Group #23762315 — subgroups

Subgroups — #23762315

Order 10112.

176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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	C₄×D₆₃₂	C₂	1	1	yes	maximal, characteristic
2	#19098642	C₂	1	2	yes	maximal, complemented
3	#19098314	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098292	C₂	1	2	yes	maximal, complemented
5	#322×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₆₃₂	C₄	1	1	yes	characteristic
7	C₂×#11929607	—	2	2	no	—
8	C₄×D₃₁₆	C₂²	1	2	yes	—
9	#14579095	C₄	1	1	yes	characteristic
10	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
11	#14579083	C₄	1	2	yes	—
12	(C₂×D₇₉)⋊C₈	—	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×D₃₁₆	C₂×C₄	1	2	yes	—
17	C₂×C₄×D₇₉	—	2	2	no	—
18	D₆₃₂	—	2	2	no	—
19	#11929607	—	4	4	no	—
20	C₂×C₇₉⋊C₈	—	2	2	no	—
21	C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
22	(C₂×D₇₉)⋊C₄	—	2	2	no	—
23	C₂×C₈×C₇₉	—	2	1	no	—
24	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	D₄	1	2	yes	—
27	C₄²×C₇₉	C₂³	1	1	yes	characteristic
28	C₂²×D₇₉	—	2	2	no	—
29	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
32	C₂×Dic₇₉	—	2	2	no	—
33	D₃₁₆	—	2	2	no	—
34	D₃₁₆	—	2	2	no	—
35	C₄×D₇₉	—	4	2	no	—
36	C₄×D₇₉	—	4	2	no	—
37	C₈×C₇₉	—	2	1	no	—
38	C₈×C₇₉	—	2	2	no	—
39	C₈×C₇₉	—	4	1	no	—
40	C₈×C₇₉	M₁₆	1	2	yes	complemented
41	C₇₉⋊C₈	—	4	2	no	—
42	C₂²×C₇₉	C₄×D₄	1	1	yes	characteristic
43	C₂×D₇₉	—	4	2	no	—
44	C₂×D₇₉	—	4	2	no	—
45	C₂×D₇₉	—	4	2	no	—
46	C₄×C₇₉	—	2	1	no	—
47	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
48	C₄×C₇₉	#131	1	1	yes	characteristic
49	C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
50	Dic₇₉	—	4	2	no	—
51	C₂×C₇₉	#436	1	1	yes	characteristic
52	C₂×C₇₉	#442	1	1	yes	characteristic
53	C₂×C₇₉	#444	1	1	yes	characteristic
54	D₇₉	—	8	2	no	—
55	#1594	—	79	1	no	maximal, Sylow
56	C₇₉	#1594	1	1	yes	characteristic, complemented, Sylow
57	C₄×D₈	—	79	1	no	—
58	#436	—	79	2	no	—
59	#334	—	79	1	no	—
60	D₄⋊C₈	—	79	2	no	—
61	#322	D₇₉	1	1	yes	characteristic, complemented
62	C₂×D₈	—	79	1	no	—
63	C₂×M₁₆	—	158	2	no	—
64	C₄×D₄	—	79	2	no	—
65	#107	—	79	1	no	—
66	C₄⋊C₈	—	79	2	no	—
67	#102	—	79	2	no	—
68	C₂²⋊C₈	—	158	2	no	—
69	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
70	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
71	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
72	C₂×D₄	—	79	2	no	—
73	C₂²×C₄	—	158	2	no	—
74	D₈	—	158	2	no	—
75	M₁₆	—	316	4	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	158	2	no	—
78	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
79	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
80	C₂×C₈	D₃₁₆	1	2	yes	—
81	C₄⋊C₄	—	79	2	no	—
82	C₂²⋊C₄	—	158	2	no	—
83	C₄²	C₂²×D₇₉	1	1	yes	characteristic
84	C₂³	—	158	2	no	—
85	D₄	—	158	2	no	—
86	D₄	—	158	2	no	—
87	C₂×C₄	—	316	2	no	—
88	C₂×C₄	—	316	2	no	—
89	C₂×C₄	—	158	2	no	—
90	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
91	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
92	C₂×C₄	#11929624	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	2	2	no	—
95	C₈	—	4	1	no	—
96	C₈	—	316	2	no	—
97	C₈	#11929607	1	2	yes	complemented
98	C₂²	—	316	2	no	—
99	C₂²	—	316	2	no	—
100	C₂²	—	316	2	no	—
101	C₂²	C₄×D₃₁₆	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	316	2	no	—
104	C₄	C₂×#11929607	1	1	yes	characteristic
105	C₄	#14579167	1	1	yes	characteristic
106	C₄	#14579189	1	2	yes	—
107	C₂	—	632	2	no	—
108	C₂	#19098642	1	1	yes	characteristic
109	C₂	#19098676	1	1	yes	characteristic
110	C₂	#19098686	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₆₃₂

