Finite Group Databasebeta

← #14724185

Subgroups — #14724185

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078677C211yesmaximal, characteristic
2#13077734C211yesmaximal, characteristic, complemented
3#13077694C211yesmaximal, characteristic, complemented
4#13067529C211yesmaximal, characteristic, complemented
5#13067517C211yesmaximal, characteristic, complemented
6#13067505C211yesmaximal, characteristic, complemented
7#13067500C211yesmaximal, characteristic, complemented
8#13067479C211yesmaximal, characteristic, complemented
9#13067472C211yesmaximal, characteristic, complemented
10#13067451C211yesmaximal, characteristic, complemented
11#13067444C211yesmaximal, characteristic, complemented
12#13067048C211yesmaximal, characteristic, complemented
13#13067014C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1573C211yesmaximal, characteristic, complemented
16#10623008C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21#10622724—21no—
22#10622724—21no—
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25#10622463C411yescharacteristic
26#10622461C411yescharacteristic
27#10622456C411yescharacteristic
28#10622455C411yescharacteristic
29#10622451C2211yescharacteristic
30#10622451C2211yescharacteristic
31#10622451C2211yescharacteristic
32#10622451C2211yescharacteristic
33#10622450—21no—
34#10622448—21no—
35#10622447C2211yescharacteristic
36#10622447C2211yescharacteristic
37#10622444C2211yescharacteristic
38#10622444C2211yescharacteristic
39#10622350C411yescharacteristic
40#10622350C411yescharacteristic
41#10622347C411yescharacteristic
42#10622347C411yescharacteristic
43#10622340—21no—
44#10622340—21no—
45#10622319—21no—
46#10622319—21no—
47C4×D88C2211yescharacteristic
48C4×D88C2211yescharacteristic
49C4×#4314C2211yescharacteristic
50C4×#4314C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622121C2211yescharacteristic
60#10622121C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C2×#4339C2×C411yescharacteristic
69C22×C8×C11—21no—
70C2×C42×C11C2311yescharacteristic
71#66983—21no—
72#66983C2×C411yescharacteristic
73#66983C2×C411yescharacteristic
74C4×C22⋊D11—21no—
75C4×C22⋊D11—21no—
76#66979C2×C411yescharacteristic
77C2×D88C2×C411yescharacteristic
78C2×D88C2×C411yescharacteristic
79C2×#4314C2×C411yescharacteristic
80C2×#4314C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87#66928—21no—
88#66927C2×C411yescharacteristic
89C4×D44—21no—
90C4×D44C2×C411yescharacteristic
91C4×D44C2311yescharacteristic
92C4×D44C2311yescharacteristic
93C4×D44C2311yescharacteristic
94#66925—21no—
95C42×D11—21no—
96#66922C2×C411yescharacteristic
97C4×Dic22C2×C411yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2×C411yescharacteristic
101C11×C4⋊C8C2×C411yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C11×C22⋊C8C2×C411yescharacteristic
108C11×C22⋊C8C2×C411yescharacteristic
109C11×#97—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)D411yescharacteristic
114C22⋊(C11⋊C8)D411yescharacteristic
115#66885C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127#66882C2×C411yescharacteristic
128#66882C2×C411yescharacteristic
129#66881C2×C411yescharacteristic
130#66881C2×C411yescharacteristic
131#66880C2×C411yescharacteristic
132#66880C2×C411yescharacteristic
133#66879—21no—
134#66879—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)D411yescharacteristic
139C4⋊(C11⋊C8)D411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17948—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151#4339—41no—
152#4339—41no—
153#4339—81no—
154#4339—81no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44C22×C411yescharacteristic
158C2×D44C22×C411yescharacteristic
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×Dic22—21no—
166C2×Dic22C22×C411yescharacteristic
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—81no—
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11#4111yescharacteristic
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203D88—41no—
204D88—41no—
205#4314—41no—
206#4314—41no—
207#4313—81no—
208#4313—81no—
209#4313—81no—
210#4313—81no—
211C8×D11—81no—
212C8×D11—81no—
213#3106—111no—
214#2989—111no—
215#2981—111no—
216#1594—111no—
217#1592—111no—
218#1590—111no—
219#1589—111no—
220#1586—111no—
221#1585—111no—
222#1582—111no—
223#1581—111no—
224#1573D1111yescharacteristic, complemented
225#1488—111no—
226#1480—111no—
227#1454—111no—
228C23×C11C4×D411yescharacteristic
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C22⋊D11—42no—
244C22⋊D11—81no—
245C22⋊D11—81no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251D44—21no—
252D44—21no—
253D44—21no—
254D44—21no—
255D44—21no—
256D44—21no—
257D44—81no—
258D44—81no—
259C4×D11—42no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—81no—
267Dic22—21no—
268Dic22—21no—
269Dic22—81no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#532—111no—
285C4×#41—111no—
286#482—111no—
287#482—111no—
288#477—111no—
289#476—111no—
290#460—111no—
291#459—111no—
292#449—111no—
293#449—111no—
294#446—111no—
295#446—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×D8—111no—
299C4×D8—111no—
300#436—111no—
301#436—111no—
302#436—111no—
