Group #23762770 — subgroups

Subgroups — #23762770

Order 10112.

156 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 61 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	#19098943	C₂	1	1	yes	maximal, characteristic
2	#19098848	C₂	1	2	yes	maximal
3	#19098316	C₂	1	1	yes	maximal, characteristic
4	#19098310	C₂	1	2	yes	maximal
5	C₈×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	—	2	1	no	—
7	C₂×Dic₃₁₆	—	2	1	no	—
8	#14579161	C₂²	1	2	yes	—
9	#14579092	—	2	2	no	—
10	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
11	#14579085	—	2	2	no	—
12	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₇₉	—	2	1	no	—
14	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₉	—	2	1	no	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₅₈	—	2	2	no	—
18	Dic₃₁₆	—	4	2	no	—
19	Dic₃₁₆	—	4	2	no	—
20	C₂×C₇₉⋊C₈	—	2	2	no	—
21	C₄⋊Dic₇₉	—	2	2	no	—
22	C₄⋊Dic₇₉	—	2	2	no	—
23	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	—	2	1	no	—
25	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
27	C₄⋊C₄×C₇₉	—	2	1	no	—
28	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
29	C₄²×C₇₉	—	2	1	no	—
30	C₄²×C₇₉	C₂³	1	1	yes	characteristic
31	Q₈×C₇₉	—	2	1	no	—
32	Q₈×C₇₉	Q₁₆	1	2	yes	complemented
33	C₂×C₄×C₇₉	—	2	1	no	—
34	C₂×C₄×C₇₉	—	2	1	no	—
35	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
38	C₂×Dic₇₉	—	4	2	no	—
39	Dic₁₅₈	—	4	2	no	—
40	Dic₁₅₈	—	4	2	no	—
41	C₈×C₇₉	—	2	1	no	—
42	C₈×C₇₉	—	4	1	no	—
43	C₈×C₇₉	SD₁₆	1	2	yes	—
44	C₇₉⋊C₈	—	4	2	no	—
45	C₂²×C₇₉	#121	1	1	yes	characteristic
46	C₄×C₇₉	—	2	2	no	—
47	C₄×C₇₉	—	2	1	no	—
48	C₄×C₇₉	—	4	1	no	—
49	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
50	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
51	C₄×C₇₉	#135	1	1	yes	characteristic
52	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
53	Dic₇₉	—	8	2	no	—
54	C₂×C₇₉	#460	1	1	yes	characteristic
55	C₂×C₇₉	#467	1	1	yes	characteristic
56	C₂×C₇₉	#473	1	1	yes	characteristic
57	#1670	—	79	1	no	maximal, Sylow
58	C₇₉	#1670	1	1	yes	characteristic, complemented, Sylow
59	#494	—	79	1	no	—
60	#475	—	79	2	no	—
61	C₈×Q₈	D₇₉	1	1	yes	characteristic
62	#335	—	79	1	no	—
63	#332	—	79	2	no	—
64	C₂×Q₁₆	—	158	1	no	—
65	C₂×Q₁₆	—	158	1	no	—
66	C₄⋊Q₈	—	79	2	no	—
67	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
68	#106	—	158	2	no	—
69	C₄⋊C₈	—	2	1	no	—
70	C₄⋊C₈	—	79	2	no	—
71	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
72	#103	—	158	2	no	—
73	C₄×C₈	—	2	1	no	—
74	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
75	C₂×Q₈	—	158	2	no	—
76	C₂×Q₈	D₃₁₆	1	1	yes	characteristic
77	Q₁₆	—	316	2	no	—
78	Q₁₆	—	316	2	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	—	158	2	no	—
81	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	158	2	no	—
85	C₄⋊C₄	—	158	2	no	—
86	C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
87	C₄²	—	2	1	no	—
88	C₄²	C₂²×D₇₉	1	1	yes	characteristic
89	Q₈	—	2	1	no	—
90	Q₈	—	316	2	no	—
91	Q₈	—	316	2	no	—
92	Q₈	Dic₃₁₆	1	2	yes	complemented
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	316	2	no	—
96	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
97	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
98	C₂×C₄	#11929624	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	4	1	no	—
101	C₈	—	316	2	no	—
102	C₈	#11929611	1	2	yes	—
103	C₂²	#14579135	1	1	yes	characteristic
104	C₄	—	2	2	no	—
105	C₄	—	2	1	no	—
106	C₄	—	4	1	no	—
107	C₄	—	632	2	no	—
108	C₄	C₂×#11929611	1	1	yes	characteristic
109	C₄	C₂×Dic₃₁₆	1	1	yes	characteristic
110	C₄	#14579183	1	1	yes	characteristic
111	C₄	#14579186	1	1	yes	characteristic
112	C₂	#19098763	1	1	yes	characteristic
113	C₂	#19098804	1	1	yes	characteristic
114	C₂	#19098838	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098943

C₂

yes

maximal, characteristic

#19098848

C₂

yes

maximal

#19098316

C₂

yes

maximal, characteristic

#19098310

C₂

yes

maximal

C₈×Q₈×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

#14579161

C₂²

yes

—

#14579092

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579085

—

C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

Q₁₆

yes

complemented

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

SD₁₆

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×SD₁₆

yes

characteristic

C₄×C₇₉

C₂×Q₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#494

—

#475

—

C₈×Q₈

D₇₉

yes

characteristic

#335

—

#332

—

C₂×Q₁₆

—

158

—

C₂×Q₁₆

—

158

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₇₉

yes

characteristic

#106

—

158

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₉

yes

characteristic

#103

—

158

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×Q₈

D₃₁₆

yes

characteristic

Q₁₆

—

316

—

Q₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

D₃₁₆

yes

characteristic

C₄²

—

C₄²

C₂²×D₇₉

yes

characteristic

Q₈

—

Q₈

—

316

—

Q₈

—

316

—

Q₈

Dic₃₁₆

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₂×C₄

#11929624

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

316

—

102

C₈

#11929611

yes

—

103

C₂²

#14579135

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

632

—

108

C₄

C₂×#11929611

yes

characteristic

109

C₄

C₂×Dic₃₁₆

yes

characteristic

110

C₄

#14579183

yes

characteristic

111

C₄

#14579186

yes

characteristic

112

C₂

#19098763

yes

characteristic

113

C₂

#19098804

yes

characteristic

114

C₂

#19098838

yes

characteristic

	subgroup	G/H
center	C₂²	#14579135
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	C₈×Q₈×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#121
hypercenter	C₈×Q₈	D₇₉
hypocenter	C₇₉	#1670
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

subgroup

G/H

center

C₂²

#14579135

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

C₈×Q₈×C₇₉

C₂

socle, prime radical

C₂²×C₇₉

#121

hypercenter

C₈×Q₈

D₇₉

hypocenter

C₇₉

#1670

LCS

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

N	H ≅ G/N	type
32. Q₈×C₇₉	Q₁₆	semidirect
58. C₇₉	#1670	semidirect
92. Q₈	Dic₃₁₆	semidirect

H ≅ G/N

type

32. Q₈×C₇₉

Q₁₆

semidirect

58. C₇₉

#1670

semidirect

92. Q₈

Dic₃₁₆

semidirect

Subgroups — #23762770

Conjugacy classes of subgroups

Complements