Group #16835210 — subgroups

Subgroups — #16835210

Order 3712.

240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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	#14272122	C₂	1	1	yes	maximal, characteristic
2	#14272099	C₂	1	1	yes	maximal, characteristic
3	(C₂×#1181)⋊C₈	C₂	1	4	yes	maximal
4	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#1181	C₂²	1	2	yes	—
6	C₂×D₂₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₈×D₂₉	C₂²	1	2	yes	—
8	C₄²×D₂₉	C₂²	1	1	yes	characteristic
9	(C₂×#1181)⋊C₄	C₄	1	4	yes	—
10	#11745218	C₄	1	4	yes	complemented
11	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic, complemented
12	C₈×Dic₂₉	C₄	1	2	yes	complemented
13	C₄×#6597	C₄	1	1	yes	characteristic, complemented
14	C₂²×#1181	C₂×C₄	1	4	yes	—
15	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
17	C₂×#6599	C₂×C₄	1	4	yes	—
18	C₄×#1181	—	2	4	no	—
19	D₂₉⋊C₈	—	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	C₂×C₄	1	2	yes	—
24	C₂×#6597	C₂×C₄	1	2	yes	—
25	C₈×D₂₉	—	2	4	no	—
26	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×#1181	—	2	4	no	—
28	C₂×#1181	—	2	8	no	—
29	C₂×C₄×C₂₉	C₄²	1	2	yes	—
30	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₂₉	C₄²	1	2	yes	—
32	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
33	C₄×D₂₉	—	2	4	no	—
34	C₄×D₂₉	#41	1	4	yes	—
35	#6599	—	2	4	no	—
36	C₈×C₂₉	—	2	2	no	—
37	#6597	—	2	2	no	—
38	#1746	—	29	1	no	maximal, Sylow
39	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
40	C₂×D₂₉	#117	1	2	yes	—
41	C₂×D₂₉	#131	1	4	yes	—
42	#1181	—	4	4	no	—
43	C₄×C₂₉	—	2	2	no	—
44	C₄×C₂₉	#117	1	2	yes	—
45	Dic₂₉	—	2	2	no	—
46	Dic₂₉	#117	1	2	yes	—
47	C₂×#97	—	29	1	no	—
48	C₂×C₄×C₈	—	29	1	no	—
49	#376	—	29	1	no	—
50	#336	—	29	4	no	—
51	C₂×C₂₉	#376	1	1	yes	characteristic
52	C₂×C₂₉	#405	1	2	yes	—
53	D₂₉	#433	1	4	yes	—
54	C₂²×C₈	—	29	2	no	—
55	C₂²×C₈	—	29	2	no	—
56	C₂×C₄²	—	29	1	no	—
57	C₂×C₄²	—	29	2	no	—
58	#97	—	29	4	no	—
59	C₄×C₈	—	29	2	no	—
60	C₄×C₈	—	29	1	no	—
61	C₄×C₈	#1181	1	1	yes	characteristic, complemented
62	#95	—	29	4	no	—
63	C₂₉	#1746	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₄	—	29	1	no	—
65	C₂²×C₄	—	29	2	no	—
66	C₂²×C₄	—	29	4	no	—
67	C₂×C₈	—	29	4	no	—
68	C₂×C₈	—	29	2	no	—
69	C₂×C₈	—	58	4	no	—
70	C₂×C₈	—	58	4	no	—
71	C₂×C₈	C₂×#1181	1	2	yes	—
72	C₄²	—	29	2	no	—
73	C₄²	—	29	1	no	—
74	C₄²	—	58	4	no	—
75	C₄²	C₂×#1181	1	1	yes	characteristic
76	C₂³	—	29	1	no	—
77	C₂×C₄	—	29	1	no	—
78	C₂×C₄	—	29	4	no	—
79	C₂×C₄	—	29	2	no	—
80	C₂×C₄	—	58	4	no	—
81	C₂×C₄	—	58	4	no	—
82	C₂×C₄	—	58	8	no	—
83	C₂×C₄	C₄×#1181	1	2	yes	—
84	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
85	C₈	—	2	2	no	—
86	C₈	—	58	4	no	—
87	C₈	—	58	2	no	—
88	C₂²	—	29	2	no	—
89	C₂²	—	29	4	no	—
90	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	29	2	no	—
93	C₄	—	58	2	no	—
94	C₄	—	116	4	no	—
95	C₄	#11745345	1	2	yes	—
96	C₂	—	29	4	no	—
97	C₂	#14272099	1	1	yes	characteristic
98	C₂	#14272126	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272122

