Finite Group Databasebeta

← #14738764

Subgroups — #14738764

Order 2816.

576 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080003C211yesmaximal, characteristic
2#13079830C211yesmaximal, characteristic, complemented
3#13077563C211yesmaximal, characteristic, complemented
4#13068195C211yesmaximal, characteristic, complemented
5#13068153C211yesmaximal, characteristic, complemented
6#13068141C211yesmaximal, characteristic, complemented
7#13068085C211yesmaximal, characteristic, complemented
8#13068071C211yesmaximal, characteristic, complemented
9#13068029C211yesmaximal, characteristic, complemented
10#13068017C211yesmaximal, characteristic, complemented
11#13067961C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067311C211yesmaximal, characteristic
14#13067306C211yesmaximal, characteristic, complemented
15C11×#3182C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#468—21no—
24C11×#468—21no—
25C11×#440—21no—
26C11×#440—21no—
27C4×C11×M16C2211yescharacteristic
28#10622735—21no—
29#10622732—21no—
30#10622707C2211yescharacteristic
31#10622707C2211yescharacteristic
32#10622704C2211yescharacteristic
33#10622704C2211yescharacteristic
34#10622704C2211yescharacteristic
35#10622704C2211yescharacteristic
36#10622688C2211yescharacteristic
37#10622688C2211yescharacteristic
38#10622682—21no—
39#10622678—21no—
40#10622655—21no—
41#10622655—21no—
42#10622632—21no—
43#10622620—21no—
44#10622609—21no—
45#10622609—21no—
46#10622539C2211yescharacteristic
47#10622537C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622314—21no—
50#10622314—21no—
51#10622292C2211yescharacteristic
52#10622292C2211yescharacteristic
53C8×Dic22C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622184C2211yescharacteristic
60#10622184C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#127C2311yescharacteristic
76C11×#125—21no—
77C11×#124—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×#121—21no—
81C11×#121—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C11×#117—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4324—21no—
89C2×#4324—21no—
90#66979—21no—
91#66977—21no—
92#66977D411yescharacteristic
93#66977D411yescharacteristic
94C2×#4318—21no—
95C22×C11⋊C8—21no—
96#66923—21no—
97#66922D411yescharacteristic
98#66922D411yescharacteristic
99C4×Dic22—21no—
100C4×Dic22C2311yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×#107—21no—
103C11×#107—21no—
104C11×#103—21no—
105C11×#103—21no—
106C11×#102—21no—
107C11×#102—21no—
108C11×#97D411yescharacteristic
109C11×#97D411yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66896—21no—
113#66896—21no—
114C22⋊(C11⋊C8)—21no—
115#66879—21no—
116#66879—21no—
117Dic11⋊C8—21no—
118Dic11⋊C8—21no—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121C8×Dic11—21no—
122C8×Dic11—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66874—21no—
127#66874—21no—
128#66874—21no—
129#66872—21no—
130#66872—21no—
131#66871—21no—
132#66871—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#19373—111nomaximal, Sylow
145C11×#41—82no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C2×Dic22—21no—
158C2×Dic22C2×D411yescharacteristic
159C2×Dic22C2×D411yescharacteristic
160C11×SD16—42no—
161C11×SD16—42no—
162C11×M16—22no—
163C11×M16—41no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C42×C11—41no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185C22⋊Dic11—21no—
186#4324—81no—
187#4324—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C2×D411yescharacteristic
192C4⋊Dic11C2×D411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207#3254—111no—
208#3237—111no—
209#3182D1111yescharacteristic
210#2962—111no—
211#1704—111no—
212#1698—111no—
213#1696—111no—
214#1686—111no—
215#1684—111no—
216#1678—111no—
217#1676—111no—
218#1666—111no—
219#1569—111no—
220#1551—111no—
221#1550—111no—
222C23×C11—41no—
223C23×C11#12111yescharacteristic
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—81no—
227Q8×C11—81no—
228D4×C11—41no—
229D4×C11—41no—
230D4×C11—41no—
231D4×C11—41no—
232D4×C11—81no—
233D4×C11—82no—
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—82no—
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—21no—
257Dic22—81no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11#13712yes—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533—111no—
269#533C2×D1111yescharacteristic
270#532C2×D1111yescharacteristic
271#501—221no—
272#500C2×D1111yescharacteristic
273#492C2×D1111yescharacteristic
274#491—221no—
275#487C2×D1111yescharacteristic
276#486C2×D1111yescharacteristic
277#485—221no—
278#485—221no—
279#477—111no—
280#477—111no—
281#477—111no—
282#477—111no—
283#475—111no—
284#475—111no—
285#474—221no—
286#468—21no—
287#468—21no—
288#468—221no—
289#468—221no—
290#461—221no—
291#460—111no—
