Group #16818987 — subgroups

Subgroups — #16818987

Order 3712.

152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14271543	C₂	1	1	yes	maximal, characteristic
2	#14271449	C₂	1	2	yes	maximal
3	#14271293	C₂	1	1	yes	maximal, characteristic
4	#14270908	C₂	1	2	yes	maximal
5	C₂₉×#334	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₆	—	2	1	no	—
7	C₂×Dic₁₁₆	—	2	1	no	—
8	#11745231	C₂²	1	2	yes	—
9	C₄×Dic₅₈	C₂²	1	1	yes	characteristic
10	C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
11	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#11745165	—	2	2	no	—
13	#11745164	—	2	2	no	—
14	#11745163	—	2	1	no	—
15	#11745162	—	2	1	no	—
16	C₄⋊#6597	C₂²	1	1	yes	characteristic
17	C₂×Dic₅₈	—	2	2	no	—
18	C₂×Dic₅₈	D₄	1	1	yes	characteristic
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
22	C₄²×C₂₉	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	—	2	2	no	—
25	C₄⋊Dic₂₉	D₄	1	1	yes	characteristic
26	#90779	—	2	1	no	—
27	C₄×Dic₂₉	—	2	1	no	—
28	C₂×#6597	—	2	1	no	—
29	Dic₁₁₆	—	4	2	no	—
30	Dic₁₁₆	—	4	2	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	#41	1	1	yes	characteristic
34	C₂×Dic₂₉	—	2	1	no	—
35	C₂×Dic₂₉	—	2	1	no	—
36	C₂×Dic₂₉	—	4	2	no	—
37	Dic₅₈	—	2	2	no	—
38	Dic₅₈	—	4	2	no	—
39	Dic₅₈	—	4	2	no	—
40	C₈×C₂₉	—	2	1	no	—
41	C₈×C₂₉	—	4	2	no	—
42	C₈×C₂₉	SD₁₆	1	2	yes	—
43	#6597	—	4	1	no	—
44	#1690	—	29	1	no	maximal, Sylow
45	C₂²×C₂₉	#121	1	1	yes	characteristic
46	C₄×C₂₉	—	2	1	no	—
47	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
48	C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
49	C₄×C₂₉	#137	1	2	yes	—
50	Dic₂₉	—	4	1	no	—
51	Dic₂₉	—	4	1	no	—
52	Dic₂₉	—	8	2	no	—
53	#494	—	29	1	no	—
54	#475	—	29	2	no	—
55	#446	—	29	1	no	—
56	#334	D₂₉	1	1	yes	characteristic
57	#332	—	29	2	no	—
58	C₂×C₂₉	#460	1	1	yes	characteristic
59	C₂×C₂₉	#470	1	1	yes	characteristic
60	C₂×C₂₉	#473	1	1	yes	characteristic
61	C₂×Q₁₆	—	58	1	no	—
62	C₂×Q₁₆	—	58	1	no	—
63	C₄⋊Q₈	—	29	2	no	—
64	C₄×Q₈	—	29	1	no	—
65	#106	—	58	2	no	—
66	C₄⋊C₈	—	29	1	no	—
67	C₄⋊C₈	—	58	1	no	—
68	C₄⋊C₈	C₂×D₂₉	1	2	yes	—
69	#103	—	58	2	no	—
70	#97	—	58	1	no	—
71	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
72	C₂₉	#1690	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₈	—	29	1	no	—
74	C₂×Q₈	—	58	2	no	—
75	Q₁₆	—	116	2	no	—
76	Q₁₆	—	116	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	58	1	no	—
79	C₂×C₈	D₁₁₆	1	1	yes	characteristic
80	C₂×C₈	D₁₁₆	1	1	yes	characteristic
81	C₄⋊C₄	—	29	1	no	—
82	C₄⋊C₄	—	58	1	no	—
83	C₄⋊C₄	—	58	2	no	—
84	C₄⋊C₄	—	58	2	no	—
85	C₄²	—	58	1	no	—
86	C₄²	C₂²×D₂₉	1	1	yes	characteristic
87	Q₈	—	58	2	no	—
88	Q₈	—	116	2	no	—
89	Q₈	—	116	2	no	—
90	C₂×C₄	—	58	1	no	—
91	C₂×C₄	—	58	1	no	—
92	C₂×C₄	—	116	2	no	—
93	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
94	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
95	C₂×C₄	#90809	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	4	2	no	—
98	C₈	—	116	1	no	—
99	C₈	#90773	1	2	yes	—
100	C₂²	#11745257	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	116	1	no	—
103	C₄	—	116	1	no	—
104	C₄	—	232	2	no	—
105	C₄	C₂×#90773	1	1	yes	characteristic
106	C₄	#11745270	1	1	yes	characteristic
107	C₄	#11745277	1	2	yes	—
108	C₂	#14271364	1	1	yes	characteristic
109	C₂	#14271422	1	1	yes	characteristic
110	C₂	#14271439	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271543

C₂

yes

maximal, characteristic

#14271449

C₂

yes

maximal

#14271293

C₂

yes

maximal, characteristic

#14270908

C₂

yes

maximal

C₂₉×#334

C₂

yes

maximal, characteristic

C₂×Dic₁₁₆

—

C₂×Dic₁₁₆

—

#11745231

C₂²

yes

—

C₄×Dic₅₈

C₂²

yes

characteristic

C₂₉×C₄⋊C₈

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×Dic₅₈

—

C₂×Dic₅₈

D₄

yes

characteristic

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

characteristic

#90779

—

C₄×Dic₂₉

—

C₂×#6597

—

Dic₁₁₆

—

Dic₁₁₆

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

SD₁₆

yes

—

—

—

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

C₂×SD₁₆

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

—

—

—

D₂₉

yes

characteristic

#332

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₂₉

yes

—

#103

—

#97

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1690

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

116

—

Q₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₁₆

yes

characteristic

C₂×C₈

D₁₁₆

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

Q₈

—

Q₈

—

116

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

D₄×D₂₉

yes

characteristic

C₂×C₄

#90809

yes

characteristic

C₈

—

C₈

—

C₈

—

116

—

C₈

#90773

yes

—

100

C₂²

#11745257

yes

characteristic

101

C₄

—

102

C₄

—

116

—

103

C₄

—

116

—

104

C₄

—

232

—

105

C₄

C₂×#90773

yes

characteristic

106

C₄

#11745270

yes

characteristic

107

C₄

#11745277

yes

—

108

C₂

#14271364

yes

characteristic

109

C₂

#14271422

yes

characteristic

110

C₂

#14271439

yes

characteristic

	subgroup	G/H
center	C₂²	#11745257
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#334	C₂
socle, prime radical	C₂²×C₂₉	#121
hypercenter	#334	D₂₉
hypocenter	C₂₉	#1690
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#11745257

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#334

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
72. C₂₉	#1690	semidirect

H ≅ G/N

type

72. C₂₉

#1690

semidirect

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

subgroup	index
#14271543	2
#14271449	2
#14271293	2
#14270908	2
C₂₉×#334	2
#1690	29

subgroup

index

C₂₉×#334

Subgroups — #16818987

Conjugacy classes of subgroups

Complements

Maximal subgroups