C₂

yes

maximal, characteristic

#14272099

C₂

yes

maximal, characteristic

(C₂×#1181)⋊C₈

C₂

yes

maximal

C₄×C₈×D₂₉

C₂

yes

maximal, characteristic

C₂×C₄×#1181

C₂²

yes

—

C₂×D₂₉⋊C₈

C₂²

yes

—

C₂×C₈×D₂₉

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

(C₂×#1181)⋊C₄

C₄

yes

—

#11745218

C₄

yes

complemented

C₄×C₈×C₂₉

C₄

yes

characteristic, complemented

C₈×Dic₂₉

C₄

yes

complemented

C₄×#6597

C₄

yes

characteristic, complemented

C₂²×#1181

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×#6599

C₂×C₄

yes

—

C₄×#1181

—

D₂₉⋊C₈

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₈×D₂₉

—

C₂²×D₂₉

C₂²×C₄

yes

characteristic

C₂×#1181

—

C₂×#1181

—

C₂×C₄×C₂₉

C₄²

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

#41

yes

—

#6599

—

C₈×C₂₉

—

#6597

—

#1746

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂×D₂₉

#117

yes

—

C₂×D₂₉

#131

yes

—

#1181

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

—

Dic₂₉

—

Dic₂₉

#117

yes

—

C₂×#97

—

C₂×C₄×C₈

—

#376

—

#336

—

C₂×C₂₉

#376

yes

characteristic

C₂×C₂₉

#405

yes

—

D₂₉

#433

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#1181

yes

characteristic, complemented

#95

—

C₂₉

#1746

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×#1181

yes

—

C₂×C₄

C₂²×#1181

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

C₂×C₄×#1181

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

116

—

C₄

#11745345

yes

—

C₂

—

C₂

#14272099

yes

characteristic

C₂

#14272126

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₄×C₈×C₂₉	C₄
prime radical	C₂²×D₂₉	C₂²×C₄
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	#1746
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#1181

commutator, socle

C₂²×C₂₉

C₂×C₄²

Fitting

C₄×C₈×C₂₉

C₄

prime radical

C₂²×D₂₉

C₂²×C₄

cosocle

C₂×C₄×D₂₉

C₂³

C₄×C₈

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ C₄×C₈

N	H ≅ G/N	type
10. #11745218	C₄	semidirect
11. C₄×C₈×C₂₉	C₄	semidirect
12. C₈×Dic₂₉	C₄	semidirect
13. C₄×#6597	C₄	semidirect
61. C₄×C₈	#1181	semidirect
63. C₂₉	#1746	semidirect

H ≅ G/N

type

10. #11745218

C₄

semidirect

11. C₄×C₈×C₂₉

C₄

semidirect

12. C₈×Dic₂₉

C₄

semidirect

13. C₄×#6597

C₄

semidirect

61. C₄×C₈

#1181

semidirect

63. C₂₉

#1746

semidirect

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

subgroup	index
#14272122	2
#14272099	2
(C₂×#1181)⋊C₈	2
C₄×C₈×D₂₉	2
#1746	29

subgroup

index

C₄×C₈×D₂₉

Subgroups — #16835210

Conjugacy classes of subgroups

Complements

Maximal subgroups