Finite Group Databasebeta

← #14767672

Subgroups — #14767672

Order 2816.

796 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079086C211yesmaximal, characteristic
2#13077534C211yesmaximal, characteristic, complemented
3#13069521C211yesmaximal, characteristic, complemented
4#13069512C211yesmaximal, characteristic, complemented
5#13069153C211yesmaximal, characteristic, complemented
6#13069148C211yesmaximal, characteristic, complemented
7#13069140C211yesmaximal, characteristic, complemented
8#13069135C211yesmaximal, characteristic, complemented
9#13069110C211yesmaximal, characteristic, complemented
10#13069103C211yesmaximal, characteristic, complemented
11#13069093C211yesmaximal, characteristic, complemented
12#13069086C211yesmaximal, characteristic, complemented
13#13068739C211yesmaximal, characteristic, complemented
14#13068371C211yesmaximal, characteristic, complemented
15C11×#2949C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C11×#519C2211yescharacteristic
18C11×#518C2211yescharacteristic
19#10623347C2211yescharacteristic
20C2×#66995C2211yescharacteristic
21#10623336C2211yescharacteristic
22C2×#66985C2211yescharacteristic
23#10623276C2211yescharacteristic
24#10623276C2211yescharacteristic
25C2×#66957C2211yescharacteristic
26C11×#440—22no—
27C4×C11×SD16—22no—
28C11×#427C2211yescharacteristic
29C11×#419C2211yescharacteristic
30C11×#418C2211yescharacteristic
31C11×#405C2211yescharacteristic
32C2×#66900C2211yescharacteristic
33#10622838C2211yescharacteristic
34C2×#66897C2211yescharacteristic
35#10622828C2211yescharacteristic
36#10622789C412yescomplemented
37#10622788C412yescomplemented
38#10622781C412yescomplemented
39#10622780C412yescomplemented
40C2×#66883C2211yescharacteristic
41#10622714C2211yescharacteristic
42#10622714C2211yescharacteristic
43#10622619C2211yescharacteristic
44#10622619C2211yescharacteristic
45#10622618C2211yescharacteristic
46#10622618C2211yescharacteristic
47#10622618C2211yescharacteristic
48#10622618C2211yescharacteristic
49#10622330—22no—
50#10622313—22no—
51C11⋊#338C2211yescharacteristic
52#10622195C2211yescharacteristic
53#10622171C2211yescharacteristic
54#10622171C2211yescharacteristic
55#10622169C2211yescharacteristic
56#10622169C2211yescharacteristic
57#10622169C2211yescharacteristic
58#10622169C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C2×#4339C2311yescharacteristic
62C2×#4339C2311yescharacteristic
63C2×C11×SD16—21no—
64C2×C11×SD16—21no—
65C2×C11×SD16—21no—
66C2×C11×SD16—21no—
67C2×C11×SD16C2×C412yes—
68C2×C11×SD16C2×C412yes—
69C2×C11×M16C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×Q8×C11—22no—
72C4×Q8×C11—41no—
73C4×D4×C11—22no—
74C4×D4×C11—41no—
75C11×#117—41no—
76C11×#117C2311yescharacteristic
77C11×#117C2311yescharacteristic
78C11×#117C2311yescharacteristic
79C2×C11×C22⋊C4—41no—
80#67006—41no—
81#67000C2×C412yescomplemented
82#66999—41no—
83#66997C2×C412yescomplemented
84C2×#4326C2×C412yescomplemented
85#66995—41no—
86#66995—41no—
87C2×#4325C2×C412yescomplemented
88#66993C2×C412yes—
89#66991—41no—
90#66989C2×C412yes—
91C2×#4324C2×C412yes—
92#66985—41no—
93#66985—41no—
94C2×#4323C2×C412yes—
95#66982—41no—
96#66979C2311yescharacteristic
97#66979C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C2×#4318C2311yescharacteristic
100C2×#4318C2311yescharacteristic
101C2×#4318C2311yescharacteristic
102#66960—41no—
103#66960—41no—
104M16×D11—41no—
105M16×D11—41no—
106C2×Dic44C2×C411yescharacteristic, complemented
107#66957—21no—
108#66957—21no—
109#66957—21no—
110#66957—21no—
111C2×D88C2×C411yescharacteristic, complemented
112C2×#4314C2×C411yescharacteristic, complemented
113C2×#4314C2×C411yescharacteristic, complemented
114#66954—22no—
115#66954—22no—
116C11×#107—21no—
117C11×#106—21no—
118C11×#103—22no—
119C11×#102—22no—
120C11×#97D412yescomplemented
121C4×C8×C11D412yescomplemented
122#66900—41no—
123#66899—41no—
124#66897—41no—
125#66896—41no—
126#66883—21no—
127#66883—21no—
128#66879—21no—
129#66879C2×C412yescomplemented
130C8×Dic11—21no—
131C8×Dic11C2×C412yescomplemented
132#66870—41no—
133#66870—41no—
134#66869—22no—
135#66869—22no—
136#66869—41no—
137#66869—41no—
138#22284—111nomaximal, Sylow
139C24×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C22×C412yes—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C22×C412yes—
152C22×C4×C11—21no—
