Group #16821067 — subgroups

Subgroups — #16821067

Order 3712.

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

normal subgroups only

This group has 158 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	#14271212	C₂	1	1	yes	maximal, characteristic
2	#14270935	C₂	1	2	yes	maximal
3	#14270923	C₂	1	2	yes	maximal
4	#14270920	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#423	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	#11745288	C₂²	1	2	yes	—
10	C₂×#90777	C₂²	1	2	yes	—
11	C₂₉×C₄⋊C₈	—	2	2	no	—
12	#11745167	—	2	2	no	—
13	C₂²×C₄×C₂₉	—	2	1	no	—
14	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	M₁₆×C₂₉	—	2	2	no	—
16	M₁₆×C₂₉	—	2	2	no	—
17	C₂×C₈×C₂₉	—	2	1	no	—
18	C₂×C₈×C₂₉	D₄	1	2	yes	—
19	C₄²×C₂₉	—	2	1	no	—
20	C₄²×C₂₉	Q₈	1	1	yes	characteristic
21	C₄²×C₂₉	Q₈	1	1	yes	characteristic
22	C₂²⋊Dic₂₉	—	2	2	no	—
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄×Dic₂₉	—	2	2	no	—
25	#90777	—	2	2	no	—
26	#90777	—	2	2	no	—
27	C₂×#6597	—	2	2	no	—
28	C₂³×C₂₉	#41	1	1	yes	characteristic
29	C₂×C₄×C₂₉	—	2	1	no	—
30	C₂×C₄×C₂₉	—	2	1	no	—
31	C₂×C₄×C₂₉	—	4	2	no	—
32	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₂₉	#41	1	2	yes	—
35	C₂×C₄×C₂₉	#41	1	2	yes	—
36	C₂×Dic₂₉	—	4	2	no	—
37	C₈×C₂₉	—	2	2	no	—
38	C₈×C₂₉	—	4	1	no	—
39	#6597	—	4	2	no	—
40	#2102	—	29	1	no	maximal, Sylow
41	C₂²×C₂₉	—	4	1	no	—
42	C₂²×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂²×C₂₉	#126	1	2	yes	—
44	C₄×C₂₉	—	2	2	no	—
45	C₄×C₂₉	—	4	1	no	—
46	C₄×C₂₉	#123	1	1	yes	characteristic
47	C₄×C₂₉	#124	1	1	yes	characteristic
48	C₄×C₂₉	#125	1	2	yes	—
49	Dic₂₉	—	8	2	no	—
50	#430	—	29	1	no	—
51	#423	D₂₉	1	1	yes	characteristic
52	#344	—	29	2	no	—
53	#339	—	29	2	no	—
54	H(3,ℤ/4)	—	29	1	no	—
55	C₂×C₂₉	—	2	2	no	—
56	C₂×C₂₉	—	2	1	no	—
57	C₂×C₂₉	#400	1	1	yes	characteristic
58	C₂×M₁₆	—	29	2	no	—
59	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
60	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
61	#117	—	29	2	no	—
62	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
63	#108	—	58	2	no	—
64	C₄⋊C₈	—	2	2	no	—
65	C₂₉	#2102	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	2	1	no	—
67	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	58	2	no	—
71	M₁₆	—	58	2	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	58	2	no	—
74	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
75	C₄⋊C₄	—	58	2	no	—
76	C₂²⋊C₄	—	58	2	no	—
77	C₄²	—	2	1	no	—
78	C₄²	—	58	2	no	—
79	C₄²	Dic₅₈	1	1	yes	characteristic
80	C₄²	Dic₅₈	1	1	yes	characteristic
81	C₂³	#90805	1	1	yes	characteristic
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	4	2	no	—
85	C₂×C₄	—	116	2	no	—
86	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
87	C₂×C₄	#90807	1	2	yes	—
88	C₂×C₄	#90809	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	4	1	no	—
92	C₈	—	116	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#11745260	1	2	yes	—
95	C₂²	#11745286	1	1	yes	characteristic
96	C₄	—	2	2	no	—
97	C₄	—	4	1	no	—
98	C₄	—	232	2	no	—
99	C₄	#11745252	1	2	yes	—
100	C₄	#11745297	1	1	yes	characteristic
101	C₄	#11745309	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	2	2	no	—
104	C₂	#14271102	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271212

C₂

yes

maximal, characteristic

#14270935

C₂

yes

maximal

#14270923

C₂

yes

maximal

#14270920

C₂

yes

maximal, characteristic

C₂₉×#423

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

#11745288

C₂²

yes

—

C₂×#90777

C₂²

yes

—

C₂₉×C₄⋊C₈

—

#11745167

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

Q₈

yes

characteristic

C₄²×C₂₉

Q₈

yes

characteristic

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

#90777

—

#90777

—

C₂×#6597

—

C₂³×C₂₉

#41

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

#6597

—

#2102

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₂₉

#126

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

Dic₂₉

—

#430

—

#423

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#400

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

characteristic

C₂×M₁₆

C₂×D₂₉

yes

characteristic

#117

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₂₉

#2102

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

Dic₅₈

yes

characteristic

C₄²

Dic₅₈

yes

characteristic

C₂³

#90805

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂×Dic₅₈

yes

characteristic

C₂×C₄

#90807

yes

—

C₂×C₄

#90809

yes

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

—

C₈

—

116

—

C₂²

—

C₂²

#11745260

yes

—

C₂²

#11745286

yes

characteristic

C₄

—

C₄

—

C₄

—

232

—

C₄

#11745252

yes

—

100

C₄

#11745297

yes

characteristic

101

C₄

#11745309

yes

characteristic

102

C₂

—

103

C₂

—

104

C₂

#14271102

yes

characteristic

	subgroup	G/H
center	C₄	#11745309
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#423	C₂
socle	C₂×C₂₉	#400
prime radical	C₂³×C₂₉	#41
hypercenter	#423	D₂₉
hypocenter	C₂₉	#2102
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #423

subgroup

G/H

center

C₄

#11745309

commutator, cosocle

C₂²×C₄×C₂₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#423

C₂

C₂×C₂₉

C₂³×C₂₉

D₂₉

C₂₉

G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #423

N	H ≅ G/N	type
65. C₂₉	#2102	semidirect

H ≅ G/N

type

65. C₂₉

#2102

semidirect

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

subgroup	index
#14271212	2
#14270935	2
#14270923	2
#14270920	2
C₂₉×#423	2
#2102	29

subgroup

index

C₂₉×#423

Subgroups — #16821067

Conjugacy classes of subgroups

Complements

Maximal subgroups