Finite Group Databasebeta

← #14723344

Subgroups — #14723344

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077581C211yesmaximal, characteristic, complemented
2C8×#4343C211yesmaximal, characteristic, complemented
3C4×#66972C211yesmaximal, characteristic
4#13067494C211yesmaximal, characteristic, complemented
5#13067491C211yesmaximal, characteristic, complemented
6#13067488C211yesmaximal, characteristic, complemented
7#13067482C211yesmaximal, characteristic, complemented
8#13067479C211yesmaximal, characteristic, complemented
9#13067476C211yesmaximal, characteristic, complemented
10#13067471C211yesmaximal, characteristic, complemented
11#13067361C211yesmaximal, characteristic, complemented
12#13066997C211yesmaximal, characteristic, complemented
13#13066997C211yesmaximal, characteristic, complemented
14D11×#322C211yesmaximal, characteristic, complemented
15C11×#1587C211yesmaximal, characteristic, complemented
16C2×#66972C411yescharacteristic
17C4×#4343C2211yescharacteristic
18C4×#4343C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22Q16×Dic11C411yescharacteristic
23C4×#4325C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622493C411yescharacteristic
28#10622485C411yescharacteristic
29#10622451C2211yescharacteristic
30#10622449—21no—
31#10622447—21no—
32#10622447C2211yescharacteristic
33#10622446—21no—
34#10622446—21no—
35#10622446C2211yescharacteristic
36#10622446C2211yescharacteristic
37#10622417C411yescharacteristic
38#10622417C411yescharacteristic
39#10622401C411yescharacteristic
40#10622401C411yescharacteristic
41#10622320—21no—
42#10622319—21no—
43C4×D88C2211yescharacteristic
44#10622301C2211yescharacteristic
45C8×D44—21no—
46C8×D44C2211yescharacteristic
47C4×C8×D11—21no—
48C4×C8×D11C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×#4343C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76#66972—24no—
77C2×D88C2×C411yescharacteristic
78C2×#4313—21no—
79C2×#4313—21no—
80C2×C8×D11—21no—
81C2×C8×D11—21no—
82C2×C8×D11—21no—
83C2×C8×D11C2×C411yescharacteristic
84C2×C8×D11C2×C411yescharacteristic
85C2×C8×D11D411yescharacteristic
86C2×C8×D11D411yescharacteristic
87#66946—21no—
88#66946—21no—
89#66946C2×C411yescharacteristic
90#66946C2×C411yescharacteristic
91#66945—21no—
92#66945—21no—
93#66945C2×C411yescharacteristic
94#66945C2×C411yescharacteristic
95C4×D44—21no—
96C4×D44—21no—
97C4×D44C2311yescharacteristic
98C4×D44C2311yescharacteristic
99C42×D11—21no—
100C42×D11—21no—
101C42×D11C2311yescharacteristic
102C11×#107C2×C411yescharacteristic
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#103C2×C411yescharacteristic
109C11×#97—21no—
110C4×C8×C11—21no—
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899C2×C411yescharacteristic
115#66899C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124#66882C2×C411yescharacteristic
125C8×Dic11—21no—
126C8×Dic11—21no—
127C8×Dic11—21no—
128C8×Dic11C2×C411yescharacteristic
129C8×Dic11C2×C411yescharacteristic
130C8×Dic11D411yescharacteristic
131C8×Dic11D411yescharacteristic
132#66873C2×C411yescharacteristic
133#66873C2×C411yescharacteristic
134#66872C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17868—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148#4343—22no—
149#4343—22no—
150#4343—22no—
151#4343M1614yescomplemented
152C2×D44—21no—
153C2×D44—21no—
154C2×D44C22×C411yescharacteristic
155C2×D44C22×C411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11C22×C411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11#4111yescharacteristic
165C11×Q16—22no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C42×C11—21no—
