Finite Group Databasebeta

← #14736254

Subgroups — #14736254

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079198C211yesmaximal, characteristic, complemented
2#13078687C211yesmaximal, characteristic
3#41×C11⋊C8C211yesmaximal, characteristic
4#13068048C211yesmaximal, characteristic, complemented
5#13068044C211yesmaximal, characteristic, complemented
6#13068041C211yesmaximal, characteristic, complemented
7#13068037C211yesmaximal, characteristic, complemented
8#13068008C211yesmaximal, characteristic, complemented
9#13068003C211yesmaximal, characteristic, complemented
10#13067984C211yesmaximal, characteristic, complemented
11#13067979C211yesmaximal, characteristic, complemented
12#13067362C211yesmaximal, characteristic, complemented
13#13067281C211yesmaximal, characteristic, complemented
14#13067280C211yesmaximal, characteristic, complemented
15C11×#3107C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#485—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#462C2211yescharacteristic
23C11×#461C2211yescharacteristic
24C11×#452—21no—
25C4×C11×Q16—21no—
26C4×C11×SD16—21no—
27C11×#431C2211yescharacteristic
28#10622852—21no—
29#10622706C2211yescharacteristic
30#10622705C2211yescharacteristic
31#10622694C2211yescharacteristic
32#10622691C2211yescharacteristic
33#10622664—21no—
34#10622664—21no—
35#10622644C2211yescharacteristic
36C4×#4326—21no—
37C4×#4326—21no—
38C4×#4326—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622632C2211yescharacteristic
43C4×#4324—21no—
44D4×C11⋊C8—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622609—21no—
50#10622538—21no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53C2×C4×C11⋊C8—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×C11×Q16—21no—
69C2×C11×SD16—21no—
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#125—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11D411yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C11×#117—21no—
85C11×#117D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4326—21no—
89C2×#4326—21no—
90C2×#4326—21no—
91C2×#4324—21no—
92#66979—21no—
93#66977—21no—
94#66977—21no—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8D411yescharacteristic
98C22×C11⋊C8D411yescharacteristic
99#66923—21no—
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102C4×Dic22—21no—
103C4×Dic22—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×C22⋊C8—21no—
113C4×C8×C11—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66874—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66872—21no—
127#66871—21no—
128#66871—21no—
129#66871—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
136C4×C11⋊C8—21no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19129—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×Dic22—21no—
159C2×Dic22—21no—
160C11×Q16—42no—
161C11×SD16—42no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—41no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—41no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186C22⋊Dic11—41no—
187#4326—42no—
188#4326—42no—
189#4326—42no—
190#4324—42no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197C4×Dic11—41no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—41no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3170—111no—
211#3107—111no—
212#3107D1111yescharacteristic
213C8×#41—111no—
214#1680—111no—
215#1680—111no—
216#1679—111no—
217#1679—111no—
218#1674—111no—
219#1673—111no—
220#1670—111no—
221#1669—111no—
222#1564—111no—
223#1544—111no—
224#1544—111no—
225C23×C11—21no—
226C23×C11#12111yescharacteristic
227Q8×C11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11#13512yes—
233D4×C11—24no—
234D4×C11—21no—
235D4×C11#13512yes—
236C2×C4×C11—24no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×Dic11—41no—
257C2×Dic11—41no—
258Dic22—41no—
259Dic22—41no—
260Dic22—41no—
261Dic22—41no—
262C8×C11—41no—
263C8×C11—41no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8#13512yes—
272#533—111no—
273#533C2×D1111yescharacteristic
274C4×#41C2×D1111yescharacteristic
275#500—111no—
276#494—111no—
277#487—111no—
278#487—111no—
279#485—21no—
280#485—221no—
281#475—111no—
282#475C2×D1111yescharacteristic
283#474—111no—
284#474C2×D1111yescharacteristic
285#467—221no—
286#467—221no—
287#462—111no—
288#462C2×D1111yescharacteristic
289#461—111no—
290#461C2×D1111yescharacteristic
291#452—21no—
292#452—221no—
293C8×Q8—111no—
294C8×Q8—111no—
295C4×Q16—21no—
296C4×Q16—221no—
297C4×Q16—221no—
298C4×Q16—221no—
299C4×SD16—21no—
300C4×SD16—221no—
301C8×D4—111no—
302C8×D4—111no—
303C8×D4—221no—
304C8×D4—221no—
305#431—111no—
306#431—111no—
307#431—221no—
308#431C2×D1111yescharacteristic
309C2×C4×C8—111no—
310C2×C4×C8—221no—
311#335—111no—
