Finite Group Databasebeta

← #16779765

Subgroups — #16779765

Order 3328.

742 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719049C211yesmaximal, characteristic
2C2×#11719060C211yesmaximal, characteristic
3#13129709C214yesmaximal
4#13117241C211yesmaximal, characteristic
5C22×C4⋊#261—21no—
6C2×#88146—21no—
7C2×C42×D13C2211yescharacteristic
8C2×(C2×#261)⋊C4—21no—
9C2×(C2×#261)⋊C4C2212yes—
10C2×#88112—21no—
11C2×#88111C2212yes—
12C2×C4×#1057—21no—
13#11719060—22no—
14#11719060C414yescomplemented
15#11719049—22no—
16#11719049C414yescomplemented
17C13×#384C411yescharacteristic, complemented
18#11718648—21no—
19#11718648C2212yes—
20#11718638—21no—
21C4⋊C4×Dic13—21no—
22C4⋊C4×Dic13C412yescomplemented
23#11718596C411yescharacteristic, complemented
24C23×#261—22no—
25C22×C4×D13D411yescharacteristic
26C22×C4×D13D411yescharacteristic
27C22×C4×D13C2311yescharacteristic
28C22×#1057—22no—
29C2×C4⋊#261—24no—
30C2×C4⋊#261—42no—
31C2×C4⋊#261—42no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C412yes—
35C2×C42×C13C2×C411yescharacteristic
36C2×#6103—22no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C412yes—
40C2×C4×Dic13—22no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44#88146—42no—
45#88146—42no—
46C42×D13C2×C412yes—
47C42×D13C2×C412yes—
48C42×D13D412yes—
49C42×D13Q812yes—
50(C2×#261)⋊C4—24no—
51(C2×#261)⋊C4—22no—
52(C2×#261)⋊C4C2×C414yes—
53#88112—24no—
54#88111—22no—
55#88111C2×C414yes—
56C4×#1057—24no—
57#88071—22no—
58#88071—22no—
59#8026—131nomaximal, Sylow
60C23×D13C2×D411yescharacteristic
61C22×#261—24no—
62C22×#261—42no—
63C22×#261—42no—
64C22×#261—42no—
65C22×#261—42no—
66C22×#261—42no—
67C22×#261—42no—
68C22×C4×C13—22no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×Dic13—22no—
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C2×D411yescharacteristic
76C2×C4×D13—41no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×C4×D13C22⋊C412yes—
81C2×C4×D13C22⋊C412yes—
82C2×C4×D13C4⋊C412yes—
83C2×C4×D13C4⋊C412yes—
84C2×C4×D13D812yes—
85C2×C4×D13SD1612yes—
86C2×C4×D13SD1612yes—
87C2×C4×D13Q1612yes—
88C2×C4×D13C22×C411yescharacteristic
89C2×C4×D13C22×C411yescharacteristic
90C2×C4×D13C2×D411yescharacteristic
91C2×C4×D13C2×Q811yescharacteristic
92C2×#1057—24no—
93C2×#1057—42no—
94C2×#1057—42no—
95C4⋊#261—48no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4—42no—
99C42×C13C4212yes—
100C42×C13C4⋊C412yes—
101#6103—42no—
102#6103—42no—
103C4⋊Dic13—42no—
104C4⋊Dic13—42no—
105C4⋊Dic13—42no—
106C4×Dic13—44no—
107C4×Dic13C4212yes—
108C4×Dic13C22⋊C412yes—
109C4×Dic13C22⋊C412yes—
110C4×Dic13C4⋊C412yes—
111C4×Dic13C4⋊C412yes—
112C4×Dic13C4⋊C412yes—
113C2×#431—131no—
114#2285—131no—
115C2×#382—131no—
116#1294—134no—
117C23×C13C2×C22⋊C411yescharacteristic
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—21no—
121C22×D13—21no—
122C22×D13C2×C22⋊C411yescharacteristic
123C22×D13C2×C4⋊C411yescharacteristic
124C22×D13C2×D811yescharacteristic
125C22×D13C2×SD1611yescharacteristic
