Group #23765233 — subgroups

Subgroups — #23765233

Order 10112.

162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14579100	C₂	1	2	yes	maximal, complemented
2	C₈×D₃₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₇₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₇₉)⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇₉	C₂²	1	2	yes	—
7	C₄×D₃₁₆	C₄	1	1	yes	characteristic
8	#14579100	—	2	4	no	—
9	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
10	C₄⋊(C₇₉⋊C₈)	C₄	1	1	yes	characteristic
11	(C₂×D₇₉)⋊C₈	C₄	1	2	yes	—
12	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×D₃₁₆	C₈	1	1	yes	characteristic
16	C₂×C₄×D₇₉	C₂×C₄	1	2	yes	—
17	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
18	C₈×D₇₉	—	2	2	no	—
19	C₈×D₇₉	—	2	2	no	—
20	C₄⋊Dic₇₉	C₈	1	1	yes	characteristic
21	(C₂×D₇₉)⋊C₄	C₈	1	2	yes	—
22	C₇₉⋊C₁₆	—	2	2	no	—
23	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
25	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
26	C₁₆×C₇₉	—	2	1	no	—
27	C₁₆×C₇₉	D₄	1	2	yes	complemented
28	C₂²×D₇₉	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₇₉	C₂×C₈	1	2	yes	—
33	D₃₁₆	—	2	2	no	—
34	C₄×D₇₉	—	2	2	no	—
35	C₄×D₇₉	—	2	2	no	—
36	C₈×C₇₉	—	2	1	no	—
37	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₇₉	#41	1	1	yes	characteristic
39	C₇₉⋊C₈	—	2	2	no	—
40	C₂²×C₇₉	C₂²×C₈	1	1	yes	characteristic
41	C₂×D₇₉	—	2	2	no	—
42	C₂×D₇₉	—	2	2	no	—
43	C₂×D₇₉	—	2	2	no	—
44	C₄×C₇₉	—	2	1	no	—
45	C₄×C₇₉	M₃₂	1	2	yes	complemented
46	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
47	C₄×C₇₉	#131	1	1	yes	characteristic
48	Dic₇₉	—	2	2	no	—
49	C₂×C₇₉	C₈×D₄	1	1	yes	characteristic
50	C₂×C₇₉	C₂×M₃₂	1	1	yes	characteristic
51	C₂×C₇₉	#504	1	1	yes	characteristic
52	D₇₉	—	4	2	no	—
53	#2169	—	79	1	no	maximal, Sylow
54	C₇₉	#2169	1	1	yes	characteristic, complemented, Sylow
55	C₂×M₃₂	—	79	2	no	—
56	C₈×D₄	—	79	1	no	—
57	C₄⋊C₁₆	—	79	1	no	—
58	C₂²⋊C₁₆	—	79	2	no	—
59	C₄×C₁₆	D₇₉	1	1	yes	characteristic, complemented
60	C₂²×C₈	—	79	2	no	—
61	C₄×D₄	—	79	1	no	—
62	M₃₂	—	158	4	no	—
63	C₂×C₁₆	—	79	2	no	—
64	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
65	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
66	C₄⋊C₈	—	79	1	no	—
67	C₂²⋊C₈	—	79	2	no	—
68	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
69	C₂×D₄	—	79	1	no	—
70	C₂²×C₄	—	79	2	no	—
71	C₂×C₈	—	79	2	no	—
72	C₂×C₈	—	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	C₄⋊C₄	—	79	1	no	—
77	C₂²⋊C₄	—	79	2	no	—
78	C₄²	C₄×D₇₉	1	1	yes	characteristic
79	C₁₆	—	2	1	no	—
80	C₁₆	—	158	2	no	—
81	C₁₆	D₃₁₆	1	2	yes	complemented
82	C₂³	—	79	2	no	—
83	D₄	—	158	2	no	—
84	C₂×C₄	—	79	2	no	—
85	C₂×C₄	—	158	2	no	—
86	C₂×C₄	—	158	2	no	—
87	C₂×C₄	C₈×D₇₉	1	1	yes	characteristic
88	C₂×C₄	C₈×D₇₉	1	1	yes	characteristic
89	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
90	C₈	—	2	1	no	—
91	C₈	—	158	2	no	—
92	C₈	C₂×D₃₁₆	1	1	yes	characteristic
93	C₈	#11929624	1	1	yes	characteristic
94	C₂²	—	158	2	no	—
95	C₂²	—	158	2	no	—
96	C₂²	—	158	2	no	—
97	C₂²	C₂×C₈×D₇₉	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	158	2	no	—
100	C₄	#14579100	1	2	yes	complemented
101	C₄	C₄×D₃₁₆	1	1	yes	characteristic
102	C₄	#14579167	1	1	yes	characteristic
103	C₂	—	316	2	no	—
104	C₂	C₈×D₃₁₆	1	1	yes	characteristic
105	C₂	C₂×#14579100	1	1	yes	characteristic
106	C₂	#19098979	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579100

