Finite Group Databasebeta

← #14724700

Subgroups — #14724700

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078645C211yesmaximal, characteristic
2#13077568C211yesmaximal, characteristic, complemented
3#13077361C211yesmaximal, characteristic
4#13067503C211yesmaximal, characteristic, complemented
5#13067458C211yesmaximal, characteristic, complemented
6#13067457C211yesmaximal, characteristic, complemented
7#13067453C211yesmaximal, characteristic, complemented
8#13067450C211yesmaximal, characteristic, complemented
9#13067419C211yesmaximal, characteristic, complemented
10C8×#4314C211yesmaximal, characteristic, complemented
11#13067385C211yesmaximal, characteristic, complemented
12#13067065C211yesmaximal, characteristic
13D11×Q8⋊C8C211yesmaximal, characteristic, complemented
14C8×#4313C211yesmaximal, characteristic, complemented
15C11×#1590C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17C4×Q8×D11C2211yescharacteristic
18#10623079C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C11×#436C2211yescharacteristic
22#10622783C411yescharacteristic
23#10622776C411yescharacteristic
24#10622740—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622476C411yescharacteristic
30#10622467C411yescharacteristic
31#10622451C2211yescharacteristic
32#10622450—21no—
33#10622450C2211yescharacteristic
34D11×C4⋊C8C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622419C411yescharacteristic
38#10622404C411yescharacteristic
39#10622390C411yescharacteristic
40#10622375C411yescharacteristic
41#10622343—21no—
42#10622340—21no—
43#10622320—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×M16—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80#66960—44no—
81C2×#4314C2×C411yescharacteristic
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313D411yescharacteristic
85C2×#4313D411yescharacteristic
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89#66948C2×C411yescharacteristic
90C4⋊C4×D11—21no—
91C4⋊C4×D11C2×C411yescharacteristic
92#66941C2×C411yescharacteristic
93#66940—21no—
94#66940C2×C411yescharacteristic
95#66938—21no—
96#66937—21no—
97C4×D44C2311yescharacteristic
98C42×D11—21no—
99C42×D11C2311yescharacteristic
100C4×Dic22—21no—
101C4×Dic22C2311yescharacteristic
102C11×#106C2×C411yescharacteristic
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×C22⋊C8—21no—
109C11×#97—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8C2×C411yescharacteristic
120(C2×D11)⋊C8C2×C411yescharacteristic
121#66881C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66879D411yescharacteristic
124#66879D411yescharacteristic
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8C2×C411yescharacteristic
130Dic11⋊C8C2×C411yescharacteristic
131C8×Dic11—21no—
132C8×Dic11—21no—
133C8×Dic11—21no—
134#66874C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17997—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152Q8×D11—22no—
153Q8×D11—41no—
154#4339—42no—
155#4339—42no—
156C2×D44—21no—
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11C22×C411yescharacteristic
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11#4111yescharacteristic
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22C22×C411yescharacteristic
167C11×SD16—41no—
168C11×M16—42no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183#4325—41no—
184#4324—22no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#4314—22no—
209#4313—22no—
210#4313—42no—
211#4313—42no—
212#4313SD1614yescomplemented
213C8×D11—42no—
214C8×D11—42no—
215C8×D11—42no—
216#3103—111no—
217Q8×M16—111no—
218#2935—111no—
219#1590—111no—
220#1590D1111yescharacteristic, complemented
221#1583—111no—
222#1583—111no—
223#1582—111no—
224#1582—111no—
225C8×SD16—111no—
226C8×SD16—111no—
227#1570—111no—
228#1492—111no—
229C2×Q8⋊C8—111no—
230C8×M16—111no—
231C23×C11—21no—
232C22×D11—21no—
233C22×D11C4×D411yescharacteristic
234Q8×C11—21no—
235Q8×C11—21no—
236D4×C11—21no—
237D4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—42no—
247C22⋊D11—42no—
248C22⋊D11—81no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11C4×D411yescharacteristic
253C2×Dic11C4×D411yescharacteristic
254C2×Dic11C4×D411yescharacteristic
255D44—21no—
256D44—21no—
257D44—42no—
258C4×D11—21no—
259C4×D11—21no—
260C4×D11—41no—
261C4×D11—42no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—81no—
265C4×D11C2×SD1612yes—
266C4×D11#13512yes—
267Dic22—21no—
268Dic22—42no—
269Dic22—42no—
270Dic22#13112yescomplemented
271C8×C11—22no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11C2×SD1612yes—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8C2×SD1612yes—
285C2×#131—221no—
286#532—111no—
287C2×C4×Q8—111no—
288#481—111no—
289#481—111no—
290#475—111no—
291#475—111no—
292#460—111no—
293#460—111no—
294#448—111no—
295#448—111no—
296#446—111no—
297#446—221no—
298#446—221no—
299#446C2×D1111yescharacteristic
300C8×Q8—111no—
301C8×Q8—111no—
302C4×SD16—111no—
303C4×SD16—111no—
304C4×SD16—111no—
305C4×SD16C2×D1111yescharacteristic
306#436—111no—
307#436C2×D1111yescharacteristic
308#435—221no—
309#435—221no—
310C8×D4—111no—
311C8×D4—111no—
312#431—111no—
313#423—111no—
314#423—221no—
315C2×C4⋊C8—111no—
316#408—221no—
317C4×M16—111no—
318C4×M16—221no—
319C2×C4×C8—111no—
320#334—111no—
321#334—111no—
322#334—111no—
323#334C2×D1111yescharacteristic
