Finite Group Databasebeta

← #14736786

Subgroups — #14736786

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078670C211yesmaximal, characteristic
2#13078398C211yesmaximal, characteristic, complemented
3#13077634C211yesmaximal, characteristic, complemented
4#13068188C211yesmaximal, characteristic, complemented
5#13068146C211yesmaximal, characteristic, complemented
6#13068136C211yesmaximal, characteristic, complemented
7#13068078C211yesmaximal, characteristic, complemented
8#13068071C211yesmaximal, characteristic, complemented
9#13068029C211yesmaximal, characteristic, complemented
10#13068017C211yesmaximal, characteristic, complemented
11#13067961C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067311C211yesmaximal, characteristic, complemented
15C11×#3182C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#468—21no—
24C11×#468—21no—
25C11×#440—21no—
26C11×#440—21no—
27C4×C11×M16C2211yescharacteristic
28#10622741—21no—
29#10622741—21no—
30#10622707C2211yescharacteristic
31#10622704C2211yescharacteristic
32#10622704C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622697C2211yescharacteristic
36#10622688C2211yescharacteristic
37#10622685C2211yescharacteristic
38#10622679—21no—
39#10622676—21no—
40#10622650—21no—
41#10622648—21no—
42C4×#4324—21no—
43C4×#4323—21no—
44#10622615—21no—
45#10622611—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622320—21no—
50#10622318—21no—
51#10622301C2211yescharacteristic
52#10622301C2211yescharacteristic
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×#4339D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#127C2311yescharacteristic
77C11×#125—21no—
78C11×#124—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×#121—21no—
82C11×#121—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C11×#117—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4324—21no—
90C2×#4323—21no—
91C4×C22⋊D11—21no—
92C4×C22⋊D11—21no—
93#66979D411yescharacteristic
94C22×C11⋊C8—21no—
95C2×#4313—21no—
96C2×#4313—21no—
97C4×D44D411yescharacteristic
98C4×D44C2311yescharacteristic
99#66925—21no—
100C42×D11—21no—
101C4×Dic22D411yescharacteristic
102C4×Dic22C2311yescharacteristic
103C11×#107—21no—
104C11×#107—21no—
105C11×#103—21no—
106C11×#103—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121C8×Dic11—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#19183—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×C22⋊D11—21no—
158#4339—22no—
159#4339—41no—
160C2×D44C2×D411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×Dic22C2×D411yescharacteristic
165C11×SD16—42no—
166C11×SD16—42no—
167C11×M16—22no—
168C11×M16—41no—
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C42×C11—41no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11#4111yescharacteristic
188C42×C11C2411yescharacteristic
189C22⋊Dic11—21no—
190#4324—42no—
191#4323—42no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194C4⋊Dic11C2×D411yescharacteristic
195C4⋊Dic11C2×D411yescharacteristic
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—42no—
208#4313—42no—
209#4313—42no—
210#3182D1111yescharacteristic, complemented
211#3106—111no—
212#3076—111no—
213#2971—111no—
214#1703—111no—
215#1697—111no—
216#1695—111no—
217#1685—111no—
218#1684—111no—
219#1678—111no—
220#1676—111no—
221#1666—111no—
222#1565—111no—
223#1554—111no—
224#1551—111no—
225C23×C11—41no—
226C23×C11#12111yescharacteristic
227C22×D11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—81no—
231Q8×C11—81no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—81no—
237D4×C11—82no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—82no—
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C22⋊D11—42no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257D44—21no—
258D44—21no—
259C4×D11—42no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—81no—
263Dic22—21no—
264Dic22#13712yes—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11#13512yes—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275#533C2×D1111yescharacteristic
276#532C2×D1111yescharacteristic
277C4×#41—111no—
278#500C2×D1111yescharacteristic
279#492C2×D1111yescharacteristic
280#487C2×D1111yescharacteristic
281#486C2×D1111yescharacteristic
282#482—221no—
283#479—221no—
284#478—221no—
285#477—111no—
286#477—111no—
287#476—111no—
288#476—111no—
289#475—111no—
290#474—111no—
291#468—21no—
292#468—21no—
293#460—111no—
294#459—111no—
295#449—221no—
296C8×Q8—111no—
297C8×Q8—111no—
298#440—21no—
299#440—21no—
300C4×SD16—221no—
301C4×D8—221no—
302#436—111no—
303#436—111no—
304#436—221no—
305#436—221no—
306#432—111no—
307#432—221no—
308#431—111no—
309#427—221no—
310C2×C4⋊C8—111no—
311#416—221no—
312C4×M16—221no—
313C4×M16C2×D1111yescharacteristic
