Finite Group Databasebeta

← #14738706

Subgroups — #14738706

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079994C211yesmaximal, characteristic
2#13079335C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13068189C211yesmaximal, characteristic, complemented
5#13068151C211yesmaximal, characteristic, complemented
6#13068137C211yesmaximal, characteristic, complemented
7#13068083C211yesmaximal, characteristic, complemented
8#13068065C211yesmaximal, characteristic, complemented
9#13068027C211yesmaximal, characteristic, complemented
10#13068013C211yesmaximal, characteristic, complemented
11#13067959C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067312C211yesmaximal, characteristic, complemented
14#13067306C211yesmaximal, characteristic, complemented
15C11×#3235C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C2×#67001—21no—
19#10623008C2211yescharacteristic
20C11×#501—21no—
21C11×#490—21no—
22C11×#482—21no—
23C11×#482—21no—
24C11×#476C2211yescharacteristic
25C11×#476C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#474C2211yescharacteristic
28C11×#432C2211yescharacteristic
29#10622847—21no—
30#10622701C2211yescharacteristic
31#10622698C2211yescharacteristic
32#10622697—21no—
33#10622694C2211yescharacteristic
34#10622691C2211yescharacteristic
35#10622685—21no—
36#10622662—21no—
37#10622662—21no—
38#10622652—21no—
39#10622652—21no—
40#10622639—21no—
41#10622639—21no—
42#10622628C2211yescharacteristic
43#10622628C2211yescharacteristic
44#10622625C2211yescharacteristic
45#10622625C2211yescharacteristic
46#10622624—21no—
47#10622624—21no—
48D4×C11⋊C8C2211yescharacteristic
49D4×C11⋊C8C2211yescharacteristic
50#10622621C2211yescharacteristic
51#10622621C2211yescharacteristic
52#10622537C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×#4339—21no—
69C11×C4⋊Q8D411yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#127D411yescharacteristic
73C11×#125—21no—
74C11×#124—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×#121—21no—
78C11×#121D411yescharacteristic
79C11×#121D411yescharacteristic
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C11×#117—21no—
86C2×C42×C11C2311yescharacteristic
87#67001—44no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4323—21no—
91C2×#4323—21no—
92#66983—21no—
93#66983—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318D411yescharacteristic
98C2×#4318D411yescharacteristic
99C22×C11⋊C8—21no—
100C22×C11⋊C8—21no—
101C22×C11⋊C8—21no—
102#66928—21no—
103#66927C2311yescharacteristic
104C4×D44—21no—
105C4×D44—21no—
106#66922C2311yescharacteristic
107C11×#107—21no—
108C11×#107—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×C4⋊C8C2311yescharacteristic
112C11×C4⋊C8C2311yescharacteristic
113C11×#102—21no—
114C11×#102—21no—
115C11×#102—21no—
116C11×#102—21no—
117C11×C22⋊C8—21no—
118C11×#97—21no—
119#66899—21no—
120#66899—21no—
121#66896—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127#66873—21no—
128#66873—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)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867D411yescharacteristic
142#66867D411yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19369—111nomaximal, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11C2×D411yescharacteristic
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C2×C22⋊D11—41no—
163#4339—82no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×C4×D11—41no—
168C2×Dic22—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—41no—
185C42×C11—41no—
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11#4111yescharacteristic
189C42×C11C2411yescharacteristic
190#4325—42no—
191#4325—42no—
192#4323—81no—
193#4323—81no—
194(C2×D11)⋊C4—41no—
195(C2×D11)⋊C4—41no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198#4318—22no—
199#4318—41no—
200#4318—42no—
201#4318—42no—
202#4318—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—42no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#3253—111no—
215#3235D1111yescharacteristic, complemented
216#3182—111no—
217#2935—111no—
218#1703—111no—
219#1697—111no—
220#1695—111no—
221#1685—111no—
222#1683—111no—
223#1677—111no—
224#1675—111no—
225#1665—111no—
226#1569—111no—
227#1551—111no—
228#1550—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11#12111yescharacteristic
232C22×D11—41no—
233Q8×C11—42no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—81no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—81no—
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—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C22⋊D11—82no—
265C2×Dic11—41no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—81no—
271C4×D11—82no—
272Dic22—81no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8AGL(1,ℤ/8)12yes—
283C2×#131—221no—
284#533C2×D1111yescharacteristic
285#532—111no—
286#532C2×D1111yescharacteristic
287#501—21no—
288#500—111no—
289#492—111no—
290#490—21no—
291#487—111no—
292#486—111no—
293#482—21no—
294#482—21no—
295#476—111no—
296#476—111no—
297#476—221no—
298#476C2×D1111yescharacteristic
299#476C2×D1111yescharacteristic
300#474C2×D1111yescharacteristic
301#474C2×D1111yescharacteristic
302#469—221no—
303#469—221no—
304#468—221no—
305#468—221no—
306#459—111no—
307#459—111no—
308#459—221no—
