Finite Group Databasebeta

← #14795283

Subgroups — #14795283

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#13078438C211yesmaximal, characteristic
2C2×#10622442C211yesmaximal, characteristic, complemented
3C4×#67004C211yesmaximal, characteristic
4#13070061C211yesmaximal, characteristic
5#13070056C211yesmaximal, characteristic
6#13069914C211yesmaximal, characteristic
7#13069914C211yesmaximal, characteristic
8#13069608C211yesmaximal, characteristic, complemented
9#13069401C211yesmaximal, characteristic, complemented
10#13069396C211yesmaximal, characteristic, complemented
11#13069392C211yesmaximal, characteristic, complemented
12#13069271C211yesmaximal, characteristic, complemented
13#13069271C211yesmaximal, characteristic, complemented
14#13068609C211yesmaximal, characteristic, complemented
15C11×#2925C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17C2×#67004C2211yescharacteristic
18C2×#66923C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C11×#433—21no—
21C11×#433—21no—
22C11×#432—21no—
23C11×#431—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#408C2211yescharacteristic
27C11×#408C2211yescharacteristic
28C11×#405C2211yescharacteristic
29C11×#405C2211yescharacteristic
30#10622845C2211yescharacteristic
31#10622845C2211yescharacteristic
32#10622845C2211yescharacteristic
33C2×#66888C2211yescharacteristic
34C2×#66888C2211yescharacteristic
35C2×#66883C2211yescharacteristic
36C2×#66883C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38C2×#66881C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41#10622643—21no—
42C4×#4326—21no—
43#10622635—21no—
44#10622635—21no—
45#10622631—21no—
46C4×#4324—21no—
47#10622622—21no—
48#10622622—21no—
49#10622617C2211yescharacteristic
50#10622608C2211yescharacteristic
51#10622608C2211yescharacteristic
52#10622608C2211yescharacteristic
53#10622537C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622442—21no—
56#10622442—21no—
57#10622442—21no—
58#10622442—21no—
59#10622192C2211yescharacteristic
60#10622192C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622190C2211yescharacteristic
66#10622190C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×Dic22C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×Q8×C11D411yescharacteristic
74C4×Q8×C11D411yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11D411yescharacteristic
78C4×D4×C11D411yescharacteristic
79C11×#117—21no—
80C11×#117C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83#67004—22no—
84#67004—22no—
85C2×#4326—21no—
86C2×#4324—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98#66923—21no—
99#66923—21no—
100#66923—21no—
101#66923—21no—
102C4×Dic22—21no—
103C4×Dic22—21no—
104C4×Dic22—21no—
105C4×Dic22—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8D411yescharacteristic
109C11×C4⋊C8D411yescharacteristic
110C11×C4⋊C8D411yescharacteristic
111C11×C4⋊C8D411yescharacteristic
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C11×C22⋊C8—21no—
116C11×#97—21no—
117C11×#97—21no—
118C4×C8×C11—21no—
119C4×C8×C11—21no—
120#66899—21no—
121#66899—21no—
122#66899—21no—
123#66896—21no—
124#66896—21no—
125#66896—21no—
126#66888—22no—
127#66888—22no—
128#66883—22no—
129#66883—22no—
130#66882—21no—
131#66882—21no—
132#66881—21no—
133#66881—21no—
134#66880—21no—
135#66880—21no—
136#66880—21no—
137#66880—21no—
138#66874—21no—
139#66874—21no—
140#66872—21no—
141#66872—21no—
142#66872—21no—
143#66871—21no—
144#66871—21no—
145#66871—21no—
146C4⋊(C11⋊C8)—21no—
147C4⋊(C11⋊C8)—21no—
148#66867—21no—
149C4×C11⋊C8—21no—
150#24725—111nomaximal, Sylow
151C11×#41—21no—
152C11×#41—21no—
153C11×#41—21no—
154C11×#41—21no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11C2×D411yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22#4112yes—
174C11×M16—21no—
175C11×M16—21no—
176C11×M16—21no—
177C11×M16—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C4⋊C4C2×D411yescharacteristic
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202#4326—24no—
203#4324—24no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210Dic11⋊C4—41no—
211Dic11⋊C4—41no—
212Dic11⋊C4—41no—
213Dic11⋊C4—41no—
214Dic11⋊C4—41no—
215Dic11⋊C4—41no—
216C4×Dic11—41no—
217C4×Dic11—41no—
218#4318—21no—
219#4318—21no—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223#4318—21no—
224#4318—21no—
225#4318#4112yes—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230#3080—111no—
231C2×#479—111no—
232C4×#137—111no—
233#2925D1111yescharacteristic
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×C11—21no—
246C23×C11C2×#4111yescharacteristic
247Q8×C11—21no—
248Q8×C11—21no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11—41no—
252D4×C11—41no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
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
272C2×Dic11—22no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—81no—
279C2×Dic11—81no—
280C2×Dic11—81no—
281Dic22—22no—
282Dic22—22no—
283Dic22—41no—
284Dic22—41no—
285C8×C11—21no—
286C8×C11—21no—
287C8×C11—21no—
288C8×C11—21no—
289C8×C11—41no—
290C8×C11—41no—
291C11⋊C8—22no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C2×#137—111no—
296C2×#125—111no—
297C4×#41C2×D1111yescharacteristic
298C2×C4×Q8—111no—
299#479—221no—
300#479—221no—
301#479—221no—
302#479—221no—
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—21no—
