Finite Group Databasebeta

← #16780161

Subgroups — #16780161

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131513C211yesmaximal, characteristic
2#13131285C211yesmaximal, characteristic
3#13129736C214yesmaximal
4#13123468C211yesmaximal, characteristic
5C2×#88237C412yes—
6C2×C42×D13C2211yescharacteristic
7#11719136C412yes—
8#11719136C2212yes—
9#11719130C412yescomplemented
10#11719127C2212yes—
11#11719119C412yescomplemented
12#11719060—21no—
13#11719059—21no—
14C4×C4⋊#261—21no—
15C4×C4⋊#261—21no—
16#11719054—21no—
17#11719052—21no—
18#11719051—21no—
19C4×#6118—21no—
20C13×#423C411yescharacteristic, complemented
21#11718787C2212yes—
22M16×Dic13C412yescomplemented
23#11718585C411yescharacteristic, complemented
24#11718496—21no—
25#11718496—21no—
26#11718494—21no—
27#11718494—21no—
28C22×C4×D13C2×C411yescharacteristic
29C22×C4×D13C2×C411yescharacteristic
30C22×C4×D13C2311yescharacteristic
31C2×C22⋊#261C2×C414yes—
32#88237—44no—
33C2×C4⋊#261—22no—
34C2×C4⋊#261—22no—
35C2×C4⋊#261—22no—
36C2×C4×#261—22no—
37C2×#6118—22no—
38C2×C13×M16C2×C412yes—
39C2×C42×C13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×#6099C2×C412yes—
44C42×D13D411yescharacteristic
45C42×D13D411yescharacteristic
46C42×D13D411yescharacteristic
47C42×D13D411yescharacteristic
48C42×D13D411yescharacteristic
49C42×D13D411yescharacteristic
50C42×D13Q811yescharacteristic
51C42×D13Q811yescharacteristic
52C22⋊#1057C2×C414yes—
53(C2×#261)⋊C4—22no—
54(C2×#261)⋊C4—22no—
55#88111—22no—
56#88110—22no—
57C4⋊#1057—22no—
58C4⋊#1057—22no—
59C4×#1057—22no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62#88060—22no—
63#88060—22no—
64#88055—22no—
65C8×Dic13—22no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68#8105—131nomaximal, Sylow
69C23×D13C22×C411yescharacteristic
70C22×#261—24no—
71C22×C4×C13C4211yescharacteristic
72C22×C4×C13C4211yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×Dic13C4211yescharacteristic
75C22×Dic13C4211yescharacteristic
76C22×Dic13C22×C411yescharacteristic
77C2×C4×D13—22no—
78C2×C4×D13—22no—
79C2×C4×D13—42no—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13C22⋊C411yescharacteristic
83C2×C4×D13C22⋊C411yescharacteristic
84C2×C4×D13C22⋊C411yescharacteristic
85C2×C4×D13C22⋊C411yescharacteristic
86C2×C4×D13C4⋊C411yescharacteristic
87C2×C4×D13C4⋊C411yescharacteristic
88C2×C4×D13C4⋊C411yescharacteristic
89C2×C4×D13C4⋊C411yescharacteristic
90C2×C4×D13C2×D411yescharacteristic
91C2×C4×D13C2×D411yescharacteristic
92C2×C4×D13C2×D411yescharacteristic
93C2×C4×D13C2×Q811yescharacteristic
94C22⋊#261—44no—
95C2×#1057—24no—
96C4⋊#261—44no—
97C4⋊#261—42no—
98C4⋊#261—42no—
99C4⋊#261—44no—
100C4×#261—44no—
101#6118—42no—
102#6118—42no—
103C13×M16—42no—
104C2×C8×C13—22no—
105C42×C13C22⋊C411yescharacteristic
106C42×C13C22⋊C411yescharacteristic
107C42×C13C4⋊C411yescharacteristic
108C42×C13C4⋊C411yescharacteristic
109C4×Dic13C22⋊C411yescharacteristic
110C4×Dic13C22⋊C411yescharacteristic
111C4×Dic13C22⋊C411yescharacteristic
112C4×Dic13C22⋊C411yescharacteristic
