Group #23765238 — subgroups

Subgroups — #23765238

Order 10112.

146 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 65 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	#19098979	C₂	1	2	yes	maximal, complemented
2	#19098681	C₂	1	1	yes	maximal, characteristic
3	#19098384	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098346	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579183	C₄	1	1	yes	characteristic
7	#14579167	C₂²	1	2	yes	—
8	#14579101	C₂²	1	2	yes	—
9	#14579100	—	2	2	no	—
10	C₁₆×D₇₉	—	2	2	no	—
11	#14579097	C₄	1	1	yes	characteristic
12	#14579089	C₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
17	Dic₃₁₆	C₈	1	1	yes	characteristic
18	#11929613	C₈	1	2	yes	—
19	D₆₃₂	C₈	1	1	yes	characteristic
20	#11929608	C₂×C₄	1	2	yes	—
21	#11929607	—	2	2	no	—
22	C₈×D₇₉	—	2	2	no	—
23	C₇₉⋊C₁₆	—	2	2	no	—
24	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
26	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₇₉	—	2	1	no	—
28	C₁₆×C₇₉	D₄	1	1	yes	characteristic
29	C₁₆×C₇₉	D₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	—	2	1	no	—
31	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²⋊D₇₉	—	2	2	no	—
33	D₃₁₆	C₂×C₈	1	2	yes	—
34	C₄×D₇₉	—	2	2	no	—
35	Dic₁₅₈	C₂×C₈	1	2	yes	—
36	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
37	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
38	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₉	#41	1	1	yes	characteristic
40	C₇₉⋊C₈	—	2	2	no	—
41	C₂²×C₇₉	#131	1	1	yes	characteristic
42	C₂×D₇₉	—	2	2	no	—
43	C₄×C₇₉	—	2	2	no	—
44	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
45	C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
46	Dic₇₉	—	2	2	no	—
47	C₂×C₇₉	—	2	1	no	—
48	C₂×C₇₉	C₈×D₄	1	1	yes	characteristic
49	D₇₉	—	4	2	no	—
50	#2170	—	79	1	no	maximal, Sylow
51	C₇₉	#2170	1	1	yes	characteristic, complemented, Sylow
52	#504	—	79	2	no	—
53	#443	—	79	1	no	—
54	#364	—	79	1	no	—
55	#350	—	79	2	no	—
56	C₄×C₁₆	D₇₉	1	1	yes	characteristic, complemented
57	#135	—	79	1	no	—
58	#131	—	79	2	no	—
59	M₃₂	—	79	2	no	—
60	M₃₂	—	158	2	no	—
61	C₂×C₁₆	—	158	2	no	—
62	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
63	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
64	#108	—	79	1	no	—
65	#104	—	79	2	no	—
66	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
67	#41	—	79	2	no	—
68	Q₁₆	—	79	1	no	—
69	SD₁₆	—	79	2	no	—
70	D₈	—	79	1	no	—
71	M₁₆	—	79	2	no	—
72	M₁₆	—	158	2	no	—
73	C₂×C₈	—	158	2	no	—
74	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
76	C₄²	C₄×D₇₉	1	1	yes	characteristic
77	C₁₆	—	2	1	no	—
78	C₁₆	—	158	2	no	—
79	C₁₆	D₃₁₆	1	1	yes	characteristic
80	C₁₆	D₃₁₆	1	1	yes	characteristic
81	Q₈	—	79	2	no	—
82	D₄	—	79	2	no	—
83	D₄	—	158	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	158	2	no	—
86	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
87	C₈	—	158	2	no	—
88	C₈	C₈×D₇₉	1	1	yes	characteristic
89	C₈	C₈×D₇₉	1	1	yes	characteristic
90	C₈	C₂×D₃₁₆	1	1	yes	characteristic
91	C₈	#11929624	1	1	yes	characteristic
92	C₂²	—	158	2	no	—
93	C₂²	#14579167	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	158	2	no	—
96	C₄	C₄×D₃₁₆	1	1	yes	characteristic
97	C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	316	2	no	—
100	C₂	C₈×D₃₁₆	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098979

