Group #23763528 — subgroups

Subgroups — #23763528

Order 10112.

248 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 141 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	#19098433	C₂	1	2	yes	maximal
2	#19098326	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₇₉	—	2	2	no	—
5	C₂×C₄⋊Dic₇₉	—	2	2	no	—
6	C₂×C₄⋊Dic₇₉	C₂²	1	4	yes	—
7	C₂²×C₈×C₇₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₇₉	C₄	1	4	yes	complemented
10	C₂²×Dic₇₉	—	2	4	no	—
11	C₄⋊Dic₇₉	—	2	8	no	—
12	C₄⋊Dic₇₉	—	4	4	no	—
13	C₄⋊Dic₇₉	—	4	4	no	—
14	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
15	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
17	C₂×C₈×C₇₉	—	2	4	no	—
18	C₂×C₈×C₇₉	C₂×C₄	1	4	yes	—
19	C₄²×C₇₉	C₂×C₄	1	2	yes	—
20	C₄²×C₇₉	Q₈	1	2	yes	—
21	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₇₉	D₈	1	2	yes	—
25	C₂×C₄×C₇₉	SD₁₆	1	4	yes	—
26	C₂×C₄×C₇₉	Q₁₆	1	2	yes	—
27	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₄×C₇₉	#41	1	4	yes	—
30	C₂×Dic₇₉	—	4	4	no	—
31	C₂×Dic₇₉	—	4	4	no	—
32	C₂×Dic₇₉	—	4	4	no	—
33	C₈×C₇₉	—	2	4	no	—
34	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₇₉	#124	1	2	yes	—
36	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
37	C₂²×C₇₉	C₂×SD₁₆	1	2	yes	—
38	C₂²×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
39	C₄×C₇₉	#106	1	4	yes	—
40	C₄×C₇₉	#107	1	4	yes	—
41	C₄×C₇₉	#117	1	2	yes	—
42	C₄×C₇₉	#125	1	2	yes	—
43	Dic₇₉	—	8	4	no	—
44	C₂×C₇₉	#382	1	1	yes	characteristic
45	C₂×C₇₉	C₂×#106	1	1	yes	characteristic
46	C₂×C₇₉	C₂×#107	1	1	yes	characteristic
47	C₂×C₇₉	#486	1	2	yes	—
48	C₂×C₇₉	#487	1	2	yes	—
49	#1834	—	79	1	no	maximal, Sylow
50	C₇₉	#1834	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₄×C₈	D₇₉	1	1	yes	characteristic
52	#384	—	79	2	no	—
53	#340	—	79	4	no	—
54	C₂²×C₈	C₂×D₇₉	1	2	yes	—
55	C₂×C₄⋊C₄	—	79	4	no	—
56	C₂×C₄⋊C₄	—	158	2	no	—
57	C₂×C₄⋊C₄	—	158	2	no	—
58	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
59	C₄×C₈	Dic₇₉	1	4	yes	complemented
60	C₂²×C₄	—	158	4	no	—
61	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
62	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
63	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
64	C₂×C₈	—	2	4	no	—
65	C₂×C₈	C₂×Dic₇₉	1	4	yes	—
66	C₄⋊C₄	—	316	4	no	—
67	C₄⋊C₄	—	316	4	no	—
68	C₄⋊C₄	—	158	8	no	—
69	C₄²	Dic₁₅₈	1	2	yes	—
70	C₄²	C₂×Dic₇₉	1	2	yes	—
71	C₂³	C₂×D₃₁₆	1	1	yes	characteristic
72	C₂×C₄	—	316	4	no	—
73	C₂×C₄	—	316	4	no	—
74	C₂×C₄	—	316	4	no	—
75	C₂×C₄	C₄⋊Dic₇₉	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₇₉	1	2	yes	—
77	C₂×C₄	D₆₃₂	1	2	yes	—
78	C₂×C₄	#11929613	1	4	yes	—
79	C₂×C₄	Dic₃₁₆	1	2	yes	—
80	C₂×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
81	C₂×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
82	C₂×C₄	#11929624	1	4	yes	—
83	C₈	—	2	4	no	—
84	C₂²	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
85	C₂²	#14579149	1	2	yes	—
86	C₂²	C₂×D₆₃₂	1	1	yes	characteristic
87	C₂²	C₂×#11929613	1	2	yes	—
88	C₂²	C₂×Dic₃₁₆	1	1	yes	characteristic
89	C₄	—	632	4	no	—
90	C₄	#14579093	1	4	yes	—
91	C₄	#14579095	1	4	yes	—
92	C₄	#14579120	1	2	yes	—
93	C₄	#14579153	1	2	yes	—
94	C₂	#19098429	1	1	yes	characteristic
95	C₂	C₂×#14579093	1	1	yes	characteristic
96	C₂	C₂×#14579095	1	1	yes	characteristic
97	C₂	#19098910	1	2	yes	—
98	C₂	#19098914	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098433