113C4×Dic13C22⋊C411yescharacteristic
114C4×Dic13C22⋊C411yescharacteristic
115C4×Dic13C4⋊C411yescharacteristic
116C4×Dic13C4⋊C411yescharacteristic
117C4×Dic13C4⋊C411yescharacteristic
118C4×Dic13C4⋊C411yescharacteristic
119C4×Dic13C4⋊C411yescharacteristic
120C4×Dic13C4⋊C411yescharacteristic
121#6099—42no—
122C2×#1055—22no—
123#2920—131no—
124#2920—131no—
125#2285—131no—
126#1305—134no—
127C23×C13C2×C4211yescharacteristic
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—41no—
131C22×D13—41no—
132C22×D13C2×C22⋊C411yescharacteristic
133C22×D13C2×C4⋊C411yescharacteristic
134C2×#261—44no—
135C2×#261—44no—
136C2×#261—44no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13#9511yescharacteristic
142C2×C4×C13#9511yescharacteristic
143C2×C4×C13#9511yescharacteristic
144C2×C4×C13#9511yescharacteristic
145C2×C4×C13C2×C22⋊C411yescharacteristic
146C2×C4×C13C2×C4⋊C411yescharacteristic
147C2×Dic13—22no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13#9511yescharacteristic
151C2×Dic13#9511yescharacteristic
152C2×Dic13#9511yescharacteristic
153C2×Dic13#9511yescharacteristic
154C2×Dic13C2×C22⋊C411yescharacteristic
155C2×Dic13C2×C4⋊C411yescharacteristic
156C4×D13—21no—
157C4×D13—21no—
158C4×D13—22no—
159C4×D13—22no—
160C4×D13—22no—
161C4×D13—21no—
162C4×D13—21no—
163C4×D13—21no—
164C4×D13—21no—
165C4×D13—22no—
166C4×D13—41no—
167C4×D13—41no—
168C4×D13—41no—
169C4×D13—41no—
170C4×D13#10012yes—
171C4×D13#10112yes—
172#1057—44no—
173C8×C13—42no—
174#1055—42no—
175C2×#117—132no—
176C22×C42—131no—
177#432—132no—
178#432—261no—
179#432—261no—
180#432—261no—
181#431—132no—
182#431—261no—
183#431—261no—
184#431—261no—
185#423—131no—
186#423—261no—
187#423#26111yescharacteristic, complemented
188#407—132no—
189#407—132no—
190C4×M16—132no—
191C4×M16—261no—
192#384—261no—
193#382—261no—
194#380—132no—
195#380—132no—
196C4×C4⋊C4—261no—
197C4×C4⋊C4—261no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13C2×#9511yescharacteristic
202C2×D13—21no—
203C2×D13—21no—
204C2×D13—21no—
205C2×D13—21no—
206C2×D13—21no—
207C2×D13—42no—
208C2×D13—42no—
209C2×D13C2×#10011yescharacteristic
210C2×D13C2×#10111yescharacteristic
211#261—84no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13#34312yes—
216C4×C13#34412yes—
217C4×C13#41011yescharacteristic
218C4×C13#41011yescharacteristic
219Dic13—21no—
220Dic13—21no—
221Dic13—21no—
222Dic13—21no—
223Dic13—21no—
224Dic13#34312yes—
225C23×C4—131no—
226C23×C4—131no—
227C23×C4—131no—
228C2×M16—132no—
229C2×M16—262no—
230C2×M16C2×#26112yes—
231#117—524no—
232C2×C4⋊C4—262no—
233C2×C4⋊C4—262no—
234C2×C4⋊C4—262no—
235C2×C22⋊C4—134no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—131no—
246C2×C42—131no—
247C2×C42—262no—
248C2×C42C2×#26111yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—262no—
252C4⋊C8—262no—
253C4⋊C8—261no—
254C4⋊C8—261no—
255C22⋊C8—134no—
256C22⋊C8—262no—
257C22⋊C8—262no—
258C22⋊C8—262no—
259#97—262no—
260#97—262no—
261C4×C8—262no—
262C4×C8—262no—
263#95—262no—
264#95—262no—
