Finite Group Databasebeta

← #14736773

Subgroups — #14736773

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079330C211yesmaximal, characteristic, complemented
2#13078687C211yesmaximal, characteristic, complemented
3#13077636C211yesmaximal, characteristic, complemented
4#13068175C211yesmaximal, characteristic, complemented
5#13068165C211yesmaximal, characteristic, complemented
6#13068127C211yesmaximal, characteristic, complemented
7#13068079C211yesmaximal, characteristic, complemented
8#13068058C211yesmaximal, characteristic, complemented
9#13068048C211yesmaximal, characteristic, complemented
10#13068008C211yesmaximal, characteristic, complemented
11#13067962C211yesmaximal, characteristic, complemented
12#13067366C211yesmaximal, characteristic, complemented
13#13067321C211yesmaximal, characteristic, complemented
14#13067314C211yesmaximal, characteristic, complemented
15C11×#3035C211yesmaximal, characteristic
16C2×C11×#135—21no—
17C11×#532C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19#10623001C2211yescharacteristic
20C11×#464—21no—
21C11×#463—21no—
22C11×#462C2211yescharacteristic
23C11×#461C2211yescharacteristic
24C11×#460C2211yescharacteristic
25C11×#459C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#416—21no—
28#10622852—21no—
29#10622706C2211yescharacteristic
30#10622691C2211yescharacteristic
31#10622689C2211yescharacteristic
32#10622683C2211yescharacteristic
33#10622655—21no—
34#10622655—21no—
35#10622644C2211yescharacteristic
36C4×#4326—21no—
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622633C2211yescharacteristic
40#10622632C2211yescharacteristic
41#10622631—21no—
42#10622631—21no—
43C4×#4324—21no—
44#10622625—21no—
45#10622625—21no—
46#10622625C2211yescharacteristic
47#10622625C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622609—21no—
50#10622539—21no—
51#10622539C2211yescharacteristic
52#10622538C2211yescharacteristic
53C4×#4318—21no—
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C11×#135—44no—
70C2×C11×Q16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×D8—21no—
74C22×C8×C11—21no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×#127C2311yescharacteristic
77C11×#124—21no—
78C11×#121—21no—
79C11×#121—21no—
80C4×Q8×C11D411yescharacteristic
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D411yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C11×#117D411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×#4326—21no—
93C2×#4324—21no—
94C2×#4324—21no—
95C2×#4324—21no—
96#66979—21no—
97#66977—21no—
98#66977—21no—
99C2×#4318—21no—
100C2×#4318—21no—
101C2×#4318D411yescharacteristic
102C2×#4318D411yescharacteristic
103#66923—21no—
104#66922C2311yescharacteristic
105#66922C2311yescharacteristic
106C4×Dic22—21no—
107C4×Dic22—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103—21no—
113C11×#102—21no—
114C11×#102—21no—
115#66899—21no—
116#66896—21no—
117#66896—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66874—21no—
127#66872—21no—
128#66871—21no—
129#66871—21no—
130#66871—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19182—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C11×#41—42no—
149C11×#41—42no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—41no—
157C2×D4×C11C2×D411yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C2×Dic22—21no—
166C2×Dic22—21no—
167C11×Q16—42no—
168C11×SD16—42no—
169C11×SD16—42no—
170C11×D8—42no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—42no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192C22⋊Dic11—41no—
193#4326—42no—
194#4324—42no—
195#4324—42no—
196#4324—42no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201Dic11⋊C4—41no—
202Dic11⋊C4—41no—
203C4×Dic11—41no—
204#4318—22no—
205#4318—41no—
206#4318—42no—
207#4318—42no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216#3182—111no—
217#3107—111no—
218#3035D1111yescharacteristic
219#2971—111no—
220#1701—111no—
221#1699—111no—
222#1693—111no—
223#1685—111no—
224#1682—111no—
225#1680—111no—
226#1674—111no—
227#1666—111no—
228#1565—111no—
229#1553—111no—
230#1552—111no—
231C23×C11—21no—
232C23×C11—41no—
233C23×C11#12111yescharacteristic
234Q8×C11—21no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11AGL(1,ℤ/8)12yes—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—42no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—81no—
246D4×C11—82no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—81no—
260C2×C4×C11—82no—
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11#12111yescharacteristic
263C2×C4×C11#12111yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×Dic11—41no—
268C2×Dic11—41no—
269Dic22—41no—
270Dic22—41no—
271Dic22—41no—
272Dic22—41no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8#13512yescomplemented
283C2×#135—21no—
284#533—111no—
285#532C2×D1111yescharacteristic
286C4×#41C2×D1111yescharacteristic
287#500—111no—
288#492—111no—
289#487—111no—
290#486—111no—
291#485—221no—
292#475—111no—
293#474—111no—
294#468—221no—
295#468—221no—
296#464—21no—
297#463—21no—
298#462—111no—
299#462C2×D1111yescharacteristic
300#461—111no—
