Finite Group Databasebeta

← #14772160

Subgroups — #14772160

Order 2816.

906 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×#10622329C211yesmaximal, characteristic
2C2×#10622466C211yesmaximal, characteristic
3C2×#10622486C211yesmaximal, characteristic
4#13071535C211yesmaximal, characteristic
5#13071530C211yesmaximal, characteristic
6#13069345C211yesmaximal, characteristic
7#13068885C211yesmaximal, characteristic
8#13068883C211yesmaximal, characteristic
9#13068871C211yesmaximal, characteristic
10#13068869C211yesmaximal, characteristic
11#13068783C211yesmaximal, characteristic
12#13068630C211yesmaximal, characteristic
13#13068620C211yesmaximal, characteristic
14#13068492C211yesmaximal, characteristic
15C11×#1944C211yesmaximal, characteristic
16C22×Dic44C2211yescharacteristic
17C2×#66940C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622590C2211yescharacteristic
37#10622589—21no—
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11—21no—
40#10622585—21no—
41#10622585—21no—
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49#10622486—24no—
50#10622466C418yescomplemented
51#10622329—24no—
52#10622263—21no—
53#10622262—21no—
54#10622260—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4D411yescharacteristic
86C2×Dic11⋊C4D411yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×Dic44C2×C414yes—
98C2×Dic44D414yes—
99C2×Dic44Q814yes—
100#66940—22no—
101#66940—22no—
102#66940—22no—
103#66940—22no—
104#66940—41no—
105#66940—41no—
106#66940C2×C414yes—
107#66940C2×C414yes—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—41no—
111C4×Dic22—41no—
112C11×#107—22no—
113C11×#106C2×C414yes—
114C11×#97—22no—
115C11×#95—21no—
116C11×#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66881—22no—
124#66880—22no—
125#66880—22no—
126#66879C2×C414yes—
127Dic11⋊C8—22no—
128C8×Dic11—22no—
129#66874—22no—
130#66874—22no—
131#66874C2×C414yes—
132#66874C2×C414yes—
133#66872—41no—
134#66871—41no—
135#22679—111nomaximal, Sylow
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22C22×C412yes—
158C2×Dic22C22×C412yes—
159C2×Dic22C2×D412yes—
160C2×Dic22C2×D412yes—
161C2×Dic22C2×Q812yes—
162C2×Dic22C2×Q812yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C22×C412yes—
167C2×C8×C11C2×D412yes—
168C2×C8×C11C2×Q812yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4C22×C412yes—
178C11×C4⋊C4C22×C412yes—
179C42×C11—21no—
180C42×C11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11—81no—
187Dic11⋊C4—24no—
188Dic11⋊C4—24no—
189Dic11⋊C4—22no—
190Dic11⋊C4—41no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—81no—
197C4×Dic11—24no—
198C4×Dic11—24no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C4×Dic11C22×C412yes—
206C4×Dic11#4112yes—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C22×C412yes—
213Dic44C4⋊C4116yescomplemented
214C2×#441—111no—
215C2×#441—111no—
216C2×C4×Q16—111no—
217#2351—111no—
218Q8×C4⋊C4—111no—
219#1944D1111yescharacteristic
220#1941—111no—
221#1865—111no—
222#1865—111no—
223#1863—111no—
224#1863—111no—
225#1847—111no—
226#1805—111no—
227#1803—111no—
228#1771—111no—
229C23×C11C22×D411yescharacteristic
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×Q811yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
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—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11C4×D412yes—
276C2×Dic11C4×D412yes—
277C2×Dic11#13712yes—
278Dic22—22no—
279Dic22—22no—
280Dic22—22no—
281Dic22—22no—
282Dic22—22no—
283Dic22—22no—
284Dic22C2×C4⋊C414yes—
285Dic22C2×C4⋊C414yes—
286C8×C11—41no—
287C8×C11C2×C4⋊C414yes—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C22×Q16—111no—
291C2×C4×Q8—111no—
292C2×C4×Q8—111no—
293C2×C4×Q8—111no—
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8—111no—
297#441—118no—
298#441—224no—
299C4×Q16—224no—
300C2×#107—111no—
301C2×#107C2×D1111yescharacteristic
302C2×#106—111no—
303C2×#106—111no—
304C2×#106C2×D1111yescharacteristic
305C2×C4⋊C8—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#97—111no—
313C2×#97C2×D1111yescharacteristic
314C2×C4×C8—111no—
315#389—111no—
316#389—111no—
317#389—221no—
318#389—221no—
319#389—221no—
320#389—221no—
321#389C2×D1111yescharacteristic
322#389C2×D1111yescharacteristic
323#384—111no—
324#384—221no—
325#382—111no—
326#382—221no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—221no—
329C4×C4⋊C4—221no—
330#340—111no—
331#340—111no—
332#340C2×D1111yescharacteristic
