Finite Group Databasebeta

← #16780205

Subgroups — #16780205

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131512C211yesmaximal, characteristic
2#13131512C211yesmaximal, characteristic
3#13129739C214yesmaximal
4#13117231C211yesmaximal, characteristic
5C22×C4×Dic13C2211yescharacteristic
6#11719169C2212yes—
7#11719169C2212yes—
8#11719130—21no—
9#11719130C412yescomplemented
10#11719129—21no—
11#11719129—21no—
12#11719128—21no—
13#11719128C412yescomplemented
14#11719125—21no—
15#11719125C412yescomplemented
16C4×#6122—21no—
17C4×#6122—21no—
18#11719119—21no—
19#11719119C412yescomplemented
20C13×#380C411yescharacteristic
21#11718873C411yescharacteristic
22#11718638—21no—
23C4⋊C4×Dic13—21no—
24#11718604C2212yes—
25C22⋊C4×Dic13C412yes—
26#11718312—21no—
27#11718309—21no—
28C23×C4×C13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2311yescharacteristic
31C2×#6122—22no—
32C2×#6122—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C22⋊C4C2×C412yes—
35C2×C22⋊Dic13C2×C412yes—
36C2×C4⋊Dic13—21no—
37C2×C4×Dic13—22no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13Q811yescharacteristic
49C2×C4×Dic13Q811yescharacteristic
50C22⋊#1057—22no—
51C22⋊#1057—22no—
52C22⋊#1057C2×C414yes—
53C22⋊#1057C2×C414yes—
54#88112—22no—
55#88112—22no—
56#88110—22no—
57#88110—22no—
58C4⋊#1057—22no—
59C4⋊#1057—22no—
60C4×#1057—22no—
61C4×#1057—22no—
62C13×#95—21no—
63#88071—21no—
64#88071—22no—
65#88071—22no—
66#88071—22no—
67#8113—131nomaximal, Sylow
68C24×C13C22×C411yescharacteristic
69C22×C4×C13—22no—
70C22×C4×C13—42no—
71C22×C4×C13C4211yescharacteristic
72C22×C4×C13C4211yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C4⋊C411yescharacteristic
76C22×C4×C13C4⋊C411yescharacteristic
77C22×Dic13—22no—
78C22×Dic13—42no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13C4211yescharacteristic
82C22×Dic13C4211yescharacteristic
83C22×Dic13C22⋊C411yescharacteristic
84C22×Dic13C22⋊C411yescharacteristic
85C22×Dic13C4⋊C411yescharacteristic
86C22×Dic13C4⋊C411yescharacteristic
87C22×Dic13C22×C411yescharacteristic
88C22×Dic13C22×C411yescharacteristic
89C22×Dic13C2×D411yescharacteristic
90C22×Dic13C2×D411yescharacteristic
91C22×Dic13C2×D411yescharacteristic
92C22×Dic13C2×Q811yescharacteristic
93#6122—42no—
94#6122—42no—
95#6122—42no—
96#6122—42no—
97C2×#1057—24no—
98C2×#1057—24no—
99C13×C4⋊C4—42no—
100C13×C22⋊C4—42no—
101C22⋊Dic13—42no—
102C4⋊Dic13—42no—
103C4×Dic13—44no—
104C4×Dic13C22⋊C411yescharacteristic
105C4×Dic13C22⋊C411yescharacteristic
106C4×Dic13C22⋊C411yescharacteristic
107C4×Dic13C22⋊C411yescharacteristic
108C4×Dic13C22⋊C411yescharacteristic
109C4×Dic13C22⋊C411yescharacteristic
110C4×Dic13C22⋊C411yescharacteristic
111C4×Dic13C22⋊C411yescharacteristic
112C4×Dic13C4⋊C411yescharacteristic
113C4×Dic13C4⋊C411yescharacteristic
114C4×Dic13C4⋊C411yescharacteristic
115C4×Dic13C4⋊C411yescharacteristic
116C4×Dic13C4⋊C411yescharacteristic
117C4×Dic13C4⋊C411yescharacteristic
118C4×Dic13C4⋊C411yescharacteristic
119C4×Dic13C4⋊C411yescharacteristic
120#2920—131no—
121#2920—131no—
122#2283—131no—
123#1306—134no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13C2×C4211yescharacteristic
129C23×C13C2×C22⋊C411yescharacteristic
130C23×C13C2×C4⋊C411yescharacteristic
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13#9511yescharacteristic
141C2×C4×C13#9511yescharacteristic
142C2×C4×C13#9511yescharacteristic
143C2×C4×C13#9511yescharacteristic
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13#9511yescharacteristic
162C2×Dic13#9511yescharacteristic
163C2×Dic13#9511yescharacteristic
164C2×Dic13#9511yescharacteristic
165C2×Dic13C2×C22⋊C411yescharacteristic
166C2×Dic13C2×C22⋊C411yescharacteristic
167C2×Dic13C2×C4⋊C411yescharacteristic
168C2×Dic13C2×C4⋊C411yescharacteristic
169#1057—44no—
170#1057—44no—
171C22×C42—131no—
172#432—132no—
173#432—132no—
174#432—261no—
175#432—261no—
176#431—132no—
177#431—132no—
178#431—261no—
179#431—261no—
180#423—261no—
181#423—261no—
182#407—132no—
183#407—132no—