126C22×D13C2×SD1611yescharacteristic
127C22×D13C2×Q1611yescharacteristic
128C2×#261—44no—
129C2×#261—44no—
130C2×#261—44no—
131C2×#261—82no—
132C2×#261—82no—
133C2×#261—82no—
134C2×#261—82no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13#9512yes—
143C2×C4×C13#9512yes—
144C2×C4×C13#10212yes—
145C2×C4×C13#10312yes—
146C2×C4×C13C2×C4211yescharacteristic
147C2×C4×C13C2×C4⋊C411yescharacteristic
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13#9512yes—
156C2×Dic13#9512yes—
157C2×Dic13#10212yes—
158C2×Dic13#10312yes—
159C2×Dic13C2×C22⋊C411yescharacteristic
160C2×Dic13C2×C4⋊C411yescharacteristic
161C4×D13—42no—
162C4×D13—42no—
163C4×D13—41no—
164C4×D13—41no—
165C4×D13—41no—
166C4×D13—41no—
167C4×D13#10214yes—
168C4×D13#10314yes—
169C4×D13#10614yes—
170C4×D13#10714yes—
171#1057—44no—
172C2×#117—261no—
173C22×C4⋊C4—261no—
174C22×C42—131no—
175#431—134no—
176#431—262no—
177C2×C4⋊C8—261no—
178C2×C22⋊C8—132no—
179C2×C4×C8—261no—
180#384—131no—
181#384#26111yescharacteristic, complemented
182#382—134no—
183#382—261no—
184#382—262no—
185#380—132no—
186#380—261no—
187C4×C4⋊C4—132no—
188C4×C4⋊C4—261no—
189C2×#95—132no—
190C2×#95—261no—
191C22×C13C2×#9511yescharacteristic
192C22×C13#41011yescharacteristic
193C22×C13#41011yescharacteristic
194C22×C13C2×#10211yescharacteristic
195C22×C13C2×#10311yescharacteristic
196C22×C13#42111yescharacteristic
197C22×C13#42111yescharacteristic
198C2×D13—21no—
199C2×D13—21no—
200C2×D13—21no—
201C2×D13—21no—
202C2×D13—21no—
203C2×D13—21no—
204C2×D13—21no—
205C2×D13—21no—
206C2×D13—21no—
207C2×D13—21no—
208C2×D13—21no—
209C2×D13—21no—
210C2×D13C2×#10211yescharacteristic
211C2×D13C2×#10311yescharacteristic
212C2×D13C2×#10611yescharacteristic
213C2×D13C2×#10711yescharacteristic
214#261—84no—
215C4×C13—22no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—82no—
219C4×C13#34014yes—
220Dic13—22no—
221Dic13—21no—
222Dic13—21no—
223Dic13—82no—
224Dic13#34014yes—
225C23×C4—131no—
226C23×C4—131no—
227C23×C4—131no—
228C23×C4—262no—
229C22×C8—262no—
230#117—522no—
231#117—522no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—132no—
235C2×C4⋊C4—264no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4—522no—
239C2×C4⋊C4—522no—
240C2×C4⋊C4C2×#26112yes—
241C2×C22⋊C4—262no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—132no—
246C2×C42—132no—
247C2×C42—132no—
248C2×C42—132no—
249C2×C42—262no—
250C2×C42C2×#26111yescharacteristic
251C4⋊C8—264no—
252C22⋊C8—134no—
253C22⋊C8—262no—
254C4×C8—264no—
255#95—134no—
256#95—262no—
257#95—262no—
258#95—262no—
259#95—264no—
260C2×C13#151711yescharacteristic
261C2×C13#151711yescharacteristic
262C2×C13#151811yescharacteristic
263C2×C13#151811yescharacteristic
264C2×C13#173311yescharacteristic
265C2×C13C2×#34011yescharacteristic
266C2×C13#174011yescharacteristic
267D13—21no—
268D13—21no—
269D13—21no—
270D13—21no—
271C24—131no—
272C22×C4—22no—
273C22×C4—131no—
274C22×C4—132no—
275C22×C4—132no—
276C22×C4—132no—
277C22×C4—132no—
278C22×C4—132no—