C₂

yes

maximal, characteristic

#19098642

C₂

yes

maximal, complemented

#19098314

C₂

yes

maximal, characteristic, complemented

#19098292

C₂

yes

maximal, complemented

#322×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×D₆₃₂

C₄

yes

characteristic

C₂×#11929607

—

C₄×D₃₁₆

C₂²

yes

—

#14579095

C₄

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579083

C₄

yes

—

(C₂×D₇₉)⋊C₈

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×D₃₁₆

C₂×C₄

yes

—

C₂×C₄×D₇₉

—

D₆₃₂

—

#11929607

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

C₂×C₄

yes

—

(C₂×D₇₉)⋊C₄

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

M₁₆

yes

complemented

C₇₉⋊C₈

—

C₂²×C₇₉

C₄×D₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×M₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#1594

—

maximal, Sylow

C₇₉

#1594

yes

characteristic, complemented, Sylow

C₄×D₈

—

#436

—

#334

—

D₄⋊C₈

—

#322

D₇₉

yes

characteristic, complemented

C₂×D₈

—

C₂×M₁₆

—

158

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

158

—

D₈

—

158

—

M₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

D₃₁₆

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

158

—

D₄

—

158

—

D₄

—

158

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

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

complemented

C₂²

—

316

—

C₂²

—

316

—

100

C₂²

—

316

—

101

C₂²

C₄×D₃₁₆

yes

characteristic

102

C₄

—

103

C₄

—

316

—

104

C₄

C₂×#11929607

yes

characteristic

105

C₄

#14579167

yes

characteristic

106

C₄

#14579189

yes

—

107

C₂

—

632

—

108

C₂

#19098642

yes

characteristic

109

C₂

#19098676

yes

characteristic

110

C₂

#19098686

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₄²	C₂²×D₇₉
Fitting	#322×C₇₉	C₂
socle	C₂²×C₇₉	C₄×D₄
prime radical	C₂×D₆₃₂	C₄
cosocle	C₄²×C₇₉	C₂³
hypercenter	#322	D₇₉
hypocenter	C₇₉	#1594
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₃₁₆

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₄²

C₂²×D₇₉

Fitting

#322×C₇₉

C₂

socle

C₂²×C₇₉

C₄×D₄

prime radical

C₂×D₆₃₂

C₄

cosocle

C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
2. #19098642	C₂	semidirect
3. #19098314	C₂	semidirect
4. #19098292	C₂	semidirect
5. #322×C₇₉	C₂	semidirect
40. C₈×C₇₉	M₁₆	semidirect
56. C₇₉	#1594	semidirect
61. #322	D₇₉	semidirect
97. C₈	#11929607	semidirect

H ≅ G/N

type

2. #19098642

C₂

semidirect

3. #19098314

C₂

semidirect

4. #19098292

C₂

semidirect

5. #322×C₇₉

C₂

semidirect

40. C₈×C₇₉

M₁₆

semidirect

56. C₇₉

#1594

semidirect

61. #322

D₇₉

semidirect

97. C₈

#11929607

semidirect

Subgroups — #23762315

Conjugacy classes of subgroups

Complements