Finite Group Databasebeta

← #14795285

Subgroups — #14795285

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078434C211yesmaximal, characteristic
2C4×#66995C211yesmaximal, characteristic
3#13077281C211yesmaximal, characteristic
4#13070062C211yesmaximal, characteristic
5#13070057C211yesmaximal, characteristic
6#13069916C211yesmaximal, characteristic
7#13069916C211yesmaximal, characteristic
8#13069610C211yesmaximal, characteristic, complemented
9#13069399C211yesmaximal, characteristic, complemented
10#13069394C211yesmaximal, characteristic, complemented
11#13069392C211yesmaximal, characteristic, complemented
12#13069268C211yesmaximal, characteristic, complemented
13#13069268C211yesmaximal, characteristic, complemented
14#13068612C211yesmaximal, characteristic, complemented
15C2×C11×#479C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66995C2211yescharacteristic
19C4×#4339C2211yescharacteristic
20C11×#479—21no—
21C11×#479—21no—
22C11×#479—21no—
23C11×#479—21no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×#66900C2211yescharacteristic
30C2×#66900C2211yescharacteristic
31#10622838C2211yescharacteristic
32#10622723C2211yescharacteristic
33#10622723C2211yescharacteristic
34C2×#66883C2211yescharacteristic
35C2×#66883C2211yescharacteristic
36#10622714C2211yescharacteristic
37#10622714C2211yescharacteristic
38#10622679—21no—
39#10622679—21no—
40#10622676—21no—
41#10622676—21no—
42#10622643—21no—
43C4×#4326—21no—
44#10622639—21no—
45C4×#4325—21no—
46#10622579C2211yescharacteristic
47#10622579C2211yescharacteristic
48#10622579C2211yescharacteristic
49#10622577C2211yescharacteristic
50#10622577C2211yescharacteristic
51#10622577C2211yescharacteristic
52#10622537C2211yescharacteristic
53#10622537C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622453—21no—
56#10622453—21no—
57#10622448—21no—
58#10622446—21no—
59#10622190C2211yescharacteristic
60#10622190C2211yescharacteristic
61#10622168C2211yescharacteristic
62#10622168C2211yescharacteristic
63#10622168C2211yescharacteristic
64#10622168C2211yescharacteristic
65#10622168C2211yescharacteristic
66#10622168C2211yescharacteristic
67C22×Q8×C11C2311yescharacteristic
68C2×#4339C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#125—21no—
72C11×#125—21no—
73C11×#125—21no—
74C11×#125—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×#4326—21no—
88#66995—22no—
89#66995—22no—
90C2×#4325—21no—
91C4×C22⋊D11—21no—
92C4×C22⋊D11—21no—
93#66979C2311yescharacteristic
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C2×#4318C2311yescharacteristic
100C4×D44D411yescharacteristic
101C4×D44D411yescharacteristic
102#66925—21no—
103C42×D11—21no—
104C4×Dic22D411yescharacteristic
105C4×Dic22D411yescharacteristic
106C11×#107—21no—
107C11×#107—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×C4⋊C8D411yescharacteristic
111C11×C4⋊C8D411yescharacteristic
112C11×C4⋊C8D411yescharacteristic
113C11×C4⋊C8D411yescharacteristic
114C11×#103—21no—
115C11×#103—21no—
116C11×#103—21no—
117C11×#103—21no—
118#66900—22no—
119#66900—22no—
120#66899—21no—
121#66899—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126#66883—22no—
127#66883—22no—
128#66879—21no—
129#66879—21no—
130C8×Dic11—21no—
131C8×Dic11—21no—
132#66874—21no—
133#66874—21no—
134#66874—21no—
135#66873—21no—
136#66873—21no—
137#66873—21no—
138#66872—21no—
139#66872—21no—
140#66872—21no—
141#66871—21no—
142#66871—21no—
143#66871—21no—
144C4⋊(C11⋊C8)—21no—
145C4⋊(C11⋊C8)—21no—
146C4⋊(C11⋊C8)—21no—
147C4⋊(C11⋊C8)—21no—
148#66867—21no—
149C4×C11⋊C8—21no—
150#24725—111nomaximal, Sylow
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11#4112yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—21no—
165#4339—21no—
166#4339—21no—
167#4339—21no—
168#4339—21no—
169C2×D44C2×D411yescharacteristic
