Group #23763547 — subgroups

Subgroups — #23763547

Order 10112.

162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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	M₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic
2	#19098333	C₂	1	2	yes	maximal
3	#19098322	C₂	1	2	yes	maximal
4	C₇₉⋊#338	C₂	1	1	yes	maximal, characteristic
5	H(3,ℤ/4)×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929608	C₂²	1	2	yes	—
7	C₂×#11929608	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
9	#14579071	C₄	1	2	yes	complemented
10	C₈×Dic₇₉	C₄	1	2	yes	complemented
11	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
12	#117×C₇₉	C₂²	1	2	yes	—
13	C₂²×Dic₇₉	—	2	1	no	—
14	#11929608	—	2	2	no	—
15	#11929608	—	2	2	no	—
16	#11929608	—	2	2	no	—
17	C₂×C₇₉⋊C₈	—	2	2	no	—
18	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
19	C₄×Dic₇₉	—	2	1	no	—
20	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
23	M₁₆×C₇₉	—	2	2	no	—
24	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
25	C₄⋊C₄×C₇₉	—	2	2	no	—
26	C₂²⋊C₄×C₇₉	—	2	2	no	—
27	C₄²×C₇₉	—	2	2	no	—
28	C₂³×C₇₉	#41	1	1	yes	characteristic
29	C₂×C₄×C₇₉	—	4	2	no	—
30	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₉	#41	1	2	yes	—
32	C₂×C₄×C₇₉	#41	1	2	yes	—
33	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
34	C₂×Dic₇₉	—	2	1	no	—
35	C₂×Dic₇₉	—	2	1	no	—
36	C₂×Dic₇₉	—	4	2	no	—
37	C₈×C₇₉	—	2	2	no	—
38	C₇₉⋊C₈	—	2	2	no	—
39	C₇₉⋊C₈	—	4	2	no	—
40	C₂²×C₇₉	—	4	1	no	—
41	C₂²×C₇₉	#117	1	1	yes	characteristic
42	C₂²×C₇₉	#126	1	2	yes	—
43	C₄×C₇₉	—	8	2	no	—
44	C₄×C₇₉	#117	1	1	yes	characteristic
45	C₄×C₇₉	#117	1	1	yes	characteristic
46	C₄×C₇₉	#126	1	2	yes	—
47	Dic₇₉	—	2	2	no	—
48	Dic₇₉	—	4	1	no	—
49	C₂×C₇₉	—	2	1	no	—
50	C₂×C₇₉	—	2	2	no	—
51	C₂×C₇₉	#383	1	1	yes	characteristic
52	#1841	—	79	1	no	maximal, Sylow
53	C₇₉	#1841	1	1	yes	characteristic, complemented, Sylow
54	C₄×M₁₆	—	79	1	no	—
55	#344	—	79	2	no	—
56	#339	—	79	2	no	—
57	#338	—	79	1	no	—
58	H(3,ℤ/4)	D₇₉	1	1	yes	characteristic
59	C₂×M₁₆	—	79	1	no	—
60	C₂×M₁₆	—	79	2	no	—
61	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
62	#117	C₂×D₇₉	1	2	yes	—
63	C₂×C₄²	—	79	1	no	—
64	#97	—	79	2	no	—
65	C₄×C₈	—	79	2	no	—
66	C₂²×C₄	—	158	1	no	—
67	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	158	2	no	—
70	M₁₆	—	158	2	no	—
71	M₁₆	—	158	2	no	—
72	C₂×C₈	—	79	2	no	—
73	C₂×C₈	—	158	2	no	—
74	C₂×C₈	C₄×D₇₉	1	2	yes	—
75	C₄⋊C₄	—	2	2	no	—
76	C₂²⋊C₄	—	2	2	no	—
77	C₄²	—	2	2	no	—
78	C₄²	—	79	1	no	—
79	C₄²	—	79	1	no	—
80	C₄²	—	158	1	no	—
81	C₂³	#11929623	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	316	2	no	—
84	C₂×C₄	—	158	1	no	—
85	C₂×C₄	—	158	1	no	—
86	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
87	C₂×C₄	#11929623	1	2	yes	—
88	C₂×C₄	#11929624	1	2	yes	—
89	C₂×C₄	#11929625	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	316	2	no	—
92	C₈	—	158	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#14579119	1	1	yes	characteristic
95	C₂²	#14579154	1	2	yes	—
96	C₄	—	8	2	no	—
97	C₄	—	316	1	no	—
98	C₄	—	158	2	no	—
99	C₄	#14579117	1	1	yes	characteristic
100	C₄	#14579118	1	1	yes	characteristic
101	C₄	#14579156	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	—	2	1	no	—
104	C₂	#19098430	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₁₆×Dic₇₉

C₂

yes

maximal, characteristic

#19098333

C₂

yes

maximal

#19098322

C₂

yes

maximal

C₇₉⋊#338

C₂

yes

maximal, characteristic

H(3,ℤ/4)×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

—

C₂×#11929608

C₂²

yes

characteristic

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

#14579071

C₄

yes

complemented

C₈×Dic₇₉

C₄

yes

complemented

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

#117×C₇₉

C₂²

yes

—

C₂²×Dic₇₉

—

#11929608

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

#41

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

#117

yes

characteristic

C₂²×C₇₉

#126

yes

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₄×M₁₆

—

—

—

—

D₇₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

characteristic

#117

C₂×D₇₉

yes

—

C₂×C₄²

—

#97

—

C₄×C₈

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

158

—

M₁₆

—

158

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

158

—

C₂³

#11929623

yes

characteristic

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

#11929623

yes

—

C₂×C₄

#11929624

yes

—

C₂×C₄

#11929625

yes

characteristic

C₈

—

C₈

—

316

—

C₈

—

158

—

C₂²

—

C₂²

#14579119

yes

characteristic

C₂²

#14579154

yes

—

C₄

—

C₄

—

316

—

C₄

—

158

—

C₄

#14579117

yes

characteristic

100

C₄

#14579118

yes

characteristic

101

C₄

#14579156

yes

—

102

C₂

—

103

C₂

—

104

C₂

#19098430

yes

characteristic

	subgroup	G/H
center	C₄	#14579118
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	H(3,ℤ/4)×C₇₉	C₂
socle	C₂×C₇₉	#383
prime radical	C₂³×C₇₉	#41
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	H(3,ℤ/4)	D₇₉
hypocenter	C₇₉	#1841
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#14579118

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

H(3,ℤ/4)×C₇₉

C₂

C₂×C₇₉

C₂³×C₇₉

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
9. #14579071	C₄	semidirect
10. C₈×Dic₇₉	C₄	semidirect
53. C₇₉	#1841	semidirect

H ≅ G/N

type

9. #14579071

C₄

semidirect

10. C₈×Dic₇₉

C₄

semidirect

53. C₇₉

#1841

semidirect

Subgroups — #23763547

Conjugacy classes of subgroups

Complements