Finite Group Databasebeta

← #14723734

Subgroups — #14723734

Order 2816.

626 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#13078636C211yesmaximal, characteristic
2#13077591C211yesmaximal, characteristic, complemented
3C8×#4339C211yesmaximal, characteristic, complemented
4#13067496C211yesmaximal, characteristic, complemented
5#13067489C211yesmaximal, characteristic, complemented
6#13067482C211yesmaximal, characteristic, complemented
7#13067475C211yesmaximal, characteristic, complemented
8#13067441C211yesmaximal, characteristic, complemented
9#13067436C211yesmaximal, characteristic, complemented
10#13067430C211yesmaximal, characteristic, complemented
11#13067430C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067051C211yesmaximal, characteristic, complemented
14#13067025C211yesmaximal, characteristic, complemented
15C11×#1452C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21#10622724—21no—
22C8×C22⋊D11—21no—
23C8×C22⋊D11—21no—
24C8×C22⋊D11—21no—
25#10622539C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622460C411yescharacteristic
28#10622458C411yescharacteristic
29#10622457C411yescharacteristic
30#10622442C411yescharacteristic
31#10622350C411yescharacteristic
32#10622347C411yescharacteristic
33#10622346C411yescharacteristic
34#10622336C411yescharacteristic
35C4×Dic44C2211yescharacteristic
36C4×D88C2211yescharacteristic
37C4×#4314C2211yescharacteristic
38C4×#4314C2211yescharacteristic
39#10622303—21no—
40#10622302—21no—
41#10622301C2211yescharacteristic
42C8×D44C2211yescharacteristic
43C8×D44C2211yescharacteristic
44C8×D44C2211yescharacteristic
45#10622298—21no—
46C4×C8×D11—21no—
47#10622292C2211yescharacteristic
48C8×Dic22C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C11×#322C2211yescharacteristic
54C11×#322C2211yescharacteristic
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622097C2211yescharacteristic
58#10622097C2211yescharacteristic
59#10622096C2211yescharacteristic
60#10622096C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622094C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C22×C8×C11D411yescharacteristic
69C22×C8×C11D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71#66983C2×C411yescharacteristic
72#66982—21no—
73C4×C22⋊D11—21no—
74C4×C22⋊D11—21no—
75C4×C22⋊D11—21no—
76#66979C2×C411yescharacteristic
77#66977C2×C411yescharacteristic
78C2×Dic44C2×C411yescharacteristic
79C2×D88C2×C411yescharacteristic
80C2×#4314C2×C411yescharacteristic
81C2×#4314C2×C411yescharacteristic
82C2×#4313—21no—
83C2×C8×D11—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86#66929—21no—
87#66928C2×C411yescharacteristic
88C4×D44C2×C411yescharacteristic
89C4×D44C2311yescharacteristic
90C4×D44C2311yescharacteristic
91#66925—21no—
92#66925—21no—
93C42×D11—21no—
94#66923C2×C411yescharacteristic
95C4×Dic22C2×C411yescharacteristic
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2×C411yescharacteristic
100C11×C4⋊C8C2×C411yescharacteristic
101C11×C22⋊C8—21no—
102C11×C22⋊C8C2×C411yescharacteristic
103C11×C22⋊C8C2×C411yescharacteristic
104C4×C8×C11D411yescharacteristic
105C4×C8×C11D411yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114#66885C2×C411yescharacteristic
115#66885C2×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#66882C2×C411yescharacteristic
123#66882C2×C411yescharacteristic
124#66881C2×C411yescharacteristic
125#66881C2×C411yescharacteristic
126#66880C2×C411yescharacteristic
127#66880C2×C411yescharacteristic
128#66880C2×C411yescharacteristic
129#66880C2×C411yescharacteristic
130#66879—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#17909—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C2×C22⋊D11—21no—
150#4339—22no—
151#4339—22no—
152C2×D44C22×C411yescharacteristic
153C2×D44C22×C411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22C22×C411yescharacteristic
159C2×Dic22C22×C411yescharacteristic
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—41no—
163C2×C8×C11—41no—
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C42×C11C22×C411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11#4111yescharacteristic
175C42×C11C2411yescharacteristic
176C22⋊Dic11—21no—
177C22⋊Dic11—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202Dic44—22no—
203D88—22no—
204#4314—22no—
205#4314—22no—
206#4313—42no—
207C8×D11—42no—
208C8×D11—42no—
209C8×D11—42no—
210#3102—111no—
211#2966—111no—
212C8×#41—111no—
213#1588—111no—
214#1587—111no—
215#1586—111no—
216#1585—111no—
217#1580—111no—
218#1579—111no—
219SD16⋊C8—111no—
220SD16⋊C8—111no—
221#1572—111no—
222#1488—111no—
223#1482—111no—
224#1452D1111yescharacteristic, complemented
225C23×C11C4×D411yescharacteristic
226C22×D11—21no—
227C22×D11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—41no—
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C22⋊D11—24no—
240C22⋊D11—42no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247D44—21no—
248D44—21no—
249D44—21no—
250D44#13112yes—
251C4×D11—24no—
252C4×D11—42no—
253C4×D11—41no—
254C4×D11—41no—
255C4×D11—41no—
256C4×D11—41no—
257Dic22—21no—
258Dic22—21no—
259Dic22—21no—
260Dic22#13112yes—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
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×D8—111no—
293#436—111no—
294#435—221no—
295C8×D4—111no—
296C8×D4—111no—
