Group #23765282 — subgroups

Subgroups — #23765282

Order 10112.

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

normal subgroups only

This group has 146 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	#19098995	C₂	1	1	yes	maximal, characteristic
2	#19098681	C₂	1	2	yes	maximal, complemented
3	#19098393	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098371	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579183	C₂²	1	2	yes	—
7	#14579167	—	2	2	no	—
8	Dic₆₃₂	C₄	1	1	yes	characteristic, complemented
9	#14579106	C₄	1	2	yes	complemented
10	D₁₂₆₄	C₄	1	1	yes	characteristic, complemented
11	#14579097	C₂²	1	2	yes	—
12	#14579089	—	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	#11929624	—	2	2	no	—
17	Dic₃₁₆	C₂×C₄	1	2	yes	—
18	#11929613	—	2	2	no	—
19	D₆₃₂	C₂×C₄	1	2	yes	—
20	#11929608	—	2	2	no	—
21	#11929607	—	4	2	no	—
22	C₈×D₇₉	—	4	2	no	—
23	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
25	C₄²×C₇₉	D₄	1	1	yes	characteristic
26	C₁₆×C₇₉	—	2	1	no	—
27	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₉	—	2	1	no	—
30	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₇₉	—	4	2	no	—
32	D₃₁₆	—	2	2	no	—
33	C₄×D₇₉	—	4	2	no	—
34	Dic₁₅₈	—	2	2	no	—
35	C₈×C₇₉	D₈	1	1	yes	characteristic
36	C₈×C₇₉	D₈	1	1	yes	characteristic
37	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₇₉	#41	1	1	yes	characteristic
39	C₇₉⋊C₈	—	4	2	no	—
40	C₂²×C₇₉	#135	1	1	yes	characteristic
41	C₂×D₇₉	—	4	2	no	—
42	C₄×C₇₉	—	2	2	no	—
43	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
44	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
45	Dic₇₉	—	4	2	no	—
46	C₂×C₇₉	—	2	1	no	—
47	C₂×C₇₉	C₄×D₈	1	1	yes	characteristic
48	D₇₉	—	8	2	no	—
49	#2178	—	79	1	no	maximal, Sylow
50	C₇₉	#2178	1	1	yes	characteristic, complemented, Sylow
51	#508	—	79	1	no	—
52	#443	—	79	2	no	—
53	#368	—	79	1	no	—
54	#359	—	79	2	no	—
55	C₄×C₁₆	D₇₉	1	1	yes	characteristic, complemented
56	#135	—	79	2	no	—
57	#131	—	158	2	no	—
58	Q₃₂	—	79	1	no	—
59	SD₃₂	—	79	2	no	—
60	D₁₆	—	79	1	no	—
61	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
62	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
63	#108	—	79	2	no	—
64	#104	—	158	2	no	—
65	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
66	#41	—	158	2	no	—
67	Q₁₆	—	79	2	no	—
68	SD₁₆	—	158	2	no	—
69	D₈	—	79	2	no	—
70	M₁₆	—	316	2	no	—
71	M₁₆	—	158	2	no	—
72	C₂×C₈	—	316	2	no	—
73	C₂×C₈	D₃₁₆	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
75	C₄²	D₃₁₆	1	1	yes	characteristic
76	C₁₆	—	2	1	no	—
77	C₁₆	C₄×D₇₉	1	1	yes	characteristic
78	C₁₆	C₄×D₇₉	1	1	yes	characteristic
79	Q₈	—	158	2	no	—
80	D₄	—	316	2	no	—
81	D₄	—	158	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	316	2	no	—
84	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
85	C₈	—	316	2	no	—
86	C₈	D₆₃₂	1	1	yes	characteristic
87	C₈	D₆₃₂	1	1	yes	characteristic
88	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
89	C₈	#11929624	1	1	yes	characteristic
90	C₂²	—	316	2	no	—
91	C₂²	#14579183	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	316	2	no	—
94	C₄	C₄×D₃₁₆	1	1	yes	characteristic
95	C₄	C₂×D₆₃₂	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	632	2	no	—
98	C₂	C₄×D₆₃₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098995

