Finite Group Databasebeta

← #14723342

Subgroups — #14723342

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#13077579C211yesmaximal, characteristic, complemented
2C8×#4341C211yesmaximal, characteristic, complemented
3C4×#66965C211yesmaximal, characteristic
4#13067497C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067489C211yesmaximal, characteristic, complemented
7#13067486C211yesmaximal, characteristic, complemented
8#13067481C211yesmaximal, characteristic, complemented
9#13067473C211yesmaximal, characteristic, complemented
10#13067470C211yesmaximal, characteristic, complemented
11#13067361C211yesmaximal, characteristic, complemented
12#13066995C211yesmaximal, characteristic, complemented
13#13066995C211yesmaximal, characteristic, complemented
14D11×#322C211yesmaximal, characteristic, complemented
15C11×#1586C211yesmaximal, characteristic, complemented
16C2×#66965C411yescharacteristic
17C4×#4341C2211yescharacteristic
18C4×#4341C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C11×#436C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22D8×Dic11C411yescharacteristic
23#10622740—21no—
24M16×Dic11—21no—
25C8×C22⋊D11—21no—
26C2×C8×Dic11—21no—
27C4×#4324C2211yescharacteristic
28C4×#4324C2211yescharacteristic
29#10622625C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622493C411yescharacteristic
32#10622486C411yescharacteristic
33#10622446C2211yescharacteristic
34#10622446C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622385C411yescharacteristic
38#10622385C411yescharacteristic
39#10622371C411yescharacteristic
40#10622371C411yescharacteristic
41#10622341—21no—
42(C22⋊D11)⋊C8—21no—
43#10622331—21no—
44#10622331—21no—
45C4×Dic44C2211yescharacteristic
46C4×C8×D11C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4341C2×C411yescharacteristic
68C2×#4341C2×C411yescharacteristic
69C2×C11×D8C2×C411yescharacteristic
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74D4×Dic11C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C4×C22⋊D11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84#66965—24no—
85C2×Dic44C2×C411yescharacteristic
86C2×C8×D11—21no—
87C2×C8×D11C2×C411yescharacteristic
88C2×C8×D11C2×C411yescharacteristic
89C2×C8×D11D411yescharacteristic
90C2×C8×D11D411yescharacteristic
91#66945C2×C411yescharacteristic
92#66945C2×C411yescharacteristic
93#66940C2×C411yescharacteristic
94#66940C2×C411yescharacteristic
95(C22⋊D11)⋊C4—21no—
96(C22⋊D11)⋊C4—21no—
97#66930—21no—
98#66930—21no—
99C42×D11C2311yescharacteristic
100C4×Dic22C2311yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×#107C2×C411yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118#66882C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66879—21no—
122#66879—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127C8×Dic11—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11—21no—
132C8×Dic11C2×C411yescharacteristic
133C8×Dic11C2×C411yescharacteristic
134C8×Dic11D411yescharacteristic
135C8×Dic11D411yescharacteristic
136#66874C2×C411yescharacteristic
137#66874C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139#66872C2×C411yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17868—111nomaximal, Sylow
146C2×D4×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156#4341—22no—
157#4341—22no—
158#4341—22no—
159#4341M1614yescomplemented
160C2×C4×D11C22×C411yescharacteristic
161C2×C4×D11C2×D411yescharacteristic
162C2×C4×D11#4111yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C2×Dic22C22×C411yescharacteristic
165C11×D8—22no—
166C11×M16—42no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—42no—
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181C22⋊Dic11—21no—
182#4324—22no—
183#4324—22no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11C22×C411yescharacteristic
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11#4111yescharacteristic
201#4318—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210Dic44—22no—
211C8×D11—24no—
212C8×D11—22no—
213C8×D11—22no—
214C8×D11—41no—
215C8×D11—41no—
216#2965—111no—
217C8×#41—111no—
218C4×#135—111no—
219#1588—111no—
220#1588—111no—
221#1587—111no—
222#1587—111no—
223#1586—111no—
224#1586D1111yescharacteristic, complemented
225#1585—111no—
226#1585—111no—
227#1564—111no—
228#1476—111no—
229#1476—111no—
230C2×#322—111no—
231C23×C11—21no—
232C23×C11—21no—
233C22×D11C4×D411yescharacteristic
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11C2×M1612yes—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—24no—
248C22⋊D11—42no—
249C2×Dic11—21no—
250C2×Dic11—24no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11C4×D411yescharacteristic
258C2×Dic11C4×D411yescharacteristic
259C2×Dic11C4×D411yescharacteristic
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—22no—
263C4×D11C2×M1612yes—
264C4×D11#13112yes—
265Dic22—21no—
266Dic22—21no—
267Dic22—21no—
268Dic22C2×M1612yes—
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#446—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C4×Q16—111no—
291C4×Q16—111no—
292C4×SD16—111no—
293C4×SD16—111no—
294C4×SD16—111no—
