Finite Group Databasebeta

← #14813878

Subgroups — #14813878

Order 2816.

792 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622703C211yesmaximal, characteristic
2C2×#10622403C211yesmaximal, characteristic
3#13072388C211yesmaximal, characteristic
4#13071535C211yesmaximal, characteristic
5#13070166C211yesmaximal, characteristic
6#13070107C211yesmaximal, characteristic
7#13070037C211yesmaximal, characteristic
8#13069294C211yesmaximal, characteristic
9#13069176C211yesmaximal, characteristic
10#13068954C211yesmaximal, characteristic
11#13068954C211yesmaximal, characteristic
12#13068954C211yesmaximal, characteristic
13#13068887C211yesmaximal, characteristic
14#13068886C211yesmaximal, characteristic
15C11×#2043C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C11×#389C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30#10622843C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622703—24no—
38#10622599—21no—
39#10622598C2211yescharacteristic
40#10622596—21no—
41#10622591—21no—
42#10622591—21no—
43#10622590C2211yescharacteristic
44C4⋊C4×Dic11—21no—
45#10622585—21no—
46C2×#66871C2211yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622403—24no—
51#10622263—21no—
52#10622260—21no—
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74Q8×Dic11—22no—
75Q8×Dic11—41no—
76C2×#4326—22no—
77C2×#4326—22no—
78C2×#4326—22no—
79C2×#4326—22no—
80C2×#4326—22no—
81C2×#4326D414yes—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4D411yescharacteristic
92C2×Dic11⋊C4D411yescharacteristic
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66940—22no—
102#66940—22no—
103#66940—22no—
104#66940—41no—
105C4×Dic22—22no—
106C4×Dic22—41no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#103—41no—
111C11×#95—21no—
112#66899—22no—
113#66899—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126#66881—41no—
127#66880—22no—
128#66880—22no—
129C8×Dic11—22no—
130#66871—22no—
131C4⋊(C11⋊C8)—22no—
132#26167—111nomaximal, Sylow
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C2×D412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22C2×D412yes—
164C2×Dic22#4112yes—
165C2×Dic22#4112yes—
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×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4#4112yes—
179C42×C11—21no—
180C42×C11—21no—
181#4326—28no—
182#4326—44no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191Dic11⋊C4—24no—
192Dic11⋊C4—22no—
193Dic11⋊C4—22no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197C4×Dic11—24no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×D412yes—
211C2×#462—111no—
212C2×C4×Q16—111no—
213#2446—111no—
214#2351—111no—
215#2097—111no—
216#2086—111no—
217#2074—111no—
218#2043D1111yescharacteristic
219#1933—111no—
220#1916—111no—
221#1878—111no—
222#1878—111no—
223#1878—111no—
224#1865—111no—
225#1865—111no—
226C23×C11C22×D411yescharacteristic
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
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×C11—41no—
252C2×C4×C11#13512yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—22no—
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—21no—
272C2×Dic11—21no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11#13712yes—
283Dic22—22no—
284Dic22—22no—
285Dic22—22no—
286Dic22#12314yes—
287C8×C11—41no—
288C8×C11—41no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291C22×Q16—111no—
292C22×Q16—111no—
293C2×C4⋊Q8C2×D1111yescharacteristic
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298#462—224no—
299C4×Q16—224no—
300C2×#107—111no—
301C2×#106—111no—
302C2×C4⋊C8—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103C2×D1111yescharacteristic
308C2×#103C2×D1111yescharacteristic
309C2×#103C2×D1111yescharacteristic
310C2×#103C2×D1111yescharacteristic
311C2×C4×C8—111no—
312#400—221no—
313#398—221no—
314#391—111no—
315#391—111no—
316#391—111no—
317#389—111no—
318#389—111no—
319#389—221no—
320#389—221no—
321#389C2×D1111yescharacteristic
322#387—221no—
323#387—221no—
324#382—111no—
325#382—221no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—221no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335#336C2×D1111yescharacteristic
