Group #23764576 — subgroups

Subgroups — #23764576

Order 10112.

278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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×#14579075	C₂	1	3	yes	maximal
2	#19098329	C₂	1	3	yes	maximal, complemented
3	#543×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
5	C₂×C₂²⋊Dic₇₉	C₂²	1	3	yes	—
6	#14579075	—	2	6	no	—
7	C₂²⋊Q₈×C₇₉	—	2	6	no	—
8	C₂×C₂²⋊C₄×C₇₉	C₂²	1	3	yes	—
9	C₂³×D₇₉	Q₈	1	1	yes	characteristic, complemented
10	C₂×C₂²⋊D₇₉	—	2	3	no	—
11	C₂×C₂²⋊D₇₉	—	2	3	no	—
12	C₂²×Dic₇₉	—	2	3	no	—
13	C₂²×Dic₇₉	Q₈	1	1	yes	characteristic, complemented
14	C₂²⋊Dic₇₉	—	2	3	no	—
15	C₂²⋊Dic₇₉	—	2	3	no	—
16	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
17	C₂×Q₈×C₇₉	—	2	2	no	—
18	C₂²×C₄×C₇₉	—	2	3	no	—
19	C₄⋊C₄×C₇₉	—	2	6	no	—
20	C₂²⋊C₄×C₇₉	—	2	3	no	—
21	C₂²⋊C₄×C₇₉	D₄	1	6	yes	—
22	C₂³×C₇₉	—	8	1	no	—
23	C₂³×C₇₉	C₂×D₄	1	3	yes	—
24	C₂³×C₇₉	C₂×Q₈	1	1	yes	characteristic
25	C₂³×C₇₉	#41	1	3	yes	—
26	C₂²×D₇₉	—	2	3	no	—
27	C₂²×D₇₉	—	8	1	no	—
28	Q₈×C₇₉	—	8	2	no	—
29	C₂×C₄×C₇₉	—	2	6	no	—
30	C₂×C₄×C₇₉	—	8	3	no	—
31	C₂²⋊D₇₉	—	4	1	no	—
32	C₂²⋊D₇₉	—	4	3	no	—
33	C₂×Dic₇₉	—	2	3	no	—
34	C₂×Dic₇₉	—	4	3	no	—
35	C₂×Dic₇₉	—	8	3	no	—
36	C₂²×C₇₉	—	4	3	no	—
37	C₂²×C₇₉	—	4	1	no	—
38	C₂²×C₇₉	—	4	3	no	—
39	C₂²×C₇₉	#120	1	1	yes	characteristic
40	C₂²×C₇₉	C₂²⋊Q₈	1	3	yes	—
41	C₂²×C₇₉	#124	1	3	yes	—
42	C₂×D₇₉	—	4	1	no	—
43	C₂×D₇₉	—	8	3	no	—
44	C₄×C₇₉	—	4	6	no	—
45	Dic₇₉	—	4	1	no	—
46	Dic₇₉	—	8	3	no	—
47	C₂×C₇₉	—	2	3	no	—
48	C₂×C₇₉	—	2	1	no	—
49	C₂×C₇₉	—	2	3	no	—
50	C₂×C₇₉	#393	1	1	yes	characteristic
51	D₇₉	—	8	1	no	—
52	#2032	—	79	1	no	maximal, Sylow
53	C₇₉	#2032	1	1	yes	characteristic, complemented, Sylow
54	#543	D₇₉	1	1	yes	characteristic, complemented
55	C₂×#99	—	79	3	no	—
56	#342	—	79	3	no	—
57	C₂²×D₄	—	79	1	no	—
58	C₂²⋊Q₈	—	2	6	no	—
59	C₂×C₂²⋊C₄	—	79	3	no	—
60	C₂×C₂²⋊C₄	C₂×D₇₉	1	3	yes	—
61	#99	—	158	6	no	—
62	C₂⁴	—	79	1	no	—
63	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
64	C₂×Q₈	—	2	2	no	—
65	C₂×D₄	—	158	3	no	—
66	C₂×D₄	—	158	3	no	—
67	C₂²×C₄	—	2	3	no	—
68	C₂²×C₄	—	79	1	no	—
69	C₂²×C₄	—	158	3	no	—
70	C₄⋊C₄	—	2	6	no	—
71	C₂²⋊C₄	—	2	3	no	—
72	C₂²⋊C₄	—	158	3	no	—
73	C₂²⋊C₄	—	158	3	no	—
74	C₂²⋊C₄	C₂²⋊D₇₉	1	6	yes	—
75	C₂³	—	8	1	no	—
76	C₂³	—	632	1	no	—
77	C₂³	—	158	3	no	—
78	C₂³	C₂×C₂²⋊D₇₉	1	3	yes	—
79	C₂³	Q₈×D₇₉	1	1	yes	characteristic
80	C₂³	#11929625	1	3	yes	—
81	Q₈	—	8	2	no	—
82	D₄	—	316	1	no	—
83	D₄	—	316	3	no	—
84	C₂×C₄	—	2	6	no	—
85	C₂×C₄	—	8	3	no	—
86	C₂×C₄	—	316	3	no	—
87	C₂×C₄	—	632	3	no	—
88	C₂×C₄	—	158	3	no	—
89	C₂²	—	4	3	no	—
90	C₂²	—	4	3	no	—
91	C₂²	—	4	1	no	—
92	C₂²	—	316	1	no	—
93	C₂²	—	632	3	no	—
94	C₂²	#14579130	1	1	yes	characteristic
95	C₂²	#14579137	1	3	yes	—
96	C₂²	#14579150	1	3	yes	—
97	C₄	—	4	6	no	—
98	C₄	—	316	1	no	—
99	C₄	—	632	3	no	—
100	C₂	—	2	1	no	—
101	C₂	—	2	3	no	—
102	C₂	—	2	3	no	—
103	C₂	—	632	1	no	—
104	C₂	#19098474	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579075

