Group #23761361 — subgroups

Subgroups — #23761361

Order 10112.

110 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 49 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	C₄×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098316	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₈×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₉⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
6	C₂×D₈×C₇₉	C₄	1	1	yes	characteristic
7	C₄×D₄×C₇₉	—	2	1	no	—
8	#107×C₇₉	C₄	1	1	yes	characteristic
9	#102×C₇₉	—	2	1	no	—
10	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₇₉⋊C₈	—	4	1	no	—
12	C₇₉⋊C₁₆	—	2	2	no	—
13	C₂×D₄×C₇₉	—	2	1	no	—
14	C₂²×C₄×C₇₉	—	4	1	no	—
15	D₈×C₇₉	—	2	1	no	—
16	D₈×C₇₉	C₈	1	2	yes	complemented
17	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
19	C₄⋊C₄×C₇₉	—	2	1	no	—
20	C₂²⋊C₄×C₇₉	—	4	1	no	—
21	C₄²×C₇₉	D₄	1	1	yes	characteristic
22	C₂³×C₇₉	—	4	1	no	—
23	D₄×C₇₉	—	2	2	no	—
24	D₄×C₇₉	—	4	1	no	—
25	C₂×C₄×C₇₉	—	4	1	no	—
26	C₂×C₄×C₇₉	—	8	1	no	—
27	C₂×C₄×C₇₉	—	8	1	no	—
28	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
31	C₈×C₇₉	—	2	1	no	—
32	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
33	C₈×C₇₉	M₁₆	1	1	yes	characteristic
34	C₇₉⋊C₈	—	8	1	no	—
35	C₂²×C₇₉	—	4	2	no	—
36	C₂²×C₇₉	—	8	1	no	—
37	C₂²×C₇₉	—	8	1	no	—
38	C₂²×C₇₉	#102	1	1	yes	characteristic
39	C₄×C₇₉	—	2	1	no	—
40	C₄×C₇₉	—	8	1	no	—
41	C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₇₉	#104	1	1	yes	characteristic
43	C₄×C₇₉	D₁₆	1	1	yes	characteristic
44	C₄×C₇₉	SD₃₂	1	1	yes	characteristic
45	C₂×C₇₉	—	8	2	no	—
46	C₂×C₇₉	D₄⋊C₈	1	1	yes	characteristic
47	C₂×C₇₉	#357	1	1	yes	characteristic
48	C₂×C₇₉	#359	1	1	yes	characteristic
49	#1331	—	79	1	no	maximal, Sylow
50	C₇₉	#1331	1	1	yes	characteristic, complemented, Sylow
51	C₄×D₈	D₇₉	1	1	yes	characteristic
52	C₄×C₁₆	—	79	1	no	—
53	#335	—	79	1	no	—
54	C₂×D₈	Dic₇₉	1	1	yes	characteristic
55	C₄×D₄	—	2	1	no	—
56	C₂×C₁₆	—	158	1	no	—
57	#107	Dic₇₉	1	1	yes	characteristic
58	C₄⋊C₈	—	158	1	no	—
59	#102	—	2	1	no	—
60	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
61	C₂×D₄	—	2	1	no	—
62	C₂²×C₄	—	4	1	no	—
63	D₈	—	2	1	no	—
64	D₈	C₇₉⋊C₈	1	2	yes	complemented
65	C₂×C₈	—	316	1	no	—
66	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
71	C₁₆	—	158	2	no	—
72	C₂³	—	4	1	no	—
73	D₄	—	2	2	no	—
74	D₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	8	1	no	—
77	C₂×C₄	—	8	1	no	—
78	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
79	C₂×C₄	#11929609	1	1	yes	characteristic
80	C₂×C₄	#11929612	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	632	1	no	—
83	C₈	C₂×C₇₉⋊C₈	1	1	yes	characteristic
84	C₈	#11929608	1	1	yes	characteristic
85	C₂²	—	4	2	no	—
86	C₂²	—	8	1	no	—
87	C₂²	—	8	1	no	—
88	C₂²	#14579082	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	8	1	no	—
91	C₄	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
92	C₄	#14579088	1	1	yes	characteristic
93	C₄	#14579102	1	1	yes	characteristic
94	C₄	#14579105	1	1	yes	characteristic
95	C₂	—	8	2	no	—
96	C₂	D₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
97	C₂	#19098364	1	1	yes	characteristic
98	C₂	#19098370	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₇₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#19098316