153C22×C4×C11—42no—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—21no—
156C2×C22⋊D11—21no—
157C2×C22⋊D11—42no—
158#4339—21no—
159#4339—21no—
160#4339—21no—
161#4339—21no—
162#4339—21no—
163#4339—21no—
164#4339—21no—
165#4339—21no—
166C2×D44C22×C411yescharacteristic
167C2×D44C22×C411yescharacteristic
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×Dic22C22×C411yescharacteristic
171C2×Dic22C22×C411yescharacteristic
172C11×SD16—22no—
173C11×SD16—22no—
174C11×SD16—22no—
175C11×SD16—22no—
176C11×M16—21no—
177C11×M16—21no—
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C22×C411yescharacteristic
180C2×C8×C11C2×D412yes—
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11#4111yescharacteristic
184C2×C8×C11#4111yescharacteristic
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—42no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—42no—
196C42×C11C2×D412yes—
197C22⋊Dic11—21no—
198C22⋊Dic11—21no—
199C22⋊Dic11—42no—
200#4326—42no—
201#4325—42no—
202#4324—42no—
203#4323—42no—
204(C2×D11)⋊C4—42no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207Dic11⋊C4—42no—
208C4×Dic11—21no—
209C4×Dic11C22×C412yes—
210#4318—21no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8C22×C412yes—
222Dic44—21no—
223Dic44—21no—
224D88—21no—
225D88—21no—
226#4314—21no—
227#4314—21no—
228#4314—21no—
229#4314—21no—
230#4313—42no—
231#4313—42no—
232C8×D11—42no—
233C8×D11—42no—
234#3154—111no—
235#2957—111no—
236#2949D1111yescharacteristic, complemented
237#1977—111no—
238#1976—111no—
239#1912—111no—
240#1911—111no—
241#1910—111no—
242#1909—111no—
243#1905—111no—
244#1904—111no—
245#1903—111no—
246#1902—111no—
247#1833—111no—
248#1747—111no—
249C23×C11—22no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—161no—
253C23×C11H(5,𝔽2)11yescharacteristic
254C22×D11—21no—
255C22×D11—21no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—41no—
259Q8×C11—41no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—162no—
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C22⋊D11—41no—
278C22⋊D11—41no—
279C22⋊D11—41no—
280C22⋊D11—41no—
281C22⋊D11—162no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—41no—
286D44—21no—
287D44—21no—
288D44—21no—
289D44—21no—
290C4×D11—41no—
291C4×D11—41no—
292C4×D11—41no—
293C4×D11—41no—
294Dic22—21no—
295Dic22—21no—
296Dic22—21no—
297Dic22—21no—
298C8×C11—22no—
299C8×C11C4×D411yescharacteristic
300C8×C11C4×D411yescharacteristic
301C8×C11C4×D411yescharacteristic
302C8×C11C4×D411yescharacteristic
303C11⋊C8—22no—
304C11⋊C8—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C2×#137—111no—
308C2×AGL(1,ℤ/8)—111no—
309C2×#135—111no—
310C22×SD16C2×D1111yescharacteristic
311#568—111no—
312#568—111no—
313#536—111no—
314#535—111no—
315#519C2×D1111yescharacteristic
316#518C2×D1111yescharacteristic
317#497—112no—
318#496—112no—
319#495—112no—
320#492—112no—
321#444—222no—
322#443—222no—
323#440—22no—
324C4×SD16—22no—
325C2×#108—111no—
326#427C2×D1111yescharacteristic
327#421—111no—
328#421—111no—
329#421—111no—
330#421—111no—
331#419—111no—
332#419C2×D1111yescharacteristic
333#418—111no—
334#418C2×D1111yescharacteristic
335C2×#101—111no—
336C2×#100—111no—
337#410—111no—
338#410—111no—
339#405—111no—
340#405—111no—
341#405C2×D1111yescharacteristic
342#344—111no—
343#344—111no—
344#338—111no—
345H(3,ℤ/4)—111no—
346H(3,ℤ/4)—111no—
347H(3,ℤ/4)—111no—
348H(3,ℤ/4)—111no—
349H(3,ℤ/4)—111no—
350C22×C11—41no—
351C22×C11—42no—
352C22×C11—82no—
353C22×C11—82no—
354C22×C11—161no—
355C22×C11#51811yescharacteristic
356C22×C11#53511yescharacteristic
357C22×C11#54011yescharacteristic
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—81no—
361C2×D11—81no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11C2×C4×D411yescharacteristic
367C4×C11#51811yescharacteristic
368C4×C11#53511yescharacteristic
369C4×C11#54011yescharacteristic
370Dic11—42no—
371Dic11—41no—
372Dic11—41no—
373Dic11—81no—
374C2×#41—111no—
375C2×#41—111no—
376C22×Q8C22×D1111yescharacteristic
377C22×D4C22×D1111yescharacteristic
378#137—441no—
379#137—441no—
380AGL(1,ℤ/8)—441no—
381AGL(1,ℤ/8)—441no—
382#135—221no—
383#135—221no—
384#135—221no—
385#135—221no—
386C2×Q16—112no—
387C2×Q16—111no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16—21no—
392C2×SD16—112no—
393C2×SD16—112no—
394C2×SD16—111no—
395C2×SD16—111no—
396C2×SD16C4×D1112yes—
397C2×SD16C4×D1112yes—
398C2×D8—112no—
