Group #23763028 — subgroups

Subgroups — #23763028

Order 10112.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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	#19098961	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098940	C₂	1	1	yes	maximal, characteristic
3	#19098936	C₂	1	2	yes	maximal, complemented
4	#19098910	C₂	1	2	yes	maximal, complemented
5	#322×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929613	—	2	4	no	—
7	C₂×D₆₃₂	—	2	2	no	—
8	#14579161	C₂²	1	2	yes	—
9	#14579158	C₂²	1	1	yes	characteristic
10	#14579158	C₂²	1	1	yes	characteristic
11	#14579093	—	2	2	no	—
12	#14579083	—	2	4	no	—
13	C₄×C₈×C₇₉	C₂²	1	2	yes	—
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	2	2	no	—
16	C₂×D₃₁₆	—	2	2	no	—
17	C₂×D₃₁₆	—	2	1	no	—
18	C₂×D₃₁₆	—	2	1	no	—
19	C₂×D₃₁₆	—	2	2	no	—
20	#11929613	—	4	8	no	—
21	D₆₃₂	—	4	4	no	—
22	C₄⋊Dic₇₉	—	2	2	no	—
23	C₄⋊Dic₇₉	—	2	2	no	—
24	C₂×C₈×C₇₉	D₄	1	4	yes	—
25	C₂×C₈×C₇₉	D₄	1	2	yes	—
26	C₄²×C₇₉	C₂³	1	1	yes	characteristic
27	C₂²×D₇₉	—	4	1	no	—
28	C₂²×D₇₉	—	4	1	no	—
29	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
31	C₂×Dic₇₉	—	4	2	no	—
32	D₃₁₆	—	4	2	no	—
33	D₃₁₆	—	4	2	no	—
34	D₃₁₆	—	4	4	no	—
35	D₃₁₆	—	4	4	no	—
36	Dic₁₅₈	—	4	4	no	—
37	C₈×C₇₉	—	2	4	no	—
38	C₈×C₇₉	SD₁₆	1	4	yes	complemented
39	C₂²×C₇₉	#127	1	1	yes	characteristic
40	C₂×D₇₉	—	8	1	no	—
41	C₂×D₇₉	—	8	1	no	—
42	C₂×D₇₉	—	8	2	no	—
43	C₂×D₇₉	—	8	2	no	—
44	C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
45	C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
46	Dic₇₉	—	8	2	no	—
47	C₂×C₇₉	#492	1	1	yes	characteristic
48	C₂×C₇₉	#496	1	2	yes	—
49	D₇₉	—	16	1	no	—
50	D₇₉	—	16	1	no	—
51	#1715	—	79	1	no	maximal, Sylow
52	C₇₉	#1715	1	1	yes	characteristic, complemented, Sylow
53	#498	—	79	1	no	—
54	#493	—	79	1	no	—
55	#492	—	79	2	no	—
56	#486	—	79	2	no	—
57	#322	D₇₉	1	1	yes	characteristic, complemented
58	C₂×SD₁₆	—	158	4	no	—
59	C₂×D₈	—	158	2	no	—
60	C₄⋊Q₈	—	79	2	no	—
61	#127	—	79	1	no	—
62	#127	—	79	1	no	—
63	#106	—	158	2	no	—
64	#102	—	158	4	no	—
65	C₄×C₈	C₂×D₇₉	1	2	yes	—
66	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
67	C₂×Q₈	—	158	2	no	—
68	C₂×D₄	—	158	2	no	—
69	C₂×D₄	—	158	1	no	—
70	C₂×D₄	—	158	1	no	—
71	C₂×D₄	—	158	2	no	—
72	SD₁₆	—	316	8	no	—
73	D₈	—	316	4	no	—
74	C₂×C₈	D₃₁₆	1	4	yes	—
75	C₂×C₈	D₃₁₆	1	2	yes	—
76	C₄⋊C₄	—	158	2	no	—
77	C₄⋊C₄	—	158	2	no	—
78	C₄²	C₂²×D₇₉	1	1	yes	characteristic
79	C₂³	—	316	1	no	—
80	C₂³	—	316	1	no	—
81	Q₈	—	316	4	no	—
82	D₄	—	316	2	no	—
83	D₄	—	316	2	no	—
84	D₄	—	316	4	no	—
85	D₄	—	316	4	no	—
86	C₂×C₄	—	316	2	no	—
87	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
88	C₂×C₄	C₂×D₃₁₆	1	2	yes	—
89	C₈	—	2	4	no	—
90	C₈	#11929613	1	4	yes	complemented
91	C₂²	—	632	1	no	—
92	C₂²	—	632	1	no	—
93	C₂²	—	632	2	no	—
94	C₂²	—	632	2	no	—
95	C₂²	#14579158	1	1	yes	characteristic
96	C₄	—	632	2	no	—
97	C₄	C₂×#11929613	1	2	yes	—
98	C₄	#14579189	1	4	yes	—
99	C₂	—	1264	1	no	—
100	C₂	—	1264	1	no	—
101	C₂	#19098936	1	1	yes	characteristic
102	C₂	#19098952	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098961

