Group #16819118 — subgroups

Subgroups — #16819118

Order 3712.

220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14271561	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271535	C₂	1	2	yes	maximal, complemented
3	#14271509	C₂	1	2	yes	maximal, complemented
4	#14270884	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	1	yes	characteristic
8	C₂₉×#127	C₂²	1	1	yes	characteristic
9	C₂×#90783	—	2	4	no	—
10	#11745231	C₂²	1	2	yes	—
11	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#11745180	—	2	4	no	—
13	#11745165	—	2	2	no	—
14	C₄×#6597	C₂²	1	2	yes	—
15	C₂×D₄×C₂₉	—	2	2	no	—
16	C₂×D₄×C₂₉	—	2	1	no	—
17	C₂×D₄×C₂₉	—	2	1	no	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×Dic₅₈	—	2	2	no	—
20	D₈×C₂₉	—	4	4	no	—
21	C₂×C₈×C₂₉	D₄	1	2	yes	—
22	C₄²×C₂₉	C₂³	1	1	yes	characteristic
23	#90783	—	4	8	no	—
24	C₄⋊Dic₂₉	—	2	2	no	—
25	C₄⋊Dic₂₉	—	2	2	no	—
26	C₂×#6597	D₄	1	4	yes	—
27	C₂³×C₂₉	—	4	1	no	—
28	C₂³×C₂₉	—	4	1	no	—
29	D₄×C₂₉	—	4	2	no	—
30	D₄×C₂₉	—	4	2	no	—
31	D₄×C₂₉	—	4	4	no	—
32	D₄×C₂₉	—	4	4	no	—
33	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₂₉	—	4	2	no	—
36	Dic₅₈	—	4	4	no	—
37	C₈×C₂₉	SD₁₆	1	4	yes	complemented
38	#6597	—	2	4	no	—
39	#1715	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	—	8	1	no	—
41	C₂²×C₂₉	—	8	1	no	—
42	C₂²×C₂₉	—	8	2	no	—
43	C₂²×C₂₉	—	8	2	no	—
44	C₂²×C₂₉	#127	1	1	yes	characteristic
45	C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
46	C₄×C₂₉	AGL(1,ℤ/8)	1	4	yes	—
47	Dic₂₉	—	8	2	no	—
48	#498	—	29	1	no	—
49	#493	D₂₉	1	1	yes	characteristic
50	#492	—	29	2	no	—
51	#486	—	29	2	no	—
52	#322	—	29	1	no	—
53	C₂×C₂₉	—	16	1	no	—
54	C₂×C₂₉	—	16	1	no	—
55	C₂×C₂₉	#492	1	1	yes	characteristic
56	C₂×C₂₉	#496	1	2	yes	—
57	C₂×SD₁₆	—	58	4	no	—
58	C₂×D₈	—	2	2	no	—
59	C₄⋊Q₈	—	29	2	no	—
60	#127	C₂×D₂₉	1	1	yes	characteristic
61	#127	C₂×D₂₉	1	1	yes	characteristic
62	#106	—	58	2	no	—
63	#102	—	58	4	no	—
64	C₄×C₈	—	29	2	no	—
65	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
66	C₂₉	#1715	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	1	no	—
71	C₂×D₄	—	2	1	no	—
72	SD₁₆	—	116	8	no	—
73	D₈	—	4	4	no	—
74	C₂×C₈	—	29	4	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	1	no	—
80	C₂³	—	4	1	no	—
81	Q₈	—	116	4	no	—
82	D₄	—	4	2	no	—
83	D₄	—	4	2	no	—
84	D₄	—	4	4	no	—
85	D₄	—	4	4	no	—
86	C₂×C₄	—	116	2	no	—
87	C₂×C₄	D₄×D₂₉	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
89	C₈	—	58	4	no	—
90	C₈	#90783	1	4	yes	complemented
91	C₂²	—	8	1	no	—
92	C₂²	—	8	1	no	—
93	C₂²	—	8	2	no	—
94	C₂²	—	8	2	no	—
95	C₂²	#11745302	1	1	yes	characteristic
96	C₄	—	232	2	no	—
97	C₄	#11745273	1	4	yes	—
98	C₄	C₂×#90783	1	2	yes	—
99	C₂	—	16	1	no	—
100	C₂	—	16	1	no	—
101	C₂	#14271535	1	1	yes	characteristic
102	C₂	#14271551	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271561

C₂

yes

maximal, characteristic, complemented

#14271535

C₂

yes

maximal, complemented

#14271509

C₂

yes

maximal, complemented

#14270884

C₂

yes

maximal, characteristic, complemented

C₂₉×#493

C₂

yes

maximal, characteristic

C₂×D₈×C₂₉

—

C₂₉×#127

C₂²

yes

characteristic

C₂₉×#127

C₂²

yes

characteristic

C₂×#90783

—

#11745231

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

—

—

C₂²

yes

—

C₂×D₄×C₂₉

—

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

—

C₂³×C₂₉

—

C₂³×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

Dic₅₈

—

C₈×C₂₉

SD₁₆

yes

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#127

yes

characteristic

C₄×C₂₉

C₂×SD₁₆

yes

—

C₄×C₂₉

AGL(1,ℤ/8)

yes

—

Dic₂₉

—

#498

—

#493

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#492

yes

characteristic

C₂×C₂₉

#496

yes

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

C₂×D₂₉

yes

characteristic

#127

C₂×D₂₉

yes

characteristic

#106

—

#102

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1715

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

116

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

C₂³

—

Q₈

—

116

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

116

—

C₂×C₄

D₄×D₂₉

yes

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

#90783

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#11745302

yes

characteristic

C₄

—

232

—

C₄

#11745273

yes

—

C₄

C₂×#90783

yes

—

C₂

—

100

C₂

—

101

C₂

#14271535

yes

characteristic

102

C₂

#14271551

yes

—

	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	#1715
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. #14271561	C₂	semidirect
2. #14271535	C₂	semidirect
3. #14271509	C₂	semidirect
4. #14270884	C₂	semidirect
37. C₈×C₂₉	SD₁₆	semidirect
66. C₂₉	#1715	semidirect
90. C₈	#90783	semidirect

H ≅ G/N

type

1. #14271561

C₂

semidirect

2. #14271535

C₂

semidirect

3. #14271509

C₂

semidirect

4. #14270884

C₂

semidirect

37. C₈×C₂₉

SD₁₆

semidirect

66. C₂₉

#1715

semidirect

90. C₈

#90783

semidirect

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

subgroup	index
#14271561	2
#14271535	2
#14271509	2
#14270884	2
C₂₉×#493	2
#1715	29

subgroup

index

C₂₉×#493

Subgroups — #16819118

Conjugacy classes of subgroups

Complements

Maximal subgroups