Group #16821003 — subgroups

Subgroups — #16821003

Order 3712.

176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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	#14271203	C₂	1	2	yes	maximal
2	#14271189	C₂	1	1	yes	maximal, characteristic
3	#14270932	C₂	1	2	yes	maximal
4	#14270928	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₉×#106	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
8	#11745288	C₂²	1	1	yes	characteristic
9	C₂×#90777	C₂²	1	1	yes	characteristic
10	C₂×#90777	C₂²	1	2	yes	—
11	C₂₉×#106	—	2	2	no	—
12	#11745162	—	2	2	no	—
13	#11745156	—	2	2	no	—
14	#11745155	—	2	2	no	—
15	C₂²×C₄×C₂₉	—	2	2	no	—
16	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂×C₈×C₂₉	—	2	2	no	—
18	C₂×C₈×C₂₉	D₄	1	2	yes	—
19	C₄⋊C₄×C₂₉	—	2	2	no	—
20	C₄⋊C₄×C₂₉	—	2	2	no	—
21	C₂²⋊Dic₂₉	—	2	1	no	—
22	C₄⋊Dic₂₉	D₄	1	2	yes	—
23	C₄×Dic₂₉	—	2	1	no	—
24	#90777	—	2	2	no	—
25	#90777	—	2	2	no	—
26	#90777	Q₈	1	4	yes	—
27	C₂×#6597	—	2	2	no	—
28	C₂×#6597	—	2	1	no	—
29	C₂³×C₂₉	#41	1	1	yes	characteristic
30	C₂×C₄×C₂₉	—	4	2	no	—
31	C₂×C₄×C₂₉	—	8	2	no	—
32	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₂₉	#41	1	2	yes	—
36	C₂×Dic₂₉	—	2	2	no	—
37	C₈×C₂₉	—	2	2	no	—
38	#6597	—	2	4	no	—
39	#6597	—	4	1	no	—
40	#2090	—	29	1	no	maximal, Sylow
41	C₂²×C₂₉	—	2	2	no	—
42	C₂²×C₂₉	#121	1	1	yes	characteristic
43	C₂²×C₂₉	#125	1	2	yes	—
44	C₄×C₂₉	—	8	2	no	—
45	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
46	C₄×C₂₉	#123	1	1	yes	characteristic
47	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
48	Dic₂₉	—	4	2	no	—
49	#428	—	29	2	no	—
50	C₂×#106	D₂₉	1	1	yes	characteristic
51	#424	—	29	1	no	—
52	#343	—	29	2	no	—
53	#341	—	29	1	no	—
54	C₂×C₂₉	—	2	2	no	—
55	C₂×C₂₉	#398	1	1	yes	characteristic
56	C₂×C₂₉	#471	1	2	yes	—
57	C₂×M₁₆	—	29	2	no	—
58	C₂×M₁₆	—	29	1	no	—
59	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
60	#117	—	29	1	no	—
61	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
62	#107	—	58	2	no	—
63	#106	—	2	2	no	—
64	#106	—	58	2	no	—
65	C₄⋊C₈	—	58	2	no	—
66	C₂₉	#2090	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	—	2	2	no	—
68	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
69	M₁₆	—	29	4	no	—
70	M₁₆	—	58	2	no	—
71	M₁₆	—	58	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	58	2	no	—
74	C₂×C₈	—	58	1	no	—
75	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	—	29	2	no	—
79	C₂²⋊C₄	—	58	1	no	—
80	C₄²	—	58	1	no	—
81	C₂³	#90807	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	8	2	no	—
84	C₂×C₄	—	58	2	no	—
85	C₂×C₄	#90805	1	2	yes	—
86	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
87	C₂×C₄	Q₈×D₂₉	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
89	C₈	—	2	2	no	—
90	C₈	—	58	4	no	—
91	C₈	—	116	1	no	—
92	C₂²	—	2	2	no	—
93	C₂²	#11745251	1	2	yes	—
94	C₂²	#11745300	1	1	yes	characteristic
95	C₄	—	8	2	no	—
96	C₄	—	116	2	no	—
97	C₄	#11745258	1	2	yes	—
98	C₄	#11745291	1	1	yes	characteristic
99	C₄	#11745306	1	1	yes	characteristic
100	C₂	—	2	2	no	—
101	C₂	#14271094	1	1	yes	characteristic
102	C₂	#14271423	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271203

C₂

yes

maximal

#14271189

C₂

yes

maximal, characteristic

#14270932

C₂

yes

maximal

#14270928

C₂

yes

maximal, characteristic

C₂×C₂₉×#106

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

#11745288

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂₉×#106

—

#11745162

—

#11745156

—

#11745155

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

—

C₄×Dic₂₉

—

#90777

—

#90777

—

#90777

Q₈

yes

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

#41

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₈×C₂₉

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

#121

yes

characteristic

C₂²×C₂₉

#125

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

C₄×C₂₉

#123

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

Dic₂₉

—

#428

—

C₂×#106

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

#398

yes

characteristic

C₂×C₂₉

#471

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₂₉

#2090

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#90807

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#90805

yes

—

C₂×C₄

D₄×D₂₉

yes

characteristic

C₂×C₄

Q₈×D₂₉

yes

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

—

C₈

—

116

—

C₂²

—

C₂²

#11745251

yes

—

C₂²

#11745300

yes

characteristic

C₄

—

C₄

—

116

—

C₄

#11745258

yes

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#14271094

yes

characteristic

102

C₂

#14271423

yes

—

	subgroup	G/H
center	C₂²	#11745300
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#106	C₂
socle	C₂²×C₂₉	#121
prime radical	C₂³×C₂₉	#41
hypercenter	C₂×#106	D₂₉
hypocenter	C₂₉	#2090
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂²

#11745300

commutator, cosocle

C₂²×C₄×C₂₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#106

C₂

C₂²×C₂₉

C₂³×C₂₉

D₂₉

C₂₉

G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
66. C₂₉	#2090	semidirect

H ≅ G/N

type

66. C₂₉

#2090

semidirect

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

subgroup	index
#14271203	2
#14271189	2
#14270932	2
#14270928	2
C₂×C₂₉×#106	2
#2090	29

subgroup

index

C₂×C₂₉×#106

Subgroups — #16821003

Conjugacy classes of subgroups

Complements

Maximal subgroups