309#440—221no—
310#440—221no—
311#436—111no—
312#436—111no—
313#435—221no—
314#435—221no—
315C8×D4—111no—
316C8×D4—111no—
317#432C2×D1111yescharacteristic
318#423—111no—
319C2×C4⋊C8—111no—
320#408—221no—
321C4×M16—111no—
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326#333—111no—
327#333—111no—
328#333—111no—
329#333—111no—
330#332—111no—
331#332—111no—
332#331—111no—
333#331—111no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11C2×#12111yescharacteristic
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C4×C11#57511yescharacteristic
357C4×C11#57711yescharacteristic
358C4×C11#57811yescharacteristic
359Dic11—81no—
360C2×#41—21no—
361C2×#41—221no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×D8—221no—
365C2×D8—221no—
366#131—444no—
367C2×M16—111no—
368C2×M16—111no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C4⋊Q8—111no—
376C4⋊Q8C22⋊D1111yescharacteristic
377C4⋊Q8C22×D1111yescharacteristic
378C4⋊Q8C22×D1111yescharacteristic
379#127—111no—
380#127C22⋊D1111yescharacteristic
381#125—21no—
382#124—21no—
383#124—221no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386#121—21no—
387#121—221no—
388#121—221no—
389#121C22⋊D1111yescharacteristic
390#121C22⋊D1111yescharacteristic
391C4×Q8—21no—
392C4×Q8—21no—
393C4×D4—21no—
394C4×D4—221no—
395C4×D4—221no—
396C4×D4C22×D1111yescharacteristic
397C4×D4C22×D1111yescharacteristic
398#117—21no—
399C2×C42C22×D1111yescharacteristic
400#107—21no—
401#107—21no—
402#107—221no—
403#107—221no—
404#106—21no—
405#106—21no—
406#106—221no—
407#106—221no—
408C4⋊C8—111no—
409C4⋊C8—111no—
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—221no—
413C4⋊C8—221no—
414C4⋊C8C22×D1111yescharacteristic
415C4⋊C8C22×D1111yescharacteristic
416#103—221no—
417#103—221no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—221no—
423#102—221no—
424#102—221no—
425#102—221no—
426#102—221no—
427#102—221no—
428C22⋊C8—21no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C22⋊C8—221no—
433#97—21no—
434#97—111no—
435#97—111no—
436C4×C8—111no—
437C4×C8—111no—
438C2×C11—41no—
439C2×C11—81no—
440C2×C11—81no—
441C2×C11#303611yescharacteristic
442C2×C11#306311yescharacteristic
443C2×C11#306811yescharacteristic
444D11—161no—
445#41—42no—
446#41—42no—
447#41—882no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—221no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—441no—
460C2×D4C2×C22⋊D1111yescharacteristic
461C2×D4C2×C22⋊D1111yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—441no—
465C22×C4D4×D1111yescharacteristic
466C22×C4#434111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468SD16—442no—
469SD16—442no—
470D8—881no—
471D8—881no—
472M16—222no—
473M16—442no—
474M16—441no—
475M16—442no—
476M16—881no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—442no—
488C2×C8—442no—
489C2×C8—442no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4C2×C22⋊D1111yescharacteristic
500C4⋊C4C2×C22⋊D1111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—441no—
507C22⋊C4—441no—
508C42—41no—
509C42D4×D1111yescharacteristic
510C42#434111yescharacteristic
511C42C2×C22⋊D1111yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1936911yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—441no—
517C23#6699211yescharacteristic
518Q8—42no—
519Q8—41no—
520Q8—41no—
521Q8—81no—
522Q8—881no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—81no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—881no—
536D4—882no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—441no—
551C2×C4—882no—
552C2×C4#6699211yescharacteristic
553C2×C4#6699211yescharacteristic
554C2×C4#6699211yescharacteristic
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×#434111yescharacteristic
557C2×C4C22×C22⋊D1111yescharacteristic
558C8—41no—
559C8—41no—
560C8—112no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—441no—
565C8—441no—
566C8—441no—
567C8—441no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22C2×#6699211yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—881no—
590C4D11×AGL(1,ℤ/8)11yescharacteristic
591C4#1062330411yescharacteristic
592C4#1062336811yescharacteristic
593C4#1062336911yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—1761no—
598C2#1307807711yescharacteristic
599C2#1307830311yescharacteristic
600C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3235C2
socleC22×C11C2×#121
prime radical#13079994C2
hypercenter#3235D11
hypocenterC11#19369
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3235

Complements

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

NH ≅ G/Ntype
2. #13079335C2semidirect
3. #13077360C2semidirect
4. #13068189C2semidirect
5. #13068151C2semidirect
6. #13068137C2semidirect
7. #13068083C2semidirect
8. #13068065C2semidirect
9. #13068027C2semidirect
10. #13068013C2semidirect
11. #13067959C2semidirect
12. #13067384C2semidirect
13. #13067312C2semidirect
14. #13067306C2semidirect
15. C11×#3235C2semidirect
215. #3235D11semidirect
513. C11#19369semidirect

Maximal subgroups

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

subgroupindex
#130799942
#130793352
#130773602
#130681892
#130681512
#130681372
#130680832
#130680652
#130680272
#130680132
#130679592
#130673842
#130673122
#130673062
C11×#32352
#1936911