Finite Group Databasebeta

← #14826495

Subgroups — #14826495

Order 2816.

728 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#13073041C211yesmaximal, characteristic
2#13071623C211yesmaximal, characteristic
3#13070025C211yesmaximal, characteristic, complemented
4#13069996C211yesmaximal, characteristic, complemented
5#13069814C211yesmaximal, characteristic
6#13069814C211yesmaximal, characteristic
7#13069345C211yesmaximal, characteristic, complemented
8#13069221C211yesmaximal, characteristic
9#13069203C211yesmaximal, characteristic, complemented
10#13069194C211yesmaximal, characteristic, complemented
11#13068885C211yesmaximal, characteristic, complemented
12#13068810C211yesmaximal, characteristic
13#13068705C211yesmaximal, characteristic
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1948C211yesmaximal, characteristic, complemented
16C2×#66951—21no—
17C2×#66950C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622606—21no—
32#10622600C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622595—21no—
37#10622594—21no—
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C4×(C2×D11)⋊C4—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622541—21no—
46#10622541C2211yescharacteristic
47#10622281—21no—
48#10622266—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×(C2×D11)⋊C4D411yescharacteristic
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×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66951—44no—
92#66950—22no—
93#66950—22no—
94C4⋊C4×D11—22no—
95C4⋊C4×D11—41no—
96#66940—22no—
97#66940—41no—
98C11×#106—22no—
99C11×#106—22no—
100C11×C4⋊C8—22no—
101C11×#95—21no—
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(C2×D11)⋊C8—22no—
113(C2×D11)⋊C8—41no—
114#66881—41no—
115#66880—22no—
116#66880—41no—
117C8×Dic11—41no—
118#66874—22no—
119#66874—22no—
120#66872—22no—
121#27034—111nomaximal, Sylow
122C23×D11C2×D411yescharacteristic
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—81no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22#4112yes—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11#4112yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4#4112yes—
167C11×C4⋊C4#4112yes—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—81no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—41no—
173(C2×D11)⋊C4—42no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4SD1614yes—
176C4⋊Dic11—24no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—42no—
184C4⋊Dic11—81no—
185Dic11⋊C4—42no—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—42no—
191C4×Dic11—42no—
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#2496—111no—
199#2360—111no—
200#2072—111no—
201#2066—111no—
202#2035—111no—
203#2035—111no—
204#1948D1111yescharacteristic, complemented
205#1941—111no—
206#1923—111no—
207#1920—111no—
208#1919—111no—
209#1865—111no—
210#1853—111no—
211#1824—111no—
212C4×#103—111no—
213C23×C11C22×D411yescharacteristic
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—21no—
219C22×D11—21no—
220C22×D11C2×SD1612yes—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
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—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C2×SD1612yes—
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—22no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
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—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11C2×SD1612yes—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—84no—
271Dic22—22no—
272Dic22—22no—
273Dic22—41no—
274Dic22—41no—
275C8×C11—22no—
276C8×C11—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C2×#126—221no—
280C2×C22⋊Q8—111no—
281C2×C4×Q8—111no—
282C22×C4⋊C4—111no—
283C2×#106—111no—
284C2×#106—111no—
285C2×#106C2×D1111yescharacteristic
286C2×#106C2×D1111yescharacteristic
287C2×C4⋊C8C2×D1111yescharacteristic
288C2×#103—111no—
289C2×#103—111no—
290C2×#103—111no—
291C2×#103—111no—
292C2×C22⋊C8—111no—
293C2×C22⋊C8—111no—
294C2×C4×C8—111no—
295#400—221no—
296#397—221no—
297#391—111no—
298#389—111no—
299#389—111no—
300#389—111no—
301#389—221no—
302#387—221no—
303#387—221no—
304#385—221no—
305#384C2×D1111yescharacteristic
306#380—111no—
307#380—111no—
308C4×C4⋊C4—111no—
309C4×C4⋊C4C2×D1111yescharacteristic
310C4×C22⋊C4—111no—
311C4×C22⋊C4—221no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340C2×D1111yescharacteristic
319#340C2×D1111yescharacteristic
320#336—111no—
321#336—111no—
322C22×C11#52511yescharacteristic
323C22×C11#54611yescharacteristic
324C22×C11#54711yescharacteristic
