Finite Group Databasebeta

← #14822237

Subgroups — #14822237

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072957C211yesmaximal, characteristic
2#13071641C211yesmaximal, characteristic
3#13069939C211yesmaximal, characteristic, complemented
4#13069820C211yesmaximal, characteristic
5#13069768C211yesmaximal, characteristic, complemented
6#13069626C211yesmaximal, characteristic
7#13069571C211yesmaximal, characteristic, complemented
8#13069306C211yesmaximal, characteristic, complemented
9#13069258C211yesmaximal, characteristic, complemented
10#13069209C211yesmaximal, characteristic, complemented
11#13068956C211yesmaximal, characteristic, complemented
12#13068926C211yesmaximal, characteristic
13#13068712C211yesmaximal, characteristic
14#13068447C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic
16C2×#66979C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C2×#66977C2211yescharacteristic
19C22×Dic44C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35#10622565—21no—
36#10622558—21no—
37#10622557—21no—
38#10622557—21no—
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622542C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622271—21no—
46#10622265—21no—
47#10622263—21no—
48#10622262—21no—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C22⋊C4D411yescharacteristic
67C2×C11×C22⋊C4D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74#66979—22no—
75#66979—41no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82#66977—22no—
83#66977—22no—
84#66977—22no—
85#66977—41no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×Dic44—22no—
97C2×Dic44—41no—
98C2×Dic44—41no—
99#66923—22no—
100#66923—41no—
101C4×Dic22—22no—
102C4×Dic22—41no—
103C11×C4⋊C8—41no—
104C11×C22⋊C8—41no—
105C11×C22⋊C8—41no—
106C11×#97—41no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66882—22no—
120#66880—22no—
121#66880—22no—
122#66880—22no—
123#66880—22no—
124#66880—41no—
125#66880—41no—
126#26749—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22#4112yes—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—41no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C22⋊Dic11—24no—
179C22⋊Dic11—42no—
180C22⋊Dic11—42no—
181C22⋊Dic11—42no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11#4112yes—
192C4⋊Dic11#4112yes—
193C4⋊Dic11#4112yes—
194Dic11⋊C4—24no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204Dic44—44no—
205#2489—111no—
206#2362—111no—
207#2056—111no—
208#2036—111no—
209#2026—111no—
210#2001—111no—
211#1989—111no—
212#1935—111no—
213#1928—111no—
214#1924D1111yescharacteristic
215#1921—111no—
216#1878—111no—
217#1873—111no—
218#1825—111no—
219#1763—111no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11C22×D411yescharacteristic
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
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×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277Dic22—22no—
278Dic22—22no—
279Dic22—41no—
280Dic22—41no—
281Dic22—41no—
282Dic22—41no—
283Dic22—41no—
284Dic22—41no—
285C8×C11—41no—
286C8×C11—41no—
287C8×C11—41no—
288C8×C11—41no—
289C22×Q16—111no—
290C2×#125—111no—
291C2×C22⋊Q8—111no—
292C2×C22⋊Q8—111no—
293C2×C4×Q8—111no—
294C2×#117—111no—
295C2×#107—111no—
296C2×C4⋊C8C2×D1111yescharacteristic
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×C22⋊C8C2×D1111yescharacteristic
304C2×C22⋊C8C2×D1111yescharacteristic
305C2×#97C2×D1111yescharacteristic
306#400—221no—
307#397—221no—
308#391—111no—
309#391—111no—
310#391—111no—
311#389—111no—
312#388—221no—
313#388—221no—
314#388—221no—
315#387—221no—
316#382—221no—
317#380—111no—
318C4×C4⋊C4—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—221no—
321C4×C22⋊C4C2×D1111yescharacteristic
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#336C2×D1111yescharacteristic
331#336C2×D1111yescharacteristic
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11#52511yescharacteristic
340C22×C11#54611yescharacteristic
341C22×C11#54611yescharacteristic
