Finite Group Databasebeta

← #16015458

Subgroups — #16015458

Order 3328.

1450 conjugacy classes of subgroups; only the 363 normal subgroups are shown.

normal subgroups only

This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 363 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718376C218yesmaximal, complemented
2C2×#11718360C212yesmaximal, complemented
3C2×#11718354C212yesmaximal
4#13123234C211yesmaximal, characteristic, complemented
5#13123193C211yesmaximal, characteristic
6C4×C13×#97C211yesmaximal, characteristic, complemented
7C22×Dic52C2218yes—
8C22×#6095C2218yes—
9C2×#88129C2214yes—
10C2×#88128C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C2×#88123C2212yes—
13C2×#88123C2214yes—
14C2×C13×#97C2214yes—
15C2×C4×C8×C13C2212yes—
16C43×C13C2211yescharacteristic
17#11718600—24no—
18#11718596—24no—
19#11718376—232no—
20#11718360—28no—
21#11718354—28no—
22C22×D52—22no—
23C22×D52C2312yes—
24C22×Dic26C2314yes—
25C22×Dic26C2312yes—
26C22×C8×C13C2314yes—
27C2×C42×C13D414yes—
28C2×C42×C13C2311yescharacteristic
29C2×C42×C13C2312yes—
30C2×#6103—28no—
31C2×C4⋊Dic13—28no—
32C2×C4⋊Dic13—24no—
33C2×C4⋊Dic13—22no—
34C2×Dic52—216no—
35C2×Dic52—232no—
36C2×#6095—216no—
37C2×#6095—232no—
38#88129—216no—
39#88128—24no—
40#88123—24no—
41#88123—24no—
42#88123—24no—
43#88123—216no—
44C13×#97D4116yescomplemented
45C4×C8×C13D418yes—
46#33305—131nomaximal, Sylow
47C23×D13—22no—
48C22×C4×C13C2×D414yes—
49C22×C4×C13C2×D412yes—
50C22×C4×C13C2411yescharacteristic
51C22×Dic13—24no—
52C22×Dic13—22no—
53C2×D52—24no—
54C2×D52—28no—
55C2×D52—44no—
56C2×D52—48no—
57C2×Dic26—24no—
58C2×Dic26—216no—
59C2×Dic26—24no—
60C2×Dic26—24no—
61C2×Dic26—28no—
62C2×C8×C13C2×D418yes—
63C2×C8×C13C2×D4116yes—
64C42×C13—28no—
65C42×C13C2×D414yes—
66C42×C13C2×D418yes—
67#6103—416no—
68C4⋊Dic13—416no—
69C4⋊Dic13—48no—
70C4⋊Dic13—44no—
71Dic52—432no—
72#6095—432no—
73C2×#497—138no—
74C2×#494—132no—
75C2×#492—132no—
76#2868—131no—
77#2858—131no—
78C4×#97D1311yescharacteristic, complemented
79C23×C13C22×D411yescharacteristic
80C22×D13—44no—
81C22×D13—42no—
82C22×D13—48no—
83C2×C4×C13—28no—
84C2×C4×C13#12718yes—
85C2×C4×C13#12714yes—
86C2×C4×C13#13718yes—
87C2×C4×C13C22×D412yes—
88C2×C4×C13C22×D414yes—
89C2×Dic13—44no—
90C2×Dic13—42no—
91C2×Dic13—48no—
92C2×Dic13—44no—
93D52—48no—
94D52—88no—
95Dic26—48no—
96Dic26—48no—
97Dic26—48no—
98C8×C13#127116yes—
99C22×Q16—138no—
100C22×SD16—138no—
101C2×C4⋊Q8—131no—
102C2×C4⋊Q8—132no—
103C2×C4⋊Q8—134no—
104C2×#127—131no—
105C2×#124—134no—
106#497—2632no—
107#494—268no—
108#492—268no—
109C2×#97C2×D1314yes—
110C2×C4×C8C2×D1312yes—
111#390—264no—
112#384—264no—
113C43C2×D1311yescharacteristic
