Group #16821711 — subgroups

Subgroups — #16821711

Order 3712.

124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14271421	C₂	1	1	yes	maximal, characteristic
2	#14270987	C₂	1	2	yes	maximal, complemented
3	#14270978	C₂	1	2	yes	maximal, complemented
4	#14270945	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#430	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₉	—	2	1	no	—
7	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
8	#11745286	—	2	1	no	—
9	C₂×Dic₁₁₆	C₂²	1	1	yes	characteristic
10	C₂₉×#108	—	2	1	no	—
11	C₂₉×#108	C₂²	1	2	yes	—
12	#11745165	C₂²	1	1	yes	characteristic
13	#11745164	—	2	1	no	—
14	#11745160	C₂²	1	2	yes	—
15	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
16	C₂×Dic₅₈	—	2	1	no	—
17	M₁₆×C₂₉	—	2	2	no	—
18	M₁₆×C₂₉	—	2	2	no	—
19	M₁₆×C₂₉	—	4	1	no	—
20	C₂×C₈×C₂₉	—	4	1	no	—
21	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
23	C₂²⋊Dic₂₉	—	4	1	no	—
24	C₄⋊Dic₂₉	—	2	1	no	—
25	#90779	—	4	1	no	—
26	Dic₁₁₆	—	2	2	no	—
27	#90768	—	2	2	no	—
28	C₂³×C₂₉	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₂₉	—	2	1	no	—
30	C₂×C₄×C₂₉	—	2	1	no	—
31	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₂₉	—	4	1	no	—
34	C₂×Dic₂₉	—	4	1	no	—
35	Dic₅₈	—	4	1	no	—
36	Dic₅₈	—	4	1	no	—
37	C₈×C₂₉	—	2	1	no	—
38	C₈×C₂₉	—	4	2	no	—
39	C₈×C₂₉	#41	1	2	yes	—
40	#2239	—	29	1	no	maximal, Sylow
41	C₂²×C₂₉	—	2	1	no	—
42	C₂²×C₂₉	—	4	1	no	—
43	C₂²×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
44	C₄×C₂₉	—	2	1	no	—
45	C₄×C₂₉	#123	1	1	yes	characteristic
46	C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
47	Dic₂₉	—	8	1	no	—
48	Dic₂₉	—	8	1	no	—
49	#470	—	29	1	no	—
50	#430	D₂₉	1	1	yes	characteristic
51	#365	—	29	2	no	—
52	#362	—	29	2	no	—
53	#349	—	29	1	no	—
54	C₂×C₂₉	—	2	1	no	—
55	C₂×C₂₉	—	4	1	no	—
56	C₂×C₂₉	#481	1	1	yes	characteristic
57	C₂×Q₁₆	—	29	1	no	—
58	C₂×M₁₆	—	2	1	no	—
59	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
60	C₂²⋊Q₈	—	58	1	no	—
61	M₃₂	—	29	2	no	—
62	#108	—	2	1	no	—
63	#108	C₂×D₂₉	1	2	yes	—
64	#106	—	29	1	no	—
65	#103	—	58	1	no	—
66	C₂₉	#2239	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	58	1	no	—
68	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
69	Q₁₆	—	58	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	2	2	no	—
72	M₁₆	—	4	1	no	—
73	C₂×C₈	—	4	1	no	—
74	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
76	C₄⋊C₄	—	58	1	no	—
77	C₄⋊C₄	—	116	1	no	—
78	C₂²⋊C₄	—	116	1	no	—
79	C₁₆	—	58	2	no	—
80	C₂³	#90784	1	1	yes	characteristic
81	Q₈	—	116	1	no	—
82	Q₈	—	116	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	116	1	no	—
86	C₂×C₄	—	116	1	no	—
87	C₂×C₄	#90784	1	1	yes	characteristic
88	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	4	2	no	—
91	C₈	#90805	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×#90784	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	232	1	no	—
97	C₄	—	232	1	no	—
98	C₄	#11745291	1	1	yes	characteristic
99	C₄	#11745294	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	#14271481	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271421

C₂

yes

maximal, characteristic

#14270987

C₂

yes

maximal, complemented

#14270978

C₂

yes

maximal, complemented

#14270945

C₂

yes

maximal, characteristic

C₂₉×#430

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

—

C₂×M₁₆×C₂₉

C₂²

yes

characteristic

#11745286

—

C₂×Dic₁₁₆

C₂²

yes

characteristic

C₂₉×#108

—

C₂₉×#108

C₂²

yes

—

#11745165

C₂²

yes

characteristic

#11745164

—

#11745160

C₂²

yes

—

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂×Dic₅₈

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

C₂³

yes

characteristic

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

#90779

—

Dic₁₁₆

—

#90768

—

C₂³×C₂₉

SD₁₆

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

SD₁₆

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

#41

yes

—

#2239

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×SD₁₆

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

#470

—

#430

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#481

yes

characteristic

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

characteristic

C₂²⋊Q₈

—

M₃₂

—

#108

—

#108

C₂×D₂₉

yes

—

#106

—

#103

—

C₂₉

#2239

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₂×C₈

C₂²×D₂₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

116

—

C₂²⋊C₄

—

116

—

C₁₆

—

C₂³

#90784

yes

characteristic

Q₈

—

116

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

#90784

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

—

C₈

#90805

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#90784

yes

characteristic

C₄

—

C₄

—

232

—

C₄

—

232

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#14271481

yes

characteristic

	subgroup	G/H
center	C₂	#14271481
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂₉×#430	C₂
socle	C₂×C₂₉	#481
prime radical	C₂³×C₂₉	SD₁₆
hypercenter	#430	D₂₉
hypocenter	C₂₉	#2239
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #430

subgroup

G/H

center

C₂

#14271481

commutator, cosocle

C₂×C₈×C₂₉

C₂³

Frattini

C₂×C₈

C₂²×D₂₉

Fitting

C₂₉×#430

C₂

socle

C₂×C₂₉

#481

prime radical

C₂³×C₂₉

SD₁₆

D₂₉

C₂₉

G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #430

N	H ≅ G/N	type
2. #14270987	C₂	semidirect
3. #14270978	C₂	semidirect
66. C₂₉	#2239	semidirect

H ≅ G/N

type

2. #14270987

C₂

semidirect

3. #14270978

C₂

semidirect

66. C₂₉

#2239

semidirect

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

subgroup	index
#14271421	2
#14270987	2
#14270978	2
#14270945	2
C₂₉×#430	2
#2239	29

subgroup

index

C₂₉×#430

Subgroups — #16821711

Conjugacy classes of subgroups

Complements

Maximal subgroups