₇₉	#2225	semidirect
82. Q₁₆	Dic₁₅₈	semidirect

H ≅ G/N

type

30. Q₁₆×C₇₉

Q₈

semidirect

60. C₇₉

#2225

semidirect

82. Q₁₆

Dic₁₅₈

semidirect

Subgroups — #23765540

Conjugacy classes of subgroups

Complements