303#436—111no—
304#435—221no—
305#435—221no—
306#435—221no—
307#435—221no—
308C8×D4—111no—
309C8×D4—111no—
310#432—221no—
311#432C2×D1111yescharacteristic
312#431—111no—
313#431—111no—
314#431C2×D1111yescharacteristic
315#423—221no—
316C2×C4⋊C8C2×D1111yescharacteristic
317#408—221no—
318#408—221no—
319#335C2×D1111yescharacteristic
320#335C2×D1111yescharacteristic
321#334C2×D1111yescharacteristic
322#334C2×D1111yescharacteristic
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331#322—111no—
332#322—111no—
333#322—111no—
334C82—111no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11C2×C4×D411yescharacteristic
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11#56811yescharacteristic
353C4×C11#56811yescharacteristic
354C4×C11#57611yescharacteristic
355C4×C11#57711yescharacteristic
356Dic11—41no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361C2×#41—111no—
362C2×#41—221no—
363C2×SD16—111no—
364C2×SD16—111no—
365C2×D8—111no—
366C2×D8—111no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16—221no—
370C2×M16—221no—
371C22×C8—21no—
372C22×C8—221no—
373C22×C8—221no—
374C4⋊Q8—111no—
375#127—111no—
376#124—221no—
377#121—111no—
378#121—111no—
379#121—221no—
380C4×Q8—111no—
381C4×Q8—111no—
382C4×D4—111no—
383C4×D4—111no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—221no—
387C4×D4—221no—
388C4×D4—221no—
389#117—111no—
390#117—221no—
391C2×C42—221no—
392C2×C42C22×D1111yescharacteristic
393#107—111no—
394#107—111no—
395#106—111no—
396#106—111no—
397C4⋊C8—21no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8C4×D1111yescharacteristic
404C4⋊C8C4×D1111yescharacteristic
405C4⋊C8C22×D1111yescharacteristic
406C4⋊C8C22×D1111yescharacteristic
407C4⋊C8C22×D1111yescharacteristic
408C4⋊C8C22×D1111yescharacteristic
409#103—111no—
410#103—111no—
411#102—111no—
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417C22⋊C8—21no—
418C22⋊C8—111no—
419C22⋊C8—111no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8C4×D1111yescharacteristic
428C22⋊C8C4×D1111yescharacteristic
429#97—21no—
430#97—221no—
431#97—221no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C2×C11—41no—
439C2×C11#293011yescharacteristic
440C2×C11#294611yescharacteristic
441C2×C11#295711yescharacteristic
442D11—81no—
443D11—81no—
444D11—81no—
445#41—441no—
446#41—441no—
447#41—881no—
448#41—881no—
449C2×Q8—111no—
450C2×Q8—221no—
451C2×D4—111no—
452C2×D4—111no—
453C2×D4—111no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4#434311yescharacteristic
467SD16—441no—
468SD16—441no—
469D8—441no—
470D8—441no—
471M16—881no—
472M16—881no—
473M16—881no—
474M16—881no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—881no—
487C2×C8—881no—
488C2×C8C2×C4×D1111yescharacteristic
489C2×C8C2×C4×D1111yescharacteristic
490C2×C8C2×C4×D1111yescharacteristic
491C2×C8C2×C4×D1111yescharacteristic
492C4⋊C4—111no—
493C4⋊C4—111no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42C2×C4×D1111yescharacteristic
510C42D4×D1111yescharacteristic
511C42#434311yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1794811yescharacteristic, complemented, Sylow
514C23—221no—
515C23—221no—
516C23—221no—
517C23#6694611yescharacteristic
518Q8—221no—
519Q8—221no—
520Q8—881no—
521D4—221no—
522D4—221no—
523D4—221no—
524D4—221no—
525D4—221no—
526D4—221no—
527D4—442no—
528D4—881no—
529D4—881no—
530D4—881no—
531D4—881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—442no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—881no—
550C2×C4#6694611yescharacteristic
551C2×C4#6694611yescharacteristic
552C2×C4#6694611yescharacteristic
553C2×C4C22×C4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4C2×#434311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—441no—
569C8—441no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—441no—
574C22—441no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22C2×#6694611yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—441no—
588C4—441no—
589C4—441no—
590C4—441no—
591C4—441no—
592C4#1062328111yescharacteristic
593C4#1062328111yescharacteristic
594C4#1062330511yescharacteristic
595C4#1062330911yescharacteristic
596C2—41no—
597C2—881no—
598C2—881no—
599C2—881no—
600C2#1307731811yescharacteristic
601C2#1307744611yescharacteristic
602C2#1307753211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1573C2
socleC22×C11C2×C4×D4
prime radical#13078677C2
cosocleC42×C11C24
hypercenter#1573D11
hypocenterC11#17948
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #13077734C2semidirect
3. #13077694C2semidirect
4. #13067529C2semidirect
5. #13067517C2semidirect
6. #13067505C2semidirect
7. #13067500C2semidirect
8. #13067479C2semidirect
9. #13067472C2semidirect
10. #13067451C2semidirect
11. #13067444C2semidirect
12. #13067048C2semidirect
13. #13067014C2semidirect
14. #13066916C2semidirect
15. C11×#1573C2semidirect
224. #1573D11semidirect
513. C11#17948semidirect

Maximal subgroups

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

subgroupindex
#130786772
#130777342
#130776942
#130675292
#130675172
#130675052
#130675002
#130674792
#130674722
#130674512
#130674442
#130670482
#130670142
#130669162
C11×#15732
#1794811