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318#333—111no—
319#333—111no—
320#333—111no—
321#333—111no—
322#332—111no—
323#332—111no—
324#331—111no—
325#331—111no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11C2×#12111yescharacteristic
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11C2×#13511yescharacteristic
344C4×C11C2×#13711yescharacteristic
345C4×C11#57511yescharacteristic
346C4×C11#57511yescharacteristic
347Dic11—22no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—21no—
351C2×#41—111no—
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16—221no—
355C2×D8—221no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16C22⋊D1111yescharacteristic
359C2×M16C22⋊D1111yescharacteristic
360C22×C8—221no—
361C4⋊Q8C22×D1111yescharacteristic
362C4⋊Q8C22×D1111yescharacteristic
363C4⋊Q8C22×D1111yescharacteristic
364#127C22×D1111yescharacteristic
365#125—21no—
366#124—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—111no—
374C4×Q8—111no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—111no—
378C4×D4—111no—
379C4×D4—221no—
380C4×D4—221no—
381#117—21no—
382#117—111no—
383#117—221no—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386#107—21no—
387#107—21no—
388#107—221no—
389#107—221no—
390#107—221no—
391#106—221no—
392#106—221no—
393#106—221no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403#103—21no—
404#103—21no—
405#103—221no—
406#103—221no—
407#103—221no—
408#102—21no—
409#102—21no—
410#102—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—221no—
420#97C22⋊D1111yescharacteristic
421#97C22⋊D1111yescharacteristic
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11—41no—
428C2×C11—161no—
429C2×C11#303511yescharacteristic
430C2×C11#305611yescharacteristic
431C2×C11#306811yescharacteristic
432D11—81no—
433#41—82no—
434#41—222no—
435#41—441no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—111no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—111no—
445C2×D4—221no—
446C22×C4—41no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4D4×D1111yescharacteristic
451C22×C4#434111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453SD16—42no—
454SD16—42no—
455SD16—442no—
456D8—442no—
457M16—22no—
458M16—41no—
459M16—442no—
460M16—442no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—442no—
468C2×C8C2×C22⋊D1111yescharacteristic
469C2×C8C2×C22⋊D1111yescharacteristic
470C2×C8C2×C22⋊D1111yescharacteristic
471C2×C8C2×C22⋊D1111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—41no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42D4×D1111yescharacteristic
495C42#434111yescharacteristic
496C42C2×C22⋊D1111yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1918311yescharacteristic, complemented, Sylow
499C23—41no—
500C23—221no—
501C23#6699111yescharacteristic
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—81no—
506Q8—112no—
507Q8—221no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—81no—
513D4—82no—
514D4—221no—
515D4—221no—
516D4—442no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—442no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—881no—
533C2×C4#6699111yescharacteristic
534C2×C4#6699111yescharacteristic
535C2×C4#6699111yescharacteristic
536C2×C4C2×D4×D1111yescharacteristic
537C2×C4C2×#434111yescharacteristic
538C2×C4C22×C22⋊D1111yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—441no—
543C8—441no—
544C8—441no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8#6700312yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22C2×#6699111yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—222no—
567C4—441no—
568C4—441no—
569C4D11×#13711yescharacteristic
570C4#1062330811yescharacteristic
571C4C2×#6700311yescharacteristic
572C4#1062335311yescharacteristic
573C2—41no—
574C2—161no—
575C2—881no—
576C2#1307806511yescharacteristic
577C2#1307824011yescharacteristic
578C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3182C2
socleC22×C11C2×#121
prime radical#13078670C2
hypercenter#3182D11
hypocenterC11#19183
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. #13078398C2semidirect
3. #13077634C2semidirect
4. #13068188C2semidirect
5. #13068146C2semidirect
6. #13068136C2semidirect
7. #13068078C2semidirect
8. #13068071C2semidirect
9. #13068029C2semidirect
10. #13068017C2semidirect
11. #13067961C2semidirect
12. #13067368C2semidirect
13. #13067326C2semidirect
14. #13067311C2semidirect
15. C11×#3182C2semidirect
210. #3182D11semidirect
498. C11#19183semidirect

Maximal subgroups

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

subgroupindex
#130786702
#130783982
#130776342
#130681882
#130681462
#130681362
#130680782
#130680712
#130680292
#130680172
#130679612
#130673682
#130673262
#130673112
C11×#31822
#1918311