Finite Group Databasebeta

← #14784649

Subgroups — #14784649

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071353C211yesmaximal, characteristic, complemented
2#13071323C211yesmaximal, characteristic
3#13070182C211yesmaximal, characteristic, complemented
4#13070176C211yesmaximal, characteristic, complemented
5#13070027C211yesmaximal, characteristic, complemented
6#13070023C211yesmaximal, characteristic
7#13069854C211yesmaximal, characteristic
8#13069853C211yesmaximal, characteristic
9#13069765C211yesmaximal, characteristic, complemented
10#13069761C211yesmaximal, characteristic
11#13068446C211yesmaximal, characteristic, complemented
12#13068444C211yesmaximal, characteristic
13C4×#66885C211yesmaximal, characteristic
14#13068367C211yesmaximal, characteristic, complemented
15C4×C11×#103C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#67000C2211yescharacteristic
18C2×#66943C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24#10622843C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29#10622602—21no—
30#10622602—21no—
31#10622601C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622589C2211yescharacteristic
34#10622589C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38#10622553—21no—
39#10622553—21no—
40C4×C4⋊Dic11C2211yescharacteristic
41#10622546—21no—
42#10622545C2211yescharacteristic
43#10622541—21no—
44C2×#66867C2211yescharacteristic
45#10622267—21no—
46#10622260—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73#67000—22no—
74#67000—22no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66943—22no—
97#66943—22no—
98C4×D44—22no—
99C4×D44—22no—
100C11×#103—22no—
101C11×#103—22no—
102C4×C8×C11—22no—
103C11×#95—21no—
104#66899—22no—
105#66899—22no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115#66885—22no—
116#66885—22no—
117#66873—22no—
118#66873—22no—
119#66867—22no—
120#23832—111nomaximal, Sylow
121C23×D11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11#4112yes—
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×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44#4112yes—
148C2×C4×D11—42no—
149C2×C4×D11—81no—
150C2×C4×D11—81no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4#4112yes—
164C42×C11—42no—
165C42×C11—81no—
166C42×C11#4112yes—
167C42×C11#4112yes—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—81no—
172(C2×D11)⋊C4—81no—
173C4⋊Dic11—24no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—81no—
180C4⋊Dic11#4112yes—
181Dic11⋊C4—24no—
182Dic11⋊C4—81no—
183Dic11⋊C4—81no—
184Dic11⋊C4—81no—
185Dic11⋊C4—81no—
186Dic11⋊C4—81no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—81no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198#2330—111no—
199#2326—111no—
200#2100—111no—
201#2099—111no—
202#2072—111no—
203#2071—111no—
204#2042—111no—
205#2042—111no—
206#2026—111no—
207#2025—111no—
208#1763—111no—
209#1762—111no—
210C4×#103D1111yescharacteristic, complemented
211C4×#102—111no—
212#1746—111no—
213C23×C11C22×D411yescharacteristic
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—41no—
224Q8×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
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#12412yes—
242C2×C4×C11#12412yes—
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—22no—
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—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270D44—22no—
271D44—22no—
272D44—41no—
273D44—41no—
274C4×D11—84no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C2×#125—111no—
280C2×#124—111no—
281C2×C4×Q8C2×D1111yescharacteristic
282C2×C4×D4—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×#103C2×D1111yescharacteristic
286C2×#103C2×D1111yescharacteristic
287C2×#102—111no—
288C2×#102—111no—
289C2×#102—111no—
290C2×#102—111no—
291C2×#97—111no—
292C2×C4×C8C2×D1111yescharacteristic
293#391—111no—
294#390—111no—
295#389—111no—
296#389—111no—
297#389—221no—
298#389—221no—
299#388—221no—
300#388—221no—
301#387—221no—
302#387—221no—
303#385—221no—
304#385—221no—
305#384—111no—
306#384—111no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4C2×D1111yescharacteristic
309#376—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340C2×D1111yescharacteristic
317#340C2×D1111yescharacteristic
318#336—111no—
319#336—111no—
320#336—111no—
321#336—111no—
322C22×C11#52511yescharacteristic