C₂

yes

maximal

#19098329

C₂

yes

maximal, complemented

#543×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₇₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₇₉

C₂²

yes

—

#14579075

—

C₂²⋊Q₈×C₇₉

—

C₂×C₂²⋊C₄×C₇₉

C₂²

yes

—

C₂³×D₇₉

Q₈

yes

characteristic, complemented

C₂×C₂²⋊D₇₉

—

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

Q₈

yes

characteristic, complemented

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂⁴×C₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

D₄

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

C₂×Q₈

yes

characteristic

C₂³×C₇₉

#41

yes

—

C₂²×D₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂²⋊D₇₉

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#120

yes

characteristic

C₂²×C₇₉

C₂²⋊Q₈

yes

—

C₂²×C₇₉

#124

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#393

yes

characteristic

D₇₉

—

#2032

—

maximal, Sylow

C₇₉

#2032

yes

characteristic, complemented, Sylow

#543

D₇₉

yes

characteristic, complemented

C₂×#99

—

#342

—

C₂²×D₄

—

C₂²⋊Q₈

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₇₉

yes

—

#99

—

158

—

C₂⁴

—

C₂⁴

C₂²×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

158

—

C₂²⋊C₄

—

158

—

C₂²⋊C₄

C₂²⋊D₇₉

yes

—

C₂³

—

C₂³

—

632

—

C₂³

—

158

—

C₂³

C₂×C₂²⋊D₇₉

yes

—

C₂³

Q₈×D₇₉

yes

characteristic

C₂³

#11929625

yes

—

Q₈

—

D₄

—

316

—

D₄

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

632

—

C₂×C₄

—

158

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

316

—

C₂²

—

632

—

C₂²

#14579130

yes

characteristic

C₂²

#14579137

yes

—

C₂²

#14579150

yes

—

C₄

—

C₄

—

316

—

C₄

—

632

—

100

C₂

—

101

C₂

—

102

C₂

—

103

C₂

—

632

—

104

C₂

#19098474

yes

characteristic

	subgroup	G/H
center	C₂	#19098474
commutator, cosocle	C₂⁴×C₇₉	C₂³
Frattini	C₂⁴	C₂²×D₇₉
Fitting	#543×C₇₉	C₂
socle	C₂×C₇₉	#393
prime radical	C₂²×C₂²⋊D₇₉	C₂²
hypercenter	#543	D₇₉
hypocenter	C₇₉	#2032
LCS	G ▷ C₂⁴×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #543

subgroup

G/H

center

C₂

#19098474

commutator, cosocle

C₂⁴×C₇₉

C₂³

Frattini

C₂⁴

C₂²×D₇₉

Fitting

#543×C₇₉

C₂

socle

C₂×C₇₉

#393

prime radical

C₂²×C₂²⋊D₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂⁴×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂⁴ ◁ #543

N	H ≅ G/N	type
2. #19098329	C₂	semidirect
3. #543×C₇₉	C₂	semidirect
9. C₂³×D₇₉	Q₈	semidirect
13. C₂²×Dic₇₉	Q₈	semidirect
53. C₇₉	#2032	semidirect
54. #543	D₇₉	semidirect

H ≅ G/N

type

2. #19098329

C₂

semidirect

3. #543×C₇₉

C₂

semidirect

9. C₂³×D₇₉

Q₈

semidirect

13. C₂²×Dic₇₉

Q₈

semidirect

53. C₇₉

#2032

semidirect

54. #543

D₇₉

semidirect

Subgroups — #23764576

Conjugacy classes of subgroups

Complements