Group #23764905 — subgroups

Subgroups — #23764905

Order 10112.

176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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	#19098606	C₂	1	2	yes	maximal
2	C₂×#14579095	C₂	1	1	yes	maximal, characteristic
3	#19098331	C₂	1	2	yes	maximal
4	#19098328	C₂	1	1	yes	maximal, characteristic
5	#424×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929608	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
8	#14579095	—	2	2	no	—
9	#14579094	—	2	2	no	—
10	#14579092	—	2	2	no	—
11	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	#117×C₇₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₉	—	2	2	no	—
15	C₂²×Dic₇₉	—	2	2	no	—
16	#11929608	—	2	2	no	—
17	#11929608	Q₈	1	4	yes	—
18	C₂×C₇₉⋊C₈	—	2	2	no	—
19	C₄⋊Dic₇₉	—	2	2	no	—
20	C₄⋊Dic₇₉	—	2	2	no	—
21	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₇₉	—	2	2	no	—
23	C₂×C₈×C₇₉	—	2	1	no	—
24	C₂×C₈×C₇₉	—	2	2	no	—
25	C₂×C₈×C₇₉	D₄	1	2	yes	—
26	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
27	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
28	C₂²⋊C₄×C₇₉	—	2	1	no	—
29	C₄²×C₇₉	—	2	1	no	—
30	C₂³×C₇₉	#41	1	1	yes	characteristic
31	C₂×C₄×C₇₉	—	2	1	no	—
32	C₂×C₄×C₇₉	—	2	1	no	—
33	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₇₉	#41	1	2	yes	—
37	C₂×Dic₇₉	—	4	2	no	—
38	C₂×Dic₇₉	—	8	2	no	—
39	C₈×C₇₉	—	2	2	no	—
40	C₈×C₇₉	—	4	1	no	—
41	C₇₉⋊C₈	—	2	4	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	—	4	1	no	—
47	C₄×C₇₉	—	4	1	no	—
48	C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
49	C₄×C₇₉	#123	1	1	yes	characteristic
50	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
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	D₇₉	1	1	yes	characteristic
61	#343	—	79	2	no	—
62	#341	—	79	1	no	—
63	C₂×M₁₆	—	79	2	no	—
64	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
65	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
66	#117	C₂×D₇₉	1	1	yes	characteristic
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	—	2	2	no	—
72	C₂²×C₄	—	158	2	no	—
73	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	79	4	no	—
76	M₁₆	—	158	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	158	2	no	—
80	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
81	C₄⋊C₄	—	158	2	no	—
82	C₄⋊C₄	—	158	2	no	—
83	C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
84	C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
85	C₂²⋊C₄	—	2	1	no	—
86	C₄²	—	2	1	no	—
87	C₂³	#11929624	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	316	2	no	—
91	C₂×C₄	—	632	2	no	—
92	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
93	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
94	C₂×C₄	Q₈×D₇₉	1	2	yes	—
95	C₂×C₄	#11929623	1	2	yes	—
96	C₈	—	2	2	no	—
97	C₈	—	4	1	no	—
98	C₈	—	158	4	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#14579135	1	1	yes	characteristic
102	C₂²	#14579151	1	2	yes	—
103	C₄	—	4	1	no	—
104	C₄	—	4	1	no	—
105	C₄	—	632	2	no	—
106	C₄	#14579141	1	2	yes	—
107	C₄	#14579142	1	1	yes	characteristic
108	C₄	#14579159	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	#19098493	1	1	yes	characteristic
111	C₂	#19098833	1	1	yes	characteristic
112	C₂	#19098838	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098606

C₂

yes

maximal

C₂×#14579095

C₂

yes

maximal, characteristic

#19098331

C₂

yes

maximal

#19098328

C₂

yes

maximal, characteristic

#424×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

#14579095

—

#14579094

—

#14579092

—

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

characteristic

#117×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂²×Dic₇₉

—

#11929608

—

#11929608

Q₈

yes

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

#41

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

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

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₂²×C₇₉

#125

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

—

C₄×C₇₉

#123

yes

characteristic

C₄×C₇₉

C₄⋊Q₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#428

—

C₂×#107

—

#424

D₇₉

yes

characteristic

#343

—

#341

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

characteristic

C₂²×C₈

C₂×D₇₉

yes

characteristic

#117

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

#107

—

158

—

#107

—

158

—

#106

—

158

—

C₄⋊C₈

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

D₃₁₆

yes

characteristic

C₄⋊C₄

D₃₁₆

yes

characteristic

C₂²⋊C₄

—

C₄²

—

C₂³

#11929624

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

632

—

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₂×C₄

Q₈×D₇₉

yes

—

C₂×C₄

#11929623

yes

—

C₈

—

C₈

—

C₈

—

158

—

C₂²

—

100

C₂²

—

101

C₂²

#14579135

yes

characteristic

102

C₂²

#14579151

yes

—

103

C₄

—

104

C₄

—

105

C₄

—

632

—

106

C₄

#14579141

yes

—

107

C₄

#14579142

yes

characteristic

108

C₄

#14579159

yes

characteristic

109

C₂

—

110

C₂

#19098493

yes

characteristic

111

C₂

#19098833

yes

characteristic

112

C₂

#19098838

yes

characteristic

	subgroup	G/H
center	C₂²	#14579135
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#424×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂³×C₇₉	#41
hypercenter	#424	D₇₉
hypocenter	C₇₉	#2089
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#14579135

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#424×C₇₉

C₂

C₂²×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

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

H ≅ G/N

type

57. C₇₉

#2089

semidirect

Subgroups — #23764905

Conjugacy classes of subgroups

Complements