Group #16835418 — subgroups

Subgroups — #16835418

Order 3712.

180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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	#14272168	C₂	1	1	yes	maximal, characteristic
2	#14272167	C₂	1	1	yes	maximal, characteristic
3	#14272039	C₂	1	4	yes	maximal
4	#97×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#90796	C₂²	1	2	yes	—
6	C₂×#90796	C₂²	1	2	yes	—
7	C₂×C₈×D₂₉	C₂²	1	2	yes	—
8	C₄²×D₂₉	C₂²	1	1	yes	characteristic
9	#11745220	—	2	2	no	—
10	C₄⋊#6599	—	2	2	no	—
11	C₂₉×#97	C₄	1	1	yes	characteristic
12	#11745163	C₄	1	2	yes	—
13	#11745151	C₄	1	1	yes	characteristic
14	C₂×C₄×D₂₉	Q₈	1	2	yes	—
15	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
16	C₂×#6599	—	2	2	no	—
17	C₂×#6599	—	2	2	no	—
18	#90796	—	2	4	no	—
19	#90796	—	2	4	no	—
20	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
21	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₂₉	D₄	1	2	yes	—
24	C₂×#6597	C₂×C₄	1	2	yes	—
25	C₈×D₂₉	—	2	2	no	—
26	C₈×D₂₉	—	2	2	no	—
27	C₂²×D₂₉	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
31	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
32	C₄×D₂₉	—	4	2	no	—
33	C₄×D₂₉	#41	1	2	yes	—
34	C₄×D₂₉	#41	1	2	yes	—
35	#6599	—	4	2	no	—
36	#6599	—	4	2	no	—
37	C₈×C₂₉	—	2	2	no	—
38	#6597	—	2	2	no	—
39	#1838	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂×D₂₉	—	2	2	no	—
42	C₂×D₂₉	#125	1	2	yes	—
43	C₄×C₂₉	—	2	2	no	—
44	C₄×C₂₉	#117	1	2	yes	—
45	Dic₂₉	—	2	2	no	—
46	Dic₂₉	#124	1	1	yes	characteristic
47	Dic₂₉	#124	1	1	yes	characteristic
48	#423	—	29	1	no	—
49	#423	—	29	1	no	—
50	C₂×#97	—	29	1	no	—
51	#341	—	29	4	no	—
52	C₂×C₂₉	#382	1	1	yes	characteristic
53	C₂×C₂₉	#430	1	2	yes	—
54	D₂₉	—	2	2	no	—
55	C₂×M₁₆	—	29	2	no	—
56	C₂×M₁₆	—	29	2	no	—
57	C₂²×C₈	—	29	2	no	—
58	C₂×C₄²	—	29	1	no	—
59	C₄⋊C₈	—	58	2	no	—
60	C₄⋊C₈	—	58	2	no	—
61	#97	—	29	2	no	—
62	#97	—	29	1	no	—
63	#97	#1181	1	1	yes	characteristic
64	C₂₉	#1838	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₄	—	29	1	no	—
66	C₂²×C₄	—	29	2	no	—
67	M₁₆	—	58	4	no	—
68	M₁₆	—	58	4	no	—
69	C₂×C₈	—	29	2	no	—
70	C₂×C₈	—	58	2	no	—
71	C₂×C₈	—	58	2	no	—
72	C₂×C₈	—	58	2	no	—
73	C₂×C₈	—	58	2	no	—
74	C₂×C₈	C₂×#1181	1	2	yes	—
75	C₄²	—	29	2	no	—
76	C₄²	—	29	1	no	—
77	C₄²	C₂×#1181	1	1	yes	characteristic
78	C₂³	—	29	1	no	—
79	C₂×C₄	—	29	1	no	—
80	C₂×C₄	—	29	2	no	—
81	C₂×C₄	—	29	2	no	—
82	C₂×C₄	—	29	2	no	—
83	C₂×C₄	—	116	2	no	—
84	C₂×C₄	C₄⋊#1181	1	2	yes	—
85	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	58	2	no	—
88	C₈	—	116	2	no	—
89	C₈	—	116	2	no	—
90	C₂²	—	29	2	no	—
91	C₂²	—	58	2	no	—
92	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	29	1	no	—
95	C₄	—	29	1	no	—
96	C₄	—	58	2	no	—
97	C₄	#11745345	1	2	yes	—
98	C₂	—	58	2	no	—
99	C₂	#14272107	1	1	yes	characteristic
100	C₂	#14272178	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272168

C₂

yes

maximal, characteristic

#14272167

C₂

yes

maximal, characteristic

#14272039

C₂

yes

maximal

#97×D₂₉

C₂

yes

maximal, characteristic

C₂×#90796

C₂²

yes

—

C₂×#90796

C₂²

yes

—

C₂×C₈×D₂₉

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745220

—

C₄⋊#6599

—

C₂₉×#97

C₄

yes

characteristic

#11745163

C₄

yes

—

#11745151

C₄

yes

characteristic

C₂×C₄×D₂₉

Q₈

yes

—

C₂×C₄×D₂₉

C₂³

yes

—

—

—

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₈×D₂₉

—

C₈×D₂₉

—

C₂²×D₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

#41

yes

—

C₄×D₂₉

#41

yes

—

#6599

—

#6599

—

C₈×C₂₉

—

#6597

—

#1838

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

#125

yes

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

—

Dic₂₉

—

Dic₂₉

yes

Dic₂₉

yes

—

—

C₂×#97

—

#341

—

C₂×C₂₉

#382

yes

characteristic

C₂×C₂₉

#430

yes

—

D₂₉

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

yes

C₂₉

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₄⋊#1181

yes

—

C₂×C₄

C₂²×#1181

yes

characteristic

C₈

—

C₈

—

C₈

—

116

—

C₈

—

116

—

C₂²

—

C₂²

—

C₂²

C₂×C₄⋊#1181

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#11745345

yes

—

C₂

—

C₂

#14272107

yes

characteristic

100

C₂

#14272178

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#97	C₄
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂²×D₂₉	C₂×Q₈
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	#97	#1181
hypocenter	C₂₉	#1838
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#97

C₄

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂²×D₂₉

C₂×Q₈

cosocle

C₂×C₄×D₂₉

C₂³

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
64. C₂₉	#1838	semidirect

H ≅ G/N

type

64. C₂₉

#1838

semidirect

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

subgroup	index
#14272168	2
#14272167	2
#14272039	2
#97×D₂₉	2
#1838	29

subgroup

index

#97×D₂₉

Subgroups — #16835418

Conjugacy classes of subgroups

Complements

Maximal subgroups