Group #16819010 — subgroups

Subgroups — #16819010

Order 3712.

152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14271568	C₂	1	1	yes	maximal, characteristic
2	#14271373	C₂	1	2	yes	maximal
3	#14270914	C₂	1	1	yes	maximal, characteristic
4	#14270908	C₂	1	2	yes	maximal
5	C₂₉×#446	C₂	1	1	yes	maximal, characteristic
6	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×#90785	—	2	2	no	—
8	#11745231	C₂²	1	2	yes	—
9	C₂₉×C₄⋊C₈	—	2	1	no	—
10	C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂₉×#97	—	2	1	no	—
12	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
13	#11745166	—	2	1	no	—
14	#11745166	—	2	1	no	—
15	#11745158	—	2	2	no	—
16	C₄⋊#6597	C₂²	1	2	yes	—
17	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
18	C₂×Dic₅₈	—	2	2	no	—
19	C₂×C₈×C₂₉	—	2	1	no	—
20	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₂₉	—	2	1	no	—
23	C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
24	C₄²×C₂₉	—	2	1	no	—
25	C₄²×C₂₉	C₂³	1	1	yes	characteristic
26	#90785	—	4	4	no	—
27	C₄⋊Dic₂₉	—	2	2	no	—
28	C₄⋊Dic₂₉	—	2	2	no	—
29	C₂×#6597	—	2	2	no	—
30	Q₈×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	—	2	1	no	—
32	C₂×C₄×C₂₉	—	2	1	no	—
33	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
36	C₂×Dic₂₉	—	4	2	no	—
37	Dic₅₈	—	4	2	no	—
38	Dic₅₈	—	4	2	no	—
39	C₈×C₂₉	—	2	1	no	—
40	C₈×C₂₉	—	4	1	no	—
41	C₈×C₂₉	Q₁₆	1	2	yes	complemented
42	#6597	—	4	2	no	—
43	#1694	—	29	1	no	maximal, Sylow
44	C₂²×C₂₉	#121	1	1	yes	characteristic
45	C₄×C₂₉	—	2	1	no	—
46	C₄×C₂₉	—	4	1	no	—
47	C₄×C₂₉	—	4	1	no	—
48	C₄×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
49	C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
50	C₄×C₂₉	#137	1	1	yes	characteristic
51	Dic₂₉	—	8	2	no	—
52	#500	—	29	1	no	—
53	#462	—	29	2	no	—
54	#446	D₂₉	1	1	yes	characteristic
55	#334	—	29	1	no	—
56	#332	—	29	2	no	—
57	C₂×C₂₉	#462	1	1	yes	characteristic
58	C₂×C₂₉	#469	1	1	yes	characteristic
59	C₂×C₂₉	#473	1	1	yes	characteristic
60	C₂×Q₁₆	—	58	2	no	—
61	C₄⋊Q₈	—	29	2	no	—
62	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic
63	#107	—	58	1	no	—
64	#107	—	58	1	no	—
65	C₄⋊C₈	—	2	1	no	—
66	C₄⋊C₈	—	29	2	no	—
67	C₄⋊C₈	C₂×D₂₉	1	1	yes	characteristic
68	#103	—	58	2	no	—
69	#97	—	2	1	no	—
70	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
71	C₂₉	#1694	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₈	—	58	2	no	—
73	C₂×Q₈	D₁₁₆	1	1	yes	characteristic
74	Q₁₆	—	116	4	no	—
75	C₂×C₈	—	2	1	no	—
76	C₂×C₈	—	58	2	no	—
77	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
79	C₄⋊C₄	—	2	1	no	—
80	C₄⋊C₄	—	58	2	no	—
81	C₄⋊C₄	—	58	2	no	—
82	C₄⋊C₄	D₁₁₆	1	1	yes	characteristic
83	C₄²	—	2	1	no	—
84	C₄²	C₂²×D₂₉	1	1	yes	characteristic
85	Q₈	—	2	2	no	—
86	Q₈	—	116	2	no	—
87	Q₈	—	116	2	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	116	2	no	—
91	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
92	C₂×C₄	#90805	1	1	yes	characteristic
93	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	4	1	no	—
96	C₈	—	116	2	no	—
97	C₈	#90785	1	2	yes	complemented
98	C₂²	#11745292	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	4	1	no	—
101	C₄	—	4	1	no	—
102	C₄	—	232	2	no	—
103	C₄	#11745270	1	2	yes	—
104	C₄	C₂×#90785	1	1	yes	characteristic
105	C₄	#11745313	1	1	yes	characteristic
106	C₂	#14271373	1	1	yes	characteristic
107	C₂	#14271416	1	1	yes	characteristic
108	C₂	#14271438	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271568

C₂

yes

maximal, characteristic

#14271373

C₂

yes

maximal

#14270914

C₂

yes

maximal, characteristic

#14270908

C₂

yes

maximal

C₂₉×#446

C₂

yes

maximal, characteristic

C₄×Q₈×C₂₉

C₂²

yes

characteristic

C₂×#90785

—

#11745231

C₂²

yes

—

C₂₉×C₄⋊C₈

—

C₂₉×C₄⋊C₈

C₂²

yes

characteristic

C₂₉×#97

—

C₄×C₈×C₂₉

C₂²

yes

—

—

—

C₂²

yes

—

C₂×Q₈×C₂₉

D₄

yes

characteristic

C₂×Dic₅₈

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

#90785

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

Q₁₆

yes

—

—

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×Q₁₆

yes

characteristic

C₄×C₂₉

AGL(1,ℤ/8)

yes

—

C₄×C₂₉

#137

yes

characteristic

Dic₂₉

—

#500

—

#462

—

#446

D₂₉

yes

characteristic

#334

—

#332

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₂₉

yes

characteristic

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₂₉

yes

characteristic

#103

—

#97

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1694

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

D₁₁₆

yes

characteristic

Q₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₁₆

yes

characteristic

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

Q₈

—

Q₈

—

116

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

#90805

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

—

C₈

—

116

—

C₈

yes

C₂²

yes

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

232

—

103

C₄

#11745270

yes

—

104

C₄

C₂×#90785

yes

characteristic

105

C₄

#11745313

yes

characteristic

106

C₂

#14271373

yes

characteristic

107

C₂

#14271416

yes

characteristic

108

C₂

#14271438

yes

characteristic

	subgroup	G/H
center	C₂²	#11745292
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#446	C₂
socle, prime radical	C₂²×C₂₉	#121
hypercenter	#446	D₂₉
hypocenter	C₂₉	#1694
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#11745292

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#446

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
41. C₈×C₂₉	Q₁₆	semidirect
71. C₂₉	#1694	semidirect
97. C₈	#90785	semidirect

H ≅ G/N

type

41. C₈×C₂₉

Q₁₆

semidirect

71. C₂₉

#1694

semidirect

97. C₈

#90785

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14271568	2
#14271373	2
#14270914	2
#14270908	2
C₂₉×#446	2
#1694	29

subgroup

index

C₂₉×#446

Subgroups — #16819010

Conjugacy classes of subgroups

Complements

Maximal subgroups