Group #23765708 — subgroups

Subgroups — #23765708

Order 10112.

106 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 35 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	#19098996	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098992	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098403	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098402	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₂×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#14579184	—	2	1	no	—
9	#14579180	—	2	1	no	—
10	Dic₆₃₂	C₂²	1	1	yes	characteristic
11	#14579105	—	2	1	no	—
12	#14579104	—	2	1	no	—
13	D₁₂₆₄	C₂²	1	1	yes	characteristic
14	C₁₆×D₇₉	C₂²	1	1	yes	characteristic
15	C₇₉⋊C₃₂	C₂²	1	1	yes	characteristic
16	Q₃₂×C₇₉	C₂²	1	1	yes	characteristic
17	D₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₃₂×C₇₉	C₂²	1	1	yes	characteristic
19	#11929625	—	4	1	no	—
20	#11929623	—	4	1	no	—
21	Dic₃₁₆	—	2	1	no	—
22	#11929612	—	4	1	no	—
23	#11929611	—	4	1	no	—
24	D₆₃₂	—	2	1	no	—
25	C₈×D₇₉	D₄	1	1	yes	characteristic
26	C₇₉⋊C₁₆	D₄	1	1	yes	characteristic
27	Q₁₆×C₇₉	—	2	1	no	—
28	D₈×C₇₉	—	2	1	no	—
29	C₁₆×C₇₉	C₂³	1	1	yes	characteristic
30	Q₈×C₇₉	—	4	1	no	—
31	D₄×C₇₉	—	4	1	no	—
32	C₂²⋊D₇₉	—	8	1	no	—
33	C₂×Dic₇₉	—	8	1	no	—
34	D₃₁₆	—	4	1	no	—
35	D₃₁₆	—	8	1	no	—
36	C₄×D₇₉	—	8	1	no	—
37	C₄×D₇₉	D₈	1	1	yes	characteristic
38	Dic₁₅₈	—	4	1	no	—
39	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
40	C₇₉⋊C₈	D₈	1	1	yes	characteristic
41	C₂²×C₇₉	—	8	1	no	—
42	C₂×D₇₉	—	8	1	no	—
43	C₂×D₇₉	D₁₆	1	1	yes	characteristic
44	C₄×C₇₉	—	8	1	no	—
45	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
46	Dic₇₉	—	8	1	no	—
47	Dic₇₉	D₁₆	1	1	yes	characteristic
48	C₂×C₇₉	—	16	1	no	—
49	C₂×C₇₉	C₂×D₁₆	1	1	yes	characteristic
50	D₇₉	—	2	1	no	—
51	D₇₉	—	16	1	no	—
52	#2262	—	79	1	no	maximal, Sylow
53	C₇₉	#2262	1	1	yes	characteristic, complemented, Sylow
54	#508	—	79	1	no	—
55	#508	—	79	1	no	—
56	Q₆₄	—	79	1	no	—
57	SD₆₄	—	79	1	no	—
58	SD₆₄	D₇₉	1	1	yes	characteristic, complemented
59	D₃₂	—	79	1	no	—
60	C₂×C₃₂	—	79	1	no	—
61	#135	—	158	1	no	—
62	#135	—	158	1	no	—
63	Q₃₂	—	79	1	no	—
64	Q₃₂	C₂×D₇₉	1	1	yes	characteristic
65	SD₃₂	—	158	1	no	—
66	SD₃₂	—	158	1	no	—
67	D₁₆	—	79	1	no	—
68	D₁₆	C₂×D₇₉	1	1	yes	characteristic
69	C₂×C₁₆	—	79	1	no	—
70	C₃₂	—	79	1	no	—
71	C₃₂	C₂×D₇₉	1	1	yes	characteristic
72	#41	—	316	1	no	—
73	#41	—	316	1	no	—
74	Q₁₆	—	2	1	no	—
75	Q₁₆	—	158	1	no	—
76	SD₁₆	—	316	1	no	—
77	SD₁₆	—	316	1	no	—
78	D₈	—	2	1	no	—
79	D₈	—	158	1	no	—
80	C₂×C₈	—	79	1	no	—
81	C₁₆	—	79	1	no	—
82	C₁₆	C₂²×D₇₉	1	1	yes	characteristic
83	Q₈	—	4	1	no	—
84	Q₈	—	316	1	no	—
85	D₄	—	4	1	no	—
86	D₄	—	316	1	no	—
87	D₄	—	632	1	no	—
88	D₄	—	632	1	no	—
89	C₂×C₄	—	79	1	no	—
90	C₂×C₄	—	632	1	no	—
91	C₂×C₄	—	632	1	no	—
92	C₈	—	79	1	no	—
93	C₈	D₄×D₇₉	1	1	yes	characteristic
94	C₂²	—	8	1	no	—
95	C₂²	—	79	1	no	—
96	C₂²	—	632	1	no	—
97	C₄	—	8	1	no	—
98	C₄	—	79	1	no	—
99	C₄	—	632	1	no	—
100	C₄	D₈×D₇₉	1	1	yes	characteristic
101	C₂	—	16	1	no	—
102	C₂	—	158	1	no	—
103	C₂	—	1264	1	no	—
104	C₂	D₁₆×D₇₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098996