297C8×D4—111no—
298C8×D4—221no—
299C8×D4—221no—
300C8×D4—221no—
301#433—221no—
302#432—111no—
303#431—111no—
304#431—221no—
305#431C2×D1111yescharacteristic
306#431C2×D1111yescharacteristic
307#405—221no—
308C2×C4×C8—221no—
309C2×C4×C8C2×D1111yescharacteristic
310#335—111no—
311#335—111no—
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⋊C8—111no—
321D4⋊C8—111no—
322#322C2×D1111yescharacteristic
323#322C2×D1111yescharacteristic
324#322C2×D1111yescharacteristic
325#322C2×D1111yescharacteristic
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11C2×C4×D411yescharacteristic
330C2×D11—22no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11C2×#13111yescharacteristic
341C4×C11C2×#13111yescharacteristic
342C4×C11#57511yescharacteristic
343C4×C11#57511yescharacteristic
344Dic11—22no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C2×Q16—111no—
352C2×SD16—111no—
353C2×SD16—111no—
354C2×D8—111no—
355C2×M16—221no—
356C22×C8—221no—
357C22×C8—221no—
358C22×C8—221no—
359C22×C8D4411yescharacteristic
360C22×C8D4411yescharacteristic
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—111no—
372C4×D4—111no—
373C4×D4—221no—
374C4×D4—221no—
375C4×D4—221no—
376#117—111no—
377#117—221no—
378#117—221no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—111no—
382#107—111no—
383#106—111no—
384#106—111no—
385C4⋊C8—21no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8C4×D1111yescharacteristic
395C4⋊C8C4×D1111yescharacteristic
396#103—111no—
397#103—111no—
398#103—111no—
399#103—111no—
400#102—111no—
401#102—111no—
402#102—111no—
403#102—111no—
404C22⋊C8—21no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8C4×D1111yescharacteristic
412C22⋊C8C4×D1111yescharacteristic
413#97—221no—
414#97—221no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8D4411yescharacteristic
420C4×C8D4411yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C4×C8C22×D1111yescharacteristic
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11—41no—
428C2×C11#292911yescharacteristic
429C2×C11#294311yescharacteristic
430C2×C11#295511yescharacteristic
431D11—42no—
432D11—81no—
433#41—222no—
434#41—222no—
435C2×Q8—111no—
436C2×Q8—111no—
437C2×D4—111no—
438C2×D4—111no—
439C2×D4—221no—
440C2×D4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4C2×D4411yescharacteristic
447C22×C4#433911yescharacteristic
448Q16—222no—
449SD16—222no—
450SD16—222no—
451D8—222no—
452M16—442no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—41no—
456C2×C8—41no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—442no—
462C2×C8—442no—
463C2×C8—442no—
464C2×C8C2×C4×D1111yescharacteristic
465C2×C8C2×C4×D1111yescharacteristic
466C2×C8C2×C4×D1111yescharacteristic
467C2×C8C2×C4×D1111yescharacteristic
468C2×C8C2×D4411yescharacteristic
469C2×C8C2×D4411yescharacteristic
470C2×C8C2×D4411yescharacteristic
471C2×C8C2×D4411yescharacteristic
472C4⋊C4—111no—
473C4⋊C4—111no—
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—221no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42C2×C4×D1111yescharacteristic
495C42C2×D4411yescharacteristic
496C42#433911yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1790911yescharacteristic, complemented, Sylow
499C23—221no—
500C23—221no—
501C23C4×D4411yescharacteristic
502Q8—112no—
503Q8—221no—
504Q8—221no—
505Q8—221no—
506D4—112no—
507D4—224no—
508D4—221no—
509D4—221no—
510D4—221no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—224no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—442no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4C4×D4411yescharacteristic
530C2×C4C4×D4411yescharacteristic
531C2×C4C4×D4411yescharacteristic
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C22×D4411yescharacteristic
534C2×C4C2×#433911yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8—441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—222no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22C2×C4×D4411yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—222no—
564C4—441no—
565C4—441no—
566C4—441no—
567C4—441no—
568C4—441no—
569C4#1062327911yescharacteristic
570C4#1062327911yescharacteristic
571C4D11×#13111yescharacteristic
572C4D11×#13111yescharacteristic
573C2—41no—
574C2—442no—
575C2—881no—
576C2#1307731211yescharacteristic
577C2#1307741811yescharacteristic
578C2#1307752011yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1452C2
socleC22×C11C2×C4×D4
prime radical#10622347C4
cosocleC42×C11C24
hypercenter#1452D11
hypocenterC11#17909
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #1452

Complements

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

NH ≅ G/Ntype
2. #13077591C2semidirect
3. C8×#4339C2semidirect
4. #13067496C2semidirect
5. #13067489C2semidirect
6. #13067482C2semidirect
7. #13067475C2semidirect
8. #13067441C2semidirect
9. #13067436C2semidirect
10. #13067430C2semidirect
11. #13067430C2semidirect
12. #13067396C2semidirect
13. #13067051C2semidirect
14. #13067025C2semidirect
15. C11×#1452C2semidirect
224. #1452D11semidirect
498. C11#17909semidirect

Maximal subgroups

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

subgroupindex
#130786362
#130775912
C8×#43392
#130674962
#130674892
#130674822
#130674752
#130674412
#130674362
#130674302
#130673962
#130670512
#130670252
C11×#14522
#1790911