Finite Group Databasebeta

← #14737517

Subgroups — #14737517

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079947C211yesmaximal, characteristic, complemented
2#13079592C211yesmaximal, characteristic
3#13077620C211yesmaximal, characteristic, complemented
4#13068181C211yesmaximal, characteristic, complemented
5#13068167C211yesmaximal, characteristic, complemented
6#13068126C211yesmaximal, characteristic, complemented
7#13068078C211yesmaximal, characteristic, complemented
8#13068050C211yesmaximal, characteristic, complemented
9#13068036C211yesmaximal, characteristic, complemented
10#13068007C211yesmaximal, characteristic, complemented
11#13067961C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067281C211yesmaximal, characteristic, complemented
14#13067265C211yesmaximal, characteristic, complemented
15C11×#3182C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#468—21no—
24C11×#468—21no—
25C11×#440—21no—
26C11×#440—21no—
27C4×C11×M16C2211yescharacteristic
28#10622852—21no—
29#10622851—21no—
30#10622741—21no—
31#10622740—21no—
32#10622707C2211yescharacteristic
33#10622703C2211yescharacteristic
34#10622703C2211yescharacteristic
35#10622700C2211yescharacteristic
36#10622696C2211yescharacteristic
37#10622696C2211yescharacteristic
38#10622688C2211yescharacteristic
39#10622685C2211yescharacteristic
40#10622672—21no—
41#10622669—21no—
42#10622664—21no—
43#10622661—21no—
44#10622641—21no—
45#10622635—21no—
46#10622538C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622322—21no—
50#10622321—21no—
51#10622301C2211yescharacteristic
52C8×D44C2211yescharacteristic
53#10622292C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622185C2211yescharacteristic
60#10622185C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#127C2311yescharacteristic
76C11×#125—21no—
77C11×#124—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×#121—21no—
81C11×#121—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C11×#117—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4326—21no—
89C2×#4326—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4324—21no—
93C2×#4323—21no—
94#66983D411yescharacteristic
95#66982—21no—
96C4×C22⋊D11—21no—
97#66977D411yescharacteristic
98C22×C11⋊C8—21no—
99C2×#4313—21no—
100C2×C8×D11—21no—
101#66929—21no—
102#66928D411yescharacteristic
103C4×D44C2311yescharacteristic
104#66925—21no—
105#66923D411yescharacteristic
106C4×Dic22C2311yescharacteristic
107C11×#107—21no—
108C11×#107—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×#97D411yescharacteristic
114C11×#97D411yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66899—21no—
121#66896—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127#66879—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130C8×Dic11—21no—
131#66874—21no—
132#66873—21no—
133#66872—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8—21no—
144#19252—111nomaximal, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×C22⋊D11—21no—
159C2×D44C2×D411yescharacteristic
160C2×C4×D11—21no—
161C2×Dic22C2×D411yescharacteristic
162C11×SD16—42no—
163C11×SD16—42no—
164C11×M16—22no—
165C11×M16—41no—
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—41no—
180C11×C22⋊C4—41no—
181C42×C11—41no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186C22⋊Dic11—21no—
187#4326—81no—
188#4326—81no—
189#4325—81no—
190#4325—81no—
191#4324—81no—
192#4323—81no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197C4⋊Dic11C2×D411yescharacteristic
198C4⋊Dic11C2×D411yescharacteristic
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201Dic11⋊C4—21no—
202Dic11⋊C4—21no—
203C4×Dic11—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—81no—
211#4313—42no—
212C8×D11—42no—
213#3248—111no—
214#3212—111no—
215#3182D1111yescharacteristic, complemented
216#2969—111no—
217#1702—111no—
218#1700—111no—
219#1693—111no—
220#1685—111no—
221#1681—111no—
222#1679—111no—
223#1674—111no—
224#1666—111no—
225#1565—111no—
226#1544—111no—
227#1540—111no—
228C23×C11—41no—
229C23×C11#12111yescharacteristic
230C22×D11—21no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—81no—
242D4×C11—82no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—82no—
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C22⋊D11—81no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262D44—21no—
263D44—21no—
264C4×D11—41no—
265C4×D11—41no—
266Dic22—21no—
267Dic22—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11#13512yes—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278#533C2×D1111yescharacteristic
279#532C2×D1111yescharacteristic
280#529—111no—
281#500C2×D1111yescharacteristic
282#495—221no—
283#492C2×D1111yescharacteristic
284#488—221no—
285#487C2×D1111yescharacteristic
286#486C2×D1111yescharacteristic
287#479—221no—
288#475—111no—
289#474—111no—
290#468—21no—
291#468—21no—
292#467—221no—
293#465—221no—
294#464—221no—
295#462—111no—
296#462—111no—
297#461—111no—
298#461—111no—
299#460—111no—
300#459—111no—
301#452—221no—
302#449—221no—
303#446—111no—
304C8×Q8—111no—