C₂

yes

maximal, complemented

#19098681

C₂

yes

maximal, characteristic

#19098384

C₂

yes

maximal, characteristic, complemented

#19098346

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579183

C₄

yes

characteristic

#14579167

C₂²

yes

—

#14579101

C₂²

yes

—

#14579100

—

C₁₆×D₇₉

—

#14579097

C₄

yes

characteristic

#14579089

C₄

yes

—

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

#11929624

C₂×C₄

yes

—

Dic₃₁₆

C₈

yes

characteristic

#11929613

C₈

yes

—

D₆₃₂

C₈

yes

characteristic

#11929608

C₂×C₄

yes

—

#11929607

—

C₈×D₇₉

—

C₇₉⋊C₁₆

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₁₆×C₇₉

—

C₁₆×C₇₉

D₄

yes

characteristic

C₁₆×C₇₉

D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²⋊D₇₉

—

D₃₁₆

C₂×C₈

yes

—

C₄×D₇₉

—

Dic₁₅₈

C₂×C₈

yes

—

C₈×C₇₉

C₂×C₈

yes

characteristic

C₈×C₇₉

C₂×C₈

yes

characteristic

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

#131

yes

characteristic

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

C₂²×C₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₈×D₄

yes

characteristic

D₇₉

—

#2170

—

maximal, Sylow

C₇₉

#2170

yes

characteristic, complemented, Sylow

—

—

—

—

C₄×C₁₆

D₇₉

yes

characteristic, complemented

#135

—

#131

—

M₃₂

—

M₃₂

—

158

—

C₂×C₁₆

—

158

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#108

—

#104

—

C₄×C₈

C₂×D₇₉

yes

characteristic

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄²

C₄×D₇₉

yes

characteristic

C₁₆

—

C₁₆

—

158

—

C₁₆

D₃₁₆

yes

characteristic

C₁₆

D₃₁₆

yes

characteristic

Q₈

—

D₄

—

D₄

—

158

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₈

—

158

—

C₈

C₈×D₇₉

yes

characteristic

C₈

C₈×D₇₉

yes

characteristic

C₈

C₂×D₃₁₆

yes

characteristic

C₈

#11929624

yes

characteristic

C₂²

—

158

—

C₂²

#14579167

yes

characteristic

C₄

—

C₄

—

158

—

C₄

C₄×D₃₁₆

yes

characteristic

C₄

C₂×C₈×D₇₉

yes

characteristic

C₂

—

C₂

—

316

—

100

C₂

C₈×D₃₁₆

yes

characteristic

	subgroup	G/H
center	C₁₆	D₃₁₆
commutator	C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₄×C₁₆×C₇₉	C₂
socle	C₂×C₇₉	C₈×D₄
prime radical	#14579183	C₄
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₄×C₁₆	D₇₉
hypocenter	C₇₉	#2170
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆

subgroup

G/H

center

C₁₆

D₃₁₆

commutator

C₄×C₇₉

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₄×C₁₆×C₇₉

C₂

socle

C₂×C₇₉

C₈×D₄

prime radical

#14579183

C₄

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₄×C₁₆

D₇₉

hypocenter

C₇₉

#2170

LCS

G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. #19098979	C₂	semidirect
3. #19098384	C₂	semidirect
4. #19098346	C₂	semidirect
5. C₄×C₁₆×C₇₉	C₂	semidirect
51. C₇₉	#2170	semidirect
56. C₄×C₁₆	D₇₉	semidirect

H ≅ G/N

type

1. #19098979

C₂

semidirect

3. #19098384

C₂

semidirect

4. #19098346

C₂

semidirect

5. C₄×C₁₆×C₇₉

C₂

semidirect

51. C₇₉

#2170

semidirect

56. C₄×C₁₆

D₇₉

semidirect

Subgroups — #23765238

Conjugacy classes of subgroups

Complements