Group #16819120 — subgroups

Subgroups — #16819120

Order 3712.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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	#14271561	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271540	C₂	1	1	yes	maximal, characteristic
3	#14271536	C₂	1	2	yes	maximal, complemented
4	#14271510	C₂	1	2	yes	maximal, complemented
5	C₂₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₂₃₂	—	2	2	no	—
7	C₂×#90773	—	2	4	no	—
8	#11745236	C₂²	1	1	yes	characteristic
9	#11745236	C₂²	1	1	yes	characteristic
10	#11745231	C₂²	1	2	yes	—
11	C₄×C₈×C₂₉	C₂²	1	2	yes	—
12	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
13	#11745169	—	2	4	no	—
14	#11745165	—	2	2	no	—
15	C₂×D₁₁₆	—	2	2	no	—
16	C₂×D₁₁₆	—	2	2	no	—
17	C₂×D₁₁₆	—	2	1	no	—
18	C₂×D₁₁₆	—	2	1	no	—
19	C₂×Dic₅₈	—	2	2	no	—
20	C₂×C₈×C₂₉	D₄	1	4	yes	—
21	C₂×C₈×C₂₉	D₄	1	2	yes	—
22	C₄²×C₂₉	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	—	2	2	no	—
25	D₂₃₂	—	4	4	no	—
26	#90773	—	4	8	no	—
27	C₂²×D₂₉	—	4	1	no	—
28	C₂²×D₂₉	—	4	1	no	—
29	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
31	C₂×Dic₂₉	—	4	2	no	—
32	D₁₁₆	—	4	2	no	—
33	D₁₁₆	—	4	2	no	—
34	D₁₁₆	—	4	4	no	—
35	D₁₁₆	—	4	4	no	—
36	Dic₅₈	—	4	4	no	—
37	C₈×C₂₉	—	2	4	no	—
38	C₈×C₂₉	SD₁₆	1	4	yes	complemented
39	#1715	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	#127	1	1	yes	characteristic
41	C₂×D₂₉	—	8	1	no	—
42	C₂×D₂₉	—	8	1	no	—
43	C₂×D₂₉	—	8	2	no	—
44	C₂×D₂₉	—	8	2	no	—
45	C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
46	C₄×C₂₉	AGL(1,ℤ/8)	1	4	yes	—
47	Dic₂₉	—	8	2	no	—
48	#498	—	29	1	no	—
49	#493	—	29	1	no	—
50	#492	—	29	2	no	—
51	#486	—	29	2	no	—
52	#322	D₂₉	1	1	yes	characteristic, complemented
53	C₂×C₂₉	#492	1	1	yes	characteristic
54	C₂×C₂₉	#496	1	2	yes	—
55	D₂₉	—	16	1	no	—
56	D₂₉	—	16	1	no	—
57	C₂×SD₁₆	—	58	4	no	—
58	C₂×D₈	—	58	2	no	—
59	C₄⋊Q₈	—	29	2	no	—
60	#127	—	29	1	no	—
61	#127	—	29	1	no	—
62	#106	—	58	2	no	—
63	#102	—	58	4	no	—
64	C₄×C₈	C₂×D₂₉	1	2	yes	—
65	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
66	C₂₉	#1715	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	58	2	no	—
68	C₂×D₄	—	58	2	no	—
69	C₂×D₄	—	58	1	no	—
70	C₂×D₄	—	58	1	no	—
71	C₂×D₄	—	58	2	no	—
72	SD₁₆	—	116	8	no	—
73	D₈	—	116	4	no	—
74	C₂×C₈	D₁₁₆	1	4	yes	—
75	C₂×C₈	D₁₁₆	1	2	yes	—
76	C₄⋊C₄	—	58	2	no	—
77	C₄⋊C₄	—	58	2	no	—
78	C₄²	C₂²×D₂₉	1	1	yes	characteristic
79	C₂³	—	116	1	no	—
80	C₂³	—	116	1	no	—
81	Q₈	—	116	4	no	—
82	D₄	—	116	2	no	—
83	D₄	—	116	2	no	—
84	D₄	—	116	4	no	—
85	D₄	—	116	4	no	—
86	C₂×C₄	—	116	2	no	—
87	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
88	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
89	C₈	—	2	4	no	—
90	C₈	#90773	1	4	yes	complemented
91	C₂²	—	232	1	no	—
92	C₂²	—	232	1	no	—
93	C₂²	—	232	2	no	—
94	C₂²	—	232	2	no	—
95	C₂²	#11745236	1	1	yes	characteristic
96	C₄	—	232	2	no	—
97	C₄	C₂×#90773	1	2	yes	—
98	C₄	#11745270	1	4	yes	—
99	C₂	—	464	1	no	—
100	C₂	—	464	1	no	—
101	C₂	#14271536	1	1	yes	characteristic
102	C₂	#14271552	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271561

