Group #23765491 — subgroups

Subgroups — #23765491

Order 10112.

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

normal subgroups only

This group has 154 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×Dic₆₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098804	C₂	1	2	yes	maximal
3	#19098389	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098368	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	C₂²	1	2	yes	—
7	#14579140	—	2	2	no	—
8	Dic₆₃₂	—	2	2	no	—
9	#14579095	C₂²	1	2	yes	—
10	#14579086	—	2	2	no	—
11	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₇₉	—	2	2	no	—
13	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	2	2	no	—
16	Dic₃₁₆	—	2	2	no	—
17	Dic₃₁₆	—	2	2	no	—
18	C₄⋊Dic₇₉	—	2	2	no	—
19	Dic₇₉⋊C₄	—	4	2	no	—
20	C₂²⋊Dic₇₉	—	4	2	no	—
21	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₇₉	—	2	1	no	—
23	C₂×C₈×C₇₉	—	2	1	no	—
24	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
26	C₁₆×C₇₉	—	2	1	no	—
27	C₁₆×C₇₉	D₄	1	2	yes	—
28	C₂³×C₇₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₇₉	—	2	1	no	—
30	C₂×C₄×C₇₉	—	2	1	no	—
31	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₇₉	—	4	2	no	—
34	C₂×Dic₇₉	—	4	2	no	—
35	Dic₁₅₈	—	4	2	no	—
36	Dic₁₅₈	—	4	2	no	—
37	C₈×C₇₉	—	2	1	no	—
38	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₉	#41	1	1	yes	characteristic
40	C₂²×C₇₉	—	2	1	no	—
41	C₂²×C₇₉	—	2	1	no	—
42	C₂²×C₇₉	Q₃₂	1	2	yes	complemented
43	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
44	C₄×C₇₉	—	2	1	no	—
45	C₄×C₇₉	#121	1	1	yes	characteristic
46	C₄×C₇₉	#135	1	1	yes	characteristic
47	Dic₇₉	—	8	2	no	—
48	Dic₇₉	—	8	2	no	—
49	C₂×C₇₉	—	2	2	no	—
50	C₂×C₇₉	#466	1	1	yes	characteristic
51	C₂×C₇₉	C₂×Q₃₂	1	1	yes	characteristic
52	C₂×C₇₉	#508	1	1	yes	characteristic
53	#2216	—	79	1	no	maximal, Sylow
54	C₇₉	#2216	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₃₂	—	79	1	no	—
56	C₂²×C₁₆	D₇₉	1	1	yes	characteristic
57	#467	—	79	2	no	—
58	#366	—	79	1	no	—
59	#358	—	79	2	no	—
60	C₂×Q₁₆	—	79	2	no	—
61	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
62	C₂²⋊Q₈	—	158	2	no	—
63	Q₃₂	—	158	2	no	—
64	C₂×C₁₆	—	2	2	no	—
65	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
66	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
67	#107	—	79	2	no	—
68	#103	—	158	2	no	—
69	C₂×Q₈	—	158	2	no	—
70	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
71	Q₁₆	—	158	2	no	—
72	Q₁₆	—	158	2	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	2	1	no	—
75	C₂×C₈	D₃₁₆	1	1	yes	characteristic
76	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
77	C₄⋊C₄	—	316	2	no	—
78	C₄⋊C₄	—	158	2	no	—
79	C₂²⋊C₄	—	316	2	no	—
80	C₁₆	—	2	1	no	—
81	C₁₆	C₂²⋊D₇₉	1	2	yes	—
82	C₂³	D₆₃₂	1	1	yes	characteristic
83	Q₈	—	316	2	no	—
84	Q₈	—	316	2	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	316	2	no	—
88	C₂×C₄	—	316	2	no	—
89	C₂×C₄	D₆₃₂	1	1	yes	characteristic
90	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
91	C₈	—	2	1	no	—
92	C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
93	C₈	#11929624	1	1	yes	characteristic
94	C₂²	—	2	1	no	—
95	C₂²	—	2	1	no	—
96	C₂²	Dic₆₃₂	1	2	yes	complemented
97	C₂²	C₂×D₆₃₂	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	632	2	no	—
100	C₄	—	632	2	no	—
101	C₄	#14579135	1	1	yes	characteristic
102	C₄	#14579183	1	1	yes	characteristic
103	C₂	—	2	2	no	—
104	C₂	#19098799	1	1	yes	characteristic
105	C₂	C₂×Dic₆₃₂	1	1	yes	characteristic
106	C₂	#19098995	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₆₃₂

C₂

yes

maximal, characteristic, complemented

#19098804

C₂

yes

maximal

#19098389

C₂

yes

maximal, characteristic, complemented

#19098368

C₂

yes

maximal, complemented

C₂²×C₁₆×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₂²

yes

—

#14579140

—

Dic₆₃₂

—

#14579095

C₂²

yes

—

#14579086

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

—

C₁₆×C₇₉

D₄

yes

—

C₂³×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

Q₃₂

yes

complemented

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#466

yes

characteristic

C₂×C₇₉

C₂×Q₃₂

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂²×C₁₆

D₇₉

yes

—

—

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂²⋊Q₈

—

158

—

Q₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

—

#103

—

158

—

C₂×Q₈

—

158

—

C₂²×C₄

D₃₁₆

yes

characteristic

Q₁₆

—

158

—

Q₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

316

—

C₁₆

—

C₁₆

C₂²⋊D₇₉

yes

—

C₂³

D₆₃₂

yes

characteristic

Q₈

—

316

—

Q₈

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

D₆₃₂

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₈

—

C₈

C₂×C₂²⋊D₇₉

yes

characteristic

C₈

#11929624

yes

characteristic

C₂²

—

C₂²

—

C₂²

Dic₆₃₂

yes

complemented

C₂²

C₂×D₆₃₂

yes

characteristic

C₄

—

C₄

—

632

—

100

C₄

—

632

—

101

C₄

#14579135

yes

characteristic

102

C₄

#14579183

yes

characteristic

103

C₂

—

104

C₂

#19098799

yes

characteristic

105

C₂

C₂×Dic₆₃₂

yes

characteristic

106

C₂

#19098995

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₆₃₂
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₂²×C₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂³×C₇₉	D₈
hypercenter	C₂²×C₁₆	D₇₉
hypocenter	C₇₉	#2216
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center

C₂²

C₂×D₆₃₂

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₂²×C₁₆×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂³×C₇₉

D₈

hypercenter

C₂²×C₁₆

D₇₉

hypocenter

C₇₉

#2216

LCS

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
1. C₂×Dic₆₃₂	C₂	semidirect
3. #19098389	C₂	semidirect
4. #19098368	C₂	semidirect
42. C₂²×C₇₉	Q₃₂	semidirect
54. C₇₉	#2216	semidirect
96. C₂²	Dic₆₃₂	semidirect

H ≅ G/N

type

1. C₂×Dic₆₃₂

C₂

semidirect

3. #19098389

C₂

semidirect

4. #19098368

C₂

semidirect

42. C₂²×C₇₉

Q₃₂

semidirect

54. C₇₉

#2216

semidirect

96. C₂²

Dic₆₃₂

semidirect

Subgroups — #23765491

Conjugacy classes of subgroups

Complements