Finite Group Databasebeta

← #14758155

Subgroups — #14758155

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622639C211yesmaximal, characteristic
2#13071267C211yesmaximal, characteristic, complemented
3#13071254C211yesmaximal, characteristic
4#13069494C211yesmaximal, characteristic
5#13069467C211yesmaximal, characteristic
6#13069353C211yesmaximal, characteristic, complemented
7#13069348C211yesmaximal, characteristic, complemented
8#13069314C211yesmaximal, characteristic
9#13069303C211yesmaximal, characteristic, complemented
10#13069300C211yesmaximal, characteristic
11#13069289C211yesmaximal, characteristic, complemented
12#13068514C211yesmaximal, characteristic, complemented
13C4×#66885C211yesmaximal, characteristic
14#13068302C211yesmaximal, characteristic, complemented
15C4×C11×#103C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C11×#103C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23#10622843C2211yescharacteristic
24#10622843C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622639C418yescomplemented
33#10622601C2211yescharacteristic
34#10622601C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622594—21no—
38#10622594—21no—
39#10622586C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622553—21no—
46#10622553—21no—
47#10622550—21no—
48#10622549—21no—
49C4×C4⋊Dic11C2211yescharacteristic
50#10622545C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52#10622280—21no—
53#10622277—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C4×Q8×C11—22no—
66C4×Q8×C11C2×C414yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×#4325—22no—
75C2×#4325—22no—
76C2×#4325C2×C414yes—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
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×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C4×D44—22no—
95C4×D44C2×C414yes—
96C11×#103—22no—
97C11×#103—22no—
98C4×C8×C11—22no—
99C11×#95—21no—
100#66899C2×C414yes—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66885—22no—
115#66885—22no—
116#66879—22no—
117#66879—22no—
118C8×Dic11—22no—
119C8×Dic11—22no—
120#66873C2×C414yes—
121#66872—22no—
122#66871—22no—
123#66871C2×C414yes—
124#66867C2×C414yes—
125#21291—111nomaximal, Sylow
126C23×D11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44C22×C412yes—
153C2×C4×D11—24no—
154C2×C4×D11—81no—
155C2×C4×D11—81no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11#4112yes—
161C2×C8×C11#4112yes—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C412yes—
169C42×C11—24no—
170C42×C11—81no—
171C42×C11C22×C412yes—
172C42×C11#4112yes—
173#4325—28no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—81no—
176(C2×D11)⋊C4—81no—
177(C2×D11)⋊C4—81no—
178(C2×D11)⋊C4—81no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—81no—
185C4⋊Dic11—81no—
186C4⋊Dic11C22×C412yes—
187Dic11⋊C4—81no—
188Dic11⋊C4—81no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—81no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8C22×C412yes—
197C2×C11⋊C8C22×C412yes—
198C2×C11⋊C8#4112yes—
199C2×C11⋊C8#4112yes—
200C2×#440—111no—
201#2320—111no—
202#2319—111no—
203#1973—111no—
204#1968—111no—
205#1943—111no—
206#1942—111no—
207#1936—111no—
208#1935—111no—
209#1934—111no—
210#1933—111no—
211#1776—111no—
212C4×#103D1111yescharacteristic, complemented
213C4×#102—111no—
214#1726—111no—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—41no—
226Q8×C11—41no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
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×C11C4×D412yes—
244C2×C4×C11C4×D412yes—
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×Dic11—22no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272D44—22no—
273D44—22no—
274D44—41no—
275D44—41no—
276C4×D11—84no—
277C8×C11—22no—
278C8×C11—22no—
279C11⋊C8—22no—
280C11⋊C8#11714yes—
281C22×SD16—111no—
282C2×C4×Q8C2×D1111yescharacteristic
283C2×C4×D4—111no—
284#440—118no—
285C2×#107—111no—
286C2×#107—111no—
287C2×#106—111no—
288C2×#103—111no—
289C2×#103C2×D1111yescharacteristic
290C2×#103C2×D1111yescharacteristic
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#97—111no—
295C2×#97—111no—
296C2×#97—111no—
297C2×C4×C8—111no—
298C2×C4×C8—111no—
299C2×C4×C8C2×D1111yescharacteristic
300#391—111no—
301#391—111no—
302#390—111no—
303#390—111no—
304#389—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#388—221no—
309#388—221no—
310#387—221no—
311#387—221no—
312#383—221no—
313#382—221no—
314#381—221no—
315#380—221no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4C2×D1111yescharacteristic
318#376—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340C2×D1111yescharacteristic
