Finite Group Databasebeta

← #14822238

Subgroups — #14822238

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#13072959C211yesmaximal, characteristic
2#13071643C211yesmaximal, characteristic
3#13069937C211yesmaximal, characteristic, complemented
4#13069820C211yesmaximal, characteristic
5#13069766C211yesmaximal, characteristic, complemented
6#13069624C211yesmaximal, characteristic
7#13069570C211yesmaximal, characteristic, complemented
8#13069303C211yesmaximal, characteristic, complemented
9#13069259C211yesmaximal, characteristic, complemented
10#13069232C211yesmaximal, characteristic
11#13069207C211yesmaximal, characteristic, complemented
12#13068954C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1873C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622825C2211yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622595—21no—
37#10622590—21no—
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43#10622566—21no—
44#10622558—21no—
45#10622558—21no—
46#10622557—21no—
47#10622546—21no—
48C4×Dic11⋊C4—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—41no—
66C11×#117—22no—
67C11×#117—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11D411yescharacteristic
78C2×C22⋊Dic11D411yescharacteristic
79C2×#4326—22no—
80C2×#4326—41no—
81C2×#4326—41no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86#66977—22no—
87#66977—22no—
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×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66943—22no—
100#66943—41no—
101#66940—22no—
102#66940—41no—
103C11×#103—22no—
104C11×#103—41no—
105C11×C22⋊C8—41no—
106#66899—22no—
107C11⋊#95—21no—
108C11⋊#95—21no—
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⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119C22⋊(C11⋊C8)—41no—
120#66882—22no—
121#66880—22no—
122#66880—41no—
123#66879—41no—
124Dic11⋊C8—41no—
125#66874—22no—
126#26749—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×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×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
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—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4#4112yes—
172C11×C4⋊C4#4112yes—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—42no—
175C42×C11—42no—
176C22⋊Dic11—24no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179C22⋊Dic11—42no—
180#4326—44no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—42no—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—24no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—42no—
197C4×Dic11—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—
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#1924—111no—
215#1921—111no—
216#1878—111no—
217#1873D1111yescharacteristic
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
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281Dic22—22no—
282Dic22—22no—
283Dic22—41no—
284Dic22—41no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—41no—
288C11⋊C8—41no—
289C22×Q16—111no—
290C2×#125—111no—
291C2×C22⋊Q8—111no—
292C2×C22⋊Q8C2×D1111yescharacteristic
293C2×C4×Q8—111no—
294C2×#117C2×D1111yescharacteristic
295C2×#107—111no—
296C2×C4⋊C8—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103C2×D1111yescharacteristic
302C2×#103C2×D1111yescharacteristic
303C2×C22⋊C8—111no—
304C2×C22⋊C8C2×D1111yescharacteristic
305C2×#97—111no—
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⋊C4—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#336—111no—
331#336—111no—
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—42no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11#52911yescharacteristic
352C4×C11#53811yescharacteristic
353C4×C11#55511yescharacteristic
354C4×C11#55911yescharacteristic
355Dic11—42no—
356Dic11—42no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—111no—
364C22×Q8C22×D1111yescharacteristic
365C23×C4C22×D1111yescharacteristic
366C2×Q16—222no—
367C2×Q16—441no—
368C2×Q16—441no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373#125—222no—
374#125—441no—
375C22⋊Q8—22no—
376C22⋊Q8—41no—
377C22⋊Q8—222no—
378C22⋊Q8—222no—
379C4×Q8—222no—
380C4×Q8—441no—
381#117—22no—
382#117—41no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—111no—
398C2×C22⋊C4—111no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C42—21no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42—221no—
407#107—222no—
408C4⋊C8—441no—
409#103—22no—
410#103—41no—
411#103—222no—
412#103—222no—
413#103—222no—
414#103—441no—
415C22⋊C8—41no—
416C22⋊C8—441no—
417#97—441no—
418#95—111no—
419#95—111no—
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#95—221no—
429#95—221no—
430C2×C11—81no—
431C2×C11#245911yescharacteristic
432C2×C11#311111yescharacteristic
433C2×C11#312711yescharacteristic
434C2×C11#331311yescharacteristic
435C2×C11#331511yescharacteristic
436C2×C11#331511yescharacteristic
437C2×C11#332711yescharacteristic
438C24D4×D1111yescharacteristic
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—112no—
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—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4D4×D1111yescharacteristic
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—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—112no—
490C4⋊C4—224no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4#433912yes—
501C4⋊C4#434112yes—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—224no—
505C22⋊C4—441no—
506C22⋊C4—441no—
507C22⋊C4—442no—
508C42—42no—
509C42—221no—
510C42—221no—
511C42—221no—
512C42—221no—
513C42—442no—
514C42—442no—
515C42—442no—
516C11#2674911yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23C2×D4×D1111yescharacteristic
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—222no—
530Q8—222no—
531Q8—441no—
532Q8—441no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—222no—
565C2×C4—222no—
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×C4C2×#433911yescharacteristic
577C2×C4C2×#434111yescharacteristic
578C2×C4#6703711yescharacteristic
579C2×C4#6703711yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#41×D1111yescharacteristic
582C8—41no—
583C8—41no—
584C8—441no—
585C8—441no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1062302111yescharacteristic
594C22#1062312211yescharacteristic
595C22#1062318711yescharacteristic
596C22#1062329911yescharacteristic
597C22#1062330211yescharacteristic
598C22#1062330811yescharacteristic
599C22#1062331011yescharacteristic
600C4—42no—
601C4—42no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—441no—
606C4—441no—
607C4—441no—
608C4—441no—
609C4—442no—
610C4—442no—
611C4—881no—
612C4—881no—
613C4#1062308811yescharacteristic
614C4#1062309011yescharacteristic
615C4#1062314411yescharacteristic
616C4#1062314711yescharacteristic
617C2—81no—
618C2#1307255211yescharacteristic
619C2#1307872811yescharacteristic
620C2#1307891211yescharacteristic
621C2#1308068311yescharacteristic
622C2#1308070811yescharacteristic
623C2#1308071611yescharacteristic
624C2#1308087711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1873D11
hypocenterC11#26749
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
3. #13069937C2semidirect
5. #13069766C2semidirect
7. #13069570C2semidirect
8. #13069303C2semidirect
9. #13069259C2semidirect
11. #13069207C2semidirect
12. #13068954C2semidirect
14. #13068445C2semidirect
516. C11#26749semidirect

Maximal subgroups

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

subgroupindex
#130729592
#130716432
#130699372
#130698202
#130697662
#130696242
#130695702
#130693032
#130692592
#130692322
#130692072
#130689542
#130687112
#130684452
C11×#18732
#2674911