Group #16827874 — subgroups

Subgroups — #16827874

Order 3712.

408 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 165 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	#14271069	C₂	1	3	yes	maximal
2	#14271061	C₂	1	3	yes	maximal
3	#14271047	C₂	1	6	yes	maximal
4	#14271031	C₂	1	2	yes	maximal
5	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₅₈	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₂₉	C₂²	1	3	yes	—
8	C₂×C₄²×C₂₉	C₂²	1	3	yes	—
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₂₉	C₂²	1	3	yes	—
11	C₂×#90779	C₂²	1	6	yes	—
12	#11745179	C₂²	1	6	yes	—
13	#11745179	C₂²	1	6	yes	—
14	#11745179	C₂²	1	6	yes	—
15	C₂²×C₄×C₂₉	C₂³	1	3	yes	—
16	C₂²×C₄×C₂₉	C₂³	1	3	yes	—
17	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₂₉	C₂³	1	6	yes	—
19	C₂²×Dic₂₉	C₂³	1	2	yes	—
20	C₂×Dic₅₈	—	2	6	no	—
21	C₄²×C₂₉	—	2	6	no	—
22	C₄²×C₂₉	—	2	6	no	—
23	C₄²×C₂₉	Q₈	1	4	yes	complemented
24	C₄⋊Dic₂₉	—	2	6	no	—
25	#90779	—	2	12	no	—
26	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
27	C₂×C₄×C₂₉	—	2	3	no	—
28	C₂×C₄×C₂₉	—	2	3	no	—
29	C₂×C₄×C₂₉	—	2	3	no	—
30	C₂×C₄×C₂₉	—	2	3	no	—
31	C₂×C₄×C₂₉	C₂×Q₈	1	6	yes	—
32	C₂×C₄×C₂₉	#41	1	6	yes	—
33	C₂×C₄×C₂₉	#41	1	6	yes	—
34	C₂×Dic₂₉	—	2	12	no	—
35	C₂×Dic₂₉	—	2	6	no	—
36	C₂×Dic₂₉	—	2	6	no	—
37	Dic₅₈	—	4	4	no	—
38	#2863	—	29	1	no	maximal, Sylow
39	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
40	C₂²×C₂₉	C₂×#41	1	3	yes	—
41	C₂²×C₂₉	C₂×#41	1	3	yes	—
42	C₄×C₂₉	—	2	6	no	—
43	C₄×C₂₉	—	2	6	no	—
44	C₄×C₂₉	#126	1	4	yes	—
45	Dic₂₉	—	4	2	no	—
46	Dic₂₉	—	4	6	no	—
47	#391	—	29	3	no	—
48	#389	—	29	3	no	—
49	#387	—	29	6	no	—
50	#383	—	29	2	no	—
51	C₄³	D₂₉	1	1	yes	characteristic
52	C₂×C₂₉	C₂×#126	1	1	yes	characteristic
53	C₂×C₂₉	#529	1	3	yes	—
54	C₂×C₂₉	#533	1	3	yes	—
55	C₂²×Q₈	—	29	1	no	—
56	C₂×C₄⋊C₄	—	29	6	no	—
57	C₂×C₄⋊C₄	—	29	3	no	—
58	C₂×C₄²	C₂×D₂₉	1	3	yes	—
59	C₂×C₄²	C₂×D₂₉	1	3	yes	—
60	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
61	#95	—	29	6	no	—
62	#95	—	29	6	no	—
63	#95	—	29	6	no	—
64	C₂₉	#2863	1	1	yes	characteristic, complemented, Sylow
65	C₂×Q₈	—	58	6	no	—
66	C₂²×C₄	—	29	2	no	—
67	C₂²×C₄	—	29	6	no	—
68	C₂²×C₄	C₂²×D₂₉	1	3	yes	—
69	C₂²×C₄	C₂²×D₂₉	1	3	yes	—
70	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
71	C₄⋊C₄	—	58	12	no	—
72	C₄⋊C₄	—	58	6	no	—
73	C₄²	—	2	6	no	—
74	C₄²	—	2	6	no	—
75	C₄²	Dic₅₈	1	4	yes	complemented
76	C₂³	C₂³×D₂₉	1	1	yes	characteristic
77	Q₈	—	116	4	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	58	6	no	—
83	C₂×C₄	—	58	12	no	—
84	C₂×C₄	—	58	6	no	—
85	C₂×C₄	C₂×Dic₅₈	1	6	yes	—
86	C₂×C₄	#90805	1	6	yes	—
87	C₂×C₄	#90805	1	6	yes	—
88	C₂²	C₂²×Dic₅₈	1	1	yes	characteristic
89	C₂²	C₂×#90805	1	3	yes	—
90	C₂²	C₂×#90805	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	2	6	no	—
93	C₄	—	116	2	no	—
94	C₄	—	116	6	no	—
95	C₄	#11745238	1	4	yes	—
96	C₂	C₂×#11745238	1	1	yes	characteristic
97	C₂	#14271697	1	3	yes	—
98	C₂	#14271720	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271069

C₂

yes

maximal

#14271061

C₂

yes

maximal

#14271047

C₂

yes

maximal

#14271031

C₂

yes

maximal

C₄³×C₂₉

C₂

yes

maximal, characteristic

C₂²×Dic₅₈

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

C₂²

yes

—

#11745179

C₂²

yes

—

#11745179

C₂²

yes

—

#11745179

C₂²

yes

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂³

yes

—

C₂²×Dic₂₉

C₂³

yes

—

C₂×Dic₅₈

—

C₄²×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

Q₈

yes

complemented

C₄⋊Dic₂₉

—

#90779

—

C₂³×C₂₉

C₂⁴

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

#2863

—

maximal, Sylow

C₂²×C₂₉

C₂²×Q₈

yes

characteristic

C₂²×C₂₉

C₂×#41

yes

—

C₂²×C₂₉

C₂×#41

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#126

yes

—

Dic₂₉

—

Dic₂₉

—

—

—

—

—

C₄³

D₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#533

yes

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

—

—

—

C₂₉

#2863

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

Dic₅₈

yes

complemented

C₂³

C₂³×D₂₉

yes

characteristic

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₅₈

yes

—

C₂×C₄

#90805

yes

—

C₂×C₄

#90805

yes

—

C₂²

C₂²×Dic₅₈

yes

characteristic

C₂²

C₂×#90805

yes

—

C₂²

C₂×#90805

yes

—

C₄

—

C₄

—

C₄

—

116

—

C₄

—

116

—

C₄

#11745238

yes

—

C₂

C₂×#11745238

yes

characteristic

C₂

#14271697

yes

—

C₂

#14271720

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator, socle, prime radical, cosocle	C₂³×C₂₉	C₂⁴
Fitting	C₄³×C₂₉	C₂
hypercenter	C₄³	D₂₉
hypocenter	C₂₉	#2863
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₂₉

commutator, socle, prime radical, cosocle

C₂³×C₂₉

C₂⁴

Fitting

C₄³×C₂₉

C₂

hypercenter

C₄³

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
23. C₄²×C₂₉	Q₈	semidirect
64. C₂₉	#2863	semidirect
75. C₄²	Dic₅₈	semidirect

H ≅ G/N

type

23. C₄²×C₂₉

Q₈

semidirect

64. C₂₉

#2863

semidirect

75. C₄²

Dic₅₈

semidirect

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

subgroup	index
#14271069	2
#14271061	2
#14271047	2
#14271031	2
C₄³×C₂₉	2
#2863	29

subgroup

index

C₄³×C₂₉

Subgroups — #16827874

Conjugacy classes of subgroups

Complements

Maximal subgroups