C₂

yes

maximal, complemented

C₈×D₃₁₆

C₂

yes

maximal, characteristic

C₄⋊(C₇₉⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

(C₂×D₇₉)⋊C₁₆

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₉

C₂²

yes

—

C₄×D₃₁₆

C₄

yes

characteristic

#14579100

—

C₂×C₇₉⋊C₁₆

C₂²

yes

—

C₄⋊(C₇₉⋊C₈)

C₄

yes

characteristic

(C₂×D₇₉)⋊C₈

C₄

yes

—

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×D₃₁₆

C₈

yes

characteristic

C₂×C₄×D₇₉

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₈×D₇₉

—

C₈×D₇₉

—

C₄⋊Dic₇₉

C₈

yes

characteristic

(C₂×D₇₉)⋊C₄

C₈

yes

—

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

complemented

C₂²×D₇₉

C₂×C₈

yes

—

C₂×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×Dic₇₉

C₂×C₈

yes

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

C₂²×C₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

M₃₂

yes

complemented

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

#131

yes

characteristic

Dic₇₉

—

C₂×C₇₉

C₈×D₄

yes

characteristic

C₂×C₇₉

C₂×M₃₂

yes

characteristic

C₂×C₇₉

#504

yes

characteristic

D₇₉

—

#2169

—

maximal, Sylow

C₇₉

#2169

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₈×D₄

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

D₇₉

yes

characteristic, complemented

C₂²×C₈

—

C₄×D₄

—

M₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₄×D₇₉

yes

characteristic

C₁₆

—

C₁₆

—

158

—

C₁₆

D₃₁₆

yes

complemented

C₂³

—

D₄

—

158

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₈×D₇₉

yes

characteristic

C₂×C₄

C₈×D₇₉

yes

characteristic

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₈

—

C₈

—

158

—

C₈

C₂×D₃₁₆

yes

characteristic

C₈

#11929624

yes

characteristic

C₂²

—

158

—

C₂²

—

158

—

C₂²

—

158

—

C₂²

C₂×C₈×D₇₉

yes

characteristic

C₄

—

C₄

—

158

—

100

C₄

#14579100

yes

complemented

101

C₄

C₄×D₃₁₆

yes

characteristic

102

C₄

#14579167

yes

characteristic

103

C₂

—

316

—

104

C₂

C₈×D₃₁₆

yes

characteristic

105

C₂

C₂×#14579100

yes

characteristic

106

C₂

#19098979

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₉
commutator, socle	C₂²×C₇₉	C₂²×C₈
Fitting	C₄×C₁₆×C₇₉	C₂
prime radical	C₂×D₃₁₆	C₈
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₄×C₁₆	D₇₉
hypocenter	C₇₉	#2169
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₇₉

commutator, socle

C₂²×C₇₉

C₂²×C₈

Fitting

C₄×C₁₆×C₇₉

C₂

prime radical

C₂×D₃₁₆

C₈

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₄×C₁₆

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. C₂×#14579100	C₂	semidirect
3. C₄⋊(C₇₉⋊C₁₆)	C₂	semidirect
4. (C₂×D₇₉)⋊C₁₆	C₂	semidirect
5. C₄×C₁₆×C₇₉	C₂	semidirect
27. C₁₆×C₇₉	D₄	semidirect
45. C₄×C₇₉	M₃₂	semidirect
54. C₇₉	#2169	semidirect
59. C₄×C₁₆	D₇₉	semidirect
81. C₁₆	D₃₁₆	semidirect
100. C₄	#14579100	semidirect

H ≅ G/N

type

1. C₂×#14579100

C₂

semidirect

3. C₄⋊(C₇₉⋊C₁₆)

C₂

semidirect

4. (C₂×D₇₉)⋊C₁₆

C₂

semidirect

5. C₄×C₁₆×C₇₉

C₂

semidirect

27. C₁₆×C₇₉

D₄

semidirect

45. C₄×C₇₉

M₃₂

semidirect

54. C₇₉

#2169

semidirect

59. C₄×C₁₆

D₇₉

semidirect

81. C₁₆

D₃₁₆

semidirect

100. C₄

#14579100

semidirect

Subgroups — #23765233

Conjugacy classes of subgroups

Complements