Group #23761442 — subgroups

Subgroups — #23761442

Order 10112.

102 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 39 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	#19098947	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₇₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	#334×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₃₁₆	C₄	1	1	yes	characteristic
5	C₂×#11929613	—	2	1	no	—
6	C₂×D₆₃₂	C₄	1	1	yes	characteristic
7	#14579149	—	2	1	no	—
8	C₂×C₇₉⋊C₁₆	—	2	1	no	—
9	C₄⋊C₈×C₇₉	—	2	1	no	—
10	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₅₈	—	2	1	no	—
12	C₂×D₃₁₆	—	2	1	no	—
13	Dic₃₁₆	—	4	1	no	—
14	#11929613	—	4	1	no	—
15	#11929613	—	4	1	no	—
16	D₆₃₂	—	4	1	no	—
17	(C₂×D₇₉)⋊C₄	—	4	1	no	—
18	(C₂×D₇₉)⋊C₄	—	4	1	no	—
19	C₇₉⋊C₁₆	—	4	1	no	—
20	C₂×C₈×C₇₉	—	4	1	no	—
21	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
23	C₄²×C₇₉	D₄	1	1	yes	characteristic
24	C₂²×D₇₉	—	4	1	no	—
25	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
27	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
28	C₂×Dic₇₉	—	4	1	no	—
29	D₃₁₆	—	4	1	no	—
30	D₃₁₆	—	4	1	no	—
31	Dic₁₅₈	—	4	1	no	—
32	Dic₁₅₈	—	4	1	no	—
33	C₈×C₇₉	—	2	1	no	—
34	C₈×C₇₉	—	8	1	no	—
35	C₈×C₇₉	D₈	1	1	yes	characteristic
36	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
37	C₂²×C₇₉	#102	1	1	yes	characteristic
38	C₂×D₇₉	—	8	1	no	—
39	C₂×D₇₉	—	8	1	no	—
40	C₂×D₇₉	—	8	1	no	—
41	C₄×C₇₉	—	2	1	no	—
42	C₄×C₇₉	—	2	1	no	—
43	C₄×C₇₉	#100	1	1	yes	characteristic
44	C₄×C₇₉	#102	1	1	yes	characteristic
45	Dic₇₉	—	8	1	no	—
46	C₂×C₇₉	#331	1	1	yes	characteristic
47	C₂×C₇₉	#359	1	1	yes	characteristic
48	C₂×C₇₉	#360	1	1	yes	characteristic
49	D₇₉	—	16	1	no	—
50	#1360	—	79	1	no	maximal, Sylow
51	C₇₉	#1360	1	1	yes	characteristic, complemented, Sylow
52	#495	—	79	1	no	—
53	C₄⋊C₁₆	—	79	1	no	—
54	#334	D₇₉	1	1	yes	characteristic, complemented
55	C₂×Q₁₆	—	79	1	no	—
56	C₂×SD₁₆	—	158	1	no	—
57	C₂×D₈	—	79	1	no	—
58	#124	—	158	1	no	—
59	C₂×C₁₆	—	158	1	no	—
60	C₄⋊C₈	—	2	1	no	—
61	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
62	C₂×Q₈	—	158	1	no	—
63	C₂×D₄	—	158	1	no	—
64	Q₁₆	—	316	1	no	—
65	SD₁₆	—	316	1	no	—
66	SD₁₆	—	316	1	no	—
67	D₈	—	316	1	no	—
68	C₂×C₈	—	4	1	no	—
69	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
70	C₂×C₈	D₃₁₆	1	1	yes	characteristic
71	C₂²⋊C₄	—	316	1	no	—
72	C₂²⋊C₄	—	316	1	no	—
73	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
74	C₁₆	—	316	1	no	—
75	C₂³	—	316	1	no	—
76	Q₈	—	316	1	no	—
77	Q₈	—	316	1	no	—
78	D₄	—	316	1	no	—
79	D₄	—	316	1	no	—
80	C₂×C₄	—	316	1	no	—
81	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
82	C₂×C₄	#11929609	1	1	yes	characteristic
83	C₂×C₄	#11929611	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	8	1	no	—
86	C₈	D₆₃₂	1	1	yes	characteristic
87	C₈	#11929613	1	1	yes	characteristic
88	C₂²	—	632	1	no	—
89	C₂²	—	632	1	no	—
90	C₂²	—	632	1	no	—
91	C₂²	#14579081	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	2	1	no	—
94	C₄	—	632	1	no	—
95	C₄	#14579077	1	1	yes	characteristic
96	C₄	#14579083	1	1	yes	characteristic
97	C₂	—	1264	1	no	—
98	C₂	#19098306	1	1	yes	characteristic
99	C₂	#19098369	1	1	yes	characteristic
100	C₂	#19098372	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098947

