Group #16835208 — subgroups

Subgroups — #16835208

Order 3712.

272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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	C₄²×#1181	C₂	1	1	yes	maximal, characteristic
3	(C₂×#1181)⋊C₈	C₂	1	4	yes	maximal
4	#97×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#1181	C₄	1	4	yes	—
6	C₂×C₄×#1181	C₂²	1	2	yes	—
7	C₂×D₂₉⋊C₈	C₂²	1	2	yes	—
8	C₂×C₈×D₂₉	C₂²	1	2	yes	—
9	C₄²×D₂₉	C₂²	1	1	yes	characteristic
10	#11745218	C₄	1	4	yes	complemented
11	C₂₉×#97	C₄	1	1	yes	characteristic, complemented
12	#11745163	C₄	1	2	yes	complemented
13	#11745151	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	8	no	—
19	C₄×#1181	—	2	4	no	—
20	D₂₉⋊C₈	—	2	4	no	—
21	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
22	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
25	C₂×#6597	C₂×C₄	1	2	yes	—
26	C₈×D₂₉	—	2	4	no	—
27	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×#1181	—	2	4	no	—
29	C₂×#1181	—	2	4	no	—
30	C₂×#1181	M₁₆	1	8	yes	—
31	C₂×C₄×C₂₉	C₄²	1	2	yes	—
32	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₂₉	C₄²	1	2	yes	—
34	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
35	C₄×D₂₉	—	2	4	no	—
36	C₄×D₂₉	#41	1	4	yes	—
37	#6599	—	2	4	no	—
38	C₈×C₂₉	—	2	2	no	—
39	#6597	—	2	2	no	—
40	#1745	—	29	1	no	maximal, Sylow
41	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
42	C₂×D₂₉	#117	1	2	yes	—
43	C₂×D₂₉	C₂×M₁₆	1	4	yes	—
44	#1181	—	2	8	no	—
45	C₄×C₂₉	—	2	2	no	—
46	C₄×C₂₉	#117	1	2	yes	—
47	Dic₂₉	—	2	2	no	—
48	Dic₂₉	#117	1	2	yes	—
49	C₂×#97	—	29	1	no	—
50	C₂×#97	—	29	1	no	—
51	C₄³	—	29	1	no	—
52	#336	—	29	4	no	—
53	C₂×C₂₉	#376	1	1	yes	characteristic
54	C₂×C₂₉	C₄×M₁₆	1	2	yes	—
55	D₂₉	#432	1	4	yes	—
56	C₂²×C₈	—	29	2	no	—
57	C₂²×C₈	—	29	2	no	—
58	C₂×C₄²	—	29	1	no	—
59	C₂×C₄²	—	29	4	no	—
60	C₂×C₄²	—	29	2	no	—
61	#97	—	29	4	no	—
62	#97	—	29	2	no	—
63	#97	—	29	1	no	—
64	#97	#1181	1	1	yes	characteristic, complemented
65	C₂₉	#1745	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	29	1	no	—
67	C₂²×C₄	—	29	4	no	—
68	C₂²×C₄	—	29	2	no	—
69	C₂×C₈	—	29	4	no	—
70	C₂×C₈	—	29	2	no	—
71	C₂×C₈	—	58	4	no	—
72	C₂×C₈	—	58	4	no	—
73	C₂×C₈	C₂×#1181	1	2	yes	—
74	C₄²	—	29	2	no	—
75	C₄²	—	29	1	no	—
76	C₄²	—	58	4	no	—
77	C₄²	—	58	8	no	—
78	C₄²	C₂×#1181	1	1	yes	characteristic
79	C₂³	—	29	1	no	—
80	C₂×C₄	—	29	1	no	—
81	C₂×C₄	—	29	4	no	—
82	C₂×C₄	—	29	8	no	—
83	C₂×C₄	—	29	2	no	—
84	C₂×C₄	—	58	4	no	—
85	C₂×C₄	—	58	4	no	—
86	C₂×C₄	—	58	4	no	—
87	C₂×C₄	C₄×#1181	1	2	yes	—
88	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
89	C₈	—	2	2	no	—
90	C₈	—	58	4	no	—
91	C₈	—	58	2	no	—
92	C₂²	—	29	2	no	—
93	C₂²	—	29	4	no	—
94	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	29	2	no	—
97	C₄	—	58	8	no	—
98	C₄	—	58	2	no	—
99	C₄	#11745345	1	2	yes	—
100	C₂	—	29	4	no	—
101	C₂	#14272099	1	1	yes	characteristic
102	C₂	M₁₆×#1181	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272122

C₂

yes

maximal, characteristic

C₄²×#1181

C₂

yes

maximal, characteristic

(C₂×#1181)⋊C₈

C₂

yes

maximal

#97×D₂₉

C₂

yes

maximal, characteristic

C₂×C₄×#1181

C₄

yes

—

C₂×C₄×#1181

C₂²

yes

—

C₂×D₂₉⋊C₈

C₂²

yes

—

C₂×C₈×D₂₉

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745218

C₄

yes

complemented

C₂₉×#97

C₄

yes

characteristic, complemented

#11745163

C₄

yes

complemented

#11745151

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

—

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

—

—

M₁₆

yes

—

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

—

#1745

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂×D₂₉

#117

yes

—

C₂×D₂₉

C₂×M₁₆

yes

—

#1181

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

—

Dic₂₉

—

Dic₂₉

#117

yes

—

C₂×#97

—

C₂×#97

—

C₄³

—

#336

—

C₂×C₂₉

#376

yes

characteristic

C₂×C₂₉

C₄×M₁₆

yes

—

D₂₉

#432

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₂₉

#1745

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

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

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

—

C₄

#11745345

yes

—

100

C₂

—

101

C₂

#14272099

yes

characteristic

102

C₂

M₁₆×#1181

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₂₉×#97	C₄
prime radical	C₂²×D₂₉	C₂²×C₄
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	#97	#1181
hypocenter	C₂₉	#1745
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#1181

commutator, socle

C₂²×C₂₉

C₂×C₄²

Fitting

C₂₉×#97

C₄

prime radical

C₂²×D₂₉

C₂²×C₄

cosocle

C₂×C₄×D₂₉

C₂³

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
10. #11745218	C₄	semidirect
11. C₂₉×#97	C₄	semidirect
12. #11745163	C₄	semidirect
13. #11745151	C₄	semidirect
64. #97	#1181	semidirect
65. C₂₉	#1745	semidirect

H ≅ G/N

type

10. #11745218

C₄

semidirect

11. C₂₉×#97

C₄

semidirect

12. #11745163

C₄

semidirect

13. #11745151

C₄

semidirect

64. #97

#1181

semidirect

65. C₂₉

#1745

semidirect

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

subgroup	index
#14272122	2
C₄²×#1181	2
(C₂×#1181)⋊C₈	2
#97×D₂₉	2
#1745	29

subgroup

index

#14272122

C₄²×#1181

(C₂×#1181)⋊C₈

#97×D₂₉

#1745

Subgroups — #16835208

Conjugacy classes of subgroups

Complements

Maximal subgroups