Group #16819393 — subgroups

Subgroups — #16819393

Order 3712.

228 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11745170	C₂	1	2	yes	maximal
2	M₁₆×Dic₂₉	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	#14270928	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90777	C₂²	1	2	yes	—
10	C₂²×#6597	C₂²	1	1	yes	characteristic
11	#11745170	C₄	1	8	yes	complemented
12	#11745163	—	2	2	no	—
13	C₈×Dic₂₉	—	2	2	no	—
14	C₈×Dic₂₉	C₄	1	4	yes	—
15	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₂₉	Q₈	1	2	yes	—
17	M₁₆×C₂₉	—	2	2	no	—
18	M₁₆×C₂₉	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
22	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
23	C₄×Dic₂₉	D₄	1	1	yes	characteristic
24	C₄×Dic₂₉	D₄	1	1	yes	characteristic
25	#90777	—	2	2	no	—
26	#90777	C₂×C₄	1	4	yes	—
27	C₂×#6597	—	2	2	no	—
28	C₂×#6597	C₂×C₄	1	2	yes	—
29	C₂×#6597	C₂×C₄	1	4	yes	—
30	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
33	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	#41	1	2	yes	—
35	C₂×Dic₂₉	—	2	4	no	—
36	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
37	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
38	C₈×C₂₉	—	2	2	no	—
39	C₈×C₂₉	—	2	4	no	—
40	#6597	—	2	4	no	—
41	#6597	C₄²	1	4	yes	—
42	C₄×#108	—	29	1	no	maximal, Sylow
43	C₂²×C₂₉	—	2	2	no	—
44	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₂₉	C₄×Q₈	1	2	yes	—
46	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
47	C₄×C₂₉	#117	1	1	yes	characteristic
48	C₄×C₂₉	C₄×D₄	1	2	yes	—
49	Dic₂₉	—	2	2	no	—
50	Dic₂₉	#108	1	4	yes	complemented
51	C₂×#108	—	29	2	no	—
52	C₄×M₁₆	—	29	2	no	—
53	C₂×C₄×C₈	—	29	1	no	—
54	#341	—	29	1	no	—
55	#341	D₂₉	1	1	yes	characteristic
56	C₂×C₂₉	—	2	2	no	—
57	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₂₉	C₂×#108	1	2	yes	—
59	C₂×M₁₆	—	29	2	no	—
60	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
61	C₂²×C₈	—	29	1	no	—
62	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
63	C₂×C₄²	—	29	1	no	—
64	#108	—	29	8	no	—
65	#97	—	58	2	no	—
66	C₄×C₈	—	29	4	no	—
67	C₄×C₈	—	58	2	no	—
68	C₂₉	C₄×#108	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₄	—	29	2	no	—
70	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	29	4	no	—
73	M₁₆	—	58	2	no	—
74	M₁₆	C₄×D₂₉	1	4	yes	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	29	2	no	—
78	C₂×C₈	—	29	4	no	—
79	C₂×C₈	—	58	2	no	—
80	C₂×C₈	C₄×D₂₉	1	2	yes	—
81	C₄²	—	29	2	no	—
82	C₄²	—	29	1	no	—
83	C₄²	—	29	1	no	—
84	C₂³	Q₈×D₂₉	1	1	yes	characteristic
85	C₂×C₄	—	29	2	no	—
86	C₂×C₄	—	29	2	no	—
87	C₂×C₄	—	58	4	no	—
88	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
89	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
90	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
91	C₂×C₄	#90807	1	2	yes	—
92	C₈	—	2	2	no	—
93	C₈	—	2	4	no	—
94	C₈	—	29	4	no	—
95	C₈	—	58	4	no	—
96	C₂²	—	2	2	no	—
97	C₂²	#11745249	1	2	yes	—
98	C₂²	C₄⋊C₄×D₂₉	1	1	yes	characteristic
99	C₄	—	29	4	no	—
100	C₄	—	58	2	no	—
101	C₄	C₄²×D₂₉	1	1	yes	characteristic
102	C₄	#11745239	1	1	yes	characteristic
103	C₄	#11745243	1	2	yes	—
104	C₂	—	2	2	no	—
105	C₂	#14271014	1	1	yes	characteristic
106	C₂	#108×D₂₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745170

C₂

yes

maximal

M₁₆×Dic₂₉

C₂

yes

maximal

C₂×C₈×Dic₂₉

C₂

yes

maximal, characteristic

#14270928

C₂

yes

maximal, characteristic

C₂₉×#341

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂²×#6597

C₂²

yes

characteristic

#11745170

C₄

yes

complemented

#11745163

—

C₈×Dic₂₉

—

C₈×Dic₂₉

C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

Q₈

yes

—

M₁₆×C₂₉

—

M₁₆×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

D₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

characteristic

#90777

—

#90777

C₂×C₄

yes

—

C₂×#6597

—

C₂×#6597

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₂³×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

#6597

—

#6597

C₄²

yes

—

C₄×#108

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

C₄×Q₈

yes

—

C₄×C₂₉

C₂×C₄²

yes

characteristic

C₄×C₂₉

#117

yes

characteristic

C₄×C₂₉

C₄×D₄

yes

—

Dic₂₉

—

Dic₂₉

#108

yes

complemented

C₂×#108

—

C₄×M₁₆

—

C₂×C₄×C₈

—

#341

—

#341

D₂₉

yes

characteristic

C₂×C₂₉

—

C₂×C₂₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₂₉

C₂×#108

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂×C₄²

—

#108

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂₉

C₄×#108

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₄×D₂₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₉

yes

—

C₄²

—

C₄²

—

C₄²

—

C₂³

Q₈×D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

C₂×C₄×D₂₉

yes

—

C₂×C₄

D₄×D₂₉

yes

characteristic

C₂×C₄

#90807

yes

—

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#11745249

yes

—

C₂²

C₄⋊C₄×D₂₉

yes

characteristic

C₄

—

100

C₄

—

101

C₄

C₄²×D₂₉

yes

characteristic

102

C₄

#11745239

yes

characteristic

103

C₄

#11745243

yes

—

104

C₂

—

105

C₂

#14271014

yes

characteristic

106

C₂

#108×D₂₉

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₉
commutator	C₄×C₂₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#341	C₂
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂³×C₂₉	C₂×Q₈
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#341	D₂₉
hypocenter	C₂₉	C₄×#108
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₂₉

commutator

C₄×C₂₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#341

C₂

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂³×C₂₉

C₂×Q₈

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
11. #11745170	C₄	semidirect
50. Dic₂₉	#108	semidirect
68. C₂₉	C₄×#108	semidirect

H ≅ G/N

type

11. #11745170

C₄

semidirect

50. Dic₂₉

#108

semidirect

68. C₂₉

C₄×#108

semidirect

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

subgroup	index
C₂×#11745170	2
M₁₆×Dic₂₉	2
C₂×C₈×Dic₂₉	2
#14270928	2
C₂₉×#341	2
C₄×#108	29

subgroup

index

C₂×#11745170

M₁₆×Dic₂₉

C₂×C₈×Dic₂₉

#14270928

C₂₉×#341

C₄×#108

Subgroups — #16819393

Conjugacy classes of subgroups

Complements

Maximal subgroups