Group #23763533 — subgroups

Subgroups — #23763533

Order 10112.

224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14579072	C₂	1	1	yes	maximal, characteristic
2	#19098433	C₂	1	1	yes	maximal, characteristic
3	#19098325	C₂	1	4	yes	maximal
4	#382×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₇₉⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₇₉	—	2	2	no	—
7	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
8	#14579072	C₄	1	4	yes	complemented
9	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
11	#95×C₇₉	—	2	2	no	—
12	C₂²×Dic₇₉	—	2	2	no	—
13	C₂×C₇₉⋊C₈	—	2	2	no	—
14	C₂×C₇₉⋊C₈	—	2	2	no	—
15	C₂×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
16	C₄⋊Dic₇₉	—	2	4	no	—
17	C₄⋊Dic₇₉	—	4	4	no	—
18	C₂²×C₄×C₇₉	—	2	2	no	—
19	C₂²×C₄×C₇₉	D₄	1	2	yes	—
20	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₇₉	—	2	4	no	—
22	C₄²×C₇₉	C₂×C₄	1	2	yes	—
23	C₄²×C₇₉	Q₈	1	2	yes	—
24	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₇₉	—	2	2	no	—
26	C₂×C₄×C₇₉	—	2	2	no	—
27	C₂×C₄×C₇₉	—	4	2	no	—
28	C₂×C₄×C₇₉	—	4	2	no	—
29	C₂×C₄×C₇₉	—	4	2	no	—
30	C₂×C₄×C₇₉	C₄⋊C₄	1	4	yes	—
31	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₇₉	#41	1	2	yes	—
34	C₂×C₄×C₇₉	#41	1	2	yes	—
35	C₂×Dic₇₉	—	4	2	no	—
36	C₂×Dic₇₉	—	4	4	no	—
37	C₇₉⋊C₈	—	2	4	no	—
38	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₇₉	#124	1	1	yes	characteristic
40	C₂²×C₇₉	#124	1	1	yes	characteristic
41	C₂²×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
42	C₂²×C₇₉	#137	1	2	yes	—
43	C₄×C₇₉	—	2	4	no	—
44	C₄×C₇₉	—	8	2	no	—
45	C₄×C₇₉	#117	1	2	yes	—
46	C₄×C₇₉	#125	1	2	yes	—
47	Dic₇₉	—	8	2	no	—
48	C₂×C₇₉	#382	1	1	yes	characteristic
49	C₂×C₇₉	#428	1	2	yes	—
50	C₂×C₇₉	#489	1	2	yes	—
51	C₂×C₇₉	#490	1	1	yes	characteristic
52	C₂×C₇₉	#491	1	1	yes	characteristic
53	#1836	—	79	1	no	maximal, Sylow
54	C₇₉	#1836	1	1	yes	characteristic, complemented, Sylow
55	C₂×#97	—	79	1	no	—
56	#384	—	79	1	no	—
57	#382	D₇₉	1	1	yes	characteristic
58	#340	—	79	4	no	—
59	C₂²×C₈	—	79	2	no	—
60	C₂×C₄⋊C₄	—	79	2	no	—
61	C₂×C₄⋊C₄	—	158	2	no	—
62	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
63	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
64	#97	—	79	4	no	—
65	#95	—	2	2	no	—
66	C₂²×C₄	—	2	2	no	—
67	C₂²×C₄	—	158	2	no	—
68	C₂²×C₄	C₂²⋊D₇₉	1	2	yes	—
69	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
70	C₂×C₈	—	79	4	no	—
71	C₂×C₈	—	158	2	no	—
72	C₂×C₈	—	158	2	no	—
73	C₄⋊C₄	—	2	4	no	—
74	C₄⋊C₄	—	316	4	no	—
75	C₄⋊C₄	—	158	4	no	—
76	C₄²	Dic₁₅₈	1	2	yes	—
77	C₄²	C₄×D₇₉	1	2	yes	—
78	C₂³	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	—	316	2	no	—
85	C₂×C₄	—	316	4	no	—
86	C₂×C₄	Dic₇₉⋊C₄	1	4	yes	—
87	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
88	C₂×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
89	C₂×C₄	#11929623	1	2	yes	—
90	C₂×C₄	#11929625	1	2	yes	—
91	C₈	—	158	4	no	—
92	C₂²	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
93	C₂²	#14579148	1	1	yes	characteristic
94	C₂²	#14579150	1	1	yes	characteristic
95	C₂²	#14579186	1	2	yes	—
96	C₂²	#14579191	1	2	yes	—
97	C₄	—	2	4	no	—
98	C₄	—	8	2	no	—
99	C₄	—	632	2	no	—
100	C₄	#14579119	1	2	yes	—
101	C₄	#14579152	1	2	yes	—
102	C₂	#19098428	1	1	yes	characteristic
103	C₂	#19098606	1	2	yes	—
104	C₂	#19098922	1	2	yes	—
105	C₂	#19098929	1	1	yes	characteristic
106	C₂	#19098933	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579072

C₂

yes

maximal, characteristic

#19098433

C₂

yes

maximal, characteristic

#19098325

C₂

yes

maximal

#382×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

#14579072

C₄

yes

complemented

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

#95×C₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

Q₈

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×C₄⋊C₄

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

—

C₂²×C₇₉

#137

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#117

yes

—

C₄×C₇₉

#125

yes

—

Dic₇₉

—

C₂×C₇₉

#382

yes

characteristic

C₂×C₇₉

#428

yes

—

C₂×C₇₉

#489

yes

—

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×#97

—

#384

—

#382

D₇₉

yes

characteristic

#340

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#97

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²⋊D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄²

Dic₁₅₈

yes

—

C₄²

C₄×D₇₉

yes

—

C₂³

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

Dic₇₉⋊C₄

yes

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

C₂×Dic₁₅₈

yes

characteristic

C₂×C₄

#11929623

yes

—

C₂×C₄

#11929625

yes

—

C₈

—

158

—

C₂²

C₂×Dic₇₉⋊C₄

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#14579191

yes

—

C₄

—

C₄

—

C₄

—

632

—

100

C₄

#14579119

yes

—

101

C₄

#14579152

yes

—

102

C₂

#19098428

yes

characteristic

103

C₂

#19098606

yes

—

104

C₂

#19098922

yes

—

105

C₂

#19098929

yes

characteristic

106

C₂

#19098933

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#382×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#382	D₇₉
hypocenter	C₇₉	#1836
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#382×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

N	H ≅ G/N	type
8. #14579072	C₄	semidirect
54. C₇₉	#1836	semidirect

H ≅ G/N

type

8. #14579072

C₄

semidirect

54. C₇₉

#1836

semidirect

Subgroups — #23763533

Conjugacy classes of subgroups

Complements