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×Dic22C2×D411yescharacteristic
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C42×C11—41no—
195C42×C11—41no—
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C22⋊Dic11—21no—
201#4326—24no—
202#4325—24no—
203(C2×D11)⋊C4—21no—
204(C2×D11)⋊C4—21no—
205C4⋊Dic11C2×D411yescharacteristic
206C4⋊Dic11C2×D411yescharacteristic
207Dic11⋊C4—21no—
208Dic11⋊C4—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318—21no—
218#4318—21no—
219#4318—21no—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223#4318#4112yes—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230#3080—111no—
231C2×#479D1111yescharacteristic, complemented
232C4×#137—111no—
233#2925—111no—
234#2079—111no—
235#2078—111no—
236#2052—111no—
237#2052—111no—
238#1998—111no—
239#1952—111no—
240#1951—111no—
241#1950—111no—
242#1930—111no—
243#1930—111no—
244#1801—111no—
245C23×C11C2×#4111yescharacteristic
246C22×D11—21no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—41no—
250Q8×C11—41no—
251C2×C4×C11—22no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—81no—
260C2×C4×C11—81no—
261C2×C4×C11—81no—
262C2×C4×C11#12111yescharacteristic
263C2×C4×C11#12111yescharacteristic
264C2×C4×C11#12111yescharacteristic
265C2×C4×C11#12111yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C22⋊D11—41no—
273C22⋊D11—41no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277D44—21no—
278D44—21no—
279C4×D11—42no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—81no—
283Dic22—21no—
284Dic22—21no—
285C8×C11—21no—
286C8×C11—21no—
287C8×C11—21no—
288C8×C11—21no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C2×#137—111no—
296C2×#125C2×D1111yescharacteristic
297C4×#41—111no—
298C2×C4×Q8C2×D1111yescharacteristic
299#479—21no—
300#479—21no—
301#479—21no—
302#479—21no—
303#479—221no—
304#479—221no—
305#478—221no—
306#478—221no—
307#441—221no—
308#440—221no—
309C4×Q16—221no—
310C4×SD16—221no—
311#433—221no—
312#433—221no—
313#432—221no—
314#431—221no—
315C2×#108—111no—
316C2×#108—111no—
317#428—111no—
318#428—111no—
319#428—111no—
320C2×#107C2×D1111yescharacteristic
321C2×#106C2×D1111yescharacteristic
322#423—111no—
323#423—111no—
324C2×C4⋊C8C2×D1111yescharacteristic
325#419—111no—
326#417—111no—
327#417—111no—
328#417—111no—
329C2×#103C2×D1111yescharacteristic
330C2×#103C2×D1111yescharacteristic
331C2×#101—111no—
332C2×#101—111no—
333#408—111no—
334#408—111no—
335#405—111no—
336#405—111no—
337C4×M16—111no—
338#343—111no—
339#343—111no—
340#343—111no—
341#343—111no—
342#343—111no—
343#343—111no—
344#341—111no—
345#341—111no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11C2×#12111yescharacteristic
349C22×C11#55211yescharacteristic
350C22×C11#55611yescharacteristic
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—42no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11#52511yescharacteristic
363C4×C11#53611yescharacteristic
364C4×C11#54711yescharacteristic
365C4×C11#54811yescharacteristic
366Dic11—41no—
367Dic11—41no—
368Dic11—41no—
369C2×#41—111no—
370C22×Q8C22×D1111yescharacteristic
371#137—222no—
372#137—222no—
373C2×Q16—221no—
374C2×SD16—221no—
375C2×M16—111no—
376C2×M16—111no—
377C2×M16—111no—
378C2×M16—111no—
379C2×M16—111no—
380C2×M16—111no—
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383#125—21no—
384#125—21no—
385#125—21no—
386#125—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—111no—
392C4×Q8—111no—
393C4×D4—111no—
394C4×D4—111no—
395C4×D4—221no—
396C4×D4—221no—
397#117—111no—
398#117—221no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C42—21no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408#108—222no—
409#108—222no—
410#107—21no—
411#107—21no—
412#107—221no—
413#107—221no—
414#107—221no—
415#106—21no—
416#106—21no—
417#106—221no—
418#106—221no—
419#106—221no—