C₂

yes

maximal, characteristic

#19098681

C₂

yes

maximal, complemented

#19098393

C₂

yes

maximal, characteristic, complemented

#19098371

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579183

C₂²

yes

—

#14579167

—

Dic₆₃₂

C₄

yes

characteristic, complemented

#14579106

C₄

yes

complemented

D₁₂₆₄

C₄

yes

characteristic, complemented

#14579097

C₂²

yes

—

#14579089

—

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

#11929624

—

Dic₃₁₆

C₂×C₄

yes

—

#11929613

—

D₆₃₂

C₂×C₄

yes

—

#11929608

—

#11929607

—

C₈×D₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₁₆×C₇₉

—

C₁₆×C₇₉

C₂×C₄

yes

characteristic

C₁₆×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²⋊D₇₉

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

D₈

yes

characteristic

C₈×C₇₉

D₈

yes

characteristic

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

#135

yes

characteristic

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₄×D₈

yes

characteristic

D₇₉

—

#2178

—

maximal, Sylow

C₇₉

#2178

yes

characteristic, complemented, Sylow

—

—

—

—

C₄×C₁₆

D₇₉

yes

characteristic, complemented

#135

—

#131

—

158

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#108

—

#104

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

#41

—

158

—

Q₁₆

—

SD₁₆

—

158

—

D₈

—

M₁₆

—

316

—

M₁₆

—

158

—

C₂×C₈

—

316

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄²

D₃₁₆

yes

characteristic

C₁₆

—

C₁₆

C₄×D₇₉

yes

characteristic

C₁₆

C₄×D₇₉

yes

characteristic

Q₈

—

158

—

D₄

—

316

—

D₄

—

158

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₈

—

316

—

C₈

D₆₃₂

yes

characteristic

C₈

D₆₃₂

yes

characteristic

C₈

C₂×C₄×D₇₉

yes

characteristic

C₈

#11929624

yes

characteristic

C₂²

—

316

—

C₂²

#14579183

yes

characteristic

C₄

—

C₄

—

316

—

C₄

C₄×D₃₁₆

yes

characteristic

C₄

C₂×D₆₃₂

yes

characteristic

C₂

—

C₂

—

632

—

C₂

C₄×D₆₃₂

yes

characteristic

	subgroup	G/H
center	C₈	D₆₃₂
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₄×C₁₆×C₇₉	C₂
socle	C₂×C₇₉	C₄×D₈
prime radical	#19098995	C₂
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₄×C₁₆	D₇₉
hypocenter	C₇₉	#2178
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₈

D₆₃₂

commutator

C₈×C₇₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₄×C₁₆×C₇₉

C₂

socle

C₂×C₇₉

C₄×D₈

prime radical

#19098995

C₂

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₄×C₁₆

D₇₉

hypocenter

C₇₉

#2178

LCS

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. #19098681	C₂	semidirect
3. #19098393	C₂	semidirect
4. #19098371	C₂	semidirect
5. C₄×C₁₆×C₇₉	C₂	semidirect
8. Dic₆₃₂	C₄	semidirect
9. #14579106	C₄	semidirect
10. D₁₂₆₄	C₄	semidirect
50. C₇₉	#2178	semidirect
55. C₄×C₁₆	D₇₉	semidirect

H ≅ G/N

type

2. #19098681

C₂

semidirect

3. #19098393

C₂

semidirect

4. #19098371

C₂

semidirect

5. C₄×C₁₆×C₇₉

C₂

semidirect

8. Dic₆₃₂

C₄

semidirect

9. #14579106

C₄

semidirect

10. D₁₂₆₄

C₄

semidirect

50. C₇₉

#2178

semidirect

55. C₄×C₁₆

D₇₉

semidirect

Subgroups — #23765282

Conjugacy classes of subgroups

Complements