Group #23765481 — subgroups

Subgroups — #23765481

Order 10112.

150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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	#19099003	C₂	1	2	yes	maximal
2	#19098943	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098384	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098378	C₂	1	2	yes	maximal, complemented
5	#443×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	—	2	1	no	—
7	C₂×Dic₃₁₆	C₂²	1	2	yes	—
8	#14579161	—	2	1	no	—
9	#14579107	—	2	2	no	—
10	#14579105	—	2	2	no	—
11	#14579101	C₂²	1	2	yes	—
12	#135×C₇₉	C₂²	1	1	yes	characteristic
13	#131×C₇₉	—	2	1	no	—
14	#108×C₇₉	C₂²	1	1	yes	characteristic
15	#104×C₇₉	—	2	1	no	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₅₈	—	2	2	no	—
18	Dic₃₁₆	—	2	2	no	—
19	Dic₃₁₆	—	2	2	no	—
20	Dic₃₁₆	—	4	1	no	—
21	Dic₃₁₆	—	4	1	no	—
22	C₄⋊Dic₇₉	—	4	2	no	—
23	C₇₉⋊C₁₆	—	2	2	no	—
24	#41×C₇₉	—	2	1	no	—
25	Q₁₆×C₇₉	D₄	1	1	yes	characteristic
26	SD₁₆×C₇₉	—	2	1	no	—
27	D₈×C₇₉	D₄	1	1	yes	characteristic
28	M₁₆×C₇₉	—	2	1	no	—
29	M₁₆×C₇₉	—	4	1	no	—
30	C₂×C₈×C₇₉	—	4	1	no	—
31	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
33	C₄²×C₇₉	D₄	1	1	yes	characteristic
34	Q₈×C₇₉	—	2	1	no	—
35	D₄×C₇₉	—	2	1	no	—
36	D₄×C₇₉	—	4	1	no	—
37	C₂×C₄×C₇₉	—	2	1	no	—
38	C₂×C₄×C₇₉	—	4	1	no	—
39	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₇₉	—	4	2	no	—
41	Dic₁₅₈	—	4	2	no	—
42	Dic₁₅₈	—	4	2	no	—
43	C₈×C₇₉	—	4	1	no	—
44	C₈×C₇₉	D₈	1	1	yes	characteristic
45	C₈×C₇₉	D₈	1	1	yes	characteristic
46	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
47	C₈×C₇₉	#41	1	1	yes	characteristic
48	C₂²×C₇₉	—	4	1	no	—
49	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
50	C₄×C₇₉	—	2	2	no	—
51	C₄×C₇₉	—	4	1	no	—
52	C₄×C₇₉	#121	1	1	yes	characteristic
53	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
54	Dic₇₉	—	8	2	no	—
55	C₂×C₇₉	—	2	1	no	—
56	C₂×C₇₉	—	8	1	no	—
57	C₂×C₇₉	#459	1	1	yes	characteristic
58	#2214	—	79	1	no	maximal, Sylow
59	C₇₉	#2214	1	1	yes	characteristic, complemented, Sylow
60	#510	—	79	2	no	—
61	#494	—	79	1	no	—
62	#443	D₇₉	1	1	yes	characteristic
63	#364	—	79	1	no	—
64	#362	—	79	2	no	—
65	#135	C₂×D₇₉	1	1	yes	characteristic
66	C₂×Q₁₆	—	79	2	no	—
67	C₂×Q₁₆	—	158	1	no	—
68	#131	—	2	1	no	—
69	C₄⋊Q₈	—	158	1	no	—
70	Q₃₂	—	158	2	no	—
71	SD₃₂	—	158	2	no	—
72	M₃₂	—	79	2	no	—
73	#108	C₂×D₇₉	1	1	yes	characteristic
74	#104	—	2	1	no	—
75	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
76	#41	—	2	1	no	—
77	C₂×Q₈	—	158	2	no	—
78	Q₁₆	—	316	1	no	—
79	Q₁₆	—	316	1	no	—
80	Q₁₆	—	158	2	no	—
81	Q₁₆	—	158	2	no	—
82	Q₁₆	D₃₁₆	1	1	yes	characteristic
83	SD₁₆	—	2	1	no	—
84	D₈	D₃₁₆	1	1	yes	characteristic
85	M₁₆	—	2	1	no	—
86	M₁₆	—	4	1	no	—
87	C₂×C₈	—	4	1	no	—
88	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
89	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
90	C₄⋊C₄	—	316	2	no	—
91	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
92	C₁₆	—	158	2	no	—
93	Q₈	—	2	1	no	—
94	Q₈	—	316	2	no	—
95	Q₈	—	316	2	no	—
96	D₄	—	2	1	no	—
97	D₄	—	4	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	4	1	no	—
100	C₂×C₄	—	316	2	no	—
101	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
102	C₈	—	4	1	no	—
103	C₈	#11929609	1	1	yes	characteristic
104	C₈	#11929609	1	1	yes	characteristic
105	C₈	C₂×D₃₁₆	1	1	yes	characteristic
106	C₈	#11929624	1	1	yes	characteristic
107	C₂²	—	4	1	no	—
108	C₂²	#14579186	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	4	1	no	—
111	C₄	—	632	2	no	—
112	C₄	#14579135	1	1	yes	characteristic
113	C₄	C₂×#11929609	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	8	1	no	—
116	C₂	#19098758	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099003

