Finite Group Databasebeta

← #14795154

Subgroups — #14795154

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622490C211yesmaximal, characteristic, complemented
2C2×#10622303C211yesmaximal, characteristic
3#13074451C211yesmaximal, characteristic
4#13071296C211yesmaximal, characteristic
5#13070055C211yesmaximal, characteristic
6#13070040C211yesmaximal, characteristic
7#13069822C211yesmaximal, characteristic
8#13069821C211yesmaximal, characteristic
9#13069570C211yesmaximal, characteristic, complemented
10#13069371C211yesmaximal, characteristic, complemented
11#13069351C211yesmaximal, characteristic, complemented
12#13069305C211yesmaximal, characteristic, complemented
13#13069292C211yesmaximal, characteristic, complemented
14#13068620C211yesmaximal, characteristic, complemented
15C11×#1942C211yesmaximal, characteristic, complemented
16C2×#66950C2211yescharacteristic
17C2×#66943C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×#66925C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622607—21no—
32#10622603—21no—
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622593—21no—
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622586—21no—
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622490—24no—
48#10622303—24no—
49#10622289—21no—
50#10622282—21no—
51#10622270—21no—
52#10622267—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4D411yescharacteristic
77C2×(C2×D11)⋊C4D411yescharacteristic
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4D411yescharacteristic
89C2×Dic11⋊C4D411yescharacteristic
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66950—22no—
96#66950—22no—
97#66943—22no—
98#66943—22no—
99#66940—22no—
100#66940—22no—
101#66925—22no—
102#66925—22no—
103C11×#107—22no—
104C11×#107—22no—
105C4×C8×C11—22no—
106C11×#95—21no—
107C11×#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117#66880—22no—
118#66880—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8D414yes—
121#66874—22no—
122#66874—22no—
123#66872—22no—
124#66871—22no—
125#66867—22no—
126#24715—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22#4112yes—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C2×D412yes—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4#4112yes—
170C42×C11—21no—
171C42×C11—21no—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—22no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—81no—
176(C2×D11)⋊C4—81no—
177(C2×D11)⋊C4—81no—
178C4⋊Dic11—24no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186Dic11⋊C4—22no—
187Dic11⋊C4—22no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192Dic11⋊C4—81no—
193C4×Dic11—42no—
194C4×Dic11—81no—
195C4×Dic11C2×D412yes—
196C4×Dic11#4112yes—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C2×D412yes—
203C2×#479—111no—
204C2×#433—111no—
205#2629—111no—
206#2323—111no—
207#2077—111no—
208#2075—111no—
209#2036—111no—
210#2036—111no—
211#1989—111no—
212#1947—111no—
213#1943—111no—
214#1942D1111yescharacteristic, complemented
215#1935—111no—
216#1933—111no—
217#1803—111no—
218C23×C11C22×D411yescharacteristic
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
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×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—21no—
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#12112yes—
270C2×Dic11#12112yes—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275Dic22—22no—
276Dic22—22no—
277Dic22—41no—
278Dic22—41no—
279C8×C11—22no—
280C8×C11—41no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C2×#125—111no—
284C2×C22⋊Q8—111no—
285C2×C4×Q8—111no—
286C2×#117—111no—
287#479—224no—
288#433—224no—
289C2×#107—111no—
290C2×#107C2×D1111yescharacteristic
291C2×#107C2×D1111yescharacteristic
292C2×#106—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×C22⋊C8—111no—
300C2×C22⋊C8—111no—
301C2×#97—111no—
302C2×C4×C8C2×D1111yescharacteristic
303#398—221no—
304#398—221no—
305#396—221no—
306#396—221no—
307#391—111no—
308#389—111no—
309#389—221no—
310#389C2×D1111yescharacteristic
311#389C2×D1111yescharacteristic
312#388—221no—
313#388—221no—
314#387—221no—
315#384—111no—
316#380—111no—
317#380—111no—
318#380—111no—
319C4×C4⋊C4—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340C2×D1111yescharacteristic
327#340C2×D1111yescharacteristic
328C22×C11C2×#12111yescharacteristic
329C22×C11#52511yescharacteristic