178C42×C11—21no—
179C42×C11C2411yescharacteristic
180#4325—22no—
181#4325—22no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206D88—22no—
207#4313—42no—
208#4313—42no—
209C8×D11—24no—
210C8×D11—22no—
211C8×D11—22no—
212C8×D11—41no—
213C8×D11—41no—
214C8×D11—42no—
215C8×D11—42no—
216#2965—111no—
217C8×#41—111no—
218C4×#135—111no—
219#1588—111no—
220#1588—111no—
221#1587—111no—
222#1587D1111yescharacteristic, complemented
223#1586—111no—
224#1586—111no—
225#1585—111no—
226#1585—111no—
227#1564—111no—
228#1476—111no—
229#1476—111no—
230C2×#322—111no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11C4×D411yescharacteristic
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—21no—
237Q8×C11C2×M1612yes—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11C4×D411yescharacteristic
248C2×Dic11C4×D411yescharacteristic
249C2×Dic11C4×D411yescharacteristic
250D44—24no—
251D44—21no—
252D44—21no—
253D44—21no—
254D44—42no—
255D44C2×M1612yes—
256C4×D11—21no—
257C4×D11—21no—
258C4×D11—24no—
259C4×D11—22no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—42no—
265C4×D11—42no—
266C4×D11—42no—
267C4×D11C2×M1612yes—
268C4×D11#13112yes—
269C8×C11—22no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—22no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C2×#135—111no—
284C4×#41—111no—
285C4×#41—111no—
286#446—111no—
287#446C2×D1111yescharacteristic
288C8×Q8—111no—
289C8×Q8C2×D1111yescharacteristic
290C4×Q16—111no—
291C4×Q16C2×D1111yescharacteristic
292C4×SD16—111no—
293C4×SD16—111no—
294C4×SD16—111no—
295C4×SD16—111no—
296C4×D8—111no—
297C4×D8—111no—
298#436—111no—
299#436—111no—
300#435—221no—
301#435—221no—
302C8×D4—111no—
303C8×D4—111no—
304C8×D4—221no—
305C8×D4—221no—
306#431—111no—
307#431—111no—
308#431—221no—
309#431—221no—
310#427—111no—
311#416—111no—
312#416—111no—
313C4×M16—221no—
314C2×C4×C8—111no—
315C2×C4×C8—111no—
316C2×C4×C8—111no—
317C2×C4×C8—221no—
318#335—111no—
319#335—111no—
320#334—111no—
321#334C2×D1111yescharacteristic
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8C2×D1111yescharacteristic
325Q8⋊C8C2×D1111yescharacteristic
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330#322—111no—
331#322—111no—
332#322—111no—
333#322C2×D1111yescharacteristic
334C22×C11C2×C4×D411yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—22no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11#43512yes—
344C4×C11—22no—
345C4×C11—21no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11C22×M1611yescharacteristic
350C4×C11C2×#13111yescharacteristic
351C4×C11#57511yescharacteristic
352C4×C11#57511yescharacteristic
353Dic11—21no—
354Dic11—41no—
355Dic11—41no—
356Dic11#43512yes—
357Dic11#44312yes—
358C2×#41—111no—
359C2×#41—111no—
360#135—224no—
361C2×Q16C4×D1111yescharacteristic
362C2×SD16—111no—
363C2×SD16—111no—
364C2×D8—111no—
365C2×M16—221no—
366C2×M16—221no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C4×Q8—111no—
375C4×Q8—111no—
376C4×Q8C22×D1111yescharacteristic
377C4×Q8C22×D1111yescharacteristic
378C4×D4—111no—
379C4×D4—111no—
380C4×D4—111no—
381C4×D4—111no—
382C4×D4—221no—
383C4×D4—221no—
384C4×D4—221no—
385C4×D4—221no—
386#117—111no—
387#117—111no—
388#117—221no—
389#117—221no—
390C2×C42—111no—
391C2×C42—221no—
392C2×C42—221no—
393#107—111no—
394#107C4×D1111yescharacteristic
395#106—111no—
396#106—111no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8C22×D1111yescharacteristic
404C4⋊C8C22×D1111yescharacteristic
405#103—111no—
406#103—111no—
407#103C4×D1111yescharacteristic
408#103C4×D1111yescharacteristic
409#102—111no—
410#102—111no—
411#102—111no—
