Group #15765758 — subgroups

Subgroups — #15765758

Order 3328.

586 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 169 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×#11718341	C₂	1	3	yes	maximal
2	#13115638	C₂	1	3	yes	maximal
3	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#88123	C₂²	1	3	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
6	C₂×#88057	—	2	6	no	—
7	C₂×#88056	—	2	6	no	—
8	#11718596	C₂²	1	1	yes	characteristic
9	#11718341	—	2	12	no	—
10	C₂²×Dic₂₆	—	2	3	no	—
11	C₂²×C₈×C₁₃	D₄	1	6	yes	—
12	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₃	—	2	6	no	—
14	C₂×C₄⋊Dic₁₃	—	2	3	no	—
15	#88123	—	2	6	no	—
16	#88123	—	2	3	no	—
17	#88123	D₄	1	6	yes	—
18	C₄×C₈×C₁₃	—	2	6	no	—
19	#88057	—	2	24	no	—
20	#88056	—	4	12	no	—
21	#10316	—	13	1	no	maximal, Sylow
22	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
23	C₂²×Dic₁₃	—	4	3	no	—
24	C₂²×Dic₁₃	—	4	1	no	—
25	C₂×Dic₂₆	—	2	6	no	—
26	C₂×Dic₂₆	—	4	6	no	—
27	C₂×Dic₂₆	—	4	6	no	—
28	C₂×Dic₂₆	—	4	3	no	—
29	C₂×C₈×C₁₃	—	2	6	no	—
30	C₂×C₈×C₁₃	—	2	6	no	—
31	C₂×C₈×C₁₃	SD₁₆	1	12	yes	—
32	C₄²×C₁₃	C₂×D₄	1	3	yes	—
33	C₄²×C₁₃	#41	1	1	yes	characteristic
34	C₄⋊Dic₁₃	—	2	12	no	—
35	C₄⋊Dic₁₃	—	4	6	no	—
36	C₄⋊Dic₁₃	—	4	6	no	—
37	C₂×#498	—	13	3	no	—
38	#1956	—	13	3	no	—
39	#1273	D₁₃	1	1	yes	characteristic
40	C₂³×C₁₃	#127	1	1	yes	characteristic
41	C₂×C₄×C₁₃	#120	1	3	yes	—
42	C₂×C₄×C₁₃	#121	1	3	yes	—
43	C₂×C₄×C₁₃	C₂×SD₁₆	1	6	yes	—
44	C₂×C₄×C₁₃	#137	1	6	yes	—
45	C₂×Dic₁₃	—	4	6	no	—
46	C₂×Dic₁₃	—	8	3	no	—
47	C₂×Dic₁₃	—	8	3	no	—
48	C₂×Dic₁₃	—	8	3	no	—
49	Dic₂₆	—	4	12	no	—
50	Dic₂₆	—	8	6	no	—
51	C₈×C₁₃	—	2	12	no	—
52	C₂×C₄⋊Q₈	—	13	3	no	—
53	#498	—	26	12	no	—
54	C₂×#106	—	26	6	no	—
55	C₂×#103	—	26	6	no	—
56	C₂×C₄×C₈	C₂×D₁₃	1	3	yes	—
57	#384	—	13	1	no	—
58	C₂²×C₁₃	#392	1	1	yes	characteristic
59	C₂²×C₁₃	#492	1	3	yes	—
60	C₂²×C₁₃	#497	1	3	yes	—
61	C₄×C₁₃	#448	1	6	yes	—
62	C₄×C₁₃	#461	1	6	yes	—
63	Dic₁₃	—	8	6	no	—
64	Dic₁₃	—	16	1	no	—
65	C₂²×Q₈	—	26	3	no	—
66	C₂²×C₈	D₅₂	1	6	yes	—
67	C₄⋊Q₈	—	13	6	no	—
68	C₄⋊Q₈	—	26	6	no	—
69	C₄⋊Q₈	—	26	3	no	—
70	C₂×C₄⋊C₄	—	26	6	no	—
71	C₂×C₄⋊C₄	—	26	3	no	—
72	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
73	#106	—	26	24	no	—
74	#103	—	52	12	no	—
75	C₄×C₈	—	2	6	no	—
76	C₂×C₁₃	#1705	1	1	yes	characteristic
77	C₂×C₁₃	#1716	1	3	yes	—
78	C₂×C₁₃	#2013	1	3	yes	—
79	C₂×Q₈	—	26	6	no	—
80	C₂×Q₈	—	52	3	no	—
81	C₂×Q₈	—	52	6	no	—
82	C₂×Q₈	—	52	6	no	—
83	C₂²×C₄	—	52	3	no	—
84	C₂²×C₄	—	52	1	no	—
85	C₂²×C₄	C₂×D₅₂	1	3	yes	—
86	C₂×C₈	—	2	6	no	—
87	C₂×C₈	—	2	6	no	—
88	C₂×C₈	#6095	1	12	yes	—
89	C₄⋊C₄	—	26	12	no	—
90	C₄⋊C₄	—	52	6	no	—
91	C₄⋊C₄	—	52	6	no	—
92	C₄²	D₄×D₁₃	1	3	yes	—
93	C₄²	#6131	1	1	yes	characteristic
94	C₁₃	#10316	1	1	yes	characteristic, complemented, Sylow
95	C₂³	#88128	1	1	yes	characteristic
96	Q₈	—	52	12	no	—
97	Q₈	—	104	6	no	—
98	C₂×C₄	—	52	6	no	—
99	C₂×C₄	—	104	3	no	—
100	C₂×C₄	—	104	3	no	—
101	C₂×C₄	—	104	3	no	—
102	C₂×C₄	#88136	1	3	yes	—
103	C₂×C₄	#88149	1	3	yes	—
104	C₂×C₄	C₂×#6095	1	6	yes	—
105	C₂×C₄	#88163	1	6	yes	—
106	C₈	—	2	12	no	—
107	C₂²	#11718332	1	1	yes	characteristic
108	C₂²	#11718354	1	3	yes	—
109	C₂²	#11718376	1	3	yes	—
110	C₄	—	104	6	no	—
111	C₄	—	208	1	no	—
112	C₄	#11718399	1	6	yes	—
113	C₄	#11718502	1	6	yes	—
114	C₂	#13114423	1	1	yes	characteristic
115	C₂	#13114469	1	3	yes	—
116	C₂	#13115921	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718341

