Finite Group Databasebeta

← #15765607

Subgroups — #15765607

Order 3328.

614 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#13125959C212yesmaximal
2#13123234C211yesmaximal, characteristic, complemented
3#13115664C211yesmaximal, characteristic
4#13113507C212yesmaximal, complemented
5C13×#1276C211yesmaximal, characteristic, complemented
6#11719182C2211yescharacteristic
7C2×#88123—22no—
8C2×#88123C2212yes—
9C13×#431C2212yes—
10C43×C13C2211yescharacteristic
11#11718596—24no—
12C2×#88045—22no—
13#11718585C2211yescharacteristic
14#11718507—24no—
15#11718397—24no—
16#11718355—22no—
17#11718343—22no—
18#11718078—24no—
19C2×#6127—21no—
20C22×Dic26—22no—
21C2×C42×C13—22no—
22C2×C42×C13D412yes—
23C2×C42×C13C2311yescharacteristic
24#88184—22no—
25C2×C4⋊Dic13—28no—
26C2×C4⋊Dic13—22no—
27C2×C4⋊Dic13D414yes—
28C2×#6099—21no—
29#88129—21no—
30#88128D411yescharacteristic
31C4×D52—22no—
32#88123—22no—
33#88123—22no—
34#88123—22no—
35#88123—22no—
36#88123—44no—
37#88123—44no—
38#88123D411yescharacteristic
39C13×C4⋊C8D414yes—
40C13×C22⋊C8—22no—
41C4×C8×C13—22no—
42#88061—28no—
43#88058—28no—
44#88045—44no—
45C4⋊#1055—22no—
46#10289—131nomaximal, Sylow
47C22×C4×C13—22no—
48C22×C4×C13C2×D411yescharacteristic
49C22×C4×C13C2×D412yes—
50C2×C22⋊D13—41no—
51C22×Dic13—24no—
52#6127—42no—
53#6127—42no—
54C2×D52—22no—
55C2×D52—21no—
56C2×C4×D13—41no—
57C2×Dic26—21no—
58C2×Dic26—42no—
59C2×Dic26—42no—
60C2×Dic26—44no—
61C2×Dic26—44no—
62C2×C8×C13—24no—
63C42×C13—28no—
64C42×C13—22no—
65C42×C13D814yes—
66C42×C13C2×D412yes—
67C42×C13C2×D411yescharacteristic
68C42×C13#4111yescharacteristic
69#6103—42no—
70C4⋊Dic13—24no—
71C4⋊Dic13—22no—
72C4⋊Dic13—24no—
73C4⋊Dic13—416no—
74C4⋊Dic13—42no—
75C4⋊Dic13—42no—
76#6099—42no—
77C2×#1055—41no—
78#3226—132no—
79#2868—131no—
80#1962—131no—
81#1546—132no—
82#1276D1311yescharacteristic, complemented
83C23×C13#12011yescharacteristic
84C22×D13—41no—
85C2×C4×C13—28no—
86C2×C4×C13—24no—
87C2×C4×C13—24no—
88C2×C4×C13#12012yes—
89C2×C4×C13#12112yes—
90C2×C4×C13#12111yescharacteristic
91C2×C4×C13#12711yescharacteristic
92C2×C4×C13C2×D812yes—
93C2×C4×C13AGL(1,ℤ/8)12yes—
94C22⋊D13—82no—
95C2×Dic13—44no—
96C2×Dic13—41no—
97C2×Dic13—48no—
98D52—44no—
99D52—42no—
100C4×D13—81no—
101C4×D13—81no—
102Dic26—42no—
103Dic26—84no—
104Dic26—82no—
105Dic26—82no—
106C8×C13—44no—
107#1055—81no—
108#532—131no—
109C2×C4⋊Q8—132no—
110C2×C4⋊Q8—262no—
111#500—262no—
112#486—262no—
113#480—264no—
114#474—264no—
115#431C2×D1312yes—
116#423—131no—
117C2×#104—262no—
118#384—264no—
119C43C2×D1311yescharacteristic
120#332—264no—
121C22×C13—22no—
122C22×C13#39211yescharacteristic
123C22×C13#44712yes—
