Finite Group Databasebeta

← #14826887

Subgroups — #14826887

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073047C211yesmaximal, characteristic
2#13071645C211yesmaximal, characteristic
3#13070026C211yesmaximal, characteristic, complemented
4#13070008C211yesmaximal, characteristic, complemented
5#13069815C211yesmaximal, characteristic
6#13069815C211yesmaximal, characteristic
7#13069379C211yesmaximal, characteristic, complemented
8#13069358C211yesmaximal, characteristic, complemented
9#13069230C211yesmaximal, characteristic
10#13069204C211yesmaximal, characteristic, complemented
11#13068881C211yesmaximal, characteristic, complemented
12#13068814C211yesmaximal, characteristic
13#13068710C211yesmaximal, characteristic
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1920C211yesmaximal, characteristic, complemented
16C2×#66950C2211yescharacteristic
17C2×#66945C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×#66880C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27#10622607—21no—
28#10622600C2211yescharacteristic
29#10622600C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622594—21no—
32C4⋊C4×Dic11C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622553—21no—
40C4×(C2×D11)⋊C4C2211yescharacteristic
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11—21no—
43#10622542C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622283—21no—
46#10622283—21no—
47#10622273—21no—
48#10622266—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66950—22no—
92#66950—22no—
93#66945—22no—
94#66945—41no—
95#66940—22no—
96#66940—41no—
97C11×#106—22no—
98C11×#95—21no—
99C11×#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109(C2×D11)⋊C8—22no—
110(C2×D11)⋊C8—41no—
111#66880—22no—
112#66880—22no—
113#66879—41no—
114#66874—22no—
115#66874—41no—
116#66872—22no—
117#66872—22no—
118#66871—41no—
119C4⋊(C11⋊C8)—22no—
120#27060—111nomaximal, Sylow
121C23×D11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22#4112yes—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4#4112yes—
162C11×C4⋊C4#4112yes—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—42no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—81no—
171(C2×D11)⋊C4—81no—
172C4⋊Dic11—24no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—42no—
180C4⋊Dic11—81no—
181C4⋊Dic11—81no—
182Dic11⋊C4—42no—
183Dic11⋊C4—81no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—42no—
187C4×Dic11—42no—
188C4×Dic11—81no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8#4112yes—
195#2497—111no—
196#2362—111no—
197#2072—111no—
198#2068—111no—
199#2035—111no—
200#2035—111no—
201#1948—111no—
202#1944—111no—
203#1924—111no—
204#1920—111no—
205#1920D1111yescharacteristic, complemented
206#1865—111no—
207#1854—111no—
208#1825—111no—
209#1763—111no—
210C23×C11C22×D411yescharacteristic
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11#13712yes—
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267Dic22—22no—
268Dic22—22no—
269Dic22—41no—
270Dic22—41no—
271C8×C11—41no—
272C8×C11—41no—
273C11⋊C8—22no—
274C11⋊C8—41no—
275C2×C22⋊Q8—111no—
276C2×C4×Q8—111no—
277C2×#117—111no—
278C2×#107—111no—
279C2×#106—111no—
280C2×#106—111no—
281C2×#106C2×D1111yescharacteristic
282C2×C4⋊C8—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×C22⋊C8—111no—
288C2×C22⋊C8—111no—
289C2×#97—111no—
290#400—221no—
291#396—221no—
292#391—111no—
293#389—111no—
294#389—111no—
295#389C2×D1111yescharacteristic
296#388—221no—
297#388—221no—
298#388—221no—
299#387—221no—
300#387—221no—
301#384—111no—
302#380—111no—
303#380—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—221no—
306C4×C4⋊C4C2×D1111yescharacteristic
307C4×C22⋊C4—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340C2×D1111yescharacteristic
314#340C2×D1111yescharacteristic
315#340C2×D1111yescharacteristic
316#336—111no—
317#336C2×D1111yescharacteristic
318C22×C11#52511yescharacteristic
319C22×C11#54611yescharacteristic
320C22×C11#54711yescharacteristic
321C22×C11C2×#13711yescharacteristic
322C22×C11#57511yescharacteristic
