Finite Group Databasebeta

← #15760608

Subgroups — #15760608

Order 3328.

498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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#13120009C211yesmaximal, characteristic
2#13113552C212yesmaximal, complemented
3#13113177C211yesmaximal, characteristic
4#13112693C212yesmaximal, complemented
5C13×#2973C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C13×#435—24no—
9C13×#432C2212yes—
10C13×#407—21no—
11C2×C13×C22⋊C8—21no—
12#11718882C412yes—
13#11718873—21no—
14#11718873—21no—
15#11718638C412yes—
16#11718608—21no—
17#11718608—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19#11718587C2212yes—
20#11718117—21no—
21#11718117—21no—
22#11718078—24no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26—21no—
27C2×C13×M16—22no—
28C22×C8×C13—22no—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C22⋊Dic13—22no—
36C2×C22⋊Dic13—22no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C412yes—
40C2×C4×Dic13C2×C412yes—
41#88123—22no—
42#88123—22no—
43C13×C4⋊C8D414yes—
44C13×C22⋊C8—22no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×#97—22no—
48#88071—22no—
49#88071—22no—
50#88071—21no—
51C22⋊#1055—22no—
52C4⋊#1055—22no—
53#88043—22no—
54#9453—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C24×C13C22⋊C411yescharacteristic
57C2×D4×C13—22no—
58C2×D4×C13—22no—
59C2×D4×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—22no—
72C22×Dic13—22no—
73C2×Dic26—42no—
74C2×Dic26—82no—
75C13×M16—82no—
76C2×C8×C13—24no—
77C2×C8×C13—82no—
78C13×C4⋊C4—22no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4—22no—
81C42×C13C2×D412yes—
82C42×C13#4112yes—
83C22⋊Dic13—82no—
84C22⋊Dic13—82no—
85C4⋊Dic13—24no—
86C4⋊Dic13—42no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4×Dic13—42no—
90C2×#1055—42no—
91#2973D1311yescharacteristic
92#2563—131no—
93#1556—132no—
94#1466—131no—
95#1285—132no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13#10112yes—
106C23×C13C2×C22⋊C411yescharacteristic
107D4×C13—44no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13C4×D412yes—
121C2×C4×C13#12011yescharacteristic
122C2×C4×C13#12112yes—
123C2×C4×C13#12311yescharacteristic
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130Dic26—84no—
131C8×C13—44no—
132#1055—82no—
133C2×C4⋊Q8—131no—
134C2×C4×D4C2×D1311yescharacteristic
135#435—24no—
136#432—132no—
137#432C2×D1312yes—
138#407—21no—
139C2×C22⋊C8—21no—
140#393—261no—
141#393—261no—
142#390—132no—
143#382—132no—
144#380—261no—
145#380—261no—
146C4×C4⋊C4—131no—
147#332—264no—
148#323—261no—
149#323—261no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—22no—
153C22×C13—42no—
154C22×C13—42no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—81no—
161C22×C13—81no—
162C22×C13#38611yescharacteristic
163C22×C13C2×#10111yescharacteristic
164C22×C13#41311yescharacteristic
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13#45512yes—
171Dic13—82no—
172Dic13—82no—
173C22×Q8—261no—
174C22×D4C4×D1311yescharacteristic
175C23×C4C22⋊D1311yescharacteristic
176C23×C4C22⋊D1311yescharacteristic
177C2×M16—22no—
178C22×C8—22no—
179C4⋊Q8—262no—
180C4⋊Q8—262no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4—132no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4C4×D1311yescharacteristic
187C2×C22⋊C4—262no—
188C2×C22⋊C4—262no—
189C2×C22⋊C4D5211yescharacteristic
190C2×C22⋊C4D5211yescharacteristic
191C2×C42—132no—
192C2×C42C22×D1311yescharacteristic
193C4⋊C8—262no—
194C4⋊C8C22⋊D1314yes—
195C22⋊C8—22no—
196C22⋊C8—22no—
197C22⋊C8—22no—
198C22⋊C8—262no—
199#97—22no—
200#97—262no—
201#95—262no—
202#95—262no—
203#95—261no—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13—42no—
207C2×C13—81no—
208C2×C13#188511yescharacteristic
209C2×C13#190111yescharacteristic
210C2×C13#191011yescharacteristic
211C24#610311yescharacteristic
212C24#610311yescharacteristic
213C2×Q8—522no—
214C2×Q8—1042no—
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—262no—
225C22×C4—262no—
226C22×C4#610311yescharacteristic
227C22×C4#610311yescharacteristic
228C22×C4C2×C4×D1311yescharacteristic
229C22×C4C2×D5211yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231M16—82no—
232C2×C8—24no—
233C2×C8—82no—
234C2×C8—522no—
235C4⋊C4—22no—
236C4⋊C4—264no—
237C4⋊C4—522no—
238C4⋊C4—521no—
239C4⋊C4—521no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—1042no—
243C22⋊C4—1042no—
244C42—522no—
245C42#612712yes—
246C42C2×C22⋊D1312yes—
247C13#945311yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23#8806412yes—
258C23C2×#610311yescharacteristic
259Q8—1044no—
260D4—44no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4—522no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4C4×C22⋊D1312yes—
280C2×C4#8818311yescharacteristic
281C2×C4#8818412yes—
282C2×C4#8820711yescharacteristic
283C8—44no—
284C8—1042no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22#1171879311yescharacteristic
298C22C2×#8806411yescharacteristic
299C22#1171887411yescharacteristic
300C4—21no—
301C4—22no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—1042no—
306C4—1042no—
307C4#1171890312yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—81no—
312C2#1311522411yescharacteristic
313C2#1311530411yescharacteristic
314C2#1311536311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2973C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2973D13
hypocenterC13#9453
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13113552C2semidirect
4. #13112693C2semidirect
247. C13#9453semidirect

Maximal subgroups

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

subgroupindex
#131200092
#131135522
#131131772
#131126932
C13×#29732
#945313