336C22×C11#52511yescharacteristic
337C22×C11D4211yescharacteristic
338C22×C11#54811yescharacteristic
339C22×C11C2×#13511yescharacteristic
340C22×C11C2×#13711yescharacteristic
341C22×C11#57811yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C2×#12311yescharacteristic
350C4×C11#53911yescharacteristic
351C4×C11#54711yescharacteristic
352C4×C11#55311yescharacteristic
353Dic11—24no—
354Dic11—22no—
355Dic11—41no—
356Dic11—41no—
357Dic11—41no—
358Dic11—81no—
359Dic11—81no—
360Dic11—81no—
361C22×Q8—111no—
362C22×Q8C22×D1111yescharacteristic
363C22×Q8C22×D1111yescharacteristic
364C2×Q16—114no—
365C2×Q16—222no—
366C2×Q16—222no—
367C2×Q16—222no—
368C2×Q16—222no—
369C2×Q16—222no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C4⋊Q8—22no—
375C4⋊Q8—41no—
376C4×Q8—222no—
377C4×Q8—222no—
378C4×Q8—222no—
379C4×Q8—222no—
380C4×Q8—222no—
381C4×Q8—441no—
382C4×Q8—441no—
383C4×Q8—441no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407#107—222no—
408#106—441no—
409C4⋊C8—222no—
410#103—22no—
411#103—22no—
412#103—22no—
413#103—41no—
414#103—222no—
415#103—222no—
416#103—222no—
417#103—222no—
418C4×C8—222no—
419#95—21no—
420#95—111no—
421#95—111no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432C2×C11#244311yescharacteristic
433C2×C11#310711yescharacteristic
434C2×C11#312711yescharacteristic
435C2×C11#327011yescharacteristic
436C2×C11#328511yescharacteristic
437C2×C11#336411yescharacteristic
438C2×C11#337411yescharacteristic
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—112no—
451C2×Q8—112no—
452C2×Q8—112no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8D4×D1112yes—
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×C4D4×D1111yescharacteristic
471C22×C4C23×D1111yescharacteristic
472Q16—228no—
473Q16—444no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—112no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—222no—
493C4⋊C4—224no—
494C4⋊C4—222no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4#434112yes—
507C42—21no—
508C42—21no—
509C42—224no—
510C42—221no—
511C42—221no—
512C42—221no—
513C42—221no—
514C42—442no—
515C42—442no—
516C42—442no—
517C11#2616711yescharacteristic, complemented, Sylow
518C23C2×D4×D1111yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—114no—
528Q8—222no—
529Q8—222no—
530Q8—222no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
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—112no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
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—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#6696912yes—
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4#6703711yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#6704311yescharacteristic
579C8—41no—
580C8—41no—
581C8—222no—
582C8—441no—
583C22#1062312111yescharacteristic
584C22#1062313711yescharacteristic
585C22#1062320811yescharacteristic
586C22C2×#6696911yescharacteristic
587C22#1062329711yescharacteristic
588C22D11×#13711yescharacteristic
589C22#1062331011yescharacteristic
590C4—22no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—222no—
597C4—224no—
598C4—441no—
599C4—441no—
600C4—441no—
601C4—881no—
602C4—881no—
603C4—881no—
604C4#1062314211yescharacteristic
605C4#1062314511yescharacteristic
606C4D11×#12311yescharacteristic
607C4#1062319111yescharacteristic
608C2#1307234411yescharacteristic
609C2#1307868411yescharacteristic
610C2#1307891411yescharacteristic
611C2#1308018911yescharacteristic
612C2#1308035011yescharacteristic
613C2#1308130611yescharacteristic
614C2#1308141611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2043C2
socle, prime radicalC23×C11C22×D4
hypercenter#2043D11
hypocenterC11#26167
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
517. C11#26167semidirect

Maximal subgroups

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

subgroupindex
C2×#106227032
C2×#106224032
#130723882
#130715352
#130701662
#130701072
#130700372
#130692942
#130691762
#130689542
#130688872
#130688862
C11×#20432
#2616711