Group #16819156 — subgroups

Subgroups — #16819156

Order 3712.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14271540	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271539	C₂	1	2	yes	maximal, complemented
3	#14271511	C₂	1	2	yes	maximal, complemented
4	#14270884	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×SD₁₆×C₂₉	—	2	2	no	—
7	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂₉×#127	C₂²	1	1	yes	characteristic
9	C₂×#90782	—	2	4	no	—
10	C₂×D₂₃₂	—	2	2	no	—
11	#11745236	C₂²	1	2	yes	—
12	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
13	#11745157	—	2	4	no	—
14	C₄×#6597	C₂²	1	2	yes	—
15	C₂×Q₈×C₂₉	—	2	1	no	—
16	C₂×D₄×C₂₉	—	2	2	no	—
17	C₂×D₄×C₂₉	—	2	1	no	—
18	C₂×D₁₁₆	—	2	2	no	—
19	C₂×D₁₁₆	—	2	2	no	—
20	C₂×D₁₁₆	—	2	2	no	—
21	SD₁₆×C₂₉	—	4	4	no	—
22	C₂×C₈×C₂₉	D₄	1	2	yes	—
23	C₄⋊C₄×C₂₉	—	2	2	no	—
24	C₄²×C₂₉	C₂³	1	1	yes	characteristic
25	#90782	—	4	8	no	—
26	C₂×#6597	D₄	1	4	yes	—
27	D₂₃₂	—	4	4	no	—
28	C₂³×C₂₉	—	4	1	no	—
29	C₂²×D₂₉	—	4	2	no	—
30	Q₈×C₂₉	—	4	2	no	—
31	D₄×C₂₉	—	4	2	no	—
32	D₄×C₂₉	—	4	4	no	—
33	C₂×C₄×C₂₉	—	4	1	no	—
34	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
36	D₁₁₆	—	4	4	no	—
37	D₁₁₆	—	4	4	no	—
38	D₁₁₆	—	4	4	no	—
39	C₈×C₂₉	D₈	1	4	yes	complemented
40	#6597	—	2	4	no	—
41	#1721	—	29	1	no	maximal, Sylow
42	C₂²×C₂₉	—	8	1	no	—
43	C₂²×C₂₉	—	8	2	no	—
44	C₂²×C₂₉	#127	1	1	yes	characteristic
45	C₂×D₂₉	—	8	2	no	—
46	C₂×D₂₉	—	8	2	no	—
47	C₂×D₂₉	—	8	2	no	—
48	C₄×C₂₉	—	8	1	no	—
49	C₄×C₂₉	C₂×D₈	1	2	yes	—
50	C₄×C₂₉	AGL(1,ℤ/8)	1	4	yes	—
51	#493	—	29	2	no	—
52	#493	—	29	1	no	—
53	#492	D₂₉	1	1	yes	characteristic, complemented
54	#486	—	29	2	no	—
55	#322	—	29	1	no	—
56	C₂×C₂₉	—	16	1	no	—
57	C₂×C₂₉	#493	1	1	yes	characteristic
58	C₂×C₂₉	#496	1	2	yes	—
59	D₂₉	—	16	2	no	—
60	C₂×SD₁₆	—	2	2	no	—
61	C₂×D₈	—	58	4	no	—
62	C₂×D₈	—	58	2	no	—
63	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
64	#127	—	29	2	no	—
65	#127	C₂×D₂₉	1	1	yes	characteristic
66	#102	—	58	4	no	—
67	C₄×C₈	—	29	2	no	—
68	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
69	C₂₉	#1721	1	1	yes	characteristic, complemented, Sylow
70	C₂×Q₈	—	2	1	no	—
71	C₂×D₄	—	2	2	no	—
72	C₂×D₄	—	2	1	no	—
73	C₂×D₄	—	58	2	no	—
74	C₂×D₄	—	58	2	no	—
75	C₂×D₄	—	58	2	no	—
76	SD₁₆	—	4	4	no	—
77	D₈	—	116	8	no	—
78	D₈	—	116	4	no	—
79	C₂×C₈	—	29	4	no	—
80	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄²	C₂²×D₂₉	1	1	yes	characteristic
83	C₂³	—	4	1	no	—
84	C₂³	—	116	2	no	—
85	Q₈	—	4	2	no	—
86	D₄	—	4	2	no	—
87	D₄	—	4	4	no	—
88	D₄	—	116	4	no	—
89	D₄	—	116	4	no	—
90	D₄	—	116	4	no	—
91	C₂×C₄	—	4	1	no	—
92	C₂×C₄	D₄×D₂₉	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
94	C₈	—	58	4	no	—
95	C₈	#90782	1	4	yes	complemented
96	C₂²	—	8	1	no	—
97	C₂²	—	8	2	no	—
98	C₂²	—	232	2	no	—
99	C₂²	—	232	2	no	—
100	C₂²	—	232	2	no	—
101	C₂²	#11745302	1	1	yes	characteristic
102	C₄	—	8	1	no	—
103	C₄	#11745276	1	4	yes	—
104	C₄	C₂×#90782	1	2	yes	—
105	C₂	—	16	1	no	—
106	C₂	—	464	2	no	—
107	C₂	#14271539	1	1	yes	characteristic
108	C₂	#14271549	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271540