C₂

yes

maximal

#13115638

C₂

yes

maximal

C₁₃×#1273

C₂

yes

maximal, characteristic

C₂×#88123

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₂×#88057

—

C₂×#88056

—

#11718596

C₂²

yes

characteristic

#11718341

—

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

#88123

—

#88123

—

#88123

D₄

yes

—

C₄×C₈×C₁₃

—

—

—

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

SD₁₆

yes

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₂×#498

—

#1956

—

#1273

D₁₃

yes

C₂³×C₁₃

yes

C₂×C₄×C₁₃

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

C₂×C₄⋊Q₈

—

#498

—

C₂×#106

—

C₂×#103

—

C₂×C₄×C₈

C₂×D₁₃

yes

—

#384

—

C₂²×C₁₃

#392

yes

characteristic

C₂²×C₁₃

#492

yes

—

C₂²×C₁₃

#497

yes

—

C₄×C₁₃

#448

yes

—

C₄×C₁₃

#461

yes

—

Dic₁₃

—

Dic₁₃

—

C₂²×Q₈

—

C₂²×C₈

D₅₂

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

#106

—

#103

—

C₄×C₈

—

C₂×C₁₃

#1705

yes

characteristic

C₂×C₁₃

#1716

yes

—

C₂×C₁₃

#2013

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₅₂

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#6095

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₄×D₁₃

yes

—

C₄²

#6131

yes

characteristic

C₁₃

#10316

yes

characteristic, complemented, Sylow

C₂³

#88128

yes

characteristic

Q₈

—

Q₈

—

104

—

C₂×C₄

—

C₂×C₄

—

104

—

100

C₂×C₄

—

104

—

101

C₂×C₄

—

104

—

102

C₂×C₄

#88136

yes

—

103

C₂×C₄

#88149

yes

—

104

C₂×C₄

C₂×#6095

yes

—

105

C₂×C₄

#88163

yes

—

106

C₈

—

107

C₂²

#11718332

yes

characteristic

108

C₂²

#11718354

yes

—

109

C₂²

#11718376

yes

—

110

C₄

—

104

—

111

C₄

—

208

—

112

C₄

#11718399

yes

—

113

C₄

#11718502

yes

—

114

C₂

#13114423

yes

characteristic

115

C₂

#13114469

yes

—

116

C₂

#13115921

yes

—

	subgroup	G/H
center	C₂³	#88128
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1273	C₂
socle, prime radical	C₂³×C₁₃	#127
hypercenter	#1273	D₁₃
hypocenter	C₁₃	#10316
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#88128

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1273

C₂

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
94. C₁₃	#10316	semidirect

H ≅ G/N

type

94. C₁₃

#10316

semidirect

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

subgroup	index
C₂×#11718341	2
#13115638	2
C₁₃×#1273	2
#10316	13

subgroup

index

C₂×#11718341

#13115638

C₁₃×#1273

#10316

Subgroups — #15765758

Conjugacy classes of subgroups

Complements

Maximal subgroups