324#340C2×D1111yescharacteristic
325C22×C11C2×C4×D411yescharacteristic
326C22×C11#53211yescharacteristic
327C22×C11#53211yescharacteristic
328C22×C11#57611yescharacteristic
329C22×C11#57711yescharacteristic
330C22×C11#57711yescharacteristic
331C22×C11#57811yescharacteristic
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C2×#11711yescharacteristic
346C4×C11C4×#4111yescharacteristic
347C4×C11#52911yescharacteristic
348C4×C11#52911yescharacteristic
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353Dic11—42no—
354Dic11—81no—
355Dic11—81no—
356C22×Q8C22×D1111yescharacteristic
357C22×D4—111no—
358C23×C4—221no—
359C2×SD16—114no—
360C2×SD16—222no—
361C2×SD16—222no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C4×Q8—22no—
367C4×Q8C4×D1114yes—
368C4×D4—114no—
369C4×D4—222no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392#107—114no—
393#107—222no—
394#106—222no—
395#103—22no—
396#103—22no—
397#103—114no—
398#102—114no—
399#102—222no—
400#102—222no—
401#97—114no—
402#97—222no—
403#97—222no—
404C4×C8—22no—
405C4×C8—222no—
406C4×C8—222no—
407#95—21no—
408#95—111no—
409#95—111no—
410#95—111no—
411#95—111no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421C2×C11#229311yescharacteristic
422C2×C11#294611yescharacteristic
423C2×C11#294711yescharacteristic
424C2×C11#317411yescharacteristic
425C2×C11#317511yescharacteristic
426C2×C11#317811yescharacteristic
427C2×C11#317911yescharacteristic
428D11—82no—
429C24—221no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×C4×D1112yes—
436C2×D4—112no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—221no—
451C22×C4—224no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—881no—
455C22×C4—881no—
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459SD16—228no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—112no—
465C2×C8—112no—
466C2×C8—112no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8#433912yes—
471C2×C8#433912yes—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—112no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—881no—
485C4⋊C4—881no—
486C4⋊C4—881no—
487C4⋊C4—881no—
488C4⋊C4C2×C4×D1112yes—
489C22⋊C4—224no—
490C22⋊C4—881no—
491C22⋊C4—881no—
492C22⋊C4—881no—
493C22⋊C4—881no—
494C42—24no—
495C42—81no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42—881no—
501C42C2×C4×D1112yes—
502C42#434112yes—
503C11#2129111yescharacteristic, complemented, Sylow
504C23—222no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23—441no—
511C23C2×D4×D1111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—222no—
517D4—222no—
518D4—441no—
519D4—441no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
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—222no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
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—884no—
558C2×C4(C22⋊D11)⋊C412yes—
559C2×C4(C22⋊D11)⋊C412yes—
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C2×#433911yescharacteristic
563C2×C4C2×#434111yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#41×D1111yescharacteristic
566C8—22no—
567C8—22no—
568C8—114no—
569C8—222no—
570C22—442no—
571C22—442no—
572C22—442no—
573C22—881no—
574C22—881no—
575C22—881no—
576C22—881no—
577C22C2×(C22⋊D11)⋊C411yescharacteristic
578C22#1062307911yescharacteristic
579C22#1062307911yescharacteristic
580C22#1062329311yescharacteristic
581C22#1062329711yescharacteristic
582C22#1062330011yescharacteristic
583C22#1062330111yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—441no—
591C4—442no—
592C4—441no—
593C4—441no—
594C4—441no—
595C4—881no—
596C4—881no—
597C4C4×#433911yescharacteristic
598C4D11×#11711yescharacteristic
599C4#1062306911yescharacteristic
600C4#1062306911yescharacteristic
601C2—882no—
602C2#1307107911yescharacteristic
603C2#1307745111yescharacteristic
604C2#1307745311yescharacteristic
605C2#1307924011yescharacteristic
606C2#1307925711yescharacteristic
607C2#1307928811yescharacteristic
608C2#1307929511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC4×#103D11
hypocenterC11#21291
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. #13071267C2semidirect
6. #13069353C2semidirect
7. #13069348C2semidirect
9. #13069303C2semidirect
11. #13069289C2semidirect
12. #13068514C2semidirect
14. #13068302C2semidirect
15. C4×C11×#103C2semidirect
32. #10622639C4semidirect
212. C4×#103D11semidirect
503. C11#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#106226392
#130712672
#130712542
#130694942
#130694672
#130693532
#130693482
#130693142
#130693032
#130693002
#130692892
#130685142
C4×#668852
#130683022
C4×C11×#1032
#2129111