Group #23765247 — subgroups

Subgroups — D₁₆×Dic₇₉ #23765247

Order 10112.

174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 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	D₈×Dic₇₉	C₂	1	2	yes	maximal, complemented
2	#19098389	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098364	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
6	D₄×Dic₇₉	—	2	2	no	—
7	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
8	#14579095	C₂²	1	2	yes	—
9	#14579082	—	2	2	no	—
10	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
11	C₂×D₈×C₇₉	C₂²	1	2	yes	—
12	D₁₆×C₇₉	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₂²×Dic₇₉	—	4	2	no	—
15	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
16	C₄⋊Dic₇₉	—	2	2	no	—
17	C₂²⋊Dic₇₉	—	4	2	no	—
18	C₄×Dic₇₉	D₄	1	1	yes	characteristic
19	C₇₉⋊C₁₆	—	2	1	no	—
20	C₂×D₄×C₇₉	—	2	2	no	—
21	D₈×C₇₉	—	2	2	no	—
22	D₈×C₇₉	C₂×C₄	1	4	yes	complemented
23	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
24	C₁₆×C₇₉	C₂×C₄	1	2	yes	complemented
25	C₂³×C₇₉	—	4	2	no	—
26	D₄×C₇₉	—	2	4	no	—
27	D₄×C₇₉	—	4	2	no	—
28	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₇₉	—	4	2	no	—
30	C₂×Dic₇₉	—	8	4	no	—
31	C₂×Dic₇₉	D₈	1	1	yes	characteristic
32	C₂×Dic₇₉	D₈	1	1	yes	characteristic
33	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₇₉	#41	1	1	yes	characteristic
35	C₇₉⋊C₈	—	2	1	no	—
36	C₂²×C₇₉	—	4	4	no	—
37	C₂²×C₇₉	—	8	2	no	—
38	C₂²×C₇₉	—	8	2	no	—
39	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
40	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
41	C₄×C₇₉	#135	1	1	yes	characteristic
42	Dic₇₉	—	2	1	no	—
43	Dic₇₉	—	8	2	no	—
44	Dic₇₉	D₁₆	1	2	yes	direct product factor
45	C₂×C₇₉	—	8	4	no	—
46	C₂×C₇₉	C₄×D₈	1	1	yes	characteristic
47	C₂×C₇₉	C₂×D₁₆	1	1	yes	characteristic
48	C₂×C₇₉	#508	1	1	yes	characteristic
49	C₄×D₁₆	—	79	1	no	maximal, Sylow
50	C₇₉	C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₁₆	D₇₉	1	1	yes	characteristic
52	C₄×D₈	—	79	2	no	—
53	#366	—	79	1	no	—
54	#357	—	79	2	no	—
55	C₄×C₁₆	—	79	1	no	—
56	C₂×D₈	C₂×D₇₉	1	2	yes	—
57	C₄×D₄	—	158	2	no	—
58	D₁₆	Dic₇₉	1	4	yes	direct product factor
59	C₂×C₁₆	—	79	1	no	—
60	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
61	#107	—	79	2	no	—
62	#102	—	158	2	no	—
63	C₄×C₈	—	79	1	no	—
64	C₂×D₄	—	2	2	no	—
65	C₂²×C₄	—	316	2	no	—
66	D₈	—	2	2	no	—
67	D₈	C₂×Dic₇₉	1	4	yes	complemented
68	C₂×C₈	—	79	1	no	—
69	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
70	C₄⋊C₄	—	158	2	no	—
71	C₂²⋊C₄	—	316	2	no	—
72	C₄²	—	79	1	no	—
73	C₁₆	—	158	1	no	—
74	C₁₆	C₂×Dic₇₉	1	2	yes	complemented
75	C₂³	—	4	2	no	—
76	D₄	—	2	4	no	—
77	D₄	—	4	2	no	—
78	C₂×C₄	—	316	2	no	—
79	C₂×C₄	—	79	1	no	—
80	C₂×C₄	—	79	1	no	—
81	C₂×C₄	—	632	4	no	—
82	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
83	C₈	—	158	1	no	—
84	C₈	C₂²×Dic₇₉	1	1	yes	characteristic
85	C₈	#11929623	1	1	yes	characteristic
86	C₂²	—	4	4	no	—
87	C₂²	—	8	2	no	—
88	C₂²	—	8	2	no	—
89	C₂²	D₈×D₇₉	1	1	yes	characteristic
90	C₄	—	79	2	no	—
91	C₄	—	632	2	no	—
92	C₄	—	158	1	no	—
93	C₄	D₄×Dic₇₉	1	1	yes	characteristic
94	C₄	#14579180	1	1	yes	characteristic
95	C₂	—	8	4	no	—
96	C₂	D₈×Dic₇₉	1	1	yes	characteristic
97	C₂	D₁₆×D₇₉	1	1	yes	characteristic
98	C₂	#19098992	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₈×Dic₇₉

