Group #16819395 — subgroups

Subgroups — C₄×#11745170 #16819395

Order 3712.

228 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 121 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	C₄×#90777	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#6597	C₂	1	1	yes	maximal, characteristic
4	#14270927	C₂	1	2	yes	maximal
5	C₄×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×#90777	C₂²	1	2	yes	—
9	C₂²×#6597	C₂²	1	1	yes	characteristic
10	C₂²×#6597	C₂²	1	1	yes	characteristic
11	C₂₉×#97	—	2	1	no	—
12	C₄×C₈×C₂₉	—	2	1	no	—
13	#11745170	C₄	1	8	yes	direct product factor
14	#11745151	—	2	1	no	—
15	C₄×#6597	—	2	1	no	—
16	C₄×#6597	C₄	1	4	yes	—
17	C₂²×C₄×C₂₉	Q₈	1	2	yes	—
18	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	M₁₆×C₂₉	—	2	2	no	—
20	M₁₆×C₂₉	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₂₉	—	2	2	no	—
22	C₄²×C₂₉	C₂×C₄	1	2	yes	—
23	C₄²×C₂₉	D₄	1	1	yes	characteristic
24	C₄²×C₂₉	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	—	2	2	no	—
29	C₂×#6597	C₂×C₄	1	2	yes	—
30	C₂×#6597	C₂×C₄	1	2	yes	—
31	C₂×#6597	C₂×C₄	1	4	yes	—
32	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₂₉	—	2	4	no	—
34	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	#41	1	2	yes	—
40	C₈×C₂₉	—	2	4	no	—
41	#6597	—	2	2	no	—
42	#6597	—	2	4	no	—
43	#6597	C₄²	1	4	yes	—
44	C₄×#108	—	29	1	no	maximal, Sylow
45	C₂²×C₂₉	—	2	2	no	—
46	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₂₉	C₄×Q₈	1	2	yes	—
48	C₄×C₂₉	—	2	2	no	—
49	C₄×C₂₉	#108	1	4	yes	complemented
50	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
51	C₄×C₂₉	#117	1	1	yes	characteristic
52	C₄×C₂₉	C₄×D₄	1	2	yes	—
53	C₂×#108	—	29	2	no	—
54	C₄×M₁₆	—	29	1	no	—
55	C₄×M₁₆	D₂₉	1	1	yes	characteristic
56	C₂×C₄×C₈	—	29	1	no	—
57	#341	—	29	2	no	—
58	C₂×C₂₉	—	2	2	no	—
59	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₂₉	C₂×#108	1	2	yes	—
61	C₂×M₁₆	—	29	2	no	—
62	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
63	C₂²×C₈	—	29	1	no	—
64	C₂²×C₈	—	29	1	no	—
65	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
66	#108	—	29	8	no	—
67	#97	—	2	1	no	—
68	#97	—	58	1	no	—
69	C₄×C₈	—	2	1	no	—
70	C₄×C₈	—	29	4	no	—
71	C₄×C₈	—	58	1	no	—
72	C₂₉	C₄×#108	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₄	Dic₅₈	1	2	yes	—
74	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
75	M₁₆	—	2	2	no	—
76	M₁₆	—	29	4	no	—
77	M₁₆	—	58	2	no	—
78	M₁₆	C₄×D₂₉	1	4	yes	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	29	2	no	—
81	C₂×C₈	—	29	4	no	—
82	C₂×C₈	—	29	2	no	—
83	C₂×C₈	—	58	2	no	—
84	C₂×C₈	—	58	2	no	—
85	C₄²	C₄×D₂₉	1	2	yes	—
86	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
87	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
88	C₂³	C₂×Dic₅₈	1	1	yes	characteristic
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	#90779	1	2	yes	—
91	C₂×C₄	#90779	1	2	yes	—
92	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
93	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
94	C₂×C₄	#90805	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
96	C₈	—	2	4	no	—
97	C₈	—	29	4	no	—
98	C₈	—	58	4	no	—
99	C₈	—	58	2	no	—
100	C₂²	—	2	2	no	—
101	C₂²	C₄×Dic₅₈	1	2	yes	—
102	C₂²	C₂×#90779	1	1	yes	characteristic
103	C₄	—	2	2	no	—
104	C₄	#11745170	1	4	yes	direct product factor
105	C₄	C₄²×D₂₉	1	1	yes	characteristic
106	C₄	#11745234	1	1	yes	characteristic
107	C₄	C₄×C₂²⋊D₂₉	1	2	yes	—
108	C₂	—	2	2	no	—
109	C₂	C₄×#90779	1	1	yes	characteristic
110	C₂	C₂×#11745170	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745170

