Finite Group Databasebeta

← #14725218

Subgroups — #14725218

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077636C211yesmaximal, characteristic, complemented
2#13077628C211yesmaximal, characteristic, complemented
3C4×#67003C211yesmaximal, characteristic
4#13067509C212yesmaximal, complemented
5#13067463C212yesmaximal, complemented
6#13067448C212yesmaximal, complemented
7#13067413C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067051C211yesmaximal, characteristic, complemented
10#13066897C211yesmaximal, characteristic, complemented
11C11×#1488C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003C411yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C11×#431C2211yescharacteristic
17#10622846C411yescharacteristic
18C4×#4326C411yescharacteristic
19C4×#4326C2211yescharacteristic
20C4×#4325C411yescharacteristic
21C4×#4325C2211yescharacteristic
22Q8×C11⋊C8C2212yes—
23C4×#4324C411yescharacteristic
24C4×#4324C2211yescharacteristic
25C4×#4323C411yescharacteristic
26C4×#4323C2211yescharacteristic
27#10622625—22no—
28#10622625C2212yes—
29#10622615C411yescharacteristic
30#10622611C411yescharacteristic
31#10622539—21no—
32#10622539C2211yescharacteristic
33C4×#4318—21no—
34C4×#4318C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622447C2212yes—
37#10622444C2212yes—
38#10622341—22no—
39#10622318—21no—
40D11×#97—21no—
41C11×Q8⋊C8C2212yes—
42C11×D4⋊C8C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45#10622097C2212yes—
46#10622094C2212yes—
47#10622092C2212yes—
48C8×C11⋊C8C2212yes—
49C2×C11×#41C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C4×Q8×C11C2×C411yescharacteristic
52C4×Q8×C11C2311yescharacteristic
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11C2×C411yescharacteristic
56C4×D4×C11C2311yescharacteristic
57C11×#117—21no—
58C11×#117C2×C411yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61#67003—24no—
62C2×#4326C2×C411yescharacteristic
63C2×#4325C2×C411yescharacteristic
64C2×#4324C2×C411yescharacteristic
65C2×#4323C2×C411yescharacteristic
66C4×C22⋊D11—21no—
67C4×C22⋊D11—21no—
68#66979C2×C411yescharacteristic
69C2×#4318—22no—
70C2×#4318D412yes—
71C22×C11⋊C8C2×C411yescharacteristic
72C22×C11⋊C8C2×C411yescharacteristic
73C2×C8×D11—22no—
74C4×D44C2×C411yescharacteristic
75C4×D44C2311yescharacteristic
76#66925—21no—
77C42×D11—21no—
78C4×Dic22C2×C411yescharacteristic
79C4×Dic22C2311yescharacteristic
80C11×C4⋊C8—21no—
81C11×C4⋊C8C2312yes—
82C11×C22⋊C8—21no—
83C11×C22⋊C8—21no—
84C11×#97—21no—
85C4×C8×C11C2312yes—
86#66899C2×C411yescharacteristic
87#66899C2×C411yescharacteristic
88#66896C2×C411yescharacteristic
89#66896C2×C411yescharacteristic
90C22⋊(C11⋊C8)—21no—
91C22⋊(C11⋊C8)—22no—
92(C2×D11)⋊C8—22no—
93#66879—22no—
94Dic11⋊C8—22no—
95#66874C2×C411yescharacteristic
96#66874C2×C411yescharacteristic
97#66873C2×C411yescharacteristic
98#66873C2×C411yescharacteristic
99#66872C2×C411yescharacteristic
100#66872C2×C411yescharacteristic
101#66871C2×C411yescharacteristic
102#66871C2×C411yescharacteristic
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)C2312yes—
105#66867—21no—
106#66867D411yescharacteristic
107#66867D411yescharacteristic
108C4×C11⋊C8—22no—
109C4×C11⋊C8C2×C411yescharacteristic
110C4×C11⋊C8C2×C411yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2312yes—
114#18037—111nomaximal, Sylow
115C11×#41—22no—
116C11×#41—41no—
117C2×Q8×C11C22×C411yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11C22×C411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—21no—
127#4339—22no—
128#4339—41no—
129C2×D44C22×C411yescharacteristic
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×Dic22C22×C411yescharacteristic
