Finite Group Databasebeta

← #14803248

Subgroups — #14803248

Order 2816.

760 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×#10622682C211yesmaximal, characteristic
2#13073601C211yesmaximal, characteristic
3#13071716C211yesmaximal, characteristic
4#13070006C211yesmaximal, characteristic
5#13069992C211yesmaximal, characteristic
6#13069861C211yesmaximal, characteristic
7#13069861C211yesmaximal, characteristic
8#13069538C211yesmaximal, characteristic
9#13069537C211yesmaximal, characteristic
10#13069537C211yesmaximal, characteristic
11#13069337C211yesmaximal, characteristic
12#13069256C211yesmaximal, characteristic
13#13069249C211yesmaximal, characteristic
14#13068446C211yesmaximal, characteristic
15C2×C11×#479C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66997C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C11×#479—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622682—24no—
36#10622598—21no—
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622596—21no—
40#10622596—21no—
41#10622594—21no—
42#10622594—21no—
43C4⋊C4×Dic11—21no—
44C4⋊C4×Dic11C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic
46#10622587C2211yescharacteristic
47#10622587C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C4×C4⋊Dic11C2211yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic
54#10622541—21no—
55#10622541—21no—
56C2×#66867C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#125—22no—
67C11×#125D414yes—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
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×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#66997—22no—
79#66997—22no—
80#66997—41no—
81#66997—41no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—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#66922—22no—
102#66922—22no—
103C11×#107—22no—
104C11×#106—22no—
105C11×C4⋊C8—22no—
106C11×#103—22no—
107C11×#103—22no—
108#66899—22no—
109#66899—22no—
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—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66880—22no—
122#66880—22no—
123#66880—41no—
124#66880—41no—
125Dic11⋊C8—41no—
126Dic11⋊C8—41no—
127#66874—22no—
128#66874—22no—
129#66874—22no—
130#66874—22no—
131#66867—22no—
132#25290—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#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
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—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—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×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4C2×D412yes—
180C11×C4⋊C4C2×D412yes—
181C42×C11—42no—
182C42×C11C2×D412yes—
183C42×C11#4112yes—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11—42no—
192C4⋊Dic11—81no—
193C4⋊Dic11#4112yes—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—81no—
204C4×Dic11—81no—
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×#491—111no—
212C2×#479D1111yescharacteristic
213#2546—111no—
214#2370—111no—
215#2068—111no—
216#2066—111no—
217#2043—111no—
218#2043—111no—
219#1981—111no—
220#1981—111no—
221#1981—111no—
222#1940—111no—
223#1928—111no—
224#1927—111no—
225#1763—111no—
226C23×C11C22×D411yescharacteristic
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—41no—
230Q8×C11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
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#12112yes—
248C2×C4×C11#12112yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
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—
277C2×Dic11#13712yes—
278C2×Dic11#13712yes—
279Dic22—41no—
280Dic22—41no—
281Dic22—41no—
282Dic22—41no—
283Dic22—41no—
284Dic22—41no—
285Dic22—41no—
286Dic22—41no—
287C8×C11—41no—
288C8×C11—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C2×C4⋊Q8—111no—
292C2×C4⋊Q8—111no—
293C2×C4⋊Q8—111no—
294C2×#125C2×D1111yescharacteristic
295C2×C4×Q8C2×D1111yescharacteristic
296#491—224no—
297#479—24no—
298C2×#107C2×D1111yescharacteristic
299C2×#106C2×D1111yescharacteristic
300C2×C4⋊C8—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8C2×D1111yescharacteristic
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103C2×D1111yescharacteristic
314C2×#103C2×D1111yescharacteristic
315C2×#97—111no—
316#398—221no—
317#398—221no—
318#391—111no—
319#391—111no—
320#389—111no—
