Group #23762726 — subgroups

Subgroups — #23762726

Order 10112.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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	C₇₉⋊#564	C₂	1	1	yes	maximal, characteristic
2	#19098969	C₂	1	2	yes	maximal
3	#19098305	C₂	1	1	yes	maximal, characteristic
4	#19098304	C₂	1	2	yes	maximal
5	#491×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#14579153	C₂²	1	2	yes	—
7	#14579152	—	2	2	no	—
8	#14579151	—	2	2	no	—
9	#14579151	—	2	2	no	—
10	#14579094	—	2	2	no	—
11	#14579092	—	2	2	no	—
12	#14579072	C₂²	1	2	yes	—
13	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	#125×C₇₉	C₂²	1	1	yes	characteristic
15	#103×C₇₉	—	2	2	no	—
16	#97×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₇₉⋊C₈	—	2	2	no	—
18	C₄⋊Dic₇₉	—	2	2	no	—
19	C₄⋊Dic₇₉	D₄	1	2	yes	—
20	C₄⋊Dic₇₉	D₄	1	2	yes	—
21	Dic₇₉⋊C₄	—	2	2	no	—
22	Dic₇₉⋊C₄	—	2	2	no	—
23	Dic₇₉⋊C₄	—	2	2	no	—
24	Dic₇₉⋊C₄	—	2	2	no	—
25	C₄×Dic₇₉	—	2	2	no	—
26	C₂×Q₈×C₇₉	—	2	1	no	—
27	C₂×C₈×C₇₉	—	2	1	no	—
28	C₄⋊C₄×C₇₉	—	2	2	no	—
29	C₄⋊C₄×C₇₉	—	2	2	no	—
30	C₄⋊C₄×C₇₉	D₄	1	2	yes	—
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	—	4	1	no	—
35	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₇₉	—	2	2	no	—
38	C₂×Dic₇₉	—	2	2	no	—
39	C₈×C₇₉	—	4	1	no	—
40	C₇₉⋊C₈	—	2	4	no	—
41	C₂²×C₇₉	#120	1	1	yes	characteristic
42	C₄×C₇₉	—	2	1	no	—
43	C₄×C₇₉	—	2	2	no	—
44	C₄×C₇₉	—	4	2	no	—
45	C₄×C₇₉	—	8	1	no	—
46	Dic₇₉	—	4	2	no	—
47	Dic₇₉	—	4	2	no	—
48	C₂×C₇₉	#454	1	1	yes	characteristic
49	C₂×C₇₉	#456	1	2	yes	—
50	#1663	—	79	1	no	maximal, Sylow
51	C₇₉	#1663	1	1	yes	characteristic, complemented, Sylow
52	#564	—	79	1	no	—
53	#501	—	79	2	no	—
54	#491	D₇₉	1	1	yes	characteristic
55	#330	—	79	1	no	—
56	#330	—	79	2	no	—
57	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
58	#125	—	79	2	no	—
59	#125	—	158	2	no	—
60	#125	—	158	2	no	—
61	#125	—	158	2	no	—
62	#125	C₂×D₇₉	1	1	yes	characteristic
63	#107	—	158	2	no	—
64	#106	—	158	2	no	—
65	#103	—	2	2	no	—
66	#97	—	79	2	no	—
67	#97	C₂×D₇₉	1	1	yes	characteristic
68	C₂×Q₈	—	2	1	no	—
69	C₂×C₈	—	2	1	no	—
70	C₂×C₈	—	158	2	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	79	2	no	—
74	C₄⋊C₄	—	79	2	no	—
75	C₄⋊C₄	—	158	2	no	—
76	C₄⋊C₄	—	158	2	no	—
77	C₄⋊C₄	—	158	2	no	—
78	C₄⋊C₄	—	158	2	no	—
79	C₄⋊C₄	—	158	2	no	—
80	C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
81	C₄²	—	158	2	no	—
82	C₄²	C₂²×D₇₉	1	1	yes	characteristic
83	Q₈	—	4	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	—	158	2	no	—
87	C₂×C₄	—	158	2	no	—
88	C₂×C₄	D₄×D₇₉	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
90	C₈	—	4	1	no	—
91	C₈	—	158	4	no	—
92	C₂²	#14579129	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	8	1	no	—
97	C₄	—	316	2	no	—
98	C₄	—	316	2	no	—
99	C₂	#19098735	1	1	yes	characteristic
100	C₂	#19098744	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₉⋊#564

C₂

yes

maximal, characteristic

#19098969

C₂

yes

maximal

#19098305

C₂

yes

maximal, characteristic

#19098304

C₂

yes

maximal

#491×C₇₉

C₂

yes

maximal, characteristic

#14579153

C₂²

yes

—

—

—

—

—

—

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#125×C₇₉

C₂²

yes

characteristic

#103×C₇₉

—

#97×C₇₉

C₂²

yes

characteristic

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

—

C₄⋊Dic₇₉

D₄

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

#120

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#454

yes

characteristic

C₂×C₇₉

#456

yes

—

#1663

—

maximal, Sylow

C₇₉

#1663

yes

characteristic, complemented, Sylow

#564

—

#501

—

#491

D₇₉

yes

characteristic

#330

—

#330

—

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

#125

—

#125

—

158

—

#125

—

158

—

#125

—

158

—

#125

C₂×D₇₉

yes

characteristic

#107

—

158

—

#106

—

158

—

#103

—

#97

—

#97

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

C₂²⋊D₇₉

yes

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

D₄×D₇₉

yes

—

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₈

—

C₈

—

158

—

C₂²

#14579129

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

316

—

C₄

—

316

—

C₂

#19098735

yes

characteristic

100

C₂

#19098744

yes

—

	subgroup	G/H
center	C₂²	#14579129
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#491×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#120
hypercenter	#491	D₇₉
hypocenter	C₇₉	#1663
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #491

subgroup

G/H

center

C₂²

#14579129

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#491×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #491

N	H ≅ G/N	type
51. C₇₉	#1663	semidirect

H ≅ G/N

type

51. C₇₉

#1663

semidirect

Subgroups — #23762726

Conjugacy classes of subgroups

Complements