Group #16818402 — subgroups

Subgroups — #16818402

Order 3712.

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

normal subgroups only

This group has 148 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	#14271293	C₂	1	2	yes	maximal
2	C₄×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic
3	#14270914	C₂	1	1	yes	maximal, characteristic
4	#14270895	C₂	1	2	yes	maximal
5	C₂₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₆	C₄	1	1	yes	characteristic
7	C₄×Dic₅₈	C₂²	1	2	yes	—
8	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#11745166	C₄	1	1	yes	characteristic
12	#11745164	C₄	1	2	yes	—
13	#11745163	—	2	2	no	—
14	#11745162	—	2	2	no	—
15	C₄⋊#6597	C₂²	1	2	yes	—
16	C₂×Dic₅₈	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₂₉	—	2	1	no	—
18	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₂₉	D₄	1	2	yes	—
21	C₄²×C₂₉	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
23	#90779	—	2	2	no	—
24	C₄×Dic₂₉	—	2	2	no	—
25	C₂×#6597	—	2	2	no	—
26	Dic₁₁₆	—	2	2	no	—
27	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
30	C₂×Dic₂₉	—	2	2	no	—
31	C₂×Dic₂₉	—	2	2	no	—
32	Dic₅₈	—	2	2	no	—
33	Dic₅₈	—	2	2	no	—
34	C₈×C₂₉	—	2	1	no	—
35	C₈×C₂₉	—	2	2	no	—
36	C₈×C₂₉	—	4	1	no	—
37	C₈×C₂₉	M₁₆	1	2	yes	—
38	#6597	—	4	2	no	—
39	#1593	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
41	C₄×C₂₉	—	2	1	no	—
42	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
43	C₄×C₂₉	#131	1	1	yes	characteristic
44	C₄×C₂₉	#137	1	2	yes	—
45	Dic₂₉	—	4	2	no	—
46	Dic₂₉	—	4	2	no	—
47	#446	—	29	2	no	—
48	C₄×Q₁₆	—	29	1	no	—
49	#334	—	29	1	no	—
50	Q₈⋊C₈	—	29	2	no	—
51	#322	D₂₉	1	1	yes	characteristic
52	C₂×C₂₉	#436	1	1	yes	characteristic
53	C₂×C₂₉	#441	1	1	yes	characteristic
54	C₂×C₂₉	#444	1	1	yes	characteristic
55	C₂×Q₁₆	—	29	1	no	—
56	C₄×Q₈	—	29	2	no	—
57	#107	—	29	1	no	—
58	C₄⋊C₈	—	29	2	no	—
59	C₄⋊C₈	—	58	2	no	—
60	#103	—	29	2	no	—
61	#97	—	58	2	no	—
62	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
63	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
64	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
65	C₂₉	#1593	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₈	—	29	2	no	—
67	Q₁₆	—	58	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	58	2	no	—
70	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
71	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
72	C₂×C₈	D₁₁₆	1	2	yes	—
73	C₄⋊C₄	—	29	2	no	—
74	C₄⋊C₄	—	58	2	no	—
75	C₄²	—	58	2	no	—
76	C₄²	C₂²×D₂₉	1	1	yes	characteristic
77	Q₈	—	58	2	no	—
78	Q₈	—	58	2	no	—
79	C₂×C₄	—	58	2	no	—
80	C₂×C₄	—	58	2	no	—
81	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
82	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
83	C₂×C₄	#90805	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	116	2	no	—
88	C₈	#90772	1	2	yes	—
89	C₂²	C₄×D₁₁₆	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	116	2	no	—
92	C₄	—	116	2	no	—
93	C₄	C₂×#90772	1	1	yes	characteristic
94	C₄	#11745263	1	1	yes	characteristic
95	C₄	#11745271	1	2	yes	—
96	C₂	#14271242	1	1	yes	characteristic
97	C₂	#14271271	1	1	yes	characteristic
98	C₂	#14271286	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271293

C₂

yes

maximal

C₄×Dic₁₁₆

C₂

yes

maximal, characteristic

#14270914

C₂

yes

maximal, characteristic

#14270895

C₂

yes

maximal

C₂₉×#322

C₂

yes

maximal, characteristic

C₂×Dic₁₁₆

C₄

yes

characteristic

C₄×Dic₅₈

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

characteristic

#11745166

C₄

yes

characteristic

#11745164

C₄

yes

—

#11745163

—

#11745162

—

C₄⋊#6597

C₂²

yes

—

C₂×Dic₅₈

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

—

C₄×Dic₂₉

—

C₂×#6597

—

Dic₁₁₆

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

M₁₆

yes

—

#6597

—

#1593

—

maximal, Sylow

C₂²×C₂₉

C₄×D₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

C₂×M₁₆

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

Dic₂₉

—

Dic₂₉

—

#446

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

D₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₄×C₈

C₂×D₂₉

yes

characteristic

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1593

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₉

yes

characteristic

C₂×C₈

C₄×D₂₉

yes

characteristic

C₂×C₈

D₁₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

#90805

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

116

—

C₈

#90772

yes

—

C₂²

C₄×D₁₁₆

yes

characteristic

C₄

—

C₄

—

116

—

C₄

—

116

—

C₄

yes

C₄

yes

C₄

yes

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁₆
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#322	C₂
socle, prime radical	C₂²×C₂₉	C₄×D₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	#322	D₂₉
hypocenter	C₂₉	#1593
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₁₁₆

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#322

C₂

socle, prime radical

C₂²×C₂₉

C₄×D₄

cosocle

C₄²×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
65. C₂₉	#1593	semidirect

H ≅ G/N

type

65. C₂₉

#1593

semidirect

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

subgroup	index
#14271293	2
C₄×Dic₁₁₆	2
#14270914	2
#14270895	2
C₂₉×#322	2
#1593	29

subgroup

index

C₄×Dic₁₁₆

C₂₉×#322

Subgroups — #16818402

Conjugacy classes of subgroups

Complements

Maximal subgroups