Finite Group Databasebeta

← #14723682

Subgroups — #14723682

Order 2816.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078630C211yesmaximal, characteristic
2#13077594C211yesmaximal, characteristic, complemented
3C8×#4341C211yesmaximal, characteristic, complemented
4#13067468C211yesmaximal, characteristic, complemented
5#13067457C211yesmaximal, characteristic, complemented
6#13067452C211yesmaximal, characteristic, complemented
7#13067422C211yesmaximal, characteristic, complemented
8#13067419C211yesmaximal, characteristic, complemented
9#13067419C211yesmaximal, characteristic, complemented
10D8×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067395C211yesmaximal, characteristic, complemented
12#13067047C211yesmaximal, characteristic, complemented
13#13067021C211yesmaximal, characteristic, complemented
14#13066901C211yesmaximal, characteristic, complemented
15C11×#1581C211yesmaximal, characteristic, complemented
16#10623088C2211yescharacteristic
17C4×#4341C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622771C411yescharacteristic
22#10622766C411yescharacteristic
23#10622740—21no—
24#10622735—21no—
25C8×C22⋊D11—21no—
26C2×C8×Dic11—21no—
27C4×#4324C2211yescharacteristic
28C4×#4324C2211yescharacteristic
29D4×C11⋊C8C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622501C411yescharacteristic
32#10622490C411yescharacteristic
33#10622448C2211yescharacteristic
34#10622446C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622397C411yescharacteristic
38#10622396C411yescharacteristic
39#10622380C411yescharacteristic
40#10622379C411yescharacteristic
41(C22⋊D11)⋊C8—21no—
42(C22⋊D11)⋊C8—21no—
43#10622333—21no—
44#10622331—21no—
45C4×Dic44C2211yescharacteristic
46#10622298C2211yescharacteristic
47#10622298C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4341C2×C411yescharacteristic
68C2×C11×D8C2×C411yescharacteristic
69C2×C11×M16—21no—
70C22×C8×C11—21no—
71C4×D4×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#66991C2×C411yescharacteristic
74#66989C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C4×C22⋊D11—21no—
80#66979—21no—
81C2×C4×Dic11—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C2×Dic44C2×C411yescharacteristic
85C2×C8×D11D411yescharacteristic
86C2×C8×D11D411yescharacteristic
87#66950C2×C411yescharacteristic
88#66945C2×C411yescharacteristic
89#66943C2×C411yescharacteristic
90#66940C2×C411yescharacteristic
91#66936—21no—
92(C22⋊D11)⋊C4—21no—
93#66932—21no—
94#66930—21no—
95C42×D11C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×#107C2×C411yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×#102C2×C411yescharacteristic
102C11×#102C2×C411yescharacteristic
103C11×C22⋊C8—21no—
104C11×C22⋊C8—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66896C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8C2×C411yescharacteristic
116(C2×D11)⋊C8C2×C411yescharacteristic
117#66882C2×C411yescharacteristic
118#66880C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66879—21no—
121#66879—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8C2×C411yescharacteristic
128Dic11⋊C8C2×C411yescharacteristic
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11—21no—
132C8×Dic11—21no—
133C8×Dic11D411yescharacteristic
134C8×Dic11D411yescharacteristic
135#66874C2×C411yescharacteristic
136#66874C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17904—111nomaximal, Sylow
145C2×D4×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153#4341—22no—
154#4341—22no—
155C2×C4×D11C22×C411yescharacteristic
156C2×C4×D11C2×D411yescharacteristic
157C2×C4×D11#4111yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C2×Dic22C22×C411yescharacteristic
160C11×D8—22no—
161C11×M16—42no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—42no—
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C42×C11C2411yescharacteristic
175C22⋊Dic11—21no—
176C22⋊Dic11—21no—
177C22⋊Dic11—21no—
178C22⋊Dic11—21no—
179#4324—22no—
180#4324—22no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11C22×C411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11#4111yescharacteristic
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—42no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207Dic44—22no—
208C8×D11—22no—
209C8×D11—22no—
210#3102—111no—
211#2966—111no—
212C8×#41—111no—
213#1584—111no—
214#1583—111no—
215#1582—111no—
216#1581D1111yescharacteristic, complemented
217C8×Q16—111no—
218C8×SD16—111no—
219C8×SD16—111no—
220C8×D8—111no—
221#1572—111no—
222#1488—111no—
223#1482—111no—
224#1450—111no—
225C23×C11—21no—
226C23×C11—21no—
227C22×D11C4×D411yescharacteristic
228D4×C11—21no—
229D4×C11—21no—
230D4×C11—21no—
231D4×C11#13112yes—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C22⋊D11—24no—
242C22⋊D11—42no—
243C2×Dic11—24no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—42no—
249C2×Dic11C4×D411yescharacteristic
250C2×Dic11C4×D411yescharacteristic
251C2×Dic11C4×D411yescharacteristic
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—41no—
257Dic22—21no—
258Dic22—21no—
259Dic22—21no—
260Dic22#13112yes—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11#13512yes—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8#13512yes—
275#529—111no—
276C4×#41—111no—
277#485—111no—
278#482—111no—
279#479—111no—
280#478—111no—
281#464—111no—
282#463—111no—
283#452—111no—
