Finite Group Databasebeta

← #15761907

Subgroups — #15761907

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊#1055C211yesmaximal, characteristic, complemented
2C2×#11718130C212yesmaximal, complemented
3C2×#11718129C212yesmaximal
4#13113063C211yesmaximal, characteristic, complemented
5C13×#2850C211yesmaximal, characteristic
6C2×C13×#124C411yescharacteristic, complemented
7C2×C13×C22⋊Q8C2211yescharacteristic
8C2×C13×#121C2211yescharacteristic
9C22×C42×C13C2211yescharacteristic
10C13×#391C411yescharacteristic, complemented
11C13×#390C411yescharacteristic, complemented
12C13×#388—21no—
13C13×#388—21no—
14C13×#386—21no—
15C13×#386—21no—
16C13×#382C411yescharacteristic, complemented
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88071C2212yes—
20C2×C22⋊#1055C2212yes—
21C2×C4×#1055—21no—
22#11718130—24no—
23#11718129—24no—
24#11718116—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C23×Dic13—22no—
32C13×#124—42no—
33C13×C22⋊Q8—22no—
34C13×C22⋊Q8—22no—
35C13×#121—22no—
36C13×#121—22no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C42×C13—42no—
47C2×C42×C13C2×C411yescharacteristic
48C2×C42×C13C2×C411yescharacteristic
49C2×C42×C13D411yescharacteristic
50C2×C42×C13D411yescharacteristic
51C22×#1055—22no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56#88071—24no—
57#88071—22no—
58#88071—22no—
59#88071—42no—
60C22⋊#1055—22no—
61C22⋊#1055D414yes—
62C4×#1055—42no—
63#9681—131nomaximal, Sylow
64C24×C13—21no—
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×D4×C13—22no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—42no—
75C2×D4×C13—42no—
76C22×C4×C13—22no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22×C411yescharacteristic
92C22×C4×C13C2×D412yes—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4112yes—
95C22×Dic13—24no—
96C22×Dic13—42no—
97C22×Dic13—42no—
98C22×Dic13—42no—
99C22×Dic13—42no—
100C22×Dic13—42no—
101C22×Dic13—42no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—42no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—42no—
112C42×C13—22no—
113C42×C13—22no—
114C42×C13—41no—
115C42×C13—41no—
116C2×#1055—24no—
117C2×#1055—42no—
118C2×#1055—42no—
119#2850D1311yescharacteristic
120C4×C22⋊C8—131no—
121C2×#328—132no—
122C2×#327—132no—
123#1434—131no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13C2×C22⋊C411yescharacteristic
136C23×C13#12411yescharacteristic
137C23×C13#12711yescharacteristic
138C23×C13#13512yes—
139C23×C13#13512yes—
140Q8×C13—82no—
141D4×C13—82no—
142D4×C13—82no—
143D4×C13—82no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—44no—
161C2×C4×C13—44no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13#9912yes—
172C2×C4×C13#10412yes—
173C2×C4×C13C4×D412yes—
174C2×C4×C13#12112yes—
175C2×Dic13—44no—
176C2×Dic13—44no—
177C2×Dic13—44no—
178C2×Dic13—82no—
179C2×Dic13—82no—
180C2×Dic13—82no—
181C2×Dic13—82no—
182#1055—44no—
183C2×#124Dic1311yescharacteristic, complemented
184C2×C22⋊Q8C2×D1311yescharacteristic
185C2×#121C2×D1311yescharacteristic
186C22×C42C2×D1311yescharacteristic
187C2×C22⋊C8—132no—
188C2×C4×C8—261no—
189#391Dic1311yescharacteristic, complemented
190#390Dic1311yescharacteristic, complemented
191#388—21no—
192#388—21no—
193#386—21no—
194#386—21no—
195#382Dic1311yescharacteristic, complemented
196C2×#95—132no—
197C2×#95—261no—
198C2×#95—261no—
199#336—261no—
200#328—264no—
201#327—264no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—22no—
207C22×C13—22no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13#39011yescharacteristic
218C22×C13C2×#9911yescharacteristic
219C22×C13#41011yescharacteristic
220C22×C13#41611yescharacteristic
221C22×C13#41611yescharacteristic
222C22×C13C2×#10411yescharacteristic
223C22×C13#42111yescharacteristic
224C22×C13#48812yes—
225C22×C13#49512yes—
226C4×C13—22no—
227C4×C13—22no—
228C4×C13—22no—
229C4×C13—22no—
230C4×C13—41no—
231C4×C13—41no—
232C4×C13—81no—
