Finite Group Databasebeta

← #14738789

Subgroups — #14738789

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079623C211yesmaximal, characteristic, complemented
2#13079350C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13068182C211yesmaximal, characteristic, complemented
5#13068158C211yesmaximal, characteristic, complemented
6#13068124C211yesmaximal, characteristic, complemented
7#13068098C211yesmaximal, characteristic, complemented
8#13068058C211yesmaximal, characteristic, complemented
9#13068034C211yesmaximal, characteristic, complemented
10#13068000C211yesmaximal, characteristic, complemented
11#13067974C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic, complemented
13#13067311C211yesmaximal, characteristic, complemented
14#13067294C211yesmaximal, characteristic, complemented
15C11×#3254C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#477C2211yescharacteristic
20C11×#477C2211yescharacteristic
21C11×#474—21no—
22C11×#468—21no—
23C11×#468—21no—
24C11×#461—21no—
25C11×#460C2211yescharacteristic
26C11×#460C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622702—21no—
29#10622701C2211yescharacteristic
30#10622699—21no—
31#10622692C2211yescharacteristic
32#10622686C2211yescharacteristic
33#10622683C2211yescharacteristic
34#10622660—21no—
35#10622660—21no—
36#10622652—21no—
37#10622652—21no—
38#10622644C2211yescharacteristic
39#10622644C2211yescharacteristic
40#10622640C2211yescharacteristic
41#10622640C2211yescharacteristic
42#10622637—21no—
43#10622637—21no—
44#10622637C2211yescharacteristic
45#10622637C2211yescharacteristic
46Q8×C11⋊C8C2211yescharacteristic
47Q8×C11⋊C8C2211yescharacteristic
48#10622627—21no—
49#10622627—21no—
50#10622612—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622184C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×#4339—21no—
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×M16—21no—
72C11×C4⋊Q8D411yescharacteristic
73C11×C4⋊Q8D411yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#127C2311yescharacteristic
76C11×#125—21no—
77C11×#124—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×C22⋊Q8D411yescharacteristic
81C11×#121—21no—
82C11×#121—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11C2311yescharacteristic
85C4×Q8×C11C2311yescharacteristic
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—21no—
91C2×#4326—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96#66983—21no—
97#66983—21no—
98C2×#4318D411yescharacteristic
99C2×#4318D411yescharacteristic
100C22×C11⋊C8—21no—
101#66928—21no—
102#66927C2311yescharacteristic
103C4×D44—21no—
104C4×D44—21no—
105#66922C2311yescharacteristic
106C11×#107—21no—
107C11×#107—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103—21no—
113C11×#102—21no—
114C11×#102—21no—
115#66896—21no—
116#66896—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66873—21no—
121#66873—21no—
122#66873—21no—
123#66873—21no—
124#66872—21no—
125#66872—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135#66867—21no—
136#66867—21no—
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19374—111nomaximal, Sylow
145C11×#41—82no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×C22⋊D11—41no—
159#4339—81no—
160#4339—81no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×C4×D11—41no—
165C2×Dic22—21no—
166C11×SD16—81no—
167C11×SD16—81no—
168C11×M16—81no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
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—21no—
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192#4326—81no—
193#4326—81no—
194#4325—81no—
195#4325—81no—
196#4323—42no—
197#4323—42no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202#4318—22no—
203#4318—41no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#3254D1111yescharacteristic, complemented
214#3216—111no—
215#3184—111no—
216#2962—111no—
217#1702—111no—
218#1698—111no—
219#1692—111no—
220#1688—111no—
221#1682—111no—
222#1678—111no—
223#1672—111no—
224#1668—111no—
225#1569—111no—
226#1551—111no—
227#1547—111no—
228C23×C11—41no—
229C23×C11#12111yescharacteristic
230C22×D11—41no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—81no—
236Q8×C11—81no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—81no—
242D4×C11—82no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—82no—
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C22⋊D11—82no—
261C2×Dic11—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—81no—
267C4×D11—82no—
268Dic22—41no—
269Dic22—41no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8#13712yes—
280#533C2×D1111yescharacteristic
281#532—111no—
282#532C2×D1111yescharacteristic
283#498—111no—
284#497—221no—
285#493—111no—
286#489—221no—
287#486—111no—
288#486—111no—
289#477C2×D1111yescharacteristic
290#477C2×D1111yescharacteristic
291#474—21no—
292#469—221no—
293#469—221no—
294#468—21no—
295#468—21no—
296#462—111no—
297#462—111no—
298#461—21no—
299#460—111no—
300#460—111no—
301#460C2×D1111yescharacteristic
