Finite Group Databasebeta

← #14739296

Subgroups — #14739296

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079748C211yesmaximal, characteristic, complemented
2#13078778C211yesmaximal, characteristic, complemented
3#13077727C211yesmaximal, characteristic, complemented
4#13068058C211yesmaximal, characteristic, complemented
5#13068051C211yesmaximal, characteristic, complemented
6#13068030C211yesmaximal, characteristic, complemented
7#13068023C211yesmaximal, characteristic, complemented
8#13068018C211yesmaximal, characteristic, complemented
9#13068013C211yesmaximal, characteristic, complemented
10#13068000C211yesmaximal, characteristic, complemented
11#13067993C211yesmaximal, characteristic, complemented
12#13067394C211yesmaximal, characteristic, complemented
13#13067311C211yesmaximal, characteristic, complemented
14#13067271C211yesmaximal, characteristic, complemented
15C11×#3106C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#482—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#460C2211yescharacteristic
23C11×#459C2211yescharacteristic
24C11×#449—21no—
25C4×C11×SD16—21no—
26C4×C11×D8—21no—
27C11×#431C2211yescharacteristic
28#10622852—21no—
29#10622692C2211yescharacteristic
30#10622691C2211yescharacteristic
31#10622683C2211yescharacteristic
32#10622683C2211yescharacteristic
33#10622648—21no—
34#10622648—21no—
35#10622644C2211yescharacteristic
36#10622643—21no—
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622634C2211yescharacteristic
40#10622632C2211yescharacteristic
41#10622631—21no—
42D4×C11⋊C8—21no—
43D4×C11⋊C8—21no—
44D4×C11⋊C8C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic
46#10622622—21no—
47#10622622—21no—
48#10622621C2211yescharacteristic
49#10622609—21no—
50#10622539C2211yescharacteristic
51#10622538—21no—
52#10622538C2211yescharacteristic
53C2×C4⋊(C11⋊C8)—21no—
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55#10622184C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×D8—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×#127C2311yescharacteristic
73C11×#124—21no—
74C11×#121—21no—
75C11×#121—21no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—21no—
85C11×#117D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4326—21no—
89C2×#4324—21no—
90#66979—21no—
91#66977—21no—
92#66977—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95C22×C11⋊C8—21no—
96#66923—21no—
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22—21no—
101C11×#107—21no—
102C11×#106—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#103—21no—
106C11×#102—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×C22⋊C8—21no—
110C4×C8×C11—21no—
111#66899—21no—
112#66896—21no—
113#66896—21no—
114#66896—21no—
115#66896—21no—
116#66896—21no—
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)D411yescharacteristic
121C22⋊(C11⋊C8)D411yescharacteristic
122#66874—21no—
123#66874—21no—
124#66872—21no—
125#66872—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)D411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19419—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—82no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—41no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C2×Dic22—21no—
164C2×Dic22—21no—
165C11×SD16—42no—
166C11×D8—42no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—41no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187C22⋊Dic11—41no—
188#4326—42no—
189#4324—42no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194Dic11⋊C4—41no—
195Dic11⋊C4—41no—
196C4×Dic11—41no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—81no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3228—111no—
209#3116—111no—
210#3106D1111yescharacteristic
211#2988—111no—
212#1682—111no—
213#1681—111no—
214#1678—111no—
215#1677—111no—
216#1676—111no—
217#1675—111no—
218#1672—111no—
219#1671—111no—
220#1572—111no—
221#1551—111no—
222#1542—111no—
223C23×C11—21no—
224C23×C11—41no—
225C23×C11#12111yescharacteristic
226Q8×C11—21no—
227Q8×C11—81no—
228Q8×C11#13512yes—
229D4×C11—24no—
230D4×C11—21no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—81no—
236D4×C11—82no—
237D4×C11#13512yes—
238C2×C4×C11—24no—
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—41no—
250C2×C4×C11—81no—
251C2×C4×C11—82no—
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×Dic11—41no—
259C2×Dic11—41no—
260Dic22—41no—
261Dic22—41no—
262Dic22—81no—
263C8×C11—41no—
264C8×C11—41no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#533—111no—
274#532C2×D1111yescharacteristic
275C4×#41C2×D1111yescharacteristic
276#500—111no—
277#498—111no—
278#486—111no—
279#486—111no—
280#485—221no—
281#482—21no—
282#482—221no—
283#482—221no—
284#478—221no—
285#478—221no—
286#477—111no—
287#477C2×D1111yescharacteristic
288#476—111no—
289#476C2×D1111yescharacteristic
290#462—111no—
291#461—111no—
292#460C2×D1111yescharacteristic
293#459C2×D1111yescharacteristic
294#452—221no—
295#449—21no—
296C8×Q8—111no—