C₂

yes

maximal

#19098943

C₂

yes

maximal, characteristic, complemented

#19098384

C₂

yes

maximal, characteristic, complemented

#19098378

C₂

yes

maximal, complemented

#443×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

C₂²

yes

—

—

—

—

C₂²

yes

—

#135×C₇₉

C₂²

yes

characteristic

#131×C₇₉

—

#108×C₇₉

C₂²

yes

characteristic

#104×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

C₄⋊Dic₇₉

—

C₇₉⋊C₁₆

—

#41×C₇₉

—

Q₁₆×C₇₉

D₄

yes

characteristic

SD₁₆×C₇₉

—

D₈×C₇₉

D₄

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

D₈

yes

characteristic

C₈×C₇₉

D₈

yes

characteristic

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#121

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#510

—

#494

—

#443

D₇₉

yes

—

—

C₂×D₇₉

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

158

—

#131

—

C₄⋊Q₈

—

158

—

Q₃₂

—

158

—

SD₃₂

—

158

—

M₃₂

—

#108

C₂×D₇₉

yes

characteristic

#104

—

C₄×C₈

C₂×D₇₉

yes

characteristic

#41

—

C₂×Q₈

—

158

—

Q₁₆

—

316

—

Q₁₆

—

316

—

Q₁₆

—

158

—

Q₁₆

—

158

—

Q₁₆

D₃₁₆

yes

characteristic

SD₁₆

—

D₈

D₃₁₆

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

C₄²

C₂²⋊D₇₉

yes

characteristic

C₁₆

—

158

—

Q₈

—

Q₈

—

316

—

Q₈

—

316

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

316

—

101

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

102

C₈

—

103

C₈

#11929609

yes

characteristic

104

C₈

#11929609

yes

characteristic

105

C₈

C₂×D₃₁₆

yes

characteristic

106

C₈

#11929624

yes

characteristic

107

C₂²

—

108

C₂²

#14579186

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

632

—

112

C₄

#14579135

yes

characteristic

113

C₄

C₂×#11929609

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

#19098758

yes

characteristic

	subgroup	G/H
center	C₂	#19098758
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#443×C₇₉	C₂
socle	C₂×C₇₉	#459
prime radical	#135×C₇₉	C₂²
hypercenter	#443	D₇₉
hypocenter	C₇₉	#2214
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

subgroup

G/H

center

C₂

#19098758

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#443×C₇₉

C₂

socle

C₂×C₇₉

#459

prime radical

#135×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

N	H ≅ G/N	type
2. #19098943	C₂	semidirect
3. #19098384	C₂	semidirect
4. #19098378	C₂	semidirect
59. C₇₉	#2214	semidirect

H ≅ G/N

type

2. #19098943

C₂

semidirect

3. #19098384

C₂

semidirect

4. #19098378

C₂

semidirect

59. C₇₉

#2214

semidirect

Subgroups — #23765481

Conjugacy classes of subgroups

Complements