Group #23762163 — subgroups

Subgroups — #23762163

Order 10112.

168 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 93 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	#19098620	C₂	1	2	yes	maximal
2	#19098316	C₂	1	2	yes	maximal, complemented
3	#19098314	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
6	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
7	#14579072	—	2	2	no	—
8	C₂²×C₈×C₇₉	C₄	1	1	yes	characteristic
9	C₂²×C₈×C₇₉	C₄	1	1	yes	characteristic
10	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₇₉	C₄	1	1	yes	characteristic
12	C₄×C₈×C₇₉	C₄	1	1	yes	characteristic
13	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×C₇₉⋊C₈	—	2	4	no	—
16	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₇₉	Q₈	1	1	yes	characteristic
19	C₂×C₈×C₇₉	—	2	2	no	—
20	C₂×C₈×C₇₉	—	2	2	no	—
21	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₇₉	D₄	1	1	yes	characteristic
27	C₄²×C₇₉	Q₈	1	1	yes	characteristic
28	C₄²×C₇₉	C₂³	1	1	yes	characteristic
29	C₂³×C₇₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	—	2	2	no	—
31	C₂×C₄×C₇₉	—	2	1	no	—
32	C₂×C₄×C₇₉	—	2	1	no	—
33	C₂×C₄×C₇₉	—	2	2	no	—
34	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
40	C₈×C₇₉	—	2	1	no	—
41	C₈×C₇₉	—	2	1	no	—
42	C₈×C₇₉	M₁₆	1	2	yes	—
43	C₈×C₇₉	M₁₆	1	2	yes	—
44	C₇₉⋊C₈	—	4	4	no	—
45	C₂²×C₇₉	—	2	1	no	—
46	C₂²×C₇₉	—	2	1	no	—
47	C₂²×C₇₉	#108	1	2	yes	—
48	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₇₉	—	2	1	no	—
50	C₄×C₇₉	—	2	1	no	—
51	C₄×C₇₉	—	2	1	no	—
52	C₄×C₇₉	—	2	1	no	—
53	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
54	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
55	C₄×C₇₉	#135	1	2	yes	—
56	C₂×C₇₉	—	2	2	no	—
57	C₂×C₇₉	#423	1	1	yes	characteristic
58	C₂×C₇₉	#427	1	1	yes	characteristic
59	C₂×C₇₉	C₂×#108	1	1	yes	characteristic
60	#1568	—	79	1	no	maximal, Sylow
61	C₇₉	#1568	1	1	yes	characteristic, complemented, Sylow
62	#432	—	79	2	no	—
63	C₂×C₄×C₈	D₇₉	1	1	yes	characteristic
64	#335	—	79	2	no	—
65	#334	—	79	2	no	—
66	C₂²×C₈	Dic₇₉	1	1	yes	characteristic
67	C₂²×C₈	Dic₇₉	1	1	yes	characteristic
68	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
69	C₄⋊C₈	—	79	4	no	—
70	C₂²⋊C₈	—	158	2	no	—
71	#97	—	158	2	no	—
72	C₄×C₈	Dic₇₉	1	1	yes	characteristic
73	C₄×C₈	Dic₇₉	1	1	yes	characteristic
74	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
75	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
76	C₂²×C₄	Dic₁₅₈	1	1	yes	characteristic
77	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
78	C₂²×C₄	C₂×Dic₇₉	1	1	yes	characteristic
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	158	4	no	—
82	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
83	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
84	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
85	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
86	C₄²	Dic₁₅₈	1	1	yes	characteristic
87	C₄²	D₃₁₆	1	1	yes	characteristic
88	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
89	C₄²	C₂²×D₇₉	1	1	yes	characteristic
90	C₂³	C₄⋊Dic₇₉	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
96	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
97	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
98	C₂×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
99	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
100	C₂×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
101	C₈	—	2	1	no	—
102	C₈	—	2	1	no	—
103	C₈	—	316	4	no	—
104	C₈	#11929608	1	2	yes	—
105	C₈	#11929608	1	2	yes	—
106	C₂²	—	2	1	no	—
107	C₂²	—	2	1	no	—
108	C₂²	#14579097	1	2	yes	—
109	C₂²	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	—	2	1	no	—
113	C₄	—	2	1	no	—
114	C₄	C₂×#11929608	1	1	yes	characteristic
115	C₄	C₂×#11929608	1	1	yes	characteristic
116	C₄	#14579183	1	2	yes	—
117	C₂	—	2	2	no	—
118	C₂	#19098587	1	1	yes	characteristic
119	C₂	#19098601	1	1	yes	characteristic
120	C₂	C₂×#14579097	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098620

