Group #23765182 — subgroups

Subgroups — #23765182

Order 10112.

152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#19098601	C₂	1	1	yes	maximal, characteristic
3	#19098390	C₂	1	2	yes	maximal, complemented
4	#19098388	C₂	1	2	yes	maximal, complemented
5	#427×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#14579120	—	2	1	no	—
7	C₂×C₇₉⋊C₁₆	C₄	1	4	yes	complemented
8	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
10	#14579095	C₂²	1	2	yes	—
11	#14579093	—	2	1	no	—
12	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	#117×C₇₉	—	2	1	no	—
14	#107×C₇₉	C₂²	1	2	yes	—
15	#106×C₇₉	—	2	1	no	—
16	C₄⋊Dic₇₉	—	2	2	no	—
17	C₂²⋊Dic₇₉	—	4	1	no	—
18	C₄×Dic₇₉	—	4	1	no	—
19	C₇₉⋊C₁₆	C₂×C₄	1	2	yes	—
20	C₇₉⋊C₁₆	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	Q₈	1	2	yes	—
25	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₇₉	—	2	2	no	—
27	C₂²⋊C₄×C₇₉	—	4	1	no	—
28	C₄²×C₇₉	—	4	1	no	—
29	C₂³×C₇₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₇₉	—	4	2	no	—
31	C₂×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
32	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
33	C₂×C₄×C₇₉	Q₁₆	1	2	yes	—
34	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₉	—	4	2	no	—
36	C₈×C₇₉	C₄⋊C₄	1	2	yes	—
37	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₇₉	—	2	2	no	—
40	C₂²×C₇₉	#107	1	2	yes	—
41	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
42	C₄×C₇₉	—	8	2	no	—
43	C₄×C₇₉	#107	1	2	yes	—
44	C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
46	Dic₇₉	—	8	2	no	—
47	C₂×C₇₉	—	2	2	no	—
48	C₂×C₇₉	C₂×#107	1	1	yes	characteristic
49	C₂×C₇₉	#508	1	2	yes	—
50	#2158	—	79	1	no	maximal, Sylow
51	C₇₉	#2158	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₁₆	—	79	1	no	—
53	#427	—	79	1	no	—
54	#427	D₇₉	1	1	yes	characteristic
55	#367	—	79	2	no	—
56	#366	—	79	2	no	—
57	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
58	#117	—	2	1	no	—
59	#117	—	158	1	no	—
60	C₂×C₁₆	—	79	1	no	—
61	C₂×C₁₆	—	79	1	no	—
62	C₂×C₁₆	—	79	4	no	—
63	#107	—	79	2	no	—
64	#107	C₂×D₇₉	1	2	yes	—
65	#106	—	2	1	no	—
66	#106	—	158	1	no	—
67	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
68	C₂×C₈	Dic₁₅₈	1	2	yes	—
69	C₂×C₈	C₄×D₇₉	1	2	yes	—
70	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	158	2	no	—
74	C₂²⋊C₄	—	4	1	no	—
75	C₂²⋊C₄	—	316	1	no	—
76	C₄²	—	4	1	no	—
77	C₄²	—	316	1	no	—
78	C₁₆	—	79	2	no	—
79	C₁₆	—	79	2	no	—
80	C₂³	#11929609	1	1	yes	characteristic
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	316	2	no	—
83	C₂×C₄	Dic₇₉⋊C₄	1	2	yes	—
84	C₂×C₄	#11929609	1	1	yes	characteristic
85	C₂×C₄	#11929614	1	2	yes	—
86	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
87	C₈	Dic₇₉⋊C₄	1	2	yes	—
88	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
89	C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#14579094	1	2	yes	—
92	C₂²	C₂×#11929609	1	1	yes	characteristic
93	C₄	—	8	2	no	—
94	C₄	—	632	2	no	—
95	C₄	#14579094	1	2	yes	—
96	C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
97	C₄	C₂×#11929614	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×#14579094	1	1	yes	characteristic
100	C₂	#19098993	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₇₉⋊C₁₆

C₂

yes

maximal, characteristic

#19098601

C₂

yes

maximal, characteristic

#19098390

C₂

yes

maximal, complemented

#19098388

C₂

yes

maximal, complemented

#427×C₇₉

C₂

yes

maximal, characteristic

#14579120

—

C₂×C₇₉⋊C₁₆

C₄

yes

complemented

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

—

#14579093

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

#117×C₇₉

—

#107×C₇₉

C₂²

yes

—

#106×C₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

C₂×C₄

yes

—

C₇₉⋊C₁₆

C₂×C₄

yes

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

Q₁₆

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₈×C₇₉

C₄⋊C₄

yes

—

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

C₂×Q₈

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

#107

yes

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

#107

yes

—

C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₉

C₂×Q₁₆

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂×#107

yes

characteristic

C₂×C₇₉

#508

yes

—

#2158

—

maximal, Sylow

C₇₉

#2158

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

#427

—

#427

D₇₉

yes

characteristic

#367

—

#366

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

#117

—

#117

—

158

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₇₉

yes

—

#106

—

#106

—

158

—

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

Dic₁₅₈

yes

—

C₂×C₈

C₄×D₇₉

yes

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

C₂²⋊C₄

—

316

—

C₄²

—

C₄²

—

316

—

C₁₆

—

C₁₆

—

C₂³

#11929609

yes

characteristic

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

Dic₇₉⋊C₄

yes

—

C₂×C₄

#11929609

yes

characteristic

C₂×C₄

#11929614

yes

—

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₈

Dic₇₉⋊C₄

yes

—

C₈

C₂×C₄×D₇₉

yes

characteristic

C₈

C₂×Dic₁₅₈

yes

characteristic

C₂²

—

C₂²

#14579094

yes

—

C₂²

C₂×#11929609

yes

characteristic

C₄

—

C₄

—

632

—

C₄

#14579094

yes

—

C₄

C₂×Dic₇₉⋊C₄

yes

characteristic

C₄

C₂×#11929614

yes

characteristic

C₂

—

C₂

C₂×#14579094

yes

characteristic

100

C₂

#19098993

yes

—

	subgroup	G/H
center	C₂×C₄	#11929609
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#427×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂³×C₇₉	D₈
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	#427	D₇₉
hypocenter	C₇₉	#2158
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

subgroup

G/H

center

C₂×C₄

#11929609

commutator

C₈×C₇₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#427×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂³×C₇₉

D₈

cosocle

C₂×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

N	H ≅ G/N	type
3. #19098390	C₂	semidirect
4. #19098388	C₂	semidirect
7. C₂×C₇₉⋊C₁₆	C₄	semidirect
51. C₇₉	#2158	semidirect

H ≅ G/N

type

3. #19098390

C₂

semidirect

4. #19098388

C₂

semidirect

7. C₂×C₇₉⋊C₁₆

C₄

semidirect

51. C₇₉

#2158

semidirect

Subgroups — #23765182

Conjugacy classes of subgroups

Complements