Finite Group Databasebeta

← #14737227

Subgroups — #14737227

Order 2816.

584 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#13079953C211yesmaximal, characteristic
2#13079198C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic
4#13068132C211yesmaximal, characteristic, complemented
5#13068127C211yesmaximal, characteristic, complemented
6#13068108C211yesmaximal, characteristic, complemented
7#13068103C211yesmaximal, characteristic, complemented
8#13068048C211yesmaximal, characteristic, complemented
9#13068044C211yesmaximal, characteristic, complemented
10#13068041C211yesmaximal, characteristic, complemented
11#13068037C211yesmaximal, characteristic, complemented
12C2×#10622118C211yesmaximal, characteristic, complemented
13#13067316C211yesmaximal, characteristic, complemented
14#13067314C211yesmaximal, characteristic, complemented
15C11×#3248C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#479—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#467—21no—
23C11×#465—21no—
24C11×#464—21no—
25C11×#462C2211yescharacteristic
26C11×#461C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622706C2211yescharacteristic
29#10622705C2211yescharacteristic
30#10622694C2211yescharacteristic
31#10622691C2211yescharacteristic
32#10622676—21no—
33#10622667—21no—
34#10622664—21no—
35#10622664—21no—
36#10622664—21no—
37#10622654—21no—
38#10622644C2211yescharacteristic
39C4×#4326—21no—
40C4×#4326—21no—
41#10622637C2211yescharacteristic
42Q8×C11⋊C8C2211yescharacteristic
43#10622633C2211yescharacteristic
44#10622632C2211yescharacteristic
45#10622625C2211yescharacteristic
46#10622624—21no—
47D4×C11⋊C8—21no—
48D4×C11⋊C8C2211yescharacteristic
49#10622620C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622118C2211yescharacteristic
66#10622118C2211yescharacteristic
67C2×C11×Q16—21no—
68C2×C11×SD16—21no—
69C22×C8×C11—21no—
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#126—21no—
73C11×#125—21no—
74C11×#125D411yescharacteristic
75C11×#124D411yescharacteristic
76C11×#123—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×#121D411yescharacteristic
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11C2311yescharacteristic
86C11×#117—21no—
87C11×#117—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4326—21no—
90C2×#4326—21no—
91C2×#4326—21no—
92C2×#4324—21no—
93#66979—21no—
94#66977—21no—
95#66977—21no—
96C2×#4318—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8D411yescharacteristic
100C22×C11⋊C8D411yescharacteristic
101#66923—21no—
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104C4×Dic22—21no—
105C4×Dic22—21no—
106C11×#107—21no—
107C11×#106—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103—21no—
113C11×#103—21no—
114C11×#102—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—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#66871—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19228—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C11×Q16—81no—
157C11×SD16—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—81no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
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—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—41no—
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—81no—
189#4324—81no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194Dic11⋊C4—41no—
195Dic11⋊C4—41no—
196C4×Dic11—41no—
197#4318—42no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—41no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8—81no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3248—111no—
211#3248D1111yescharacteristic
212#3170—111no—
213#2966—111no—
214#1694—111no—
215#1693—111no—
216#1690—111no—
217#1689—111no—
218#1680—111no—
219#1680—111no—
220#1679—111no—
221#1679—111no—
222C2×#334—111no—
223#1552—111no—
224#1552—111no—
225C23×C11—21no—
226C23×C11#12111yescharacteristic
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—42no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
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
272#529C2×D1111yescharacteristic
273#500—111no—
274#494—111no—
275#487—111no—
276#487—111no—
277#479—21no—
278#479—221no—
279#475—111no—
280#475C2×D1111yescharacteristic
281#474—111no—
282#474C2×D1111yescharacteristic
283#467—21no—
284#467—221no—
285#467—221no—
286#467—221no—
287#465—21no—
288#465—221no—
289#464—21no—
290#464—221no—
291#462—111no—
292#462C2×D1111yescharacteristic
293#461—111no—
294#461C2×D1111yescharacteristic
295#446—111no—
296C8×Q8—111no—
297C4×Q16—221no—
298C4×Q16—221no—
