Group #16821247 — subgroups

Subgroups — #16821247

Order 3712.

172 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11745160	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	#14270981	C₂	1	4	yes	maximal, complemented
4	C₂×C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
7	C₂²×#6597	C₄	1	1	yes	characteristic
8	C₂₉×M₃₂	—	2	2	no	—
9	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
10	C₈×Dic₂₉	C₄	1	2	yes	—
11	C₈×Dic₂₉	C₂²	1	2	yes	—
12	#11745160	—	2	2	no	—
13	C₂×#90768	C₂²	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₂₉	C₈	1	2	yes	—
16	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₂₉	D₄	1	2	yes	—
18	C₂×C₈×C₂₉	Q₈	1	2	yes	—
19	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
20	C₄×Dic₂₉	C₈	1	1	yes	characteristic
21	C₄×Dic₂₉	C₈	1	1	yes	characteristic
22	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
23	C₂×#6597	—	2	2	no	—
24	C₂×#6597	C₂×C₄	1	2	yes	—
25	C₁₆×C₂₉	—	2	2	no	—
26	#90768	—	2	2	no	—
27	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
31	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₂₉	—	2	4	no	—
33	C₂×Dic₂₉	C₂×C₈	1	2	yes	—
34	C₂×Dic₂₉	C₂×C₈	1	2	yes	—
35	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
36	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
37	C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
38	#6597	—	2	2	no	—
39	#2150	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	—	2	2	no	—
41	C₂²×C₂₉	C₄⋊C₈	1	2	yes	—
42	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
43	C₄×C₂₉	C₄⋊C₈	1	2	yes	—
44	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
46	Dic₂₉	—	2	2	no	—
47	Dic₂₉	M₃₂	1	4	yes	complemented
48	C₂×M₃₂	—	29	1	no	—
49	C₂×M₃₂	D₂₉	1	1	yes	characteristic
50	C₂×C₄×C₈	—	29	1	no	—
51	C₄⋊C₁₆	—	29	4	no	—
52	C₂×C₂₉	—	2	2	no	—
53	C₂×C₂₉	C₂×C₄⋊C₈	1	1	yes	characteristic
54	C₂×C₂₉	C₂×M₃₂	1	2	yes	—
55	C₂²×C₈	—	29	1	no	—
56	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
57	C₂×C₄²	—	29	1	no	—
58	M₃₂	—	2	2	no	—
59	M₃₂	—	58	2	no	—
60	C₂×C₁₆	—	29	2	no	—
61	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
62	C₄×C₈	—	29	2	no	—
63	C₄×C₈	—	29	2	no	—
64	C₂₉	#2150	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₄	—	29	2	no	—
66	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
67	C₂×C₈	—	29	2	no	—
68	C₂×C₈	—	58	2	no	—
69	C₂×C₈	Dic₅₈	1	2	yes	—
70	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
71	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
72	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
73	C₄²	—	29	1	no	—
74	C₄²	—	29	1	no	—
75	C₄²	—	29	2	no	—
76	C₁₆	—	2	2	no	—
77	C₁₆	—	58	2	no	—
78	C₂³	C₈×D₂₉	1	1	yes	characteristic
79	C₂×C₄	—	29	2	no	—
80	C₂×C₄	—	29	2	no	—
81	C₂×C₄	—	58	4	no	—
82	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
83	C₂×C₄	#90772	1	2	yes	—
84	C₂×C₄	#90779	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
86	C₈	—	58	2	no	—
87	C₈	#90779	1	2	yes	—
88	C₈	C₂×Dic₅₈	1	1	yes	characteristic
89	C₈	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#11745162	1	2	yes	—
92	C₂²	C₂×C₈×D₂₉	1	1	yes	characteristic
93	C₄	—	29	4	no	—
94	C₄	—	58	2	no	—
95	C₄	#11745162	1	2	yes	—
96	C₄	C₂×#90772	1	1	yes	characteristic
97	C₄	C₂×#90779	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×#11745162	1	1	yes	characteristic
100	C₂	M₃₂×D₂₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745160

