Finite Group Databasebeta

← #14816867

Subgroups — #14816867

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622679C211yesmaximal, characteristic
2C2×#10622465C211yesmaximal, characteristic
3#13072473C211yesmaximal, characteristic, complemented
4#13071525C211yesmaximal, characteristic
5#13070161C211yesmaximal, characteristic, complemented
6#13070101C211yesmaximal, characteristic, complemented
7#13069994C211yesmaximal, characteristic, complemented
8#13069343C211yesmaximal, characteristic, complemented
9#13069176C211yesmaximal, characteristic, complemented
10#13068951C211yesmaximal, characteristic
11#13068949C211yesmaximal, characteristic
12#13068878C211yesmaximal, characteristic
13#13068871C211yesmaximal, characteristic, complemented
14#13068860C211yesmaximal, characteristic
15C11×#2059C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622679—24no—
29#10622602—21no—
30#10622600—21no—
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622597—21no—
34#10622595—21no—
35#10622591—21no—
36#10622590C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586—21no—
39#10622586C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48#10622542C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622465—24no—
51#10622281—21no—
52D11×#95—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#125—22no—
69C11×#125—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×#4314—22no—
95C2×#4314—22no—
96C2×#4314Q814yes—
97#66946—22no—
98#66946—22no—
99#66946—22no—
100#66946—41no—
101#66940—22no—
102#66940—41no—
103C4×D44—22no—
104C4×D44—41no—
105C11×#107—41no—
106C11×#106—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
119#66885—22no—
120#66880—41no—
121C8×Dic11—22no—
122#66874—22no—
123#66874—22no—
124#66873—22no—
125#66873D414yes—
126#66872—22no—
127#66872—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130#26378—111nomaximal, Sylow
131C23×D11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44C2×D412yes—
150C2×D44C2×Q812yes—
151C2×D44#4112yes—
152C2×C4×D11—24no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×C4×D11—81no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22C2×Q812yes—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×Q812yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4C2×D412yes—
183C11×C4⋊C4#4112yes—
184C42×C11—21no—
185C42×C11—21no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C4⋊Dic11—81no—
195Dic11⋊C4—22no—
196Dic11⋊C4—41no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C2×D412yes—
210#4314—28no—
211C2×#478—111no—
212C2×C4×SD16—111no—
213#2453—111no—
214#2349—111no—
215#2097—111no—
216#2085—111no—
217#2066—111no—
218#2059D1111yescharacteristic, complemented
219#1941—111no—
220#1916—111no—
221#1877—111no—
222#1877—111no—
223#1864—111no—
224#1863—111no—
225#1862—111no—
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
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—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×C11C22×D411yescharacteristic
253C2×C4×C11C22×Q811yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11#13512yes—
279D44—22no—
280D44—22no—
281D44—22no—
282D44C22⋊Q814yes—
283C4×D11—84no—
284C4×D11—84no—
285C4×D11—84no—
286Dic22—22no—
287Dic22—22no—
288Dic22—41no—
289Dic22—41no—
290C8×C11—22no—
291C8×C11—41no—
292C11⋊C8—22no—
293C11⋊C8—41no—
294C22×SD16—111no—
295C2×#125C2×D1111yescharacteristic
296C2×C4×Q8—111no—
297C2×C4×D4—111no—
298C2×C4×D4—111no—
299C2×C4×D4—111no—
300#478—224no—
301C4×SD16—224no—
302C2×#107—111no—
303C2×#107C2×D1111yescharacteristic
304C2×#106—111no—
305C2×#106—111no—
306C2×#106C2×D1111yescharacteristic
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×C4×C8—111no—
315#400—221no—
316#398—221no—
317#391—111no—
318#391—111no—
319#389—111no—
320#389—111no—
321#389—111no—
322#389—221no—
323#389C2×D1111yescharacteristic
324#387—221no—
325#385—221no—
326#385—221no—
327#382—111no—
328#380—221no—
329C4×C4⋊C4—111no—
330C2×#95—221no—
331#340—111no—
332#340—111no—
333#340C2×D1111yescharacteristic
334#340C2×D1111yescharacteristic
335#336—111no—
336#336—111no—
337#336—111no—
338#336C2×D1111yescharacteristic
339C22×C11#52511yescharacteristic
340C22×C11D4211yescharacteristic
341C22×C11D4×Q811yescharacteristic
342C22×C11C2×#13511yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57711yescharacteristic
345C22×C11#57711yescharacteristic
346C2×D11—24no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C4×C11—42no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11C2×C22⋊Q811yescharacteristic