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4C22×C411yescharacteristic
139C11×C4⋊C4C22×C411yescharacteristic
140C11×C22⋊C4—21no—
141C11×C22⋊C4—21no—
142C11×C22⋊C4—21no—
143C42×C11—21no—
144C42×C11—21no—
145C42×C11—21no—
146C42×C11C22×C411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11#4111yescharacteristic
149C42×C11C2411yescharacteristic
150C22⋊Dic11—21no—
151#4326—22no—
152#4325M1614yescomplemented
153#4324—22no—
154#4323—22no—
155(C2×D11)⋊C4—21no—
156(C2×D11)⋊C4—21no—
157C4⋊Dic11C22×C411yescharacteristic
158C4⋊Dic11C22×C411yescharacteristic
159Dic11⋊C4—21no—
160Dic11⋊C4—21no—
161C4×Dic11—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164#4318—24no—
165#4318—44no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—41no—
169C2×C11⋊C8C22×C411yescharacteristic
170C2×C11⋊C8C22×C411yescharacteristic
171C2×C11⋊C8C22×C411yescharacteristic
172C2×C11⋊C8C22×C411yescharacteristic
173C2×C11⋊C8C2×D412yes—
174C2×C11⋊C8C2×D412yes—
175C8×D11—44no—
176#2971—111no—
177#2970—111no—
178C4×#135—111no—
179#1590—112no—
180#1584—112no—
181#1581—112no—
182C8×SD16—112no—
183#1568—111no—
184#1488—111no—
185#1488D1111yescharacteristic, complemented
186C8×M16—111no—
187C23×C11—21no—
188C23×C11C4×D411yescharacteristic
189C22×D11—21no—
190Q8×C11—21no—
191Q8×C11C2×M1612yes—
192D4×C11—21no—
193D4×C11—21no—
194D4×C11—42no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—81no—
205C2×C4×C11C4×D411yescharacteristic
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C22⋊D11—42no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215D44—21no—
216D44C2×M1612yes—
217C4×D11—42no—
218C4×D11—42no—
219C4×D11—81no—
220Dic22—21no—
221Dic22—21no—
222C8×C11—42no—
223C8×C11—42no—
224C11⋊C8—21no—
225C11⋊C8—21no—
226C11⋊C8—21no—
227C11⋊C8—22no—
228C11⋊C8—42no—
229C11⋊C8C2×M1612yes—
230C11⋊C8#13514yescomplemented
231C2×#135—111no—
232C4×#41—111no—
233C4×#41C2×D1111yescharacteristic
234#446—112no—
235C8×Q8—112no—
236C4×Q16—111no—
237C4×Q16—111no—
238C4×SD16—111no—
239C4×SD16—111no—
240C4×SD16—111no—
241C4×SD16—111no—
242C4×D8—111no—
243C4×D8—111no—
244#436—112no—
245#436—222no—
246#435—222no—
247C8×D4—112no—
248#432—111no—
249#432—221no—
250#432—221no—
251#432C2×D1111yescharacteristic
252#431C2×D1111yescharacteristic
253#427—111no—
254#416—111no—
255#416—111no—
256C4×M16—111no—
257C4×M16—221no—
258C2×#97—221no—
259C2×C4×C8—111no—
260#335—112no—
261#334—112no—
262Q8⋊C8—112no—
263Q8⋊C8C2×D1112yes—
264D4⋊C8—112no—
265D4⋊C8C2×D1112yes—
266#322—112no—
267C82—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11C2×C4×D411yescharacteristic
275C2×D11—22no—
276C2×D11—41no—
277C2×D11—41no—
278C4×C11—21no—
279C4×C11—22no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11C22×M1611yescharacteristic
286C4×C11#56811yescharacteristic
287C4×C11C2×#13512yes—
288Dic11—41no—
289Dic11—41no—
290Dic11—41no—
291C2×#41—111no—
292C2×#41C4×D1111yescharacteristic
293#135—224no—
294C2×Q16—111no—
295C2×SD16—111no—
296C2×SD16—111no—
297C2×D8—111no—
298C2×M16—112no—
299C2×M16—222no—
300C22×C8—111no—
301C22×C8—111no—
302C22×C8—222no—
303C4×Q8—111no—
304C4×Q8—111no—
305C4×Q8C4×D1111yescharacteristic
306C4×Q8C22×D1111yescharacteristic
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—111no—
310C4×D4—111no—
311C4×D4—221no—
312C4×D4—221no—
313C4×D4C4×D1111yescharacteristic
314C4×D4C22×D1111yescharacteristic
315#117—21no—
316#117—111no—
317#117—221no—
318#117C4×D1111yescharacteristic
319C2×C42—21no—
320C2×C42—221no—
321C2×C42C22×D1111yescharacteristic
322#107—111no—
323#107—111no—
324#106—111no—
325#106—111no—
326C4⋊C8—21no—
327C4⋊C8—112no—
328C4⋊C8—222no—
329C4⋊C8—222no—