265C2×C13—41no—
266C2×C13#174011yescharacteristic
267C2×C13C2×#34311yescharacteristic
268C2×C13C2×#34411yescharacteristic
269D13—21no—
270D13—21no—
271D13—41no—
272C24—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—262no—
289C22×C4—262no—
290C22×C4—264no—
291C22×C4—522no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4C4×#26111yescharacteristic
295C22×C4C4×#26111yescharacteristic
296C22×C4C22×#26111yescharacteristic
297M16—42no—
298M16—522no—
299M16—522no—
300M16—522no—
301C2×C8—22no—
302C2×C8—264no—
303C2×C8—262no—
304C4⋊C4—524no—
305C4⋊C4—524no—
306C4⋊C4—522no—
307C4⋊C4—522no—
308C22⋊C4—524no—
309C42—131no—
310C42—131no—
311C42—131no—
312C42—131no—
313C42—131no—
314C42—131no—
315C42—131no—
316C42—131no—
317C42—131no—
318C42—131no—
319C42—131no—
320C42—131no—
321C42—524no—
322C42C4⋊#26111yescharacteristic
323C42C4⋊#26111yescharacteristic
324C42C22⋊#26111yescharacteristic
325C42C22⋊#26111yescharacteristic
326C13#810511yescharacteristic, complemented, Sylow
327C23—131no—
328C23—131no—
329C23—261no—
330C23—261no—
331C23—521no—
332C23—521no—
333C23C2×C4×#26111yescharacteristic
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—131no—
339C2×C4—132no—
340C2×C4—132no—
341C2×C4—131no—
342C2×C4—131no—
343C2×C4—131no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—262no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—262no—
350C2×C4—262no—
351C2×C4—262no—
352C2×C4—262no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—524no—
364C2×C4—524no—
365C2×C4—524no—
366C2×C4(C2×#261)⋊C411yescharacteristic
367C2×C4(C2×#261)⋊C411yescharacteristic
368C2×C4(C2×#261)⋊C411yescharacteristic
369C2×C4(C2×#261)⋊C411yescharacteristic
370C2×C4C2×C4⋊#26111yescharacteristic
371C2×C4C2×C22⋊#26111yescharacteristic
372C8—42no—
373C8—524no—
374C8—522no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—131no—
379C22—131no—
380C22—261no—
381C22—261no—
382C22—261no—
383C22—261no—
384C22—261no—
385C22—522no—
386C22—522no—
387C22C2×(C2×#261)⋊C411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—132no—
392C4—261no—
393C4—261no—
394C4—261no—
395C4—261no—
396C4—261no—
397C4—1044no—
398C4#1171827112yes—
399C4#1171827412yes—
400C4#1171914211yescharacteristic
401C4#1171915611yescharacteristic
402C2—41no—
403C2—261no—
404C2—261no—
405C2—521no—
406C2#1313053611yescharacteristic
407C2C2×#1171827111yescharacteristic
408C2C2×#1171827411yescharacteristic
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC23×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#423C4
socleC22×C13C2×#95
prime radicalC23×D13C22×C4
cosocleC22×C4×D13C23
hypercenter#423#261
hypocenterC13#8105
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
9. #11719130C4semidirect
11. #11719119C4semidirect
20. C13×#423C4semidirect
22. M16×Dic13C4semidirect
23. #11718585C4semidirect
187. #423#261semidirect
326. C13#8105semidirect

Maximal subgroups

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

subgroupindex
#131315132
#131312852
#131297362
#131234682
#810513