Group #14668448 — subgroups

Subgroups — #14668448

Order 2816.

258 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 91 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	#13070898	C₂	1	1	yes	maximal, characteristic
2	#13070869	C₂	1	1	yes	maximal, characteristic
3	#13070844	C₂	1	2	yes	maximal
4	#13068213	C₂	1	2	yes	maximal
5	C₁₁×#1311	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₈	—	2	2	no	—
7	#10622312	C₂²	1	2	yes	—
8	#10622295	C₂²	1	2	yes	—
9	#10622294	—	2	2	no	—
10	#10622293	—	2	2	no	—
11	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
12	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
13	C₈²×C₁₁	C₂²	1	1	yes	characteristic
14	#10622143	—	2	2	no	—
15	#10622141	—	2	4	no	—
16	C₂×Dic₄₄	—	2	2	no	—
17	C₂×Dic₄₄	—	2	2	no	—
18	#66922	—	2	2	no	—
19	#66922	—	2	2	no	—
20	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
21	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
22	C₄×C₈×C₁₁	D₄	1	2	yes	—
23	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
24	#66882	—	2	2	no	—
25	#66882	—	2	2	no	—
26	#66881	—	4	4	no	—
27	#66880	—	4	4	no	—
28	Dic₈₈	—	4	4	no	—
29	#12507	—	11	1	no	maximal, Sylow
30	C₂×Dic₂₂	—	4	2	no	—
31	C₂×Dic₂₂	—	4	2	no	—
32	C₂×C₈×C₁₁	D₈	1	4	yes	—
33	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
34	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
35	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₄⋊Dic₁₁	—	4	2	no	—
37	C₄⋊Dic₁₁	—	4	2	no	—
38	C₄⋊Dic₁₁	—	4	2	no	—
39	C₄⋊Dic₁₁	—	4	2	no	—
40	Dic₄₄	—	4	4	no	—
41	Dic₄₄	—	4	4	no	—
42	C₁₁×C₁₆	—	2	2	no	—
43	C₁₁×C₁₆	SD₁₆	1	4	yes	—
44	#2254	—	11	1	no	—
45	#2247	—	11	1	no	—
46	#2241	—	11	2	no	—
47	#1707	—	11	2	no	—
48	#1311	D₁₁	1	1	yes	characteristic
49	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
50	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
51	C₂×Dic₁₁	—	8	2	no	—
52	C₂×Dic₁₁	—	8	2	no	—
53	Dic₂₂	—	8	2	no	—
54	Dic₂₂	—	8	2	no	—
55	Dic₂₂	—	8	4	no	—
56	C₈×C₁₁	—	2	4	no	—
57	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
58	C₈×C₁₁	#135	1	2	yes	—
59	C₂×Q₃₂	—	22	2	no	—
60	#500	—	11	2	no	—
61	#498	—	22	2	no	—
62	#494	—	11	2	no	—
63	#487	—	22	2	no	—
64	#367	—	22	2	no	—
65	#358	—	22	4	no	—
66	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
67	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
68	C₈²	C₂×D₁₁	1	1	yes	characteristic
69	C₂²×C₁₁	#493	1	1	yes	characteristic
70	C₄×C₁₁	#492	1	1	yes	characteristic
71	C₄×C₁₁	#495	1	1	yes	characteristic
72	C₄×C₁₁	#510	1	4	yes	—
73	Dic₁₁	—	16	2	no	—
74	Dic₁₁	—	16	2	no	—
75	C₂×Q₁₆	—	22	2	no	—
76	C₂×Q₁₆	—	22	2	no	—
77	C₄⋊Q₈	—	22	2	no	—
78	C₄⋊Q₈	—	22	2	no	—
79	Q₃₂	—	44	4	no	—
80	C₂×C₁₆	D₄₄	1	2	yes	—
81	C₂×C₁₆	D₄₄	1	2	yes	—
82	#107	—	22	2	no	—
83	#107	—	22	2	no	—
84	#106	—	44	4	no	—
85	#103	—	44	4	no	—
86	C₄×C₈	D₄₄	1	2	yes	—
87	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
88	C₂×C₁₁	#1706	1	1	yes	characteristic
89	C₂×C₁₁	#2251	1	2	yes	—
90	C₂×Q₈	—	44	2	no	—
91	C₂×Q₈	—	44	2	no	—
92	Q₁₆	—	44	4	no	—
93	Q₁₆	—	44	4	no	—
94	C₂×C₈	D₈₈	1	4	yes	—
95	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
96	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
97	C₄⋊C₄	—	44	2	no	—
98	C₄⋊C₄	—	44	2	no	—
99	C₄⋊C₄	—	44	2	no	—
100	C₄⋊C₄	—	44	2	no	—
101	C₄²	C₂×D₄₄	1	1	yes	characteristic
102	C₁₆	—	2	2	no	—
103	C₁₆	#4314	1	4	yes	—
104	C₁₁	#12507	1	1	yes	characteristic, complemented, Sylow
105	Q₈	—	88	4	no	—
106	Q₈	—	88	2	no	—
107	Q₈	—	88	2	no	—
108	C₂×C₄	—	88	2	no	—
109	C₂×C₄	—	88	2	no	—
110	C₂×C₄	#66927	1	1	yes	characteristic
111	C₂×C₄	C₂×D₈₈	1	2	yes	—
112	C₈	—	2	4	no	—
113	C₈	C₂×#4314	1	2	yes	—
114	C₈	#66957	1	2	yes	—
115	C₂²	#10622308	1	1	yes	characteristic
116	C₄	—	176	2	no	—
117	C₄	—	176	2	no	—
118	C₄	#10622306	1	1	yes	characteristic
119	C₄	#10622309	1	1	yes	characteristic
120	C₄	#10622522	1	4	yes	—
121	C₂	#13068208	1	1	yes	characteristic
122	C₂	#13070887	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13070898

