Group #23765661 — subgroups

Subgroups — #23765661

Order 10112.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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×Dic₆₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14579106	C₂	1	2	yes	maximal, complemented
3	C₂×D₁₂₆₄	C₂	1	1	yes	maximal, characteristic
4	#19098947	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₃₁₆	C₂²	1	2	yes	—
7	C₂×#11929613	—	2	2	no	—
8	C₂×D₆₃₂	C₂²	1	2	yes	—
9	#14579149	—	2	2	no	—
10	Dic₆₃₂	—	2	2	no	—
11	#14579106	—	2	4	no	—
12	D₁₂₆₄	—	2	2	no	—
13	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₅₈	—	2	2	no	—
17	C₂×D₃₁₆	—	2	2	no	—
18	Dic₃₁₆	—	2	2	no	—
19	Dic₃₁₆	—	2	2	no	—
20	#11929613	—	4	4	no	—
21	D₆₃₂	—	2	2	no	—
22	D₆₃₂	—	2	2	no	—
23	(C₂×D₇₉)⋊C₄	—	4	4	no	—
24	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
26	C₄²×C₇₉	D₄	1	1	yes	characteristic
27	C₁₆×C₇₉	D₄	1	2	yes	—
28	C₁₆×C₇₉	D₄	1	2	yes	—
29	C₂²×D₇₉	—	4	2	no	—
30	C₂×C₄×C₇₉	D₈	1	2	yes	—
31	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₇₉	—	4	2	no	—
33	D₃₁₆	—	4	2	no	—
34	D₃₁₆	—	4	2	no	—
35	Dic₁₅₈	—	4	2	no	—
36	Dic₁₅₈	—	4	2	no	—
37	C₈×C₇₉	D₈	1	2	yes	—
38	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
41	C₂×D₇₉	—	8	2	no	—
42	C₂×D₇₉	—	8	4	no	—
43	C₄×C₇₉	—	2	2	no	—
44	C₄×C₇₉	#127	1	1	yes	characteristic
45	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
46	Dic₇₉	—	8	2	no	—
47	C₂×C₇₉	#493	1	1	yes	characteristic
48	C₂×C₇₉	#508	1	2	yes	—
49	D₇₉	—	16	2	no	—
50	#2249	—	79	1	no	maximal, Sylow
51	C₇₉	#2249	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₃₂	—	79	1	no	—
53	C₂×SD₃₂	—	79	2	no	—
54	C₂×D₁₆	—	79	1	no	—
55	#495	—	79	2	no	—
56	C₄×C₁₆	D₇₉	1	1	yes	characteristic, complemented
57	C₂×Q₁₆	—	79	2	no	—
58	C₂×SD₁₆	—	158	2	no	—
59	C₂×D₈	—	79	2	no	—
60	#124	—	158	2	no	—
61	Q₃₂	—	158	2	no	—
62	SD₃₂	—	158	4	no	—
63	D₁₆	—	158	2	no	—
64	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
65	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
66	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
67	C₂×Q₈	—	158	2	no	—
68	C₂×D₄	—	158	2	no	—
69	Q₁₆	—	158	2	no	—
70	Q₁₆	—	158	2	no	—
71	SD₁₆	—	316	4	no	—
72	D₈	—	158	2	no	—
73	D₈	—	158	2	no	—
74	C₂×C₈	D₃₁₆	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
76	C₂²⋊C₄	—	316	4	no	—
77	C₄²	D₃₁₆	1	1	yes	characteristic
78	C₁₆	D₃₁₆	1	2	yes	—
79	C₁₆	D₃₁₆	1	2	yes	—
80	C₂³	—	316	2	no	—
81	Q₈	—	316	2	no	—
82	Q₈	—	316	2	no	—
83	D₄	—	316	2	no	—
84	D₄	—	316	2	no	—
85	C₂×C₄	—	316	2	no	—
86	C₂×C₄	D₆₃₂	1	2	yes	—
87	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
88	C₈	D₆₃₂	1	2	yes	—
89	C₈	C₂×D₃₁₆	1	1	yes	characteristic
90	C₈	C₂×D₃₁₆	1	1	yes	characteristic
91	C₂²	—	632	2	no	—
92	C₂²	—	632	4	no	—
93	C₂²	C₂×D₆₃₂	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	632	2	no	—
96	C₄	#14579158	1	1	yes	characteristic
97	C₄	C₂×D₆₃₂	1	1	yes	characteristic
98	C₂	—	1264	2	no	—
99	C₂	#19098940	1	1	yes	characteristic
100	C₂	#19098995	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₆₃₂