292#460—111no—
293#446—111no—
294#446—111no—
295#446—221no—
296#446—221no—
297C8×Q8—111no—
298C8×Q8—111no—
299#440—21no—
300#440—21no—
301#432—111no—
302#424—221no—
303#423—111no—
304C2×C4⋊C8—111no—
305#405—221no—
306C4×M16C2×D1111yescharacteristic
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311#333—111no—
312#333—111no—
313#333—111no—
314#333—111no—
315#332—111no—
316#332—111no—
317#331—111no—
318#331—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11C2×#12111yescharacteristic
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11C2×#13711yescharacteristic
334C4×C11#57511yescharacteristic
335C4×C11#57711yescharacteristic
336C4×C11#57811yescharacteristic
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341C2×#41—21no—
342C2×SD16—21no—
343C2×SD16—21no—
344C2×SD16—221no—
345C2×SD16—221no—
346C2×M16—221no—
347C2×M16C22⋊D1111yescharacteristic
348C2×M16C22⋊D1111yescharacteristic
349C22×C8—221no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8C22×D1111yescharacteristic
353C4⋊Q8C22×D1111yescharacteristic
354C4⋊Q8C22×D1111yescharacteristic
355#127C22×D1111yescharacteristic
356#125—21no—
357#125—221no—
358#124—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—111no—
362C22⋊Q8—111no—
363C22⋊Q8—221no—
364#121—21no—
365#121—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—221no—
371C4×D4—21no—
372C4×D4—21no—
373#117—21no—
374#117—221no—
375C2×C42C22×D1111yescharacteristic
376#107—21no—
377#107—21no—
378#107—221no—
379#107—221no—
380#107—221no—
381#107—221no—
382#106—221no—
383#106—221no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396#103—21no—
397#103—21no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#102—21no—
405#102—21no—
406#102—221no—
407#102—221no—
408C22⋊C8—221no—
409#97—221no—
410#97—221no—
411#97—221no—
412#97C22⋊D1111yescharacteristic
413#97C22⋊D1111yescharacteristic
414C4×C8—221no—
415C4×C8—221no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11—41no—
419C2×C11—161no—
420C2×C11#303711yescharacteristic
421C2×C11#306311yescharacteristic
422C2×C11#306811yescharacteristic
423#41—82no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—111no—
428C2×Q8—111no—
429C2×Q8—221no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—41no—
434C22×C4—41no—
435C22×C4D4×D1111yescharacteristic
436C22×C4#434111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438SD16—42no—
439SD16—42no—
440SD16—881no—
441SD16—881no—
442M16—22no—
443M16—41no—
444M16—881no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—442no—
452C2×C8C2×C22⋊D1111yescharacteristic
453C2×C8C2×C22⋊D1111yescharacteristic
454C2×C8C2×C22⋊D1111yescharacteristic
455C2×C8C2×C22⋊D1111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—111no—
465C4⋊C4—111no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—41no—
479C42—221no—
480C42—221no—
481C42D4×D1111yescharacteristic
482C42#434111yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1937311yescharacteristic, complemented, Sylow
486C23—41no—
487C23#6699111yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—81no—
491Q8—81no—
492Q8—221no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8—881no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—81no—
502D4—82no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—82no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4#6699111yescharacteristic
517C2×C4#6699111yescharacteristic
518C2×C4#6699111yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—441no—
526C8—441no—
527C8—441no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8#6700412yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22C2×#6699111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—441no—
547C4—441no—
548C4—441no—
549C4—441no—
550C4#1062330911yescharacteristic
551C4#1062331011yescharacteristic
552C4#1062335311yescharacteristic
553C4C2×#6700411yescharacteristic
554C2—41no—
555C2—161no—
556C2#1307808411yescharacteristic
557C2#1307830111yescharacteristic
558C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3182C2
socleC22×C11C2×#121
prime radicalC11×#532C22
hypercenter#3182D11
hypocenterC11#19373
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
2. #13079830C2semidirect
3. #13077563C2semidirect
4. #13068195C2semidirect
5. #13068153C2semidirect
6. #13068141C2semidirect
7. #13068085C2semidirect
8. #13068071C2semidirect
9. #13068029C2semidirect
10. #13068017C2semidirect
11. #13067961C2semidirect
12. #13067383C2semidirect
14. #13067306C2semidirect
485. C11#19373semidirect

Maximal subgroups

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

subgroupindex
#130800032
#130798302
#130775632
#130681952
#130681532
#130681412
#130680852
#130680712
#130680292
#130680172
#130679612
#130673832
#130673112
#130673062
C11×#31822
#1937311