323C22×C11#57711yescharacteristic
324C22×C11#57711yescharacteristic
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C4×C11—22no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11#52911yescharacteristic
339C4×C11#53911yescharacteristic
340C4×C11#55311yescharacteristic
341C4×C11#55611yescharacteristic
342Dic11—41no—
343Dic11—42no—
344Dic11—41no—
345Dic11—41no—
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349C22×Q8—111no—
350C23×C4—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355C22⋊Q8—222no—
356C22⋊Q8—222no—
357C4×Q8—222no—
358C4×Q8—441no—
359#117—222no—
360#117—441no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—111no—
376C2×C22⋊C4—111no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C42—21no—
382C2×C42—111no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42C22×D1111yescharacteristic
387#107—441no—
388#106—22no—
389#106—222no—
390#106—222no—
391C4⋊C8—222no—
392#103—222no—
393#103—222no—
394#103—222no—
395#103—441no—
396C22⋊C8—222no—
397C22⋊C8—441no—
398#97—441no—
399#95—21no—
400#95—21no—
401#95—111no—
402#95—111no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410C2×C11#246611yescharacteristic
411C2×C11#311611yescharacteristic
412C2×C11#312611yescharacteristic
413C2×C11#332111yescharacteristic
414C2×C11#333111yescharacteristic
415C2×C11#334411yescharacteristic
416C2×C11#335011yescharacteristic
417D11—81no—
418C24—111no—
419C2×Q8—112no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—112no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—42no—
464C4⋊C4—224no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—442no—
472C4⋊C4—442no—
473C4⋊C4—881no—
474C4⋊C4—881no—
475C4⋊C4—881no—
476C4⋊C4#433912yes—
477C4⋊C4#434312yes—
478C22⋊C4—224no—
479C22⋊C4—222no—
480C22⋊C4—441no—
481C22⋊C4—442no—
482C22⋊C4—881no—
483C22⋊C4—881no—
484C42—21no—
485C42—21no—
486C42—42no—
487C42—221no—
488C42—221no—
489C42—442no—
490C42—442no—
491C42—881no—
492C11#2706011yescharacteristic, complemented, Sylow
493C23—221no—
494C23—221no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23C2×D4×D1111yescharacteristic
501Q8—222no—
502Q8—222no—
503Q8—441no—
504Q8—441no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—222no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4#6696812yes—
548C2×C4C2×#433911yescharacteristic
549C2×C4C2×#434311yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C2×C4#6704211yescharacteristic
553C2×C4#6704311yescharacteristic
554C8—41no—
555C8—41no—
556C8—222no—
557C8—441no—
558C22—441no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22—441no—
565C22#1062308111yescharacteristic
566C22#1062315811yescharacteristic
567C22#1062318611yescharacteristic
568C22C2×#6696811yescharacteristic
569C22#1062330111yescharacteristic
570C22#1062330411yescharacteristic
571C22#1062330911yescharacteristic
572C4—22no—
573C4—41no—
574C4—42no—
575C4—42no—
576C4—81no—
577C4—81no—
578C4—441no—
579C4—442no—
580C4—441no—
581C4—441no—
582C4—881no—
583C4—881no—
584C4—881no—
585C4#1062305911yescharacteristic
586C4#1062311511yescharacteristic
587C4#1062322611yescharacteristic
588C4#1062323811yescharacteristic
589C2—881no—
590C2#1307265911yescharacteristic
591C2#1307878011yescharacteristic
592C2#1307890911yescharacteristic
593C2#1308080711yescharacteristic
594C2#1308093411yescharacteristic
595C2#1308107511yescharacteristic
596C2#1308115411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1920C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1920D11
hypocenterC11#27060
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
3. #13070026C2semidirect
4. #13070008C2semidirect
7. #13069379C2semidirect
8. #13069358C2semidirect
10. #13069204C2semidirect
11. #13068881C2semidirect
14. #13068445C2semidirect
15. C11×#1920C2semidirect
205. #1920D11semidirect
492. C11#27060semidirect

Maximal subgroups

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

subgroupindex
#130730472
#130716452
#130700262
#130700082
#130698152
#130693792
#130693582
#130692302
#130692042
#130688812
#130688142
#130687102
#130684452
C11×#19202
#2706011