Group #16827855 — subgroups

Subgroups — #16827855

Order 3712.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 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	C₂×#11745232	C₂	1	2	yes	maximal
2	#14271061	C₂	1	8	yes	maximal
3	#14271033	C₂	1	2	yes	maximal
4	#14271029	C₂	1	2	yes	maximal
5	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄²×C₂₉	C₂²	1	4	yes	—
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₂₉	C₂²	1	4	yes	—
11	C₂×C₄⋊Dic₂₉	C₂²	1	8	yes	—
12	C₂×#90779	C₂²	1	8	yes	—
13	#11745232	—	2	8	no	—
14	#11745179	C₂²	1	8	yes	—
15	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
16	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
17	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
19	C₂²×Dic₂₉	C₂³	1	8	yes	—
20	C₄²×C₂₉	—	2	8	no	—
21	C₄²×C₂₉	D₄	1	4	yes	—
22	C₄²×C₂₉	Q₈	1	4	yes	—
23	C₄²×C₂₉	Q₈	1	4	yes	—
24	C₄⋊Dic₂₉	—	2	8	no	—
25	C₄⋊Dic₂₉	—	2	16	no	—
26	#90779	—	2	16	no	—
27	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₂₉	—	2	4	no	—
29	C₂×C₄×C₂₉	—	2	4	no	—
30	C₂×C₄×C₂₉	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₂₉	C₂×Q₈	1	4	yes	—
33	C₂×C₄×C₂₉	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₂₉	#41	1	8	yes	—
37	C₂×Dic₂₉	—	2	8	no	—
38	C₂×Dic₂₉	—	2	16	no	—
39	#2859	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
41	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
43	C₂²×C₂₉	C₂×#41	1	4	yes	—
44	C₄×C₂₉	—	2	4	no	—
45	C₄×C₂₉	—	2	4	no	—
46	C₄×C₂₉	#125	1	8	yes	complemented
47	C₄×C₂₉	C₄⋊Q₈	1	4	yes	—
48	Dic₂₉	—	4	8	no	—
49	C₂×#125	—	29	2	no	—
50	#389	—	29	8	no	—
51	#384	—	29	2	no	—
52	#382	—	29	2	no	—
53	C₄³	D₂₉	1	1	yes	characteristic
54	C₂×C₂₉	C₂×#125	1	2	yes	—
55	C₂×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
56	C₂×C₂₉	#532	1	2	yes	—
57	C₂×C₂₉	#533	1	2	yes	—
58	#125	—	58	8	no	—
59	C₂×C₄⋊C₄	—	29	8	no	—
60	C₂×C₄⋊C₄	—	29	4	no	—
61	C₂×C₄⋊C₄	—	29	8	no	—
62	C₂×C₄²	C₂×D₂₉	1	4	yes	—
63	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
64	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
66	#95	—	29	8	no	—
67	C₂₉	#2859	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	—	29	8	no	—
69	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
70	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
71	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
73	C₄⋊C₄	—	58	16	no	—
74	C₄⋊C₄	—	58	8	no	—
75	C₄⋊C₄	—	58	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	Dic₅₈	1	4	yes	—
78	C₄²	Dic₅₈	1	4	yes	—
79	C₄²	D₁₁₆	1	4	yes	—
80	C₂³	C₂³×D₂₉	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	58	8	no	—
84	C₂×C₄	—	58	16	no	—
85	C₂×C₄	C₂×Dic₅₈	1	4	yes	—
86	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
87	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
88	C₂×C₄	C₂×Dic₅₈	1	4	yes	—
89	C₂×C₄	C₂×D₁₁₆	1	4	yes	—
90	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
91	C₂×C₄	#90805	1	8	yes	—
92	C₂²	C₂²×Dic₅₈	1	1	yes	characteristic
93	C₂²	C₂²×Dic₅₈	1	1	yes	characteristic
94	C₂²	C₂²×D₁₁₆	1	1	yes	characteristic
95	C₂²	C₂×#90805	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	116	8	no	—
99	C₄	#11745231	1	4	yes	—
100	C₄	#11745232	1	8	yes	complemented
101	C₂	C₂×#11745232	1	2	yes	—
102	C₂	C₂×#11745231	1	1	yes	characteristic
103	C₂	#14271713	1	2	yes	—
104	C₂	#14271720	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745232

C₂

yes

maximal

#14271061

C₂

yes

maximal

#14271033

C₂

yes

maximal

#14271029

C₂

yes

maximal

C₄³×C₂₉

C₂

yes

maximal, characteristic

C₂×C₄²×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

C₂²

yes

—

#11745232

—

#11745179

C₂²

yes

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×Dic₂₉

C₂³

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

Q₈

yes

—

C₄²×C₂₉

Q₈

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

#90779

—

C₂³×C₂₉

C₂⁴

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#2859

—

maximal, Sylow

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₂²×C₂₉

C₂²×Q₈

yes

characteristic

C₂²×C₂₉

C₂²×Q₈

yes

characteristic

C₂²×C₂₉

C₂×#41

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#125

yes

complemented

C₄×C₂₉

C₄⋊Q₈

yes

—

Dic₂₉

—

—

—

—

—

C₄³

D₂₉

yes

characteristic

C₂×C₂₉

C₂×#125

yes

—

C₂×C₂₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₂₉

#532

yes

—

C₂×C₂₉

#533

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₂×C₄²

C₂×D₂₉

yes

characteristic

#95

—

C₂₉

#2859

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂²×C₄

C₂²×D₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₅₈

yes

—

C₄²

Dic₅₈

yes

—

C₄²

D₁₁₆

yes

—

C₂³

C₂³×D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₅₈

yes

—

C₂×C₄

C₂×Dic₅₈

yes

—

C₂×C₄

C₂×Dic₅₈

yes

—

C₂×C₄

C₂×Dic₅₈

yes

—

C₂×C₄

C₂×D₁₁₆

yes

—

C₂×C₄

C₂×D₁₁₆

yes

—

C₂×C₄

#90805

yes

—

C₂²

C₂²×Dic₅₈

yes

characteristic

C₂²

C₂²×Dic₅₈

yes

characteristic

C₂²

C₂²×D₁₁₆

yes

characteristic

C₂²

C₂×#90805

yes

—

C₄

—

C₄

—

C₄

—

116

—

C₄

#11745231

yes

—

100

C₄

#11745232

yes

complemented

101

C₂

C₂×#11745232

yes

—

102

C₂

C₂×#11745231

yes

characteristic

103

C₂

#14271713

yes

—

104

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	#2859
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
46. C₄×C₂₉	#125	semidirect
67. C₂₉	#2859	semidirect
100. C₄	#11745232	semidirect

H ≅ G/N

type

46. C₄×C₂₉

#125

semidirect

67. C₂₉

#2859

semidirect

100. C₄

#11745232

semidirect

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

subgroup	index
C₂×#11745232	2
#14271061	2
#14271033	2
#14271029	2
C₄³×C₂₉	2
#2859	29

subgroup

index

C₄³×C₂₉

Subgroups — #16827855

Conjugacy classes of subgroups

Complements

Maximal subgroups