Group #23763556 — subgroups

Subgroups — #23763556

Order 10112.

280 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₂×#14579092	C₂	1	4	yes	maximal
2	C₂×C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#19098433	C₂	1	1	yes	maximal, characteristic
4	#384×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₇₉⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₇₉	—	2	2	no	—
7	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
8	#14579092	—	2	8	no	—
9	C₄×C₇₉⋊C₈	C₄	1	4	yes	complemented
10	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
11	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×Dic₇₉	—	2	2	no	—
14	C₂×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
15	C₂×C₇₉⋊C₈	D₄	1	4	yes	—
16	C₂×C₇₉⋊C₈	Q₈	1	4	yes	—
17	C₄⋊Dic₇₉	—	2	4	no	—
18	C₄⋊Dic₇₉	—	4	4	no	—
19	C₂²×C₄×C₇₉	—	2	2	no	—
20	C₂²×C₄×C₇₉	D₄	1	2	yes	—
21	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₇₉	—	2	4	no	—
23	C₄⋊C₄×C₇₉	—	4	4	no	—
24	C₄²×C₇₉	C₂×C₄	1	2	yes	—
25	C₄²×C₇₉	Q₈	1	2	yes	—
26	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₇₉	—	4	2	no	—
28	C₂×C₄×C₇₉	—	4	4	no	—
29	C₂×C₄×C₇₉	C₄⋊C₄	1	4	yes	—
30	C₂×C₄×C₇₉	SD₁₆	1	4	yes	—
31	C₂×C₄×C₇₉	SD₁₆	1	4	yes	—
32	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
36	C₂×Dic₇₉	—	4	2	no	—
37	C₂×Dic₇₉	—	4	4	no	—
38	C₇₉⋊C₈	C₄⋊C₄	1	8	yes	complemented
39	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₇₉	#127	1	1	yes	characteristic
41	C₂²×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₇₉	C₂×SD₁₆	1	2	yes	—
43	C₂²×C₇₉	C₂×SD₁₆	1	2	yes	—
44	C₄×C₇₉	—	8	2	no	—
45	C₄×C₇₉	#106	1	8	yes	complemented
46	C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
47	C₄×C₇₉	C₄⋊Q₈	1	2	yes	—
48	Dic₇₉	—	8	2	no	—
49	C₂×C₇₉	#384	1	1	yes	characteristic
50	C₂×C₇₉	C₂×#106	1	2	yes	—
51	C₂×C₇₉	#492	1	1	yes	characteristic
52	C₂×C₇₉	#492	1	1	yes	characteristic
53	C₂×C₇₉	#498	1	2	yes	—
54	#1844	—	79	1	no	maximal, Sylow
55	C₇₉	#1844	1	1	yes	characteristic, complemented, Sylow
56	C₂×#106	—	79	4	no	—
57	C₂×C₄×C₈	—	79	1	no	—
58	#384	—	79	1	no	—
59	#384	D₇₉	1	1	yes	characteristic
60	C₂²×C₈	—	79	2	no	—
61	C₂×C₄⋊C₄	—	2	2	no	—
62	C₂×C₄⋊C₄	—	79	2	no	—
63	C₂×C₄⋊C₄	—	158	2	no	—
64	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
65	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
66	#106	—	158	8	no	—
67	C₄×C₈	—	79	4	no	—
68	C₂²×C₄	—	2	2	no	—
69	C₂²×C₄	—	158	2	no	—
70	C₂²×C₄	C₂²⋊D₇₉	1	2	yes	—
71	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
72	C₂×C₈	—	79	4	no	—
73	C₂×C₈	—	79	4	no	—
74	C₂×C₈	—	79	4	no	—
75	C₄⋊C₄	—	2	4	no	—
76	C₄⋊C₄	—	4	4	no	—
77	C₄⋊C₄	—	316	4	no	—
78	C₄⋊C₄	—	158	4	no	—
79	C₄²	Dic₁₅₈	1	2	yes	—
80	C₄²	C₄×D₇₉	1	2	yes	—
81	C₂³	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	4	4	no	—
84	C₂×C₄	—	316	2	no	—
85	C₂×C₄	—	316	4	no	—
86	C₂×C₄	Dic₇₉⋊C₄	1	4	yes	—
87	C₂×C₄	#11929611	1	4	yes	—
88	C₂×C₄	#11929612	1	4	yes	—
89	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
90	C₂×C₄	D₄×D₇₉	1	2	yes	—
91	C₂×C₄	Q₈×D₇₉	1	2	yes	—
92	C₂×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
93	C₈	—	79	8	no	—
94	C₂²	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
95	C₂²	#14579157	1	1	yes	characteristic
96	C₂²	#14579159	1	1	yes	characteristic
97	C₂²	C₂×#11929611	1	2	yes	—
98	C₂²	C₂×#11929612	1	2	yes	—
99	C₄	—	8	2	no	—
100	C₄	—	632	2	no	—
101	C₄	#14579092	1	8	yes	complemented
102	C₄	C₄⋊C₄×D₇₉	1	2	yes	—
103	C₄	#14579160	1	2	yes	—
104	C₂	#19098432	1	1	yes	characteristic
105	C₂	C₂×#14579092	1	2	yes	—
106	C₂	#19098935	1	1	yes	characteristic
107	C₂	#19098937	1	1	yes	characteristic
108	C₂	#19098959	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579092

