Group #23761681 — subgroups

Subgroups — #23761681

Order 10112.

224 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11929608	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#19098285	C₂	1	2	yes	maximal, complemented
4	C₈×C₇₉⋊C₈	C₂	1	2	yes	maximal, complemented
5	#431×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929608	C₄	1	2	yes	—
7	C₂²×C₇₉⋊C₈	C₄	1	2	yes	—
8	#14579072	C₄	1	2	yes	—
9	C₄×C₇₉⋊C₈	C₄	1	2	yes	—
10	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₉	C₄	1	2	yes	—
15	C₂²⋊C₈×C₇₉	C₄	1	2	yes	—
16	C₄×C₈×C₇₉	C₂²	1	2	yes	—
17	#11929608	C₈	1	8	yes	complemented
18	C₂×C₇₉⋊C₈	—	2	4	no	—
19	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
20	C₂×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
21	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	C₂×C₄	1	4	yes	—
26	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₇₉	C₂³	1	1	yes	characteristic
30	C₂³×C₇₉	C₄²	1	1	yes	characteristic
31	C₂×C₄×C₇₉	—	2	2	no	—
32	C₂×C₄×C₇₉	—	2	2	no	—
33	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
35	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₂×C₈	1	4	yes	—
37	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
40	C₈×C₇₉	—	2	4	no	—
41	C₇₉⋊C₈	—	2	2	no	—
42	C₇₉⋊C₈	C₂×C₈	1	8	yes	complemented
43	C₇₉⋊C₈	M₁₆	1	4	yes	complemented
44	C₂²×C₇₉	—	2	1	no	—
45	C₂²×C₇₉	—	2	1	no	—
46	C₂²×C₇₉	C₄×C₈	1	2	yes	—
47	C₂²×C₇₉	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₇₉	—	2	1	no	—
49	C₄×C₇₉	—	2	1	no	—
50	C₄×C₇₉	C₄×C₈	1	2	yes	—
51	C₄×C₇₉	C₂²×C₈	1	2	yes	—
52	C₄×C₇₉	C₂×M₁₆	1	2	yes	—
53	C₄×C₇₉	#131	1	2	yes	—
54	C₂×C₇₉	—	2	2	no	—
55	C₂×C₇₉	C₂×C₄×C₈	1	1	yes	characteristic
56	C₂×C₇₉	C₄×M₁₆	1	1	yes	characteristic
57	C₂×C₇₉	#405	1	1	yes	characteristic
58	C₈×M₁₆	—	79	1	no	maximal, Sylow
59	C₇₉	C₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
60	#431	D₇₉	1	1	yes	characteristic
61	C₄×M₁₆	—	79	1	no	—
62	C₂×C₄×C₈	—	79	1	no	—
63	#322	—	79	2	no	—
64	C₈²	—	79	2	no	—
65	C₂×M₁₆	—	79	2	no	—
66	C₂²×C₈	—	79	2	no	—
67	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
68	C₄⋊C₈	Dic₇₉	1	2	yes	—
69	C₂²⋊C₈	Dic₇₉	1	2	yes	—
70	#97	—	79	2	no	—
71	C₄×C₈	—	79	1	no	—
72	C₄×C₈	—	79	2	no	—
73	C₄×C₈	—	79	1	no	—
74	C₄×C₈	—	79	2	no	—
75	C₄×C₈	C₂×D₇₉	1	2	yes	—
76	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
77	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
78	C₂²×C₄	C₂×Dic₇₉	1	1	yes	characteristic
79	M₁₆	—	79	8	no	—
80	C₂×C₈	—	79	2	no	—
81	C₂×C₈	—	79	4	no	—
82	C₂×C₈	—	79	2	no	—
83	C₂×C₈	—	158	4	no	—
84	C₂×C₈	C₂×Dic₇₉	1	4	yes	—
85	C₄²	C₄×D₇₉	1	1	yes	characteristic
86	C₄²	C₄×D₇₉	1	1	yes	characteristic
87	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
88	C₄²	C₂²×D₇₉	1	1	yes	characteristic
89	C₂³	C₄×Dic₇₉	1	1	yes	characteristic
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
93	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
94	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
95	C₂×C₄	C₈×D₇₉	1	4	yes	—
96	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
97	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
98	C₂×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
99	C₈	—	2	4	no	—
100	C₈	—	79	8	no	—
101	C₈	—	79	4	no	—
102	C₈	—	158	2	no	—
103	C₂²	—	2	1	no	—
104	C₂²	—	2	1	no	—
105	C₂²	C₈×Dic₇₉	1	2	yes	—
106	C₂²	C₂×C₄×Dic₇₉	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	C₈×Dic₇₉	1	2	yes	—
110	C₄	C₂×C₈×D₇₉	1	2	yes	—
111	C₄	M₁₆×D₇₉	1	2	yes	—
112	C₄	#14579168	1	2	yes	—
113	C₂	—	2	2	no	—
114	C₂	C₂×C₈×Dic₇₉	1	1	yes	characteristic
115	C₂	M₁₆×Dic₇₉	1	1	yes	characteristic
116	C₂	#19098519	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#11929608

