Group #16819081 — subgroups

Subgroups — #16819081

Order 3712.

224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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, complemented
2	#14271535	C₂	1	2	yes	maximal, complemented
3	#14271509	C₂	1	2	yes	maximal, complemented
4	C₈×#6597	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#493	C₂	1	1	yes	maximal, characteristic
6	C₂×D₈×C₂₉	—	2	2	no	—
7	C₂₉×#127	C₂²	1	2	yes	—
8	C₂×#90783	—	2	4	no	—
9	#11745231	C₂²	1	2	yes	—
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#11745180	—	2	4	no	—
12	#11745166	—	2	2	no	—
13	C₄×#6597	C₂²	1	1	yes	characteristic
14	C₄×#6597	C₂²	1	1	yes	characteristic
15	C₂×D₄×C₂₉	—	2	2	no	—
16	C₂×D₄×C₂₉	—	2	2	no	—
17	C₂×D₄×C₂₉	—	2	2	no	—
18	C₂×Dic₅₈	—	2	2	no	—
19	D₈×C₂₉	—	4	4	no	—
20	C₂×C₈×C₂₉	D₄	1	2	yes	—
21	C₄²×C₂₉	C₂³	1	1	yes	characteristic
22	#90783	—	4	8	no	—
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	—	2	2	no	—
25	C₂×#6597	D₄	1	2	yes	—
26	C₂×#6597	D₄	1	2	yes	—
27	C₂³×C₂₉	—	4	2	no	—
28	D₄×C₂₉	—	4	4	no	—
29	D₄×C₂₉	—	4	4	no	—
30	D₄×C₂₉	—	4	4	no	—
31	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₂₉	—	4	2	no	—
35	Dic₅₈	—	4	4	no	—
36	C₈×C₂₉	SD₁₆	1	4	yes	complemented
37	#6597	—	2	2	no	—
38	#6597	D₈	1	4	yes	complemented
39	#1706	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	—	8	2	no	—
41	C₂²×C₂₉	—	8	2	no	—
42	C₂²×C₂₉	—	8	2	no	—
43	C₂²×C₂₉	#127	1	1	yes	characteristic
44	C₄×C₂₉	C₂×D₈	1	2	yes	—
45	C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
46	C₄×C₂₉	#135	1	2	yes	—
47	Dic₂₉	—	8	2	no	—
48	#500	—	29	1	no	—
49	#493	D₂₉	1	1	yes	characteristic
50	#492	—	29	2	no	—
51	#486	—	29	2	no	—
52	C₈²	—	29	1	no	—
53	C₂×C₂₉	—	16	2	no	—
54	C₂×C₂₉	#492	1	1	yes	characteristic
55	C₂×C₂₉	#493	1	1	yes	characteristic
56	C₂×C₂₉	#495	1	1	yes	characteristic
57	C₂×SD₁₆	—	58	4	no	—
58	C₂×D₈	—	2	2	no	—
59	C₄⋊Q₈	—	29	2	no	—
60	#127	C₂×D₂₉	1	2	yes	—
61	#107	—	58	2	no	—
62	#102	—	58	4	no	—
63	C₄×C₈	—	29	1	no	—
64	C₄×C₈	—	29	1	no	—
65	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
66	C₂₉	#1706	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	58	2	no	—
68	C₂×D₄	—	2	2	no	—
69	C₂×D₄	—	2	2	no	—
70	C₂×D₄	—	2	2	no	—
71	SD₁₆	—	116	8	no	—
72	D₈	—	4	4	no	—
73	C₂×C₈	—	29	2	no	—
74	C₂×C₈	—	29	2	no	—
75	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
76	C₄⋊C₄	—	58	2	no	—
77	C₄⋊C₄	—	58	2	no	—
78	C₄²	C₂²×D₂₉	1	1	yes	characteristic
79	C₂³	—	4	2	no	—
80	Q₈	—	116	4	no	—
81	D₄	—	4	4	no	—
82	D₄	—	4	4	no	—
83	D₄	—	4	4	no	—
84	C₂×C₄	—	116	2	no	—
85	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
86	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
87	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
88	C₈	—	29	4	no	—
89	C₈	—	58	2	no	—
90	C₈	#90783	1	4	yes	complemented
91	C₂²	—	8	2	no	—
92	C₂²	—	8	2	no	—
93	C₂²	—	8	2	no	—
94	C₂²	#11745302	1	1	yes	characteristic
95	C₄	—	232	2	no	—
96	C₄	D₈×D₂₉	1	2	yes	—
97	C₄	#11745274	1	2	yes	—
98	C₄	C₂×#90783	1	2	yes	—
99	C₂	—	16	2	no	—
100	C₂	#14271535	1	1	yes	characteristic
101	C₂	#14271538	1	1	yes	characteristic
102	C₂	#14271546	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271568

