Finite Group Databasebeta

← #14738759

Subgroups — #14738759

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079623C211yesmaximal, characteristic
2#13079335C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13068186C211yesmaximal, characteristic, complemented
5#13068168C211yesmaximal, characteristic, complemented
6#13068132C211yesmaximal, characteristic, complemented
7#13068090C211yesmaximal, characteristic, complemented
8#13068062C211yesmaximal, characteristic, complemented
9#13068044C211yesmaximal, characteristic, complemented
10#13068008C211yesmaximal, characteristic, complemented
11#13067966C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic, complemented
13#13067316C211yesmaximal, characteristic, complemented
14#13067294C211yesmaximal, characteristic
15C11×#3255C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#475—21no—
20C11×#475C2211yescharacteristic
21C11×#475C2211yescharacteristic
22C11×#470—21no—
23C11×#470—21no—
24C11×#462—21no—
25C11×#462C2211yescharacteristic
26C11×#462C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622702—21no—
29#10622701C2211yescharacteristic
30#10622699—21no—
31#10622698C2211yescharacteristic
32#10622694C2211yescharacteristic
33#10622691C2211yescharacteristic
34#10622662—21no—
35#10622662—21no—
36#10622660—21no—
37#10622660—21no—
38#10622644C2211yescharacteristic
39#10622644C2211yescharacteristic
40#10622640C2211yescharacteristic
41#10622640C2211yescharacteristic
42#10622639—21no—
43#10622639—21no—
44#10622637—21no—
45#10622637—21no—
46#10622637C2211yescharacteristic
47#10622637C2211yescharacteristic
48Q8×C11⋊C8C2211yescharacteristic
49Q8×C11⋊C8C2211yescharacteristic
50#10622612—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×M16—21no—
71C11×C4⋊Q8D411yescharacteristic
72C11×C4⋊Q8D411yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#125—21no—
76C11×#125—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8D411yescharacteristic
81C11×C22⋊Q8D411yescharacteristic
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11C2311yescharacteristic
86C4×Q8×C11C2311yescharacteristic
87C11×#117—21no—
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—21no—
91C2×#4326—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4325—21no—
95C2×#4325—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×#106—21no—
107C11×#106—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103—21no—
113C11×#103—21no—
114C11×#103—21no—
115#66899—21no—
116#66899—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66873—21no—
121#66873—21no—
122#66873—21no—
123#66873—21no—
124#66871—21no—
125#66871—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#19372—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C2×C22⋊D11—41no—
154#4339—81no—
155#4339—81no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×C4×D11—41no—
160C2×Dic22—21no—
161C11×Q16—81no—
162C11×Q16—81no—
163C11×M16—81no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C11×C4⋊C4—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—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—41no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—41no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191#4326—81no—
192#4326—81no—
193#4325—42no—
194#4325—42no—
195#4325—81no—
196#4325—81no—
197(C2×D11)⋊C4—41no—
198(C2×D11)⋊C4—41no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201#4318—22no—
202#4318—41no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—42no—
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#3255D1111yescharacteristic, complemented
213#3216—111no—
214#3182—111no—
215#2962—111no—
216#1702—111no—
217#1700—111no—
218#1694—111no—
219#1686—111no—
220#1682—111no—
221#1680—111no—
222#1674—111no—
223#1666—111no—
224#1569—111no—
225#1552—111no—
226#1547—111no—
227C23×C11#12111yescharacteristic
228C22×D11—41no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—81no—
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—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C22⋊D11—82no—
256C2×Dic11—41no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—81no—
262C4×D11—82no—
263Dic22—41no—
264Dic22—41no—
265C8×C11—41no—
266C8×C11—41no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8#13712yes—
275#533C2×D1111yescharacteristic
276#533C2×D1111yescharacteristic
277#532—111no—
278#500—111no—
279#497—221no—
280#492—111no—
281#489—221no—
282#487—111no—
283#486—111no—
284#475—21no—
285#475C2×D1111yescharacteristic
286#475C2×D1111yescharacteristic
287#470—21no—
288#470—21no—
289#468—221no—
290#468—221no—
291#462—21no—
292#462—111no—
293#462—111no—
294#462C2×D1111yescharacteristic
