Finite Group Databasebeta

← #14738854

Subgroups — #14738854

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079983C211yesmaximal, characteristic
2#13079837C211yesmaximal, characteristic
3#13077620C211yesmaximal, characteristic
4#13068141C211yesmaximal, characteristic, complemented
5#13068136C211yesmaximal, characteristic, complemented
6#13068119C211yesmaximal, characteristic, complemented
7#13068112C211yesmaximal, characteristic, complemented
8#13068017C211yesmaximal, characteristic, complemented
9#13068012C211yesmaximal, characteristic, complemented
10#13067995C211yesmaximal, characteristic, complemented
11#13067988C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067297C211yesmaximal, characteristic, complemented
15C11×#3165C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#501—21no—
20C11×#501—21no—
21C11×#500C2211yescharacteristic
22C11×#500C2211yescharacteristic
23C11×#498C2211yescharacteristic
24C11×#498C2211yescharacteristic
25C11×#428—21no—
26C11×#428—21no—
27C4×C11×M16C2211yescharacteristic
28#10622741—21no—
29#10622740—21no—
30#10622704C2211yescharacteristic
31#10622704C2211yescharacteristic
32#10622704C2211yescharacteristic
33#10622703C2211yescharacteristic
34#10622702—21no—
35#10622697C2211yescharacteristic
36#10622697C2211yescharacteristic
37#10622697C2211yescharacteristic
38#10622696C2211yescharacteristic
39#10622693—21no—
40#10622665—21no—
41#10622662—21no—
42#10622641—21no—
43#10622635—21no—
44#10622584—21no—
45#10622580—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622322—21no—
50#10622321—21no—
51#10622301C2211yescharacteristic
52C8×D44C2211yescharacteristic
53#10622292C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622184C2211yescharacteristic
60#10622184C2211yescharacteristic
61#10622184C2211yescharacteristic
62#10622184C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C22×Q8×C11—21no—
68C2×C11×M16D411yescharacteristic
69C2×C11×M16D411yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×#125—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C11×#117—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4325—21no—
88#66983D411yescharacteristic
89#66982—21no—
90C4×C22⋊D11—21no—
91#66977D411yescharacteristic
92C2×#4318—21no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95#66929—21no—
96#66928D411yescharacteristic
97C4×D44C2311yescharacteristic
98#66925—21no—
99#66923D411yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×#107—21no—
102C11×#107—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899—21no—
114#66899—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122C8×Dic11—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66872—21no—
130#66872—21no—
131#66872—21no—
132#66871—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#19379—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11—82no—
151C22×C4×C11—41no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C2×C22⋊D11—21no—
156C2×D44C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×Dic22C2×D411yescharacteristic
159C11×M16—22no—
160C11×M16—22no—
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C22⋊C4—41no—
178C42×C11—41no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11#4111yescharacteristic
182C42×C11C2411yescharacteristic
183C22⋊Dic11—21no—
184#4326—81no—
185#4325—81no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11C2×D411yescharacteristic
191C4⋊Dic11C2×D411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204#4313—42no—
205C8×D11—42no—
206#3252—111no—
207#3238—111no—
208#3165D1111yescharacteristic, complemented
209#2969—111no—
210#1696—111no—
211#1695—111no—
212#1692—111no—
213#1691—111no—
214#1676—111no—
215#1675—111no—
216#1672—111no—
217#1671—111no—
218#1569—111no—
219#1554—111no—
220#1548—111no—
221C23×C11#12111yescharacteristic
222C22×D11—21no—
223Q8×C11—41no—
224Q8×C11—41no—
225Q8×C11—81no—
226Q8×C11—81no—
227Q8×C11—81no—
228Q8×C11—82no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—82no—
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C22⋊D11—81no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249D44—21no—
250D44—21no—
251C4×D11—41no—
252C4×D11—41no—
253Dic22—21no—
254Dic22—21no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11#13712yes—
258C8×C11#13712yes—
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265#533C2×D1111yescharacteristic
266C2×C4⋊Q8C2×D1111yescharacteristic
267#529—111no—
268#501—21no—
269#501—21no—
270#501—221no—
271#500C2×D1111yescharacteristic
272#500C2×D1111yescharacteristic
273#498C2×D1111yescharacteristic
274#498C2×D1111yescharacteristic
275#489—221no—
276#483—221no—
277#480—221no—
278#479—221no—
279#477—111no—
280#477—111no—
281#477—111no—
282#476—111no—
283#476—111no—
284#476—111no—
285#470—221no—
286#468—221no—
287#464—221no—
288#462—111no—
289#461—111no—
290#446—111no—
291C8×Q8—111no—
292#436—111no—
293#436—221no—
294#435—221no—
295C8×D4—111no—
296#433—221no—
