Finite Group Databasebeta

← #14857006

Subgroups — #14857006

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074579C211yesmaximal, characteristic
2#13071267C211yesmaximal, characteristic, complemented
3#13070120C211yesmaximal, characteristic, complemented
4#13069995C211yesmaximal, characteristic, complemented
5#13069985C211yesmaximal, characteristic
6#13069930C211yesmaximal, characteristic
7#13069467C211yesmaximal, characteristic
8#13069345C211yesmaximal, characteristic, complemented
9#13069314C211yesmaximal, characteristic
10#13069308C211yesmaximal, characteristic, complemented
11#13069244C211yesmaximal, characteristic
12#13069198C211yesmaximal, characteristic, complemented
13#13068971C211yesmaximal, characteristic
14#13068472C211yesmaximal, characteristic, complemented
15C11×#1865C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#103C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C11×#389C2211yescharacteristic
22#10622843C2211yescharacteristic
23#10622843C2211yescharacteristic
24C2×#66899C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622607—21no—
33#10622606—21no—
34#10622601C2211yescharacteristic
35#10622601C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622594—21no—
40#10622594—21no—
41#10622586C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44#10622552C2211yescharacteristic
45#10622550—21no—
46#10622549—21no—
47C4×C4⋊Dic11C2211yescharacteristic
48#10622545C2211yescharacteristic
49#10622288—21no—
50#10622287—21no—
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4325—22no—
73C2×#4325—22no—
74C2×#4325—41no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C11×#106—22no—
94C11×#103—22no—
95C11×#103—22no—
96C11×#95—21no—
97#66899—41no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110C11⋊#95D411yescharacteristic
111#66885—22no—
112#66885—41no—
113#66881—41no—
114#66879—41no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117C8×Dic11—41no—
118#66873—22no—
119#66872—22no—
120#29442—111nomaximal, Sylow
121C23×D11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11#4112yes—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—81no—
161C11×C4⋊C4#4112yes—
162C42×C11—24no—
163C42×C11—21no—
164C42×C11—21no—
165#4325—44no—
166(C2×D11)⋊C4—81no—
167(C2×D11)⋊C4—81no—
168(C2×D11)⋊C4—81no—
169(C2×D11)⋊C4—81no—
170(C2×D11)⋊C4—81no—
171(C2×D11)⋊C4—81no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—81no—
179C4⋊Dic11—81no—
180C4⋊Dic11—81no—
181Dic11⋊C4—81no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—81no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8#4112yes—
193#2644—111no—
194#2320—111no—
195#2088—111no—
196#2066—111no—
197#2065—111no—
198#2055—111no—
199#1968—111no—
200#1941—111no—
201#1936—111no—
202#1935—111no—
203#1926—111no—
204#1920—111no—
205#1880—111no—
206#1865D1111yescharacteristic, complemented
207#1768—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—41no—
269C8×C11—22no—
270C8×C11—41no—
271C11⋊C8—22no—
272C11⋊C8—41no—
273C22×SD16—111no—
274C2×C4×Q8C2×D1111yescharacteristic
275C2×#106—111no—
276C2×#106—111no—
277C2×#106C2×D1111yescharacteristic
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×#103—111no—
281C2×#103C2×D1111yescharacteristic
282C2×#103C2×D1111yescharacteristic
283C2×#102—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×#97—111no—
287C2×C4×C8—111no—
288#397—221no—
289#397—221no—
290#397—221no—
291#396—221no—
292#391—111no—
293#391—111no—
294#390—111no—
295#390—111no—
296#390—111no—
297#389—111no—
298#389—111no—
299#389—111no—
300#389—111no—
301#389C2×D1111yescharacteristic
302#387—221no—
303#387—221no—
304#383—221no—
305#382—221no—
306C4×C4⋊C4—111no—
307#376—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340C2×D1111yescharacteristic
314#336—111no—
315#336C2×D1111yescharacteristic
316C22×C11#52511yescharacteristic
317C22×C11#53211yescharacteristic
318C22×C11#53711yescharacteristic
319C22×C11#57711yescharacteristic
320C22×C11#57711yescharacteristic
321C22×C11#57711yescharacteristic
322C22×C11#57711yescharacteristic
