Group #23765164 — subgroups

Subgroups — #23765164

Order 10112.

152 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 75 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	M₃₂×D₇₉	C₂	1	2	yes	maximal
2	#19098517	C₂	1	1	yes	maximal, characteristic
3	#19098384	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098383	C₂	1	2	yes	maximal, complemented
5	#364×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929607	C₄	1	1	yes	characteristic
7	C₂×C₈×D₇₉	C₂²	1	1	yes	characteristic
8	#14579118	C₄	1	1	yes	characteristic
9	#14579101	C₂²	1	2	yes	—
10	#14579100	—	2	2	no	—
11	C₁₆×D₇₉	—	2	2	no	—
12	#14579072	C₄	1	1	yes	characteristic
13	#14579071	C₄	1	1	yes	characteristic
14	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
15	M₃₂×C₇₉	C₂²	1	2	yes	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
18	#11929607	C₈	1	4	yes	—
19	C₂×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
20	C₂×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
21	C₈×D₇₉	D₄	1	2	yes	—
22	C₈×D₇₉	Q₈	1	2	yes	—
23	Dic₇₉⋊C₄	—	2	1	no	—
24	(C₂×D₇₉)⋊C₄	—	2	1	no	—
25	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
26	C₇₉⋊C₁₆	—	2	2	no	—
27	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
29	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
30	C₁₆×C₇₉	—	2	2	no	—
31	C₂²×D₇₉	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₉	—	2	1	no	—
33	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₇₉	—	2	1	no	—
35	C₂×Dic₇₉	M₁₆	1	1	yes	characteristic
36	C₄×D₇₉	C₄⋊C₄	1	2	yes	—
37	C₄×D₇₉	C₂×C₈	1	2	yes	—
38	C₈×C₇₉	C₂×C₈	1	2	yes	—
39	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
40	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
41	C₇₉⋊C₈	C₄⋊C₄	1	2	yes	—
42	C₇₉⋊C₈	C₂×C₈	1	2	yes	—
43	C₂²×C₇₉	C₂×M₁₆	1	1	yes	characteristic
44	C₂×D₇₉	—	4	1	no	—
45	C₂×D₇₉	C₄⋊C₈	1	2	yes	—
46	C₄×C₇₉	—	4	1	no	—
47	C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
49	Dic₇₉	—	4	1	no	—
50	Dic₇₉	C₄⋊C₈	1	2	yes	—
51	C₂×C₇₉	—	2	1	no	—
52	C₂×C₇₉	C₂×C₄⋊C₈	1	1	yes	characteristic
53	D₇₉	—	2	2	no	—
54	#2153	—	79	1	no	maximal, Sylow
55	C₇₉	#2153	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₃₂	—	79	2	no	—
57	#405	—	79	1	no	—
58	#364	—	79	2	no	—
59	#364	—	79	1	no	—
60	#364	D₇₉	1	1	yes	characteristic, complemented
61	C₂×M₁₆	—	79	1	no	—
62	C₂²×C₈	—	79	1	no	—
63	#117	—	79	1	no	—
64	M₃₂	—	79	2	no	—
65	M₃₂	—	158	2	no	—
66	M₃₂	C₂×D₇₉	1	2	yes	—
67	C₂×C₁₆	—	158	2	no	—
68	#97	—	79	1	no	—
69	#97	—	79	1	no	—
70	C₄×C₈	—	79	1	no	—
71	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
72	C₂²×C₄	—	79	1	no	—
73	M₁₆	—	79	4	no	—
74	C₂×C₈	—	79	1	no	—
75	C₂×C₈	—	79	1	no	—
76	C₂×C₈	—	79	2	no	—
77	C₂×C₈	—	79	2	no	—
78	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
79	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
80	C₄⋊C₄	—	158	1	no	—
81	C₂²⋊C₄	—	158	1	no	—
82	C₄²	—	79	1	no	—
83	C₄²	C₄×D₇₉	1	1	yes	characteristic
84	C₁₆	—	2	2	no	—
85	C₁₆	—	158	2	no	—
86	C₂³	—	79	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	79	1	no	—
89	C₂×C₄	—	79	2	no	—
90	C₂×C₄	—	79	2	no	—
91	C₂×C₄	—	158	1	no	—
92	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
93	C₈	—	79	2	no	—
94	C₈	—	79	2	no	—
95	C₈	C₈×D₇₉	1	2	yes	—
96	C₈	D₄×D₇₉	1	1	yes	characteristic
97	C₈	Q₈×D₇₉	1	1	yes	characteristic
98	C₂²	—	316	1	no	—
99	C₂²	—	79	2	no	—
100	C₂²	M₁₆×D₇₉	1	1	yes	characteristic
101	C₄	—	4	1	no	—
102	C₄	—	316	1	no	—
103	C₄	—	79	2	no	—
104	C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
105	C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
106	C₂	—	2	1	no	—
107	C₂	—	158	2	no	—
108	C₂	C₄⋊C₈×D₇₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₃₂×D₇₉

