Finite Group Databasebeta

← #14739230

Subgroups — #14739230

Order 2816.

628 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#13079572C211yesmaximal, characteristic, complemented
2#13078687C211yesmaximal, characteristic, complemented
3#13077727C211yesmaximal, characteristic, complemented
4#13068058C211yesmaximal, characteristic, complemented
5#13068051C211yesmaximal, characteristic, complemented
6#13068044C211yesmaximal, characteristic, complemented
7#13068037C211yesmaximal, characteristic, complemented
8#13067984C211yesmaximal, characteristic, complemented
9#13067979C211yesmaximal, characteristic, complemented
10#13067962C211yesmaximal, characteristic, complemented
11#13067955C211yesmaximal, characteristic, complemented
12#13067397C211yesmaximal, characteristic, complemented
13#13067317C211yesmaximal, characteristic, complemented
14#13067265C211yesmaximal, characteristic, complemented
15C11×#3115C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#482—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#460C2211yescharacteristic
23C11×#459C2211yescharacteristic
24C11×#449—21no—
25C11×#442—21no—
26C11×#440—21no—
27C11×#432C2211yescharacteristic
28#10622852—21no—
29#10622852—21no—
30#10622852—21no—
31#10622705C2211yescharacteristic
32#10622694C2211yescharacteristic
33#10622689C2211yescharacteristic
34#10622683C2211yescharacteristic
35#10622667—21no—
36#10622667—21no—
37#10622644C2211yescharacteristic
38C4×#4326—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622632C2211yescharacteristic
43C4×#4324—21no—
44D4×C11⋊C8—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622609—21no—
50#10622538—21no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53C2×C4⋊(C11⋊C8)—21no—
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
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×#4326—21no—
90C2×#4326—21no—
91C2×#4324—21no—
92C2×#4324—21no—
93C2×#4324—21no—
94#66979—21no—
95#66977—21no—
96#66977—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8—21no—
100#66923—21no—
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103C4×Dic22—21no—
104C4×Dic22—21no—
105C11×#107—21no—
106C11×#106—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#102—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×C22⋊C8—21no—
114C11×#97—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)D411yescharacteristic
125C22⋊(C11⋊C8)D411yescharacteristic
126#66874—21no—
127#66874—21no—
128#66872—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
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19413—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—81no—
148C11×#41—81no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C2×Dic22—21no—
165C2×Dic22—21no—
166C11×SD16—42no—
167C11×D8—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—41no—
180C11×C22⋊C4—41no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4326—42no—
190#4326—81no—
191#4326—81no—
192#4324—42no—
193#4324—81no—
194#4324—81no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199Dic11⋊C4—41no—
200Dic11⋊C4—41no—
201C4×Dic11—41no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8—81no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#3210—111no—
214#3115D1111yescharacteristic
215#3107—111no—
216#2988—111no—
217#1682—111no—
218#1681—111no—
219#1680—111no—
220#1679—111no—
221#1670—111no—
222#1669—111no—
223#1666—111no—
224#1665—111no—
225#1572—111no—
226#1552—111no—
227#1540—111no—
228C23×C11—21no—
229C23×C11—41no—
230C23×C11#12111yescharacteristic
231Q8×C11—21no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11#13512yes—
235D4×C11—24no—
236D4×C11—21no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—81no—
242D4×C11—82no—
243D4×C11#13512yes—
244C2×C4×C11—24no—
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—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—81no—
257C2×C4×C11—82no—
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×Dic11—41no—
265C2×Dic11—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—41no—
269Dic22—41no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#533—111no—
281#532C2×D1111yescharacteristic
282C4×#41C2×D1111yescharacteristic
283#494—111no—
284#492—111no—
285#487—111no—
286#486—111no—
287#485—221no—
288#482—21no—
289#475—111no—
290#475C2×D1111yescharacteristic
291#474—111no—
292#474C2×D1111yescharacteristic
293#464—221no—
294#464—221no—
295#462—111no—
296#461—111no—
297#460C2×D1111yescharacteristic
298#459C2×D1111yescharacteristic
299#452—221no—
300#452—221no—
301#452—221no—
302#449—21no—
303C8×Q8—111no—
304C8×Q8—111no—
305#442—21no—
306#440—21no—
307C4×Q16—221no—
