Finite Group Databasebeta

← #14739294

Subgroups — #14739294

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#13078772C211yesmaximal, characteristic, complemented
2#13078670C211yesmaximal, characteristic
3#13077724C211yesmaximal, characteristic, complemented
4#13068057C211yesmaximal, characteristic, complemented
5#13068050C211yesmaximal, characteristic, complemented
6#13068029C211yesmaximal, characteristic, complemented
7#13068022C211yesmaximal, characteristic, complemented
8#13068017C211yesmaximal, characteristic, complemented
9#13068012C211yesmaximal, characteristic, complemented
10#13067995C211yesmaximal, characteristic, complemented
11#13067988C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067311C211yesmaximal, characteristic, complemented
14#13067273C211yesmaximal, characteristic, complemented
15C11×#3228C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#486C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#482—21no—
24C11×#482—21no—
25C11×#478—21no—
26C11×#478—21no—
27C11×#431C2211yescharacteristic
28#10622704C2211yescharacteristic
29#10622704C2211yescharacteristic
30#10622703C2211yescharacteristic
31#10622697C2211yescharacteristic
32#10622697C2211yescharacteristic
33#10622696C2211yescharacteristic
34#10622688C2211yescharacteristic
35#10622685C2211yescharacteristic
36#10622660—21no—
37#10622658—21no—
38#10622650—21no—
39#10622648—21no—
40#10622643—21no—
41#10622639—21no—
42C4×#4324—21no—
43C4×#4323—21no—
44#10622539C2211yescharacteristic
45#10622538C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622446—21no—
48D11×C4⋊C8—21no—
49(C22⋊D11)⋊C8—21no—
50(C22⋊D11)⋊C8—21no—
51C8×D44C2211yescharacteristic
52C8×D44C2211yescharacteristic
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
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#127C2311yescharacteristic
73C11×#125—21no—
74C11×#124—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×#121—21no—
78C11×#121—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C11×#117—21no—
84C2×C42×C11C2311yescharacteristic
85C2×#4326—21no—
86C2×#4325—21no—
87C2×#4324—21no—
88C2×#4323—21no—
89C4×C22⋊D11—21no—
90C4×C22⋊D11—21no—
91#66979D411yescharacteristic
92C22×C11⋊C8—21no—
93C2×C8×D11—21no—
94C2×C8×D11—21no—
95C4×D44D411yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98C42×D11—21no—
99C4×Dic22D411yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×#107—21no—
102C11×#107—21no—
103C11×#106—21no—
104C11×#106—21no—
105C11×C4⋊C8D411yescharacteristic
106C11×C4⋊C8D411yescharacteristic
107C11×#102—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×C22⋊C8D411yescharacteristic
112C11×C22⋊C8D411yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899—21no—
116#66899—21no—
117#66896—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126C8×Dic11—21no—
127#66874—21no—
128#66874—21no—
129#66873—21no—
130#66873—21no—
131#66872—21no—
132#66872—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#19419—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—22no—
160C2×D44C2×D411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×Dic22C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
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×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—41no—
180C42×C11—41no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186#4326—42no—
187#4325—42no—
188#4324—42no—
189#4323—42no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192C4⋊Dic11C2×D411yescharacteristic
193C4⋊Dic11C2×D411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—81no—
206C8×D11—81no—
207C8×D11—81no—
208#3228D1111yescharacteristic, complemented
209#3116—111no—
210#3106—111no—
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—41no—
224C23×C11#12111yescharacteristic
225C22×D11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—81no—
229Q8×C11—81no—
230D4×C11—41no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—81no—
235D4×C11—82no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—82no—
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—24no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255D44—21no—
256D44#13512yes—
257C4×D11—24no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—81no—
261Dic22—21no—
262Dic22#13512yes—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#533C2×D1111yescharacteristic
274#532C2×D1111yescharacteristic
275C4×#41—111no—
276#500C2×D1111yescharacteristic
277#498C2×D1111yescharacteristic
278#486C2×D1111yescharacteristic
279#486C2×D1111yescharacteristic
280#485—221no—
281#482—21no—
282#482—21no—
283#482—221no—
284#478—21no—
