Group #23765649 — subgroups

Subgroups — #23765649

Order 10112.

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

normal subgroups only

This group has 216 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	C₂×#14579102	C₂	1	4	yes	maximal, complemented
2	#19098940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#493×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₆₃₂	—	2	1	no	—
6	C₂×D₆₃₂	C₂²	1	2	yes	—
7	#14579158	—	2	1	no	—
8	#14579102	—	2	8	no	—
9	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
10	C₂×D₈×C₇₉	—	2	1	no	—
11	C₂×D₈×C₇₉	C₂²	1	2	yes	—
12	#127×C₇₉	—	2	1	no	—
13	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×D₃₁₆	—	2	2	no	—
15	C₂×D₃₁₆	—	4	2	no	—
16	D₆₃₂	—	2	4	no	—
17	D₆₃₂	—	4	2	no	—
18	C₇₉⋊C₁₆	D₄	1	4	yes	complemented
19	C₂×D₄×C₇₉	—	2	2	no	—
20	C₂×D₄×C₇₉	—	4	2	no	—
21	D₈×C₇₉	—	2	4	no	—
22	D₈×C₇₉	—	4	2	no	—
23	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
25	C₄²×C₇₉	D₄	1	1	yes	characteristic
26	C₂³×C₇₉	—	4	2	no	—
27	C₂²×D₇₉	—	4	2	no	—
28	D₄×C₇₉	—	4	2	no	—
29	D₄×C₇₉	—	4	2	no	—
30	D₄×C₇₉	—	8	4	no	—
31	C₂×C₄×C₇₉	D₈	1	2	yes	—
32	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
33	D₃₁₆	—	4	2	no	—
34	D₃₁₆	—	4	2	no	—
35	D₃₁₆	—	8	4	no	—
36	C₈×C₇₉	D₈	1	2	yes	—
37	C₈×C₇₉	C₂×D₄	1	2	yes	—
38	C₂²×C₇₉	—	8	2	no	—
39	C₂²×C₇₉	—	8	4	no	—
40	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
41	C₂×D₇₉	—	8	2	no	—
42	C₂×D₇₉	—	8	4	no	—
43	C₄×C₇₉	D₁₆	1	4	yes	complemented
44	C₄×C₇₉	#127	1	1	yes	characteristic
45	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
46	C₂×C₇₉	—	16	2	no	—
47	C₂×C₇₉	#493	1	1	yes	characteristic
48	C₂×C₇₉	C₂×D₁₆	1	2	yes	—
49	D₇₉	—	16	2	no	—
50	#2246	—	79	1	no	maximal, Sylow
51	C₇₉	#2246	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₁₆	—	79	4	no	—
53	#493	—	79	1	no	—
54	#493	D₇₉	1	1	yes	characteristic, complemented
55	C₄×C₁₆	—	79	1	no	—
56	C₂×D₈	—	2	1	no	—
57	C₂×D₈	—	79	2	no	—
58	C₂×D₈	—	158	1	no	—
59	C₂×D₈	C₂×D₇₉	1	2	yes	—
60	#127	—	2	1	no	—
61	#127	—	158	1	no	—
62	D₁₆	—	158	8	no	—
63	C₂×C₁₆	—	79	2	no	—
64	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
65	C₂×D₄	—	2	2	no	—
66	C₂×D₄	—	4	2	no	—
67	C₂×D₄	—	316	2	no	—
68	C₂×D₄	—	158	2	no	—
69	D₈	—	2	4	no	—
70	D₈	—	4	2	no	—
71	D₈	—	316	2	no	—
72	D₈	—	158	4	no	—
73	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
75	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
76	C₁₆	—	79	4	no	—
77	C₂³	—	4	2	no	—
78	C₂³	—	316	2	no	—
79	D₄	—	4	2	no	—
80	D₄	—	4	2	no	—
81	D₄	—	8	4	no	—
82	D₄	—	316	2	no	—
83	D₄	—	316	2	no	—
84	D₄	—	632	4	no	—
85	C₂×C₄	#11929609	1	2	yes	—
86	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
87	C₈	#11929609	1	2	yes	—
88	C₈	D₄×D₇₉	1	2	yes	—
89	C₂²	—	8	2	no	—
90	C₂²	—	8	4	no	—
91	C₂²	—	632	2	no	—
92	C₂²	—	632	4	no	—
93	C₂²	C₂×#11929609	1	1	yes	characteristic
94	C₄	#14579102	1	4	yes	complemented
95	C₄	#14579157	1	1	yes	characteristic
96	C₄	C₂×#11929609	1	1	yes	characteristic
97	C₂	—	16	2	no	—
98	C₂	—	1264	2	no	—
99	C₂	#19098939	1	1	yes	characteristic
100	C₂	C₂×#14579102	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579102

