Group #16817400 — subgroups

Subgroups — #16817400

Order 3712.

192 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14271127	C₂	1	2	yes	maximal
2	C₂₉×#381	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
4	C₂×C₂²⋊C₄×C₂₉	C₄	1	2	yes	—
5	C₂×#90777	—	2	2	no	—
6	C₂₉×#95	—	2	2	no	—
7	C₂²⋊#6597	—	2	2	no	—
8	C₂²⋊#6597	C₄	1	4	yes	complemented
9	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₂₉	—	2	2	no	—
11	C₂²×C₄×C₂₉	—	4	2	no	—
12	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₂₉	D₄	1	2	yes	—
15	C₂²×C₄×C₂₉	Q₈	1	1	yes	characteristic
16	C₂²⋊C₄×C₂₉	—	4	2	no	—
17	#90777	—	4	4	no	—
18	C₂×#6597	—	2	4	no	—
19	C₂³×C₂₉	—	2	2	no	—
20	C₂³×C₂₉	—	4	2	no	—
21	C₂³×C₂₉	C₄²	1	1	yes	characteristic
22	C₂³×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂³×C₂₉	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉	—	2	4	no	—
25	C₂×C₄×C₂₉	—	4	2	no	—
26	C₂×C₄×C₂₉	—	4	1	no	—
27	C₂×C₄×C₂₉	—	4	1	no	—
28	C₂×C₄×C₂₉	—	4	4	no	—
29	C₂×C₄×C₂₉	—	4	2	no	—
30	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
32	#6597	—	4	4	no	—
33	#1306	—	29	1	no	maximal, Sylow
34	C₂²×C₂₉	—	2	2	no	—
35	C₂²×C₂₉	—	2	1	no	—
36	C₂²×C₂₉	—	2	1	no	—
37	C₂²×C₂₉	—	2	2	no	—
38	C₂²×C₂₉	—	2	2	no	—
39	C₂²×C₂₉	—	4	4	no	—
40	C₂²×C₂₉	#95	1	1	yes	characteristic
41	C₂²×C₂₉	#99	1	2	yes	—
42	C₄×C₂₉	—	2	2	no	—
43	C₄×C₂₉	—	2	2	no	—
44	C₄×C₂₉	—	8	2	no	—
45	#407	—	29	2	no	—
46	#381	D₂₉	1	1	yes	characteristic
47	C₂×C₂₉	—	2	2	no	—
48	C₂×C₂₉	—	4	1	no	—
49	C₂×C₂₉	—	4	1	no	—
50	C₂×C₂₉	#342	1	1	yes	characteristic
51	C₂×C₂₉	#344	1	2	yes	—
52	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
53	C₂×M₁₆	—	58	2	no	—
54	C₂×C₂²⋊C₄	Dic₂₉	1	2	yes	—
55	C₂²⋊C₈	—	29	4	no	—
56	C₂²⋊C₈	—	58	2	no	—
57	#95	—	2	2	no	—
58	C₂₉	#1306	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	C₂×Dic₂₉	1	1	yes	characteristic
60	C₂²×C₄	—	2	2	no	—
61	C₂²×C₄	—	4	2	no	—
62	C₂²×C₄	Dic₅₈	1	1	yes	characteristic
63	C₂²×C₄	C₄×D₂₉	1	2	yes	—
64	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
65	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
66	M₁₆	—	116	4	no	—
67	C₂×C₈	—	58	4	no	—
68	C₂²⋊C₄	—	4	2	no	—
69	C₂³	—	2	2	no	—
70	C₂³	—	4	2	no	—
71	C₂³	C₄×Dic₂₉	1	1	yes	characteristic
72	C₂³	C₄⋊Dic₂₉	1	1	yes	characteristic
73	C₂³	C₂²⋊Dic₂₉	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	4	4	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	#90779	1	2	yes	—
81	C₂×C₄	#90781	1	2	yes	—
82	C₈	—	116	4	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	2	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	4	4	no	—
89	C₂²	#11745179	1	1	yes	characteristic
90	C₂²	#11745182	1	2	yes	—
91	C₄	—	2	2	no	—
92	C₄	—	2	2	no	—
93	C₄	—	8	2	no	—
94	C₂	—	2	2	no	—
95	C₂	—	4	1	no	—
96	C₂	—	4	1	no	—
97	C₂	#14270930	1	1	yes	characteristic
98	C₂	#14270933	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271127

C₂

yes

maximal

C₂₉×#381

C₂

yes

maximal, characteristic

C₂³×C₄×C₂₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₂₉

C₄

yes

—

C₂×#90777

—

C₂₉×#95

—

C₂²⋊#6597

—

C₂²⋊#6597

C₄

yes

complemented

C₂⁴×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

Q₈

yes

characteristic

C₂²⋊C₄×C₂₉

—

#90777

—

C₂×#6597

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

C₄²

yes

characteristic

C₂³×C₂₉

C₂²⋊C₄

yes

characteristic

C₂³×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

#6597

—

#1306

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#95

yes

characteristic

C₂²×C₂₉

#99

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

#407

—

#381

D₂₉

yes

characteristic

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#342

yes

characteristic

C₂×C₂₉

#344

yes

—

C₂³×C₄

C₂×D₂₉

yes

characteristic

C₂×M₁₆

—

C₂×C₂²⋊C₄

Dic₂₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#95

—

C₂₉

#1306

yes

characteristic, complemented, Sylow

C₂⁴

C₂×Dic₂₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₅₈

yes

characteristic

C₂²×C₄

C₄×D₂₉

yes

—

C₂²×C₄

D₁₁₆

yes

characteristic

C₂²×C₄

C₂²⋊D₂₉

yes

—

M₁₆

—

116

—

C₂×C₈

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

C₄×Dic₂₉

yes

characteristic

C₂³

C₄⋊Dic₂₉

yes

characteristic

C₂³

C₂²⋊Dic₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#90779

yes

—

C₂×C₄

#90781

yes

—

C₈

—

116

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#11745179

yes

characteristic

C₂²

#11745182

yes

—

C₄

—

C₄

—

C₄

—

C₂

—

C₂

—

C₂

—

C₂

#14270930

yes

characteristic

C₂

#14270933

yes

—

	subgroup	G/H
center	C₂²	#11745179
commutator	C₂³×C₂₉	C₄²
Frattini	C₂³×C₄	C₂×D₂₉
Fitting	C₂₉×#381	C₂
socle	C₂²×C₂₉	#95
prime radical	C₂⁴×C₂₉	C₂×C₄
cosocle	C₂³×C₄×C₂₉	C₂²
hypercenter	#381	D₂₉
hypocenter	C₂₉	#1306
LCS	G ▷ C₂³×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

subgroup

G/H

center

C₂²

#11745179

commutator

C₂³×C₂₉

C₄²

Frattini

C₂³×C₄

C₂×D₂₉

Fitting

C₂₉×#381

C₂

socle

C₂²×C₂₉

#95

prime radical

C₂⁴×C₂₉

C₂×C₄

cosocle

C₂³×C₄×C₂₉

C₂²

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

N	H ≅ G/N	type
8. C₂²⋊#6597	C₄	semidirect
58. C₂₉	#1306	semidirect

H ≅ G/N

type

8. C₂²⋊#6597

C₄

semidirect

58. C₂₉

#1306

semidirect

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

subgroup	index
#14271127	2
C₂₉×#381	2
#1306	29

subgroup

index

#14271127

C₂₉×#381

#1306

Subgroups — #16817400

Conjugacy classes of subgroups

Complements

Maximal subgroups