Finite Group Databasebeta

← #14853539

Subgroups — #14853539

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074592C211yesmaximal, characteristic, complemented
2#13071324C211yesmaximal, characteristic
3#13070178C211yesmaximal, characteristic, complemented
4#13069858C211yesmaximal, characteristic
5#13069857C211yesmaximal, characteristic
6#13069314C211yesmaximal, characteristic
7#13069304C211yesmaximal, characteristic, complemented
8#13069297C211yesmaximal, characteristic
9#13069293C211yesmaximal, characteristic, complemented
10#13068630C211yesmaximal, characteristic, complemented
11#13068625C211yesmaximal, characteristic
12#13068620C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic
14#13068472C211yesmaximal, characteristic, complemented
15C11×#2099C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66940C2211yescharacteristic
18C2×#66928C2211yescharacteristic
19C11×#389C2211yescharacteristic
20C11×#384C2211yescharacteristic
21C2×#66885C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66880C2211yescharacteristic
24C2×#66880C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622603—21no—
30#10622603—21no—
31#10622602—21no—
32#10622602—21no—
33#10622601C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622597—21no—
36#10622593—21no—
37#10622590C2211yescharacteristic
38#10622589C2211yescharacteristic
39#10622587C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45#10622545C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622272—21no—
48#10622271—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
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)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90#66946—22no—
91#66946—22no—
92#66940—22no—
93#66940—22no—
94#66928—22no—
95#66928—22no—
96C11×#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95D411yescharacteristic
105C11⋊#95D411yescharacteristic
106C11⋊#95D411yescharacteristic
107C11⋊#95D411yescharacteristic
108#66885—22no—
109#66885—41no—
110#66880—22no—
111#66880—41no—
112#66879—41no—
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115C8×Dic11—41no—
116#66874—22no—
117#66874—41no—
118#66873—22no—
119#66873—41no—
120#29134—111nomaximal, Sylow
121C23×D11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44#4112yes—
142C2×C4×D11—42no—
143C2×C4×D11—81no—
144C2×C4×D11—81no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22#4112yes—
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—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4—81no—
168C42×C11—21no—
169C42×C11—21no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—42no—
173(C2×D11)⋊C4—81no—
174(C2×D11)⋊C4—81no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—81no—
180Dic11⋊C4—42no—
181Dic11⋊C4—81no—
182Dic11⋊C4—81no—
183Dic11⋊C4—81no—
184Dic11⋊C4—81no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—42no—
188C4×Dic11#4112yes—
189C4×Dic11#4112yes—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196#2647—111no—
197#2326—111no—
198#2100—111no—
199#2099D1111yescharacteristic, complemented
200#2042—111no—
201#2042—111no—
202#1936—111no—
203#1935—111no—
204#1934—111no—
205#1933—111no—
206#1805—111no—
207#1804—111no—
208#1803—111no—
209#1802—111no—
210#1768—111no—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
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×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11#12412yes—
263C2×Dic11#12412yes—
264D44—22no—
265D44—22no—
266D44—41no—
267D44—41no—
268C4×D11—84no—
269Dic22—22no—
270Dic22—22no—
271Dic22—41no—
272Dic22—41no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C2×#124—111no—
278C2×C4×Q8—111no—
279C2×C4×D4—111no—
280C2×C4⋊C8—111no—
281C2×C4⋊C8—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#102—111no—
287C2×#102—111no—
288C2×#102—111no—
289C2×#102—111no—
290C2×#97—111no—
291C2×C4×C8—111no—
292#400—221no—
293#400—221no—
294#398—221no—
295#398—221no—
296#391—111no—
297#390—111no—
298#389—111no—
299#389—111no—
300#389—111no—
301#389C2×D1111yescharacteristic
302#388—221no—
303#388—221no—
304#385—221no—
305#385—221no—
306#384—111no—
307#384C2×D1111yescharacteristic
308#382—111no—
309#376—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340C2×D1111yescharacteristic
315#340C2×D1111yescharacteristic
316#340C2×D1111yescharacteristic
