Group #23765648 — subgroups

Subgroups — #23765648

Order 10112.

216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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	C₂×D₁₂₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14579102	C₂	1	2	yes	maximal, complemented
3	#19098938	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, complemented
6	C₂×D₆₃₂	C₂²	1	2	yes	—
7	C₂×#11929609	—	2	2	no	—
8	#14579157	—	2	2	no	—
9	D₁₂₆₄	—	2	2	no	—
10	#14579102	—	2	4	no	—
11	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
13	C₂×D₈×C₇₉	C₂²	1	2	yes	—
14	D₁₆×C₇₉	—	2	2	no	—
15	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×D₃₁₆	—	2	2	no	—
17	C₂×C₂²⋊D₇₉	—	4	4	no	—
18	D₆₃₂	—	2	2	no	—
19	D₆₃₂	—	2	2	no	—
20	#11929609	—	4	4	no	—
21	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
22	C₄×Dic₇₉	D₄	1	1	yes	characteristic
23	C₇₉⋊C₁₆	D₄	1	2	yes	complemented
24	C₂×D₄×C₇₉	—	2	2	no	—
25	D₈×C₇₉	—	2	2	no	—
26	D₈×C₇₉	—	2	2	no	—
27	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
28	C₁₆×C₇₉	D₄	1	2	yes	complemented
29	C₂³×C₇₉	—	4	2	no	—
30	C₂²×D₇₉	—	4	2	no	—
31	D₄×C₇₉	—	4	2	no	—
32	D₄×C₇₉	—	4	2	no	—
33	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
34	C₂²⋊D₇₉	—	8	8	no	—
35	C₂×Dic₇₉	D₈	1	2	yes	—
36	D₃₁₆	—	4	2	no	—
37	D₃₁₆	—	4	2	no	—
38	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
40	C₇₉⋊C₈	D₈	1	2	yes	—
41	C₂²×C₇₉	—	8	2	no	—
42	C₂²×C₇₉	—	8	4	no	—
43	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
44	C₂×D₇₉	—	8	2	no	—
45	C₂×D₇₉	—	8	4	no	—
46	C₄×C₇₉	#127	1	1	yes	characteristic
47	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
48	Dic₇₉	D₁₆	1	4	yes	complemented
49	C₂×C₇₉	—	16	2	no	—
50	C₂×C₇₉	#493	1	1	yes	characteristic
51	C₂×C₇₉	C₂×D₁₆	1	2	yes	—
52	D₇₉	—	16	2	no	—
53	#2246	—	79	1	no	maximal, Sylow
54	C₇₉	#2246	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₁₆	—	79	2	no	—
56	C₂×D₁₆	—	79	1	no	—
57	C₂×D₁₆	D₇₉	1	1	yes	characteristic, complemented
58	#493	—	79	2	no	—
59	C₄×C₁₆	—	79	1	no	—
60	C₂×D₈	—	79	2	no	—
61	C₂×D₈	—	158	2	no	—
62	C₂×D₈	C₂×D₇₉	1	2	yes	—
63	#127	—	158	2	no	—
64	D₁₆	—	2	2	no	—
65	D₁₆	—	158	4	no	—
66	D₁₆	—	158	2	no	—
67	C₂×C₁₆	—	79	1	no	—
68	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
69	C₄×C₈	—	79	1	no	—
70	C₂×D₄	—	2	2	no	—
71	C₂×D₄	—	316	4	no	—
72	C₂×D₄	—	158	2	no	—
73	D₈	—	2	2	no	—
74	D₈	—	2	2	no	—
75	D₈	—	316	4	no	—
76	D₈	—	158	2	no	—
77	D₈	—	158	2	no	—
78	C₂×C₈	—	79	1	no	—
79	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
80	C₄²	—	79	1	no	—
81	C₁₆	—	79	2	no	—
82	C₁₆	C₂²⋊D₇₉	1	2	yes	complemented
83	C₂³	—	4	2	no	—
84	C₂³	—	316	2	no	—
85	D₄	—	4	2	no	—
86	D₄	—	4	2	no	—
87	D₄	—	316	2	no	—
88	D₄	—	316	2	no	—
89	D₄	—	632	8	no	—
90	C₂×C₄	—	79	2	no	—
91	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
92	C₈	—	79	2	no	—
93	C₈	D₄×D₇₉	1	1	yes	characteristic
94	C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
95	C₂²	—	8	2	no	—
96	C₂²	—	8	4	no	—
97	C₂²	—	632	2	no	—
98	C₂²	—	632	4	no	—
99	C₂²	D₈×D₇₉	1	1	yes	characteristic
100	C₄	—	79	4	no	—
101	C₄	#14579157	1	1	yes	characteristic
102	C₄	D₈×D₇₉	1	1	yes	characteristic
103	C₂	—	16	2	no	—
104	C₂	—	1264	2	no	—
105	C₂	#19098938	1	1	yes	characteristic
106	C₂	D₁₆×D₇₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₁₂₆₄