C₂

yes

maximal, characteristic

C₂×C₈×Dic₂₉

C₂

yes

maximal, characteristic

#14270981

C₂

yes

maximal, complemented

C₂×C₂₉×M₃₂

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

characteristic

C₂²×#6597

C₄

yes

characteristic

C₂₉×M₃₂

—

C₂×C₁₆×C₂₉

C₂²

yes

—

C₈×Dic₂₉

C₄

yes

—

C₈×Dic₂₉

C₂²

yes

—

#11745160

—

C₂×#90768

C₂²

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₈

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

Q₈

yes

—

C₂×C₈×C₂₉

C₂³

yes

characteristic

C₄×Dic₂₉

C₈

yes

characteristic

C₄×Dic₂₉

C₈

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

—

C₂×#6597

—

C₂×#6597

C₂×C₄

yes

—

C₁₆×C₂₉

—

#90768

—

C₂³×C₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₈×C₂₉

C₄⋊C₄

yes

—

C₈×C₂₉

C₂×D₄

yes

characteristic

C₈×C₂₉

C₂×Q₈

yes

—

—

C₂²×C₂₉

—

C₂²×C₂₉

C₄⋊C₈

yes

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₄×C₂₉

C₄⋊C₈

yes

—

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₂×M₁₆

yes

characteristic

Dic₂₉

—

Dic₂₉

M₃₂

yes

complemented

C₂×M₃₂

—

C₂×M₃₂

D₂₉

yes

characteristic

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂×C₂₉

—

C₂×C₂₉

C₂×C₄⋊C₈

yes

characteristic

C₂×C₂₉

C₂×M₃₂

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₂₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₂₉

#2150

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₄×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₅₈

yes

—

C₂×C₈

C₄×D₂₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₉

yes

—

C₂×C₈

C₂²×D₂₉

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

C₈×D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₂₉

yes

characteristic

C₂×C₄

#90772

yes

—

C₂×C₄

#90779

yes

—

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

C₈

—

C₈

#90779

yes

—

C₈

C₂×Dic₅₈

yes

characteristic

C₈

C₂×C₂²⋊D₂₉

yes

characteristic

C₂²

—

C₂²

#11745162

yes

—

C₂²

C₂×C₈×D₂₉

yes

characteristic

C₄

—

C₄

—

C₄

#11745162

yes

—

C₄

yes

C₄

yes

C₂

—

C₂

C₂×#11745162

yes

characteristic

100

C₂

M₃₂×D₂₉

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂²×C₈
Fitting	C₂×C₂₉×M₃₂	C₂
prime radical	C₂³×C₂₉	C₂×C₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	C₂×M₃₂	D₂₉
hypocenter	C₂₉	#2150
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₂₉

commutator, socle

C₂²×C₂₉

C₂²×C₈

Fitting

C₂×C₂₉×M₃₂

C₂

prime radical

C₂³×C₂₉

C₂×C₈

cosocle

C₂×C₈×C₂₉

C₂³

hypercenter

C₂×M₃₂

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #14270981	C₂	semidirect
47. Dic₂₉	M₃₂	semidirect
64. C₂₉	#2150	semidirect

H ≅ G/N

type

3. #14270981

C₂

semidirect

47. Dic₂₉

M₃₂

semidirect

64. C₂₉

#2150

semidirect

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

subgroup	index
C₂×#11745160	2
C₂×C₈×Dic₂₉	2
#14270981	2
C₂×C₂₉×M₃₂	2
#2150	29

subgroup

index

C₂×#11745160

C₂×C₈×Dic₂₉

#14270981

C₂×C₂₉×M₃₂

#2150

Subgroups — #16821247

Conjugacy classes of subgroups

Complements

Maximal subgroups