297#432—111no—
298#431—111no—
299#428—21no—
300#428—21no—
301#423—111no—
302#405—221no—
303C4×M16C2×D1111yescharacteristic
304#335—111no—
305#335—111no—
306#334—111no—
307#334—111no—
308#333—111no—
309#333—111no—
310#333—111no—
311#333—111no—
312#333—111no—
313#333—111no—
314#332—111no—
315#332—111no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11C2×#12111yescharacteristic
320C2×D11—41no—
321C2×D11—41no—
322C2×D11—41no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—81no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11C2×#13711yescharacteristic
332C4×C11C2×#13711yescharacteristic
333C4×C11#57711yescharacteristic
334C4×C11#57811yescharacteristic
335Dic11—41no—
336Dic11—41no—
337Dic11—41no—
338C22×Q8—21no—
339C2×Q16—221no—
340C2×SD16—221no—
341C2×M16—221no—
342C2×M16—221no—
343C2×M16C22⋊D1111yescharacteristic
344C2×M16C22⋊D1111yescharacteristic
345C22×C8—221no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8C22×D1111yescharacteristic
350C4⋊Q8C22×D1111yescharacteristic
351C4⋊Q8C22×D1111yescharacteristic
352C4⋊Q8C22×D1111yescharacteristic
353#126—221no—
354#125—21no—
355#125—111no—
356#124—111no—
357#123—221no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—111no—
361#121—111no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—111no—
365C4×D4—111no—
366C4×D4—221no—
367#117—21no—
368#117—221no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C42C22×D1111yescharacteristic
372#107—21no—
373#107—21no—
374#107—21no—
375#107—21no—
376#107—221no—
377#107—221no—
378#107—221no—
379#106—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—221no—
384#106—221no—
385#106—221no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#102—221no—
401#102—221no—
402#102—221no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—221no—
408#97—221no—
409#97C22⋊D1111yescharacteristic
410#97C22⋊D1111yescharacteristic
411C4×C8—221no—
412C4×C8—221no—
413C4×C8C22×D1111yescharacteristic
414C4×C8C22×D1111yescharacteristic
415C2×C11—41no—
416C2×C11#303911yescharacteristic
417C2×C11#306311yescharacteristic
418C2×C11#306811yescharacteristic
419D11—81no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—41no—
425C2×Q8—82no—
426C2×Q8—111no—
427C2×D4—111no—
428C2×D4—221no—
429C22×C4—41no—
430C22×C4—221no—
431C22×C4D4×D1111yescharacteristic
432C22×C4#434111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434Q16—881no—
435SD16—881no—
436M16—22no—
437M16—22no—
438M16—442no—
439M16—881no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—442no—
447C2×C8C2×C22⋊D1111yescharacteristic
448C2×C8C2×C22⋊D1111yescharacteristic
449C2×C8C2×C22⋊D1111yescharacteristic
450C2×C8C2×C22⋊D1111yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—111no—
464C4⋊C4—111no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C22⋊C4—41no—
470C22⋊C4—221no—
471C22⋊C4—221no—
472C22⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C42—41no—
476C42—221no—
477C42D4×D1111yescharacteristic
478C42#434111yescharacteristic
479C42C2×C22⋊D1111yescharacteristic
480C42C23×D1111yescharacteristic
481C11#1937911yescharacteristic, complemented, Sylow
482C23—221no—
483C23#6699111yescharacteristic
484Q8—41no—
485Q8—41no—
486Q8—81no—
487Q8—81no—
488Q8—81no—
489Q8—82no—
490Q8—221no—
491Q8—221no—
492D4—221no—
493D4—221no—
494D4—881no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4#6699111yescharacteristic
511C2×C4#6699111yescharacteristic
512C2×C4#6699111yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4C2×#434111yescharacteristic
515C2×C4C22×C22⋊D1111yescharacteristic
516C8—21no—
517C8—21no—
518C8—441no—
519C8—441no—
520C8—441no—
521C8—441no—
522C8—441no—
523C8—441no—
524C8#6699512yes—
525C8#6699512yes—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—441no—
530C22—441no—
531C22—441no—
532C22C2×#6699111yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4—441no—
542C4—441no—
543C4—441no—
544C4#1062330911yescharacteristic
545C4#1062331011yescharacteristic
546C4C2×#6699511yescharacteristic
547C4C2×#6699511yescharacteristic
548C2—41no—
549C2—881no—
550C2#1307809911yescharacteristic
551C2#1307830111yescharacteristic
552C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3165C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#3165D11
hypocenterC11#19379
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
4. #13068141C2semidirect
5. #13068136C2semidirect
6. #13068119C2semidirect
7. #13068112C2semidirect
8. #13068017C2semidirect
9. #13068012C2semidirect
10. #13067995C2semidirect
11. #13067988C2semidirect
12. #13067383C2semidirect
13. #13067326C2semidirect
14. #13067297C2semidirect
15. C11×#3165C2semidirect
208. #3165D11semidirect
481. C11#19379semidirect

Maximal subgroups

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

subgroupindex
#130799832
#130798372
#130776202
#130681412
#130681362
#130681192
#130681122
#130680172
#130680122
#130679952
#130679882
#130673832
#130673262
#130672972
C11×#31652
#1937911