Group #16818820 — subgroups

Subgroups — #16818820

Order 3712.

172 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14271573	C₂	1	2	yes	maximal
2	#14271533	C₂	1	1	yes	maximal, characteristic
3	#14270905	C₂	1	1	yes	maximal, characteristic
4	#14270905	C₂	1	2	yes	maximal
5	C₂₉×#564	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#125	—	2	2	no	—
7	C₂₉×#125	—	2	2	no	—
8	C₂₉×#125	—	2	2	no	—
9	C₂₉×#125	C₂²	1	1	yes	characteristic
10	C₂₉×#125	C₂²	1	2	yes	—
11	#11745231	C₂²	1	1	yes	characteristic
12	#11745158	—	2	2	no	—
13	#11745156	—	2	2	no	—
14	#11745155	—	2	2	no	—
15	#11745151	C₂²	1	1	yes	characteristic
16	#11745151	C₂²	1	2	yes	—
17	C₂×Dic₅₈	—	2	1	no	—
18	C₄⋊C₄×C₂₉	—	2	2	no	—
19	C₄⋊C₄×C₂₉	—	2	2	no	—
20	C₄⋊C₄×C₂₉	—	2	2	no	—
21	C₄⋊C₄×C₂₉	—	2	2	no	—
22	C₄⋊C₄×C₂₉	—	2	2	no	—
23	C₄⋊C₄×C₂₉	—	2	2	no	—
24	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
25	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
26	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
27	C₄²×C₂₉	—	2	2	no	—
28	C₄²×C₂₉	C₂³	1	1	yes	characteristic
29	C₄⋊Dic₂₉	—	2	2	no	—
30	C₂×#6597	—	2	2	no	—
31	C₂×#6597	—	2	1	no	—
32	C₂×C₄×C₂₉	—	2	2	no	—
33	C₂×C₄×C₂₉	—	2	2	no	—
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₂₉	—	4	1	no	—
38	Dic₅₈	—	4	2	no	—
39	#6597	—	2	4	no	—
40	#6597	—	4	1	no	—
41	#1663	—	29	1	no	maximal, Sylow
42	C₂²×C₂₉	#120	1	1	yes	characteristic
43	C₄×C₂₉	—	2	1	no	—
44	C₄×C₂₉	—	2	2	no	—
45	C₄×C₂₉	—	4	2	no	—
46	C₄×C₂₉	—	4	2	no	—
47	C₄×C₂₉	—	4	2	no	—
48	Dic₂₉	—	8	1	no	—
49	#564	D₂₉	1	1	yes	characteristic
50	#501	—	29	2	no	—
51	#491	—	29	1	no	—
52	#330	—	29	2	no	—
53	#330	—	29	1	no	—
54	C₂×C₂₉	#454	1	1	yes	characteristic
55	C₂×C₂₉	#456	1	2	yes	—
56	C₄⋊Q₈	—	29	1	no	—
57	#125	—	2	2	no	—
58	#125	—	2	2	no	—
59	#125	—	2	2	no	—
60	#125	C₂×D₂₉	1	1	yes	characteristic
61	#125	C₂×D₂₉	1	2	yes	—
62	#107	—	58	2	no	—
63	#106	—	58	2	no	—
64	#103	—	58	2	no	—
65	#97	—	29	1	no	—
66	#97	—	29	2	no	—
67	C₂₉	#1663	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₈	—	58	1	no	—
69	C₂×C₈	—	58	2	no	—
70	C₂×C₈	—	58	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	—	2	2	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	58	2	no	—
78	C₄⋊C₄	C₂²⋊D₂₉	1	2	yes	—
79	C₄⋊C₄	C₂²⋊D₂₉	1	2	yes	—
80	C₄⋊C₄	C₂²⋊D₂₉	1	2	yes	—
81	C₄²	—	2	2	no	—
82	C₄²	C₂²×D₂₉	1	1	yes	characteristic
83	Q₈	—	116	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	116	1	no	—
88	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
90	C₈	—	58	4	no	—
91	C₈	—	116	1	no	—
92	C₂²	#11745315	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	4	2	no	—
97	C₄	—	4	2	no	—
98	C₄	—	232	1	no	—
99	C₂	#14271336	1	1	yes	characteristic
100	C₂	#14271346	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271573

C₂

yes

maximal

#14271533

C₂

yes

maximal, characteristic

#14270905

C₂

yes

maximal, characteristic

#14270905

C₂

yes

maximal

C₂₉×#564

C₂

yes

maximal, characteristic

C₂₉×#125

—

C₂₉×#125

—

C₂₉×#125

—

C₂₉×#125

C₂²

yes

characteristic

C₂₉×#125

C₂²

yes

—

#11745231

C₂²

yes

—

—

—

C₂²

yes

characteristic

#11745151

C₂²

yes

—

C₂×Dic₅₈

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

Dic₅₈

—

—

—

—

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

#564

D₂₉

yes

—

—

—

—

C₂×C₂₉

#454

yes

characteristic

C₂×C₂₉

#456

yes

—

C₄⋊Q₈

—

—

—

—

C₂×D₂₉

yes

characteristic

#125

C₂×D₂₉

yes

—

—

—

—

—

—

C₂₉

#1663

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₂₉

yes

—

C₄⋊C₄

C₂²⋊D₂₉

yes

—

C₄⋊C₄

C₂²⋊D₂₉

yes

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

—

116

—

C₂²

#11745315

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

232

—

C₂

#14271336

yes

characteristic

100

C₂

#14271346

yes

—

	subgroup	G/H
center	C₂²	#11745315
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#564	C₂
socle, prime radical	C₂²×C₂₉	#120
hypercenter	#564	D₂₉
hypocenter	C₂₉	#1663
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

subgroup

G/H

center

C₂²

#11745315

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#564

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #564

N	H ≅ G/N	type
67. C₂₉	#1663	semidirect

H ≅ G/N

type

67. C₂₉

#1663

semidirect

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

subgroup	index
#14271573	2
#14271533	2
#14270905	2
C₂₉×#564	2
#1663	29

subgroup

index

C₂₉×#564

Subgroups — #16818820

Conjugacy classes of subgroups

Complements

Maximal subgroups