Group #23761272 — subgroups

Subgroups — #23761272

Order 10112.

138 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 57 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	1	yes	maximal, characteristic
2	#19098620	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
5	C₄⋊(C₇₉⋊C₈)	C₄	1	2	yes	—
6	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
7	C₂²⋊(C₇₉⋊C₈)	C₄	1	2	yes	—
8	#14579072	—	2	1	no	—
9	#14579072	—	2	1	no	—
10	C₂×M₁₆×C₇₉	—	2	1	no	—
11	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
12	#97×C₇₉	—	2	1	no	—
13	C₄×C₈×C₇₉	C₄	1	2	yes	—
14	C₂×C₇₉⋊C₈	—	2	2	no	—
15	C₂×C₇₉⋊C₈	—	2	2	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	M₁₆×C₇₉	—	2	4	no	—
20	C₂×C₈×C₇₉	—	2	2	no	—
21	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₇₉	D₄	1	1	yes	characteristic
24	C₄²×C₇₉	D₄	1	1	yes	characteristic
25	C₂³×C₇₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₇₉	—	2	2	no	—
27	C₂×C₄×C₇₉	—	4	1	no	—
28	C₂×C₄×C₇₉	—	4	1	no	—
29	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
35	C₈×C₇₉	—	2	4	no	—
36	C₇₉⋊C₈	—	4	2	no	—
37	C₇₉⋊C₈	—	4	2	no	—
38	C₂²×C₇₉	—	2	1	no	—
39	C₂²×C₇₉	—	2	1	no	—
40	C₂²×C₇₉	—	2	1	no	—
41	C₂²×C₇₉	#95	1	1	yes	characteristic
42	C₄×C₇₉	—	2	1	no	—
43	C₄×C₇₉	—	2	1	no	—
44	C₄×C₇₉	—	2	1	no	—
45	C₄×C₇₉	—	2	1	no	—
46	C₄×C₇₉	—	2	1	no	—
47	C₄×C₇₉	#104	1	2	yes	—
48	C₂×C₇₉	—	4	1	no	—
49	C₂×C₇₉	#338	1	1	yes	characteristic
50	C₂×C₇₉	#339	1	1	yes	characteristic
51	C₂×C₇₉	#344	1	1	yes	characteristic
52	#1291	—	79	1	no	maximal, Sylow
53	C₇₉	#1291	1	1	yes	characteristic, complemented, Sylow
54	#432	—	79	1	no	—
55	#432	—	79	1	no	—
56	C₄×M₁₆	D₇₉	1	1	yes	characteristic
57	C₂×M₁₆	—	2	1	no	—
58	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
59	C₄⋊C₈	—	79	2	no	—
60	C₄⋊C₈	—	158	1	no	—
61	C₂²⋊C₈	—	79	2	no	—
62	C₂²⋊C₈	—	158	1	no	—
63	#97	—	2	1	no	—
64	#97	—	158	1	no	—
65	#97	—	158	1	no	—
66	C₄×C₈	Dic₇₉	1	2	yes	—
67	C₂²×C₄	Dic₁₅₈	1	1	yes	characteristic
68	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
69	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
70	M₁₆	—	2	4	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	158	2	no	—
73	C₂×C₈	—	158	2	no	—
74	C₄²	C₄×D₇₉	1	1	yes	characteristic
75	C₄²	D₃₁₆	1	1	yes	characteristic
76	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
77	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
78	C₂³	Dic₇₉⋊C₄	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	4	1	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
83	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
84	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
85	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
86	C₂×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
87	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
88	C₈	—	2	4	no	—
89	C₈	—	316	2	no	—
90	C₈	—	316	2	no	—
91	C₂²	—	2	1	no	—
92	C₂²	—	2	1	no	—
93	C₂²	—	2	1	no	—
94	C₂²	C₇₉⋊#95	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	2	1	no	—
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	#14579089	1	2	yes	—
101	C₂	—	4	1	no	—
102	C₂	C₇₉⋊#338	1	1	yes	characteristic
103	C₂	#19098323	1	1	yes	characteristic
104	C₂	#19098334	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098620

C₂

yes

maximal, characteristic

#19098620

C₂

yes

maximal, characteristic

C₄×M₁₆×C₇₉

C₂

yes

maximal, characteristic

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

C₄

yes

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

C₄

yes

—

#14579072

—

#14579072

—

C₂×M₁₆×C₇₉

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

#97×C₇₉

—

C₄×C₈×C₇₉

C₄

yes

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

Q₈

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₂³×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#95

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#104

yes

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#432

—

#432

—

C₄×M₁₆

D₇₉

yes

characteristic

C₂×M₁₆

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

158

—

C₂²⋊C₈

—

C₂²⋊C₈

—

158

—

#97

—

#97

—

158

—

#97

—

158

—

C₄×C₈

Dic₇₉

yes

—

C₂²×C₄

Dic₁₅₈

yes

characteristic

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₄²

C₄×D₇₉

yes

characteristic

C₄²

D₃₁₆

yes

characteristic

C₄²

C₂×Dic₇₉

yes

characteristic

C₄²

C₂²⋊D₇₉

yes

characteristic

C₂³

Dic₇₉⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₇₉

yes

characteristic

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₇₉

yes

characteristic

C₂×C₄

Dic₇₉⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

C₈

—

C₈

—

316

—

C₈

—

316

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₇₉⋊#95

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

100

C₄

#14579089

yes

—

101

C₂

—

102

C₂

C₇₉⋊#338

yes

characteristic

103

C₂

#19098323

yes

characteristic

104

C₂

#19098334

yes

characteristic

	subgroup	G/H
center	C₂²	C₇₉⋊#95
commutator	C₂×C₄×C₇₉	C₄²
Frattini	C₂×C₄²	C₂×D₇₉
Fitting	C₄×M₁₆×C₇₉	C₂
socle	C₂²×C₇₉	#95
prime radical	C₂³×C₇₉	C₄⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂²
hypercenter	C₄×M₁₆	D₇₉
hypocenter	C₇₉	#1291
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₇₉⋊#95

commutator

C₂×C₄×C₇₉

C₄²

Frattini

C₂×C₄²

C₂×D₇₉

Fitting

C₄×M₁₆×C₇₉

C₂

socle

C₂²×C₇₉

#95

prime radical

C₂³×C₇₉

C₄⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂²

hypercenter

C₄×M₁₆

D₇₉

hypocenter

C₇₉

#1291

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
53. C₇₉	#1291	semidirect

H ≅ G/N

type

53. C₇₉

#1291

semidirect

Subgroups — #23761272

Conjugacy classes of subgroups

Complements