Group #23765163 — subgroups

Subgroups — C₂×#19098384 #23765163

Order 10112.

168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14579101	C₂	1	2	yes	maximal
2	#19098384	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579101	—	2	2	no	—
5	#14579101	C₂²	1	4	yes	—
6	C₂×C₇₉⋊C₁₆	—	2	2	no	—
7	C₂²×C₈×C₇₉	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₇₉	C₄	1	1	yes	characteristic
10	C₄×C₈×C₇₉	C₄	1	2	yes	—
11	C₄×C₈×C₇₉	C₂²	1	2	yes	—
12	C₇₉⋊C₁₆	—	2	4	no	—
13	C₂²×C₄×C₇₉	—	2	1	no	—
14	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₇₉	C₈	1	2	yes	—
16	C₂×C₈×C₇₉	C₈	1	2	yes	—
17	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
22	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
23	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
24	C₄²×C₇₉	—	2	1	no	—
25	C₄²×C₇₉	C₂×C₄	1	2	yes	—
26	C₂³×C₇₉	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₇₉	—	2	4	no	—
28	C₂×C₄×C₇₉	—	2	2	no	—
29	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₇₉	M₁₆	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
36	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
37	C₈×C₇₉	C₂×C₈	1	4	yes	—
38	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
40	C₂²×C₇₉	—	2	2	no	—
41	C₂²×C₇₉	C₄⋊C₈	1	1	yes	characteristic
42	C₂²×C₇₉	C₄⋊C₈	1	1	yes	characteristic
43	C₂²×C₇₉	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₇₉	—	2	4	no	—
45	C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
46	C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
49	C₂×C₇₉	—	2	1	no	—
50	C₂×C₇₉	—	2	1	no	—
51	C₂×C₇₉	#364	1	2	yes	complemented
52	C₂×C₇₉	C₂×C₄⋊C₈	1	1	yes	characteristic
53	C₂×#364	—	79	1	no	maximal, Sylow
54	C₇₉	C₂×#364	1	1	yes	characteristic, complemented, Sylow
55	C₂×M₃₂	—	79	2	no	—
56	C₂×C₄×C₈	D₇₉	1	1	yes	characteristic
57	#364	—	79	4	no	—
58	C₂²×C₈	Dic₇₉	1	1	yes	characteristic
59	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
60	C₂×C₄²	Dic₇₉	1	1	yes	characteristic
61	M₃₂	—	79	4	no	—
62	M₃₂	—	158	2	no	—
63	C₂×C₁₆	—	158	2	no	—
64	C₄×C₈	Dic₇₉	1	2	yes	—
65	C₄×C₈	C₂×D₇₉	1	2	yes	—
66	C₂²×C₄	—	2	1	no	—
67	C₂²×C₄	C₂×Dic₇₉	1	1	yes	characteristic
68	C₂×C₈	C₇₉⋊C₈	1	2	yes	—
69	C₂×C₈	C₇₉⋊C₈	1	2	yes	—
70	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
71	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
72	C₂×C₈	D₃₁₆	1	1	yes	characteristic
73	C₂×C₈	D₃₁₆	1	1	yes	characteristic
74	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
75	C₂×C₈	C₂×Dic₇₉	1	2	yes	—
76	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
77	C₄²	—	2	1	no	—
78	C₄²	C₂×Dic₇₉	1	2	yes	—
79	C₁₆	—	158	4	no	—
80	C₂³	#11929608	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
84	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
85	C₂×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
86	C₂×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
87	C₂×C₄	#11929608	1	1	yes	characteristic
88	C₂×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
89	C₈	C₄⋊Dic₇₉	1	1	yes	characteristic
90	C₈	C₄⋊Dic₇₉	1	1	yes	characteristic
91	C₈	C₂×C₇₉⋊C₈	1	4	yes	—
92	C₈	C₂×D₃₁₆	1	1	yes	characteristic
93	C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
94	C₂²	—	2	2	no	—
95	C₂²	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
96	C₂²	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
97	C₂²	C₂×#11929608	1	1	yes	characteristic
98	C₄	—	2	4	no	—
99	C₄	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
100	C₄	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
101	C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
102	C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	2	1	no	—
105	C₂	#19098384	1	2	yes	direct product factor
106	C₂	C₂×C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579101