C₂

yes

maximal, characteristic, complemented

C₂×#14579102

C₂

yes

maximal, complemented

#19098938

C₂

yes

maximal, complemented

C₁₆×Dic₇₉

C₂

yes

maximal, characteristic, complemented

C₂×D₁₆×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×D₆₃₂

C₂²

yes

—

C₂×#11929609

—

#14579157

—

D₁₂₆₄

—

#14579102

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×D₈×C₇₉

C₂²

yes

—

D₁₆×C₇₉

—

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

D₆₃₂

—

D₆₃₂

—

#11929609

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

D₄

yes

complemented

C₂×D₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

D₄

yes

complemented

C₂³×C₇₉

—

C₂²×D₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

D₈

yes

—

D₃₁₆

—

D₃₁₆

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

C₂×D₄

yes

characteristic

C₇₉⋊C₈

D₈

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

#127

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

Dic₇₉

D₁₆

yes

complemented

C₂×C₇₉

—

C₂×C₇₉

#493

yes

characteristic

C₂×C₇₉

C₂×D₁₆

yes

—

D₇₉

—

#2246

—

maximal, Sylow

C₇₉

#2246

yes

characteristic, complemented, Sylow

C₂×D₁₆

—

C₂×D₁₆

—

C₂×D₁₆

D₇₉

yes

characteristic, complemented

#493

—

C₄×C₁₆

—

C₂×D₈

—

C₂×D₈

—

158

—

C₂×D₈

C₂×D₇₉

yes

—

#127

—

158

—

D₁₆

—

D₁₆

—

158

—

D₁₆

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₄×C₈

—

C₂×D₄

—

C₂×D₄

—

316

—

C₂×D₄

—

158

—

D₈

—

D₈

—

D₈

—

316

—

D₈

—

158

—

D₈

—

158

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄²

—

C₁₆

—

C₁₆

C₂²⋊D₇₉

yes

complemented

C₂³

—

C₂³

—

316

—

D₄

—

D₄

—

D₄

—

316

—

D₄

—

316

—

D₄

—

632

—

C₂×C₄

—

C₂×C₄

D₄×D₇₉

yes

characteristic

C₈

—

C₈

D₄×D₇₉

yes

characteristic

C₈

C₂×C₂²⋊D₇₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

632

—

C₂²

—

632

—

C₂²

D₈×D₇₉

yes

characteristic

100

C₄

—

101

C₄

#14579157

yes

characteristic

102

C₄

D₈×D₇₉

yes

characteristic

103

C₂

—

104

C₂

—

1264

—

105

C₂

#19098938

yes

characteristic

106

C₂

D₁₆×D₇₉

yes

—

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₂×D₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
hypercenter	C₂×D₁₆	D₇₉
hypocenter	C₇₉	#2246
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₂×D₁₆×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

hypercenter

C₂×D₁₆

D₇₉

hypocenter

C₇₉

#2246

LCS

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. C₂×D₁₂₆₄	C₂	semidirect
2. C₂×#14579102	C₂	semidirect
3. #19098938	C₂	semidirect
4. C₁₆×Dic₇₉	C₂	semidirect
5. C₂×D₁₆×C₇₉	C₂	semidirect
23. C₇₉⋊C₁₆	D₄	semidirect
28. C₁₆×C₇₉	D₄	semidirect
48. Dic₇₉	D₁₆	semidirect
54. C₇₉	#2246	semidirect
57. C₂×D₁₆	D₇₉	semidirect
82. C₁₆	C₂²⋊D₇₉	semidirect

H ≅ G/N

type

1. C₂×D₁₂₆₄

C₂

semidirect

2. C₂×#14579102

C₂

semidirect

3. #19098938

C₂

semidirect

4. C₁₆×Dic₇₉

C₂

semidirect

5. C₂×D₁₆×C₇₉

C₂

semidirect

23. C₇₉⋊C₁₆

D₄

semidirect

28. C₁₆×C₇₉

D₄

semidirect

48. Dic₇₉

D₁₆

semidirect

54. C₇₉

#2246

semidirect

57. C₂×D₁₆

D₇₉

semidirect

82. C₁₆

C₂²⋊D₇₉

semidirect

Subgroups — #23765648

Conjugacy classes of subgroups

Complements