412#102—111no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—21no—
420#97—221no—
421C4×C8—21no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—221no—
430C4×C8—221no—
431C4×C8—221no—
432C4×C8—221no—
433C4×C8C22×D1111yescharacteristic
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C2×C11C2×#43511yescharacteristic
437C2×C11#294311yescharacteristic
438C2×C11C2×#44311yescharacteristic
439D11—22no—
440D11—42no—
441D11—81no—
442#41—114no—
443#41—222no—
444#41—222no—
445#41—222no—
446C2×Q8C2×C4×D1111yescharacteristic
447C2×Q8C2×C4×D1111yescharacteristic
448C2×D4—111no—
449C2×D4—111no—
450C2×D4—221no—
451C2×D4—221no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461Q16—22no—
462SD16—222no—
463SD16—222no—
464D8—222no—
465M16—442no—
466M16—442no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—224no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—441no—
481C2×C8—441no—
482C2×C8—442no—
483C2×C8—442no—
484C2×C8C2×C4×D1111yescharacteristic
485C2×C8C2×C4×D1111yescharacteristic
486C2×C8D4×D1111yescharacteristic
487C2×C8D4×D1111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—111no—
491C4⋊C4—111no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4C2×C4×D1111yescharacteristic
495C4⋊C4C2×C4×D1111yescharacteristic
496C22⋊C4—221no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C42—21no—
503C42—21no—
504C42—111no—
505C42—111no—
506C42—111no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42C23×D1111yescharacteristic
512C11#1786811yescharacteristic, complemented, Sylow
513C23—111no—
514C23—221no—
515C23—221no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8M16×D1112yes—
520D4—112no—
521D4—224no—
522D4—221no—
523D4—221no—
524D4—221no—
525D4—442no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—111no—
531C2×C4—111no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—111no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4C22×C4×D1111yescharacteristic
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C8—22no—
552C8—21no—
553C8—21no—
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—222no—
559C8—221no—
560C8—221no—
561C8—221no—
562C8—221no—
563C8—441no—
564C8—441no—
565C22—112no—
566C22—221no—
567C22—221no—
568C22—222no—
569C22—441no—
570C22—441no—
571C22—441no—
572C22—441no—
573C22—441no—
574C22C4×D4×D1111yescharacteristic
575C4—22no—
576C4—21no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—112no—
581C4—112no—
582C4—221no—
583C4—441no—
584C4—441no—
585C4C2×M16×D1111yescharacteristic
586C4D11×#13111yescharacteristic
587C4#1062330811yescharacteristic
588C4#1062330811yescharacteristic
589C2—222no—
590C2—442no—
591C2—881no—
592C2D11×#43511yescharacteristic
593C2#1307741511yescharacteristic
594C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1587C2
socleC22×C11C2×C4×D4
prime radicalC2×#66972C4
cosocleC42×C11C24
hypercenter#1587D11
hypocenterC11#17868
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
1. #13077581C2semidirect
2. C8×#4343C2semidirect
4. #13067494C2semidirect
5. #13067491C2semidirect
6. #13067488C2semidirect
7. #13067482C2semidirect
8. #13067479C2semidirect
9. #13067476C2semidirect
10. #13067471C2semidirect
11. #13067361C2semidirect
12. #13066997C2semidirect
13. #13066997C2semidirect
14. D11×#322C2semidirect
15. C11×#1587C2semidirect
151. #4343M16semidirect
222. #1587D11semidirect
512. C11#17868semidirect

Maximal subgroups

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

subgroupindex
#130775812
C8×#43432
C4×#669722
#130674942
#130674912
#130674882
#130674822
#130674792
#130674762
#130674712
#130673612
#130669972
D11×#3222
C11×#15872
#1786811