Group #23762309 — subgroups

Subgroups — #23762309

Order 10112.

148 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 71 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	#19098694	C₂	1	2	yes	maximal
2	#19098314	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊(C₇₉⋊C₈)	C₂	1	2	yes	maximal
4	#19098284	C₂	1	1	yes	maximal, characteristic
5	C₄×Q₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
7	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
8	#14579072	—	2	2	no	—
9	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×Q₁₆×C₇₉	C₄	1	1	yes	characteristic
12	C₄×Q₈×C₇₉	C₂²	1	2	yes	—
13	#107×C₇₉	C₄	1	1	yes	characteristic
14	#103×C₇₉	C₄	1	2	yes	—
15	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₇₉⋊C₈	—	2	2	no	—
17	C₂×C₇₉⋊C₈	—	2	1	no	—
18	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
19	C₂×Q₈×C₇₉	C₂×C₄	1	2	yes	—
20	Q₁₆×C₇₉	—	2	2	no	—
21	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₄⋊C₄×C₇₉	—	2	2	no	—
24	C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
25	C₄²×C₇₉	—	2	2	no	—
26	C₄²×C₇₉	C₂³	1	1	yes	characteristic
27	Q₈×C₇₉	—	2	2	no	—
28	Q₈×C₇₉	—	2	2	no	—
29	C₂×C₄×C₇₉	—	2	2	no	—
30	C₂×C₄×C₇₉	—	2	2	no	—
31	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
34	C₈×C₇₉	—	2	1	no	—
35	C₈×C₇₉	M₁₆	1	2	yes	—
36	C₇₉⋊C₈	—	2	2	no	—
37	C₇₉⋊C₈	—	4	1	no	—
38	C₇₉⋊C₈	—	4	2	no	—
39	C₂²×C₇₉	C₄×D₄	1	1	yes	characteristic
40	C₄×C₇₉	—	2	1	no	—
41	C₄×C₇₉	—	4	2	no	—
42	C₄×C₇₉	—	4	2	no	—
43	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₇₉	#131	1	1	yes	characteristic
45	C₄×C₇₉	#137	1	2	yes	—
46	C₂×C₇₉	#436	1	1	yes	characteristic
47	C₂×C₇₉	#441	1	1	yes	characteristic
48	C₂×C₇₉	#444	1	1	yes	characteristic
49	#1593	—	79	1	no	maximal, Sylow
50	C₇₉	#1593	1	1	yes	characteristic, complemented, Sylow
51	#446	—	79	2	no	—
52	C₄×Q₁₆	D₇₉	1	1	yes	characteristic
53	#334	—	79	1	no	—
54	Q₈⋊C₈	—	79	2	no	—
55	#322	—	79	1	no	—
56	C₂×Q₁₆	Dic₇₉	1	1	yes	characteristic
57	C₄×Q₈	C₂×D₇₉	1	2	yes	—
58	#107	Dic₇₉	1	1	yes	characteristic
59	C₄⋊C₈	—	79	2	no	—
60	C₄⋊C₈	—	158	2	no	—
61	#103	Dic₇₉	1	2	yes	—
62	#97	—	158	2	no	—
63	C₄×C₈	—	79	1	no	—
64	C₄×C₈	—	79	1	no	—
65	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
66	C₂×Q₈	C₂×Dic₇₉	1	2	yes	—
67	Q₁₆	—	2	2	no	—
68	C₂×C₈	—	79	2	no	—
69	C₂×C₈	—	158	2	no	—
70	C₂×C₈	—	158	1	no	—
71	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
72	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
75	C₄²	—	2	2	no	—
76	C₄²	C₂²×D₇₉	1	1	yes	characteristic
77	Q₈	—	2	2	no	—
78	Q₈	—	2	2	no	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
82	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
83	C₂×C₄	#11929623	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	316	1	no	—
86	C₈	—	316	2	no	—
87	C₈	—	158	2	no	—
88	C₈	#11929608	1	2	yes	—
89	C₂²	D₄×Dic₇₉	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	4	2	no	—
92	C₄	—	4	2	no	—
93	C₄	C₂×#11929608	1	1	yes	characteristic
94	C₄	#14579168	1	1	yes	characteristic
95	C₄	#14579193	1	2	yes	—
96	C₂	#19098641	1	1	yes	characteristic
97	C₂	#19098670	1	1	yes	characteristic
98	C₂	#19098685	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098694

C₂

yes

maximal

#19098314

C₂

yes

maximal, characteristic

Q₈⋊(C₇₉⋊C₈)

C₂

yes

maximal

#19098284

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₇₉

C₂

yes

maximal, characteristic

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579072

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×Q₁₆×C₇₉

C₄

yes

characteristic

C₄×Q₈×C₇₉

C₂²

yes

—

#107×C₇₉

C₄

yes

characteristic

#103×C₇₉

C₄

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₂×Q₈×C₇₉

C₂×C₄

yes

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

M₁₆

yes

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×M₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#446

—

C₄×Q₁₆

D₇₉

yes

characteristic

#334

—

Q₈⋊C₈

—

#322

—

C₂×Q₁₆

Dic₇₉

yes

characteristic

C₄×Q₈

C₂×D₇₉

yes

—

#107

Dic₇₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

158

—

#103

Dic₇₉

yes

—

#97

—

158

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

C₂×Dic₇₉

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₇₉

yes

—

C₄²

—

C₄²

C₂²×D₇₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₇₉

yes

characteristic

C₂×C₄

D₄×D₇₉

yes

characteristic

C₂×C₄

#11929623

yes

characteristic

C₈

—

C₈

—

316

—

C₈

—

316

—

C₈

—

158

—

C₈

#11929608

yes

—

C₂²

D₄×Dic₇₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₄

yes

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₄²	C₂²×D₇₉
Fitting	C₄×Q₁₆×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₄×D₄
cosocle	C₄²×C₇₉	C₂³
hypercenter	C₄×Q₁₆	D₇₉
hypocenter	C₇₉	#1593
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

subgroup

G/H

center

C₂×C₄

D₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₄²

C₂²×D₇₉

Fitting

C₄×Q₁₆×C₇₉

C₂

socle, prime radical

C₂²×C₇₉

C₄×D₄

cosocle

C₄²×C₇₉

C₂³

hypercenter

C₄×Q₁₆

D₇₉

hypocenter

C₇₉

#1593

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

N	H ≅ G/N	type
50. C₇₉	#1593	semidirect

H ≅ G/N

type

50. C₇₉

#1593

semidirect

Subgroups — #23762309

Conjugacy classes of subgroups

Complements