399C2×D8—111no—
400#131—222no—
401#131—222no—
402#131—441no—
403#131—441no—
404C2×M16—111no—
405C2×M16—111no—
406C2×M16—111no—
407C2×M16—111no—
408C2×M16—441no—
409C2×M16—441no—
410C2×M16C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412C4⋊Q8—112no—
413#127—112no—
414#124—112no—
415#124—112no—
416#123—441no—
417C22⋊Q8—441no—
418#121—441no—
419#120—441no—
420C4×Q8—22no—
421C4×Q8—41no—
422C4×D4—22no—
423C4×D4—41no—
424#117—41no—
425#117—111no—
426#117—111no—
427#117C22×D1111yescharacteristic
428#117C22×D1111yescharacteristic
429#117C22×D1111yescharacteristic
430C2×C22⋊C4—41no—
431#108—221no—
432#108—221no—
433#107—21no—
434#106—21no—
435#104—222no—
436#104—222no—
437#104—441no—
438#104—441no—
439#103—22no—
440#103—441no—
441#102—22no—
442#102—441no—
443#101—441no—
444#100—441no—
445#99—441no—
446#99—441no—
447#97—112no—
448#97—221no—
449#97C22⋊D1112yescomplemented
450C4×C8—112no—
451C4×C8—221no—
452C4×C8C22⋊D1112yescomplemented
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—21no—
456C2×C11—82no—
457C2×C11#232811yescharacteristic
458D11—81no—
459D11—81no—
460C24—21no—
461#41—221no—
462#41—221no—
463#41—221no—
464#41—221no—
465#41—221no—
466#41—221no—
467#41—221no—
468#41—221no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—111no—
475C2×Q8—111no—
476C2×Q8C2×C4×D1112yes—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—111no—
483C2×D4—111no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—442no—
487C2×D4C2×C4×D1112yes—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4C23×D1111yescharacteristic
493Q16—221no—
494Q16—221no—
495Q16—442no—
496SD16—22no—
497SD16—22no—
498SD16—22no—
499SD16—22no—
500SD16—221no—
501SD16—221no—
502SD16—221no—
503SD16—221no—
504SD16—442no—
505SD16—442no—
506D8—221no—
507D8—221no—
508D8—442no—
509M16—21no—
510M16—21no—
511M16—221no—
512M16—221no—
513M16—221no—
514M16—221no—
515M16—221no—
516M16—221no—
517M16—221no—
518M16—221no—
519M16—442no—
520M16—442no—
521C2×C8—112no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—442no—
526C2×C8—442no—
527C2×C8C2×C4×D1111yescharacteristic
528C2×C8C2×C4×D1111yescharacteristic
529C2×C8#433911yescharacteristic
530C2×C8#433911yescharacteristic
531C2×C8C2×C22⋊D1112yes—
532C2×C8C2×C22⋊D1111yescharacteristic
533C2×C8C2×C22⋊D1111yescharacteristic
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—442no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—42no—
545C22⋊C4—221no—
546C22⋊C4—221no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—112no—
553C42—221no—
554C42C2×C22⋊D1112yes—
555C11#2228411yescharacteristic, complemented, Sylow
556C23—22no—
557C23—41no—
558C23—41no—
559C23—161no—
560C23—221no—
561C23—221no—
562C23#6703711yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8—221no—
568Q8—221no—
569Q8—221no—
570Q8—221no—
571D4—22no—
572D4—22no—
573D4—41no—
574D4—41no—
575D4—221no—
576D4—221no—
577D4—221no—
578D4—221no—
579D4—441no—
580D4—441no—
581D4—441no—
582D4—441no—
583D4—1762no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—162no—
591C2×C4—222no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4C22×C4×D1111yescharacteristic
600C2×C4C2×#433911yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4#6704211yescharacteristic
603C2×C4#6704211yescharacteristic
604C2×C4C22×C22⋊D1111yescharacteristic
605C8—22no—
606C8—222no—
607C8—441no—
608C8—441no—
609C8—441no—
610C8C4×C22⋊D1111yescharacteristic
611C8C4×C22⋊D1111yescharacteristic
612C8C4×C22⋊D1111yescharacteristic
613C8C4×C22⋊D1111yescharacteristic
614C22—41no—
615C22—42no—
616C22—82no—
617C22—82no—
618C22—161no—
619C22—441no—
620C22—441no—
621C22—881no—
622C22—881no—
623C22#1062307611yescharacteristic
624C22#1062309311yescharacteristic
625C22#1062333611yescharacteristic
626C4—42no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—442no—
631C4—441no—
632C4—441no—
633C4—881no—
634C4#1062307611yescharacteristic
635C4#1062309311yescharacteristic
636C4C2×C4×C22⋊D1111yescharacteristic
637C4#1062336111yescharacteristic
638C2—21no—
639C2—21no—
640C2—21no—
641C2—82no—
642C2—881no—
643C2—881no—
644C2#1307133811yescharacteristic
subgroupG/H
centerC2#13071338
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2949C2
socleC2×C11#2328
prime radical#13079086C2
cosocleC22×C4×C11C24
hypercenter#2949D11
hypocenterC11#22284
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2949