C₂

yes

maximal, characteristic

#13070869

C₂

yes

maximal, characteristic

#13070844

C₂

yes

maximal

#13068213

C₂

yes

maximal

C₁₁×#1311

C₂

yes

maximal, characteristic

C₂×Dic₈₈

—

#10622312

C₂²

yes

—

#10622295

C₂²

yes

—

#10622294

—

#10622293

—

C₄×C₁₁×C₁₆

C₂²

yes

characteristic

C₄×C₁₁×C₁₆

C₂²

yes

characteristic

C₈²×C₁₁

C₂²

yes

characteristic

#10622143

—

#10622141

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

#66922

—

#66922

—

C₂×C₁₁×C₁₆

D₄

yes

—

C₂×C₁₁×C₁₆

D₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

C₂³

yes

—

—

—

—

Dic₈₈

—

#12507

—

maximal, Sylow

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₄₄

—

Dic₄₄

—

C₁₁×C₁₆

—

C₁₁×C₁₆

SD₁₆

yes

—

—

—

—

—

D₁₁

yes

characteristic

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

C₂×SD₁₆

yes

—

C₈×C₁₁

#135

yes

—

C₂×Q₃₂

—

—

—

—

—

—

—

C₄×C₁₆

C₂×D₁₁

yes

characteristic

C₄×C₁₆

C₂×D₁₁

yes

characteristic

C₈²

C₂×D₁₁

yes

C₂²×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

Dic₁₁

—

Dic₁₁

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

Q₃₂

—

C₂×C₁₆

D₄₄

yes

—

C₂×C₁₆

D₄₄

yes

—

—

—

—

—

C₄×C₈

D₄₄

yes

—

C₄×C₈

C₂²×D₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

D₈₈

yes

—

C₂×C₈

C₂×D₄₄

yes

characteristic

C₂×C₈

C₂×D₄₄

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

C₂×D₄₄

yes

characteristic

102

C₁₆

—

103

C₁₆

#4314

yes

—

104

C₁₁

#12507

yes

characteristic, complemented, Sylow

105

Q₈

—

106

Q₈

—

107

Q₈

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

#66927

yes

characteristic

111

C₂×C₄

C₂×D₈₈

yes

—

112

C₈

—

113

C₈

C₂×#4314

yes

—

114

C₈

#66957

yes

—

115

C₂²

#10622308

yes

characteristic

116

C₄

—

176

—

117

C₄

—

176

—

118

C₄

#10622306

yes

characteristic

119

C₄

#10622309

yes

characteristic

120

C₄

#10622522

yes

—

121

C₂

#13068208

yes

characteristic

122

C₂

#13070887

yes

—

	subgroup	G/H
center	C₂²	#10622308
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#1311	C₂
socle, prime radical	C₂²×C₁₁	#493
hypercenter	#1311	D₁₁
hypocenter	C₁₁	#12507
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1311

subgroup

G/H

center

C₂²

#10622308

commutator, cosocle

C₄×C₈×C₁₁

C₂³

Frattini

C₄×C₈

C₂²×D₁₁

Fitting

C₁₁×#1311

C₂

C₂²×C₁₁

D₁₁

C₁₁

G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1311

N	H ≅ G/N	type
104. C₁₁	#12507	semidirect

H ≅ G/N

type

104. C₁₁

#12507

semidirect

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

subgroup	index
#13070898	2
#13070869	2
#13070844	2
#13068213	2
C₁₁×#1311	2
#12507	11

subgroup

index

C₁₁×#1311

Subgroups — #14668448

Conjugacy classes of subgroups

Complements

Maximal subgroups