C₂

yes

maximal

#19098384

C₂

yes

maximal, direct product factor

C₂×C₄×C₈×C₇₉

C₂

yes

maximal, characteristic

#14579101

—

#14579101

C₂²

yes

—

C₂×C₇₉⋊C₁₆

—

C₂²×C₈×C₇₉

C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₄

yes

characteristic

C₄×C₈×C₇₉

C₄

yes

—

C₄×C₈×C₇₉

C₂²

yes

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₈

yes

—

C₂×C₈×C₇₉

C₈

yes

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

—

C₂³×C₇₉

M₁₆

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

M₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₈×C₇₉

C₂×C₈

yes

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

C₂×Q₈

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

C₄⋊C₈

yes

characteristic

C₂²×C₇₉

C₄⋊C₈

yes

characteristic

C₂²×C₇₉

C₂×M₁₆

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₄⋊C₈

yes

characteristic

C₄×C₇₉

C₄⋊C₈

yes

characteristic

C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₉

C₂²×C₈

yes

characteristic

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#364

yes

complemented

C₂×C₇₉

C₂×C₄⋊C₈

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×C₄×C₈

D₇₉

yes

characteristic

#364

—

C₂²×C₈

Dic₇₉

yes

characteristic

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂×C₄²

Dic₇₉

yes

characteristic

M₃₂

—

M₃₂

—

158

—

C₂×C₁₆

—

158

—

C₄×C₈

Dic₇₉

yes

—

C₄×C₈

C₂×D₇₉

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₇₉⋊C₈

yes

—

C₂×C₈

C₇₉⋊C₈

yes

—

C₂×C₈

Dic₁₅₈

yes

characteristic

C₂×C₈

Dic₁₅₈

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄²

—

C₄²

C₂×Dic₇₉

yes

—

C₁₆

—

158

—

C₂³

#11929608

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

C₂×C₄

C₂×C₇₉⋊C₈

yes

characteristic

C₂×C₄

C₂×C₇₉⋊C₈

yes

characteristic

C₂×C₄

#11929608

yes

characteristic

C₂×C₄

C₂²×Dic₇₉

yes

characteristic

C₈

C₄⋊Dic₇₉

yes

characteristic

C₈

C₄⋊Dic₇₉

yes

characteristic

C₈

C₂×C₇₉⋊C₈

yes

—

C₈

C₂×D₃₁₆

yes

characteristic

C₈

C₂×Dic₁₅₈

yes

characteristic

C₂²

—

C₂²

C₄⋊(C₇₉⋊C₈)

yes

characteristic

C₂²

C₄⋊(C₇₉⋊C₈)

yes

characteristic

C₂²

C₂×#11929608

yes

characteristic

C₄

—

C₄

C₄⋊(C₇₉⋊C₈)

yes

characteristic

100

C₄

C₄⋊(C₇₉⋊C₈)

yes

characteristic

101

C₄

C₂×C₄⋊Dic₇₉

yes

characteristic

102

C₄

C₂²×C₇₉⋊C₈

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

#19098384

yes

direct product factor

106

C₂

C₂×C₄⋊(C₇₉⋊C₈)

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₃₁₆
commutator	C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₂×C₄×C₈×C₇₉	C₂
socle	C₂²×C₇₉	C₄⋊C₈
prime radical	C₂³×C₇₉	M₁₆
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₂×C₄×C₈	D₇₉
hypocenter	C₇₉	C₂×#364
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₈

D₃₁₆

commutator

C₄×C₇₉

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₂×C₄×C₈×C₇₉

C₂

socle

C₂²×C₇₉

C₄⋊C₈

prime radical

C₂³×C₇₉

M₁₆

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₂×C₄×C₈

D₇₉

hypocenter

C₇₉

C₂×#364

LCS

G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #19098384	C₂	direct (N × H)
51. C₂×C₇₉	#364	semidirect
54. C₇₉	C₂×#364	semidirect
105. C₂	#19098384	direct (N × H)

H ≅ G/N

type

2. #19098384

C₂

direct (N × H)

51. C₂×C₇₉

#364

semidirect

54. C₇₉

C₂×#364

semidirect

105. C₂

#19098384

direct (N × H)

Subgroups — C₂×#19098384 #23765163

Conjugacy classes of subgroups

Complements

Subgroups — C2×#19098384 #23765163

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19098384 #23765163