C₂

yes

maximal, complemented

#19098940

C₂

yes

maximal, characteristic, complemented

C₄×C₇₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#493×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×D₆₃₂

—

C₂×D₆₃₂

C₂²

yes

—

#14579158

—

#14579102

—

C₂×C₇₉⋊C₁₆

C₂²

yes

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

C₂²

yes

—

#127×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×D₃₁₆

—

C₂×D₃₁₆

—

D₆₃₂

—

D₆₃₂

—

C₇₉⋊C₁₆

D₄

yes

complemented

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

D₈

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₈×C₇₉

D₈

yes

—

C₈×C₇₉

C₂×D₄

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

D₁₆

yes

complemented

C₄×C₇₉

#127

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

C₂×C₇₉

—

C₂×C₇₉

#493

yes

characteristic

C₂×C₇₉

C₂×D₁₆

yes

—

D₇₉

—

#2246

—

maximal, Sylow

C₇₉

#2246

yes

characteristic, complemented, Sylow

C₂×D₁₆

—

#493

—

#493

D₇₉

yes

characteristic, complemented

C₄×C₁₆

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

158

—

C₂×D₈

C₂×D₇₉

yes

—

#127

—

#127

—

158

—

D₁₆

—

158

—

C₂×C₁₆

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

316

—

C₂×D₄

—

158

—

D₈

—

D₈

—

D₈

—

316

—

D₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄²

C₂²⋊D₇₉

yes

characteristic

C₁₆

—

C₂³

—

C₂³

—

316

—

D₄

—

D₄

—

D₄

—

D₄

—

316

—

D₄

—

316

—

D₄

—

632

—

C₂×C₄

#11929609

yes

—

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₈

#11929609

yes

—

C₈

D₄×D₇₉

yes

—

C₂²

—

C₂²

—

C₂²

—

632

—

C₂²

—

632

—

C₂²

yes

C₄

yes

C₄

yes

C₄

yes

C₂

—

C₂

—

1264

—

C₂

#19098939

yes

characteristic

100

C₂

C₂×#14579102

yes

—

	subgroup	G/H
center	C₂²	C₂×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#493×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
hypercenter	#493	D₇₉
hypocenter	C₇₉	#2246
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂²

C₂×#11929609

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#493×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
1. C₂×#14579102	C₂	semidirect
2. #19098940	C₂	semidirect
3. C₄×C₇₉⋊C₁₆	C₂	semidirect
4. #493×C₇₉	C₂	semidirect
18. C₇₉⋊C₁₆	D₄	semidirect
43. C₄×C₇₉	D₁₆	semidirect
51. C₇₉	#2246	semidirect
54. #493	D₇₉	semidirect
94. C₄	#14579102	semidirect

H ≅ G/N

type

1. C₂×#14579102

C₂

semidirect

2. #19098940

C₂

semidirect

3. C₄×C₇₉⋊C₁₆

C₂

semidirect

4. #493×C₇₉

C₂

semidirect

18. C₇₉⋊C₁₆

D₄

semidirect

43. C₄×C₇₉

D₁₆

semidirect

51. C₇₉

#2246

semidirect

54. #493

D₇₉

semidirect

94. C₄

#14579102

semidirect

Subgroups — #23765649

Conjugacy classes of subgroups

Complements