Finite Group Databasebeta

← #14738669

Subgroups — #14738669

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079978C211yesmaximal, characteristic
2#13078941C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068200C211yesmaximal, characteristic, complemented
5#13068193C211yesmaximal, characteristic, complemented
6#13068186C211yesmaximal, characteristic, complemented
7#13068179C211yesmaximal, characteristic, complemented
8#13068048C211yesmaximal, characteristic, complemented
9#13068041C211yesmaximal, characteristic, complemented
10#13068034C211yesmaximal, characteristic, complemented
11#13068027C211yesmaximal, characteristic, complemented
12#13067371C211yesmaximal, characteristic, complemented
13#13067346C211yesmaximal, characteristic, complemented
14#13067336C211yesmaximal, characteristic, complemented
15C11×#3252C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#479—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#470—21no—
23C11×#468—21no—
24C11×#464—21no—
25C11×#462C2211yescharacteristic
26C11×#461C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622706C2211yescharacteristic
29#10622706C2211yescharacteristic
30#10622701C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622681—21no—
33#10622681—21no—
34#10622679—21no—
35#10622670—21no—
36#10622662—21no—
37#10622652—21no—
38#10622640C2211yescharacteristic
39#10622637C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622628C2211yescharacteristic
43#10622625C2211yescharacteristic
44#10622624—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47#10622620C2211yescharacteristic
48#10622615—21no—
49#10622615—21no—
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53#10622537C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622123C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622118C2211yescharacteristic
66#10622118C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×Q16—21no—
69C2×C11×SD16—21no—
70C2×C11×M16—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#126—21no—
74C11×#125—21no—
75C11×#125D411yescharacteristic
76C11×#124D411yescharacteristic
77C11×#123—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8D411yescharacteristic
81C11×#121D411yescharacteristic
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11C2311yescharacteristic
85C4×D4×C11—21no—
86C4×D4×C11C2311yescharacteristic
87C11×#117—21no—
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4325—21no—
91C2×#4323—21no—
92#66983—21no—
93#66983—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8D411yescharacteristic
98C22×C11⋊C8D411yescharacteristic
99#66928—21no—
100#66927C2311yescharacteristic
101C4×D44—21no—
102C4×D44—21no—
103#66922C2311yescharacteristic
104C11×#107—21no—
105C11×#106—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113#66899—21no—
114#66896—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66874—21no—
121#66874—21no—
122#66873—21no—
123#66873—21no—
124#66873—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66872—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#19366—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×C22⋊D11—41no—
155#4339—42no—
156#4339—42no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×C4×D11—41no—
161C2×Dic22—21no—
162C11×Q16—81no—
163C11×SD16—81no—
164C11×M16—81no—
165C2×C8×C11—21no—
166C2×C8×C11—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—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—41no—
185C42×C11—21no—
186C42×C11—41no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191#4325—81no—
192#4323—81no—
193(C2×D11)⋊C4—41no—
194(C2×D11)⋊C4—41no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197#4318—42no—
198#4318—81no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—41no—
204C2×C11⋊C8—41no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3252D1111yescharacteristic, complemented
211#3251—111no—
212#3131—111no—
213#2966—111no—
214#1704—111no—
215#1703—111no—
216#1702—111no—
217#1701—111no—
218#1680—111no—
219#1679—111no—
220#1678—111no—
221#1677—111no—
222#1566—111no—
223#1559—111no—
224#1557—111no—
225C23×C11—21no—
226C23×C11#12111yescharacteristic
227C22×D11—41no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—81no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—42no—
236C2×C4×C11—21no—
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—41no—
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
254C22⋊D11—82no—
255C2×Dic11—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—81no—
261C4×D11—82no—
262Dic22—41no—
263Dic22—41no—
264C8×C11—41no—
265C8×C11—41no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274#533C2×D1111yescharacteristic
275#532—111no—
276#529C2×D1111yescharacteristic
277#488—221no—
278#488—221no—
279#487—111no—
280#487—111no—
281#486—111no—
282#486—111no—
283#479—21no—
284#478—221no—
285#477C2×D1111yescharacteristic
286#476C2×D1111yescharacteristic
287#475—111no—
288#474—111no—
289#470—21no—
290#469—221no—
291#468—21no—
292#468—221no—
293#464—21no—
294#463—221no—
295#462C2×D1111yescharacteristic
