Finite Group Databasebeta

← #14736818

Subgroups — #14736818

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079357C211yesmaximal, characteristic, complemented
2#13078687C211yesmaximal, characteristic
3#13077636C211yesmaximal, characteristic
4#13068193C211yesmaximal, characteristic, complemented
5#13068161C211yesmaximal, characteristic, complemented
6#13068117C211yesmaximal, characteristic, complemented
7#13068103C211yesmaximal, characteristic, complemented
8#13068076C211yesmaximal, characteristic, complemented
9#13068044C211yesmaximal, characteristic, complemented
10#13068000C211yesmaximal, characteristic, complemented
11#13067984C211yesmaximal, characteristic, complemented
12#13067366C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067314C211yesmaximal, characteristic, complemented
15C11×#3076C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#479—21no—
20C11×#478—21no—
21C11×#477C2211yescharacteristic
22C11×#476C2211yescharacteristic
23C11×#475C2211yescharacteristic
24C11×#474C2211yescharacteristic
25C11×#427—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#416—21no—
28#10622852—21no—
29#10622706C2211yescharacteristic
30#10622705C2211yescharacteristic
31#10622694C2211yescharacteristic
32#10622692C2211yescharacteristic
33#10622665—21no—
34#10622665—21no—
35#10622644C2211yescharacteristic
36#10622643—21no—
37#10622643—21no—
38C4×#4326—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622632C2211yescharacteristic
43C4×#4324—21no—
44#10622625—21no—
45#10622625—21no—
46#10622625C2211yescharacteristic
47#10622625C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622609—21no—
50#10622539—21no—
51#10622539C2211yescharacteristic
52#10622538C2211yescharacteristic
53C4×#4318—21no—
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C22×C8×C11—21no—
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#125—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11D411yescharacteristic
81C4×D4×C11C2311yescharacteristic
82C11×#117—21no—
83C11×#117—21no—
84C11×#117D411yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×#4326—21no—
88C2×#4326—21no—
89C2×#4326—21no—
90C2×#4324—21no—
91#66979—21no—
92#66977—21no—
93#66977—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318D411yescharacteristic
97C2×#4318D411yescharacteristic
98#66923—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113C11×#102—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66874—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66872—21no—
127#66872—21no—
128#66872—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867D411yescharacteristic
138#66867D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19185—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—42no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4C2×D411yescharacteristic
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—41no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—41no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—41no—
186#4326—42no—
187#4326—42no—
188#4326—42no—
189#4324—42no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194Dic11⋊C4—41no—
195Dic11⋊C4—41no—
196C4×Dic11—41no—
197#4318—22no—
198#4318—41no—
199#4318—42no—
200#4318—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209#3185—111no—
210#3107—111no—
211#3076D1111yescharacteristic
212#2971—111no—
213#1703—111no—
214#1699—111no—
215#1691—111no—
216#1689—111no—
217#1684—111no—
218#1680—111no—
219#1672—111no—
220#1670—111no—
221#1565—111no—
222#1554—111no—
223#1552—111no—
224C23×C11—21no—
225C23×C11#12111yescharacteristic
226Q8×C11—21no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—81no—
230Q8×C11#13712yes—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—42no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—81no—
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×Dic11—41no—
255C2×Dic11—41no—
256Dic22—41no—
257Dic22—41no—
258Dic22—41no—
259Dic22—41no—
260C8×C11—41no—
261C8×C11—41no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8#13512yes—
270#533—111no—
271#533C2×D1111yescharacteristic
272C4×#41C2×D1111yescharacteristic
273#498—111no—
274#494—111no—
275#487—111no—
276#487—111no—
277#485—221no—
278#479—21no—
279#478—21no—
280#477C2×D1111yescharacteristic
281#476C2×D1111yescharacteristic
282#475—111no—
283#475C2×D1111yescharacteristic
284#474—111no—
285#474C2×D1111yescharacteristic
286#470—221no—
287#470—221no—
288#462—111no—
289#461—111no—
290#452—221no—
291C8×Q8—111no—
292C8×Q8—111no—
293#441—221no—
294#441—221no—
295C4×Q16—221no—