302#460C2×D1111yescharacteristic
303#452—221no—
304#452—221no—
305#446—111no—
306#446—111no—
307#446—221no—
308#446—221no—
309C8×Q8—111no—
310C8×Q8—111no—
311#442—221no—
312#442—221no—
313#432—111no—
314#424—221no—
315#423C2×D1111yescharacteristic
316C2×C4⋊C8—111no—
317#405—221no—
318C4×M16—111no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323#333—111no—
324#333—111no—
325#332—111no—
326#332—111no—
327#331—111no—
328#331—111no—
329#331—111no—
330#331—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11C2×#12111yescharacteristic
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—81no—
350C4×C11C2×#13711yescharacteristic
351C4×C11#57511yescharacteristic
352C4×C11#57611yescharacteristic
353C4×C11#57711yescharacteristic
354Dic11—81no—
355C2×#41—21no—
356C2×#41—221no—
357C2×Q16—221no—
358C2×Q16—221no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—221no—
362C2×SD16—221no—
363C2×D8—221no—
364C2×D8—221no—
365C2×M16—21no—
366C2×M16—111no—
367C2×M16—111no—
368C22×C8—221no—
369C4⋊Q8—111no—
370C4⋊Q8C22⋊D1111yescharacteristic
371C4⋊Q8C22⋊D1111yescharacteristic
372C4⋊Q8C22×D1111yescharacteristic
373#127—111no—
374#127C22×D1111yescharacteristic
375#125—21no—
376#124—21no—
377#124—221no—
378C22⋊Q8—21no—
379C22⋊Q8C22⋊D1111yescharacteristic
380C22⋊Q8C22⋊D1111yescharacteristic
381#121—21no—
382#121—21no—
383#121—221no—
384#121—221no—
385C4×Q8—21no—
386C4×Q8C22×D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—221no—
391C4×D4—221no—
392#117—21no—
393C2×C42C22×D1111yescharacteristic
394#107—21no—
395#107—21no—
396#106—221no—
397#106—221no—
398C4⋊C8—21no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—21no—
411#103—21no—
412#103—221no—
413#103—221no—
414#102—21no—
415#102—21no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422C22⋊C8—221no—
423#97—111no—
424#97—111no—
425#97—221no—
426#97—221no—
427#97—221no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—221no—
431C4×C8—221no—
432C2×C11—41no—
433C2×C11—161no—
434C2×C11#303711yescharacteristic
435C2×C11#306211yescharacteristic
436C2×C11#306811yescharacteristic
437D11—161no—
438#41—82no—
439#41—881no—
440#41—881no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—221no—
444C2×Q8C2×C22⋊D1111yescharacteristic
445C2×Q8C2×C22⋊D1111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—441no—
454C22×C4—41no—
455C22×C4—441no—
456C22×C4D4×D1111yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459Q16—881no—
460Q16—881no—
461SD16—81no—
462SD16—81no—
463SD16—881no—
464SD16—881no—
465D8—442no—
466D8—442no—
467M16—81no—
468M16—222no—
469M16—441no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—442no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4C2×C22⋊D1111yescharacteristic
493C4⋊C4C2×C22⋊D1111yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C42—21no—
501C42—21no—
502C42D4×D1111yescharacteristic
503C42#434111yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1937411yescharacteristic, complemented, Sylow
507C23—41no—
508C23—441no—
509C23#6699211yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—81no—
515Q8—81no—
516Q8—441no—
517Q8—441no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—82no—
524D4—441no—
525D4—441no—
526D4—441no—
527D4—441no—
528D4—881no—
529D4—882no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—441no—
542C2×C4—882no—
543C2×C4#6699211yescharacteristic
544C2×C4#6699211yescharacteristic
545C2×C4#6699211yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4C2×#434111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—41no—
550C8—41no—
551C8—112no—
552C8—221no—
553C8—221no—
554C8—221no—
555C8—441no—
556C8—441no—
557C8—441no—
558C8—441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22C2×#6699211yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—881no—
579C4D11×#13711yescharacteristic
580C4#1062330811yescharacteristic
581C4#1062336611yescharacteristic
582C4#1062336811yescharacteristic
583C2—41no—
584C2—161no—
585C2—1761no—
586C2#1307808511yescharacteristic
587C2#1307829811yescharacteristic
588C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3254C2
socleC22×C11C2×#121
prime radical#13079350C2
hypercenter#3254D11
hypocenterC11#19374
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3254

Complements

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

NH ≅ G/Ntype
1. #13079623C2semidirect
3. #13077565C2semidirect
4. #13068182C2semidirect
5. #13068158C2semidirect
6. #13068124C2semidirect
7. #13068098C2semidirect
8. #13068058C2semidirect
9. #13068034C2semidirect
10. #13068000C2semidirect
11. #13067974C2semidirect
12. #13067381C2semidirect
13. #13067311C2semidirect
14. #13067294C2semidirect
15. C11×#3254C2semidirect
213. #3254D11semidirect
506. C11#19374semidirect

Maximal subgroups

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

subgroupindex
#130796232
#130793502
#130775652
#130681822
#130681582
#130681242
#130680982
#130680582
#130680342
#130680002
#130679742
#130673812
#130673112
#130672942
C11×#32542
#1937411