Group #23762220 — subgroups

Subgroups — #23762220

Order 10112.

160 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₈×Dic₁₅₈	C₂	1	2	yes	maximal
2	C₄×Dic₃₁₆	C₂	1	1	yes	maximal, characteristic
3	#19098314	C₂	1	1	yes	maximal, characteristic
4	#19098295	C₂	1	2	yes	maximal
5	#322×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	C₄	1	1	yes	characteristic
7	C₄×Dic₁₅₈	C₂²	1	2	yes	—
8	#14579095	C₄	1	1	yes	characteristic
9	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
10	Dic₇₉⋊C₈	—	2	2	no	—
11	#14579086	C₄	1	2	yes	—
12	C₈×Dic₇₉	—	2	2	no	—
13	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₅₈	C₂×C₄	1	2	yes	—
17	Dic₃₁₆	C₈	1	4	yes	complemented
18	C₂×C₇₉⋊C₈	—	2	2	no	—
19	C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
20	Dic₇₉⋊C₄	—	2	2	no	—
21	C₄×Dic₇₉	—	2	2	no	—
22	C₂×C₈×C₇₉	—	2	1	no	—
23	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	D₄	1	2	yes	—
26	C₄²×C₇₉	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
30	C₂×Dic₇₉	—	2	2	no	—
31	C₂×Dic₇₉	—	2	2	no	—
32	Dic₁₅₈	—	2	2	no	—
33	Dic₁₅₈	C₂×C₈	1	4	yes	—
34	C₈×C₇₉	—	2	1	no	—
35	C₈×C₇₉	—	2	2	no	—
36	C₈×C₇₉	—	4	1	no	—
37	C₈×C₇₉	C₂×C₈	1	2	yes	—
38	C₇₉⋊C₈	—	4	2	no	—
39	C₂²×C₇₉	C₄×D₄	1	1	yes	characteristic
40	C₄×C₇₉	—	2	1	no	—
41	C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₇₉	#131	1	1	yes	characteristic
43	C₄×C₇₉	#137	1	2	yes	—
44	Dic₇₉	—	2	4	no	—
45	Dic₇₉	—	4	2	no	—
46	C₂×C₇₉	C₈×D₄	1	1	yes	characteristic
47	C₂×C₇₉	#441	1	1	yes	characteristic
48	C₂×C₇₉	#444	1	1	yes	characteristic
49	#1579	—	79	1	no	maximal, Sylow
50	C₇₉	#1579	1	1	yes	characteristic, complemented, Sylow
51	C₈×Q₈	—	79	2	no	—
52	C₄×Q₁₆	—	79	1	no	—
53	#334	—	79	1	no	—
54	Q₈⋊C₈	—	79	2	no	—
55	#322	D₇₉	1	1	yes	characteristic
56	C₂×Q₁₆	—	79	1	no	—
57	C₄×Q₈	—	79	2	no	—
58	#107	—	79	1	no	—
59	C₄⋊C₈	—	79	2	no	—
60	C₄⋊C₈	—	158	2	no	—
61	#103	—	79	2	no	—
62	C₄×C₈	—	158	2	no	—
63	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
64	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
65	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
66	C₂×Q₈	—	79	2	no	—
67	Q₁₆	—	79	4	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	158	2	no	—
70	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
71	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
72	C₂×C₈	D₃₁₆	1	2	yes	—
73	C₄⋊C₄	—	79	2	no	—
74	C₄⋊C₄	—	158	2	no	—
75	C₄²	—	158	2	no	—
76	C₄²	C₂²×D₇₉	1	1	yes	characteristic
77	Q₈	—	79	4	no	—
78	Q₈	—	158	2	no	—
79	C₂×C₄	—	158	2	no	—
80	C₂×C₄	—	158	2	no	—
81	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
82	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
83	C₂×C₄	#11929624	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	316	2	no	—
88	C₈	C₈×D₇₉	1	2	yes	—
89	C₂²	C₄×D₃₁₆	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	316	2	no	—
92	C₄	—	158	4	no	—
93	C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
94	C₄	#14579167	1	1	yes	characteristic
95	C₄	#14579194	1	2	yes	—
96	C₂	C₈×D₃₁₆	1	1	yes	characteristic
97	C₂	#19098671	1	1	yes	characteristic
98	C₂	#19098686	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₁₅₈

C₂

yes

maximal

C₄×Dic₃₁₆

C₂

yes

maximal, characteristic

#19098314

C₂

yes

maximal, characteristic

#19098295

C₂

yes

maximal

#322×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₄

yes

characteristic

C₄×Dic₁₅₈

C₂²

yes

—

#14579095

C₄

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

Dic₇₉⋊C₈

—

#14579086

C₄

yes

—

C₈×Dic₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

C₂×C₄

yes

—

Dic₃₁₆

C₈

yes

complemented

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

C₂×C₄

yes

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

C₂×C₈

yes

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

C₂×C₈

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₂²×C₈

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

C₈×D₄

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₈×Q₈

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

D₇₉

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

158

—

#103

—

C₄×C₈

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

D₃₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

Q₈

—

Q₈

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₂×C₄

#11929624

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

316

—

C₈

C₈×D₇₉

yes

—

C₂²

C₄×D₃₁₆

yes

characteristic

C₄

—

C₄

—

316

—

C₄

—

158

—

C₄

C₂×C₈×D₇₉

yes

C₄

yes

C₄

yes

—

C₂

C₈×D₃₁₆

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₃₁₆
commutator	C₄×C₇₉	C₂²×C₈
Frattini	C₄²	C₂²×D₇₉
Fitting	#322×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₄×D₄
cosocle	C₄²×C₇₉	C₂³
hypercenter	#322	D₇₉
hypocenter	C₇₉	#1579
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₃₁₆

commutator

C₄×C₇₉

C₂²×C₈

Frattini

C₄²

C₂²×D₇₉

Fitting

#322×C₇₉

C₂

socle, prime radical

C₂²×C₇₉

C₄×D₄

cosocle

C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
17. Dic₃₁₆	C₈	semidirect
50. C₇₉	#1579	semidirect

H ≅ G/N

type

17. Dic₃₁₆

C₈

semidirect

50. C₇₉

#1579

semidirect

Subgroups — #23762220

Conjugacy classes of subgroups

Complements