C₂

yes

maximal, characteristic, complemented

#14271540

C₂

yes

maximal, characteristic

#14271536

C₂

yes

maximal, complemented

#14271510

C₂

yes

maximal, complemented

C₂₉×#322

C₂

yes

maximal, characteristic, complemented

C₂×D₂₃₂

—

C₂×#90773

—

#11745236

C₂²

yes

characteristic

#11745236

C₂²

yes

characteristic

#11745231

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

characteristic

#11745169

—

#11745165

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

D₂₃₂

—

#90773

—

C₂²×D₂₉

—

C₂²×D₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

—

D₁₁₆

—

D₁₁₆

—

D₁₁₆

—

D₁₁₆

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

SD₁₆

yes

—

C₂²×C₂₉

yes

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

C₂×SD₁₆

yes

—

C₄×C₂₉

AGL(1,ℤ/8)

yes

—

Dic₂₉

—

—

—

—

—

D₂₉

yes

characteristic, complemented

C₂×C₂₉

#492

yes

characteristic

C₂×C₂₉

#496

yes

—

D₂₉

—

D₂₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

—

—

—

—

C₄×C₈

C₂×D₂₉

yes

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1715

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

116

—

D₈

—

116

—

C₂×C₈

D₁₁₆

yes

—

C₂×C₈

D₁₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

116

—

C₂³

—

116

—

Q₈

—

116

—

D₄

—

116

—

D₄

—

116

—

D₄

—

116

—

D₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

C₂×D₁₁₆

yes

—

C₈

—

C₈

#90773

yes

complemented

C₂²

—

232

—

C₂²

—

232

—

C₂²

—

232

—

C₂²

—

232

—

C₂²

#11745236

yes

characteristic

C₄

—

232

—

C₄

C₂×#90773

yes

—

C₄

#11745270

yes

—

C₂

—

464

—

100

C₂

—

464

—

101

C₂

#14271536

yes

characteristic

102

C₂

#14271552

yes

—

	subgroup	G/H
center	C₂²	#11745236
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#322	C₂
socle	C₂²×C₂₉	#127
prime radical	#14271540	C₂
hypercenter	#322	D₂₉
hypocenter	C₂₉	#1715
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#11745236

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#322

C₂

C₂²×C₂₉

C₂

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
1. #14271561	C₂	semidirect
3. #14271536	C₂	semidirect
4. #14271510	C₂	semidirect
5. C₂₉×#322	C₂	semidirect
38. C₈×C₂₉	SD₁₆	semidirect
52. #322	D₂₉	semidirect
66. C₂₉	#1715	semidirect
90. C₈	#90773	semidirect

H ≅ G/N

type

1. #14271561

C₂

semidirect

3. #14271536

C₂

semidirect

4. #14271510

C₂

semidirect

5. C₂₉×#322

C₂

semidirect

38. C₈×C₂₉

SD₁₆

semidirect

52. #322

D₂₉

semidirect

66. C₂₉

#1715

semidirect

90. C₈

#90773

semidirect

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

subgroup	index
#14271561	2
#14271540	2
#14271536	2
#14271510	2
C₂₉×#322	2
#1715	29

subgroup

index

C₂₉×#322

Subgroups — #16819120

Conjugacy classes of subgroups

Complements

Maximal subgroups