C₂

yes

maximal, characteristic, complemented

#14271539

C₂

yes

maximal, complemented

#14271511

C₂

yes

maximal, complemented

#14270884

C₂

yes

maximal, characteristic, complemented

C₂₉×#492

C₂

yes

maximal, characteristic, complemented

C₂×SD₁₆×C₂₉

—

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂₉×#127

C₂²

yes

characteristic

C₂×#90782

—

C₂×D₂₃₂

—

#11745236

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

characteristic

#11745157

—

C₄×#6597

C₂²

yes

—

C₂×Q₈×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

SD₁₆×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

#90782

—

C₂×#6597

D₄

yes

—

D₂₃₂

—

C₂³×C₂₉

—

C₂²×D₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

D₁₁₆

—

D₁₁₆

—

D₁₁₆

—

C₈×C₂₉

D₈

yes

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#127

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×D₈

yes

—

C₄×C₂₉

AGL(1,ℤ/8)

yes

—

#493

—

#493

—

#492

D₂₉

yes

characteristic, complemented

#486

—

#322

—

C₂×C₂₉

—

C₂×C₂₉

#493

yes

characteristic

C₂×C₂₉

#496

yes

—

D₂₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

#127

—

#127

C₂×D₂₉

yes

characteristic

#102

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1721

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

D₈

—

116

—

D₈

—

116

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

—

C₄⋊C₄

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

C₂³

—

116

—

Q₈

—

D₄

—

D₄

—

D₄

—

116

—

D₄

—

116

—

D₄

—

116

—

C₂×C₄

—

C₂×C₄

D₄×D₂₉

yes

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

#90782

yes

complemented

C₂²

—

C₂²

—

C₂²

—

232

—

C₂²

—

232

—

100

C₂²

—

232

—

101

C₂²

#11745302

yes

characteristic

102

C₄

—

103

C₄

#11745276

yes

—

104

C₄

C₂×#90782

yes

—

105

C₂

—

106

C₂

—

464

—

107

C₂

#14271539

yes

characteristic

108

C₂

#14271549

yes

—

	subgroup	G/H
center	C₂²	#11745302
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#492	C₂
socle	C₂²×C₂₉	#127
hypercenter	#492	D₂₉
hypocenter	C₂₉	#1721
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#11745302

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#492

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
1. #14271540	C₂	semidirect
2. #14271539	C₂	semidirect
3. #14271511	C₂	semidirect
4. #14270884	C₂	semidirect
5. C₂₉×#492	C₂	semidirect
39. C₈×C₂₉	D₈	semidirect
53. #492	D₂₉	semidirect
69. C₂₉	#1721	semidirect
95. C₈	#90782	semidirect

H ≅ G/N

type

1. #14271540

C₂

semidirect

2. #14271539

C₂

semidirect

3. #14271511

C₂

semidirect

4. #14270884

C₂

semidirect

5. C₂₉×#492

C₂

semidirect

39. C₈×C₂₉

D₈

semidirect

53. #492

D₂₉

semidirect

69. C₂₉

#1721

semidirect

95. C₈

#90782

semidirect

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

subgroup	index
#14271540	2
#14271539	2
#14271511	2
#14270884	2
C₂₉×#492	2
#1721	29

subgroup

index

C₂₉×#492

Subgroups — #16819156

Conjugacy classes of subgroups

Complements

Maximal subgroups