Group #23762791 — subgroups

Subgroups — #23762791

Order 10112.

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

normal subgroups only

This group has 156 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	#19098770	C₂	1	2	yes	maximal
2	C₈×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic
3	#19098316	C₂	1	1	yes	maximal, characteristic
4	#19098309	C₂	1	2	yes	maximal
5	#500×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929614	—	2	2	no	—
7	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
8	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
9	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
10	Dic₇₉⋊C₈	—	2	1	no	—
11	#14579085	—	2	2	no	—
12	C₈×Dic₇₉	—	2	1	no	—
13	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
14	#107×C₇₉	—	2	1	no	—
15	#107×C₇₉	—	2	1	no	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₅₈	D₄	1	1	yes	characteristic
18	#11929614	—	4	4	no	—
19	C₂×C₇₉⋊C₈	—	2	1	no	—
20	C₂×C₇₉⋊C₈	—	2	2	no	—
21	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
22	Dic₇₉⋊C₄	—	2	1	no	—
23	C₄×Dic₇₉	—	2	1	no	—
24	C₂×Q₈×C₇₉	—	2	2	no	—
25	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
27	C₄⋊C₄×C₇₉	—	2	2	no	—
28	C₄⋊C₄×C₇₉	—	2	2	no	—
29	C₄²×C₇₉	C₂³	1	1	yes	characteristic
30	Q₈×C₇₉	—	4	2	no	—
31	Q₈×C₇₉	—	4	2	no	—
32	C₂×C₄×C₇₉	—	4	2	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	#41	1	1	yes	characteristic
36	C₂×Dic₇₉	—	2	1	no	—
37	C₂×Dic₇₉	—	2	1	no	—
38	Dic₁₅₈	—	2	1	no	—
39	Dic₁₅₈	D₈	1	2	yes	—
40	C₈×C₇₉	—	2	1	no	—
41	C₈×C₇₉	Q₁₆	1	2	yes	complemented
42	C₇₉⋊C₈	—	4	2	no	—
43	C₇₉⋊C₈	—	4	1	no	—
44	C₂²×C₇₉	#121	1	1	yes	characteristic
45	C₄×C₇₉	—	2	1	no	—
46	C₄×C₇₉	—	8	2	no	—
47	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
48	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
49	C₄×C₇₉	#135	1	1	yes	characteristic
50	C₄×C₇₉	#137	1	1	yes	characteristic
51	Dic₇₉	—	2	2	no	—
52	Dic₇₉	—	4	1	no	—
53	C₂×C₇₉	#462	1	1	yes	characteristic
54	C₂×C₇₉	#466	1	1	yes	characteristic
55	C₂×C₇₉	#473	1	1	yes	characteristic
56	#1674	—	79	1	no	maximal, Sylow
57	C₇₉	#1674	1	1	yes	characteristic, complemented, Sylow
58	#500	D₇₉	1	1	yes	characteristic
59	#462	—	79	2	no	—
60	C₈×Q₈	—	79	1	no	—
61	#335	—	79	1	no	—
62	#332	—	79	2	no	—
63	C₂×Q₁₆	—	158	2	no	—
64	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
65	C₄×Q₈	—	79	1	no	—
66	#107	—	2	1	no	—
67	#107	—	2	1	no	—
68	C₄⋊C₈	—	79	1	no	—
69	C₄⋊C₈	—	79	2	no	—
70	C₄⋊C₈	—	158	1	no	—
71	#103	—	158	2	no	—
72	C₄×C₈	—	158	1	no	—
73	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
74	C₂×Q₈	—	2	2	no	—
75	C₂×Q₈	—	79	1	no	—
76	Q₁₆	—	316	4	no	—
77	C₂×C₈	—	158	2	no	—
78	C₂×C₈	—	158	1	no	—
79	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	79	1	no	—
84	C₄⋊C₄	—	158	1	no	—
85	C₄²	—	158	1	no	—
86	C₄²	C₂²×D₇₉	1	1	yes	characteristic
87	Q₈	—	4	2	no	—
88	Q₈	—	4	2	no	—
89	Q₈	—	79	2	no	—
90	Q₈	—	158	1	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	—	158	1	no	—
93	C₂×C₄	—	158	1	no	—
94	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
95	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
96	C₂×C₄	#11929623	1	1	yes	characteristic
97	C₈	—	2	1	no	—
98	C₈	—	316	2	no	—
99	C₈	—	316	1	no	—
100	C₈	#11929614	1	2	yes	complemented
101	C₂²	#14579132	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	8	2	no	—
104	C₄	—	316	1	no	—
105	C₄	—	158	2	no	—
106	C₄	D₈×D₇₉	1	1	yes	characteristic
107	C₄	C₂×#11929614	1	1	yes	characteristic
108	C₄	#14579180	1	1	yes	characteristic
109	C₄	#14579192	1	1	yes	characteristic
110	C₂	#19098770	1	1	yes	characteristic
111	C₂	#19098796	1	1	yes	characteristic
112	C₂	#19098835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098770

C₂

yes

maximal

C₈×Dic₁₅₈

C₂

yes

maximal, characteristic

#19098316

C₂

yes

maximal, characteristic

#19098309

C₂

yes

maximal

#500×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929614

—

C₄×Dic₁₅₈

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

Dic₇₉⋊C₈

—

#14579085

—

C₈×Dic₇₉

—

C₄⋊Q₈×C₇₉

C₂²

yes

—

#107×C₇₉

—

#107×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

D₄

yes

characteristic

#11929614

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

D₄

yes

characteristic

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

D₈

yes

—

C₈×C₇₉

—

C₈×C₇₉

Q₁₆

yes

complemented

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

C₂×Q₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#500

D₇₉

yes

characteristic

#462

—

C₈×Q₈

—

#335

—

#332

—

C₂×Q₁₆

—

158

—

C₄⋊Q₈

C₂×D₇₉

yes

—

C₄×Q₈

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

158

—

#103

—

158

—

C₄×C₈

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

316

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

158

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

D₄×D₇₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

#11929623

yes

characteristic

C₈

—

C₈

—

316

—

C₈

—

316

—

100

C₈

#11929614

yes

complemented

101

C₂²

#14579132

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

316

—

105

C₄

—

158

—

106

C₄

D₈×D₇₉

yes

characteristic

107

C₄

C₂×#11929614

yes

characteristic

108

C₄

#14579180

yes

characteristic

109

C₄

#14579192

yes

characteristic

110

C₂

#19098770

yes

characteristic

111

C₂

#19098796

yes

characteristic

112

C₂

#19098835

yes

characteristic

	subgroup	G/H
center	C₂²	#14579132
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#500×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#121
hypercenter	#500	D₇₉
hypocenter	C₇₉	#1674
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#14579132

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#500×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
41. C₈×C₇₉	Q₁₆	semidirect
57. C₇₉	#1674	semidirect
100. C₈	#11929614	semidirect

H ≅ G/N

type

41. C₈×C₇₉

Q₁₆

semidirect

57. C₇₉

#1674

semidirect

100. C₈

#11929614

semidirect

Subgroups — #23762791

Conjugacy classes of subgroups

Complements