Finite Group Databasebeta

← #14738914

Subgroups — #14738914

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079972C211yesmaximal, characteristic
2#13079643C211yesmaximal, characteristic, complemented
3#13077620C211yesmaximal, characteristic, complemented
4#13068181C211yesmaximal, characteristic, complemented
5#13068174C211yesmaximal, characteristic, complemented
6#13068167C211yesmaximal, characteristic, complemented
7#13068160C211yesmaximal, characteristic, complemented
8#13068057C211yesmaximal, characteristic, complemented
9#13068050C211yesmaximal, characteristic, complemented
10#13068043C211yesmaximal, characteristic, complemented
11#13068036C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067321C211yesmaximal, characteristic, complemented
14#13067288C211yesmaximal, characteristic, complemented
15C11×#3141C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#489—21no—
20C11×#489—21no—
21C11×#487C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#486C2211yescharacteristic
25C11×#417—21no—
26C11×#417—21no—
27C4×C11×M16C2211yescharacteristic
28#10622841—21no—
29#10622840—21no—
30#10622741—21no—
31#10622740—21no—
32#10622707C2211yescharacteristic
33#10622703C2211yescharacteristic
34#10622703C2211yescharacteristic
35#10622700C2211yescharacteristic
36#10622699—21no—
37#10622696C2211yescharacteristic
38#10622696C2211yescharacteristic
39#10622695—21no—
40#10622688C2211yescharacteristic
41#10622685C2211yescharacteristic
42#10622655—21no—
43#10622652—21no—
44#10622629—21no—
45#10622622—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48#10622537C2211yescharacteristic
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—
68C22×Q8×C11—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×#127C2311yescharacteristic
78C11×#124—21no—
79C11×#121—21no—
80C11×#121—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4326—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4324—21no—
91C2×#4323—21no—
92#66983D411yescharacteristic
93#66982—21no—
94C4×C22⋊D11—21no—
95#66977D411yescharacteristic
96C2×#4318—21no—
97C2×#4313—21no—
98C2×C8×D11—21no—
99#66929—21no—
100#66928D411yescharacteristic
101C4×D44C2311yescharacteristic
102#66925—21no—
103#66923D411yescharacteristic
104C4×Dic22C2311yescharacteristic
105C11×#103—21no—
106C11×#103—21no—
107C11×#103—21no—
108C11×#103—21no—
109C11×#102—21no—
110C11×#102—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
142#66867—21no—
143C4×C11⋊C8—21no—
144#19383—111nomaximal, Sylow
145C11×#41—42no—
146C11×#41—42no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—81no—
152C2×Q8×C11—81no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C2×C22⋊D11—21no—
163C2×D44C2×D411yescharacteristic
164C2×C4×D11—21no—
165C2×Dic22C2×D411yescharacteristic
166C11×M16—41no—
167C11×M16—41no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—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—
204#4318—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211#4313—42no—
212C8×D11—42no—
213#3251—111no—
214#3218—111no—
215#3141D1111yescharacteristic, complemented
216#2969—111no—
217#1702—111no—
218#1701—111no—
219#1700—111no—
220#1699—111no—
221#1682—111no—
222#1681—111no—
223#1680—111no—
224#1679—111no—
225#1569—111no—
226#1553—111no—
227#1546—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—
237Q8×C11—82no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—81no—
243D4×C11—82no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—82no—
253C2×C4×C11—82no—
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C22⋊D11—81no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264D44—21no—
265D44—21no—
266C4×D11—41no—
267C4×D11—41no—
268Dic22—21no—
269Dic22—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#532C2×D1111yescharacteristic
281C2×C4⋊Q8C2×D1111yescharacteristic
282#529—111no—
283#497—221no—
284#491—221no—
285#489—21no—
286#489—21no—
287#487C2×D1111yescharacteristic
288#487C2×D1111yescharacteristic
289#486C2×D1111yescharacteristic
290#486C2×D1111yescharacteristic
291#478—221no—
292#475—111no—
293#474—111no—
294#469—221no—
295#468—221no—
296#463—221no—
297#462—111no—
298#462—111no—
299#461—111no—
300#461—111no—
301#460—111no—
302#459—111no—
303#451—221no—
304#448—221no—
305#446—111no—
306C8×Q8—111no—
307#436—111no—
308#436—221no—
309#435—221no—
310C8×D4—111no—
311#433—221no—
312#432—111no—
313#431—111no—
314#423—111no—
315#417—21no—
316#417—21no—
317#405—221no—
318C4×M16C2×D1111yescharacteristic
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329#331—111no—
