Group #16835138 — subgroups

Subgroups — #16835138

Order 3712.

148 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 56 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	#14272213	C₂	1	2	yes	maximal
2	#14272024	C₂	1	1	yes	maximal, characteristic
3	#14272013	C₂	1	2	yes	maximal
4	#14272004	C₂	1	1	yes	maximal, characteristic
5	#14271257	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₆	C₄	1	1	yes	characteristic
7	#11745249	C₂²	1	2	yes	—
8	#11745218	—	2	2	no	—
9	C₄⋊#6599	—	2	2	no	—
10	C₄⋊#6599	C₂²	1	2	yes	—
11	C₄×#6599	C₂²	1	1	yes	characteristic
12	C₄×#6599	C₂²	1	1	yes	characteristic
13	C₂₉×#107	C₄	1	1	yes	characteristic
14	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
15	#11745158	C₄	1	2	yes	—
16	C₂×Dic₅₈	C₂×C₄	1	2	yes	—
17	C₂×#6599	—	2	2	no	—
18	C₂×#6599	—	2	1	no	—
19	C₂×#6599	D₄	1	2	yes	—
20	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
22	#90779	—	2	2	no	—
23	C₄×Dic₂₉	—	2	2	no	—
24	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
25	C₂×#6597	C₂×C₄	1	1	yes	characteristic
26	Dic₁₁₆	—	2	2	no	—
27	C₂×C₄×C₂₉	—	2	2	no	—
28	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×Dic₂₉	—	2	2	no	—
30	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₂₉	#41	1	1	yes	characteristic
32	Dic₅₈	—	2	2	no	—
33	Dic₅₈	—	2	2	no	—
34	#6599	—	2	2	no	—
35	#6599	—	4	1	no	—
36	#6599	—	4	2	no	—
37	C₈×C₂₉	M₁₆	1	2	yes	—
38	#6597	—	2	1	no	—
39	#1593	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
41	C₄×C₂₉	—	4	2	no	—
42	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
43	C₄×C₂₉	#131	1	1	yes	characteristic
44	Dic₂₉	—	2	1	no	—
45	Dic₂₉	—	4	2	no	—
46	Dic₂₉	#137	1	2	yes	—
47	#446	—	29	2	no	—
48	C₄×Q₁₆	—	29	1	no	—
49	#334	—	29	1	no	—
50	Q₈⋊C₈	—	29	2	no	—
51	#322	—	29	1	no	—
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	#1181	1	1	yes	characteristic
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	—	29	1	no	—
63	C₄×C₈	—	29	1	no	—
64	C₄×C₈	—	29	1	no	—
65	C₂₉	#1593	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₈	—	29	2	no	—
67	Q₁₆	—	58	2	no	—
68	C₂×C₈	—	29	2	no	—
69	C₂×C₈	—	29	1	no	—
70	C₂×C₈	—	58	1	no	—
71	C₂×C₈	—	58	2	no	—
72	C₂×C₈	C₂×#1181	1	1	yes	characteristic
73	C₄⋊C₄	—	58	2	no	—
74	C₄⋊C₄	C₂×#1181	1	2	yes	—
75	C₄²	—	29	1	no	—
76	C₄²	—	58	2	no	—
77	Q₈	—	58	2	no	—
78	Q₈	—	58	2	no	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	29	1	no	—
81	C₂×C₄	—	29	1	no	—
82	C₂×C₄	—	58	2	no	—
83	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
84	C₈	—	58	2	no	—
85	C₈	—	58	1	no	—
86	C₈	—	116	2	no	—
87	C₈	—	116	1	no	—
88	C₈	#90796	1	2	yes	—
89	C₂²	D₄×#1181	1	1	yes	characteristic
90	C₄	—	4	2	no	—
91	C₄	—	29	2	no	—
92	C₄	—	58	1	no	—
93	C₄	—	116	2	no	—
94	C₄	C₂×#90796	1	1	yes	characteristic
95	C₄	#11745348	1	1	yes	characteristic
96	C₂	#14272197	1	1	yes	characteristic
97	C₂	#14272203	1	1	yes	characteristic
98	C₂	#14272210	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272213

C₂

yes

maximal

#14272024

C₂

yes

maximal, characteristic

#14272013

C₂

yes

maximal

#14272004

C₂

yes

maximal, characteristic

#14271257

C₂

yes

maximal, characteristic

C₂×Dic₁₁₆

C₄

yes

characteristic

#11745249

C₂²

yes

—

#11745218

—

C₄⋊#6599

—

C₄⋊#6599

C₂²

yes

—

C₄×#6599

C₂²

yes

characteristic

C₄×#6599

C₂²

yes

characteristic

C₂₉×#107

C₄

yes

characteristic

C₈×Dic₂₉

C₂²

yes

characteristic

#11745158

C₄

yes

—

C₂×Dic₅₈

C₂×C₄

yes

—

C₂×#6599

—

C₂×#6599

—

C₂×#6599

D₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂³

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

Dic₁₁₆

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

#41

yes

characteristic

Dic₅₈

—

Dic₅₈

—

#6599

—

#6599

—

#6599

—

C₈×C₂₉

M₁₆

yes

—

#6597

—

#1593

—

maximal, Sylow

C₂²×C₂₉

C₄×D₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

C₂×M₁₆

yes

characteristic

C₄×C₂₉

#131

yes

characteristic

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#137

yes

—

#446

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×Q₁₆

—

C₄×Q₈

—

#107

#1181

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂₉

#1593

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×#1181

yes

—

C₄²

—

C₄²

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×#1181

yes

characteristic

C₈

—

C₈

—

C₈

—

116

—

C₈

—

116

—

C₈

#90796

yes

—

C₂²

D₄×#1181

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

116

—

C₄

yes

C₄

yes

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	D₄×#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#107	C₄
socle, prime radical	C₂²×C₂₉	C₄×D₄
cosocle	C₄×Dic₂₉	C₂³
hypercenter	#107	#1181
hypocenter	C₂₉	#1593
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

subgroup

G/H

center

C₂²

D₄×#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#107

C₄

socle, prime radical

C₂²×C₂₉

C₄×D₄

cosocle

C₄×Dic₂₉

C₂³

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

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
#14272213	2
#14272024	2
#14272013	2
#14272004	2
#14271257	2
#1593	29

subgroup

index

Subgroups — #16835138

Conjugacy classes of subgroups

Complements

Maximal subgroups