312#335—111no—
313#334—111no—
314#334—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—22no—
326C22×C11—21no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×#12111yescharacteristic
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—22no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11#47312yes—
339C4×C11C2×#13511yescharacteristic
340C4×C11C2×#13511yescharacteristic
341C4×C11C2×#13511yescharacteristic
342C4×C11#57511yescharacteristic
343Dic11—81no—
344Dic11—81no—
345C2×#41C22⋊D1111yescharacteristic
346C2×Q16—21no—
347C2×Q16—221no—
348C2×Q16—221no—
349C2×Q16—221no—
350C2×SD16—21no—
351C2×SD16—221no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—221no—
355C22×C8—221no—
356C4⋊Q8—111no—
357C4⋊Q8—111no—
358C4⋊Q8C22×D1111yescharacteristic
359C4⋊Q8C22×D1111yescharacteristic
360#125—21no—
361#125—221no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—221no—
365C22⋊Q8—221no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—221no—
369C4×Q8—221no—
370C4×Q8C22⋊D1111yescharacteristic
371C4×Q8C22×D1111yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4C22⋊D1111yescharacteristic
375C4×D4C22×D1111yescharacteristic
376#117—21no—
377#117—21no—
378#117—221no—
379#117C22⋊D1111yescharacteristic
380C2×C42—21no—
381C2×C42C22×D1111yescharacteristic
382#107—21no—
383#107—221no—
384#107—221no—
385#107—221no—
386#106—21no—
387#106—221no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#103—221no—
405#103—221no—
406#102—21no—
407#102—221no—
408C22⋊C8—21no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C4×C8—21no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—221no—
419C4×C8—221no—
420C4×C8—221no—
421C4×C8—221no—
422C2×C11—41no—
423C2×C11—42no—
424C2×C11#303511yescharacteristic
425C2×C11#305011yescharacteristic
426C2×C11C2×#47311yescharacteristic
427#41—22no—
428#41—22no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8C2×C22⋊D1111yescharacteristic
434C2×D4—21no—
435C2×D4C2×C22⋊D1111yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4D4×D1111yescharacteristic
440C22×C4#434111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442Q16—42no—
443Q16—442no—
444Q16—442no—
445Q16—442no—
446SD16—42no—
447SD16—442no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—222no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—442no—
460C2×C8—441no—
461C2×C8—442no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—441no—
475C4⋊C4—441no—
476C4⋊C4C2×C22⋊D1111yescharacteristic
477C4⋊C4C2×C22⋊D1111yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—41no—
482C22⋊C4—441no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—41no—
487C42—441no—
488C42D4×D1111yescharacteristic
489C42#434111yescharacteristic
490C42C2×C22⋊D1111yescharacteristic
491C42C23×D1111yescharacteristic
492C11#1912911yescharacteristic, complemented, Sylow
493C23—21no—
494C23#6699211yescharacteristic
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—441no—
501Q8—441no—
502Q8—441no—
503Q8—441no—
504Q8#6700312yes—
505D4—24no—
506D4—21no—
507D4#6700312yes—
508C2×C4—24no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4#6699211yescharacteristic
525C2×C4#6699211yescharacteristic
526C2×C4#6699211yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×#434111yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—41no—
531C8—41no—
532C8—112no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—441no—
537C8—441no—
538C8—441no—
539C8—441no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—22no—
544C22—41no—
545C22—41no—
546C22C2×#6699211yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—881no—
556C4—881no—
557C4#1062281712yes—
558C4D11×#13511yescharacteristic
559C4#1062329911yescharacteristic
560C4C2×#6700311yescharacteristic
561C4C2×#6700311yescharacteristic
562C2—41no—
563C2—42no—
564C2#1307806711yescharacteristic
565C2#1307819411yescharacteristic
566C2C2×#1062281711yescharacteristic
subgroupG/H
centerC2×C4#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3107C2
socleC22×C11C2×#121
prime radicalC2×C11×#41D4
hypercenter#3107D11
hypocenterC11#19129
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
1. #13079198C2semidirect
4. #13068048C2semidirect
5. #13068044C2semidirect
6. #13068041C2semidirect
7. #13068037C2semidirect
8. #13068008C2semidirect
9. #13068003C2semidirect
10. #13067984C2semidirect
11. #13067979C2semidirect
12. #13067362C2semidirect
13. #13067281C2semidirect
14. #13067280C2semidirect
492. C11#19129semidirect

Maximal subgroups

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

subgroupindex
#130791982
#130786872
#41×C11⋊C82
#130680482
#130680442
#130680412
#130680372
#130680082
#130680032
#130679842
#130679792
#130673622
#130672812
#130672802
C11×#31072
#1912911