Finite Group Databasebeta

← #14738916

Subgroups — #14738916

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#13079640C211yesmaximal, characteristic, complemented
2#13079009C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13068182C211yesmaximal, characteristic, complemented
5#13068175C211yesmaximal, characteristic, complemented
6#13068168C211yesmaximal, characteristic, complemented
7#13068161C211yesmaximal, characteristic, complemented
8#13068058C211yesmaximal, characteristic, complemented
9#13068051C211yesmaximal, characteristic, complemented
10#13068044C211yesmaximal, characteristic, complemented
11#13068037C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic, complemented
13#13067321C211yesmaximal, characteristic, complemented
14#13067289C211yesmaximal, characteristic, complemented
15C11×#3251C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C11×#529C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C11×#478—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#469—21no—
23C11×#468—21no—
24C11×#463—21no—
25C11×#460C2211yescharacteristic
26C11×#459C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622845—21no—
29#10622845—21no—
30#10622694C2211yescharacteristic
31#10622694C2211yescharacteristic
32#10622683C2211yescharacteristic
33#10622683C2211yescharacteristic
34#10622682—21no—
35#10622673—21no—
36#10622668—21no—
37#10622668—21no—
38#10622663—21no—
39#10622653—21no—
40#10622644C2211yescharacteristic
41#10622644C2211yescharacteristic
42#10622637C2211yescharacteristic
43Q8×C11⋊C8C2211yescharacteristic
44#10622632C2211yescharacteristic
45#10622632C2211yescharacteristic
46#10622625—21no—
47#10622625C2211yescharacteristic
48#10622624—21no—
49D4×C11⋊C8C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53#10622538C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C22×Dic22—21no—
69C2×C11×SD16—21no—
70C2×C11×D8—21no—
71C2×C11×M16—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#126—21no—
75C11×#125D411yescharacteristic
76C11×#124—21no—
77C11×#124D411yescharacteristic
78C11×#123—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×#121—21no—
81C11×#121—21no—
82C11×#121D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—21no—
91C2×#4326—21no—
92C2×#4324—21no—
93C2×#4324—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×#4318—21no—
97C2×#4318D411yescharacteristic
98C2×#4318D411yescharacteristic
99C22×C11⋊C8—21no—
100#66922—21no—
101#66922—21no—
102#66922—21no—
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C11×#107—21no—
106C11×#106—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×#102—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121#66896—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126#66874—21no—
127#66874—21no—
128#66874—21no—
129#66874—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19383—111nomaximal, Sylow
145C11×#41—42no—
146C11×#41—42no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—41no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×Dic11—41no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—41no—
164C2×Dic22—81no—
165C2×Dic22—81no—
166C11×SD16—81no—
167C11×D8—81no—
168C11×M16—81no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—21no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191#4326—81no—
192#4326—81no—
193#4324—81no—
194#4324—81no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—41no—
200C4⋊Dic11—41no—
201#4318—41no—
202#4318—41no—
203#4318—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#3251D1111yescharacteristic
214#3218—111no—
215#3141—111no—
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—21no—
229C23×C11—41no—
230C23×C11#12111yescharacteristic
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—41no—
234Q8×C11—41no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—81no—
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—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—82no—
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—82no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—41no—
269Dic22—82no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#532C2×D1111yescharacteristic
281C2×C4⋊Q8—111no—
282#529C2×D1111yescharacteristic
283#497—221no—
284#491—221no—
285#489—221no—
286#489—221no—
287#487—111no—
288#487—111no—
289#486—111no—
290#486—111no—
291#478—21no—
292#475C2×D1111yescharacteristic
293#474C2×D1111yescharacteristic
294#469—21no—
295#468—21no—
296#463—21no—
297#462—111no—
298#462—111no—
299#461—111no—
300#461—111no—
301#460C2×D1111yescharacteristic
302#459C2×D1111yescharacteristic
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#423C2×D1111yescharacteristic
