Finite Group Databasebeta

← #15765605

Subgroups — #15765605

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#13125957C212yesmaximal
2#13115664C211yesmaximal, characteristic
3#13113508C212yesmaximal, complemented
4#13112669C211yesmaximal, characteristic, complemented
5C13×#2868C211yesmaximal, characteristic, complemented
6C2×C13×C4⋊Q8—22no—
7C2×C13×C4⋊Q8C2212yes—
8#11719182C2211yescharacteristic
9C13×#384—24no—
10C43×C13C2211yescharacteristic
11#11718749—22no—
12#11718748—24no—
13#11718739—22no—
14#11718628—24no—
15C2×#88045—22no—
16#11718586C2212yes—
17#11718585C2211yescharacteristic
18#11718139—24no—
19C22×Q8×C13—22no—
20C2×#6127—21no—
21C13×C4⋊Q8—22no—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—22no—
25C13×C4⋊Q8—44no—
26C13×C4⋊Q8—44no—
27C2×C13×C4⋊C4—28no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4D414yes—
30C2×C42×C13—22no—
31C2×C42×C13D412yes—
32C2×C42×C13C2311yescharacteristic
33#88184—22no—
34C2×#6099—21no—
35#88129—21no—
36#88128D411yescharacteristic
37C4×D52—22no—
38#88123D411yescharacteristic
39C22⋊#1055—22no—
40#88049—28no—
41#88047—28no—
42#88045—44no—
43C4⋊#1055—22no—
44C4⋊#1055D414yes—
45C4×#1055—22no—
46#10289—131nomaximal, Sylow
47C2×Q8×C13—42no—
48C2×Q8×C13—42no—
49C2×Q8×C13—44no—
50C2×Q8×C13—44no—
51C22×C4×C13—22no—
52C22×C4×C13—24no—
53C22×C4×C13C2×D412yes—
54C22×C4×C13C2×D411yescharacteristic
55C2×C22⋊D13—41no—
56#6127—42no—
57#6127—42no—
58C2×D52—22no—
59C2×D52—21no—
60C2×C4×D13—41no—
61C2×Dic26—21no—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—24no—
64C13×C4⋊C4—416no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—42no—
67C42×C13—28no—
68C42×C13—22no—
69C42×C13D814yes—
70C42×C13C2×D411yescharacteristic
71C42×C13C2×D412yes—
72C42×C13#4111yescharacteristic
73#6103—42no—
74C4⋊Dic13—22no—
75#6099—42no—
76C2×#1055—24no—
77C2×#1055—41no—
78#3226—132no—
79#2868D1311yescharacteristic, complemented
80#1962—131no—
81#1546—132no—
82#1276—131no—
83C23×C13#12011yescharacteristic
84C22×D13—41no—
85Q8×C13—84no—
86Q8×C13—82no—
87Q8×C13—82no—
88C2×C4×C13—28no—
89C2×C4×C13—24no—
90C2×C4×C13—24no—
91C2×C4×C13—44no—
92C2×C4×C13—48no—
93C2×C4×C13#12012yes—
94C2×C4×C13#12112yes—
95C2×C4×C13#12111yescharacteristic
96C2×C4×C13#12711yescharacteristic
97C2×C4×C13C2×D812yes—
98C2×C4×C13AGL(1,ℤ/8)12yes—
99C22⋊D13—82no—
100C2×Dic13—41no—
101D52—44no—
102D52—42no—
103C4×D13—81no—
104C4×D13—81no—
105Dic26—42no—
106#1055—44no—
107#1055—81no—
108#532—131no—
109C2×C4⋊Q8—22no—
110C2×C4⋊Q8C2×D1312yes—
111#500—262no—
112#486—262no—
113#480—264no—
114#474—264no—
115#431—132no—
116#423—131no—
117C2×#104—262no—
118#384—24no—
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—84no—
129C4×C13#45614yes—
130C4×C13#45912yes—
131C4×C13#49311yescharacteristic
132C4×C13#49611yescharacteristic
133Dic13—81no—
134C2×#41—261no—
135C22×Q8—22no—
136C2×M16—261no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—22no—
140C4⋊Q8—22no—
141C4⋊Q8—44no—
142C4⋊Q8—44no—
143C4⋊Q8—131no—
144#127—131no—
145#124—261no—
146#121—262no—
147C4×D4—262no—
148C2×C4⋊C4—28no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4C22⋊D1314yes—
151C2×C42—22no—
152C2×C42C22⋊D1312yes—
153C2×C42C22×D1311yescharacteristic
154#107—268no—
155C4⋊C8—134no—
156C4⋊C8—262no—
157#104—524no—
158#102—268no—
159C22⋊C8—262no—
160C4×C8—262no—
161C2×C13—22no—
162C2×C13#200512yes—
163C2×C13#201111yescharacteristic
164D13—161no—
165#41—522no—
166#41—522no—
167C2×Q8—44no—
168C2×Q8—44no—
169C2×Q8—42no—
170C2×Q8—42no—
171C2×Q8—261no—
172C2×D4—262no—
173C2×D4—261no—
174C2×D4—521no—
175C22×C4—22no—
176C22×C4—24no—
177C22×C4—521no—
178C22×C4C2×C22⋊D1312yes—
179C22×C4C2×C22⋊D1311yescharacteristic
180M16—522no—
181C2×C8—264no—
182C2×C8—521no—
183C4⋊C4—24no—
184C4⋊C4—24no—
185C4⋊C4—416no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—262no—
189C22⋊C4—522no—
190C42—28no—
191C42—22no—
192C42#610414yes—
193C42D4×D1311yescharacteristic
194C42D4×D1312yes—
195C42#612911yescharacteristic
196C13#1028911yescharacteristic, complemented, Sylow
197C23—521no—
198C23#8820711yescharacteristic
199Q8—84no—
200Q8—82no—
201Q8—82no—
202Q8—522no—
203D4—522no—
204D4—524no—
205D4—1042no—
206C2×C4—28no—
207C2×C4—24no—
208C2×C4—24no—
209C2×C4—48no—
210C2×C4—44no—
211C2×C4—521no—
212C2×C4—1041no—
213C2×C4—1041no—
214C2×C4C2×#610412yes—
215C2×C4#8818612yes—
216C2×C4#8819112yes—
217C2×C4#8819211yescharacteristic
218C2×C4#8819312yes—
219C2×C4#8819411yescharacteristic
220C8—524no—
221C8—1041no—
222C22—22no—
223C22—1041no—
224C22—1042no—
225C22#1171887812yes—
226C22#1171888411yescharacteristic
227C4—28no—
228C4—22no—
229C4—84no—
230C4—1041no—
231C4#1171873312yes—
232C4#1171873411yescharacteristic
233C4#1171873511yescharacteristic
234C4#1171875614yes—
235C2—22no—
236C2—2081no—
237C2#1311587212yes—
238C2#1311590711yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2868C2
socleC22×C13#392
prime radical#11719182C22
hypercenter#2868D13
hypocenterC13#10289
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2868

Complements

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

NH ≅ G/Ntype
3. #13113508C2semidirect
4. #13112669C2semidirect
5. C13×#2868C2semidirect
79. #2868D13semidirect
196. C13#10289semidirect

Maximal subgroups

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

subgroupindex
#131259572
#131156642
#131135082
#131126692
C13×#28682
#1028913