C₂

yes

maximal

C₂×C₄×C₇₉⋊C₈

C₂

yes

maximal, characteristic

#19098433

C₂

yes

maximal, characteristic

#384×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

#14579092

—

C₄×C₇₉⋊C₈

C₄

yes

complemented

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₂×C₇₉⋊C₈

Q₈

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

Q₈

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

SD₁₆

yes

—

C₂×C₄×C₇₉

SD₁₆

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₇₉⋊C₈

C₄⋊C₄

yes

complemented

C₂²×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₉

#127

yes

characteristic

C₂²×C₇₉

C₄⋊Q₈

yes

characteristic

C₂²×C₇₉

C₂×SD₁₆

yes

—

C₂²×C₇₉

C₂×SD₁₆

yes

—

C₄×C₇₉

—

C₄×C₇₉

#106

yes

complemented

C₄×C₇₉

C₂×C₄⋊C₄

yes

—

C₄×C₇₉

C₄⋊Q₈

yes

—

Dic₇₉

—

C₂×C₇₉

#384

yes

characteristic

C₂×C₇₉

C₂×#106

yes

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

#1844

—

maximal, Sylow

C₇₉

#1844

yes

characteristic, complemented, Sylow

C₂×#106

—

C₂×C₄×C₈

—

#384

—

#384

D₇₉

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#106

—

158

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²⋊D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄²

Dic₁₅₈

yes

—

C₄²

C₄×D₇₉

yes

—

C₂³

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

Dic₇₉⋊C₄

yes

—

C₂×C₄

#11929611

yes

—

C₂×C₄

#11929612

yes

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

D₄×D₇₉

yes

—

C₂×C₄

Q₈×D₇₉

yes

—

C₂×C₄

C₂×Dic₁₅₈

yes

characteristic

C₈

—

C₂²

C₂×Dic₇₉⋊C₄

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×#11929612

yes

—

C₄

—

100

C₄

—

632

—

101

C₄

#14579092

yes

complemented

102

C₄

C₄⋊C₄×D₇₉

yes

—

103

C₄

#14579160

yes

—

104

C₂

#19098432

yes

characteristic

105

C₂

C₂×#14579092

yes

—

106

C₂

#19098935

yes

characteristic

107

C₂

#19098937

yes

characteristic

108

C₂

#19098959

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#384×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#384	D₇₉
hypocenter	C₇₉	#1844
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#384×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
9. C₄×C₇₉⋊C₈	C₄	semidirect
38. C₇₉⋊C₈	C₄⋊C₄	semidirect
45. C₄×C₇₉	#106	semidirect
55. C₇₉	#1844	semidirect
101. C₄	#14579092	semidirect

H ≅ G/N

type

9. C₄×C₇₉⋊C₈

C₄

semidirect

38. C₇₉⋊C₈

C₄⋊C₄

semidirect

45. C₄×C₇₉

#106

semidirect

55. C₇₉

#1844

semidirect

101. C₄

#14579092

semidirect

Subgroups — #23763556

Conjugacy classes of subgroups

Complements