325C22×C11C22×SD1611yescharacteristic
326C22×C11#57511yescharacteristic
327C22×C11#57711yescharacteristic
328C22×C11#57811yescharacteristic
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#52911yescharacteristic
343C4×C11#53911yescharacteristic
344C4×C11#55311yescharacteristic
345C4×C11#55611yescharacteristic
346Dic11—22no—
347Dic11—42no—
348Dic11—41no—
349Dic11—41no—
350Dic11—81no—
351Dic11—81no—
352Dic11—81no—
353C22×Q8—111no—
354C23×C4—111no—
355C23×C4—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360#126—444no—
361C22⋊Q8—222no—
362C22⋊Q8—222no—
363C4×Q8—222no—
364C4×Q8—441no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—441no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—111no—
383C2×C22⋊C4—111no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C42—21no—
388C2×C42—111no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392#106—22no—
393#106—22no—
394#106—222no—
395#106—441no—
396C4⋊C8—22no—
397#103—222no—
398#103—222no—
399#103—222no—
400#103—441no—
401C22⋊C8—222no—
402C22⋊C8—441no—
403C4×C8—441no—
404#95—21no—
405#95—111no—
406#95—111no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415C2×C11#246611yescharacteristic
416C2×C11#310311yescharacteristic
417C2×C11#312011yescharacteristic
418C2×C11#329811yescharacteristic
419C2×C11#331111yescharacteristic
420C2×C11#333511yescharacteristic
421C2×C11#335211yescharacteristic
422D11—42no—
423C24—111no—
424C2×Q8—112no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×Q8—221no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—442no—
448C22×C4—442no—
449C22×C4—881no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
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—
464C2×C8#433912yes—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—224no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—442no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—881no—
485C4⋊C4#434112yes—
486C4⋊C4#434312yes—
487C22⋊C4—114no—
488C22⋊C4—224no—
489C22⋊C4—441no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C42—21no—
493C42—21no—
494C42—81no—
495C42—221no—
496C42—221no—
497C42—442no—
498C42—442no—
499C11#2703411yescharacteristic, complemented, Sylow
500C23—112no—
501C23—221no—
502C23—221no—
503C23—221no—
504C23—221no—
505C23—221no—
506C23—221no—
507C23C2×D4×D1111yescharacteristic
508Q8—222no—
509Q8—222no—
510Q8—441no—
511Q8—441no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
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—112no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—222no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
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—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—884no—
555C2×C4SD16×D1112yes—
556C2×C4C2×#433911yescharacteristic
557C2×C4C2×#434111yescharacteristic
558C2×C4C2×#434311yescharacteristic
559C2×C4#6704011yescharacteristic
560C2×C4#41×D1111yescharacteristic
561C2×C4#6704211yescharacteristic
562C8—22no—
563C8—41no—
564C8—441no—
565C8—441no—
566C22—222no—
567C22—222no—
568C22—222no—
569C22—441no—
570C22—441no—
571C22—441no—
572C22—441no—
573C22#1062303811yescharacteristic
574C22#1062313711yescharacteristic
575C22#1062316111yescharacteristic
576C22C2×SD16×D1111yescharacteristic
577C22#1062329311yescharacteristic
578C22#1062330411yescharacteristic
579C22#1062331011yescharacteristic
580C4—22no—
581C4—42no—
582C4—42no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—222no—
587C4—441no—
588C4—442no—
589C4—441no—
590C4—881no—
591C4—881no—
592C4—881no—
593C4#1062309611yescharacteristic
594C4#1062311111yescharacteristic
595C4#1062322311yescharacteristic
596C4#1062326311yescharacteristic
597C2—442no—
598C2#1307265711yescharacteristic
599C2#1307864611yescharacteristic
600C2#1307882711yescharacteristic
601C2#1308047811yescharacteristic
602C2#1308064911yescharacteristic
603C2#1308096911yescharacteristic
604C2#1308118711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1948D11
hypocenterC11#27034
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #13070025C2semidirect
4. #13069996C2semidirect
7. #13069345C2semidirect
9. #13069203C2semidirect
10. #13069194C2semidirect
11. #13068885C2semidirect
14. #13068435C2semidirect
15. C11×#1948C2semidirect
204. #1948D11semidirect
499. C11#27034semidirect

Maximal subgroups

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

subgroupindex
#130730412
#130716232
#130700252
#130699962
#130698142
#130693452
#130692212
#130692032
#130691942
#130688852
#130688102
#130687052
#130684352
C11×#19482
#2703411