308C4×SD16—221no—
309C8×D4—111no—
310C8×D4—111no—
311C8×D4—221no—
312C8×D4—221no—
313#432C2×D1111yescharacteristic
314#431—111no—
315#431—111no—
316#431—221no—
317C2×C4⋊C8—111no—
318C2×C4⋊C8—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329#331—111no—
330#331—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—22no—
334C22×C11—21no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11C2×#12111yescharacteristic
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—81no—
349C4×C11C2×#13511yescharacteristic
350C4×C11C2×#13511yescharacteristic
351C4×C11#57611yescharacteristic
352C4×C11#57711yescharacteristic
353Dic11—81no—
354Dic11—81no—
355C2×#41—21no—
356C2×#41C22⋊D1111yescharacteristic
357C2×Q16—221no—
358C2×Q16—221no—
359C2×Q16—221no—
360C2×SD16—21no—
361C2×SD16—221no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×D8—21no—
365C22×C8—221no—
366C22×C8—221no—
367C22×C8—221no—
368C4⋊Q8—111no—
369C4⋊Q8—111no—
370C4⋊Q8C22×D1111yescharacteristic
371#127C22×D1111yescharacteristic
372#125—221no—
373#124—21no—
374C22⋊Q8—221no—
375C22⋊Q8—221no—
376#121—21no—
377#121—21no—
378C4×Q8—221no—
379C4×Q8—221no—
380C4×Q8C22⋊D1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C22⋊D1111yescharacteristic
387C4×D4C22×D1111yescharacteristic
388#117—21no—
389#117—221no—
390#117C22⋊D1111yescharacteristic
391C2×C42—21no—
392C2×C42C22×D1111yescharacteristic
393#107—21no—
394#107—221no—
395#106—21no—
396#106—221no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8C22×D1111yescharacteristic
407C4⋊C8C22×D1111yescharacteristic
408#103—21no—
409#103—221no—
410#103—221no—
411#103—221no—
412#103—221no—
413#103—221no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—21no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426#97—21no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—221no—
430C4×C8—221no—
431C4×C8—221no—
432C2×C11—41no—
433C2×C11—42no—
434C2×C11—161no—
435C2×C11#304511yescharacteristic
436C2×C11#305011yescharacteristic
437C2×C11#306911yescharacteristic
438#41—22no—
439#41—22no—
440#41—81no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8C2×C22⋊D1111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4C2×C22⋊D1111yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4D4×D1111yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459Q16—442no—
460Q16—881no—
461Q16—881no—
462SD16—42no—
463SD16—442no—
464SD16—881no—
465SD16—881no—
466D8—42no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—881no—
478C2×C8—881no—
479C2×C8—881no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—441no—
489C4⋊C4—441no—
490C4⋊C4C2×C22⋊D1111yescharacteristic
491C4⋊C4C2×C22⋊D1111yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—441no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—441no—
502C42D4×D1111yescharacteristic
503C42#434111yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1941311yescharacteristic, complemented, Sylow
507C23—21no—
508C23—41no—
509C23#6699211yescharacteristic
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—441no—
514Q8—441no—
515Q8—441no—
516Q8—441no—
517Q8#6700312yes—
518D4—24no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4#6700312yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—81no—
540C2×C4—82no—
541C2×C4—441no—
542C2×C4—441no—
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—221no—
552C8—221no—
553C8—221no—
554C8—221no—
555C8—441no—
556C8—441no—
557C8—441no—
558C8—441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×#6699211yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—881no—
578C4—881no—
579C4#1062330511yescharacteristic
580C4#1062330611yescharacteristic
581C4C2×#6700311yescharacteristic
582C4C2×#6700311yescharacteristic
583C2—41no—
584C2—42no—
585C2—161no—
586C2#1307815911yescharacteristic
587C2#1307819411yescharacteristic
588C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3115C2
socleC22×C11C2×#121
hypercenter#3115D11
hypocenterC11#19413
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #13079572C2semidirect
2. #13078687C2semidirect
3. #13077727C2semidirect
4. #13068058C2semidirect
5. #13068051C2semidirect
6. #13068044C2semidirect
7. #13068037C2semidirect
8. #13067984C2semidirect
9. #13067979C2semidirect
10. #13067962C2semidirect
11. #13067955C2semidirect
12. #13067397C2semidirect
13. #13067317C2semidirect
14. #13067265C2semidirect
506. C11#19413semidirect

Maximal subgroups

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

subgroupindex
#130795722
#130786872
#130777272
#130680582
#130680512
#130680442
#130680372
#130679842
#130679792
#130679622
#130679552
#130673972
#130673172
#130672652
C11×#31152
#1941311