C₂

yes

maximal, characteristic

C₄⋊(C₇₉⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#334×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

C₄

yes

characteristic

C₂×#11929613

—

C₂×D₆₃₂

C₄

yes

characteristic

#14579149

—

C₂×C₇₉⋊C₁₆

—

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

Dic₃₁₆

—

#11929613

—

#11929613

—

D₆₃₂

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₇₉⋊C₁₆

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₂²×D₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

D₈

yes

characteristic

C₈×C₇₉

SD₁₆

yes

characteristic

C₂²×C₇₉

#102

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#1360

—

maximal, Sylow

C₇₉

#1360

yes

characteristic, complemented, Sylow

#495

—

C₄⋊C₁₆

—

#334

D₇₉

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×SD₁₆

—

158

—

C₂×D₈

—

#124

—

158

—

C₂×C₁₆

—

158

—

C₄⋊C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

—

158

—

Q₁₆

—

316

—

SD₁₆

—

316

—

SD₁₆

—

316

—

D₈

—

316

—

C₂×C₈

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₂²⋊C₄

—

316

—

C₂²⋊C₄

—

316

—

C₄²

C₂²⋊D₇₉

yes

characteristic

C₁₆

—

316

—

C₂³

—

316

—

Q₈

—

316

—

Q₈

—

316

—

D₄

—

316

—

D₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

D₆₃₂

yes

characteristic

C₈

#11929613

yes

characteristic

C₂²

—

632

—

C₂²

—

632

—

C₂²

—

632

—

C₂²

#14579081

yes

characteristic

C₄

—

C₄

—

C₄

—

632

—

C₄

yes

C₄

yes

C₂

—

1264

—

C₂

yes

C₂

yes

100

C₂

#19098372

yes

characteristic

	subgroup	G/H
center	C₂²	#14579081
commutator	C₂×C₈×C₇₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₉
Fitting	#334×C₇₉	C₂
socle	C₂²×C₇₉	#102
prime radical	C₂×D₆₃₂	C₄
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	#334	D₇₉
hypocenter	C₇₉	#1360
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

subgroup

G/H

center

C₂²

#14579081

commutator

C₂×C₈×C₇₉

C₂×C₄

Frattini

C₄×C₈

C₂×D₇₉

Fitting

#334×C₇₉

C₂

socle

C₂²×C₇₉

#102

prime radical

C₂×D₆₃₂

C₄

cosocle

C₄×C₈×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

N	H ≅ G/N	type
2. C₄⋊(C₇₉⋊C₁₆)	C₂	semidirect
3. #334×C₇₉	C₂	semidirect
51. C₇₉	#1360	semidirect
54. #334	D₇₉	semidirect

H ≅ G/N

type

2. C₄⋊(C₇₉⋊C₁₆)

C₂

semidirect

3. #334×C₇₉

C₂

semidirect

51. C₇₉

#1360

semidirect

54. #334

D₇₉

semidirect

Subgroups — #23761442

Conjugacy classes of subgroups

Complements