295#462C2×D1111yescharacteristic
296#460—111no—
297#460—111no—
298#452—221no—
299#452—221no—
300#446—111no—
301#446—111no—
302#446—221no—
303#446—221no—
304C8×Q8—111no—
305C8×Q8—111no—
306#440—221no—
307#440—221no—
308#432—111no—
309#424—221no—
310#423C2×D1111yescharacteristic
311C2×C4⋊C8—111no—
312#405—221no—
313C4×M16—111no—
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#331—111no—
325#331—111no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11C2×#12111yescharacteristic
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11C2×#13711yescharacteristic
344C4×C11#57511yescharacteristic
345C4×C11#57611yescharacteristic
346C4×C11#57711yescharacteristic
347Dic11—81no—
348C2×#41—221no—
349C2×Q16—21no—
350C2×Q16—21no—
351C2×Q16—221no—
352C2×Q16—221no—
353C2×SD16—221no—
354C2×SD16—221no—
355C2×SD16—221no—
356C2×SD16—221no—
357C2×M16—21no—
358C2×M16—111no—
359C2×M16—111no—
360C22×C8—221no—
361C4⋊Q8—111no—
362C4⋊Q8C22⋊D1111yescharacteristic
363C4⋊Q8C22⋊D1111yescharacteristic
364C4⋊Q8C22×D1111yescharacteristic
365C4⋊Q8C22×D1111yescharacteristic
366#127—111no—
367#125—21no—
368#125—21no—
369#124—221no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8C22⋊D1111yescharacteristic
374C22⋊Q8C22⋊D1111yescharacteristic
375#121—221no—
376#121—221no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C22×D1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—221no—
383C4×D4—221no—
384#117—21no—
385#117—21no—
386C2×C42C22×D1111yescharacteristic
387#107—221no—
388#107—221no—
389#106—21no—
390#106—21no—
391C4⋊C8—21no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415C22⋊C8—221no—
416#97—111no—
417#97—111no—
418#97—221no—
419#97—221no—
420#97—221no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C2×C11—41no—
426C2×C11#303711yescharacteristic
427C2×C11#306211yescharacteristic
428C2×C11#306911yescharacteristic
429D11—161no—
430#41—881no—
431#41—881no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—221no—
436C2×Q8C2×C22⋊D1111yescharacteristic
437C2×Q8C2×C22⋊D1111yescharacteristic
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—441no—
442C22×C4—441no—
443C22×C4D4×D1111yescharacteristic
444C22×C4#434111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446Q16—81no—
447Q16—81no—
448Q16—881no—
449Q16—881no—
450SD16—442no—
451SD16—442no—
452SD16—881no—
453SD16—881no—
454M16—81no—
455M16—222no—
456M16—441no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—442no—
468C4⋊C4—21no—
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—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4C2×C22⋊D1111yescharacteristic
484C4⋊C4C2×C22⋊D1111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42D4×D1111yescharacteristic
494C42#434111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C23×D1111yescharacteristic
497C11#1937211yescharacteristic, complemented, Sylow
498C23—441no—
499C23#6699211yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—81no—
509Q8—441no—
510Q8—441no—
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—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—441no—
529C2×C4—882no—
530C2×C4#6699211yescharacteristic
531C2×C4#6699211yescharacteristic
532C2×C4#6699211yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4C2×#434111yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—41no—
537C8—41no—
538C8—112no—
539C8—221no—
540C8—221no—
541C8—221no—
542C8—441no—
543C8—441no—
544C8—441no—
545C8—441no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22C2×#6699211yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—881no—
564C4D11×#13711yescharacteristic
565C4#1062330811yescharacteristic
566C4#1062336611yescharacteristic
567C4#1062336811yescharacteristic
568C2—41no—
569C2—1761no—
570C2#1307808511yescharacteristic
571C2#1307829811yescharacteristic
572C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3255C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3255D11
hypocenterC11#19372
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
3. #13077565C2semidirect
4. #13068186C2semidirect
5. #13068168C2semidirect
6. #13068132C2semidirect
7. #13068090C2semidirect
8. #13068062C2semidirect
9. #13068044C2semidirect
10. #13068008C2semidirect
11. #13067966C2semidirect
12. #13067381C2semidirect
13. #13067316C2semidirect
15. C11×#3255C2semidirect
212. #3255D11semidirect
497. C11#19372semidirect

Maximal subgroups

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

subgroupindex
#130796232
#130793352
#130775652
#130681862
#130681682
#130681322
#130680902
#130680622
#130680442
#130680082
#130679662
#130673812
#130673162
#130672942
C11×#32552
#1937211