Finite Group Databasebeta

← #14814539

Subgroups — #14814539

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072045C211yesmaximal, characteristic
2#13070178C211yesmaximal, characteristic, complemented
3#13070052C211yesmaximal, characteristic, complemented
4#13070025C211yesmaximal, characteristic, complemented
5#13069819C211yesmaximal, characteristic, complemented
6#13069250C211yesmaximal, characteristic, complemented
7#13069187C211yesmaximal, characteristic, complemented
8#13069037C211yesmaximal, characteristic, complemented
9#13068928C211yesmaximal, characteristic, complemented
10#13068928C211yesmaximal, characteristic, complemented
11#13068909C211yesmaximal, characteristic
12#13068813C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14#13068332C211yesmaximal, characteristic, complemented
15C11×#2354C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#390—21no—
24C11×#388—21no—
25C11×#388—21no—
26C11×#384C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C4×C11×C4⋊C4—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31#10622835—21no—
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622585—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622565—21no—
44#10622558—21no—
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C11×#117—22no—
66C11×#117—22no—
67C11×#117—41no—
68C11×#117—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90#66979—22no—
91#66979—41no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—22no—
96#66977—22no—
97#66977—22no—
98#66977—41no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—41no—
105C22×C11⋊C8—41no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118C22⋊(C11⋊C8)—41no—
119C22⋊(C11⋊C8)—41no—
120#66874—22no—
121#66874—41no—
122#66874—41no—
123#66874—41no—
124#66872—41no—
125#66871—22no—
126#26211—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D411yescharacteristic
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4#4112yes—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—81no—
179C11×C22⋊C4—81no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—42no—
183C42×C11—42no—
184C42×C11—42no—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198C4×Dic11—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—44no—
212#2415—111no—
213#2354D1111yescharacteristic
214#2100—111no—
215#2077—111no—
216#2072—111no—
217#2036—111no—
218#1927—111no—
219#1918—111no—
220#1892—111no—
221#1873—111no—
222#1873—111no—
223#1869—111no—
224#1854—111no—
225#1825—111no—
226#1735—111no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11#12312yes—
241C23×C11C22×D411yescharacteristic
242D4×C11—44no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11#12312yes—
274C2×C4×C11#13512yes—
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×Dic11—22no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296Dic22—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C23×C8—111no—
302C2×C22⋊Q8—111no—
303C2×C22⋊Q8—111no—
304C2×C4×D4C2×D1111yescharacteristic
305C2×#117—111no—
306C2×#117C2×D1111yescharacteristic
307C2×#117C2×D1111yescharacteristic
308C2×#107—111no—
309C2×#106—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317#397—221no—
318#394—221no—
319#391—111no—
320#390—21no—
321#389—111no—
322#389—221no—
323#388—21no—
324#388—21no—
325#388—221no—
326#384C2×D1111yescharacteristic
327#380—111no—
328#380C2×D1111yescharacteristic
329#380C2×D1111yescharacteristic
330C4×C4⋊C4—21no—
331C4×C4⋊C4C2×D1111yescharacteristic
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336—111no—
343#336—111no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11C2×#12311yescharacteristic
359C22×C11#54611yescharacteristic
360C22×C11#54611yescharacteristic
361C22×C11C2×#13511yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57711yescharacteristic
364C22×C11#57811yescharacteristic
365C4×C11—22no—
366C4×C11—22no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—42no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11#52911yescharacteristic
374C4×C11#53811yescharacteristic
375C4×C11#55311yescharacteristic
376C4×C11#55311yescharacteristic
377Dic11—42no—
378Dic11—81no—
379Dic11—81no—
380Dic11—81no—
381C22×Q8—111no—
382C22×D4C22⋊D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—222no—
390C22×C8—441no—
391C22×C8—441no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C22⋊Q8—441no—
396C4×D4—22no—
397C4×D4—22no—
398#117—22no—
399#117—22no—
400#117—41no—
401#117—41no—
402#117—222no—
403#117—441no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4C22⋊D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4C22⋊D1111yescharacteristic
426C2×C22⋊C4C22⋊D1111yescharacteristic
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432#107—222no—
433#106—441no—
434#103—222no—
435#103—441no—
436#103—441no—
437#103—441no—
438C22⋊C8—222no—
439C22⋊C8—441no—
440C22⋊C8—441no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11—42no—
449C2×C11—81no—
450C2×C11#244411yescharacteristic
451C2×C11#309111yescharacteristic
452C2×C11#309711yescharacteristic
453C2×C11#330211yescharacteristic
454C2×C11#330311yescharacteristic
455C2×C11#331311yescharacteristic
456C2×C11#331711yescharacteristic
457C24C2×C22⋊D1111yescharacteristic
458C24C2×C22⋊D1111yescharacteristic
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—41no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4#433912yes—
487C22×C4#433912yes—
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—444no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—81no—
516C4⋊C4—112no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4#434112yes—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—81no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C42—21no—
537C42—21no—
538C42—42no—
539C42—42no—
540C42—42no—
541C42—442no—
542C11#2621111yescharacteristic, complemented, Sylow
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23#6698212yes—
557C23C22×C22⋊D1111yescharacteristic
558Q8—441no—
559Q8—441no—
560Q8—441no—
561Q8—441no—
562D4—44no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—222no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4#6698212yes—
606C2×C4#6700312yes—
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4C2×#434111yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#6704211yescharacteristic
613C8—441no—
614C8—441no—
615C8—441no—
616C8—441no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22C2×#6698211yescharacteristic
632C22#1062333711yescharacteristic
633C22C2×#6700311yescharacteristic
634C22#1062335311yescharacteristic
635C22#1062336011yescharacteristic
636C22#1062336711yescharacteristic
637C22#1062336911yescharacteristic
638C4—22no—
639C4—22no—
640C4—41no—
641C4—42no—
642C4—41no—
643C4—81no—
644C4—81no—
645C4—81no—
646C4—442no—
647C4—881no—
648C4—881no—
649C4—881no—
650C4#1062306911yescharacteristic
651C4#1062307111yescharacteristic
652C4#1062309111yescharacteristic
653C4#1062309611yescharacteristic
654C2—42no—
655C2—81no—
656C2#1307236011yescharacteristic
657C2#1307852911yescharacteristic
658C2#1307858511yescharacteristic
659C2#1308053311yescharacteristic
660C2#1308053811yescharacteristic
661C2#1308067611yescharacteristic
662C2#1308074211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2354D11
hypocenterC11#26211
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13070178C2semidirect
3. #13070052C2semidirect
4. #13070025C2semidirect
5. #13069819C2semidirect
6. #13069250C2semidirect
7. #13069187C2semidirect
8. #13069037C2semidirect
9. #13068928C2semidirect
10. #13068928C2semidirect
12. #13068813C2semidirect
13. #13068711C2semidirect
14. #13068332C2semidirect
542. C11#26211semidirect

Maximal subgroups

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

subgroupindex
#130720452
#130701782
#130700522
#130700252
#130698192
#130692502
#130691872
#130690372
#130689282
#130689092
#130688132
#130687112
#130683322
C11×#23542
#2621111