279C22×C4—132no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—132no—
283C22×C4—132no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—264no—
289C22×C4—262no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4—522no—
295C22×C4—522no—
296C22×C4—522no—
297C22×C4—522no—
298C22×C4—522no—
299C22×C4—522no—
300C22×C4C22⋊#26111yescharacteristic
301C22×C4C22⋊#26111yescharacteristic
302C22×C4C22×#26111yescharacteristic
303C2×C8—264no—
304C2×C8—522no—
305C2×C8—522no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—522no—
310C4⋊C4—522no—
311C4⋊C4—528no—
312C4⋊C4—522no—
313C22⋊C4—522no—
314C22⋊C4—522no—
315C42—132no—
316C42—132no—
317C42—132no—
318C42—132no—
319C42—132no—
320C42—132no—
321C42—524no—
322C42C4×#26112yes—
323C42C4⋊#26112yes—
324C13#802611yescharacteristic, complemented, Sylow
325C23—131no—
326C23—131no—
327C23—131no—
328C23—131no—
329C23—131no—
330C23—131no—
331C23—261no—
332C23—261no—
333C23—261no—
334C23—261no—
335C23C2×C22⋊#26111yescharacteristic
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—132no—
344C2×C4—132no—
345C2×C4—132no—
346C2×C4—134no—
347C2×C4—134no—
348C2×C4—134no—
349C2×C4—134no—
350C2×C4—131no—
351C2×C4—132no—
352C2×C4—131no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—524no—
364C2×C4—524no—
365C2×C4—524no—
366C2×C4—522no—
367C2×C4—522no—
368C2×C4—522no—
369C2×C4—1042no—
370C2×C4—1042no—
371C2×C4—1042no—
372C2×C4—1042no—
373C2×C4(C2×#261)⋊C412yes—
374C2×C4(C2×#261)⋊C412yes—
375C2×C4#8811512yes—
376C2×C4#8811712yes—
377C2×C4C2×C4×#26111yescharacteristic
378C2×C4C2×C4⋊#26111yescharacteristic
379C8—524no—
380C22—131no—
381C22—131no—
382C22—131no—
383C22—131no—
384C22—261no—
385C22—261no—
386C22—261no—
387C22—261no—
388C22—261no—
389C22—261no—
390C22—261no—
391C22—261no—
392C22—261no—
393C22—261no—
394C22—261no—
395C22—261no—
396C22C2×(C2×#261)⋊C411yescharacteristic
397C22C2×#8811511yescharacteristic
398C22#1171914011yescharacteristic
399C22#1171914211yescharacteristic
400C22C2×#8811711yescharacteristic
401C22#1171915511yescharacteristic
402C22#1171915611yescharacteristic
403C4—22no—
404C4—21no—
405C4—21no—
406C4—82no—
407C4—134no—
408C4—262no—
409C4—261no—
410C4—261no—
411C4—1044no—
412C4—1042no—
413C4#1171824614yes—
414C2—261no—
415C2—261no—
416C2—261no—
417C2—261no—
418C2#1313026511yescharacteristic
419C2#1313026711yescharacteristic
420C2#1313026811yescharacteristic
421C2#1313027011yescharacteristic
422C2#1313051511yescharacteristic
423C2C2×#1171824611yescharacteristic
424C2#1313053611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenter#384#261
hypocenterC13#8026
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
14. #11719060C4semidirect
16. #11719049C4semidirect
17. C13×#384C4semidirect
22. C4⋊C4×Dic13C4semidirect
23. #11718596C4semidirect
181. #384#261semidirect
324. C13#8026semidirect

Maximal subgroups

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

subgroupindex
C2×#117190492
C2×#117190602
#131297092
#131172412
#802613