285#478—21no—
286#477—111no—
287#477—111no—
288#476—111no—
289#476—111no—
290#462—111no—
291#461—111no—
292#460—111no—
293#459—111no—
294#452—221no—
295#449—221no—
296C8×Q8—111no—
297C8×Q8—111no—
298#441—221no—
299#440—221no—
300C4×SD16—221no—
301C4×D8—221no—
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—21no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11C2×#12111yescharacteristic
331C2×D11—22no—
332C2×D11—41no—
333C2×D11—41no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11C2×#13511yescharacteristic
342C4×C11C2×#13511yescharacteristic
343C4×C11#57711yescharacteristic
344C4×C11#57811yescharacteristic
345Dic11—22no—
346Dic11—41no—
347Dic11—41no—
348C2×#41—21no—
349C2×#41—111no—
350C2×Q16—221no—
351C2×SD16—221no—
352C2×SD16—221no—
353C2×D8—221no—
354C22×C8—221no—
355C22×C8—221no—
356C22×C8—221no—
357C4⋊Q8C22×D1111yescharacteristic
358C4⋊Q8C22×D1111yescharacteristic
359C4⋊Q8C22×D1111yescharacteristic
360#127C22×D1111yescharacteristic
361#125—21no—
362#124—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365#121—21no—
366#121—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—111no—
374C4×D4—111no—
375C4×D4—221no—
376C4×D4—221no—
377#117—21no—
378#117—111no—
379#117—221no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382#107—21no—
383#107—21no—
384#107—221no—
385#107—221no—
386#106—21no—
387#106—21no—
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—221no—
402#103—221no—
403#103—221no—
404#103—221no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8C22⋊D1111yescharacteristic
418C22⋊C8C22⋊D1111yescharacteristic
419#97—221no—
420C4×C8—221no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C2×C11—41no—
426C2×C11—161no—
427C2×C11#304611yescharacteristic
428C2×C11#305011yescharacteristic
429C2×C11#306811yescharacteristic
430D11—42no—
431#41—82no—
432#41—222no—
433#41—222no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—111no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—111no—
443C2×D4—221no—
444C22×C4—41no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4D4×D1111yescharacteristic
449C22×C4#434111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451Q16—442no—
452SD16—442no—
453SD16—442no—
454D8—442no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—881no—
462C2×C8—881no—
463C2×C8—881no—
464C2×C8C2×C22⋊D1111yescharacteristic
465C2×C8C2×C22⋊D1111yescharacteristic
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C42—41no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42D4×D1111yescharacteristic
491C42#434111yescharacteristic
492C42C2×C22⋊D1111yescharacteristic
493C42C23×D1111yescharacteristic
494C11#1941911yescharacteristic, complemented, Sylow
495C23—41no—
496C23—221no—
497C23#6699111yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502Q8—112no—
503Q8—221no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—82no—
510D4—112no—
511D4—224no—
512D4—221no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—224no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—881no—
529C2×C4#6699111yescharacteristic
530C2×C4#6699111yescharacteristic
531C2×C4#6699111yescharacteristic
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4C2×#434111yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—441no—
540C8—441no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—222no—
552C22—441no—
553C22—441no—
554C22C2×#6699111yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—222no—
563C4—441no—
564C4—441no—
565C4D11×#13511yescharacteristic
566C4D11×#13511yescharacteristic
567C4#1062336811yescharacteristic
568C4#1062336911yescharacteristic
569C2—41no—
570C2—161no—
571C2—442no—
572C2#1307816211yescharacteristic
573C2#1307819311yescharacteristic
574C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3228C2
socleC22×C11C2×#121
prime radical#13078670C2
hypercenter#3228D11
hypocenterC11#19419
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
1. #13078772C2semidirect
3. #13077724C2semidirect
4. #13068057C2semidirect
5. #13068050C2semidirect
6. #13068029C2semidirect
7. #13068022C2semidirect
8. #13068017C2semidirect
9. #13068012C2semidirect
10. #13067995C2semidirect
11. #13067988C2semidirect
12. #13067396C2semidirect
13. #13067311C2semidirect
14. #13067273C2semidirect
15. C11×#3228C2semidirect
208. #3228D11semidirect
494. C11#19419semidirect

Maximal subgroups

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

subgroupindex
#130787722
#130786702
#130777242
#130680572
#130680502
#130680292
#130680222
#130680172
#130680122
#130679952
#130679882
#130673962
#130673112
#130672732
C11×#32282
#1941911