330C22×C11#53611yescharacteristic
331C22×C11#57611yescharacteristic
332C22×C11#57711yescharacteristic
333C22×C11#57811yescharacteristic
334C22×C11#57811yescharacteristic
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—41no—
342C4×C11—42no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11#54711yescharacteristic
349C4×C11#54811yescharacteristic
350C4×C11#55211yescharacteristic
351C4×C11#55611yescharacteristic
352Dic11—22no—
353Dic11—22no—
354Dic11—42no—
355Dic11—41no—
356Dic11—81no—
357Dic11—81no—
358Dic11—81no—
359C22×Q8—111no—
360C23×C4—111no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365#125—222no—
366#125—222no—
367C22⋊Q8—222no—
368C22⋊Q8—222no—
369C4×Q8—222no—
370C4×Q8—222no—
371#117—222no—
372#117—222no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—111no—
392C2×C22⋊C4—111no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C42—111no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42C22×D1111yescharacteristic
401#107—22no—
402#107—22no—
403#107—222no—
404#106—222no—
405C4⋊C8—114no—
406C4⋊C8—222no—
407#103—222no—
408#103—222no—
409#103—222no—
410#103—222no—
411C22⋊C8—222no—
412C22⋊C8—222no—
413#97—222no—
414C4×C8—22no—
415#95—21no—
416#95—21no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424C2×C11#241511yescharacteristic
425C2×C11#306111yescharacteristic
426C2×C11#306311yescharacteristic
427C2×C11#311911yescharacteristic
428C2×C11#312711yescharacteristic
429C2×C11#324211yescharacteristic
430C2×C11#324311yescharacteristic
431D11—81no—
432C24—111no—
433C2×Q8—112no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—112no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8D4×D1112yes—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—222no—
481C4⋊C4—222no—
482C4⋊C4—224no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—442no—
492C4⋊C4—881no—
493C4⋊C4—881no—
494C4⋊C4—881no—
495C4⋊C4#433912yes—
496C22⋊C4—222no—
497C22⋊C4—222no—
498C22⋊C4—224no—
499C22⋊C4—881no—
500C22⋊C4—881no—
501C22⋊C4—881no—
502C42—21no—
503C42—21no—
504C42—112no—
505C42—112no—
506C42—442no—
507C42—881no—
508C11#2471511yescharacteristic, complemented, Sylow
509C23—221no—
510C23—221no—
511C23—221no—
512C23—221no—
513C23—221no—
514C23—221no—
515C23—221no—
516C23C2×D4×D1111yescharacteristic
517Q8—222no—
518Q8—222no—
519Q8—441no—
520Q8—441no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—112no—
540C2×C4—112no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—222no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
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×C4C2×#433911yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4#6704011yescharacteristic
567C2×C4#6704011yescharacteristic
568C2×C4#41×D1111yescharacteristic
569C2×C4#41×D1111yescharacteristic
570C8—22no—
571C8—41no—
572C8—222no—
573C8—441no—
574C22—441no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22#1062307811yescharacteristic
582C22D11×#12111yescharacteristic
583C22#1062325511yescharacteristic
584C22#1062328811yescharacteristic
585C22#1062329711yescharacteristic
586C22#1062330111yescharacteristic
587C22#1062330211yescharacteristic
588C4—41no—
589C4—42no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—222no—
595C4—222no—
596C4—441no—
597C4—442no—
598C4—881no—
599C4—881no—
600C4—881no—
601C4#1062303811yescharacteristic
602C4#1062309911yescharacteristic
603C4#1062316411yescharacteristic
604C4#1062322411yescharacteristic
605C2—881no—
606C2#1307204411yescharacteristic
607C2#1307828111yescharacteristic
608C2#1307830611yescharacteristic
609C2#1307881111yescharacteristic
610C2#1307891311yescharacteristic
611C2#1307988711yescharacteristic
612C2#1307990211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1942C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1942D11
hypocenterC11#24715
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
1. C2×#10622490C2semidirect
9. #13069570C2semidirect
10. #13069371C2semidirect
11. #13069351C2semidirect
12. #13069305C2semidirect
13. #13069292C2semidirect
14. #13068620C2semidirect
15. C11×#1942C2semidirect
214. #1942D11semidirect
508. C11#24715semidirect

Maximal subgroups

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

subgroupindex
C2×#106224902
C2×#106223032
#130744512
#130712962
#130700552
#130700402
#130698222
#130698212
#130695702
#130693712
#130693512
#130693052
#130692922
#130686202
C11×#19422
#2471511