297C8×Q8—111no—
298#441—221no—
299#440—221no—
300C4×SD16—21no—
301C4×D8—21no—
302C8×D4—111no—
303C8×D4—111no—
304C8×D4—221no—
305C8×D4—221no—
306#432—111no—
307#431—111no—
308#431—221no—
309#431C2×D1111yescharacteristic
310C2×C4⋊C8—111no—
311C2×C4⋊C8—221no—
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316#333—111no—
317#333—111no—
318#333—111no—
319#333—111no—
320#332—111no—
321#332—111no—
322#331—111no—
323#331—111no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—22no—
327C22×C11—21no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11C2×#12111yescharacteristic
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11C2×#13511yescharacteristic
343C4×C11C2×#13511yescharacteristic
344C4×C11#57711yescharacteristic
345C4×C11#57811yescharacteristic
346Dic11—81no—
347Dic11—81no—
348C2×#41—21no—
349C2×#41C22⋊D1111yescharacteristic
350C2×Q16—221no—
351C2×SD16—21no—
352C2×SD16—221no—
353C2×D8—21no—
354C22×C8—221no—
355C22×C8—221no—
356C22×C8—221no—
357C4⋊Q8—111no—
358C4⋊Q8—111no—
359C4⋊Q8C22×D1111yescharacteristic
360#127C22×D1111yescharacteristic
361#125—221no—
362#124—21no—
363C22⋊Q8—221no—
364C22⋊Q8—221no—
365#121—21no—
366#121—21no—
367C4×Q8—221no—
368C4×Q8—221no—
369C4×Q8C22⋊D1111yescharacteristic
370C4×Q8C22×D1111yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4C22⋊D1111yescharacteristic
376C4×D4C22×D1111yescharacteristic
377#117—21no—
378#117—221no—
379#117C22⋊D1111yescharacteristic
380C2×C42—21no—
381C2×C42C22×D1111yescharacteristic
382#107—21no—
383#107—221no—
384#107—221no—
385#107—221no—
386#106—21no—
387#106—221no—
388#106—221no—
389#106—221no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—21no—
402#103—221no—
403#103—221no—
404#103—221no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413C22⋊C8—21no—
414C22⋊C8—111no—
415C22⋊C8—111no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—221no—
420C4×C8—21no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C2×C11—41no—
426C2×C11—42no—
427C2×C11—161no—
428C2×C11#304611yescharacteristic
429C2×C11#305011yescharacteristic
430C2×C11#306811yescharacteristic
431#41—22no—
432#41—22no—
433#41—82no—
434C2×Q8—21no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8C2×C22⋊D1111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4C2×C22⋊D1111yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—41no—
448C22×C4D4×D1111yescharacteristic
449C22×C4#434111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451Q16—442no—
452SD16—42no—
453SD16—442no—
454D8—42no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—881no—
466C2×C8—881no—
467C2×C8—881no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—441no—
477C4⋊C4—441no—
478C4⋊C4C2×C22⋊D1111yescharacteristic
479C4⋊C4C2×C22⋊D1111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—441no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—441no—
490C42D4×D1111yescharacteristic
491C42#434111yescharacteristic
492C42C2×C22⋊D1111yescharacteristic
493C42C23×D1111yescharacteristic
494C11#1941911yescharacteristic, complemented, Sylow
495C23—21no—
496C23—41no—
497C23#6699211yescharacteristic
498Q8—21no—
499Q8—81no—
500Q8—441no—
501Q8—441no—
502Q8—881no—
503Q8#6700312yes—
504D4—24no—
505D4—21no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—81no—
511D4—82no—
512D4#6700312yes—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
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—81no—
526C2×C4—82no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4#6699211yescharacteristic
530C2×C4#6699211yescharacteristic
531C2×C4#6699211yescharacteristic
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4C2×#434111yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—41no—
536C8—41no—
537C8—221no—
538C8—221no—
539C8—221no—
540C8—221no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22C2×#6699211yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—881no—
564C4—881no—
565C4#1062330111yescharacteristic
566C4#1062330211yescharacteristic
567C4C2×#6700311yescharacteristic
568C4C2×#6700311yescharacteristic
569C2—41no—
570C2—42no—
571C2—161no—
572C2#1307816411yescharacteristic
573C2#1307819411yescharacteristic
574C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3106C2
socleC22×C11C2×#121
hypercenter#3106D11
hypocenterC11#19419
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #13079748C2semidirect
2. #13078778C2semidirect
3. #13077727C2semidirect
4. #13068058C2semidirect
5. #13068051C2semidirect
6. #13068030C2semidirect
7. #13068023C2semidirect
8. #13068018C2semidirect
9. #13068013C2semidirect
10. #13068000C2semidirect
11. #13067993C2semidirect
12. #13067394C2semidirect
13. #13067311C2semidirect
14. #13067271C2semidirect
494. C11#19419semidirect

Maximal subgroups

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

subgroupindex
#130797482
#130787782
#130777272
#130680582
#130680512
#130680302
#130680232
#130680182
#130680132
#130680002
#130679932
#130673942
#130673112
#130672712
C11×#31062
#1941911