305#440—21no—
306#440—21no—
307#436—111no—
308#436—221no—
309#435—221no—
310C8×D4—111no—
311#433—221no—
312#431—111no—
313#431—111no—
314C2×C4⋊C8—111no—
315#405—221no—
316C4×M16C2×D1111yescharacteristic
317#335—111no—
318#335—111no—
319#334—111no—
320#334—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#331—111no—
328#331—111no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11C2×#12111yescharacteristic
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11C2×#13511yescharacteristic
347C4×C11#57511yescharacteristic
348C4×C11#57611yescharacteristic
349C4×C11#57711yescharacteristic
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353C2×#41—21no—
354C2×Q16—221no—
355C2×Q16—221no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—221no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×D8—221no—
362C2×M16—221no—
363C2×M16C22⋊D1111yescharacteristic
364C2×M16C22⋊D1111yescharacteristic
365C22×C8—221no—
366C22×C8—221no—
367C4⋊Q8C22×D1111yescharacteristic
368C4⋊Q8C22×D1111yescharacteristic
369C4⋊Q8C22×D1111yescharacteristic
370#127C22×D1111yescharacteristic
371#126—221no—
372#125—21no—
373#125—111no—
374#124—21no—
375#124—111no—
376#123—221no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—111no—
380#121—21no—
381#121—21no—
382#121—111no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—111no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—111no—
389C4×D4—221no—
390#117—21no—
391#117—221no—
392C2×C42C22×D1111yescharacteristic
393#107—21no—
394#107—21no—
395#107—221no—
396#106—221no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406#103—21no—
407#103—21no—
408#103—221no—
409#103—221no—
410#103—221no—
411#103—221no—
412#103—221no—
413#102—21no—
414#102—21no—
415#102—221no—
416#102—221no—
417#102—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422#97—221no—
423#97C22⋊D1111yescharacteristic
424#97C22⋊D1111yescharacteristic
425C4×C8—221no—
426C4×C8—221no—
427C4×C8—221no—
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C2×C11—41no—
431C2×C11—161no—
432C2×C11#303511yescharacteristic
433C2×C11#306211yescharacteristic
434C2×C11#306911yescharacteristic
435D11—81no—
436#41—81no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—111no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—111no—
447C2×D4—221no—
448C22×C4—41no—
449C22×C4—221no—
450C22×C4D4×D1111yescharacteristic
451C22×C4#434111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453Q16—881no—
454Q16—881no—
455SD16—42no—
456SD16—42no—
457SD16—881no—
458SD16—881no—
459SD16—881no—
460D8—881no—
461M16—22no—
462M16—41no—
463M16—442no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—442no—
471C2×C8—881no—
472C2×C8C2×C22⋊D1111yescharacteristic
473C2×C8C2×C22⋊D1111yescharacteristic
474C2×C8C2×C22⋊D1111yescharacteristic
475C2×C8C2×C22⋊D1111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—111no—
485C4⋊C4—111no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—221no—
494C22⋊C4—221no—
495C22⋊C4—221no—
496C22⋊C4—221no—
497C22⋊C4—221no—
498C42—41no—
499C42—221no—
500C42D4×D1111yescharacteristic
501C42#434111yescharacteristic
502C42C2×C22⋊D1111yescharacteristic
503C42C23×D1111yescharacteristic
504C11#1925211yescharacteristic, complemented, Sylow
505C23—41no—
506C23—221no—
507C23#6699111yescharacteristic
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—221no—
515Q8—221no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—81no—
521D4—82no—
522D4—221no—
523D4—221no—
524D4—881no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4#6699111yescharacteristic
540C2×C4#6699111yescharacteristic
541C2×C4#6699111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—441no—
549C8—441no—
550C8—441no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8#6700312yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22C2×#6699111yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—441no—
573C4—441no—
574C4—441no—
575C4#1062330511yescharacteristic
576C4#1062330611yescharacteristic
577C4C2×#6700311yescharacteristic
578C4#1062335311yescharacteristic
579C2—41no—
580C2—161no—
581C2—881no—
582C2#1307806511yescharacteristic
583C2#1307829011yescharacteristic
584C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3182C2
socleC22×C11C2×#121
prime radical#13079592C2
hypercenter#3182D11
hypocenterC11#19252
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
1. #13079947C2semidirect
3. #13077620C2semidirect
4. #13068181C2semidirect
5. #13068167C2semidirect
6. #13068126C2semidirect
7. #13068078C2semidirect
8. #13068050C2semidirect
9. #13068036C2semidirect
10. #13068007C2semidirect
11. #13067961C2semidirect
12. #13067368C2semidirect
13. #13067281C2semidirect
14. #13067265C2semidirect
15. C11×#3182C2semidirect
215. #3182D11semidirect
504. C11#19252semidirect

Maximal subgroups

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

subgroupindex
#130799472
#130795922
#130776202
#130681812
#130681672
#130681262
#130680782
#130680502
#130680362
#130680072
#130679612
#130673682
#130672812
#130672652
C11×#31822
#1925211