360C4×C11#53911yescharacteristic
361C4×C11#54711yescharacteristic
362C4×C11#55411yescharacteristic
363Dic11—22no—
364Dic11—41no—
365Dic11—41no—
366Dic11—42no—
367Dic11—41no—
368Dic11—81no—
369Dic11—81no—
370C22×Q8—111no—
371C22×D4—111no—
372C23×C4—221no—
373C23×C4—221no—
374C23×C4—221no—
375C2×SD16—114no—
376C2×SD16—222no—
377C2×SD16—222no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382#125—22no—
383#125—41no—
384C4×Q8—222no—
385C4×Q8—441no—
386C4×D4—222no—
387C4×D4—222no—
388C4×D4—222no—
389C4×D4—222no—
390C4×D4—441no—
391C4×D4—441no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414#107—41no—
415#107—222no—
416#106—22no—
417#106—222no—
418#106—222no—
419C4⋊C8—222no—
420#103—222no—
421#103—222no—
422#103—441no—
423#102—114no—
424#102—222no—
425#102—222no—
426C4×C8—222no—
427#95—21no—
428#95—111no—
429#95—111no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439C2×C11#244911yescharacteristic
440C2×C11#310211yescharacteristic
441C2×C11#312311yescharacteristic
442C2×C11#326711yescharacteristic
443C2×C11#328211yescharacteristic
444C2×C11#338111yescharacteristic
445C2×C11#338811yescharacteristic
446D11—44no—
447C24—221no—
448C2×Q8—112no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×D4—112no—
455C2×D4—112no—
456C2×D4—112no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—224no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—881no—
477C22×C4—881no—
478C22×C4—881no—
479C22×C4—881no—
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483SD16—228no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—112no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8Q8×D1112yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—81no—
505C4⋊C4—222no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—441no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—881no—
515C4⋊C4D4×D1112yes—
516C4⋊C4#434312yes—
517C22⋊C4—224no—
518C22⋊C4—442no—
519C22⋊C4—442no—
520C42—21no—
521C42—21no—
522C42—221no—
523C42—221no—
524C42—221no—
525C42—221no—
526C42—442no—
527C11#2637811yescharacteristic, complemented, Sylow
528C23—222no—
529C23—222no—
530C23—222no—
531C23—441no—
532C23—441no—
533C23—441no—
534C23—441no—
535C23C2×D4×D1111yescharacteristic
536Q8—222no—
537Q8—222no—
538Q8—441no—
539Q8—441no—
540D4—114no—
541D4—222no—
542D4—222no—
543D4—222no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—112no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—222no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—884no—
584C2×C4—884no—
585C2×C4—884no—
586C2×C4C2×D4×D1111yescharacteristic
587C2×C4#6703711yescharacteristic
588C2×C4C2×Q8×D1111yescharacteristic
589C2×C4C2×#434311yescharacteristic
590C2×C4#6704011yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C8—22no—
593C8—41no—
594C8—222no—
595C8—441no—
596C22—224no—
597C22—442no—
598C22—442no—
599C22—442no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22#1062312111yescharacteristic
604C22#1062315811yescharacteristic
605C22#1062325811yescharacteristic
606C22D11×#13511yescharacteristic
607C22#1062330111yescharacteristic
608C22#1062330611yescharacteristic
609C22#1062330811yescharacteristic
610C4—41no—
611C4—41no—
612C4—42no—
613C4—42no—
614C4—81no—
615C4—81no—
616C4—222no—
617C4—442no—
618C4—441no—
619C4—441no—
620C4—441no—
621C4—881no—
622C4—881no—
623C4D11×C22⋊Q811yescharacteristic
624C4#1062316911yescharacteristic
625C4#1062325711yescharacteristic
626C4#1062326111yescharacteristic
627C2—444no—
628C2#1307241811yescharacteristic
629C2#1307864111yescharacteristic
630C2#1307887011yescharacteristic
631C2#1308014411yescharacteristic
632C2#1308032611yescharacteristic
633C2#1308148811yescharacteristic
634C2#1308156011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2059C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2059D11
hypocenterC11#26378
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2059

Complements

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

NH ≅ G/Ntype
3. #13072473C2semidirect
5. #13070161C2semidirect
6. #13070101C2semidirect
7. #13069994C2semidirect
8. #13069343C2semidirect
9. #13069176C2semidirect
13. #13068871C2semidirect
15. C11×#2059C2semidirect
218. #2059D11semidirect
527. C11#26378semidirect

Maximal subgroups

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

subgroupindex
C2×#106226792
C2×#106224652
#130724732
#130715252
#130701612
#130701012
#130699942
#130693432
#130691762
#130689512
#130689492
#130688782
#130688712
#130688602
C11×#20592
#2637811