295C4×SD16—111no—
296C4×D8—111no—
297C4×D8C2×D1111yescharacteristic
298#436—111no—
299#436C2×D1111yescharacteristic
300#435—221no—
301#435—221no—
302C8×D4—111no—
303C8×D4—221no—
304C8×D4—221no—
305C8×D4C2×D1111yescharacteristic
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⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8C2×D1111yescharacteristic
329D4⋊C8C2×D1111yescharacteristic
330#322—111no—
331#322—111no—
332#322—111no—
333#322C2×D1111yescharacteristic
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11C2×C4×D411yescharacteristic
341C2×D11—21no—
342C2×D11—21no—
343C2×D11#43512yes—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11C22×M1611yescharacteristic
348C4×C11C2×#13111yescharacteristic
349C4×C11#57511yescharacteristic
350C4×C11#57511yescharacteristic
351Dic11—22no—
352Dic11—21no—
353Dic11—41no—
354Dic11—41no—
355Dic11—41no—
356Dic11#43512yes—
357Dic11#44312yes—
358C2×#41—111no—
359C2×#41—111no—
360#135—224no—
361C2×Q16—111no—
362C2×SD16—111no—
363C2×SD16—111no—
364C2×D8C4×D1111yescharacteristic
365C2×M16—21no—
366C2×M16—221no—
367C22×C8—21no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—221no—
373C22×C8—221no—
374C4×Q8—111no—
375C4×Q8—111no—
376C4×Q8—111no—
377C4×Q8—111no—
378C4×D4—111no—
379C4×D4—111no—
380C4×D4—221no—
381C4×D4—221no—
382C4×D4—221no—
383C4×D4—221no—
384C4×D4C22×D1111yescharacteristic
385C4×D4C22×D1111yescharacteristic
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—111no—
398C4⋊C8—111no—
399C4⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8C22×D1111yescharacteristic
404C4⋊C8C22×D1111yescharacteristic
405#103—111no—
406#103—111no—
407#103—111no—
408#103—111no—
409#102—111no—
410#102—111no—
411#102C4×D1111yescharacteristic
412#102C4×D1111yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—221no—
420#97—221no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—221no—
429C4×C8—221no—
430C4×C8—221no—
431C4×C8—221no—
432C4×C8—221no—
433C4×C8C22×D1111yescharacteristic
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C2×C11—42no—
437C2×C11—81no—
438C2×C11C2×#43511yescharacteristic
439C2×C11#294311yescharacteristic
440C2×C11C2×#44311yescharacteristic
441D11—22no—
442#41—114no—
443#41—222no—
444#41—222no—
445#41—222no—
446C2×Q8—111no—
447C2×Q8—111no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4C2×C4×D1111yescharacteristic
451C2×D4C2×C4×D1111yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461Q16—222no—
462SD16—222no—
463SD16—222no—
464D8—22no—
465M16—42no—
466M16—442no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—42no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—224no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—441no—
482C2×C8—441no—
483C2×C8—442no—
484C2×C8C2×C4×D1111yescharacteristic
485C2×C8C2×C4×D1111yescharacteristic
486C2×C8D4×D1111yescharacteristic
487C2×C8D4×D1111yescharacteristic
488C4⋊C4—111no—
489C4⋊C4—111no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4C2×C4×D1111yescharacteristic
495C4⋊C4C2×C4×D1111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C42—111no—
503C42—111no—
504C42—111no—
505C42—221no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42C23×D1111yescharacteristic
512C11#1786811yescharacteristic, complemented, Sylow
513C23—21no—
514C23—21no—
515C23—111no—
516Q8—112no—
517Q8—221no—
518Q8—221no—
519Q8—221no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—224no—
524D4—442no—
525D4M16×D1112yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—111no—
533C2×C4—111no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—111no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
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—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—112no—
572C22—221no—
573C22—221no—
574C22C4×D4×D1111yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—112no—
579C4—112no—
580C4—222no—
581C4—221no—
582C4—441no—
583C4—441no—
584C4—441no—
585C4C2×M16×D1111yescharacteristic
586C4D11×#13111yescharacteristic
587C4#1062330411yescharacteristic
588C4#1062330411yescharacteristic
589C2—42no—
590C2—81no—
591C2—222no—
592C2D11×#43511yescharacteristic
593C2#1307741311yescharacteristic
594C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1586C2
socleC22×C11C2×C4×D4
prime radicalC2×#66965C4
cosocleC42×C11C24
hypercenter#1586D11
hypocenterC11#17868
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
1. #13077579C2semidirect
2. C8×#4341C2semidirect
4. #13067497C2semidirect
5. #13067492C2semidirect
6. #13067489C2semidirect
7. #13067486C2semidirect
8. #13067481C2semidirect
9. #13067473C2semidirect
10. #13067470C2semidirect
11. #13067361C2semidirect
12. #13066995C2semidirect
13. #13066995C2semidirect
14. D11×#322C2semidirect
15. C11×#1586C2semidirect
159. #4341M16semidirect
224. #1586D11semidirect
512. C11#17868semidirect

Maximal subgroups

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

subgroupindex
#130775792
C8×#43412
C4×#669652
#130674972
#130674922
#130674892
#130674862
#130674812
#130674732
#130674702
#130673612
#130669952
D11×#3222
C11×#15862
#1786811