Finite Group Databasebeta

← #14739300

Subgroups — #14739300

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079754C211yesmaximal, characteristic, complemented
2#13078778C211yesmaximal, characteristic, complemented
3#13078676C211yesmaximal, characteristic
4#13068060C211yesmaximal, characteristic, complemented
5#13068053C211yesmaximal, characteristic, complemented
6#13068032C211yesmaximal, characteristic, complemented
7#13068025C211yesmaximal, characteristic, complemented
8#13068020C211yesmaximal, characteristic, complemented
9#13068015C211yesmaximal, characteristic, complemented
10#13067998C211yesmaximal, characteristic, complemented
11#13067991C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067309C211yesmaximal, characteristic, complemented
14#13067274C211yesmaximal, characteristic, complemented
15C11×#2988C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623001C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C8×D4×C11—21no—
22C8×D4×C11—21no—
23C8×D4×C11C2211yescharacteristic
24C8×D4×C11C2211yescharacteristic
25C11×#431—21no—
26C11×#431C2211yescharacteristic
27C2×C11×C4⋊C8—21no—
28C2×C11×C4⋊C8C2211yescharacteristic
29#10622852—21no—
30#10622851—21no—
31#10622644C2211yescharacteristic
32#10622643—21no—
33#10622640C2211yescharacteristic
34C4×#4325—21no—
35#10622634C2211yescharacteristic
36#10622634C2211yescharacteristic
37#10622632C2211yescharacteristic
38#10622631—21no—
39#10622628C2211yescharacteristic
40C4×#4323—21no—
41#10622621C2211yescharacteristic
42#10622621C2211yescharacteristic
43#10622616—21no—
44#10622609—21no—
45#10622539C2211yescharacteristic
46#10622538C2211yescharacteristic
47#10622460—21no—
48#10622460—21no—
49#10622350—21no—
50#10622350—21no—
51#10622307C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622295C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622119C2211yescharacteristic
60#10622119C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C4×Q8×C11D411yescharacteristic
73C4×Q8×C11C2311yescharacteristic
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11D411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C11×#117D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—21no—
83C2×#4325—21no—
84C2×#4324—21no—
85C2×#4323—21no—
86#66983—21no—
87#66983—21no—
88#66979—21no—
89#66977—21no—
90#66977—21no—
91#66928—21no—
92#66927C2311yescharacteristic
93C4×D44—21no—
94C4×D44—21no—
95#66923—21no—
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8D411yescharacteristic
105C11×C4⋊C8D411yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8D411yescharacteristic
111C11×C22⋊C8D411yescharacteristic
112C4×C8×C11—21no—
113C4×C8×C11—21no—
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66885—21no—
123#66885—21no—
124#66885—21no—
125#66885—21no—
126#66882—21no—
127#66882—21no—
128#66881—21no—
129#66881—21no—
130#66874—21no—
131#66874—21no—
132#66873—21no—
133#66873—21no—
134#66872—21no—
135#66872—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#19419—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—41no—
157#4339—82no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×C4×D11—41no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—81no—
168C2×C8×C11—81no—
169C2×C8×C11—81no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4326—42no—
190#4325—42no—
191#4324—42no—
192#4323—42no—
193(C2×D11)⋊C4—41no—
194(C2×D11)⋊C4—41no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201Dic11⋊C4—41no—
202Dic11⋊C4—41no—
203C4×Dic11—41no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208#3228—111no—
209#3116—111no—
210#3106—111no—
211#2988D1111yescharacteristic, complemented
212#1682—111no—
213#1681—111no—
214#1678—111no—
215#1677—111no—
216#1676—111no—
217#1675—111no—
218#1672—111no—
219#1671—111no—
220#1572—111no—
221#1551—111no—
222#1542—111no—
223C23×C11—21no—
224C23×C11#12111yescharacteristic
225C22×D11—41no—
226Q8×C11—21no—
227Q8×C11#13512yes—
228D4×C11—24no—
229D4×C11—21no—
230D4×C11#13512yes—
231C2×C4×C11—24no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—81no—
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—82no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253D44—41no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—81no—
258C4×D11—82no—
259Dic22—41no—
260Dic22—41no—
261Dic22—81no—
262Dic22—81no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#533—111no—
274#532—111no—
275C4×#41C2×D1111yescharacteristic
276#500—111no—
277#498—111no—
278#486—111no—
279#486—111no—
280#485—221no—
281#482—221no—
282#482—221no—
283#482—221no—
284#478—221no—
285#478—221no—
286#477—111no—
287#477—111no—
288#476—111no—
289#476—111no—
290#462—111no—
291#461—111no—
292#460—111no—
293#459—111no—
294#452—221no—
295#449—221no—
296C8×Q8C2×D1111yescharacteristic
297C8×Q8C2×D1111yescharacteristic
298#441—221no—
299#440—221no—
300C4×SD16—221no—
301C4×D8—221no—
302C8×D4—21no—
303C8×D4—21no—
304C8×D4C2×D1111yescharacteristic
305C8×D4C2×D1111yescharacteristic