333#340C2×D1111yescharacteristic
334#336—111no—
335#336—111no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11D4211yescharacteristic
338C22×C11D4×Q811yescharacteristic
339C22×C11C2×#13711yescharacteristic
340C22×C11#57511yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C22×C4⋊C411yescharacteristic
350C4×C11#52011yescharacteristic
351C4×C11#54711yescharacteristic
352C4×C11#55411yescharacteristic
353Dic11—24no—
354Dic11—24no—
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361C22×Q8—111no—
362C22×Q8—111no—
363C2×Q16—114no—
364C2×Q16—114no—
365C2×Q16—114no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C4×Q8—114no—
371C4×Q8—114no—
372C4×Q8—222no—
373C4×Q8—222no—
374C4×Q8—222no—
375C4×Q8—222no—
376C4×Q8—222no—
377C4×Q8—222no—
378C4×Q8—441no—
379C4×Q8—441no—
380C4×Q8—441no—
381C4×Q8—441no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
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×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411#107—22no—
412#107—441no—
413#106—222no—
414#106—441no—
415#106C4×D1114yes—
416C4⋊C8—222no—
417#103—114no—
418#103—114no—
419#103—222no—
420#103—222no—
421#103—222no—
422#103—222no—
423#97—22no—
424#97—114no—
425C4×C8—222no—
426#95—21no—
427#95—21no—
428#95—111no—
429#95—111no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434C2×C11D4×C4⋊C411yescharacteristic
435C2×C11C4×#13711yescharacteristic
436C2×C11#294711yescharacteristic
437C2×C11#327011yescharacteristic
438C2×C11#327111yescharacteristic
439C2×C11#338711yescharacteristic
440C2×C11#339011yescharacteristic
441C2×Q8—112no—
442C2×Q8—112no—
443C2×Q8—112no—
444C2×Q8—112no—
445C2×Q8—112no—
446C2×Q8—112no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4D4×D1111yescharacteristic
466C22×C4D4×D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468Q16—1116no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—112no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8C2×C4×D1112yes—
479C2×C8D4×D1112yes—
480C2×C8Q8×D1112yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—81no—
489C4⋊C4—222no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—441no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—881no—
504C4⋊C4—881no—
505C4⋊C4C2×C4×D1112yes—
506C4⋊C4C2×C4×D1112yes—
507C42—21no—
508C42—21no—
509C42—112no—
510C42—112no—
511C42—224no—
512C42—224no—
513C42—221no—
514C42—221no—
515C42—442no—
516C42—442no—
517C42—442no—
518C42—442no—
519C11#2267911yescharacteristic, complemented, Sylow
520C23C2×D4×D1111yescharacteristic
521Q8—114no—
522Q8—114no—
523Q8—222no—
524Q8—222no—
525Q8—222no—
526Q8—222no—
527Q8—222no—
528Q8—222no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
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—112no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—221no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4C22×C4×D1111yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×Q8×D1111yescharacteristic
574C2×C4#6704011yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C2×C4#6704211yescharacteristic
577C8—41no—
578C8—222no—
579C8—441no—
580C8C4⋊C4×D1114yes—
581C22C4×D4×D1111yescharacteristic
582C22#1062314011yescharacteristic
583C22#1062325811yescharacteristic
584C22#1062330411yescharacteristic
585C22#1062330611yescharacteristic
586C22D11×#13711yescharacteristic
587C22#1062331011yescharacteristic
588C4—41no—
589C4—41no—
590C4—42no—
591C4—42no—
592C4—81no—
593C4—81no—
594C4—222no—
595C4—224no—
596C4—224no—
597C4—222no—
598C4—222no—
599C4—441no—
600C4—881no—
601C4—881no—
602C4C2×C4⋊C4×D1111yescharacteristic
603C4#1062310511yescharacteristic
604C4#1062316211yescharacteristic
605C4#1062322111yescharacteristic
606C2#1307151711yescharacteristic
607C2#1307743811yescharacteristic
608C2#1307745611yescharacteristic
609C2#1308019311yescharacteristic
610C2#1308020811yescharacteristic
611C2#1308154511yescharacteristic
612C2#1308158011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1944C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1944D11
hypocenterC11#22679
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
50. #10622466C4semidirect
213. Dic44C4⋊C4semidirect
519. C11#22679semidirect

Maximal subgroups

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

subgroupindex
C2×#106223292
C2×#106224662
C2×#106224862
#130715352
#130715302
#130693452
#130688852
#130688832
#130688712
#130688692
#130687832
#130686302
#130686202
#130684922
C11×#19442
#2267911