Finite Group Databasebeta

← #14736232

Subgroups — #14736232

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079175C211yesmaximal, characteristic, complemented
2#13078687C211yesmaximal, characteristic, complemented
3#13078676C211yesmaximal, characteristic
4#13068074C211yesmaximal, characteristic, complemented
5#13068067C211yesmaximal, characteristic, complemented
6#13068060C211yesmaximal, characteristic, complemented
7#13068053C211yesmaximal, characteristic, complemented
8#13067998C211yesmaximal, characteristic, complemented
9#13067991C211yesmaximal, characteristic, complemented
10#13067964C211yesmaximal, characteristic, complemented
11#13067957C211yesmaximal, characteristic, complemented
12#13067364C211yesmaximal, characteristic, complemented
13#13067280C211yesmaximal, characteristic, complemented
14#13067276C211yesmaximal, characteristic, complemented
15C8×C11×#41C211yesmaximal, 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×C4×C8×C11—21no—
28C2×C4×C8×C11C2211yescharacteristic
29#10622852—21no—
30#10622851—21no—
31#10622727—21no—
32#10622727—21no—
33#10622644C2211yescharacteristic
34C4×#4326—21no—
35#10622640C2211yescharacteristic
36C4×#4325—21no—
37#10622634C2211yescharacteristic
38#10622633C2211yescharacteristic
39#10622632C2211yescharacteristic
40C4×#4324—21no—
41#10622628C2211yescharacteristic
42C4×#4323—21no—
43#10622621C2211yescharacteristic
44#10622620C2211yescharacteristic
45#10622616—21no—
46#10622609—21no—
47#10622538C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622307C2211yescharacteristic
50#10622306C2211yescharacteristic
51C4×#4314—21no—
52C4×#4314—21no—
53#10622294C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
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×C11D411yescharacteristic
72C22×C8×C11D411yescharacteristic
73C4×Q8×C11D411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11D411yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C11×#117—21no—
80C11×#117D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4326—21no—
84C2×#4325—21no—
85C2×#4324—21no—
86C2×#4323—21no—
87#66983—21no—
88#66983—21no—
89#66979—21no—
90#66977—21no—
91#66977—21no—
92C2×#4314—21no—
93C2×#4314—21no—
94#66928—21no—
95#66927C2311yescharacteristic
96C4×D44—21no—
97C4×D44—21no—
98#66923—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102C4×Dic22—21no—
103C4×Dic22—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112C4×C8×C11—21no—
113C4×C8×C11—21no—
114C4×C8×C11D411yescharacteristic
115C4×C8×C11D411yescharacteristic
116C4×C8×C11C2311yescharacteristic
117C4×C8×C11C2311yescharacteristic
118#66899—21no—
119#66899—21no—
120#66896—21no—
121#66896—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124#66885—21no—
125#66885—21no—
126#66881—21no—
127#66881—21no—
128#66880—21no—
129#66880—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
142C4×C11⋊C8—21no—
143C4×C11⋊C8—21no—
144#19127—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—22no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—41no—
169C2×C8×C11—42no—
170C2×C8×C11—42no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
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—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11#4111yescharacteristic
188C42×C11C2411yescharacteristic
189C22⋊Dic11—41no—
190#4326—42no—
191#4325—42no—
192#4324—42no—
193#4323—42no—
194(C2×D11)⋊C4—41no—
195(C2×D11)⋊C4—41no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202Dic11⋊C4—41no—
203Dic11⋊C4—41no—
204C4×Dic11—41no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209#4314—42no—
210#4314—42no—
211#3167—111no—
212#3107—111no—
213#3106—111no—
214C8×#41D1111yescharacteristic, complemented
215#1684—111no—
216#1683—111no—
217#1682—111no—
218#1681—111no—
219#1672—111no—
220#1671—111no—
221#1666—111no—
222#1665—111no—
223#1564—111no—
224#1544—111no—
225#1543—111no—
226C23×C11—21no—
227C23×C11#12111yescharacteristic
228C22×D11—41no—
229Q8×C11—21no—
230Q8×C11#13512yes—
231D4×C11—24no—
232D4×C11—21no—
233D4×C11#13512yes—
234C2×C4×C11—24no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—82no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—81no—
261C4×D11—82no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—81no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11#13512yes—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277#533—111no—
278#532—111no—
279C4×#41C2×D1111yescharacteristic
280#498—111no—
281#492—111no—
282#487—111no—
283#486—111no—
284#485—221no—
285#482—221no—
286#477—111no—
287#476—111no—
288#475—111no—
289#474—111no—
290#465—221no—
291#465—221no—
292#462—111no—
293#461—111no—
294#460—111no—
295#459—111no—
296#452—221no—
297#449—221no—
298C8×Q8C2×D1111yescharacteristic
299C8×Q8C2×D1111yescharacteristic
300C4×Q16—221no—
301C4×SD16—221no—
302C4×SD16—221no—
303C4×SD16—221no—
304C4×SD16—221no—
305C4×D8—221no—
306C8×D4—21no—
307C8×D4—21no—
308C8×D4C2×D1111yescharacteristic
309C8×D4C2×D1111yescharacteristic
310#431—21no—
311#431—111no—
312#431—111no—
