Finite Group Databasebeta

← #14739220

Subgroups — #14739220

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#13078761C211yesmaximal, characteristic
2#13078681C211yesmaximal, characteristic, complemented
3#13077724C211yesmaximal, characteristic, complemented
4#13068057C211yesmaximal, characteristic, complemented
5#13068050C211yesmaximal, characteristic, complemented
6#13068043C211yesmaximal, characteristic, complemented
7#13068036C211yesmaximal, characteristic, complemented
8#13067983C211yesmaximal, characteristic, complemented
9#13067978C211yesmaximal, characteristic, complemented
10#13067961C211yesmaximal, characteristic, complemented
11#13067954C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067316C211yesmaximal, characteristic, complemented
14#13067265C211yesmaximal, characteristic, complemented
15C11×#3210C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#494C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#464—21no—
24C11×#464—21no—
25C11×#452—21no—
26C11×#452—21no—
27C11×#431C2211yescharacteristic
28#10622707C2211yescharacteristic
29#10622707C2211yescharacteristic
30#10622703C2211yescharacteristic
31#10622700C2211yescharacteristic
32#10622700C2211yescharacteristic
33#10622696C2211yescharacteristic
34#10622688C2211yescharacteristic
35#10622685C2211yescharacteristic
36#10622660—21no—
37#10622658—21no—
38#10622650—21no—
39#10622648—21no—
40C4×#4326—21no—
41C4×#4325—21no—
42#10622631—21no—
43#10622627—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#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622185C2211yescharacteristic
60#10622185C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C2×#4339D411yescharacteristic
69C2×C11×Q16—21no—
70C2×C11×Q16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#127C2311yescharacteristic
77C11×#125—21no—
78C11×#124—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×#121—21no—
82C11×#121—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C11×#117—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4326—21no—
90C2×#4325—21no—
91C2×#4324—21no—
92C2×#4323—21no—
93C4×C22⋊D11—21no—
94C4×C22⋊D11—21no—
95#66979D411yescharacteristic
96C22×C11⋊C8—21no—
97C2×C8×D11—21no—
98C2×C8×D11—21no—
99C4×D44D411yescharacteristic
100C4×D44C2311yescharacteristic
101#66925—21no—
102C42×D11—21no—
103C4×Dic22D411yescharacteristic
104C4×Dic22C2311yescharacteristic
105C11×C4⋊C8D411yescharacteristic
106C11×C4⋊C8D411yescharacteristic
107C11×#103—21no—
108C11×#103—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#19413—111nomaximal, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
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—21no—
159#4339—22no—
160#4339—22no—
161C2×D44C2×D411yescharacteristic
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×Dic22C2×D411yescharacteristic
166C11×Q16—81no—
167C11×Q16—81no—
168C11×SD16—81no—
169C11×SD16—81no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
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⋊C4—41no—
181C11×C4⋊C4—41no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C42×C11—41no—
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11#4111yescharacteristic
189C42×C11C2411yescharacteristic
190C22⋊Dic11—21no—
191#4326—42no—
192#4325—42no—
193#4324—42no—
194#4323—42no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197C4⋊Dic11C2×D411yescharacteristic
198C4⋊Dic11C2×D411yescharacteristic
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—81no—
211C8×D11—81no—
212C8×D11—81no—
213#3210D1111yescharacteristic, complemented
214#3115—111no—
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—41no—
229C23×C11#12111yescharacteristic
230C22×D11—21no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
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—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
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
258C22⋊D11—24no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262D44—21no—
263D44#13512yes—
264C4×D11—24no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—81no—
268Dic22—21no—
269Dic22#13512yes—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#533C2×D1111yescharacteristic
281#532C2×D1111yescharacteristic
282C4×#41—111no—
283#494C2×D1111yescharacteristic
284#492C2×D1111yescharacteristic
285#487C2×D1111yescharacteristic
286#486C2×D1111yescharacteristic
287#485—221no—
288#482—221no—
289#475—111no—
290#475—111no—
291#474—111no—
292#474—111no—
293#464—21no—
294#464—21no—
295#462—111no—
296#461—111no—
297#460—111no—
298#459—111no—
299#452—21no—
300#452—21no—
301#452—221no—
302#449—221no—
303C8×Q8—111no—
304C8×Q8—111no—
305#442—221no—
306#440—221no—
307C4×Q16—221no—