323C22×C11#52511yescharacteristic
324C22×C11C2×#12411yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57711yescharacteristic
328C22×C11#57811yescharacteristic
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—81no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#52911yescharacteristic
343C4×C11#52911yescharacteristic
344C4×C11#52911yescharacteristic
345C4×C11#52911yescharacteristic
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—42no—
350Dic11—41no—
351Dic11—81no—
352Dic11—81no—
353C22×Q8C22×D1111yescharacteristic
354C22×D4—111no—
355C23×C4—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360#125—222no—
361#125—222no—
362#124—222no—
363#124—222no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×D4—222no—
367C4×D4—222no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—221no—
393C2×C42C22×D1111yescharacteristic
394#103—22no—
395#103—22no—
396#103—222no—
397#103—222no—
398#102—222no—
399#102—222no—
400#102—222no—
401#102—222no—
402#97—222no—
403C4×C8—22no—
404#95—21no—
405#95—111no—
406#95—111no—
407#95—111no—
408#95—111no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414C2×C11#239811yescharacteristic
415C2×C11#311911yescharacteristic
416C2×C11#312011yescharacteristic
417C2×C11#312411yescharacteristic
418C2×C11#312511yescharacteristic
419C2×C11#313611yescharacteristic
420C2×C11#313711yescharacteristic
421D11—82no—
422C24—221no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#433912yes—
429C2×D4—112no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—442no—
447C22×C4—881no—
448C22×C4—881no—
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1111yescharacteristic
451C22×C4C23×D1111yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—42no—
470C4⋊C4—112no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—881no—
479C4⋊C4—881no—
480C4⋊C4—881no—
481C4⋊C4—881no—
482C4⋊C4—881no—
483C4⋊C4—881no—
484C4⋊C4#433912yes—
485C22⋊C4—224no—
486C22⋊C4—224no—
487C22⋊C4—442no—
488C22⋊C4—881no—
489C22⋊C4—881no—
490C42—42no—
491C42—81no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42—881no—
497C42#433912yes—
498C42#434112yes—
499C11#2383211yescharacteristic, complemented, Sylow
500C23—222no—
501C23—441no—
502C23—441no—
503C23—441no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23C2×D4×D1111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—222no—
513D4—222no—
514D4—441no—
515D4—441no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—222no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—884no—
554C2×C4#6693812yes—
555C2×C4#6693812yes—
556C2×C4C2×#433911yescharacteristic
557C2×C4C2×#433911yescharacteristic
558C2×C4C2×#433911yescharacteristic
559C2×C4C2×#434111yescharacteristic
560C2×C4#41×D1111yescharacteristic
561C2×C4#41×D1111yescharacteristic
562C8—41no—
563C8—41no—
564C8—441no—
565C8—441no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—881no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22C2×#6693811yescharacteristic
574C22#1062307811yescharacteristic
575C22#1062307811yescharacteristic
576C22#1062329311yescharacteristic
577C22#1062329711yescharacteristic
578C22#1062330011yescharacteristic
579C22#1062330111yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—441no—
587C4—441no—
588C4—441no—
589C4—442no—
590C4—441no—
591C4—881no—
592C4—881no—
593C4#1062301011yescharacteristic
594C4#1062305911yescharacteristic
595C4#1062306911yescharacteristic
596C4#1062308811yescharacteristic
597C2—882no—
598C2#1307190311yescharacteristic
599C2#1307882111yescharacteristic
600C2#1307883611yescharacteristic
601C2#1307888411yescharacteristic
602C2#1307888911yescharacteristic
603C2#1307897411yescharacteristic
604C2#1307897911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC4×#103D11
hypocenterC11#23832
LCSG ▷ C22×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
1. #13071353C2semidirect
3. #13070182C2semidirect
4. #13070176C2semidirect
5. #13070027C2semidirect
9. #13069765C2semidirect
11. #13068446C2semidirect
14. #13068367C2semidirect
15. C4×C11×#103C2semidirect
210. C4×#103D11semidirect
499. C11#23832semidirect

Maximal subgroups

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

subgroupindex
#130713532
#130713232
#130701822
#130701762
#130700272
#130700232
#130698542
#130698532
#130697652
#130697612
#130684462
#130684442
C4×#668852
#130683672
C4×C11×#1032
#2383211