C₂

yes

maximal, characteristic, complemented

C₄×D₈×C₇₉

C₂

yes

maximal, characteristic

C₂×C₇₉⋊C₁₆

—

C₄⋊(C₇₉⋊C₈)

—

C₂×D₈×C₇₉

C₄

yes

characteristic

C₄×D₄×C₇₉

—

#107×C₇₉

C₄

yes

characteristic

#102×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₇₉⋊C₈

—

C₇₉⋊C₁₆

—

C₂×D₄×C₇₉

—

C₂²×C₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

C₈

yes

complemented

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

D₄

yes

characteristic

C₂³×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

C₂×C₈

yes

characteristic

C₈×C₇₉

M₁₆

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#102

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊C₈

yes

characteristic

C₄×C₇₉

#104

yes

characteristic

C₄×C₇₉

D₁₆

yes

characteristic

C₄×C₇₉

SD₃₂

yes

characteristic

C₂×C₇₉

—

C₂×C₇₉

D₄⋊C₈

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₄×D₈

D₇₉

yes

characteristic

C₄×C₁₆

—

#335

—

C₂×D₈

Dic₇₉

yes

characteristic

C₄×D₄

—

C₂×C₁₆

—

158

—

#107

Dic₇₉

yes

characteristic

C₄⋊C₈

—

158

—

#102

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

C₇₉⋊C₈

yes

complemented

C₂×C₈

—

316

—

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₇₉

yes

characteristic

C₁₆

—

158

—

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₇₉

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

632

—

C₈

C₂×C₇₉⋊C₈

yes

characteristic

C₈

#11929608

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

#14579082

yes

characteristic

C₄

—

C₄

—

C₄

C₂²⋊(C₇₉⋊C₈)

yes

C₄

yes

C₄

yes

C₄

yes

C₂

—

C₂

D₄⋊(C₇₉⋊C₈)

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	#11929609
commutator	C₈×C₇₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₉
Fitting	C₄×D₈×C₇₉	C₂
socle	C₂²×C₇₉	#102
prime radical	C₂×D₈×C₇₉	C₄
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	C₄×D₈	D₇₉
hypocenter	C₇₉	#1331
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

subgroup

G/H

center

C₂×C₄

#11929609

commutator

C₈×C₇₉

C₂×C₈

Frattini

C₄×C₈

C₂×D₇₉

Fitting

C₄×D₈×C₇₉

C₂

socle

C₂²×C₇₉

#102

prime radical

C₂×D₈×C₇₉

C₄

cosocle

C₄×C₈×C₇₉

C₂²

hypercenter

C₄×D₈

D₇₉

hypocenter

C₇₉

#1331

LCS

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

N	H ≅ G/N	type
1. C₄×C₇₉⋊C₁₆	C₂	semidirect
2. #19098316	C₂	semidirect
16. D₈×C₇₉	C₈	semidirect
50. C₇₉	#1331	semidirect
64. D₈	C₇₉⋊C₈	semidirect

H ≅ G/N

type

1. C₄×C₇₉⋊C₁₆

C₂

semidirect

2. #19098316

C₂

semidirect

16. D₈×C₇₉

C₈

semidirect

50. C₇₉

#1331

semidirect

64. D₈

C₇₉⋊C₈

semidirect

Subgroups — #23761361

Conjugacy classes of subgroups

Complements