114C22×C13C2×#12711yescharacteristic
115C22×C13C2×#12712yes—
116C22×C13C2×#13714yes—
117C2×D13—82no—
118C2×D13—84no—
119C2×D13—88no—
120C4×C13—28no—
121C4×C13#49718yescomplemented
122C4×C13C2×#12714yes—
123Dic13—84no—
124Dic13—82no—
125C22×Q8—132no—
126C22×Q8—134no—
127C22×D4—132no—
128C22×D4—262no—
129C2×Q16—2616no—
130C2×Q16—2632no—
131C2×SD16—2616no—
132C2×SD16—2632no—
133C22×C8C22×D1314yes—
134C4⋊Q8—264no—
135C4⋊Q8—264no—
136C4⋊Q8—264no—
137C4⋊Q8—2616no—
138#127—264no—
139#124—2616no—
140C2×C4⋊C4—268no—
141C2×C4⋊C4—264no—
142C2×C4⋊C4—262no—
143C2×C22⋊C4—268no—
144C2×C42D5214yes—
145C2×C42C22×D1312yes—
146C2×C42C22×D1311yescharacteristic
147#97D52116yescomplemented
148C4×C8D5218yes—
149C2×C13#286711yescharacteristic
150C2×C13C2×#49712yes—
151C2×C13#315214yes—
152D13—162no—
153C24—262no—
154C2×Q8—268no—
155C2×Q8—264no—
156C2×Q8—2616no—
157C2×Q8—264no—
158C2×Q8—264no—
159C2×D4—268no—
160C2×D4—264no—
161C2×D4—524no—
162C2×D4—528no—
163C22×C4—262no—
164C22×C4—264no—
165C22×C4C2×D5214yes—
166C22×C4C2×D5212yes—
167C22×C4C23×D1311yescharacteristic
168Q16—5232no—
169SD16—5232no—
170C2×C8C2×D5218yes—
171C2×C8C2×D52116yes—
172C4⋊C4—5216no—
173C4⋊C4—528no—
174C4⋊C4—524no—
175C22⋊C4—5216no—
176C42—28no—
177C42C2×D5214yes—
178C42C2×D5218yes—
179C13#3330511yescharacteristic, complemented, Sylow
180C23—524no—
181C23—522no—
182C23—528no—
183C23C22×D5211yescharacteristic
184Q8—528no—
185Q8—528no—
186Q8—528no—
187D4—528no—
188D4—1048no—
189C2×C4—28no—
190C2×C4—524no—
191C2×C4—522no—
192C2×C4—524no—
193C2×C4—528no—
194C2×C4#8812818yes—
195C2×C4#8812814yes—
196C2×C4#8816318yes—
197C2×C4C22×D5212yes—
198C2×C4C22×D5214yes—
199C8#88128116yes—
200C22—1044no—
201C22—1042no—
202C22—1048no—
203C22C2×#8812811yescharacteristic
204C22C2×#8812812yes—
205C22C2×#8816314yes—
206C4—28no—
207C4—1042no—
208C4—1044no—
209C4#1171837618yescomplemented
210C4C2×#8812814yes—
211C2—2082no—
212C2#1312323111yescharacteristic
213C2C2×#1171837612yes—
214C2#1312529514yes—
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC4×C13×#97C2
socleC23×C13C22×D4
prime radicalC2×#88128C22
hypercenterC4×#97D13
hypocenterC13#33305
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×#97

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11718376C2semidirect
2. C2×#11718360C2semidirect
4. #13123234C2semidirect
6. C4×C13×#97C2semidirect
44. C13×#97D4semidirect
78. C4×#97D13semidirect
121. C4×C13#497semidirect
147. #97D52semidirect
179. C13#33305semidirect
209. C4#11718376semidirect

Maximal subgroups

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

subgroupindex
C2×#117183762
C2×#117183602
C2×#117183542
#131232342
#131231932
C4×C13×#972
#3330513