330#331—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11C2×#12111yescharacteristic
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—41no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11#57511yescharacteristic
349C4×C11#57511yescharacteristic
350C4×C11#57611yescharacteristic
351C4×C11#57711yescharacteristic
352Dic11—41no—
353Dic11—41no—
354Dic11—41no—
355C2×#41—21no—
356C22×Q8—21no—
357C2×Q16—221no—
358C2×Q16—221no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×SD16—221no—
362C2×D8—221no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16C22⋊D1111yescharacteristic
366C2×M16C22⋊D1111yescharacteristic
367C22×C8—221no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8C22×D1111yescharacteristic
372C4⋊Q8C22×D1111yescharacteristic
373C4⋊Q8C22×D1111yescharacteristic
374#127C22×D1111yescharacteristic
375#126—221no—
376#125—111no—
377#124—21no—
378#124—111no—
379#123—221no—
380C22⋊Q8—111no—
381#121—21no—
382#121—21no—
383#121—111no—
384C4×Q8—111no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—111no—
388C4×D4—221no—
389#117—221no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C42C22×D1111yescharacteristic
393#107—221no—
394#106—221no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404#103—21no—
405#103—21no—
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—21no—
416#102—21no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424#97—221no—
425#97—221no—
426#97C22⋊D1111yescharacteristic
427#97C22⋊D1111yescharacteristic
428C4×C8—221no—
429C4×C8—221no—
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—41no—
433C2×C11—161no—
434C2×C11#304011yescharacteristic
435C2×C11#306211yescharacteristic
436C2×C11#306911yescharacteristic
437D11—81no—
438#41—42no—
439#41—42no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—81no—
445C2×Q8—81no—
446C2×Q8—111no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—111no—
452C2×D4—221no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—221no—
456C22×C4D4×D1111yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459Q16—881no—
460Q16—881no—
461SD16—881no—
462SD16—881no—
463SD16—881no—
464D8—881no—
465M16—41no—
466M16—41no—
467M16—442no—
468M16—881no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—442no—
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—111no—
489C4⋊C4—111no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—221no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C42—221no—
502C42D4×D1111yescharacteristic
503C42#434111yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1938311yescharacteristic, complemented, Sylow
507C23—41no—
508C23—221no—
509C23#6699111yescharacteristic
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—82no—
517Q8—221no—
518Q8—221no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525D4—221no—
526D4—221no—
527D4—881no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4#6699111yescharacteristic
544C2×C4#6699111yescharacteristic
545C2×C4#6699111yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4C2×#434111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—441no—
554C8—441no—
555C8—441no—
556C8—441no—
557C8—441no—
558C8—441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—441no—
566C22—441no—
567C22—441no—
568C22C2×#6699111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—441no—
577C4—441no—
578C4—441no—
579C4#1062330511yescharacteristic
580C4#1062330611yescharacteristic
581C4#1062335311yescharacteristic
582C4#1062335311yescharacteristic
583C2—41no—
584C2—161no—
585C2—881no—
586C2#1307810611yescharacteristic
587C2#1307829011yescharacteristic
588C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3141C2
socleC22×C11C2×#121
prime radical#13079972C2
hypercenter#3141D11
hypocenterC11#19383
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #13079643C2semidirect
3. #13077620C2semidirect
4. #13068181C2semidirect
5. #13068174C2semidirect
6. #13068167C2semidirect
7. #13068160C2semidirect
8. #13068057C2semidirect
9. #13068050C2semidirect
10. #13068043C2semidirect
11. #13068036C2semidirect
12. #13067383C2semidirect
13. #13067321C2semidirect
14. #13067288C2semidirect
15. C11×#3141C2semidirect
215. #3141D11semidirect
506. C11#19383semidirect

Maximal subgroups

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

subgroupindex
#130799722
#130796432
#130776202
#130681812
#130681742
#130681672
#130681602
#130680572
#130680502
#130680432
#130680362
#130673832
#130673212
#130672882
C11×#31412
#1938311