301#461C2×D1111yescharacteristic
302#460C2×D1111yescharacteristic
303#459C2×D1111yescharacteristic
304#452—221no—
305C8×Q8—111no—
306C8×Q8—111no—
307#440—221no—
308#440—221no—
309C4×Q16—221no—
310C4×SD16—221no—
311#436—111no—
312#436—111no—
313#436—221no—
314#436—221no—
315#432—111no—
316#432—221no—
317#431—111no—
318C2×C4⋊C8C2×D1111yescharacteristic
319#416—21no—
320C4×M16—111no—
321C4×M16—221no—
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329#332—111no—
330#332—111no—
331#332—111no—
332#331—111no—
333#331—111no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11C2×#12111yescharacteristic
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—22no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11C2×#13511yescharacteristic
353C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
354C4×C11#57511yescharacteristic
355C4×C11#57511yescharacteristic
356Dic11—81no—
357Dic11—81no—
358C2×#41—21no—
359C2×#41C22⋊D1111yescharacteristic
360#135—44no—
361C2×Q16—21no—
362C2×Q16—221no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×D8—21no—
369C2×M16—111no—
370C2×M16—111no—
371C2×M16—221no—
372C2×M16—221no—
373C22×C8—21no—
374C4⋊Q8—111no—
375C4⋊Q8—111no—
376C4⋊Q8C22×D1111yescharacteristic
377#127C22×D1111yescharacteristic
378#125—221no—
379#124—21no—
380C22⋊Q8—221no—
381C22⋊Q8—221no—
382#121—21no—
383#121—21no—
384C4×Q8—221no—
385C4×Q8—221no—
386C4×Q8C22⋊D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C22⋊D1111yescharacteristic
393C4×D4C22×D1111yescharacteristic
394#117—21no—
395#117—221no—
396#117C22⋊D1111yescharacteristic
397C2×C42—21no—
398C2×C42C22×D1111yescharacteristic
399#107—221no—
400#107—221no—
401#107—221no—
402#106—221no—
403C4⋊C8—21no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412#103—21no—
413#103—21no—
414#103—221no—
415#103—221no—
416#103—221no—
417#103—221no—
418#103—221no—
419#102—21no—
420#102—21no—
421#102—221no—
422#102—221no—
423#102—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428#97—111no—
429#97—111no—
430#97—221no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—221no—
434C4×C8—221no—
435C4×C8—221no—
436C2×C11—41no—
437C2×C11—81no—
438C2×C11—161no—
439C2×C11#303511yescharacteristic
440C2×C11#305511yescharacteristic
441C2×C11#306911yescharacteristic
442#41—22no—
443#41—41no—
444#41—42no—
445#41—42no—
446C2×Q8—21no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8C2×C22⋊D1111yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4C2×C22⋊D1111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4D4×D1111yescharacteristic
461C22×C4#434111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463Q16—42no—
464Q16—442no—
465SD16—42no—
466SD16—42no—
467SD16—442no—
468SD16—442no—
469SD16—442no—
470D8—42no—
471M16—222no—
472M16—442no—
473M16—441no—
474M16—442no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—441no—
495C4⋊C4—441no—
496C4⋊C4C2×C22⋊D1111yescharacteristic
497C4⋊C4C2×C22⋊D1111yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—441no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—441no—
508C42D4×D1111yescharacteristic
509C42#434111yescharacteristic
510C42C2×C22⋊D1111yescharacteristic
511C42C23×D1111yescharacteristic
512C11#1918211yescharacteristic, complemented, Sylow
513C23—21no—
514C23—41no—
515C23#6699211yescharacteristic
516Q8—21no—
517Q8—41no—
518Q8—41no—
519Q8—441no—
520Q8—441no—
521Q8—441no—
522Q8—441no—
523Q8#6698512yes—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—81no—
532D4—82no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—81no—
546C2×C4—82no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4#6699211yescharacteristic
550C2×C4#6699211yescharacteristic
551C2×C4#6699211yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C2×C4C22×C22⋊D1111yescharacteristic
555C8—41no—
556C8—41no—
557C8—112no—
558C8—221no—
559C8—221no—
560C8—221no—
561C8—441no—
562C8—441no—
563C8—441no—
564C8—441no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22C2×#6699211yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—881no—
584C4—881no—
585C4D11×#13511yescharacteristic
586C4#1062329911yescharacteristic
587C4C2×#6698511yescharacteristic
588C4#1062335311yescharacteristic
589C2—41no—
590C2—81no—
591C2—161no—
592C2#1307806711yescharacteristic
593C2#1307823111yescharacteristic
594C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3035C2
socleC22×C11C2×#121
hypercenter#3035D11
hypocenterC11#19182
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #13079330C2semidirect
2. #13078687C2semidirect
3. #13077636C2semidirect
4. #13068175C2semidirect
5. #13068165C2semidirect
6. #13068127C2semidirect
7. #13068079C2semidirect
8. #13068058C2semidirect
9. #13068048C2semidirect
10. #13068008C2semidirect
11. #13067962C2semidirect
12. #13067366C2semidirect
13. #13067321C2semidirect
14. #13067314C2semidirect
282. C11⋊C8#135semidirect
512. C11#19182semidirect

Maximal subgroups

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

subgroupindex
#130793302
#130786872
#130776362
#130681752
#130681652
#130681272
#130680792
#130680582
#130680482
#130680082
#130679622
#130673662
#130673212
#130673142
C11×#30352
#1918211