Group #23761298 — subgroups

Subgroups — #23761298

Order 10112.

144 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 61 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	#19098616	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579072	C₂	1	1	yes	maximal, characteristic
3	#432×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₇₉⋊C₈	—	2	1	no	—
5	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
6	C₂²⋊(C₇₉⋊C₈)	C₄	1	2	yes	—
7	#14579072	—	2	1	no	—
8	#14579072	C₄	1	2	yes	—
9	C₄×C₇₉⋊C₈	—	2	1	no	—
10	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₇₉	C₄	1	2	yes	—
12	C₂²⋊C₈×C₇₉	—	2	1	no	—
13	#97×C₇₉	—	2	1	no	—
14	C₂×C₇₉⋊C₈	—	2	4	no	—
15	C₂×C₇₉⋊C₈	—	2	2	no	—
16	C₂×C₇₉⋊C₈	—	2	2	no	—
17	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₇₉	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₇₉	—	2	2	no	—
21	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₇₉	D₄	1	1	yes	characteristic
24	C₄²×C₇₉	D₄	1	1	yes	characteristic
25	C₂³×C₇₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₇₉	—	2	2	no	—
27	C₂×C₄×C₇₉	—	2	2	no	—
28	C₂×C₄×C₇₉	—	4	1	no	—
29	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
35	C₈×C₇₉	—	4	2	no	—
36	C₇₉⋊C₈	—	2	4	no	—
37	C₇₉⋊C₈	—	4	2	no	—
38	C₂²×C₇₉	—	2	1	no	—
39	C₂²×C₇₉	—	2	1	no	—
40	C₂²×C₇₉	#95	1	1	yes	characteristic
41	C₂²×C₇₉	#108	1	2	yes	—
42	C₄×C₇₉	—	2	1	no	—
43	C₄×C₇₉	—	2	1	no	—
44	C₄×C₇₉	—	2	1	no	—
45	C₄×C₇₉	—	2	1	no	—
46	C₄×C₇₉	—	2	1	no	—
47	C₄×C₇₉	#104	1	2	yes	—
48	C₂×C₇₉	—	2	2	no	—
49	C₂×C₇₉	#339	1	1	yes	characteristic
50	C₂×C₇₉	#341	1	1	yes	characteristic
51	C₂×C₇₉	#344	1	1	yes	characteristic
52	#1302	—	79	1	no	maximal, Sylow
53	C₇₉	#1302	1	1	yes	characteristic, complemented, Sylow
54	#432	D₇₉	1	1	yes	characteristic
55	#431	—	79	1	no	—
56	C₂×#97	—	79	1	no	—
57	C₂²×C₈	—	158	1	no	—
58	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
59	C₄⋊C₈	—	158	1	no	—
60	C₄⋊C₈	Dic₇₉	1	2	yes	—
61	C₂²⋊C₈	—	2	1	no	—
62	C₂²⋊C₈	—	79	2	no	—
63	#97	—	2	1	no	—
64	#97	—	79	2	no	—
65	#97	—	158	1	no	—
66	C₄×C₈	—	158	1	no	—
67	C₂²×C₄	Dic₁₅₈	1	1	yes	characteristic
68	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
69	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
70	C₂×C₈	—	2	2	no	—
71	C₂×C₈	—	158	2	no	—
72	C₂×C₈	—	158	4	no	—
73	C₂×C₈	—	158	2	no	—
74	C₄²	C₄×D₇₉	1	1	yes	characteristic
75	C₄²	D₃₁₆	1	1	yes	characteristic
76	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
77	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
78	C₂³	Dic₇₉⋊C₄	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
83	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
84	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
85	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
86	C₂×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
87	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
88	C₈	—	4	2	no	—
89	C₈	—	316	2	no	—
90	C₈	—	158	4	no	—
91	C₂²	—	2	1	no	—
92	C₂²	—	2	1	no	—
93	C₂²	C₇₉⋊#95	1	1	yes	characteristic
94	C₂²	#14579096	1	2	yes	—
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	2	1	no	—
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	#14579088	1	2	yes	—
101	C₂	—	2	2	no	—
102	C₂	#19098322	1	1	yes	characteristic
103	C₂	#19098327	1	1	yes	characteristic
104	C₂	#19098334	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098616

C₂

yes

maximal, characteristic

C₂×#14579072

C₂

yes

maximal, characteristic

#432×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

C₄

yes

—

#14579072

—

#14579072

C₄

yes

—

C₄×C₇₉⋊C₈

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₄

yes

—

C₂²⋊C₈×C₇₉

—

#97×C₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

Q₈

yes

characteristic

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₂³×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#95

yes

characteristic

C₂²×C₇₉

#108

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#104

yes

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#432

D₇₉

yes

characteristic

#431

—

C₂×#97

—

C₂²×C₈

—

158

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₄⋊C₈

—

158

—

C₄⋊C₈

Dic₇₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

#97

—

158

—

C₄×C₈

—

158

—

C₂²×C₄

Dic₁₅₈

yes

characteristic

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₄²

C₄×D₇₉

yes

characteristic

C₄²

D₃₁₆

yes

characteristic

C₄²

C₂×Dic₇₉

yes

characteristic

C₄²

C₂²⋊D₇₉

yes

characteristic

C₂³

Dic₇₉⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₇₉

yes

characteristic

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₇₉

yes

characteristic

C₂×C₄

Dic₇₉⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

C₈

—

C₈

—

316

—

C₈

—

158

—

C₂²

—

C₂²

—

C₂²

C₇₉⋊#95

yes

characteristic

C₂²

#14579096

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

100

C₄

#14579088

yes

—

101

C₂

—

102

C₂

#19098322

yes

characteristic

103

C₂

#19098327

yes

characteristic

104

C₂

#19098334

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₇₉
commutator	C₂×C₄×C₇₉	C₄²
Frattini	C₂×C₄²	C₂×D₇₉
Fitting	#432×C₇₉	C₂
socle	C₂²×C₇₉	#95
prime radical	C₂³×C₇₉	C₄⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂²
hypercenter	#432	D₇₉
hypocenter	C₇₉	#1302
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #432

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₇₉

commutator

C₂×C₄×C₇₉

C₄²

Frattini

C₂×C₄²

C₂×D₇₉

Fitting

#432×C₇₉

C₂

socle

C₂²×C₇₉

#95

prime radical

C₂³×C₇₉

C₄⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #432

N	H ≅ G/N	type
53. C₇₉	#1302	semidirect

H ≅ G/N

type

53. C₇₉

#1302

semidirect

Subgroups — #23761298

Conjugacy classes of subgroups

Complements