Complements

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

NH ≅ G/Ntype
2. #13077534C2semidirect
3. #13069521C2semidirect
4. #13069512C2semidirect
5. #13069153C2semidirect
6. #13069148C2semidirect
7. #13069140C2semidirect
8. #13069135C2semidirect
9. #13069110C2semidirect
10. #13069103C2semidirect
11. #13069093C2semidirect
12. #13069086C2semidirect
13. #13068739C2semidirect
14. #13068371C2semidirect
15. C11×#2949C2semidirect
36. #10622789C4semidirect
37. #10622788C4semidirect
38. #10622781C4semidirect
39. #10622780C4semidirect
81. #67000C2×C4semidirect
83. #66997C2×C4semidirect
84. C2×#4326C2×C4semidirect
87. C2×#4325C2×C4semidirect
106. C2×Dic44C2×C4semidirect
111. C2×D88C2×C4semidirect
112. C2×#4314C2×C4semidirect
113. C2×#4314C2×C4semidirect
120. C11×#97D4semidirect
121. C4×C8×C11D4semidirect
129. #66879C2×C4semidirect
131. C8×Dic11C2×C4semidirect
236. #2949D11semidirect
449. #97C22⋊D11semidirect
452. C4×C8C22⋊D11semidirect
555. C11#22284semidirect

Maximal subgroups

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

subgroupindex
#130790862
#130775342
#130695212
#130695122
#130691532
#130691482
#130691402
#130691352
#130691102
#130691032
#130690932
#130690862
#130687392
#130683712
C11×#29492
#2228411