296#461C2×D1111yescharacteristic
297#460—111no—
298#459—111no—
299#446—111no—
300C8×Q8—111no—
301#436—111no—
302#435—221no—
303C8×D4—111no—
304C8×D4—221no—
305#433—221no—
306#432—111no—
307#423—111no—
308#423C2×D1111yescharacteristic
309#416—221no—
310#416—221no—
311#405—221no—
312C2×C4×C8—111no—
313#334—111no—
314#334—111no—
315#334—111no—
316#334—111no—
317#333—111no—
318#333—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323#331—111no—
324#331—111no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11C2×#12111yescharacteristic
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11#57511yescharacteristic
345C4×C11#57511yescharacteristic
346C4×C11#57711yescharacteristic
347C4×C11#57711yescharacteristic
348Dic11—81no—
349C2×#41—221no—
350C2×Q16—21no—
351C2×SD16—21no—
352C2×SD16—221no—
353C2×D8—221no—
354C2×M16—21no—
355C2×M16—221no—
356C2×M16—221no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—221no—
360C4⋊Q8—111no—
361C4⋊Q8C22×D1111yescharacteristic
362C4⋊Q8C22×D1111yescharacteristic
363#127—111no—
364#126—21no—
365#125—21no—
366#125C22⋊D1111yescharacteristic
367#124—221no—
368#124C22⋊D1111yescharacteristic
369#123—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8C22⋊D1111yescharacteristic
373#121—221no—
374#121—221no—
375#121C22⋊D1111yescharacteristic
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C22×D1111yescharacteristic
379C4×D4—21no—
380C4×D4—221no—
381C4×D4—221no—
382C4×D4C22×D1111yescharacteristic
383#117—21no—
384#117—21no—
385C2×C42C22×D1111yescharacteristic
386#107—21no—
387#107—221no—
388#106—21no—
389#106—221no—
390C4⋊C8—21no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—221no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#102—21no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415#102—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—221no—
420#97—221no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—221no—
426C2×C11—41no—
427C2×C11—81no—
428C2×C11#304011yescharacteristic
429C2×C11#306011yescharacteristic
430C2×C11#306711yescharacteristic
431D11—161no—
432#41—442no—
433#41—442no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—221no—
437C2×Q8C2×C22⋊D1111yescharacteristic
438C2×D4—21no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—441no—
443C2×D4C2×C22⋊D1111yescharacteristic
444C22×C4—21no—
445C22×C4—441no—
446C22×C4D4×D1111yescharacteristic
447C22×C4#434111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449Q16—81no—
450SD16—81no—
451SD16—881no—
452D8—881no—
453M16—81no—
454M16—442no—
455M16—881no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—441no—
467C2×C8—441no—
468C2×C8—442no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4C2×C22⋊D1111yescharacteristic
482C4⋊C4C2×C22⋊D1111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C42—21no—
492C42—41no—
493C42D4×D1111yescharacteristic
494C42#434111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C23×D1111yescharacteristic
497C11#1936611yescharacteristic, complemented, Sylow
498C23—21no—
499C23—441no—
500C23#6699211yescharacteristic
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—441no—
507Q8—441no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—441no—
512D4—441no—
513D4—441no—
514D4—441no—
515D4—881no—
516D4—882no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—441no—
530C2×C4—882no—
531C2×C4#6699211yescharacteristic
532C2×C4#6699211yescharacteristic
533C2×C4#6699211yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×#434111yescharacteristic
536C2×C4C22×C22⋊D1111yescharacteristic
537C8—41no—
538C8—41no—
539C8—221no—
540C8—221no—
541C8—221no—
542C8—221no—
543C8—441no—
544C8—441no—
545C8—441no—
546C8—441no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22C2×#6699211yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—881no—
567C4#1062330811yescharacteristic
568C4#1062330811yescharacteristic
569C4#1062336711yescharacteristic
570C4#1062336811yescharacteristic
571C2—41no—
572C2—81no—
573C2—1761no—
574C2#1307811211yescharacteristic
575C2#1307827511yescharacteristic
576C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3252C2
socleC22×C11C2×#121
prime radical#13079978C2
hypercenter#3252D11
hypocenterC11#19366
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3252

Complements

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

NH ≅ G/Ntype
2. #13078941C2semidirect
3. #13077592C2semidirect
4. #13068200C2semidirect
5. #13068193C2semidirect
6. #13068186C2semidirect
7. #13068179C2semidirect
8. #13068048C2semidirect
9. #13068041C2semidirect
10. #13068034C2semidirect
11. #13068027C2semidirect
12. #13067371C2semidirect
13. #13067346C2semidirect
14. #13067336C2semidirect
15. C11×#3252C2semidirect
210. #3252D11semidirect
497. C11#19366semidirect

Maximal subgroups

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

subgroupindex
#130799782
#130789412
#130775922
#130682002
#130681932
#130681862
#130681792
#130680482
#130680412
#130680342
#130680272
#130673712
#130673462
#130673362
C11×#32522
#1936611