C₂

yes

maximal

#19098316

C₂

yes

maximal, complemented

#19098314

C₂

yes

maximal, complemented

C₂×C₄×C₈×C₇₉

C₂

yes

maximal, characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₂²×C₈×C₇₉

C₄

yes

characteristic

C₂²×C₈×C₇₉

C₄

yes

characteristic

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₄

yes

characteristic

C₄×C₈×C₇₉

C₄

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₇₉⋊C₈

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

Q₈

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

Q₈

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

M₁₆

yes

—

C₈×C₇₉

M₁₆

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#108

yes

—

C₂²×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×M₁₆

yes

characteristic

C₄×C₇₉

C₂×M₁₆

yes

characteristic

C₄×C₇₉

#135

yes

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#432

—

C₂×C₄×C₈

D₇₉

yes

characteristic

#335

—

#334

—

C₂²×C₈

Dic₇₉

yes

characteristic

C₂²×C₈

Dic₇₉

yes

characteristic

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

158

—

#97

—

158

—

C₄×C₈

Dic₇₉

yes

characteristic

C₄×C₈

Dic₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂²×C₄

Dic₁₅₈

yes

characteristic

C₂²×C₄

D₃₁₆

yes

characteristic

C₂²×C₄

C₂×Dic₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₄²

Dic₁₅₈

yes

characteristic

C₄²

D₃₁₆

yes

characteristic

C₄²

C₂×Dic₇₉

yes

characteristic

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

C₄⋊Dic₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

C₂×C₄

C₂²×Dic₇₉

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

100

C₂×C₄

C₂×Dic₁₅₈

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

316

—

104

C₈

#11929608

yes

—

105

C₈

#11929608

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

#14579097

yes

—

109

C₂²

C₂×C₄⋊Dic₇₉

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

C₂×#11929608

yes

characteristic

115

C₄

C₂×#11929608

yes

characteristic

116

C₄

#14579183

yes

—

117

C₂

—

118

C₂

#19098587

yes

characteristic

119

C₂

#19098601

yes

characteristic

120

C₂

C₂×#14579097

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₄²	C₂²×D₇₉
Fitting	C₂×C₄×C₈×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄⋊C₄
prime radical	C₂³×C₇₉	C₄⋊C₄
cosocle	C₄²×C₇₉	C₂³
hypercenter	C₂×C₄×C₈	D₇₉
hypocenter	C₇₉	#1568
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄

C₂×D₃₁₆

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₄²

C₂²×D₇₉

Fitting

C₂×C₄×C₈×C₇₉

C₂

socle

C₂²×C₇₉

C₂×C₄⋊C₄

prime radical

C₂³×C₇₉

C₄⋊C₄

cosocle

C₄²×C₇₉

C₂³

hypercenter

C₂×C₄×C₈

D₇₉

hypocenter

C₇₉

#1568

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #19098316	C₂	semidirect
3. #19098314	C₂	semidirect
61. C₇₉	#1568	semidirect

H ≅ G/N

type

2. #19098316

C₂

semidirect

3. #19098314

C₂

semidirect

61. C₇₉

#1568

semidirect

Subgroups — #23762163

Conjugacy classes of subgroups

Complements