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326Q8⋊C8—111no—
327Q8⋊C8C2×D1111yescharacteristic
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8C2×D1111yescharacteristic
332#322—111no—
333#322—111no—
334C82—111no—
335C82C2×D1111yescharacteristic
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×C4×D411yescharacteristic
340C2×D11—21no—
341C2×D11—21no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11C4×SD1612yes—
346C4×C11—21no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11C2×#13111yescharacteristic
351C4×C11#56811yescharacteristic
352C4×C11C22×SD1611yescharacteristic
353C4×C11C2×#13511yescharacteristic
354Dic11—22no—
355Dic11—21no—
356Dic11—21no—
357Dic11—41no—
358Dic11—41no—
359Dic11C4×SD1612yes—
360C2×#41—221no—
361C22×Q8—111no—
362C2×SD16—111no—
363C2×SD16—111no—
364C2×SD16—111no—
365C2×SD16C4×D1111yescharacteristic
366#131—444no—
367C2×M16—21no—
368C2×M16—111no—
369C2×M16—111no—
370C2×M16—221no—
371C2×M16—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C22×C8—221no—
376C4⋊Q8—111no—
377#127—111no—
378#124—221no—
379#121—111no—
380#121—111no—
381#121—221no—
382C4×Q8—111no—
383C4×Q8—111no—
384C4×Q8—111no—
385C4×Q8—221no—
386C4×Q8—221no—
387C4×Q8C22×D1111yescharacteristic
388C4×D4—111no—
389C4×D4—221no—
390C4×D4C22×D1111yescharacteristic
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C42—111no—
394C2×C42—221no—
395#106—111no—
396#106—111no—
397#106—111no—
398#106C4×D1111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8C22×D1111yescharacteristic
410C4⋊C8C22×D1111yescharacteristic
411#103—111no—
412#103—111no—
413#103—111no—
414#103C4×D1111yescharacteristic
415#102—111no—
416#102—111no—
417#102—111no—
418#102C4×D1111yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425#97—21no—
426#97—111no—
427#97—111no—
428#97—221no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—221no—
433C4×C8—221no—
434C4×C8—221no—
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C2×C11—81no—
439C2×C11#293311yescharacteristic
440C2×C11C2×C4×SD1611yescharacteristic
441C2×C11#295611yescharacteristic
442D11—22no—
443D11—81no—
444#41—442no—
445#41—442no—
446C2×Q8—111no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—222no—
450C2×Q8—441no—
451C2×Q8C2×C4×D1111yescharacteristic
452C2×D4—111no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4C2×C4×D1111yescharacteristic
458C22×C4—21no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465SD16—41no—
466SD16—222no—
467SD16—222no—
468SD16—441no—
469M16—42no—
470M16—114no—
471M16—222no—
472M16—442no—
473M16—442no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—442no—
485C2×C8—442no—
486C2×C8—442no—
487C2×C8—442no—
488C2×C8C2×C4×D1111yescharacteristic
489C2×C8C2×C4×D1111yescharacteristic
490C2×C8D4×D1111yescharacteristic
491C2×C8D4×D1111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—111no—
494C4⋊C4—111no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4C2×C4×D1111yescharacteristic
501C4⋊C4C2×C4×D1111yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C42—21no—
507C42—111no—
508C42—111no—
509C42—111no—
510C42—221no—
511C42—221no—
512C42—221no—
513C42C23×D1111yescharacteristic
514C11#1799711yescharacteristic, complemented, Sylow
515C23—21no—
516C23—111no—
517C23—221no—
518Q8—21no—
519Q8—21no—
520Q8—112no—
521Q8—221no—
522Q8—442no—
523Q8—442no—
524D4—21no—
525D4—21no—
526D4—221no—
527D4—221no—
528D4—442no—
529D4—442no—
530D4—442no—
531D4—881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—111no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—441no—
548C2×C4—442no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—881no—
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C8—22no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—112no—
562C8—221no—
563C8—221no—
564C8—221no—
565C8—441no—
566C8—441no—
567C8—441no—
568C8SD16×D1112yes—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—112no—
573C22—221no—
574C22—221no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22C4×D4×D1111yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—112no—
584C4—221no—
585C4—221no—
586C4—222no—
587C4—441no—
588C4—441no—
589C4#1062327611yescharacteristic
590C4D11×#13111yescharacteristic
591C4C2×SD16×D1111yescharacteristic
592C4D11×#13511yescharacteristic
593C2—81no—
594C2—222no—
595C2—881no—
596C2#1307734511yescharacteristic
597C2C4×SD16×D1111yescharacteristic
598C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1590C2
socleC22×C11C2×C4×D4
prime radical#10623079C22
cosocleC42×C11C24
hypercenter#1590D11
hypocenterC11#17997
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #13077568C2semidirect
4. #13067503C2semidirect
5. #13067458C2semidirect
6. #13067457C2semidirect
7. #13067453C2semidirect
8. #13067450C2semidirect
9. #13067419C2semidirect
10. C8×#4314C2semidirect
11. #13067385C2semidirect
13. D11×Q8⋊C8C2semidirect
14. C8×#4313C2semidirect
15. C11×#1590C2semidirect
212. #4313SD16semidirect
220. #1590D11semidirect
270. Dic22#131semidirect
514. C11#17997semidirect

Maximal subgroups

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

subgroupindex
#130786452
#130775682
#130773612
#130675032
#130674582
#130674572
#130674532
#130674502
#130674192
C8×#43142
#130673852
#130670652
D11×Q8⋊C82
C8×#43132
C11×#15902
#1799711