306#432—111no—
307#431—21no—
308#431—111no—
309#431C2×D1111yescharacteristic
310C2×C4⋊C8—21no—
311C2×C4⋊C8C2×D1111yescharacteristic
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316#333—111no—
317#333—111no—
318#333—111no—
319#333—111no—
320#332—111no—
321#332—111no—
322#331—111no—
323#331—111no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—22no—
327C22×C11—21no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11C2×#12111yescharacteristic
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11C2×#13511yescharacteristic
342C4×C11C2×#13511yescharacteristic
343C4×C11#57711yescharacteristic
344C4×C11#57811yescharacteristic
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348C2×#41—221no—
349C2×#41D4411yescharacteristic
350C2×Q16—221no—
351C2×SD16—221no—
352C2×SD16—221no—
353C2×D8—221no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C4⋊Q8—111no—
358C4⋊Q8—111no—
359C4⋊Q8—111no—
360#127—111no—
361#125—221no—
362#124—221no—
363C22⋊Q8—221no—
364C22⋊Q8—221no—
365#121—221no—
366#121—221no—
367C4×Q8—221no—
368C4×Q8—221no—
369C4×Q8D4411yescharacteristic
370C4×Q8C22×D1111yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—221no—
374C4×D4—221no—
375C4×D4D4411yescharacteristic
376C4×D4C22×D1111yescharacteristic
377#117—21no—
378#117—221no—
379#117D4411yescharacteristic
380C2×C42—21no—
381C2×C42C22×D1111yescharacteristic
382#107—221no—
383#107—221no—
384#107—221no—
385#107—221no—
386#106—221no—
387#106—221no—
388#106—221no—
389#106—221no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8C22⋊D1111yescharacteristic
398C4⋊C8C22⋊D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—221no—
402#103—221no—
403#103—221no—
404#103—221no—
405#102—221no—
406#102—221no—
407#102—221no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8C22⋊D1111yescharacteristic
418C22⋊C8C22⋊D1111yescharacteristic
419#97—221no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—221no—
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C2×C11—41no—
426C2×C11—42no—
427C2×C11#304611yescharacteristic
428C2×C11#305011yescharacteristic
429C2×C11#306811yescharacteristic
430D11—161no—
431#41—22no—
432#41—22no—
433#41—882no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8C2×D4411yescharacteristic
438C2×D4—21no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—441no—
443C2×D4C2×D4411yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—441no—
448C22×C4C2×D4411yescharacteristic
449C22×C4#433911yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451Q16—442no—
452SD16—442no—
453SD16—442no—
454D8—442no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—81no—
458C2×C8—81no—
459C2×C8—81no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8C2×C22⋊D1111yescharacteristic
465C2×C8C2×C22⋊D1111yescharacteristic
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—441no—
477C4⋊C4—441no—
478C4⋊C4C2×D4411yescharacteristic
479C4⋊C4C2×D4411yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—441no—
490C42C2×D4411yescharacteristic
491C42#433911yescharacteristic
492C42C2×C22⋊D1111yescharacteristic
493C42C23×D1111yescharacteristic
494C11#1941911yescharacteristic, complemented, Sylow
495C23—21no—
496C23—441no—
497C23#6698311yescharacteristic
498Q8—21no—
499Q8—441no—
500Q8—441no—
501Q8—881no—
502Q8—881no—
503Q8#6695712yes—
504D4—24no—
505D4—21no—
506D4—441no—
507D4—441no—
508D4—441no—
509D4—441no—
510D4—881no—
511D4—882no—
512D4#6695712yes—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—81no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—882no—
529C2×C4#6698311yescharacteristic
530C2×C4#6698311yescharacteristic
531C2×C4#6698311yescharacteristic
532C2×C4C22×D4411yescharacteristic
533C2×C4C2×#433911yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22C2×#6698311yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—881no—
563C4—881no—
564C4—881no—
565C4C2×#6695711yescharacteristic
566C4C2×#6695711yescharacteristic
567C4#1062336711yescharacteristic
568C4#1062336911yescharacteristic
569C2—41no—
570C2—42no—
571C2—1761no—
572C2#1307816611yescharacteristic
573C2#1307819711yescharacteristic
574C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×#121
prime radical#13078676C2
hypercenter#2988D11
hypocenterC11#19419
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13079754C2semidirect
2. #13078778C2semidirect
4. #13068060C2semidirect
5. #13068053C2semidirect
6. #13068032C2semidirect
7. #13068025C2semidirect
8. #13068020C2semidirect
9. #13068015C2semidirect
10. #13067998C2semidirect
11. #13067991C2semidirect
12. #13067396C2semidirect
13. #13067309C2semidirect
14. #13067274C2semidirect
15. C11×#2988C2semidirect
211. #2988D11semidirect
494. C11#19419semidirect

Maximal subgroups

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

subgroupindex
#130797542
#130787782
#130786762
#130680602
#130680532
#130680322
#130680252
#130680202
#130680152
#130679982
#130679912
#130673962
#130673092
#130672742
C11×#29882
#1941911