C₂

yes

maximal

#19098326

C₂

yes

maximal

C₂×C₄×C₈×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₄

yes

complemented

C₂²×Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

Q₈

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

D₈

yes

—

C₂×C₄×C₇₉

SD₁₆

yes

—

C₂×C₄×C₇₉

Q₁₆

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₂²×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₉

#124

yes

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂²×C₇₉

C₂×SD₁₆

yes

—

C₂²×C₇₉

C₂×Q₁₆

yes

characteristic

C₄×C₇₉

#106

yes

—

C₄×C₇₉

#107

yes

—

C₄×C₇₉

#117

yes

—

C₄×C₇₉

#125

yes

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂×C₇₉

#487

yes

—

#1834

—

maximal, Sylow

C₇₉

#1834

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

D₇₉

yes

characteristic

#384

—

#340

—

C₂²×C₈

C₂×D₇₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₄×C₈

Dic₇₉

yes

complemented

C₂²×C₄

—

158

—

C₂²×C₄

D₃₁₆

yes

characteristic

C₂²×C₄

D₃₁₆

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×Dic₇₉

yes

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄²

Dic₁₅₈

yes

—

C₄²

C₂×Dic₇₉

yes

—

C₂³

C₂×D₃₁₆

yes

characteristic

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

C₄⋊Dic₇₉

yes

—

C₂×C₄

C₄⋊Dic₇₉

yes

—

C₂×C₄

D₆₃₂

yes

—

C₂×C₄

#11929613

yes

—

C₂×C₄

Dic₃₁₆

yes

—

C₂×C₄

C₂²×Dic₇₉

yes

characteristic

C₂×C₄

C₂×Dic₁₅₈

yes

characteristic

C₂×C₄

#11929624

yes

—

C₈

—

C₂²

C₂×C₄⋊Dic₇₉

yes

characteristic

C₂²

#14579149

yes

—

C₂²

C₂×D₆₃₂

yes

characteristic

C₂²

C₂×#11929613

yes

—

C₂²

C₂×Dic₃₁₆

yes

characteristic

C₄

—

632

—

C₄

#14579093

yes

—

C₄

#14579095

yes

—

C₄

#14579120

yes

—

C₄

#14579153

yes

—

C₂

yes

C₂

yes

C₂

yes

C₂

yes

—

C₂

#19098914

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×C₄×C₈×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	C₂×C₄×C₈	D₇₉
hypocenter	C₇₉	#1834
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₃₁₆

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×C₄×C₈×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

cosocle

C₂²×C₄×C₇₉

C₂³

hypercenter

C₂×C₄×C₈

D₇₉

hypocenter

C₇₉

#1834

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. C₄×C₈×C₇₉	C₄	semidirect
50. C₇₉	#1834	semidirect
59. C₄×C₈	Dic₇₉	semidirect

H ≅ G/N

type

9. C₄×C₈×C₇₉

C₄

semidirect

50. C₇₉

#1834

semidirect

59. C₄×C₈

Dic₇₉

semidirect

Subgroups — #23763528

Conjugacy classes of subgroups

Complements