299#436—111no—
300#435—221no—
301C8×D4—111no—
302C8×D4—221no—
303#433—221no—
304#432—111no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8C2×D1111yescharacteristic
307#405—221no—
308C2×C4×C8—111no—
309#334—111no—
310#334—111no—
311#334—111no—
312#334—111no—
313#332—111no—
314#332—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—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11#47312yes—
327C22×C11C2×#12111yescharacteristic
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11C2×#13511yescharacteristic
338C4×C11#57511yescharacteristic
339C4×C11#57711yescharacteristic
340C4×C11#57711yescharacteristic
341Dic11—81no—
342Dic11—81no—
343C2×Q16—21no—
344C2×Q16—221no—
345C2×Q16—221no—
346C2×Q16—221no—
347C2×SD16—21no—
348C2×SD16—221no—
349C2×M16—221no—
350C22×C8—21no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—221no—
354C22×C8—221no—
355C4⋊Q8—111no—
356C4⋊Q8—111no—
357C4⋊Q8C22×D1111yescharacteristic
358C4⋊Q8C22×D1111yescharacteristic
359#126—21no—
360#125—21no—
361#125—221no—
362#125C22⋊D1111yescharacteristic
363#124C22⋊D1111yescharacteristic
364#123—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369C22⋊Q8C22⋊D1111yescharacteristic
370#121C22⋊D1111yescharacteristic
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—221no—
374C4×Q8—221no—
375C4×Q8C22×D1111yescharacteristic
376C4×D4—21no—
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379#117—21no—
380#117—221no—
381C2×C42C22×D1111yescharacteristic
382#107—21no—
383#107—221no—
384#107—221no—
385#107—221no—
386#106—21no—
387#106—221no—
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8C22×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—221no—
402#103—221no—
403#103—221no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#102—21no—
409#102—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—221no—
414#97—221no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—221no—
420C2×C11—22no—
421C2×C11—81no—
422C2×C11#303511yescharacteristic
423C2×C11#306011yescharacteristic
424C2×C11C2×#47311yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×Q8C2×C22⋊D1111yescharacteristic
430C2×D4—21no—
431C2×D4C2×C22⋊D1111yescharacteristic
432C22×C4—21no—
433C22×C4D4×D1111yescharacteristic
434C22×C4#434111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436Q16—81no—
437Q16—442no—
438Q16—442no—
439Q16—881no—
440SD16—81no—
441SD16—881no—
442M16—442no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—222no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—441no—
456C2×C8—442no—
457C2×C8—881no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—441no—
473C4⋊C4—441no—
474C4⋊C4C2×C22⋊D1111yescharacteristic
475C4⋊C4C2×C22⋊D1111yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—41no—
482C22⋊C4—441no—
483C42—21no—
484C42—41no—
485C42—441no—
486C42D4×D1111yescharacteristic
487C42#434111yescharacteristic
488C42C2×C22⋊D1111yescharacteristic
489C42C23×D1111yescharacteristic
490C11#1922811yescharacteristic, complemented, Sylow
491C23—21no—
492C23#6699211yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—441no—
500Q8—441no—
501Q8—441no—
502Q8—441no—
503D4—21no—
504D4—21no—
505D4—42no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
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—41no—
539C22—41no—
540C22—41no—
541C22#1062281712yes—
542C22C2×#6699211yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—881no—
553C4—881no—
554C4D11×#13511yescharacteristic
555C4#1062329911yescharacteristic
556C4#1062336711yescharacteristic
557C4#1062336811yescharacteristic
558C2—22no—
559C2—81no—
560C2#1307806711yescharacteristic
561C2#1307827511yescharacteristic
562C2C2×#1062281711yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3248C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#3248D11
hypocenterC11#19228
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3248

Complements

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

NH ≅ G/Ntype
2. #13079198C2semidirect
4. #13068132C2semidirect
5. #13068127C2semidirect
6. #13068108C2semidirect
7. #13068103C2semidirect
8. #13068048C2semidirect
9. #13068044C2semidirect
10. #13068041C2semidirect
11. #13068037C2semidirect
12. C2×#10622118C2semidirect
13. #13067316C2semidirect
14. #13067314C2semidirect
490. C11#19228semidirect

Maximal subgroups

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

subgroupindex
#130799532
#130791982
#130775922
#130681322
#130681272
#130681082
#130681032
#130680482
#130680442
#130680412
#130680372
C2×#106221182
#130673162
#130673142
C11×#32482
#1922811