C₂

yes

maximal, characteristic, complemented

C₂×#14579106

C₂

yes

maximal, complemented

C₂×D₁₂₆₄

C₂

yes

maximal, characteristic

#19098947

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

C₂²

yes

—

C₂×#11929613

—

C₂×D₆₃₂

C₂²

yes

—

#14579149

—

Dic₆₃₂

—

#14579106

—

D₁₂₆₄

—

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929613

—

D₆₃₂

—

D₆₃₂

—

(C₂×D₇₉)⋊C₄

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₁₆×C₇₉

D₄

yes

—

C₁₆×C₇₉

D₄

yes

—

C₂²×D₇₉

—

C₂×C₄×C₇₉

D₈

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

D₈

yes

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#127

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

#493

yes

characteristic

C₂×C₇₉

#508

yes

—

D₇₉

—

#2249

—

maximal, Sylow

C₇₉

#2249

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×C₁₆

D₇₉

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×SD₁₆

—

158

—

C₂×D₈

—

#124

—

158

—

Q₃₂

—

158

—

SD₃₂

—

158

—

D₁₆

—

158

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

—

158

—

Q₁₆

—

158

—

Q₁₆

—

158

—

SD₁₆

—

316

—

D₈

—

158

—

D₈

—

158

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₂²⋊C₄

—

316

—

C₄²

D₃₁₆

yes

characteristic

C₁₆

D₃₁₆

yes

—

C₁₆

D₃₁₆

yes

—

C₂³

—

316

—

Q₈

—

316

—

Q₈

—

316

—

D₄

—

316

—

D₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

D₆₃₂

yes

—

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₈

D₆₃₂

yes

—

C₈

C₂×D₃₁₆

yes

characteristic

C₈

C₂×D₃₁₆

yes

characteristic

C₂²

—

632

—

C₂²

—

632

—

C₂²

C₂×D₆₃₂

yes

characteristic

C₄

—

C₄

—

632

—

C₄

#14579158

yes

characteristic

C₄

C₂×D₆₃₂

yes

characteristic

C₂

—

1264

—

C₂

#19098940

yes

characteristic

100

C₂

#19098995

yes

—

	subgroup	G/H
center	C₂²	C₂×D₆₃₂
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₄×C₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂×D₁₂₆₄	C₂
hypercenter	C₄×C₁₆	D₇₉
hypocenter	C₇₉	#2249
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×D₆₃₂

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₄×C₁₆×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂×D₁₂₆₄

C₂

hypercenter

C₄×C₁₆

D₇₉

hypocenter

C₇₉

#2249

LCS

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. C₂×Dic₆₃₂	C₂	semidirect
2. C₂×#14579106	C₂	semidirect
4. #19098947	C₂	semidirect
5. C₄×C₁₆×C₇₉	C₂	semidirect
51. C₇₉	#2249	semidirect
56. C₄×C₁₆	D₇₉	semidirect

H ≅ G/N

type

1. C₂×Dic₆₃₂

C₂

semidirect

2. C₂×#14579106

C₂

semidirect

4. #19098947

C₂

semidirect

5. C₄×C₁₆×C₇₉

C₂

semidirect

51. C₇₉

#2249

semidirect

56. C₄×C₁₆

D₇₉

semidirect

Subgroups — #23765661

Conjugacy classes of subgroups

Complements