C₂

yes

maximal, complemented

#19098389

C₂

yes

maximal, characteristic, complemented

#19098364

C₂

yes

maximal, complemented

C₁₆×Dic₇₉

C₂

yes

maximal, characteristic, complemented

C₂×D₁₆×C₇₉

C₂

yes

maximal, characteristic

D₄×Dic₇₉

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

—

#14579082

—

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×D₈×C₇₉

C₂²

yes

—

D₁₆×C₇₉

C₄

yes

complemented

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

C₂×D₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

C₂×C₄

yes

complemented

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

C₂×C₄

yes

complemented

C₂³×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₂×Dic₇₉

D₈

yes

characteristic

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

#135

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

D₁₆

yes

direct product factor

C₂×C₇₉

—

C₂×C₇₉

C₄×D₈

yes

characteristic

C₂×C₇₉

C₂×D₁₆

yes

characteristic

C₂×C₇₉

#508

yes

characteristic

C₄×D₁₆

—

maximal, Sylow

C₇₉

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₁₆

D₇₉

yes

characteristic

C₄×D₈

—

#366

—

#357

—

C₄×C₁₆

—

C₂×D₈

C₂×D₇₉

yes

—

C₄×D₄

—

158

—

D₁₆

Dic₇₉

yes

direct product factor

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

—

#102

—

158

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

316

—

D₈

—

D₈

C₂×Dic₇₉

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

316

—

C₄²

—

C₁₆

—

158

—

C₁₆

C₂×Dic₇₉

yes

complemented

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

632

—

C₂×C₄

D₄×D₇₉

yes

characteristic

C₈

—

158

—

C₈

C₂²×Dic₇₉

yes

characteristic

C₈

#11929623

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

D₈×D₇₉

yes

characteristic

C₄

—

C₄

—

632

—

C₄

—

158

—

C₄

D₄×Dic₇₉

yes

characteristic

C₄

#14579180

yes

characteristic

C₂

—

C₂

D₈×Dic₇₉

yes

characteristic

C₂

D₁₆×D₇₉

yes

characteristic

C₂

#19098992

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting, prime radical	C₂×D₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₂×D₁₆	D₇₉
hypocenter	C₇₉	C₄×D₁₆
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator

C₈×C₇₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₉

Fitting, prime radical

C₂×D₁₆×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₂×D₁₆

D₇₉

hypocenter

C₇₉

C₄×D₁₆

LCS

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. D₈×Dic₇₉	C₂	semidirect
2. #19098389	C₂	semidirect
3. #19098364	C₂	semidirect
4. C₁₆×Dic₇₉	C₂	semidirect
12. D₁₆×C₇₉	C₄	semidirect
22. D₈×C₇₉	C₂×C₄	semidirect
24. C₁₆×C₇₉	C₂×C₄	semidirect
44. Dic₇₉	D₁₆	direct (N × H)
50. C₇₉	C₄×D₁₆	semidirect
58. D₁₆	Dic₇₉	direct (N × H)
67. D₈	C₂×Dic₇₉	semidirect
74. C₁₆	C₂×Dic₇₉	semidirect

H ≅ G/N

type

1. D₈×Dic₇₉

C₂

semidirect

2. #19098389

C₂

semidirect

3. #19098364

C₂

semidirect

4. C₁₆×Dic₇₉

C₂

semidirect

12. D₁₆×C₇₉

C₄

semidirect

22. D₈×C₇₉

C₂×C₄

semidirect

24. C₁₆×C₇₉

C₂×C₄

semidirect

44. Dic₇₉

D₁₆

direct (N × H)

50. C₇₉

C₄×D₁₆

semidirect

58. D₁₆

Dic₇₉

direct (N × H)

67. D₈

C₂×Dic₇₉

semidirect

74. C₁₆

C₂×Dic₇₉

semidirect

Subgroups — D₁₆×Dic₇₉ #23765247

Conjugacy classes of subgroups

Complements

Subgroups — D16×Dic79 #23765247

Conjugacy classes of subgroups

Complements

Subgroups — D₁₆×Dic₇₉ #23765247