Group #23764392 — subgroups

Subgroups — #23764392

Order 10112.

228 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14579153	C₂	1	1	yes	maximal, characteristic
2	C₄×#11929608	C₂	1	1	yes	maximal, characteristic
3	#19098331	C₂	1	4	yes	maximal
4	#423×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#11929608	C₂²	1	2	yes	—
6	#14579153	—	2	2	no	—
7	#14579153	—	2	1	no	—
8	#14579153	—	2	1	no	—
9	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
10	C₂×Dic₇₉⋊C₄	C₄	1	4	yes	—
11	#14579072	—	2	1	no	—
12	C₄×C₇₉⋊C₈	—	2	1	no	—
13	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
15	C₄⋊C₈×C₇₉	—	2	2	no	—
16	C₂²×Dic₇₉	C₂×C₄	1	4	yes	—
17	#11929608	—	2	2	no	—
18	#11929608	Q₈	1	4	yes	—
19	C₂×C₇₉⋊C₈	—	2	2	no	—
20	C₄⋊Dic₇₉	—	2	2	no	—
21	C₄⋊Dic₇₉	—	2	2	no	—
22	Dic₇₉⋊C₄	—	2	4	no	—
23	Dic₇₉⋊C₄	—	2	4	no	—
24	C₂²×C₄×C₇₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
26	M₁₆×C₇₉	—	2	4	no	—
27	C₂×C₈×C₇₉	—	2	2	no	—
28	C₄²×C₇₉	D₄	1	2	yes	—
29	C₄²×C₇₉	D₄	1	1	yes	characteristic
30	C₄²×C₇₉	D₄	1	1	yes	characteristic
31	C₂³×C₇₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	—	4	2	no	—
33	C₂×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₇₉	#41	1	2	yes	—
39	C₂×Dic₇₉	—	2	4	no	—
40	C₂×Dic₇₉	—	4	4	no	—
41	C₈×C₇₉	—	4	2	no	—
42	C₇₉⋊C₈	—	2	4	no	—
43	C₂²×C₇₉	—	2	2	no	—
44	C₂²×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₇₉	C₄×Q₈	1	2	yes	—
46	C₄×C₇₉	—	2	2	no	—
47	C₄×C₇₉	—	2	2	no	—
48	C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
49	C₄×C₇₉	#124	1	1	yes	characteristic
50	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
51	Dic₇₉	—	4	4	no	—
52	C₂×C₇₉	—	2	2	no	—
53	C₂×C₇₉	#391	1	1	yes	characteristic
54	C₂×C₇₉	#413	1	2	yes	—
55	#1998	—	79	1	no	maximal, Sylow
56	C₇₉	#1998	1	1	yes	characteristic, complemented, Sylow
57	C₂×#125	—	79	1	no	—
58	#423	D₇₉	1	1	yes	characteristic
59	C₄×M₁₆	—	79	1	no	—
60	#343	—	79	4	no	—
61	C₂×M₁₆	—	79	2	no	—
62	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
63	#125	—	158	2	no	—
64	#125	—	158	1	no	—
65	#125	—	158	1	no	—
66	C₂×C₄⋊C₄	—	79	2	no	—
67	C₂×C₄⋊C₄	—	79	4	no	—
68	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
69	C₄⋊C₈	—	2	2	no	—
70	#97	—	158	1	no	—
71	C₄×C₈	—	158	1	no	—
72	C₂²×C₄	—	79	4	no	—
73	C₂²×C₄	C₄×D₇₉	1	2	yes	—
74	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
75	M₁₆	—	2	4	no	—
76	M₁₆	—	79	4	no	—
77	M₁₆	—	158	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	158	2	no	—
80	C₄⋊C₄	—	158	4	no	—
81	C₄⋊C₄	—	158	4	no	—
82	C₄⋊C₄	—	158	2	no	—
83	C₄⋊C₄	—	158	2	no	—
84	C₄²	D₃₁₆	1	1	yes	characteristic
85	C₄²	D₃₁₆	1	1	yes	characteristic
86	C₄²	C₂²⋊D₇₉	1	2	yes	—
87	C₂³	C₂×C₄×D₇₉	1	1	yes	characteristic
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	316	4	no	—
90	C₂×C₄	—	158	4	no	—
91	C₂×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
92	C₂×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
94	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
95	C₂×C₄	Q₈×D₇₉	1	2	yes	—
96	C₂×C₄	#11929623	1	2	yes	—
97	C₈	—	4	2	no	—
98	C₈	—	158	4	no	—
99	C₂²	—	2	2	no	—
100	C₂²	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
101	C₂²	#14579126	1	2	yes	—
102	C₄	—	2	2	no	—
103	C₄	—	2	2	no	—
104	C₄	—	316	4	no	—
105	C₄	#14579141	1	2	yes	—
106	C₄	#14579148	1	1	yes	characteristic
107	C₄	#14579159	1	1	yes	characteristic
108	C₂	—	2	2	no	—
109	C₂	#19098468	1	1	yes	characteristic
110	C₂	#19098545	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579153

C₂

yes

maximal, characteristic

C₄×#11929608

C₂

yes

maximal, characteristic

#19098331

C₂

yes

maximal

#423×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

—

#14579153

—

#14579153

—

#14579153

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₄

yes

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂²×Dic₇₉

C₂×C₄

yes

—

#11929608

—

#11929608

Q₈

yes

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

D₄

yes

—

C₄²×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₂³×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₉

C₄×Q₈

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

—

C₄×C₇₉

#124

yes

characteristic

C₄×C₇₉

C₄⋊Q₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#391

yes

characteristic

C₂×C₇₉

#413

yes

—

#1998

—

maximal, Sylow

C₇₉

#1998

yes

characteristic, complemented, Sylow

C₂×#125

—

#423

D₇₉

yes

characteristic

C₄×M₁₆

—

#343

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

—

#125

—

158

—

#125

—

158

—

#125

—

158

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₄⋊C₈

—

#97

—

158

—

C₄×C₈

—

158

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

D₃₁₆

yes

characteristic

C₄²

D₃₁₆

yes

characteristic

C₄²

C₂²⋊D₇₉

yes

—

C₂³

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

158

—

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

—

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

—

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₂×C₄

Q₈×D₇₉

yes

—

C₂×C₄

#11929623

yes

—

C₈

—

C₈

—

158

—

C₂²

—

100

C₂²

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

101

C₂²

#14579126

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

316

—

105

C₄

#14579141

yes

—

106

C₄

#14579148

yes

characteristic

107

C₄

#14579159

yes

characteristic

108

C₂

—

109

C₂

#19098468

yes

characteristic

110

C₂

#19098545

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₇₉)⋊C₄
commutator, prime radical	C₂³×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#423×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#423	D₇₉
hypocenter	C₇₉	#1998
LCS	G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂×(C₂×D₇₉)⋊C₄

commutator, prime radical

C₂³×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#423×C₇₉

C₂

socle

C₂²×C₇₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
56. C₇₉	#1998	semidirect

H ≅ G/N

type

56. C₇₉

#1998

semidirect

Subgroups — #23764392

Conjugacy classes of subgroups

Complements