C₂

yes

maximal, characteristic

C₂×C₄×C₇₉⋊C₈

C₂

yes

maximal, characteristic

#19098285

C₂

yes

maximal, complemented

C₈×C₇₉⋊C₈

C₂

yes

maximal, complemented

#431×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₄

yes

—

C₂²×C₇₉⋊C₈

C₄

yes

—

#14579072

C₄

yes

—

C₄×C₇₉⋊C₈

C₄

yes

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₄

yes

—

C₂²⋊C₈×C₇₉

C₄

yes

—

C₄×C₈×C₇₉

C₂²

yes

—

#11929608

C₈

yes

complemented

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₂×C₈

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

C₂×C₈

yes

complemented

C₇₉⋊C₈

M₁₆

yes

complemented

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₄×C₈

yes

—

C₂²×C₇₉

C₂×C₄²

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄×C₈

yes

—

C₄×C₇₉

C₂²×C₈

yes

—

C₄×C₇₉

C₂×M₁₆

yes

—

C₄×C₇₉

#131

yes

—

C₂×C₇₉

—

C₂×C₇₉

C₂×C₄×C₈

yes

characteristic

C₂×C₇₉

C₄×M₁₆

yes

characteristic

C₂×C₇₉

#405

yes

characteristic

C₈×M₁₆

—

maximal, Sylow

C₇₉

C₈×M₁₆

yes

characteristic, complemented, Sylow

#431

D₇₉

yes

characteristic

C₄×M₁₆

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₄⋊C₈

Dic₇₉

yes

—

C₂²⋊C₈

Dic₇₉

yes

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

—

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

C₂×Dic₇₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₂×Dic₇₉

yes

—

C₄²

C₄×D₇₉

yes

characteristic

C₄²

C₄×D₇₉

yes

characteristic

C₄²

C₂×Dic₇₉

yes

characteristic

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

C₄×Dic₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₇₉

yes

characteristic

C₂×C₄

C₄×Dic₇₉

yes

characteristic

C₂×C₄

C₄×Dic₇₉

yes

characteristic

C₂×C₄

C₈×D₇₉

yes

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

C₂²×Dic₇₉

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

102

C₈

—

158

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₈×Dic₇₉

yes

—

106

C₂²

C₂×C₄×Dic₇₉

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

C₈×Dic₇₉

yes

—

110

C₄

C₂×C₈×D₇₉

yes

—

111

C₄

M₁₆×D₇₉

yes

—

112

C₄

#14579168

yes

—

113

C₂

—

114

C₂

C₂×C₈×Dic₇₉

yes

characteristic

115

C₂

M₁₆×Dic₇₉

yes

characteristic

116

C₂

#19098519

yes

characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₇₉
commutator	C₂×C₇₉	C₂×C₄×C₈
Fitting	#431×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄²
prime radical	C₂³×C₇₉	C₄²
cosocle	C₄²×C₇₉	C₂³
hypercenter	#431	D₇₉
hypocenter	C₇₉	C₈×M₁₆
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄² ◁ #431

subgroup

G/H

center, Frattini

C₄²

C₂²×D₇₉

commutator

C₂×C₇₉

C₂×C₄×C₈

Fitting

#431×C₇₉

C₂

socle

C₂²×C₇₉

C₂×C₄²

prime radical

C₂³×C₇₉

C₄²

cosocle

C₄²×C₇₉

C₂³

hypercenter

#431

D₇₉

hypocenter

C₇₉

C₈×M₁₆

LCS

G ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₄² ◁ #431

N	H ≅ G/N	type
3. #19098285	C₂	semidirect
4. C₈×C₇₉⋊C₈	C₂	semidirect
17. #11929608	C₈	semidirect
42. C₇₉⋊C₈	C₂×C₈	semidirect
43. C₇₉⋊C₈	M₁₆	semidirect
59. C₇₉	C₈×M₁₆	semidirect

H ≅ G/N

type

3. #19098285

C₂

semidirect

4. C₈×C₇₉⋊C₈

C₂

semidirect

17. #11929608

C₈

semidirect

42. C₇₉⋊C₈

C₂×C₈

semidirect

43. C₇₉⋊C₈

M₁₆

semidirect

59. C₇₉

C₈×M₁₆

semidirect

Subgroups — #23761681

Conjugacy classes of subgroups

Complements