233C4×C13—81no—
234C4×C13—81no—
235Dic13—84no—
236C22×Q8C2×Dic1311yescharacteristic
237C22×D4—21no—
238C22×D4C2×Dic1311yescharacteristic
239C23×C4—262no—
240C23×C4C22⋊D1311yescharacteristic
241C23×C4C22⋊D1311yescharacteristic
242C23×C4C22×D1311yescharacteristic
243C22×C8—262no—
244#124—42no—
245C22⋊Q8—22no—
246C22⋊Q8—22no—
247#121—22no—
248#121—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4C2×Dic1311yescharacteristic
251C2×C4⋊C4C2×Dic1311yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C42—42no—
259C2×C42C2×Dic1311yescharacteristic
260C2×C42C2×Dic1311yescharacteristic
261C2×C42C22⋊D1311yescharacteristic
262C2×C42C22⋊D1311yescharacteristic
263C22⋊C8—134no—
264C22⋊C8—262no—
265C4×C8—522no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—264no—
271#95—262no—
272#95—262no—
273#95—522no—
274C2×C13—22no—
275C2×C13—22no—
276C2×C13—161no—
277C2×C13#150011yescharacteristic
278C2×C13#150111yescharacteristic
279C2×C13#151611yescharacteristic
280C2×C13#152111yescharacteristic
281C2×C13#195811yescharacteristic
282C2×C13#196411yescharacteristic
283C2×C13#198011yescharacteristic
284C24—21no—
285C24C2×C22⋊D1311yescharacteristic
286C2×Q8—22no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—22no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—42no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—264no—
308C22×C4—522no—
309C22×C4—522no—
310C22×C4—522no—
311C22×C4—522no—
312C22×C4—522no—
313C22×C4—522no—
314C22×C4C22⋊Dic1311yescharacteristic
315C22×C4C22⋊Dic1311yescharacteristic
316C22×C4C22⋊Dic1311yescharacteristic
317C22×C4C22⋊Dic1311yescharacteristic
318C22×C4D4×D1312yes—
319C22×C4#612912yes—
320C22×C4C22×Dic1311yescharacteristic
321C22×C4C2×C22⋊D1311yescharacteristic
322C2×C8—264no—
323C2×C8—522no—
324C2×C8—522no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C42—22no—
336C42—22no—
337C42—41no—
338C42—41no—
339C13#968111yescharacteristic, complemented, Sylow
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23#8819011yescharacteristic
352C23#8819411yescharacteristic
353C23#8820412yes—
354C23#8820412yes—
355C23C2×C22⋊Dic1311yescharacteristic
356Q8—82no—
357D4—82no—
358D4—82no—
359D4—82no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—524no—
388C2×C4—524no—
389C2×C4—524no—
390C2×C4—1042no—
391C2×C4—1042no—
392C2×C4—1042no—
393C2×C4—1042no—
394C2×C4#8807412yes—
395C2×C4#8807712yes—
396C2×C4D4×Dic1312yes—
397C2×C4#8819212yes—
398C8—524no—
399C22—21no—
400C22—21no—
401C22—22no—
402C22—22no—
403C22—21no—
404C22—21no—
405C22—22no—
406C22—22no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22#1171871712yes—
415C22#1171872012yes—
416C22C2×#8807411yescharacteristic
417C22#1171888211yescharacteristic
418C22#1171889411yescharacteristic
419C22#1171889411yescharacteristic
420C22C2×#8807711yescharacteristic
421C22#1171889711yescharacteristic
422C22#1171890111yescharacteristic
423C4—22no—
424C4—22no—
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—81no—
430C4—81no—
431C4—81no—
432C4—1044no—
433C2—22no—
434C2—22no—
435C2—161no—
436C2#1311332211yescharacteristic
437C2#1311332711yescharacteristic
438C2#1311339211yescharacteristic
439C2#1311341311yescharacteristic
440C2#1311564811yescharacteristic
441C2#1311567311yescharacteristic
442C2#1311575611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2850C2
socleC23×C13C2×C22⋊C4
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2850D13
hypocenterC13#9681
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
1. C4×C22⋊#1055C2semidirect
2. C2×#11718130C2semidirect
4. #13113063C2semidirect
6. C2×C13×#124C4semidirect
10. C13×#391C4semidirect
11. C13×#390C4semidirect
16. C13×#382C4semidirect
183. C2×#124Dic13semidirect
189. #391Dic13semidirect
190. #390Dic13semidirect
195. #382Dic13semidirect
339. C13#9681semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#10552
C2×#117181302
C2×#117181292
#131130632
C13×#28502
#968113