C₂

yes

maximal

C₄×#90777

C₂

yes

maximal, characteristic

C₂×C₄×#6597

C₂

yes

maximal, characteristic

#14270927

C₂

yes

maximal

C₄×M₁₆×C₂₉

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂²×#6597

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

characteristic

C₂₉×#97

—

C₄×C₈×C₂₉

—

#11745170

C₄

yes

direct product factor

#11745151

—

C₄×#6597

—

C₄×#6597

C₄

yes

—

C₂²×C₄×C₂₉

Q₈

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

D₄

yes

characteristic

#90777

—

#90777

C₂×C₄

yes

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₂³×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

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

—

C₈×C₂₉

—

#6597

—

#6597

—

#6597

C₄²

yes

—

C₄×#108

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

C₄×Q₈

yes

—

C₄×C₂₉

—

C₄×C₂₉

#108

yes

complemented

C₄×C₂₉

C₂×C₄²

yes

characteristic

C₄×C₂₉

#117

yes

characteristic

C₄×C₂₉

C₄×D₄

yes

—

C₂×#108

—

C₄×M₁₆

—

C₄×M₁₆

D₂₉

yes

characteristic

C₂×C₄×C₈

—

#341

—

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×C₄²

C₂×D₂₉

yes

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂₉

C₄×#108

yes

characteristic, complemented, Sylow

C₂²×C₄

Dic₅₈

yes

—

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

—

C₄²

C₄×D₂₉

yes

—

C₄²

C₂²⋊D₂₉

yes

characteristic

C₄²

C₂²⋊D₂₉

yes

characteristic

C₂³

C₂×Dic₅₈

yes

characteristic

C₂×C₄

—

C₂×C₄

#90779

yes

—

C₂×C₄

#90779

yes

—

C₂×C₄

C₂×C₄×D₂₉

yes

—

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

#90805

yes

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

100

C₂²

—

101

C₂²

C₄×Dic₅₈

yes

—

102

C₂²

C₂×#90779

yes

characteristic

103

C₄

—

104

C₄

#11745170

yes

direct product factor

105

C₄

C₄²×D₂₉

yes

characteristic

106

C₄

#11745234

yes

characteristic

107

C₄

C₄×C₂²⋊D₂₉

yes

—

108

C₂

—

109

C₂

C₄×#90779

yes

characteristic

110

C₂

C₂×#11745170

yes

—

	subgroup	G/H
center	C₄²	C₂²⋊D₂₉
commutator	C₄×C₂₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₄×M₁₆×C₂₉	C₂
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂³×C₂₉	C₂×Q₈
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₄×M₁₆	D₂₉
hypocenter	C₂₉	C₄×#108
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₄²

C₂²⋊D₂₉

commutator

C₄×C₂₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₄×M₁₆×C₂₉

C₂

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂³×C₂₉

C₂×Q₈

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₄×M₁₆

D₂₉

hypocenter

C₂₉

C₄×#108

LCS

G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
13. #11745170	C₄	direct (N × H)
49. C₄×C₂₉	#108	semidirect
72. C₂₉	C₄×#108	semidirect
104. C₄	#11745170	direct (N × H)

H ≅ G/N

type

13. #11745170

C₄

direct (N × H)

49. C₄×C₂₉

#108

semidirect

72. C₂₉

C₄×#108

semidirect

104. C₄

#11745170

direct (N × H)

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

subgroup	index
C₂×#11745170	2
C₄×#90777	2
C₂×C₄×#6597	2
#14270927	2
C₄×M₁₆×C₂₉	2
C₄×#108	29

subgroup

index

C₂×C₄×#6597

C₄×M₁₆×C₂₉

Subgroups — C₄×#11745170 #16819395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×#11745170 #16819395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11745170 #16819395