342C22×C11#57511yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57811yescharacteristic
345C22×C11#57811yescharacteristic
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11#52911yescharacteristic
352C4×C11#53811yescharacteristic
353C4×C11#55511yescharacteristic
354C4×C11#55911yescharacteristic
355Dic11—42no—
356Dic11—42no—
357Dic11—42no—
358Dic11—42no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—111no—
364C22×Q8—111no—
365C23×C4C22×D1111yescharacteristic
366C2×Q16—222no—
367C2×Q16—441no—
368C2×Q16—441no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373#125—222no—
374#125—441no—
375C22⋊Q8—222no—
376C22⋊Q8—222no—
377C22⋊Q8—222no—
378C22⋊Q8—441no—
379C4×Q8—222no—
380C4×Q8—441no—
381#117—222no—
382#117—441no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4D4411yescharacteristic
400C2×C22⋊C4D4411yescharacteristic
401C2×C42—221no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406C2×C42C22×D1111yescharacteristic
407#107—222no—
408C4⋊C8—41no—
409#103—222no—
410#103—222no—
411#103—222no—
412#103—222no—
413#103—441no—
414#103—441no—
415C22⋊C8—41no—
416C22⋊C8—41no—
417#97—41no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95D4411yescharacteristic
429#95D4411yescharacteristic
430C2×C11—81no—
431C2×C11#245911yescharacteristic
432C2×C11#311111yescharacteristic
433C2×C11#312711yescharacteristic
434C2×C11#331311yescharacteristic
435C2×C11#331511yescharacteristic
436C2×C11#331511yescharacteristic
437C2×C11#332711yescharacteristic
438C24C2×D4411yescharacteristic
439C2×Q8—112no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4C2×D4411yescharacteristic
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×D4411yescharacteristic
469C22×C4C2×D4411yescharacteristic
470C22×C4C23×D1111yescharacteristic
471Q16—444no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C4⋊C4—112no—
485C4⋊C4—112no—
486C4⋊C4—112no—
487C4⋊C4—224no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—224no—
505C22⋊C4—442no—
506C22⋊C4—442no—
507C22⋊C4—442no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—442no—
513C42—442no—
514C42—442no—
515C42—442no—
516C11#2674911yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23C22×D4411yescharacteristic
525Q8—222no—
526Q8—222no—
527Q8—441no—
528Q8—441no—
529Q8—441no—
530Q8—441no—
531Q8—441no—
532Q8—441no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4#6703711yescharacteristic
577C2×C4#6703711yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#41×D1111yescharacteristic
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1062305511yescharacteristic
594C22#1062308511yescharacteristic
595C22#1062308511yescharacteristic
596C22#1062327911yescharacteristic
597C22#1062327911yescharacteristic
598C22#1062328411yescharacteristic
599C22#1062328411yescharacteristic
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—442no—
606C4—442no—
607C4—442no—
608C4—442no—
609C4—881no—
610C4—881no—
611C4—881no—
612C4—881no—
613C4#1062314411yescharacteristic
614C4#1062319511yescharacteristic
615C4#1062320111yescharacteristic
616C4#1062323711yescharacteristic
617C2—81no—
618C2#1307255111yescharacteristic
619C2#1307872711yescharacteristic
620C2#1307891711yescharacteristic
621C2#1308068411yescharacteristic
622C2#1308071411yescharacteristic
623C2#1308071411yescharacteristic
624C2#1308088611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1924C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1924D11
hypocenterC11#26749
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
3. #13069939C2semidirect
5. #13069768C2semidirect
7. #13069571C2semidirect
8. #13069306C2semidirect
9. #13069258C2semidirect
10. #13069209C2semidirect
11. #13068956C2semidirect
14. #13068447C2semidirect
516. C11#26749semidirect

Maximal subgroups

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

subgroupindex
#130729572
#130716412
#130699392
#130698202
#130697682
#130696262
#130695712
#130693062
#130692582
#130692092
#130689562
#130689262
#130687122
#130684472
C11×#19242
#2674911