Group #23762919 — subgroups

Subgroups — #23762919

Order 10112.

152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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	#19098968	C₂	1	1	yes	maximal, characteristic
2	#19098774	C₂	1	2	yes	maximal
3	#19098693	C₂	1	1	yes	maximal, characteristic
4	#19098310	C₂	1	2	yes	maximal
5	#334×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	—	2	2	no	—
7	#14579161	C₂²	1	2	yes	—
8	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
9	#14579095	—	2	1	no	—
10	#14579095	—	2	1	no	—
11	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
12	Dic₇₉⋊C₈	—	2	1	no	—
13	#14579086	—	2	2	no	—
14	#14579071	—	2	1	no	—
15	C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₅₈	—	2	2	no	—
18	C₂×Dic₁₅₈	D₄	1	1	yes	characteristic
19	Dic₃₁₆	—	4	4	no	—
20	C₂×C₇₉⋊C₈	—	2	1	no	—
21	C₄⋊Dic₇₉	—	2	2	no	—
22	C₄⋊Dic₇₉	—	2	2	no	—
23	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
24	Dic₇₉⋊C₄	—	2	1	no	—
25	C₄×Dic₇₉	—	2	1	no	—
26	C₂×C₈×C₇₉	—	2	2	no	—
27	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
28	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
29	C₄²×C₇₉	C₂³	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
33	C₂×Dic₇₉	—	2	1	no	—
34	C₂×Dic₇₉	—	2	1	no	—
35	C₂×Dic₇₉	—	4	2	no	—
36	Dic₁₅₈	—	2	2	no	—
37	Dic₁₅₈	—	4	2	no	—
38	Dic₁₅₈	—	4	2	no	—
39	C₈×C₇₉	—	2	1	no	—
40	C₈×C₇₉	—	4	2	no	—
41	C₈×C₇₉	Q₁₆	1	2	yes	complemented
42	C₇₉⋊C₈	—	4	1	no	—
43	C₂²×C₇₉	#121	1	1	yes	characteristic
44	C₄×C₇₉	—	2	1	no	—
45	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
47	C₄×C₇₉	#137	1	1	yes	characteristic
48	Dic₇₉	—	4	1	no	—
49	Dic₇₉	—	4	1	no	—
50	Dic₇₉	—	8	2	no	—
51	C₂×C₇₉	#462	1	1	yes	characteristic
52	C₂×C₇₉	#469	1	1	yes	characteristic
53	C₂×C₇₉	#473	1	1	yes	characteristic
54	#1694	—	79	1	no	maximal, Sylow
55	C₇₉	#1694	1	1	yes	characteristic, complemented, Sylow
56	#500	—	79	1	no	—
57	#462	—	79	2	no	—
58	#446	—	79	1	no	—
59	#334	D₇₉	1	1	yes	characteristic
60	#332	—	79	2	no	—
61	C₂×Q₁₆	—	158	2	no	—
62	C₄⋊Q₈	—	79	2	no	—
63	C₄×Q₈	—	79	1	no	—
64	#107	—	158	1	no	—
65	#107	—	158	1	no	—
66	C₄⋊C₈	—	79	1	no	—
67	C₄⋊C₈	—	158	1	no	—
68	C₄⋊C₈	C₂×D₇₉	1	2	yes	—
69	#103	—	158	2	no	—
70	#97	—	158	1	no	—
71	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
72	C₂×Q₈	—	79	1	no	—
73	C₂×Q₈	—	158	2	no	—
74	Q₁₆	—	316	4	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	158	1	no	—
77	C₂×C₈	D₃₁₆	1	1	yes	characteristic
78	C₂×C₈	D₃₁₆	1	1	yes	characteristic
79	C₄⋊C₄	—	79	1	no	—
80	C₄⋊C₄	—	158	2	no	—
81	C₄⋊C₄	—	158	2	no	—
82	C₄⋊C₄	—	158	1	no	—
83	C₄²	—	158	1	no	—
84	C₄²	C₂²×D₇₉	1	1	yes	characteristic
85	Q₈	—	316	2	no	—
86	Q₈	—	316	2	no	—
87	Q₈	—	158	2	no	—
88	C₂×C₄	—	316	2	no	—
89	C₂×C₄	—	158	1	no	—
90	C₂×C₄	—	158	1	no	—
91	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
92	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
93	C₂×C₄	#11929625	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	4	2	no	—
96	C₈	—	316	1	no	—
97	C₈	Dic₃₁₆	1	2	yes	complemented
98	C₂²	#14579136	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	316	1	no	—
101	C₄	—	316	1	no	—
102	C₄	—	632	2	no	—
103	C₄	C₂×Dic₃₁₆	1	1	yes	characteristic
104	C₄	#14579188	1	2	yes	—
105	C₄	#14579194	1	1	yes	characteristic
106	C₂	#19098774	1	1	yes	characteristic
107	C₂	#19098817	1	1	yes	characteristic
108	C₂	#19098839	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098968

C₂

yes

maximal, characteristic

#19098774

C₂

yes

maximal

#19098693

C₂

yes

maximal, characteristic

#19098310

C₂

yes

maximal

#334×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

—

#14579161

C₂²

yes

—

C₄×Dic₁₅₈

C₂²

yes

characteristic

#14579095

—

#14579095

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

Dic₇₉⋊C₈

—

#14579086

—

#14579071

—

C₄⋊C₈×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₄

yes

characteristic

Dic₃₁₆

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

characteristic

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

Q₁₆

yes

complemented

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₂×Q₁₆

yes

characteristic

C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₄×C₇₉

#137

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic

#332

—

C₂×Q₁₆

—

158

—

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

158

—

#107

—

158

—

C₄⋊C₈

—

C₄⋊C₈

—

158

—

C₄⋊C₈

C₂×D₇₉

yes

—

#103

—

158

—

#97

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

158

—

Q₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

Q₈

—

316

—

Q₈

—

316

—

Q₈

—

158

—

C₂×C₄

—

316

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

D₄×D₇₉

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₂×C₄

#11929625

yes

characteristic

C₈

—

C₈

—

C₈

—

316

—

C₈

Dic₃₁₆

yes

complemented

C₂²

#14579136

yes

characteristic

C₄

—

100

C₄

—

316

—

101

C₄

—

316

—

102

C₄

—

632

—

103

C₄

C₂×Dic₃₁₆

yes

characteristic

104

C₄

#14579188

yes

—

105

C₄

#14579194

yes

characteristic

106

C₂

#19098774

yes

characteristic

107

C₂

#19098817

yes

characteristic

108

C₂

#19098839

yes

characteristic

	subgroup	G/H
center	C₂²	#14579136
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#334×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#121
hypercenter	#334	D₇₉
hypocenter	C₇₉	#1694
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#14579136

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#334×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
41. C₈×C₇₉	Q₁₆	semidirect
55. C₇₉	#1694	semidirect
97. C₈	Dic₃₁₆	semidirect

H ≅ G/N

type

41. C₈×C₇₉

Q₁₆

semidirect

55. C₇₉

#1694

semidirect

97. C₈

Dic₃₁₆

semidirect

Subgroups — #23762919

Conjugacy classes of subgroups

Complements