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C4×C11—42no—
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11#55111yescharacteristic
337C4×C11#55211yescharacteristic
338C4×C11#55311yescharacteristic
339C4×C11#55611yescharacteristic
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347C22×Q8C22×D1111yescharacteristic
348C22×D4—111no—
349C2×SD16—222no—
350C2×SD16—222no—
351C2×SD16—441no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C4×Q8—22no—
357C4×Q8—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C42—21no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#106—22no—
382#106—222no—
383#106—441no—
384C4⋊C8—222no—
385C4⋊C8—222no—
386#103—22no—
387#103—22no—
388#103—441no—
389#102—222no—
390#102—222no—
391#102—441no—
392#97—441no—
393C4×C8—441no—
394#95—21no—
395#95—111no—
396#95—111no—
397#95—111no—
398#95—111no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408C2×C11#260111yescharacteristic
409C2×C11#312511yescharacteristic
410C2×C11#312611yescharacteristic
411C2×C11#317311yescharacteristic
412C2×C11#317411yescharacteristic
413C2×C11#326011yescharacteristic
414C2×C11#326311yescharacteristic
415D11—161no—
416C24—221no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8#434112yes—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—221no—
426C2×D4—221no—
427C2×D4—221no—
428C2×D4—221no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443SD16—444no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—112no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8#433912yes—
456C4⋊C4—24no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—81no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—881no—
470C4⋊C4—881no—
471C4⋊C4—881no—
472C4⋊C4—881no—
473C4⋊C4#434112yes—
474C22⋊C4—881no—
475C22⋊C4—881no—
476C22⋊C4—881no—
477C22⋊C4—881no—
478C22⋊C4—881no—
479C22⋊C4—881no—
480C42—24no—
481C42—21no—
482C42—21no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—881no—
488C11#2944211yescharacteristic, complemented, Sylow
489C23—441no—
490C23—441no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23C2×D4×D1111yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501D4—441no—
502D4—441no—
503D4—441no—
504D4—441no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4C2×#433911yescharacteristic
545C2×C4C2×#434111yescharacteristic
546C2×C4C2×#434111yescharacteristic
547C2×C4#6704011yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#6704211yescharacteristic
550C8—22no—
551C8—41no—
552C8—222no—
553C8—441no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22—881no—
558C22—881no—
559C22—881no—
560C22—881no—
561C22#1062307911yescharacteristic
562C22#1062311711yescharacteristic
563C22#1062316011yescharacteristic
564C22#1062329311yescharacteristic
565C22#1062330111yescharacteristic
566C22#1062330911yescharacteristic
567C22#1062330911yescharacteristic
568C4—42no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—441no—
575C4—441no—
576C4—441no—
577C4—441no—
578C4—881no—
579C4—881no—
580C4—881no—
581C4#1062304411yescharacteristic
582C4#1062309611yescharacteristic
583C4#1062317211yescharacteristic
584C4#1062318911yescharacteristic
585C2—1761no—
586C2#1307421711yescharacteristic
587C2#1307888611yescharacteristic
588C2#1307890111yescharacteristic
589C2#1307923611yescharacteristic
590C2#1307924011yescharacteristic
591C2#1308006111yescharacteristic
592C2#1308008511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1865D11
hypocenterC11#29442
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
2. #13071267C2semidirect
3. #13070120C2semidirect
4. #13069995C2semidirect
8. #13069345C2semidirect
10. #13069308C2semidirect
12. #13069198C2semidirect
14. #13068472C2semidirect
15. C11×#1865C2semidirect
206. #1865D11semidirect
488. C11#29442semidirect

Maximal subgroups

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

subgroupindex
#130745792
#130712672
#130701202
#130699952
#130699852
#130699302
#130694672
#130693452
#130693142
#130693082
#130692442
#130691982
#130689712
#130684722
C11×#18652
#2944211