330C4⋊C8C22×D1112yes—
331#103—111no—
332#103—111no—
333#103—111no—
334#103—111no—
335#102—111no—
336#102—111no—
337#102—111no—
338#102—111no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—222no—
342C22⋊C8—222no—
343C22⋊C8—221no—
344#97—21no—
345#97—111no—
346#97—111no—
347#97—222no—
348#97—221no—
349C4×C8—111no—
350C4×C8—111no—
351C4×C8—111no—
352C4×C8—112no—
353C4×C8—111no—
354C4×C8—222no—
355C4×C8C22×D1112yes—
356C2×C11—41no—
357C2×C11—81no—
358C2×C11D4×M1611yescharacteristic
359C2×C11C4×#13511yescharacteristic
360C2×C11#295711yescharacteristic
361D11—42no—
362#41—22no—
363#41—41no—
364#41—222no—
365#41—441no—
366C2×Q8—111no—
367C2×Q8C2×C4×D1111yescharacteristic
368C2×D4—21no—
369C2×D4—111no—
370C2×D4—221no—
371C2×D4C2×C4×D1111yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4C2×C4×D1111yescharacteristic
379C22×C4D4×D1111yescharacteristic
380C22×C4#434111yescharacteristic
381Q16—222no—
382SD16—114no—
383SD16—222no—
384D8—222no—
385M16—224no—
386M16—444no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—111no—
390C2×C8—112no—
391C2×C8—111no—
392C2×C8—111no—
393C2×C8—111no—
394C2×C8—112no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—444no—
398C2×C8—441no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—111no—
402C4⋊C4—111no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4C2×C4×D1111yescharacteristic
406C4⋊C4C2×C4×D1111yescharacteristic
407C22⋊C4—21no—
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—221no—
411C22⋊C4—221no—
412C22⋊C4—221no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—221no—
417C42—221no—
418C42—221no—
419C42C2×C4×D1111yescharacteristic
420C42D4×D1111yescharacteristic
421C42#434111yescharacteristic
422C42C23×D1111yescharacteristic
423C11#1803711yescharacteristic, complemented, Sylow
424C23—21no—
425C23—221no—
426C23(C22⋊D11)⋊C411yescharacteristic
427Q8—21no—
428Q8—221no—
429Q8—221no—
430Q8M16×D1112yes—
431D4—21no—
432D4—21no—
433D4—42no—
434D4—112no—
435D4—221no—
436D4—442no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—881no—
453C2×C4(C22⋊D11)⋊C411yescharacteristic
454C2×C4(C22⋊D11)⋊C411yescharacteristic
455C2×C4(C22⋊D11)⋊C411yescharacteristic
456C2×C4C22×C4×D1111yescharacteristic
457C2×C4C2×D4×D1111yescharacteristic
458C2×C4C2×#434111yescharacteristic
459C8—42no—
460C8—42no—
461C8—112no—
462C8—114no—
463C8—221no—
464C8—221no—
465C8—221no—
466C8—222no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—222no—
475C22—441no—
476C22—441no—
477C22C2×(C22⋊D11)⋊C411yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—22no—
482C4—21no—
483C4—41no—
484C4—41no—
485C4—441no—
486C4—441no—
487C4—441no—
488C4C2×M16×D1111yescharacteristic
489C4#1062327611yescharacteristic
490C4D11×#13512yes—
491C2—41no—
492C2—81no—
493C2—442no—
494C2#1307734811yescharacteristic
495C2#1307738411yescharacteristic
496C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1488C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C4
cosocleC42×C11C24
hypercenter#1488D11
hypocenterC11#18037
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
1. #13077636C2semidirect
2. #13077628C2semidirect
4. #13067509C2semidirect
5. #13067463C2semidirect
6. #13067448C2semidirect
7. #13067413C2semidirect
8. #13067377C2semidirect
9. #13067051C2semidirect
10. #13066897C2semidirect
11. C11×#1488C2semidirect
152. #4325M16semidirect
185. #1488D11semidirect
230. C11⋊C8#135semidirect
423. C11#18037semidirect

Maximal subgroups

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

subgroupindex
#130776362
#130776282
C4×#670032
#130675092
#130674632
#130674482
#130674132
#130673772
#130670512
#130668972
C11×#14882
#1803711