Group #23762541 — subgroups

Subgroups — #23762541

Order 10112.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 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	#19099293	C₂	1	1	yes	maximal, characteristic
2	#19098942	C₂	1	1	yes	maximal, characteristic
3	#19098859	C₂	1	2	yes	maximal
4	#19098293	C₂	1	2	yes	maximal
5	#333×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929614	—	2	2	no	—
7	#14579161	C₂²	1	1	yes	characteristic
8	#14579160	—	2	2	no	—
9	#14579159	—	2	2	no	—
10	C₄×Dic₁₅₈	C₂²	1	2	yes	—
11	#14579126	—	2	2	no	—
12	#14579095	—	2	2	no	—
13	#14579086	—	2	2	no	—
14	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
17	C₂×Dic₁₅₈	—	2	2	no	—
18	C₂×Dic₁₅₈	—	2	1	no	—
19	C₂×Dic₁₅₈	D₄	1	2	yes	—
20	#11929614	—	4	4	no	—
21	C₂×C₇₉⋊C₈	—	2	1	no	—
22	C₄⋊Dic₇₉	—	2	2	no	—
23	C₄⋊Dic₇₉	D₄	1	2	yes	—
24	Dic₇₉⋊C₄	—	2	4	no	—
25	Dic₇₉⋊C₄	—	2	2	no	—
26	C₄×Dic₇₉	—	2	2	no	—
27	C₄×Dic₇₉	—	2	2	no	—
28	C₂×Q₈×C₇₉	D₄	1	2	yes	—
29	C₂×C₈×C₇₉	—	2	2	no	—
30	C₄⋊C₄×C₇₉	—	2	2	no	—
31	C₄²×C₇₉	C₂³	1	1	yes	characteristic
32	Q₈×C₇₉	—	4	2	no	—
33	C₂×C₄×C₇₉	—	2	2	no	—
34	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₇₉	—	2	2	no	—
37	C₂×Dic₇₉	—	2	2	no	—
38	C₂×Dic₇₉	—	4	1	no	—
39	Dic₁₅₈	—	2	2	no	—
40	Dic₁₅₈	—	4	2	no	—
41	Dic₁₅₈	—	8	2	no	—
42	Dic₁₅₈	Q₁₆	1	4	yes	complemented
43	C₈×C₇₉	—	4	2	no	—
44	C₇₉⋊C₈	—	2	2	no	—
45	C₂²×C₇₉	#120	1	1	yes	characteristic
46	C₄×C₇₉	—	2	1	no	—
47	C₄×C₇₉	—	4	2	no	—
48	C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
49	C₄×C₇₉	#137	1	2	yes	—
50	Dic₇₉	—	2	4	no	—
51	Dic₇₉	—	4	2	no	—
52	Dic₇₉	—	8	1	no	—
53	C₂×C₇₉	#451	1	2	yes	—
54	C₂×C₇₉	#453	1	1	yes	characteristic
55	#1633	—	79	1	no	maximal, Sylow
56	C₇₉	#1633	1	1	yes	characteristic, complemented, Sylow
57	Q₈²	—	79	1	no	—
58	#494	—	79	1	no	—
59	#477	—	79	2	no	—
60	#333	D₇₉	1	1	yes	characteristic
61	Q₈⋊C₈	—	79	2	no	—
62	C₂×Q₁₆	—	158	2	no	—
63	C₄⋊Q₈	—	79	1	no	—
64	C₄⋊Q₈	—	158	2	no	—
65	C₄⋊Q₈	—	158	2	no	—
66	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
67	C₄×Q₈	—	79	2	no	—
68	C₄×Q₈	—	158	2	no	—
69	#107	—	158	2	no	—
70	C₄⋊C₈	C₂×D₇₉	1	2	yes	—
71	#103	—	158	2	no	—
72	C₄×C₈	—	79	1	no	—
73	C₂×Q₈	—	79	2	no	—
74	C₂×Q₈	—	158	2	no	—
75	C₂×Q₈	—	158	1	no	—
76	C₂×Q₈	D₃₁₆	1	2	yes	—
77	Q₁₆	—	316	4	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	158	1	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	79	2	no	—
82	C₄⋊C₄	—	158	4	no	—
83	C₄⋊C₄	—	158	2	no	—
84	C₄⋊C₄	—	158	2	no	—
85	C₄²	—	158	2	no	—
86	C₄²	—	158	2	no	—
87	C₄²	C₂²×D₇₉	1	1	yes	characteristic
88	Q₈	—	4	2	no	—
89	Q₈	—	316	2	no	—
90	Q₈	—	79	4	no	—
91	Q₈	—	632	2	no	—
92	Q₈	—	158	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	316	1	no	—
95	C₂×C₄	—	158	2	no	—
96	C₂×C₄	—	158	2	no	—
97	C₂×C₄	D₄×D₇₉	1	2	yes	—
98	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
99	C₈	—	4	2	no	—
100	C₈	—	158	2	no	—
101	C₂²	#14579131	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	4	2	no	—
104	C₄	—	316	2	no	—
105	C₄	—	632	1	no	—
106	C₄	—	158	4	no	—
107	C₄	Q₁₆×D₇₉	1	2	yes	—
108	C₄	#14579190	1	2	yes	—
109	C₂	#19098720	1	2	yes	—
110	C₂	#19098733	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099293

C₂

yes

maximal, characteristic

#19098942

C₂

yes

maximal, characteristic

#19098859

C₂

yes

maximal

#19098293

C₂

yes

maximal

#333×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929614

—

#14579161

C₂²

yes

characteristic

#14579160

—

#14579159

—

C₄×Dic₁₅₈

C₂²

yes

—

#14579126

—

#14579095

—

#14579086

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₄

yes

—

#11929614

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

D₄

yes

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

Q₁₆

yes

complemented

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

#120

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×Q₁₆

yes

—

C₄×C₇₉

#137

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#451

yes

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

Q₈²

—

#494

—

#477

—

#333

D₇₉

yes

characteristic

Q₈⋊C₈

—

C₂×Q₁₆

—

158

—

C₄⋊Q₈

—

C₄⋊Q₈

—

158

—

C₄⋊Q₈

—

158

—

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

158

—

#107

—

158

—

C₄⋊C₈

C₂×D₇₉

yes

—

#103

—

158

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

C₂×Q₈

D₃₁₆

yes

—

Q₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

Q₈

—

Q₈

—

316

—

Q₈

—

Q₈

—

632

—

Q₈

—

158

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

D₄×D₇₉

yes

—

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₈

—

100

C₈

—

158

—

101

C₂²

#14579131

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

316

—

105

C₄

—

632

—

106

C₄

—

158

—

107

C₄

Q₁₆×D₇₉

yes

—

108

C₄

#14579190

yes

—

109

C₂

#19098720

yes

—

110

C₂

#19098733

yes

characteristic

	subgroup	G/H
center	C₂²	#14579131
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#333×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#120
hypercenter	#333	D₇₉
hypocenter	C₇₉	#1633
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#14579131

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#333×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
42. Dic₁₅₈	Q₁₆	semidirect
56. C₇₉	#1633	semidirect

H ≅ G/N

type

42. Dic₁₅₈

Q₁₆

semidirect

56. C₇₉

#1633

semidirect

Subgroups — #23762541

Conjugacy classes of subgroups

Complements