Group #23763067 — subgroups

Subgroups — #23763067

Order 10112.

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

normal subgroups only

This group has 242 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	#19098939	C₂	1	2	yes	maximal, complemented
2	#19098936	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098909	C₂	1	2	yes	maximal, complemented
4	#19098284	C₂	1	1	yes	maximal, characteristic, complemented
5	#493×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929613	—	2	2	no	—
7	C₂×#11929609	—	2	4	no	—
8	#14579161	C₂²	1	1	yes	characteristic
9	#14579158	C₂²	1	1	yes	characteristic
10	#14579082	—	2	4	no	—
11	C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
12	C₂×D₈×C₇₉	—	2	2	no	—
13	#127×C₇₉	C₂²	1	2	yes	—
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	2	1	no	—
16	C₂×D₃₁₆	—	2	2	no	—
17	C₂×D₃₁₆	—	2	1	no	—
18	#11929613	—	4	4	no	—
19	#11929609	—	4	8	no	—
20	C₂×C₇₉⋊C₈	D₄	1	4	yes	—
21	C₄⋊Dic₇₉	—	2	2	no	—
22	C₂×D₄×C₇₉	—	2	2	no	—
23	C₂×D₄×C₇₉	—	2	2	no	—
24	C₂×D₄×C₇₉	—	2	2	no	—
25	D₈×C₇₉	—	4	4	no	—
26	C₂×C₈×C₇₉	D₄	1	2	yes	—
27	C₄²×C₇₉	C₂³	1	1	yes	characteristic
28	C₂³×C₇₉	—	4	2	no	—
29	C₂²×D₇₉	—	4	1	no	—
30	D₄×C₇₉	—	4	4	no	—
31	D₄×C₇₉	—	4	4	no	—
32	D₄×C₇₉	—	4	4	no	—
33	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₉	—	4	1	no	—
36	D₃₁₆	—	4	2	no	—
37	D₃₁₆	—	4	4	no	—
38	Dic₁₅₈	—	4	2	no	—
39	C₈×C₇₉	D₈	1	4	yes	complemented
40	C₇₉⋊C₈	—	2	4	no	—
41	C₂²×C₇₉	—	8	2	no	—
42	C₂²×C₇₉	—	8	2	no	—
43	C₂²×C₇₉	—	8	2	no	—
44	C₂²×C₇₉	#127	1	1	yes	characteristic
45	C₂×D₇₉	—	8	1	no	—
46	C₂×D₇₉	—	8	2	no	—
47	C₄×C₇₉	C₂×D₈	1	2	yes	—
48	C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
49	Dic₇₉	—	8	1	no	—
50	C₂×C₇₉	—	16	2	no	—
51	C₂×C₇₉	#493	1	1	yes	characteristic
52	C₂×C₇₉	#496	1	2	yes	—
53	D₇₉	—	16	1	no	—
54	#1721	—	79	1	no	maximal, Sylow
55	C₇₉	#1721	1	1	yes	characteristic, complemented, Sylow
56	#493	—	79	2	no	—
57	#493	D₇₉	1	1	yes	characteristic, complemented
58	#492	—	79	1	no	—
59	#486	—	79	2	no	—
60	#322	—	79	1	no	—
61	C₂×SD₁₆	—	158	2	no	—
62	C₂×D₈	—	2	2	no	—
63	C₂×D₈	—	158	4	no	—
64	C₄⋊Q₈	—	79	1	no	—
65	#127	—	79	1	no	—
66	#127	C₂×D₇₉	1	2	yes	—
67	#102	—	158	4	no	—
68	C₄×C₈	—	79	2	no	—
69	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
70	C₂×Q₈	—	158	1	no	—
71	C₂×D₄	—	2	2	no	—
72	C₂×D₄	—	2	2	no	—
73	C₂×D₄	—	2	2	no	—
74	C₂×D₄	—	158	2	no	—
75	C₂×D₄	—	158	1	no	—
76	SD₁₆	—	316	4	no	—
77	D₈	—	4	4	no	—
78	D₈	—	316	8	no	—
79	C₂×C₈	—	79	4	no	—
80	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
81	C₄⋊C₄	—	158	2	no	—
82	C₄²	C₂²×D₇₉	1	1	yes	characteristic
83	C₂³	—	4	2	no	—
84	C₂³	—	316	1	no	—
85	Q₈	—	316	2	no	—
86	D₄	—	4	4	no	—
87	D₄	—	4	4	no	—
88	D₄	—	4	4	no	—
89	D₄	—	316	2	no	—
90	D₄	—	316	4	no	—
91	C₂×C₄	—	316	1	no	—
92	C₂×C₄	D₄×D₇₉	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
94	C₈	—	158	4	no	—
95	C₈	#11929609	1	4	yes	complemented
96	C₂²	—	8	2	no	—
97	C₂²	—	8	2	no	—
98	C₂²	—	8	2	no	—
99	C₂²	—	632	1	no	—
100	C₂²	—	632	2	no	—
101	C₂²	#14579157	1	1	yes	characteristic
102	C₄	—	632	1	no	—
103	C₄	C₂×#11929609	1	2	yes	—
104	C₄	#14579185	1	4	yes	—
105	C₂	—	16	2	no	—
106	C₂	—	1264	1	no	—
107	C₂	#19098939	1	1	yes	characteristic
108	C₂	#19098951	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098939