312#433—21no—
313#432—21no—
314#431—21no—
315C2×#108—111no—
316C2×#108—111no—
317#428—111no—
318#428—111no—
319#428—111no—
320C2×#107—111no—
321C2×#106—111no—
322#423—111no—
323#423C2×D1111yescharacteristic
324C2×C4⋊C8C2×D1111yescharacteristic
325#419—111no—
326#417—111no—
327#417—111no—
328#417—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#101—111no—
332C2×#101—111no—
333#408C2×D1111yescharacteristic
334#408C2×D1111yescharacteristic
335#405C2×D1111yescharacteristic
336#405C2×D1111yescharacteristic
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×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11C2×#12111yescharacteristic
352C22×C11#55211yescharacteristic
353C22×C11#55611yescharacteristic
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11#52511yescharacteristic
362C4×C11#53611yescharacteristic
363C4×C11#54711yescharacteristic
364C4×C11#54811yescharacteristic
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C2×#41C22×D1111yescharacteristic
370C22×Q8—111no—
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×M16C22×D1111yescharacteristic
380C2×M16C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383#125—221no—
384#125—221no—
385#125—221no—
386#125—221no—
387C4×Q8—221no—
388C4×Q8—221no—
389C4×Q8—221no—
390C4×Q8—221no—
391C4×Q8D4411yescharacteristic
392C4×Q8D4411yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4D4411yescharacteristic
396C4×D4D4411yescharacteristic
397#117—21no—
398#117C22×D1111yescharacteristic
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C42—21no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408#108—222no—
409#108—222no—
410#107—221no—
411#107—221no—
412#107—221no—
413#107—221no—
414#107—221no—
415#106—221no—
416#106—221no—
417#106—221no—
418#106—221no—
419#106—221no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—221no—
423C4⋊C8—221no—
424C4⋊C8C22⋊D1111yescharacteristic
425C4⋊C8C22⋊D1111yescharacteristic
426C4⋊C8C22⋊D1111yescharacteristic
427C4⋊C8C22⋊D1111yescharacteristic
428#103—221no—
429#103—221no—
430#103—221no—
431#103—221no—
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—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446#97—21no—
447#97—21no—
448#97—221no—
449C4×C8—21no—
450C4×C8—21no—
451C4×C8—221no—
452C2×C11—21no—
453C2×C11—21no—
454C2×C11—81no—
455C2×C11#241511yescharacteristic
456C2×C11#306711yescharacteristic
457C2×C11#306911yescharacteristic
458#41—21no—
459#41—21no—
460#41—21no—
461#41—21no—
462C2×Q8—112no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8C2×D4411yescharacteristic
469C2×D4—21no—
470C2×D4C2×D4411yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4#433911yescharacteristic
479C22×C4#433911yescharacteristic
480C22×C4C23×D1111yescharacteristic
481Q16—224no—
482SD16—224no—
483M16—21no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—112no—
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—21no—
500C2×C8—21no—
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—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—441no—
518C4⋊C4—441no—
519C4⋊C4—441no—
520C4⋊C4—441no—
521C4⋊C4—441no—
522C4⋊C4—441no—
523C4⋊C4C2×D4411yescharacteristic
524C4⋊C4C2×D4411yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—441no—
532C42—441no—
533C42C2×D4411yescharacteristic
534C42C2×D4411yescharacteristic
535C42C2×C22⋊D1111yescharacteristic
536C42C2×C22⋊D1111yescharacteristic
537C11#2472511yescharacteristic, complemented, Sylow
538C23—21no—
539C23C2×#433911yescharacteristic
540Q8—21no—
541Q8—21no—
542Q8—222no—
543Q8—222no—
544Q8—441no—
545Q8—441no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—81no—
559C2×C4—222no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—881no—
566C2×C4—881no—
567C2×C4—881no—
568C2×C4#6698311yescharacteristic
569C2×C4#6698311yescharacteristic
570C2×C4#6698311yescharacteristic
571C2×C4#6698311yescharacteristic
572C2×C4C22×D4411yescharacteristic
573C2×C4#41×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#6704311yescharacteristic
576C2×C4#6704311yescharacteristic
577C2×C4C22×C22⋊D1111yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—222no—
585C8—441no—
586C8—441no—
587C8—441no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1062306011yescharacteristic
594C22#1062306411yescharacteristic
595C22C2×#6698311yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—442no—
604C4—881no—
605C4—881no—
606C4—881no—
607C4#1062305511yescharacteristic
608C4#1062305711yescharacteristic
609C4#1062335511yescharacteristic
610C4#1062336211yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2#1307203911yescharacteristic
615C2#1307833611yescharacteristic
616C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2925C2
socleC22×C11C2×#121
prime radicalC2×C11×#41C23
hypercenter#2925D11
hypocenterC11#24725
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. C2×#10622442C2semidirect
8. #13069608C2semidirect
9. #13069401C2semidirect
10. #13069396C2semidirect
11. #13069392C2semidirect
12. #13069271C2semidirect
13. #13069271C2semidirect
14. #13068609C2semidirect
537. C11#24725semidirect

Maximal subgroups

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

subgroupindex
#130784382
C2×#106224422
C4×#670042
#130700612
#130700562
#130699142
#130696082
#130694012
#130693962
#130693922
#130692712
#130686092
C11×#29252
#2472511