321#389—111no—
322#389—221no—
323#389—221no—
324#389—221no—
325#387—221no—
326#387—221no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—221no—
332#340—111no—
333#340—111no—
334#336—111no—
335#336—111no—
336C22×C11C2×#12111yescharacteristic
337C22×C11#54611yescharacteristic
338C22×C11#54811yescharacteristic
339C22×C11C2×#13711yescharacteristic
340C22×C11C2×#13711yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—81no—
349C4×C11#52911yescharacteristic
350C4×C11#54211yescharacteristic
351C4×C11#54811yescharacteristic
352C4×C11#55011yescharacteristic
353Dic11—22no—
354Dic11—22no—
355Dic11—42no—
356Dic11—41no—
357Dic11—41no—
358Dic11—81no—
359Dic11—81no—
360Dic11—81no—
361C22×Q8—111no—
362C22×Q8—111no—
363C22×Q8C22×D1111yescharacteristic
364C22×C8—111no—
365C22×C8—111no—
366C22×C8C22×D1111yescharacteristic
367C22×C8C22×D1111yescharacteristic
368C4⋊Q8—222no—
369C4⋊Q8—222no—
370C4⋊Q8—222no—
371C4⋊Q8—222no—
372C4⋊Q8—441no—
373C4⋊Q8—441no—
374#125—22no—
375#125C22⋊D1114yes—
376C4×Q8—22no—
377C4×Q8—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C42—21no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42C22×D1111yescharacteristic
403#107—22no—
404#106—22no—
405C4⋊C8—22no—
406C4⋊C8—441no—
407C4⋊C8—441no—
408#103—22no—
409#103—22no—
410#103—222no—
411#103—222no—
412#103—222no—
413#103—222no—
414#103—222no—
415#103—222no—
416#103—222no—
417#103—222no—
418#103—441no—
419#103—441no—
420#97—222no—
421#95—111no—
422#95—111no—
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#242611yescharacteristic
433C2×C11#303911yescharacteristic
434C2×C11#304611yescharacteristic
435C2×C11#331211yescharacteristic
436C2×C11#332011yescharacteristic
437C2×C11#337211yescharacteristic
438C2×C11#337411yescharacteristic
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8#434312yes—
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
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—24no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—112no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—881no—
505C4⋊C4C2×C22⋊D1112yes—
506C4⋊C4C2×C22⋊D1112yes—
507C42—42no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42—221no—
512C42—442no—
513C42—881no—
514C42—881no—
515C42#434112yes—
516C42C2×C22⋊D1112yes—
517C11#2529011yescharacteristic, complemented, Sylow
518C23C2×D4×D1111yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—41no—
522Q8—41no—
523Q8—441no—
524Q8—441no—
525Q8—441no—
526Q8—441no—
527Q8—441no—
528Q8—441no—
529Q8—441no—
530Q8—441no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
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—112no—
548C2×C4—112no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—222no—
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#6699212yes—
572C2×C4#6699212yes—
573C2×C4C2×#434111yescharacteristic
574C2×C4C2×#434311yescharacteristic
575C2×C4#6704011yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#6704211yescharacteristic
578C2×C4C22×C22⋊D1111yescharacteristic
579C8—41no—
580C8—41no—
581C8—441no—
582C8—441no—
583C22#1062316111yescharacteristic
584C22#1062316411yescharacteristic
585C22#1062330111yescharacteristic
586C22#1062330211yescharacteristic
587C22D11×#13711yescharacteristic
588C22D11×#13711yescharacteristic
589C22C2×#6699211yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—81no—
596C4—222no—
597C4—222no—
598C4—442no—
599C4—441no—
600C4—441no—
601C4—881no—
602C4—881no—
603C4—881no—
604C4#1062315511yescharacteristic
605C4#1062317411yescharacteristic
606C4#1062334811yescharacteristic
607C4#1062336511yescharacteristic
608C2#1307218411yescharacteristic
609C2#1307810111yescharacteristic
610C2#1307816411yescharacteristic
611C2#1308066411yescharacteristic
612C2#1308078411yescharacteristic
613C2#1308140011yescharacteristic
614C2#1308142211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#479C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#479D11
hypocenterC11#25290
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
517. C11#25290semidirect

Maximal subgroups

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

subgroupindex
C2×#106226822
#130736012
#130717162
#130700062
#130699922
#130698612
#130695382
#130695372
#130693372
#130692562
#130692492
#130684462
C2×C11×#4792
#2529011