420C4⋊C8—221no—
421C4⋊C8—221no—
422C4⋊C8—221no—
423C4⋊C8—221no—
424C4⋊C8C22⋊D1111yescharacteristic
425C4⋊C8C22⋊D1111yescharacteristic
426C4⋊C8C22⋊D1111yescharacteristic
427C4⋊C8C22⋊D1111yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103—221no—
433#103—221no—
434#103—221no—
435#103—221no—
436#103—221no—
437#102—221no—
438#102—221no—
439#102—221no—
440#101—222no—
441#101—222no—
442C22⋊C8—221no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445C22⋊C8—221no—
446#97—221no—
447#97—221no—
448#97—221no—
449C4×C8—221no—
450C4×C8—221no—
451C4×C8—221no—
452C2×C11—21no—
453C2×C11—21no—
454C2×C11#241511yescharacteristic
455C2×C11#306711yescharacteristic
456C2×C11#306911yescharacteristic
457D11—81no—
458#41—221no—
459#41—221no—
460#41—221no—
461#41—221no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—111no—
468C2×Q8#434312yes—
469C2×D4—111no—
470C2×D4—221no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4#434111yescharacteristic
479C22×C4#434111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481Q16—224no—
482SD16—224no—
483M16—112no—
484M16—221no—
485M16—221no—
486M16—221no—
487M16—221no—
488M16—221no—
489M16—221no—
490M16—221no—
491M16—221no—
492M16—221no—
493M16—221no—
494M16—221no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8C2×C22⋊D1111yescharacteristic
506C2×C8C2×C22⋊D1111yescharacteristic
507C2×C8C2×C22⋊D1111yescharacteristic
508C2×C8C2×C22⋊D1111yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—111no—
522C4⋊C4—111no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C22⋊C4—221no—
526C22⋊C4—221no—
527C22⋊C4—221no—
528C42—41no—
529C42—41no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42D4×D1111yescharacteristic
534C42D4×D1111yescharacteristic
535C42C2×C22⋊D1111yescharacteristic
536C42C2×C22⋊D1111yescharacteristic
537C11#2472511yescharacteristic, complemented, Sylow
538C23—221no—
539C23C2×#434111yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—41no—
543Q8—41no—
544Q8—221no—
545Q8—221no—
546D4—221no—
547D4—221no—
548D4—441no—
549D4—441no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—442no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—881no—
568C2×C4#6699111yescharacteristic
569C2×C4#6699111yescharacteristic
570C2×C4#6699111yescharacteristic
571C2×C4#6699111yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×#434311yescharacteristic
574C2×C4#6704011yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C2×C4#6704311yescharacteristic
577C2×C4C22×C22⋊D1111yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—222no—
583C8—441no—
584C8—441no—
585C8—441no—
586C8—441no—
587C8—441no—
588C22—21no—
589C22—21no—
590C22—441no—
591C22—441no—
592C22—441no—
593C22#1062317211yescharacteristic
594C22#1062317311yescharacteristic
595C22C2×#6699111yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—441no—
605C4—441no—
606C4—441no—
607C4#1062315811yescharacteristic
608C4#1062315911yescharacteristic
609C4#1062334811yescharacteristic
610C4#1062335511yescharacteristic
611C2—21no—
612C2—21no—
613C2—881no—
614C2#1307204111yescharacteristic
615C2#1307833211yescharacteristic
616C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#479C2
socleC22×C11C2×#121
prime radicalC2×#4339C23
hypercenterC2×#479D11
hypocenterC11#24725
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
8. #13069610C2semidirect
9. #13069399C2semidirect
10. #13069394C2semidirect
11. #13069392C2semidirect
12. #13069268C2semidirect
13. #13069268C2semidirect
14. #13068612C2semidirect
15. C2×C11×#479C2semidirect
231. C2×#479D11semidirect
537. C11#24725semidirect

Maximal subgroups

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

subgroupindex
#130784342
C4×#669952
#130772812
#130700622
#130700572
#130699162
#130696102
#130693992
#130693942
#130693922
#130692682
#130686122
C2×C11×#4792
#2472511