308C4×SD16—221no—
309C8×D4—111no—
310C8×D4—111no—
311C8×D4—221no—
312C8×D4—221no—
313#432—111no—
314#431—111no—
315#431—221no—
316#431C2×D1111yescharacteristic
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—21no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11C2×#12111yescharacteristic
338C2×D11—22no—
339C2×D11—41no—
340C2×D11—41no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11C2×#13511yescharacteristic
349C4×C11C2×#13511yescharacteristic
350C4×C11#57611yescharacteristic
351C4×C11#57711yescharacteristic
352Dic11—22no—
353Dic11—41no—
354Dic11—41no—
355C2×#41—21no—
356C2×#41—111no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—221no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×D8—221no—
365C22×C8—221no—
366C22×C8—221no—
367C22×C8—221no—
368C4⋊Q8C22×D1111yescharacteristic
369C4⋊Q8C22×D1111yescharacteristic
370C4⋊Q8C22×D1111yescharacteristic
371#127C22×D1111yescharacteristic
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—111no—
381C4×Q8—111no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—221no—
387C4×D4—221no—
388#117—21no—
389#117—111no—
390#117—221no—
391C2×C42—221no—
392C2×C42C22×D1111yescharacteristic
393#107—221no—
394#107—221no—
395#106—221no—
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—21no—
410#103—221no—
411#103—221no—
412#103—221no—
413#103—221no—
414#102—21no—
415#102—21no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8C22⋊D1111yescharacteristic
425C22⋊C8C22⋊D1111yescharacteristic
426#97—221no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8—221no—
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—41no—
433C2×C11—161no—
434C2×C11#304511yescharacteristic
435C2×C11#305011yescharacteristic
436C2×C11#306911yescharacteristic
437D11—42no—
438#41—81no—
439#41—81no—
440#41—222no—
441#41—222no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—111no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4—111no—
451C2×D4—221no—
452C22×C4—41no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4D4×D1111yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459Q16—81no—
460Q16—81no—
461Q16—442no—
462SD16—81no—
463SD16—81no—
464SD16—442no—
465SD16—442no—
466D8—442no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—881no—
474C2×C8—881no—
475C2×C8—881no—
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—111no—
489C4⋊C4—111no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—221no—
496C22⋊C4—221no—
497C22⋊C4—221no—
498C42—41no—
499C42—221no—
500C42—221no—
501C42—221no—
502C42D4×D1111yescharacteristic
503C42#434111yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1941311yescharacteristic, complemented, Sylow
507C23—41no—
508C23—221no—
509C23#6699111yescharacteristic
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—112no—
517Q8—221no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—82no—
524D4—112no—
525D4—224no—
526D4—221no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—224no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—881no—
543C2×C4#6699111yescharacteristic
544C2×C4#6699111yescharacteristic
545C2×C4#6699111yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4C2×#434111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—441no—
554C8—441no—
555C8—441no—
556C8—441no—
557C8—441no—
558C8—441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—222no—
566C22—441no—
567C22—441no—
568C22C2×#6699111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—222no—
577C4—441no—
578C4—441no—
579C4D11×#13511yescharacteristic
580C4D11×#13511yescharacteristic
581C4#1062336611yescharacteristic
582C4#1062336711yescharacteristic
583C2—41no—
584C2—161no—
585C2—442no—
586C2#1307815111yescharacteristic
587C2#1307819311yescharacteristic
588C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3210C2
socleC22×C11C2×#121
prime radical#13078761C2
hypercenter#3210D11
hypocenterC11#19413
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3210

Complements

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

NH ≅ G/Ntype
2. #13078681C2semidirect
3. #13077724C2semidirect
4. #13068057C2semidirect
5. #13068050C2semidirect
6. #13068043C2semidirect
7. #13068036C2semidirect
8. #13067983C2semidirect
9. #13067978C2semidirect
10. #13067961C2semidirect
11. #13067954C2semidirect
12. #13067396C2semidirect
13. #13067316C2semidirect
14. #13067265C2semidirect
15. C11×#3210C2semidirect
213. #3210D11semidirect
506. C11#19413semidirect

Maximal subgroups

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

subgroupindex
#130787612
#130786812
#130777242
#130680572
#130680502
#130680432
#130680362
#130679832
#130679782
#130679612
#130679542
#130673962
#130673162
#130672652
C11×#32102
#1941311