184C4×M16—261no—
185C4×M16—261no—
186#383—261no—
187#382—261no—
188#381—132no—
189#380—131no—
190#380#26111yescharacteristic
191C4×C4⋊C4—261no—
192C4×C22⋊C4—132no—
193#376—261no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—42no—
203C22×C13—42no—
204C22×C13C2×#9511yescharacteristic
205C22×C13#41011yescharacteristic
206C22×C13#41011yescharacteristic
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—82no—
211C4×C13#34412yes—
212Dic13—21no—
213Dic13—21no—
214Dic13—21no—
215Dic13—21no—
216Dic13—21no—
217Dic13—21no—
218Dic13—21no—
219Dic13—82no—
220Dic13#34412yes—
221C23×C4—131no—
222C23×C4—131no—
223C23×C4C2×#26111yescharacteristic
224C2×M16—262no—
225C2×M16—262no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—261no—
228C2×C22⋊C4—132no—
229C2×C22⋊C4C2×#26112yes—
230C2×C42—131no—
231C2×C42—131no—
232C2×C42—131no—
233C2×C42—131no—
234C2×C42—131no—
235C2×C42—131no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—262no—
243C4⋊C8—262no—
244C4⋊C8—262no—
245C4⋊C8—262no—
246C4⋊C8—262no—
247C22⋊C8—134no—
248C22⋊C8—134no—
249C22⋊C8—262no—
250C22⋊C8—262no—
251#97—262no—
252#97—262no—
253C4×C8—262no—
254C4×C8—262no—
255#95—21no—
256#95—262no—
257#95—262no—
258#95—262no—
259#95—261no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13—41no—
263C2×C13—41no—
264C2×C13#174011yescharacteristic
265C2×C13C2×#34411yescharacteristic
266C2×C13C2×#34411yescharacteristic
267C24C22×#26111yescharacteristic
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—131no—
271C22×C4—131no—
272C22×C4—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—262no—
283C22×C4—522no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4C4×#26111yescharacteristic
287C22×C4C4×#26111yescharacteristic
288C22×C4C4⋊#26111yescharacteristic
289C22×C4C4⋊#26111yescharacteristic
290C22×C4C22⋊#26111yescharacteristic
291C22×C4C22⋊#26111yescharacteristic
292M16—522no—
293M16—522no—
294M16—522no—
295M16—522no—
296C2×C8—264no—
297C2×C8—264no—
298C4⋊C4—42no—
299C4⋊C4—522no—
300C22⋊C4—42no—
301C22⋊C4—522no—
302C42—131no—
303C42—131no—
304C42—131no—
305C42—131no—
306C42—131no—
307C42—131no—
308C42—131no—
309C42—131no—
310C42—131no—
311C42—131no—
312C42—131no—
313C42—131no—
314C42—131no—
315C42—131no—
316C42—131no—
317C42—131no—
318C42—524no—
319C13#811311yescharacteristic, complemented, Sylow
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23C2×C4×#26111yescharacteristic
325C23C2×C4⋊#26111yescharacteristic
326C23C2×C22⋊#26111yescharacteristic
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—131no—
337C2×C4—131no—
338C2×C4—131no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—131no—
342C2×C4—131no—
343C2×C4—131no—
344C2×C4—262no—
345C2×C4—262no—
346C2×C4—262no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—522no—
359C2×C4—522no—
360C2×C4—522no—
361C2×C4(C2×#261)⋊C411yescharacteristic
362C2×C4(C2×#261)⋊C411yescharacteristic
363C2×C4(C2×#261)⋊C411yescharacteristic
364C2×C4(C2×#261)⋊C411yescharacteristic
365C8—524no—
366C8—524no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—42no—
376C22—42no—
377C22C2×(C2×#261)⋊C411yescharacteristic
378C22#1171914211yescharacteristic
379C22#1171915611yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—132no—
385C4—261no—
386C4—261no—
387C4—261no—
388C4—261no—
389C4—261no—
390C4—261no—
391C4—261no—
392C4—1042no—
393C4#1171823912yes—
394C2—21no—
395C2—21no—
396C2—41no—
397C2—41no—
398C2#1313053611yescharacteristic
399C2C2×#1171823911yescharacteristic
400C2#1313054411yescharacteristic
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC13×#380C4
socleC22×C13C2×#95
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenter#380#261
hypocenterC13#8113
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
9. #11719130C4semidirect
13. #11719128C4semidirect
15. #11719125C4semidirect
19. #11719119C4semidirect
319. C13#8113semidirect

Maximal subgroups

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

subgroupindex
#131315122
#131297392
#131172312
#811313