Group #23762298 — subgroups

Subgroups — #23762298

Order 10112.

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

normal subgroups only

This group has 152 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	#19098693	C₂	1	2	yes	maximal
2	C₄×Dic₃₁₆	C₂	1	1	yes	maximal, characteristic
3	#19098316	C₂	1	1	yes	maximal, characteristic
4	#19098295	C₂	1	2	yes	maximal
5	C₈²×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	C₄	1	1	yes	characteristic
7	C₄×Dic₁₅₈	C₂²	1	2	yes	—
8	#14579095	C₄	1	1	yes	characteristic
9	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
10	Dic₇₉⋊C₈	—	2	2	no	—
11	#14579086	C₄	1	2	yes	—
12	#14579071	—	2	2	no	—
13	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₅₈	C₂×C₄	1	2	yes	—
17	Dic₃₁₆	—	2	2	no	—
18	C₂×C₇₉⋊C₈	—	2	2	no	—
19	C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
20	Dic₇₉⋊C₄	—	2	2	no	—
21	C₄×Dic₇₉	—	2	2	no	—
22	C₂×C₈×C₇₉	—	2	1	no	—
23	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
27	C₄²×C₇₉	C₂³	1	1	yes	characteristic
28	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
31	C₂×Dic₇₉	—	2	2	no	—
32	C₂×Dic₇₉	—	2	2	no	—
33	Dic₁₅₈	—	2	2	no	—
34	Dic₁₅₈	—	2	2	no	—
35	C₈×C₇₉	—	2	2	no	—
36	C₈×C₇₉	—	2	1	no	—
37	C₈×C₇₉	—	2	1	no	—
38	C₈×C₇₉	M₁₆	1	2	yes	—
39	C₈×C₇₉	Q₁₆	1	2	yes	complemented
40	C₇₉⋊C₈	—	4	2	no	—
41	C₂²×C₇₉	C₄×D₄	1	1	yes	characteristic
42	C₄×C₇₉	—	2	1	no	—
43	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₇₉	#131	1	1	yes	characteristic
45	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₇₉	#135	1	1	yes	characteristic
47	Dic₇₉	—	4	2	no	—
48	Dic₇₉	—	4	2	no	—
49	C₂×C₇₉	#436	1	1	yes	characteristic
50	C₂×C₇₉	C₄×Q₁₆	1	1	yes	characteristic
51	C₂×C₇₉	#443	1	1	yes	characteristic
52	#1591	—	79	1	no	maximal, Sylow
53	C₇₉	#1591	1	1	yes	characteristic, complemented, Sylow
54	#446	—	79	2	no	—
55	C₄×Q₁₆	—	79	1	no	—
56	#335	—	79	1	no	—
57	Q₈⋊C₈	—	79	2	no	—
58	C₈²	D₇₉	1	1	yes	characteristic
59	C₂×Q₁₆	—	79	1	no	—
60	C₄×Q₈	—	79	2	no	—
61	#107	—	79	1	no	—
62	C₄⋊C₈	—	79	2	no	—
63	C₄⋊C₈	—	158	2	no	—
64	#103	—	79	2	no	—
65	#97	—	158	2	no	—
66	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
67	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
68	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
69	C₂×Q₈	—	79	2	no	—
70	Q₁₆	—	158	2	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	158	2	no	—
73	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
74	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
75	C₂×C₈	D₃₁₆	1	1	yes	characteristic
76	C₂×C₈	D₃₁₆	1	1	yes	characteristic
77	C₄⋊C₄	—	79	2	no	—
78	C₄⋊C₄	—	158	2	no	—
79	C₄²	—	158	2	no	—
80	C₄²	C₂²×D₇₉	1	1	yes	characteristic
81	Q₈	—	158	2	no	—
82	Q₈	—	158	2	no	—
83	C₂×C₄	—	158	2	no	—
84	C₂×C₄	—	158	2	no	—
85	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
86	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
87	C₂×C₄	#11929624	1	1	yes	characteristic
88	C₈	—	2	2	no	—
89	C₈	—	2	1	no	—
90	C₈	—	2	1	no	—
91	C₈	—	316	2	no	—
92	C₈	#11929607	1	2	yes	—
93	C₈	Dic₃₁₆	1	2	yes	complemented
94	C₂²	C₄×D₃₁₆	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	316	2	no	—
97	C₄	—	316	2	no	—
98	C₄	C₂×#11929607	1	1	yes	characteristic
99	C₄	#14579167	1	1	yes	characteristic
100	C₄	C₂×Dic₃₁₆	1	1	yes	characteristic
101	C₄	#14579183	1	1	yes	characteristic
102	C₂	#19098642	1	1	yes	characteristic
103	C₂	C₄×Dic₃₁₆	1	1	yes	characteristic
104	C₂	#19098681	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098693

C₂

yes

maximal

C₄×Dic₃₁₆

C₂

yes

maximal, characteristic

#19098316

C₂

yes

maximal, characteristic

#19098295

C₂

yes

maximal

C₈²×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₄

yes

characteristic

C₄×Dic₁₅₈

C₂²

yes

—

#14579095

C₄

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

Dic₇₉⋊C₈

—

#14579086

C₄

yes

—

#14579071

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

C₂×C₄

yes

—

Dic₃₁₆

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

C₂×C₄

yes

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

M₁₆

yes

—

C₈×C₇₉

Q₁₆

yes

complemented

C₇₉⋊C₈

—

C₂²×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₂×M₁₆

yes

characteristic

C₄×C₇₉

#131

yes

characteristic

C₄×C₇₉

C₂×Q₁₆

yes

characteristic

C₄×C₇₉

#135

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#436

yes

characteristic

C₂×C₇₉

C₄×Q₁₆

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#446

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

D₇₉

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

158

—

#103

—

#97

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

Q₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

Q₈

—

158

—

Q₈

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₂×C₄

#11929624

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

316

—

C₈

#11929607

yes

—

C₈

Dic₃₁₆

yes

complemented

C₂²

C₄×D₃₁₆

yes

characteristic

C₄

—

C₄

—

316

—

C₄

—

316

—

C₄

yes

C₄

yes

100

C₄

C₂×Dic₃₁₆

yes

characteristic

101

C₄

#14579183

yes

characteristic

102

C₂

#19098642

yes

characteristic

103

C₂

C₄×Dic₃₁₆

yes

characteristic

104

C₂

#19098681

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₄²	C₂²×D₇₉
Fitting	C₈²×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₄×D₄
cosocle	C₄²×C₇₉	C₂³
hypercenter	C₈²	D₇₉
hypocenter	C₇₉	#1591
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈²

subgroup

G/H

center

C₂×C₄

C₂×D₃₁₆

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₄²

C₂²×D₇₉

Fitting

C₈²×C₇₉

C₂

socle, prime radical

C₂²×C₇₉

C₄×D₄

cosocle

C₄²×C₇₉

C₂³

hypercenter

C₈²

D₇₉

hypocenter

C₇₉

#1591

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈²

N	H ≅ G/N	type
39. C₈×C₇₉	Q₁₆	semidirect
53. C₇₉	#1591	semidirect
93. C₈	Dic₃₁₆	semidirect

H ≅ G/N

type

39. C₈×C₇₉

Q₁₆

semidirect

53. C₇₉

#1591

semidirect

93. C₈

Dic₃₁₆

semidirect

Subgroups — #23762298

Conjugacy classes of subgroups

Complements