C₂

yes

maximal

#19098517

C₂

yes

maximal, characteristic

#19098384

C₂

yes

maximal, characteristic, complemented

#19098383

C₂

yes

maximal, complemented

#364×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929607

C₄

yes

characteristic

C₂×C₈×D₇₉

C₂²

yes

characteristic

#14579118

C₄

yes

characteristic

#14579101

C₂²

yes

—

#14579100

—

C₁₆×D₇₉

—

#14579072

C₄

yes

characteristic

#14579071

C₄

yes

characteristic

C₈×Dic₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄×D₇₉

C₂×C₄

yes

characteristic

#11929607

C₈

yes

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₈×D₇₉

D₄

yes

—

C₈×D₇₉

Q₈

yes

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₇₉⋊C₁₆

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₁₆×C₇₉

—

C₂²×D₇₉

M₁₆

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

M₁₆

yes

characteristic

C₄×D₇₉

C₄⋊C₄

yes

—

C₄×D₇₉

C₂×C₈

yes

—

C₈×C₇₉

C₂×C₈

yes

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

C₂×Q₈

yes

characteristic

C₇₉⋊C₈

C₄⋊C₄

yes

—

C₇₉⋊C₈

C₂×C₈

yes

—

C₂²×C₇₉

C₂×M₁₆

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

C₄⋊C₈

yes

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₉

C₂²×C₈

yes

characteristic

Dic₇₉

—

Dic₇₉

C₄⋊C₈

yes

—

C₂×C₇₉

—

C₂×C₇₉

C₂×C₄⋊C₈

yes

characteristic

D₇₉

—

#2153

—

maximal, Sylow

C₇₉

#2153

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

—

—

—

D₇₉

yes

characteristic, complemented

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

158

—

M₃₂

C₂×D₇₉

yes

—

C₂×C₁₆

—

158

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

158

—

C₄²

—

C₄²

C₄×D₇₉

yes

characteristic

C₁₆

—

C₁₆

—

158

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₈

—

C₈

—

C₈

C₈×D₇₉

yes

—

C₈

D₄×D₇₉

yes

characteristic

C₈

Q₈×D₇₉

yes

characteristic

C₂²

—

316

—

C₂²

—

100

C₂²

M₁₆×D₇₉

yes

characteristic

101

C₄

—

102

C₄

—

316

—

103

C₄

—

104

C₄

C₄⋊C₄×D₇₉

yes

characteristic

105

C₄

C₂×C₈×D₇₉

yes

characteristic

106

C₂

—

107

C₂

—

158

—

108

C₂

C₄⋊C₈×D₇₉

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₇₉
commutator	C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#364×C₇₉	C₂
socle	C₂×C₇₉	C₂×C₄⋊C₈
prime radical	C₂²×D₇₉	M₁₆
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	#364	D₇₉
hypocenter	C₇₉	#2153
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×D₇₉

commutator

C₄×C₇₉

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#364×C₇₉

C₂

socle

C₂×C₇₉

C₂×C₄⋊C₈

prime radical

C₂²×D₇₉

M₁₆

cosocle

C₂×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
3. #19098384	C₂	semidirect
4. #19098383	C₂	semidirect
5. #364×C₇₉	C₂	semidirect
55. C₇₉	#2153	semidirect
60. #364	D₇₉	semidirect

H ≅ G/N

type

3. #19098384

C₂

semidirect

4. #19098383

C₂

semidirect

5. #364×C₇₉

C₂

semidirect

55. C₇₉

#2153

semidirect

60. #364

D₇₉

semidirect

Subgroups — #23765164

Conjugacy classes of subgroups

Complements