315#417—221no—
316#417—221no—
317#405—221no—
318C4×M16—111no—
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—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11C2×#12111yescharacteristic
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—81no—
349C4×C11#57511yescharacteristic
350C4×C11#57511yescharacteristic
351C4×C11#57611yescharacteristic
352C4×C11#57711yescharacteristic
353Dic11—81no—
354Dic11—81no—
355C2×#41—21no—
356C22×Q8—221no—
357C2×Q16—221no—
358C2×Q16—221no—
359C2×SD16—21no—
360C2×SD16—221no—
361C2×SD16—221no—
362C2×D8—21no—
363C2×M16—21no—
364C2×M16—111no—
365C2×M16—111no—
366C2×M16—221no—
367C22×C8—221no—
368C4⋊Q8—111no—
369C4⋊Q8—111no—
370C4⋊Q8—221no—
371C4⋊Q8—221no—
372C4⋊Q8—221no—
373C4⋊Q8C22×D1111yescharacteristic
374#127C22×D1111yescharacteristic
375#126—21no—
376#125C22⋊D1111yescharacteristic
377#124—21no—
378#124C22⋊D1111yescharacteristic
379#123—21no—
380C22⋊Q8C22⋊D1111yescharacteristic
381#121—21no—
382#121—21no—
383#121C22⋊D1111yescharacteristic
384C4×Q8C22×D1111yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4C22×D1111yescharacteristic
389#117—21no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C42C22×D1111yescharacteristic
393#107—21no—
394#106—21no—
395C4⋊C8—21no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402C4⋊C8C22×D1111yescharacteristic
403C4⋊C8C22×D1111yescharacteristic
404#103—21no—
405#103—221no—
406#103—221no—
407#103—221no—
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—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424#97—111no—
425#97—111no—
426#97—221no—
427#97—221no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—221no—
431C4×C8—221no—
432C2×C11—41no—
433C2×C11—81no—
434C2×C11—161no—
435C2×C11#304011yescharacteristic
436C2×C11#306211yescharacteristic
437C2×C11#306911yescharacteristic
438#41—42no—
439#41—42no—
440C2×Q8—21no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—441no—
444C2×Q8—881no—
445C2×Q8—881no—
446C2×Q8C2×C22⋊D1111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4C2×C22⋊D1111yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—441no—
456C22×C4D4×D1111yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459Q16—881no—
460Q16—881no—
461SD16—81no—
462SD16—881no—
463SD16—881no—
464D8—81no—
465M16—81no—
466M16—441no—
467M16—441no—
468M16—442no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—442no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—441no—
491C4⋊C4—441no—
492C4⋊C4C2×C22⋊D1111yescharacteristic
493C4⋊C4C2×C22⋊D1111yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—21no—
502C42D4×D1111yescharacteristic
503C42#434111yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1938311yescharacteristic, complemented, Sylow
507C23—21no—
508C23—41no—
509C23#6699211yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—441no—
515Q8—441no—
516Q8—441no—
517Q8—441no—
518Q8—882no—
519D4—21no—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4—81no—
527D4—82no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—882no—
543C2×C4#6699211yescharacteristic
544C2×C4#6699211yescharacteristic
545C2×C4#6699211yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4C2×#434111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—41no—
550C8—41no—
551C8—221no—
552C8—221no—
553C8—221no—
554C8—221no—
555C8—441no—
556C8—441no—
557C8—441no—
558C8—441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×#6699211yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—881no—
578C4—881no—
579C4#1062330411yescharacteristic
580C4#1062330411yescharacteristic
581C4#1062336611yescharacteristic
582C4#1062336811yescharacteristic
583C2—41no—
584C2—81no—
585C2—161no—
586C2#1307810811yescharacteristic
587C2#1307829811yescharacteristic
588C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3251C2
socleC22×C11C2×#121
hypercenter#3251D11
hypocenterC11#19383
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3251

Complements

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

NH ≅ G/Ntype
1. #13079640C2semidirect
2. #13079009C2semidirect
3. #13077621C2semidirect
4. #13068182C2semidirect
5. #13068175C2semidirect
6. #13068168C2semidirect
7. #13068161C2semidirect
8. #13068058C2semidirect
9. #13068051C2semidirect
10. #13068044C2semidirect
11. #13068037C2semidirect
12. #13067381C2semidirect
13. #13067321C2semidirect
14. #13067289C2semidirect
506. C11#19383semidirect

Maximal subgroups

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

subgroupindex
#130796402
#130790092
#130776212
#130681822
#130681752
#130681682
#130681612
#130680582
#130680512
#130680442
#130680372
#130673812
#130673212
#130672892
C11×#32512
#1938311