C₂

yes

maximal, characteristic, complemented

#19098940

C₂

yes

maximal, characteristic

#19098936

C₂

yes

maximal, complemented

#19098910

C₂

yes

maximal, complemented

#322×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929613

—

C₂×D₆₃₂

—

#14579161

C₂²

yes

—

#14579158

C₂²

yes

characteristic

#14579158

C₂²

yes

characteristic

#14579093

—

#14579083

—

C₄×C₈×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

#11929613

—

D₆₃₂

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₂×C₈×C₇₉

D₄

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

SD₁₆

yes

complemented

C₂²×C₇₉

#127

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

C₂×SD₁₆

yes

—

C₄×C₇₉

AGL(1,ℤ/8)

yes

—

Dic₇₉

—

C₂×C₇₉

#492

yes

characteristic

C₂×C₇₉

#496

yes

—

D₇₉

—

D₇₉

—

#1715

—

maximal, Sylow

C₇₉

#1715

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic, complemented

C₂×SD₁₆

—

158

—

C₂×D₈

—

158

—

C₄⋊Q₈

—

#127

—

#127

—

#106

—

158

—

#102

—

158

—

C₄×C₈

C₂×D₇₉

yes

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

SD₁₆

—

316

—

D₈

—

316

—

C₂×C₈

D₃₁₆

yes

—

C₂×C₈

D₃₁₆

yes

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

316

—

C₂³

—

316

—

Q₈

—

316

—

D₄

—

316

—

D₄

—

316

—

D₄

—

316

—

D₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

—

C₈

—

C₈

#11929613

yes

complemented

C₂²

—

632

—

C₂²

—

632

—

C₂²

—

632

—

C₂²

—

632

—

C₂²

#14579158

yes

characteristic

C₄

—

632

—

C₄

C₂×#11929613

yes

—

C₄

#14579189

yes

—

C₂

—

1264

—

100

C₂

—

1264

—

101

C₂

#19098936

yes

characteristic

102

C₂

#19098952

yes

—

	subgroup	G/H
center	C₂²	#14579158
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#322×C₇₉	C₂
socle	C₂²×C₇₉	#127
prime radical	#19098940	C₂
hypercenter	#322	D₇₉
hypocenter	C₇₉	#1715
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#14579158

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#322×C₇₉

C₂

C₂²×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
1. #19098961	C₂	semidirect
3. #19098936	C₂	semidirect
4. #19098910	C₂	semidirect
5. #322×C₇₉	C₂	semidirect
38. C₈×C₇₉	SD₁₆	semidirect
52. C₇₉	#1715	semidirect
57. #322	D₇₉	semidirect
90. C₈	#11929613	semidirect

H ≅ G/N

type

1. #19098961

C₂

semidirect

3. #19098936

C₂

semidirect

4. #19098910

C₂

semidirect

5. #322×C₇₉

C₂

semidirect

38. C₈×C₇₉

SD₁₆

semidirect

52. C₇₉

#1715

semidirect

57. #322

D₇₉

semidirect

90. C₈

#11929613

semidirect

Subgroups — #23763028

Conjugacy classes of subgroups

Complements