284#449—111no—
285#446—111no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292C4×D8C2×D1111yescharacteristic
293#436C2×D1111yescharacteristic
294#435—221no—
295C8×D4—111no—
296C8×D4—111no—
297C8×D4—221no—
298C8×D4—221no—
299C8×D4—221no—
300C8×D4C2×D1111yescharacteristic
301#433—221no—
302#432—111no—
303#431—111no—
304#431—111no—
305#431—111no—
306#431—221no—
307#405—221no—
308C2×C4×C8—111no—
309C2×C4×C8—221no—
310#335—111no—
311#335C2×D1111yescharacteristic
312#334—111no—
313#334—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318D4⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8C2×D1111yescharacteristic
321D4⋊C8C2×D1111yescharacteristic
322#322—111no—
323#322C2×D1111yescharacteristic
324C82—111no—
325C82—111no—
326C22×C11—22no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4×D411yescharacteristic
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—21no—
336C4×C11—21no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11C2×#13111yescharacteristic
340C4×C11C2×#13111yescharacteristic
341C4×C11C2×#13511yescharacteristic
342C4×C11C2×#13511yescharacteristic
343Dic11—22no—
344Dic11—21no—
345Dic11—21no—
346Dic11—21no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C2×Q16—111no—
352C2×SD16—111no—
353C2×SD16—111no—
354C2×D8C4×D1111yescharacteristic
355C2×M16—21no—
356C22×C8—21no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—221no—
360C22×C8—221no—
361#126—221no—
362#125—111no—
363#124—111no—
364#123—221no—
365C22⋊Q8—111no—
366#121—111no—
367C4×Q8—111no—
368C4×Q8—111no—
369C4×Q8—111no—
370C4×D4—111no—
371C4×D4—221no—
372C4×D4—221no—
373C4×D4—221no—
374C4×D4C22×D1111yescharacteristic
375C4×D4C22×D1111yescharacteristic
376#117—111no—
377#117—221no—
378#117—221no—
379C2×C42—111no—
380C2×C42—221no—
381#107—111no—
382#107C4×D1111yescharacteristic
383#106—111no—
384#106—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
396#103—111no—
397#103—111no—
398#103—111no—
399#103—111no—
400#102—111no—
401#102—111no—
402#102C4×D1111yescharacteristic
403#102C4×D1111yescharacteristic
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—111no—
407C22⋊C8—111no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—221no—
414#97—221no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—221no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8C22×D1111yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11—42no—
428C2×C11—81no—
429C2×C11#292911yescharacteristic
430C2×C11C4×#13511yescharacteristic
431C2×C11#295511yescharacteristic
432D11—41no—
433#41—222no—
434#41—222no—
435C2×Q8—111no—
436C2×Q8—111no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4C2×C4×D1111yescharacteristic
440C2×D4C2×C4×D1111yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—221no—
447C22×C4—221no—
448Q16—222no—
449SD16—222no—
450SD16—222no—
451D8—22no—
452M16—42no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—42no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—442no—
467C2×C8—442no—
468C2×C8C2×C4×D1111yescharacteristic
469C2×C8C2×C4×D1111yescharacteristic
470C2×C8D4×D1111yescharacteristic
471C2×C8D4×D1111yescharacteristic
472C4⋊C4—111no—
473C4⋊C4—111no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4C2×C4×D1111yescharacteristic
481C4⋊C4C2×C4×D1111yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—111no—
491C42—111no—
492C42—111no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42C23×D1111yescharacteristic
498C11#1790411yescharacteristic, complemented, Sylow
499C23—21no—
500C23—21no—
501C23—111no—
502Q8—112no—
503Q8—221no—
504Q8—221no—
505Q8—221no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—224no—
510D4—442no—
511D4#6696012yes—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—111no—
519C2×C4—111no—
520C2×C4—111no—
521C2×C4—224no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—442no—
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—112no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8#6696512yes—
549C22—22no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—221no—
556C22—221no—
557C22—221no—
558C22C4×D4×D1111yescharacteristic
559C4—21no—
560C4—41no—
561C4—41no—
562C4—221no—
563C4—221no—
564C4—222no—
565C4—221no—
566C4—441no—
567C4—441no—
568C4—441no—
569C4C2×#6696011yescharacteristic
570C4D11×#13111yescharacteristic
571C4C2×#6696511yescharacteristic
572C4D11×#13511yescharacteristic
573C2—42no—
574C2—81no—
575C2—441no—
576C2#1307730711yescharacteristic
577C2C4×#6696511yescharacteristic
578C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1581C2
socleC22×C11C2×C4×D4
prime radical#10622771C4
cosocleC42×C11C24
hypercenter#1581D11
hypocenterC11#17904
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #13077594C2semidirect
3. C8×#4341C2semidirect
4. #13067468C2semidirect
5. #13067457C2semidirect
6. #13067452C2semidirect
7. #13067422C2semidirect
8. #13067419C2semidirect
9. #13067419C2semidirect
10. D8×C11⋊C8C2semidirect
11. #13067395C2semidirect
12. #13067047C2semidirect
13. #13067021C2semidirect
14. #13066901C2semidirect
15. C11×#1581C2semidirect
216. #1581D11semidirect
498. C11#17904semidirect

Maximal subgroups

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

subgroupindex
#130786302
#130775942
C8×#43412
#130674682
#130674572
#130674522
#130674222
#130674192
D8×C11⋊C82
#130673952
#130670472
#130670212
#130669012
C11×#15812
#1790411