Group #34209291 — subgroups

Subgroups — #34209291

Order 20224.

146 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 63 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	#23765677	C₂	1	2	yes	maximal
2	#23761601	C₂	1	2	yes	maximal
3	#23761600	C₂	1	1	yes	maximal, characteristic
4	C₃₂×Dic₇₉	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#1423	C₂	1	1	yes	maximal, characteristic
6	#19098964	—	2	2	no	—
7	C₂×C₇₉⋊C₃₂	C₂²	1	1	yes	characteristic
8	#19098390	—	2	2	no	—
9	#19098389	C₂²	1	2	yes	—
10	C₁₆×Dic₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
12	#366×C₇₉	C₂²	1	2	yes	—
13	#14579152	—	4	2	no	—
14	C₂×C₇₉⋊C₁₆	D₄	1	1	yes	characteristic
15	#14579095	—	2	2	no	—
16	#14579092	—	4	2	no	—
17	C₈×Dic₇₉	D₄	1	1	yes	characteristic
18	C₇₉⋊C₃₂	Q₈	1	2	yes	—
19	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
20	#107×C₇₉	—	2	2	no	—
21	C₃₂×C₇₉	Q₈	1	2	yes	—
22	C₂×C₇₉⋊C₈	D₈	1	1	yes	characteristic
23	C₄⋊Dic₇₉	—	4	2	no	—
24	C₄⋊Dic₇₉	—	8	2	no	—
25	Dic₇₉⋊C₄	—	8	2	no	—
26	C₄×Dic₇₉	D₈	1	1	yes	characteristic
27	C₇₉⋊C₁₆	Q₁₆	1	2	yes	—
28	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
29	C₄⋊C₄×C₇₉	—	4	2	no	—
30	C₁₆×C₇₉	C₂×Q₈	1	1	yes	characteristic
31	C₁₆×C₇₉	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₇₉	—	8	2	no	—
33	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
34	C₂×Dic₇₉	—	8	2	no	—
35	C₂×Dic₇₉	D₁₆	1	1	yes	characteristic
36	C₂×Dic₇₉	D₁₆	1	1	yes	characteristic
37	C₈×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
38	C₈×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
39	C₇₉⋊C₈	Q₃₂	1	2	yes	—
40	C₂²×C₇₉	C₂×D₁₆	1	1	yes	characteristic
41	C₄×C₇₉	—	16	2	no	—
42	C₄×C₇₉	#500	1	1	yes	characteristic
43	C₄×C₇₉	C₂×Q₃₂	1	1	yes	characteristic
44	Dic₇₉	—	2	1	no	—
45	Dic₇₉	—	2	1	no	—
46	Dic₇₉	—	16	2	no	—
47	#13732	—	79	1	no	maximal, Sylow
48	C₂×C₇₉	#2252	1	1	yes	characteristic
49	C₂×C₇₉	#2262	1	1	yes	characteristic
50	C₂×C₇₉	#2262	1	1	yes	characteristic
51	#2253	—	79	2	no	—
52	#1424	—	79	2	no	—
53	#1423	—	79	1	no	—
54	#1423	D₇₉	1	1	yes	characteristic
55	C₄×C₃₂	—	79	1	no	—
56	C₇₉	#13732	1	1	yes	characteristic, complemented, Sylow
57	#499	—	158	2	no	—
58	C₂×C₃₂	—	79	1	no	—
59	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
60	#367	—	158	2	no	—
61	#366	—	79	2	no	—
62	#366	C₂×D₇₉	1	2	yes	—
63	C₄×C₁₆	—	79	1	no	—
64	#125	—	316	2	no	—
65	C₂×C₁₆	—	79	1	no	—
66	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
67	#107	—	2	2	no	—
68	#107	—	158	2	no	—
69	#106	—	316	2	no	—
70	C₄×C₈	—	79	1	no	—
71	C₃₂	—	79	2	no	—
72	C₃₂	Dic₁₅₈	1	2	yes	—
73	C₂×C₈	—	79	1	no	—
74	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
75	C₄⋊C₄	—	4	2	no	—
76	C₄⋊C₄	—	316	2	no	—
77	C₄⋊C₄	—	632	2	no	—
78	C₄⋊C₄	—	632	2	no	—
79	C₄²	—	79	1	no	—
80	C₁₆	—	79	2	no	—
81	C₁₆	Q₈×D₇₉	1	1	yes	characteristic
82	C₁₆	C₂×Dic₁₅₈	1	1	yes	characteristic
83	C₂×C₄	—	8	2	no	—
84	C₂×C₄	—	79	1	no	—
85	C₂×C₄	—	79	1	no	—
86	C₂×C₄	—	632	2	no	—
87	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
88	C₈	—	79	2	no	—
89	C₈	#14579160	1	1	yes	characteristic
90	C₈	Q₁₆×D₇₉	1	1	yes	characteristic
91	C₂²	D₁₆×D₇₉	1	1	yes	characteristic
92	C₄	—	16	2	no	—
93	C₄	—	158	1	no	—
94	C₄	—	158	1	no	—
95	C₄	—	1264	2	no	—
96	C₄	#19098967	1	1	yes	characteristic
97	C₄	Q₃₂×D₇₉	1	1	yes	characteristic
98	C₂	#23765674	1	1	yes	characteristic
99	C₂	#23765706	1	1	yes	characteristic
100	C₂	#23765710	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23765677