296C4×SD16—221no—
297#436—111no—
298#436—111no—
299#436—221no—
300#436—221no—
301#432—111no—
302#432—221no—
303#431—111no—
304#427—21no—
305C2×C4⋊C8C2×D1111yescharacteristic
306#416—21no—
307C4×M16—111no—
308C4×M16—221no—
309#335—111no—
310#335—111no—
311#334—111no—
312#334—111no—
313#333—111no—
314#333—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11C2×#12111yescharacteristic
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—22no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11C2×#13511yescharacteristic
338C4×C11C2×#13711yescharacteristic
339C4×C11#57511yescharacteristic
340C4×C11#57511yescharacteristic
341Dic11—81no—
342Dic11—81no—
343C2×#41C22⋊D1111yescharacteristic
344C2×Q16—221no—
345C2×Q16—221no—
346C2×Q16—221no—
347C2×SD16—221no—
348C2×M16—111no—
349C2×M16—111no—
350C2×M16—221no—
351C2×M16—221no—
352C22×C8—21no—
353C4⋊Q8—111no—
354C4⋊Q8—111no—
355C4⋊Q8C22×D1111yescharacteristic
356C4⋊Q8C22×D1111yescharacteristic
357#125—21no—
358#125—221no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—221no—
362C22⋊Q8—221no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—221no—
366C4×Q8—221no—
367C4×Q8C22⋊D1111yescharacteristic
368C4×Q8C22×D1111yescharacteristic
369C4×D4—21no—
370C4×D4—21no—
371C4×D4C22⋊D1111yescharacteristic
372C4×D4C22×D1111yescharacteristic
373#117—21no—
374#117—21no—
375#117—221no—
376#117C22⋊D1111yescharacteristic
377C2×C42—21no—
378C2×C42C22×D1111yescharacteristic
379#107—21no—
380#107—21no—
381#107—221no—
382#106—21no—
383#106—21no—
384#106—221no—
385#106—221no—
386#106—221no—
387C4⋊C8—21no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
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#103—221no—
405#102—21no—
406#102—21no—
407#102—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412#97—111no—
413#97—111no—
414#97—221no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8—221no—
420C2×C11—41no—
421C2×C11—81no—
422C2×C11#303511yescharacteristic
423C2×C11#305611yescharacteristic
424C2×C11#306911yescharacteristic
425#41—22no—
426#41—41no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8C2×C22⋊D1111yescharacteristic
432C2×D4—21no—
433C2×D4C2×C22⋊D1111yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4D4×D1111yescharacteristic
438C22×C4#434111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440Q16—442no—
441Q16—442no—
442Q16—442no—
443SD16—442no—
444M16—222no—
445M16—442no—
446M16—441no—
447M16—442no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—441no—
472C4⋊C4—441no—
473C4⋊C4C2×C22⋊D1111yescharacteristic
474C4⋊C4C2×C22⋊D1111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—441no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—41no—
484C42—441no—
485C42D4×D1111yescharacteristic
486C42#434111yescharacteristic
487C42C2×C22⋊D1111yescharacteristic
488C42C23×D1111yescharacteristic
489C11#1918511yescharacteristic, complemented, Sylow
490C23—21no—
491C23#6699211yescharacteristic
492Q8—21no—
493Q8—41no—
494Q8—41no—
495Q8—81no—
496Q8—441no—
497Q8—441no—
498Q8—441no—
499Q8—441no—
500Q8#6699512yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—81no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4#6699211yescharacteristic
521C2×C4#6699211yescharacteristic
522C2×C4#6699211yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—41no—
527C8—41no—
528C8—112no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8—441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×#6699211yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—881no—
553C4—881no—
554C4D11×#13511yescharacteristic
555C4#1062329911yescharacteristic
556C4C2×#6699511yescharacteristic
557C4#1062335311yescharacteristic
558C2—41no—
559C2—81no—
560C2#1307806711yescharacteristic
561C2#1307824211yescharacteristic
562C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3076C2
socleC22×C11C2×#121
prime radicalC2×C11×#41D4
hypercenter#3076D11
hypocenterC11#19185
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #13079357C2semidirect
4. #13068193C2semidirect
5. #13068161C2semidirect
6. #13068117C2semidirect
7. #13068103C2semidirect
8. #13068076C2semidirect
9. #13068044C2semidirect
10. #13068000C2semidirect
11. #13067984C2semidirect
12. #13067366C2semidirect
13. #13067326C2semidirect
14. #13067314C2semidirect
489. C11#19185semidirect

Maximal subgroups

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

subgroupindex
#130793572
#130786872
#130776362
#130681932
#130681612
#130681172
#130681032
#130680762
#130680442
#130680002
#130679842
#130673662
#130673262
#130673142
C11×#30762
#1918511