313#431C2×D1111yescharacteristic
314C2×C4×C8—21no—
315C2×C4×C8C2×D1111yescharacteristic
316#335—111no—
317#335—111no—
318#334—111no—
319#334—111no—
320#333—111no—
321#333—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#331—111no—
327#331—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—22no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11C2×#12111yescharacteristic
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—22no—
341C4×C11—21no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11#47112yes—
345C4×C11C2×#13511yescharacteristic
346C4×C11C2×#13511yescharacteristic
347C4×C11C2×#13511yescharacteristic
348C4×C11#57511yescharacteristic
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352C2×#41—221no—
353C2×#41D4411yescharacteristic
354C2×Q16—221no—
355C2×SD16—221no—
356C2×SD16—221no—
357C2×SD16—221no—
358C2×SD16—221no—
359C2×D8—221no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8C22⋊D1111yescharacteristic
363C22×C8C22⋊D1111yescharacteristic
364C4⋊Q8—111no—
365C4⋊Q8—111no—
366C4⋊Q8—111no—
367#127—111no—
368#125—221no—
369#124—221no—
370C22⋊Q8—221no—
371C22⋊Q8—221no—
372#121—221no—
373#121—221no—
374C4×Q8—221no—
375C4×Q8—221no—
376C4×Q8D4411yescharacteristic
377C4×Q8C22×D1111yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—221no—
381C4×D4—221no—
382C4×D4D4411yescharacteristic
383C4×D4C22×D1111yescharacteristic
384#117—21no—
385#117—221no—
386#117D4411yescharacteristic
387C2×C42—21no—
388C2×C42C22×D1111yescharacteristic
389#107—221no—
390#107—221no—
391#106—221no—
392#106—221no—
393#106—221no—
394#106—221no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403#103—221no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8C22⋊D1111yescharacteristic
426C4×C8C22⋊D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C2×C11—41no—
430C2×C11—42no—
431C2×C11#303511yescharacteristic
432C2×C11#305011yescharacteristic
433C2×C11C2×#47111yescharacteristic
434D11—161no—
435#41—22no—
436#41—22no—
437#41—882no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8C2×D4411yescharacteristic
442C2×D4—21no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—441no—
447C2×D4C2×D4411yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—441no—
452C22×C4C2×D4411yescharacteristic
453C22×C4#433911yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455Q16—442no—
456SD16—442no—
457SD16—442no—
458SD16—442no—
459SD16—442no—
460D8—442no—
461C2×C8—22no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—41no—
465C2×C8—42no—
466C2×C8—42no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8C2×C22⋊D1111yescharacteristic
472C2×C8C2×C22⋊D1111yescharacteristic
473C2×C8C2×C22⋊D1111yescharacteristic
474C2×C8C2×C22⋊D1111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C4⋊C4C2×D4411yescharacteristic
486C4⋊C4C2×D4411yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—441no—
497C42C2×D4411yescharacteristic
498C42#433911yescharacteristic
499C42C2×C22⋊D1111yescharacteristic
500C42C23×D1111yescharacteristic
501C11#1912711yescharacteristic, complemented, Sylow
502C23—21no—
503C23—441no—
504C23#6698311yescharacteristic
505Q8—21no—
506Q8—441no—
507Q8—441no—
508Q8—441no—
509Q8—441no—
510Q8—881no—
511Q8#6695712yes—
512D4—24no—
513D4—21no—
514D4—441no—
515D4—441no—
516D4—441no—
517D4—441no—
518D4—881no—
519D4—882no—
520D4#6695712yes—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—882no—
537C2×C4#6698311yescharacteristic
538C2×C4#6698311yescharacteristic
539C2×C4#6698311yescharacteristic
540C2×C4C22×D4411yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—441no—
549C8—441no—
550C8—441no—
551C8—441no—
552C8#6700312yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—881no—
560C22—881no—
561C22—881no—
562C22C2×#6698311yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—881no—
570C4—881no—
571C4—881no—
572C4#1062275412yes—
573C4C2×#6695711yescharacteristic
574C4C2×#6695711yescharacteristic
575C4C2×#6700311yescharacteristic
576C4#1062335311yescharacteristic
577C2—41no—
578C2—42no—
579C2—1761no—
580C2#1307807111yescharacteristic
581C2#1307819711yescharacteristic
582C2C2×#1062275411yescharacteristic
subgroupG/H
centerC2×C4#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C2×#121
prime radical#13078676C2
hypercenterC8×#41D11
hypocenterC11#19127
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. #13079175C2semidirect
2. #13078687C2semidirect
4. #13068074C2semidirect
5. #13068067C2semidirect
6. #13068060C2semidirect
7. #13068053C2semidirect
8. #13067998C2semidirect
9. #13067991C2semidirect
10. #13067964C2semidirect
11. #13067957C2semidirect
12. #13067364C2semidirect
13. #13067280C2semidirect
14. #13067276C2semidirect
15. C8×C11×#41C2semidirect
214. C8×#41D11semidirect
501. C11#19127semidirect

Maximal subgroups

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

subgroupindex
#130791752
#130786872
#130786762
#130680742
#130680672
#130680602
#130680532
#130679982
#130679912
#130679642
#130679572
#130673642
#130672802
#130672762
C8×C11×#412
#1912711