Group #23761391 — subgroups

Subgroups — #23761391

Order 10112.

110 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 33 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	#19098345	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
3	#469×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929608	—	2	1	no	—
5	#14579101	—	2	1	no	—
6	C₂×D₈×C₇₉	C₄	1	1	yes	characteristic
7	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
8	#121×C₇₉	—	2	1	no	—
9	#106×C₇₉	C₄	1	1	yes	characteristic
10	#102×C₇₉	—	2	1	no	—
11	#11929608	—	4	1	no	—
12	#11929608	—	4	1	no	—
13	C₂×C₇₉⋊C₈	—	2	2	no	—
14	C₇₉⋊C₁₆	—	4	1	no	—
15	C₂×D₄×C₇₉	—	2	1	no	—
16	C₂×D₄×C₇₉	—	4	1	no	—
17	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
18	D₈×C₇₉	—	4	1	no	—
19	M₁₆×C₇₉	—	4	1	no	—
20	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₇₉	—	2	1	no	—
23	C₂²⋊C₄×C₇₉	—	4	1	no	—
24	C₂³×C₇₉	—	4	1	no	—
25	C₂³×C₇₉	SD₁₆	1	1	yes	characteristic
26	D₄×C₇₉	—	4	1	no	—
27	D₄×C₇₉	—	4	1	no	—
28	D₄×C₇₉	—	8	2	no	—
29	C₂×C₄×C₇₉	—	2	1	no	—
30	C₂×C₄×C₇₉	—	2	1	no	—
31	C₂×C₄×C₇₉	—	4	1	no	—
32	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
34	C₈×C₇₉	—	2	1	no	—
35	C₈×C₇₉	—	2	1	no	—
36	C₇₉⋊C₈	—	4	2	no	—
37	C₂²×C₇₉	—	2	1	no	—
38	C₂²×C₇₉	—	4	1	no	—
39	C₂²×C₇₉	—	8	1	no	—
40	C₂²×C₇₉	—	8	1	no	—
41	C₂²×C₇₉	—	8	1	no	—
42	C₂²×C₇₉	#102	1	1	yes	characteristic
43	C₄×C₇₉	—	2	1	no	—
44	C₄×C₇₉	—	8	1	no	—
45	C₄×C₇₉	#99	1	1	yes	characteristic
46	C₄×C₇₉	#104	1	1	yes	characteristic
47	C₂×C₇₉	—	2	1	no	—
48	C₂×C₇₉	—	4	1	no	—
49	C₂×C₇₉	—	16	1	no	—
50	C₂×C₇₉	#327	1	1	yes	characteristic
51	#1341	—	79	1	no	maximal, Sylow
52	C₇₉	#1341	1	1	yes	characteristic, complemented, Sylow
53	#469	D₇₉	1	1	yes	characteristic
54	#349	—	79	1	no	—
55	#338	—	79	1	no	—
56	C₂×D₈	Dic₇₉	1	1	yes	characteristic
57	C₂×M₁₆	—	158	1	no	—
58	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
59	#121	—	2	1	no	—
60	M₃₂	—	158	1	no	—
61	#106	Dic₇₉	1	1	yes	characteristic
62	#102	—	2	1	no	—
63	C₂×D₄	—	2	1	no	—
64	C₂×D₄	—	4	1	no	—
65	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
66	D₈	—	4	1	no	—
67	M₁₆	—	4	1	no	—
68	M₁₆	—	316	1	no	—
69	M₁₆	—	316	1	no	—
70	C₂×C₈	—	158	2	no	—
71	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
72	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
73	C₄⋊C₄	—	2	1	no	—
74	C₂²⋊C₄	—	4	1	no	—
75	C₁₆	—	316	1	no	—
76	C₂³	—	4	1	no	—
77	C₂³	#11929612	1	1	yes	characteristic
78	D₄	—	4	1	no	—
79	D₄	—	4	1	no	—
80	D₄	—	8	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
85	C₂×C₄	#11929609	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	2	1	no	—
88	C₈	—	316	2	no	—
89	C₂²	—	2	1	no	—
90	C₂²	—	4	1	no	—
91	C₂²	—	8	1	no	—
92	C₂²	—	8	1	no	—
93	C₂²	—	8	1	no	—
94	C₂²	#14579082	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	8	1	no	—
97	C₄	#14579076	1	1	yes	characteristic
98	C₄	#14579088	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	4	1	no	—
101	C₂	—	16	1	no	—
102	C₂	#19098297	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098345

C₂

yes

maximal, characteristic, complemented

C₇₉⋊#338

C₂

yes

maximal, characteristic, complemented

#469×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

—

#14579101

—

C₂×D₈×C₇₉

C₄

yes

characteristic

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

#121×C₇₉

—

#106×C₇₉

C₄

yes

characteristic

#102×C₇₉

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₇₉⋊C₁₆

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

D₈×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

SD₁₆

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

D₈

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#102

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#469

D₇₉

yes

characteristic

#349

—

#338

—

C₂×D₈

Dic₇₉

yes

characteristic

C₂×M₁₆

—

158

—

C₂×M₁₆

C₂×D₇₉

yes

characteristic

#121

—

M₃₂

—

158

—

#106

Dic₇₉

yes

characteristic

#102

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

316

—

M₁₆

—

316

—

C₂×C₈

—

158

—

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

316

—

C₂³

—

C₂³

#11929612

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₇₉

yes

characteristic

C₂×C₄

#11929609

yes

characteristic

C₈

—

C₈

—

C₈

—

316

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#14579082

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

—

102

C₂

#19098297

yes

characteristic

	subgroup	G/H
center	C₂	#19098297
commutator	C₂×C₈×C₇₉	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₇₉
Fitting, prime radical	#469×C₇₉	C₂
socle	C₂×C₇₉	#327
cosocle	C₂×M₁₆×C₇₉	C₂²
hypercenter	#469	D₇₉
hypocenter	C₇₉	#1341
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

subgroup

G/H

center

C₂

#19098297

commutator

C₂×C₈×C₇₉

C₂×C₄

Frattini

C₂×M₁₆

C₂×D₇₉

Fitting, prime radical

#469×C₇₉

C₂

socle

C₂×C₇₉

#327

cosocle

C₂×M₁₆×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

N	H ≅ G/N	type
1. #19098345	C₂	semidirect
2. C₇₉⋊#338	C₂	semidirect
52. C₇₉	#1341	semidirect

H ≅ G/N

type

1. #19098345

C₂

semidirect

2. C₇₉⋊#338

C₂

semidirect

52. C₇₉

#1341

semidirect

Subgroups — #23761391

Conjugacy classes of subgroups

Complements