124C2×D13—82no—
125C2×D13—81no—
126C4×C13—28no—
127C4×C13—22no—
128C4×C13#45614yes—
129C4×C13#45912yes—
130C4×C13#49311yescharacteristic
131C4×C13#49611yescharacteristic
132Dic13—81no—
133Dic13—84no—
134C2×#41—261no—
135C22×Q8—262no—
136C2×M16—261no—
137C4⋊Q8—131no—
138C4⋊Q8—262no—
139C4⋊Q8—262no—
140C4⋊Q8—262no—
141C4⋊Q8—262no—
142C4⋊Q8—524no—
143C4⋊Q8—524no—
144#127—131no—
145#124—261no—
146#121—262no—
147C4×D4—262no—
148C2×C4⋊C4—134no—
149C2×C4⋊C4—268no—
150C2×C4⋊C4—262no—
151C2×C42—22no—
152C2×C42D5212yes—
153C2×C42C22×D1311yescharacteristic
154#107—268no—
155C4⋊C8—262no—
156C4⋊C8D5214yes—
157#104—524no—
158#102—268no—
159C22⋊C8—22no—
160C4×C8—22no—
161C2×C13—22no—
162C2×C13#200512yes—
163C2×C13#201111yescharacteristic
164D13—161no—
165#41—522no—
166#41—522no—
167C2×Q8—261no—
168C2×Q8—522no—
169C2×Q8—522no—
170C2×Q8—524no—
171C2×Q8—524no—
172C2×D4—262no—
173C2×D4—261no—
174C2×D4—521no—
175C22×C4—22no—
176C22×C4—264no—
177C22×C4—521no—
178C22×C4C2×D5211yescharacteristic
179C22×C4D4×D1312yes—
180M16—522no—
181C2×C8—24no—
182C2×C8—521no—
183C4⋊C4—264no—
184C4⋊C4—262no—
185C4⋊C4—264no—
186C4⋊C4—5216no—
187C4⋊C4—522no—
188C4⋊C4—522no—
189C22⋊C4—522no—
190C42—28no—
191C42—22no—
192C42D10414yes—
193C42C2×D5212yes—
194C42D4×D1311yescharacteristic
195C42#613111yescharacteristic
196C13#1028911yescharacteristic, complemented, Sylow
197C23—521no—
198C23#8813611yescharacteristic
199Q8—522no—
200Q8—1044no—
201Q8—1042no—
202Q8—1042no—
203D4—524no—
204D4—522no—
205D4—1042no—
206C2×C4—28no—
207C2×C4—24no—
208C2×C4—24no—
209C2×C4—521no—
210C2×C4—524no—
211C2×C4—528no—
212C2×C4—1041no—
213C2×C4—1041no—
214C2×C4#8812811yescharacteristic
215C2×C4#8813612yes—
216C2×C4#8814912yes—
217C2×C4#8814911yescharacteristic
218C2×C4C2×D10412yes—
219C2×C4#8816212yes—
220C8—44no—
221C8—1041no—
222C22—22no—
223C22—1041no—
224C22—1042no—
225C22#1171833211yescharacteristic
226C22#1171839312yes—
227C4—28no—
228C4—22no—
229C4—1044no—
230C4—1041no—
231C4#1171835611yescharacteristic
232C4#1171837311yescharacteristic
233C4#1171848714yes—
234C4#1171850412yes—
235C2—22no—
236C2—2081no—
237C2#1311587512yes—
238C2#1311590911yescharacteristic
subgroupG/H
centerC22#11718332
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#392
prime radical#11719182C22
hypercenter#1276D13
hypocenterC13#10289
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
2. #13123234C2semidirect
4. #13113507C2semidirect
5. C13×#1276C2semidirect
82. #1276D13semidirect
196. C13#10289semidirect

Maximal subgroups

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

subgroupindex
#131259592
#131232342
#131156642
#131135072
C13×#12762
#1028913