Group #23764907 — subgroups

Subgroups — #23764907

Order 10112.

176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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	#19098605	C₂	1	2	yes	maximal
2	C₂×#14579095	C₂	1	1	yes	maximal, characteristic
3	#19098589	C₂	1	1	yes	maximal, characteristic
4	#19098331	C₂	1	2	yes	maximal
5	#341×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929608	C₂²	1	1	yes	characteristic
7	#14579120	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	#14579095	—	2	2	no	—
10	#14579095	—	2	2	no	—
11	#14579093	—	2	2	no	—
12	Dic₇₉⋊C₈	—	2	2	no	—
13	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×Dic₇₉	—	2	2	no	—
16	#11929608	—	2	2	no	—
17	C₂×C₇₉⋊C₈	—	2	1	no	—
18	C₄⋊Dic₇₉	—	2	2	no	—
19	C₄⋊Dic₇₉	—	2	2	no	—
20	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
21	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
22	C₂²⋊Dic₇₉	—	2	1	no	—
23	C₄×Dic₇₉	—	2	1	no	—
24	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
25	M₁₆×C₇₉	—	2	2	no	—
26	M₁₆×C₇₉	Q₈	1	4	yes	—
27	C₂×C₈×C₇₉	—	2	2	no	—
28	C₂×C₈×C₇₉	—	2	2	no	—
29	C₂×C₈×C₇₉	D₄	1	2	yes	—
30	C₂³×C₇₉	#41	1	1	yes	characteristic
31	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₇₉	#41	1	2	yes	—
35	C₂×Dic₇₉	—	2	1	no	—
36	C₂×Dic₇₉	—	2	1	no	—
37	C₂×Dic₇₉	—	4	2	no	—
38	C₂×Dic₇₉	—	8	2	no	—
39	C₈×C₇₉	—	2	4	no	—
40	C₈×C₇₉	—	2	2	no	—
41	C₇₉⋊C₈	—	4	1	no	—
42	C₂²×C₇₉	—	2	1	no	—
43	C₂²×C₇₉	—	2	1	no	—
44	C₂²×C₇₉	#121	1	1	yes	characteristic
45	C₂²×C₇₉	#125	1	2	yes	—
46	C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
47	C₄×C₇₉	#123	1	1	yes	characteristic
48	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
49	Dic₇₉	—	4	1	no	—
50	Dic₇₉	—	4	1	no	—
51	Dic₇₉	—	8	2	no	—
52	C₂×C₇₉	—	2	2	no	—
53	C₂×C₇₉	#398	1	1	yes	characteristic
54	C₂×C₇₉	#472	1	1	yes	characteristic
55	C₂×C₇₉	#473	1	1	yes	characteristic
56	#2089	—	79	1	no	maximal, Sylow
57	C₇₉	#2089	1	1	yes	characteristic, complemented, Sylow
58	#428	—	79	2	no	—
59	C₂×#107	—	79	1	no	—
60	#424	—	79	1	no	—
61	#343	—	79	2	no	—
62	#341	D₇₉	1	1	yes	characteristic
63	C₂×M₁₆	—	79	1	no	—
64	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
65	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
66	#117	—	79	1	no	—
67	C₂×C₄⋊C₄	—	79	2	no	—
68	#107	—	158	2	no	—
69	#107	—	158	2	no	—
70	#106	—	158	2	no	—
71	C₄⋊C₈	—	158	2	no	—
72	C₂²×C₄	—	158	2	no	—
73	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	158	2	no	—
76	M₁₆	Dic₁₅₈	1	4	yes	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	158	1	no	—
80	C₂×C₈	D₃₁₆	1	2	yes	—
81	C₄⋊C₄	—	79	1	no	—
82	C₄⋊C₄	—	79	1	no	—
83	C₄⋊C₄	—	158	2	no	—
84	C₄⋊C₄	—	158	2	no	—
85	C₂²⋊C₄	—	158	1	no	—
86	C₄²	—	158	1	no	—
87	C₂³	#11929625	1	1	yes	characteristic
88	C₂×C₄	—	316	2	no	—
89	C₂×C₄	—	632	2	no	—
90	C₂×C₄	—	158	1	no	—
91	C₂×C₄	—	158	1	no	—
92	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
93	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
94	C₂×C₄	C₂×Dic₁₅₈	1	2	yes	—
95	C₂×C₄	#11929623	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	2	2	no	—
98	C₈	—	316	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#14579136	1	1	yes	characteristic
102	C₂²	#14579152	1	2	yes	—
103	C₄	—	316	1	no	—
104	C₄	—	316	1	no	—
105	C₄	—	632	2	no	—
106	C₄	#14579138	1	2	yes	—
107	C₄	#14579145	1	1	yes	characteristic
108	C₄	#14579161	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	#19098495	1	1	yes	characteristic
111	C₂	#19098834	1	1	yes	characteristic
112	C₂	#19098839	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098605

C₂

yes

maximal

C₂×#14579095

C₂

yes

maximal, characteristic

#19098589

C₂

yes

maximal, characteristic

#19098331

C₂

yes

maximal

#341×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

characteristic

#14579120

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

#14579095

—

#14579095

—

#14579093

—

Dic₇₉⋊C₈

—

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

characteristic

C₄⋊Dic₇₉

D₄

yes

characteristic

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

Q₈

yes

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₂³×C₇₉

#41

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₂²×C₇₉

#125

yes

—

C₄×C₇₉

C₂²⋊Q₈

yes

—

C₄×C₇₉

#123

yes

characteristic

C₄×C₇₉

C₄⋊Q₈

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#107

—

158

—

#107

—

158

—

#106

—

158

—

C₄⋊C₈

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

158

—

M₁₆

Dic₁₅₈

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

D₃₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

158

—

C₄²

—

158

—

C₂³

#11929625

yes

characteristic

C₂×C₄

—

316

—

C₂×C₄

—

632

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

D₄×D₇₉

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₂×C₄

C₂×Dic₁₅₈

yes

—

C₂×C₄

#11929623

yes

—

C₈

—

C₈

—

C₈

—

316

—

C₂²

—

100

C₂²

—

101

C₂²

#14579136

yes

characteristic

102

C₂²

#14579152

yes

—

103

C₄

—

316

—

104

C₄

—

316

—

105

C₄

—

632

—

106

C₄

#14579138

yes

—

107

C₄

#14579145

yes

characteristic

108

C₄

#14579161

yes

characteristic

109

C₂

—

110

C₂

#19098495

yes

characteristic

111

C₂

#19098834

yes

characteristic

112

C₂

#19098839

yes

characteristic

	subgroup	G/H
center	C₂²	#14579136
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#341×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂³×C₇₉	#41
hypercenter	#341	D₇₉
hypocenter	C₇₉	#2089
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#14579136

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#341×C₇₉

C₂

C₂²×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
57. C₇₉	#2089	semidirect

H ≅ G/N

type

57. C₇₉

#2089

semidirect

Subgroups — #23764907

Conjugacy classes of subgroups

Complements