C₂

yes

maximal, characteristic, complemented

#19098992

C₂

yes

maximal, characteristic, complemented

#19098403

C₂

yes

maximal, characteristic, complemented

#19098402

C₂

yes

maximal, characteristic, complemented

#19098398

C₂

yes

maximal, characteristic, complemented

C₃₂×D₇₉

C₂

yes

maximal, characteristic, complemented

SD₆₄×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579184

—

#14579180

—

Dic₆₃₂

C₂²

yes

characteristic

#14579105

—

#14579104

—

D₁₂₆₄

C₂²

yes

characteristic

C₁₆×D₇₉

C₂²

yes

characteristic

C₇₉⋊C₃₂

C₂²

yes

characteristic

Q₃₂×C₇₉

C₂²

yes

characteristic

D₁₆×C₇₉

C₂²

yes

characteristic

C₃₂×C₇₉

C₂²

yes

characteristic

#11929625

—

#11929623

—

Dic₃₁₆

—

#11929612

—

#11929611

—

D₆₃₂

—

C₈×D₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

D₄

yes

characteristic

Q₁₆×C₇₉

—

D₈×C₇₉

—

C₁₆×C₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

D₄×C₇₉

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

D₈

yes

characteristic

Dic₁₅₈

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₇₉⋊C₈

D₈

yes

characteristic

C₂²×C₇₉

—

C₂×D₇₉

—

C₂×D₇₉

D₁₆

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₂×D₈

yes

characteristic

Dic₇₉

—

Dic₇₉

D₁₆

yes

characteristic

C₂×C₇₉

—

C₂×C₇₉

C₂×D₁₆

yes

characteristic

D₇₉

—

D₇₉

—

#2262

—

maximal, Sylow

C₇₉

#2262

yes

characteristic, complemented, Sylow

#508

—

#508

—

Q₆₄

—

SD₆₄

—

SD₆₄

D₇₉

yes

characteristic, complemented

D₃₂

—

C₂×C₃₂

—

#135

—

158

—

#135

—

158

—

Q₃₂

—

Q₃₂

C₂×D₇₉

yes

characteristic

SD₃₂

—

158

—

SD₃₂

—

158

—

D₁₆

—

D₁₆

C₂×D₇₉

yes

characteristic

C₂×C₁₆

—

C₃₂

—

C₃₂

C₂×D₇₉

yes

characteristic

#41

—

316

—

#41

—

316

—

Q₁₆

—

Q₁₆

—

158

—

SD₁₆

—

316

—

SD₁₆

—

316

—

D₈

—

D₈

—

158

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂²×D₇₉

yes

characteristic

Q₈

—

Q₈

—

316

—

D₄

—

D₄

—

316

—

D₄

—

632

—

D₄

—

632

—

C₂×C₄

—

C₂×C₄

—

632

—

C₂×C₄

—

632

—

C₈

—

C₈

D₄×D₇₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

632

—

C₄

—

C₄

—

C₄

—

632

—

100

C₄

D₈×D₇₉

yes

characteristic

101

C₂

—

102

C₂

—

158

—

103

C₂

—

1264

—

104

C₂

D₁₆×D₇₉

yes

characteristic

	subgroup	G/H
center	C₂	D₁₆×D₇₉
commutator, cosocle	C₁₆×C₇₉	C₂³
Frattini	C₁₆	C₂²×D₇₉
Fitting	SD₆₄×C₇₉	C₂
socle	C₂×C₇₉	C₂×D₁₆
hypercenter	SD₆₄	D₇₉
hypocenter	C₇₉	#2262
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

subgroup

G/H

center

C₂

D₁₆×D₇₉

commutator, cosocle

C₁₆×C₇₉

C₂³

Frattini

C₁₆

C₂²×D₇₉

Fitting

SD₆₄×C₇₉

C₂

socle

C₂×C₇₉

C₂×D₁₆

hypercenter

SD₆₄

D₇₉

hypocenter

C₇₉

#2262

LCS

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

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

N	H ≅ G/N	type
1. #19098996	C₂	semidirect
2. #19098992	C₂	semidirect
3. #19098403	C₂	semidirect
4. #19098402	C₂	semidirect
5. #19098398	C₂	semidirect
6. C₃₂×D₇₉	C₂	semidirect
7. SD₆₄×C₇₉	C₂	semidirect
53. C₇₉	#2262	semidirect
58. SD₆₄	D₇₉	semidirect

H ≅ G/N

type

1. #19098996

C₂

semidirect

2. #19098992

C₂

semidirect

3. #19098403

C₂

semidirect

4. #19098402

C₂

semidirect

5. #19098398

C₂

semidirect

6. C₃₂×D₇₉

C₂

semidirect

7. SD₆₄×C₇₉

C₂

semidirect

53. C₇₉

#2262

semidirect

58. SD₆₄

D₇₉

semidirect

Subgroups — #23765708

Conjugacy classes of subgroups

Complements