C₂

yes

maximal, complemented

#19098936

C₂

yes

maximal, characteristic, complemented

#19098909

C₂

yes

maximal, complemented

#19098284

C₂

yes

maximal, characteristic, complemented

#493×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929613

—

C₂×#11929609

—

#14579161

C₂²

yes

characteristic

#14579158

C₂²

yes

characteristic

#14579082

—

C₄×C₇₉⋊C₈

C₂²

yes

—

C₂×D₈×C₇₉

—

#127×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

#11929613

—

#11929609

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₄⋊Dic₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

Dic₁₅₈

—

C₈×C₇₉

D₈

yes

complemented

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#127

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

C₂×D₈

yes

—

C₄×C₇₉

AGL(1,ℤ/8)

yes

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#493

yes

characteristic

C₂×C₇₉

#496

yes

—

D₇₉

—

#1721

—

maximal, Sylow

C₇₉

#1721

yes

characteristic, complemented, Sylow

#493

—

#493

D₇₉

yes

characteristic, complemented

#492

—

#486

—

#322

—

C₂×SD₁₆

—

158

—

C₂×D₈

—

C₂×D₈

—

158

—

C₄⋊Q₈

—

#127

—

#127

C₂×D₇₉

yes

—

#102

—

158

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

SD₁₆

—

316

—

D₈

—

D₈

—

316

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₉

yes

—

C₄⋊C₄

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

C₂³

—

316

—

Q₈

—

316

—

D₄

—

D₄

—

D₄

—

D₄

—

316

—

D₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

D₄×D₇₉

yes

—

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₈

—

158

—

C₈

#11929609

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

632

—

100

C₂²

—

632

—

101

C₂²

#14579157

yes

characteristic

102

C₄

—

632

—

103

C₄

C₂×#11929609

yes

—

104

C₄

#14579185

yes

—

105

C₂

—

106

C₂

—

1264

—

107

C₂

#19098939

yes

characteristic

108

C₂

#19098951

yes

—

	subgroup	G/H
center	C₂²	#14579157
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#493×C₇₉	C₂
socle	C₂²×C₇₉	#127
hypercenter	#493	D₇₉
hypocenter	C₇₉	#1721
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#14579157

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#493×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #19098939	C₂	semidirect
2. #19098936	C₂	semidirect
3. #19098909	C₂	semidirect
4. #19098284	C₂	semidirect
5. #493×C₇₉	C₂	semidirect
39. C₈×C₇₉	D₈	semidirect
55. C₇₉	#1721	semidirect
57. #493	D₇₉	semidirect
95. C₈	#11929609	semidirect

H ≅ G/N

type

1. #19098939

C₂

semidirect

2. #19098936

C₂

semidirect

3. #19098909

C₂

semidirect

4. #19098284

C₂

semidirect

5. #493×C₇₉

C₂

semidirect

39. C₈×C₇₉

D₈

semidirect

55. C₇₉

#1721

semidirect

57. #493

D₇₉

semidirect

95. C₈

#11929609

semidirect

Subgroups — #23763067

Conjugacy classes of subgroups

Complements