C₂

yes

maximal

#23761601

C₂

yes

maximal

#23761600

C₂

yes

maximal, characteristic

C₃₂×Dic₇₉

C₂

yes

maximal, characteristic

C₇₉×#1423

C₂

yes

maximal, characteristic

#19098964

—

C₂×C₇₉⋊C₃₂

C₂²

yes

characteristic

#19098390

—

#19098389

C₂²

yes

—

C₁₆×Dic₇₉

C₂²

yes

characteristic

C₂×C₃₂×C₇₉

C₂²

yes

characteristic

#366×C₇₉

C₂²

yes

—

#14579152

—

C₂×C₇₉⋊C₁₆

D₄

yes

characteristic

#14579095

—

#14579092

—

C₈×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₃₂

Q₈

yes

—

C₂×C₁₆×C₇₉

C₂³

yes

characteristic

#107×C₇₉

—

C₃₂×C₇₉

Q₈

yes

—

C₂×C₇₉⋊C₈

D₈

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

D₈

yes

characteristic

C₇₉⋊C₁₆

Q₁₆

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

C₂×Q₈

yes

characteristic

C₁₆×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

D₁₆

yes

characteristic

C₂×Dic₇₉

D₁₆

yes

characteristic

C₈×C₇₉

C₄⋊Q₈

yes

characteristic

C₈×C₇₉

C₂×Q₁₆

yes

characteristic

C₇₉⋊C₈

Q₃₂

yes

—

C₂²×C₇₉

C₂×D₁₆

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

#500

yes

characteristic

C₄×C₇₉

C₂×Q₃₂

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

—

—

D₇₉

yes

characteristic

C₄×C₃₂

—

C₇₉

#13732

yes

characteristic, complemented, Sylow

#499

—

158

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₇₉

yes

characteristic

#367

—

158

—

#366

—

#366

C₂×D₇₉

yes

—

C₄×C₁₆

—

#125

—

316

—

C₂×C₁₆

—

C₂×C₁₆

C₂²×D₇₉

yes

characteristic

#107

—

#107

—

158

—

#106

—

316

—

C₄×C₈

—

C₃₂

—

C₃₂

Dic₁₅₈

yes

—

C₂×C₈

—

C₂×C₈

D₄×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

632

—

C₄⋊C₄

—

632

—

C₄²

—

C₁₆

—

C₁₆

Q₈×D₇₉

yes

characteristic

C₁₆

C₂×Dic₁₅₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

632

—

C₂×C₄

D₈×D₇₉

yes

characteristic

C₈

—

C₈

#14579160

yes

characteristic

C₈

Q₁₆×D₇₉

yes

characteristic

C₂²

D₁₆×D₇₉

yes

characteristic

C₄

—

C₄

—

158

—

C₄

—

158

—

C₄

—

1264

—

C₄

#19098967

yes

characteristic

C₄

Q₃₂×D₇₉

yes

C₂

yes

C₂

yes

100

C₂

#23765710

yes

characteristic

	subgroup	G/H
center	C₂²	D₁₆×D₇₉
commutator, cosocle	C₂×C₁₆×C₇₉	C₂³
Frattini	C₂×C₁₆	C₂²×D₇₉
Fitting	C₇₉×#1423	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₁₆
hypercenter	#1423	D₇₉
hypocenter	C₇₉	#13732
LCS	G ▷ C₂×C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1423

subgroup

G/H

center

C₂²

D₁₆×D₇₉

commutator, cosocle

C₂×C₁₆×C₇₉

C₂³

Frattini

C₂×C₁₆

C₂²×D₇₉

Fitting

C₇₉×#1423

C₂

socle, prime radical

C₂²×C₇₉

C₂×D₁₆

D₇₉

C₇₉

G ▷ C₂×C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1423

N	H ≅ G/N	type
56. C₇₉	#13732	semidirect

H ≅ G/N

type

56. C₇₉

#13732

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23765677	2
#23761601	2
#23761600	2
C₃₂×Dic₇₉	2
C₇₉×#1423	2
#13732	79

subgroup

index

#23765677

#23761601

#23761600

C₃₂×Dic₇₉

C₇₉×#1423

#13732

Subgroups — #34209291

Conjugacy classes of subgroups

Complements

Maximal subgroups