Finite Group Databasebeta

← #14822450

Subgroups — #14822450

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073139C211yesmaximal, characteristic, complemented
2#13071686C211yesmaximal, characteristic
3#13070004C211yesmaximal, characteristic
4#13069855C211yesmaximal, characteristic
5#13069855C211yesmaximal, characteristic
6#13069293C211yesmaximal, characteristic, complemented
7#13069255C211yesmaximal, characteristic, complemented
8#13069193C211yesmaximal, characteristic, complemented
9#13069185C211yesmaximal, characteristic, complemented
10#13069176C211yesmaximal, characteristic, complemented
11#13068887C211yesmaximal, characteristic, complemented
12#13068879C211yesmaximal, characteristic
13#13068618C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic
15C11×#2071C211yesmaximal, characteristic
16C2×#66989C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C11×#390C2211yescharacteristic
22C11×#384C2211yescharacteristic
23C2×#66896C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622598C2211yescharacteristic
30#10622597—21no—
31#10622596—21no—
32#10622591—21no—
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622587C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622585—21no—
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622559—21no—
43#10622558—21no—
44#10622557—21no—
45C22⋊C4×Dic11—21no—
46C4×Dic11⋊C4C2211yescharacteristic
47#10622541C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75#66989—22no—
76#66989—22no—
77D4×Dic11—22no—
78D4×Dic11—41no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C4×Dic22—22no—
97C4×Dic22—41no—
98C11×#102—22no—
99C11×#102—22no—
100#66896—22no—
101#66896—41no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112#66881—22no—
113#66880—22no—
114#66880—41no—
115C8×Dic11—41no—
116#66874—22no—
117#66874—22no—
118#66871—22no—
119C4⋊(C11⋊C8)—41no—
120#26763—111nomaximal, Sylow
121C24×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11—81no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22#4112yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—81no—
164C11×C4⋊C4—81no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—81no—
167C42×C11—21no—
168C42×C11—21no—
169C22⋊Dic11—24no—
170C22⋊Dic11—24no—
171C22⋊Dic11—42no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—81no—
177C4⋊Dic11#4112yes—
178C4⋊Dic11#4112yes—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183Dic11⋊C4—81no—
184Dic11⋊C4—81no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—42no—
190C4×Dic11—81no—
191C4×Dic11—81no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198#2507—111no—
199#2367—111no—
200#2071D1111yescharacteristic
201#2067—111no—
202#2042—111no—
203#2042—111no—
204#1933—111no—
205#1928—111no—
206#1919—111no—
207#1918—111no—
208#1916—111no—
209#1865—111no—
210#1864—111no—
211#1803—111no—
212C4×#102—111no—
213C23×C11—22no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11C22×D411yescharacteristic
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—41no—
224D4×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11#13512yes—
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C112−1+411yescharacteristic
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—22no—
251C2×Dic11—21no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—84no—
270C2×Dic11#13712yes—
271Dic22—22no—
272Dic22—22no—
273Dic22—41no—
274Dic22—41no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C2×#124—111no—
280C2×C4×Q8—111no—
281C2×C4×D4—111no—
282C2×#107—111no—
283C2×#106—111no—
284C2×C4⋊C8—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103—111no—
288C2×#103—111no—
289C2×#102—111no—
290C2×#102—111no—
291C2×#102C2×D1111yescharacteristic
292C2×#102C2×D1111yescharacteristic
293C2×C4×C8—111no—
294#398—221no—
295#398—221no—
296#391—111no—
297#390C2×D1111yescharacteristic
298#389—111no—
299#389—111no—
300#389—111no—
301#389—111no—
302#389—221no—
303#388—221no—
304#388—221no—
305#387—221no—
306#385—221no—
307#384C2×D1111yescharacteristic
308C4×C4⋊C4—111no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—111no—
311C4×C22⋊C4—221no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340C2×D1111yescharacteristic
317#340C2×D1111yescharacteristic
318#336—111no—
319#336—111no—