317#340C2×D1111yescharacteristic
318#336—111no—
319#336C2×D1111yescharacteristic
320C22×C11#52511yescharacteristic
321C22×C11C2×#12411yescharacteristic
322C22×C11#53711yescharacteristic
323C22×C11#57611yescharacteristic
324C22×C11#57711yescharacteristic
325C22×C11#57711yescharacteristic
326C22×C11#57811yescharacteristic
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11#55211yescharacteristic
341C4×C11#55211yescharacteristic
342C4×C11#55311yescharacteristic
343C4×C11#55311yescharacteristic
344Dic11—22no—
345Dic11—22no—
346Dic11—42no—
347Dic11—41no—
348Dic11—41no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8—111no—
352C22×D4—111no—
353C23×C4—221no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358#124—222no—
359#124—222no—
360C4×Q8—222no—
361C4×Q8—222no—
362C4×D4—222no—
363C4×D4—222no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388C4⋊C8—222no—
389C4⋊C8—222no—
390#103—222no—
391#103—222no—
392#103—441no—
393#103—441no—
394#102—222no—
395#102—222no—
396#102—441no—
397#102—441no—
398#97—441no—
399C4×C8—441no—
400#95—21no—
401#95—111no—
402#95—111no—
403#95—111no—
404#95—111no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412C2×C11#256211yescharacteristic
413C2×C11#311911yescharacteristic
414C2×C11#312011yescharacteristic
415C2×C11#313611yescharacteristic
416C2×C11#313711yescharacteristic
417C2×C11#326211yescharacteristic
418C2×C11#326311yescharacteristic
419D11—82no—
420C24—221no—
421C2×Q8—112no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×D4—112no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—442no—
445C22×C4—881no—
446C22×C4—881no—
447C22×C4D4×D1111yescharacteristic
448C22×C4D4×D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—442no—
478C4⋊C4—881no—
479C4⋊C4—881no—
480C4⋊C4—881no—
481C4⋊C4—881no—
482C4⋊C4—881no—
483C22⋊C4—224no—
484C22⋊C4—224no—
485C22⋊C4—442no—
486C22⋊C4—881no—
487C22⋊C4—881no—
488C42—21no—
489C42—21no—
490C42—112no—
491C42—112no—
492C42—221no—
493C42—221no—
494C42—442no—
495C11#2913411yescharacteristic, complemented, Sylow
496C23—222no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23—441no—
501C23—441no—
502C23—441no—
503C23C2×D4×D1111yescharacteristic
504Q8—222no—
505Q8—222no—
506Q8—441no—
507Q8—441no—
508D4—222no—
509D4—222no—
510D4—441no—
511D4—441no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
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—112no—
531C2×C4—112no—
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—222no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—884no—
552C2×C4#6704011yescharacteristic
553C2×C4#41×D1111yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#6704211yescharacteristic
558C8—41no—
559C8—41no—
560C8—441no—
561C8—441no—
562C22—442no—
563C22—442no—
564C22—442no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22#1062316011yescharacteristic
570C22#1062318711yescharacteristic
571C22D11×#12411yescharacteristic
572C22#1062328811yescharacteristic
573C22#1062329311yescharacteristic
574C22#1062330911yescharacteristic
575C22#1062331011yescharacteristic
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—222no—
583C4—222no—
584C4—441no—
585C4—441no—
586C4—442no—
587C4—881no—
588C4—881no—
589C4#1062322411yescharacteristic
590C4#1062322411yescharacteristic
591C4#1062324011yescharacteristic
592C4#1062324011yescharacteristic
593C2—882no—
594C2#1307377811yescharacteristic
595C2#1307881811yescharacteristic
596C2#1307883311yescharacteristic
597C2#1307896511yescharacteristic
598C2#1307898211yescharacteristic
599C2#1308007611yescharacteristic
600C2#1308008511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2099C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2099D11
hypocenterC11#29134
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
1. #13074592C2semidirect
3. #13070178C2semidirect
7. #13069304C2semidirect
9. #13069293C2semidirect
10. #13068630C2semidirect
12. #13068620C2semidirect
14. #13068472C2semidirect
15. C11×#2099C2semidirect
199. #2099D11semidirect
495. C11#29134semidirect

Maximal subgroups

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

subgroupindex
#130745922
#130713242
#130701782
#130698582
#130698572
#130693142
#130693042
#130692972
#130692932
#130686302
#130686252
#130686202
#130686152
#130684722
C11×#20992
#2913411