Group #23765505 — subgroups

Subgroups — #23765505

Order 10112.

150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14579100	C₂	1	1	yes	maximal, characteristic
2	#19098801	C₂	1	2	yes	maximal
3	#19098391	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098367	C₂	1	2	yes	maximal, complemented
5	C₂×Q₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇₉	C₂²	1	1	yes	characteristic
7	#14579137	—	2	2	no	—
8	#14579100	—	2	2	no	—
9	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
10	#14579095	C₂²	1	2	yes	—
11	#14579085	—	2	2	no	—
12	C₂×Q₁₆×C₇₉	C₂²	1	2	yes	—
13	Q₃₂×C₇₉	—	2	2	no	—
14	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
16	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
17	C₈×D₇₉	—	2	1	no	—
18	C₈×D₇₉	—	2	1	no	—
19	C₄⋊Dic₇₉	—	2	2	no	—
20	Dic₇₉⋊C₄	—	4	2	no	—
21	(C₂×D₇₉)⋊C₄	—	4	2	no	—
22	C₇₉⋊C₁₆	—	2	1	no	—
23	C₂×Q₈×C₇₉	—	2	2	no	—
24	Q₁₆×C₇₉	—	2	2	no	—
25	Q₁₆×C₇₉	—	2	2	no	—
26	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
27	C₁₆×C₇₉	D₄	1	2	yes	—
28	C₂²×D₇₉	D₈	1	1	yes	characteristic
29	Q₈×C₇₉	—	4	2	no	—
30	Q₈×C₇₉	—	4	2	no	—
31	C₂×C₄×C₇₉	—	4	2	no	—
32	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₇₉	—	4	2	no	—
34	C₂×Dic₇₉	D₈	1	1	yes	characteristic
35	C₄×D₇₉	—	2	1	no	—
36	C₄×D₇₉	—	2	1	no	—
37	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₇₉	#41	1	1	yes	characteristic
39	C₇₉⋊C₈	—	2	1	no	—
40	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
41	C₂×D₇₉	—	2	1	no	—
42	C₂×D₇₉	—	2	2	no	—
43	C₄×C₇₉	—	8	2	no	—
44	C₄×C₇₉	#121	1	1	yes	characteristic
45	C₄×C₇₉	#135	1	1	yes	characteristic
46	Dic₇₉	—	2	1	no	—
47	Dic₇₉	—	8	2	no	—
48	C₂×C₇₉	#466	1	1	yes	characteristic
49	C₂×C₇₉	#510	1	2	yes	—
50	D₇₉	—	4	1	no	—
51	#2219	—	79	1	no	maximal, Sylow
52	C₇₉	#2219	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₃₂	D₇₉	1	1	yes	characteristic, complemented
54	C₂×M₃₂	—	79	1	no	—
55	#467	—	79	2	no	—
56	#367	—	79	1	no	—
57	#358	—	79	2	no	—
58	C₂×Q₁₆	C₂×D₇₉	1	2	yes	—
59	C₂²×C₈	—	79	1	no	—
60	C₂²⋊Q₈	—	158	2	no	—
61	Q₃₂	—	2	2	no	—
62	M₃₂	—	158	2	no	—
63	C₂×C₁₆	—	79	1	no	—
64	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
65	#107	—	79	2	no	—
66	#103	—	158	2	no	—
67	C₂×Q₈	—	2	2	no	—
68	C₂²×C₄	—	79	1	no	—
69	Q₁₆	—	2	2	no	—
70	Q₁₆	—	2	2	no	—
71	C₂×C₈	—	79	1	no	—
72	C₂×C₈	—	158	1	no	—
73	C₂×C₈	—	158	1	no	—
74	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
75	C₄⋊C₄	—	316	2	no	—
76	C₄⋊C₄	—	158	2	no	—
77	C₂²⋊C₄	—	316	2	no	—
78	C₁₆	—	158	1	no	—
79	C₁₆	C₂²⋊D₇₉	1	2	yes	—
80	C₂³	—	79	1	no	—
81	Q₈	—	4	2	no	—
82	Q₈	—	4	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	—	316	2	no	—
85	C₂×C₄	—	79	1	no	—
86	C₂×C₄	—	158	1	no	—
87	C₂×C₄	—	158	1	no	—
88	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
89	C₈	—	158	1	no	—
90	C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
91	C₈	#11929623	1	1	yes	characteristic
92	C₂²	—	158	2	no	—
93	C₂²	—	158	1	no	—
94	C₂²	D₈×D₇₉	1	1	yes	characteristic
95	C₄	—	8	2	no	—
96	C₄	—	632	2	no	—
97	C₄	—	158	1	no	—
98	C₄	#14579132	1	1	yes	characteristic
99	C₄	#14579180	1	1	yes	characteristic
100	C₂	—	316	1	no	—
101	C₂	#19098796	1	1	yes	characteristic
102	C₂	#19099005	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579100

C₂

yes

maximal, characteristic

#19098801

C₂

yes

maximal

#19098391

C₂

yes

maximal, characteristic, complemented

#19098367

C₂

yes

maximal, complemented

C₂×Q₃₂×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₉

C₂²

yes

characteristic

#14579137

—

#14579100

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

—

#14579085

—

C₂×Q₁₆×C₇₉

C₂²

yes

—

Q₃₂×C₇₉

—

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₈×D₇₉

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₇₉⋊C₁₆

—

C₂×Q₈×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

D₄

yes

—

C₂²×D₇₉

D₈

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#466

yes

characteristic

C₂×C₇₉

#510

yes

—

D₇₉

—

#2219

—

maximal, Sylow

C₇₉

#2219

yes

characteristic, complemented, Sylow

C₂×Q₃₂

D₇₉

yes

characteristic, complemented

C₂×M₃₂

—

#467

—

#367

—

#358

—

C₂×Q₁₆

C₂×D₇₉

yes

—

C₂²×C₈

—

C₂²⋊Q₈

—

158

—

Q₃₂

—

M₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

—

#103

—

158

—

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

316

—

C₁₆

—

158

—

C₁₆

C₂²⋊D₇₉

yes

—

C₂³

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

D₄×D₇₉

yes

characteristic

C₈

—

158

—

C₈

C₂×C₂²⋊D₇₉

yes

characteristic

C₈

#11929623

yes

characteristic

C₂²

—

158

—

C₂²

—

158

—

C₂²

D₈×D₇₉

yes

characteristic

C₄

—

C₄

—

632

—

C₄

—

158

—

C₄

yes

C₄

yes

100

C₂

—

316

—

101

C₂

#19098796

yes

characteristic

102

C₂

#19099005

yes

—

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₂×Q₃₂×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂²×D₇₉	D₈
hypercenter	C₂×Q₃₂	D₇₉
hypocenter	C₇₉	#2219
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₂×Q₃₂×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂²×D₇₉

D₈

hypercenter

C₂×Q₃₂

D₇₉

hypocenter

C₇₉

#2219

LCS

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
3. #19098391	C₂	semidirect
4. #19098367	C₂	semidirect
5. C₂×Q₃₂×C₇₉	C₂	semidirect
52. C₇₉	#2219	semidirect
53. C₂×Q₃₂	D₇₉	semidirect

H ≅ G/N

type

3. #19098391

C₂

semidirect

4. #19098367

C₂

semidirect

5. C₂×Q₃₂×C₇₉

C₂

semidirect

52. C₇₉

#2219

semidirect

53. C₂×Q₃₂

D₇₉

semidirect

Subgroups — #23765505

Conjugacy classes of subgroups

Complements