C₂

yes

maximal, characteristic, complemented

#14271535

C₂

yes

maximal, complemented

#14271509

C₂

yes

maximal, complemented

C₈×#6597

C₂

yes

maximal, characteristic, complemented

C₂₉×#493

C₂

yes

maximal, characteristic

C₂×D₈×C₂₉

—

C₂₉×#127

C₂²

yes

—

C₂×#90783

—

#11745231

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

—

—

C₂²

yes

characteristic

C₄×#6597

C₂²

yes

characteristic

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×Dic₅₈

—

D₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

#90783

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

D₄

yes

—

C₂×#6597

D₄

yes

—

C₂³×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

Dic₅₈

—

C₈×C₂₉

SD₁₆

yes

complemented

#6597

—

#6597

D₈

yes

complemented

#1706

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#127

yes

characteristic

C₄×C₂₉

C₂×D₈

yes

—

C₄×C₂₉

C₂×SD₁₆

yes

—

C₄×C₂₉

#135

yes

—

Dic₂₉

—

#500

—

#493

D₂₉

yes

characteristic

#492

—

#486

—

C₈²

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

C₂×D₂₉

yes

—

#107

—

#102

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1706

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

116

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

Q₈

—

116

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

116

—

C₂×C₄

D₄×D₂₉

yes

characteristic

C₂×C₄

D₄×D₂₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

—

C₈

#90783

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

#11745302

yes

characteristic

C₄

—

232

—

C₄

D₈×D₂₉

yes

—

C₄

#11745274

yes

—

C₄

C₂×#90783

yes

—

C₂

—

100

C₂

#14271535

yes

characteristic

101

C₂

#14271538

yes

characteristic

102

C₂

#14271546

yes

characteristic

	subgroup	G/H
center	C₂²	#11745302
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting, prime radical	C₂₉×#493	C₂
socle	C₂²×C₂₉	#127
hypercenter	#493	D₂₉
hypocenter	C₂₉	#1706
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#11745302

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting, prime radical

C₂₉×#493

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #14271568	C₂	semidirect
2. #14271535	C₂	semidirect
3. #14271509	C₂	semidirect
4. C₈×#6597	C₂	semidirect
36. C₈×C₂₉	SD₁₆	semidirect
38. #6597	D₈	semidirect
66. C₂₉	#1706	semidirect
90. C₈	#90783	semidirect

H ≅ G/N

type

1. #14271568

C₂

semidirect

2. #14271535

C₂

semidirect

3. #14271509

C₂

semidirect

4. C₈×#6597

C₂

semidirect

36. C₈×C₂₉

SD₁₆

semidirect

38. #6597

D₈

semidirect

66. C₂₉

#1706

semidirect

90. C₈

#90783

semidirect

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

subgroup	index
#14271568	2
#14271535	2
#14271509	2
C₈×#6597	2
C₂₉×#493	2
#1706	29

subgroup

index

C₂₉×#493

Subgroups — #16819081

Conjugacy classes of subgroups

Complements

Maximal subgroups