320#336—111no—
321#336C2×D1111yescharacteristic
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11#52511yescharacteristic
330C22×C11#54611yescharacteristic
331C22×C11#54811yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C22×C11#57611yescharacteristic
335C22×C11#57711yescharacteristic
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#52911yescharacteristic
342C4×C11#53911yescharacteristic
343C4×C11#55211yescharacteristic
344C4×C11#55311yescharacteristic
345Dic11—22no—
346Dic11—42no—
347Dic11—41no—
348Dic11—41no—
349Dic11—42no—
350Dic11—41no—
351Dic11—42no—
352Dic11—81no—
353C22×Q8—111no—
354C22×D4C22×D1111yescharacteristic
355C23×C4—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360#124—222no—
361#124—222no—
362C4×Q8—222no—
363C4×Q8—441no—
364C4×D4—222no—
365C4×D4—441no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—221no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392#107—222no—
393#106—222no—
394C4⋊C8—441no—
395#103—222no—
396#103—222no—
397#103—222no—
398#103—441no—
399#102—22no—
400#102—22no—
401#102—222no—
402#102—441no—
403C4×C8—441no—
404#95—111no—
405#95—111no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414C2×C11—82no—
415C2×C11#246011yescharacteristic
416C2×C11#310711yescharacteristic
417C2×C11#311911yescharacteristic
418C2×C11#330111yescharacteristic
419C2×C11#331411yescharacteristic
420C2×C11#336111yescharacteristic
421C2×C11#336911yescharacteristic
422C24—21no—
423C2×Q8—112no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4#434112yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4—881no—
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1111yescharacteristic
451C22×C4C23×D1111yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—112no—
473C4⋊C4—112no—
474C4⋊C4—222no—
475C4⋊C4—222no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—442no—
481C4⋊C4—442no—
482C4⋊C4—881no—
483C4⋊C4—881no—
484C4⋊C4—881no—
485C22⋊C4—42no—
486C22⋊C4—81no—
487C22⋊C4—224no—
488C22⋊C4—224no—
489C22⋊C4—442no—
490C42—21no—
491C42—21no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42—442no—
497C42—881no—
498C42—881no—
499C11#2676311yescharacteristic, complemented, Sylow
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C2×D4×D1111yescharacteristic
508Q8—222no—
509Q8—222no—
510Q8—441no—
511Q8—441no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—112no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—222no—
542C2×C4—221no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—884no—
555C2×C4#6696912yes—
556C2×C4C2×#434111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C2×C4#6704211yescharacteristic
561C2×C4#6704311yescharacteristic
562C8—41no—
563C8—41no—
564C8—441no—
565C8—441no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#1062313711yescharacteristic
574C22#1062318511yescharacteristic
575C22#1062320811yescharacteristic
576C22#1062328811yescharacteristic
577C22C2×#6696911yescharacteristic
578C22#1062330611yescharacteristic
579C22D11×#13711yescharacteristic
580C4—22no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—222no—
586C4—441no—
587C4—442no—
588C4—441no—
589C4—442no—
590C4—442no—
591C4—441no—
592C4—881no—
593C4#1062318011yescharacteristic
594C4#1062319611yescharacteristic
595C4#1062323911yescharacteristic
596C4#1062324011yescharacteristic
597C2—82no—
598C2#1307256911yescharacteristic
599C2#1307868411yescharacteristic
600C2#1307881211yescharacteristic
601C2#1308051611yescharacteristic
602C2#1308070011yescharacteristic
603C2#1308128111yescharacteristic
604C2#1308135311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2071C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2071D11
hypocenterC11#26763
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
1. #13073139C2semidirect
6. #13069293C2semidirect
7. #13069255C2semidirect
8. #13069193C2semidirect
9. #13069185C2semidirect
10. #13069176C2semidirect
11. #13068887C2semidirect
13. #13068618C2semidirect
499. C11#26763semidirect

Maximal subgroups

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

subgroupindex
#130731392
#130716862
#130700042
#130698552
#130692932
#130692552
#130691932
#130691852
#130691762
#130688872
#130688792
#130686182
#102×Dic112
C11×#20712
#2676311