Group #23761503 — subgroups

Subgroups — #23761503

Order 10112.

124 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 69 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	1	yes	maximal, characteristic
2	C₂×#14579097	C₂	1	1	yes	maximal, characteristic
3	C₂×#108×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929608	—	2	1	no	—
5	#14579101	—	2	1	no	—
6	#14579101	—	2	1	no	—
7	C₂×C₇₉⋊C₁₆	C₄	1	2	yes	—
8	#14579097	—	2	1	no	—
9	#14579097	C₄	1	2	yes	—
10	C₂×M₁₆×C₇₉	—	2	1	no	—
11	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
12	#108×C₇₉	—	2	1	no	—
13	#108×C₇₉	C₄	1	2	yes	—
14	#11929608	—	2	2	no	—
15	#11929608	—	4	1	no	—
16	C₂×C₇₉⋊C₈	—	4	1	no	—
17	C₇₉⋊C₁₆	—	2	2	no	—
18	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
19	M₁₆×C₇₉	—	2	2	no	—
20	M₁₆×C₇₉	—	4	1	no	—
21	C₂×C₈×C₇₉	—	4	1	no	—
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	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
28	C₂³×C₇₉	Q₁₆	1	1	yes	characteristic
29	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
33	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
35	C₈×C₇₉	—	4	2	no	—
36	C₈×C₇₉	C₄²	1	1	yes	characteristic
37	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
40	C₇₉⋊C₈	—	4	2	no	—
41	C₂²×C₇₉	—	4	1	no	—
42	C₂²×C₇₉	#103	1	1	yes	characteristic
43	C₂²×C₇₉	#103	1	1	yes	characteristic
44	C₂²×C₇₉	#107	1	1	yes	characteristic
45	C₄×C₇₉	#95	1	1	yes	characteristic
46	C₄×C₇₉	#102	1	1	yes	characteristic
47	C₄×C₇₉	#102	1	1	yes	characteristic
48	C₄×C₇₉	#106	1	1	yes	characteristic
49	C₂×C₇₉	—	2	1	no	—
50	C₂×C₇₉	—	2	1	no	—
51	C₂×C₇₉	—	2	1	no	—
52	C₂×C₇₉	#340	1	1	yes	characteristic
53	#1385	—	79	1	no	maximal, Sylow
54	C₇₉	#1385	1	1	yes	characteristic, complemented, Sylow
55	C₂×M₃₂	—	79	1	no	—
56	C₂×#108	—	79	1	no	—
57	C₂×#108	D₇₉	1	1	yes	characteristic
58	C₂×M₁₆	—	2	1	no	—
59	C₂×M₁₆	—	158	1	no	—
60	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
61	M₃₂	—	158	1	no	—
62	M₃₂	—	158	1	no	—
63	C₂×C₁₆	—	79	2	no	—
64	#108	—	2	1	no	—
65	#108	—	79	2	no	—
66	#108	—	158	1	no	—
67	#108	Dic₇₉	1	2	yes	—
68	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	4	1	no	—
71	M₁₆	—	316	1	no	—
72	M₁₆	—	158	2	no	—
73	C₂×C₈	—	4	1	no	—
74	C₂×C₈	—	316	1	no	—
75	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
76	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
77	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
78	C₂×C₈	D₃₁₆	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
81	C₁₆	—	158	2	no	—
82	C₂³	#11929614	1	1	yes	characteristic
83	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
84	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
85	C₂×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
86	C₂×C₄	#11929609	1	1	yes	characteristic
87	C₂×C₄	#11929611	1	1	yes	characteristic
88	C₂×C₄	#11929612	1	1	yes	characteristic
89	C₈	—	4	2	no	—
90	C₈	—	316	2	no	—
91	C₈	C₄×Dic₇₉	1	1	yes	characteristic
92	C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
93	C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
94	C₈	C₄⋊Dic₇₉	1	1	yes	characteristic
95	C₂²	—	4	1	no	—
96	C₂²	#14579084	1	1	yes	characteristic
97	C₂²	#14579085	1	1	yes	characteristic
98	C₂²	#14579094	1	1	yes	characteristic
99	C₄	C₇₉⋊#95	1	1	yes	characteristic
100	C₄	#14579081	1	1	yes	characteristic
101	C₄	#14579082	1	1	yes	characteristic
102	C₄	#14579092	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	2	1	no	—
105	C₂	—	2	1	no	—
106	C₂	#19098325	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579101

C₂

yes

maximal, characteristic

C₂×#14579097

C₂

yes

maximal, characteristic

C₂×#108×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

—

#14579101

—

#14579101

—

C₂×C₇₉⋊C₁₆

C₄

yes

—

#14579097

—

#14579097

C₄

yes

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

#108×C₇₉

—

#108×C₇₉

C₄

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

M₁₆×C₇₉

—

M₁₆×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

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

characteristic

C₂³×C₇₉

Q₁₆

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

D₈

yes

characteristic

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

C₄²

yes

characteristic

C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

—

C₂×#108

D₇₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

158

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

M₃₂

—

158

—

M₃₂

—

158

—

C₂×C₁₆

—

#108

—

#108

—

#108

—

158

—

#108

Dic₇₉

yes

—

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

316

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

316

—

C₂×C₈

Dic₁₅₈

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₁₆

—

158

—

C₂³

#11929614

yes

characteristic

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₇₉

yes

characteristic

C₂×C₄

Dic₇₉⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

316

—

C₈

C₄×Dic₇₉

yes

characteristic

C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

C₈

Dic₇₉⋊C₄

yes

characteristic

C₈

C₄⋊Dic₇₉

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

C₇₉⋊#95

yes

characteristic

100

C₄

#14579081

yes

characteristic

101

C₄

#14579082

yes

characteristic

102

C₄

#14579092

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

—

106

C₂

#19098325

yes

characteristic

	subgroup	G/H
center	C₄	#14579092
commutator	C₈×C₇₉	C₄²
Frattini	C₂²×C₈	C₂×D₇₉
Fitting	C₂×#108×C₇₉	C₂
socle	C₂×C₇₉	#340
prime radical	C₂³×C₇₉	Q₁₆
cosocle	C₂²×C₈×C₇₉	C₂²
hypercenter	C₂×#108	D₇₉
hypocenter	C₇₉	#1385
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₄

#14579092

commutator

C₈×C₇₉

C₄²

Frattini

C₂²×C₈

C₂×D₇₉

Fitting

C₂×#108×C₇₉

C₂

socle

C₂×C₇₉

#340

prime radical

C₂³×C₇₉

Q₁₆

cosocle

C₂²×C₈×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
54. C₇₉	#1385	semidirect

H ≅ G/N

type

54. C₇₉

#1385

semidirect

Subgroups — #23761503

Conjugacy classes of subgroups

Complements