Finite Group Databasebeta

← #14722227

Subgroups — #14722227

Order 2816.

964 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082432C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic
3#13077181C211yesmaximal, characteristic
4#13067304C211yesmaximal, characteristic, complemented
5#13067303C212yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067295C212yesmaximal, complemented
8#13067274C211yesmaximal, characteristic, complemented
9#13067270C212yesmaximal, complemented
10D11×#333C212yesmaximal, complemented
11C2×C11×#333C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13Q8×C22⋊D11C414yes—
14C2×#66954—21no—
15#10623261—21no—
16#10623260—22no—
17#10623259C2212yes—
18#10623258C412yes—
19D11×C4⋊Q8C2212yes—
20#10623253—21no—
21#10623252C412yes—
22#10623042—22no—
23#10623035—21no—
24#10623031—21no—
25C4×#4339C2211yescharacteristic
26#10623001C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C8×C22⋊D11—22no—
30#10622715—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622452—22no—
34#10622450C2212yes—
35#10622447—21no—
36#10622446C2212yes—
37D11×C4⋊C8C2212yes—
38D11×C4⋊C8C2212yes—
39#10622443—21no—
40C11×#333C2212yes—
41C11×#333C2212yes—
42#10622184C2212yes—
43#10622184C2212yes—
44#10622124C2211yescharacteristic
45#10622124C2211yescharacteristic
46#10622120C2212yes—
47#10622119C2211yescharacteristic
48#10622119C2212yes—
49#10622119C2211yescharacteristic
50C22×Q8×C11C2×C412yes—
51C2×Q8×D11C2×C414yes—
52C2×#4339D411yescharacteristic
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2×C412yes—
58C11×C4⋊Q8C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62#66999—24no—
63#66999C2×C414yes—
64Q8×Dic11C2×C414yes—
65#66997—24no—
66#66997C2×C414yes—
67C4×C22⋊D11—24no—
68C4×C22⋊D11C2×C412yes—
69C4×C22⋊D11D412yes—
70#66979—21no—
71#66979D411yescharacteristic
72#66977—21no—
73#66977—24no—
74#66977C2×C412yes—
75C2×#4318—21no—
76#66954—44no—
77C2×#4313—22no—
78C2×C8×D11—22no—
79C2×C8×D11—22no—
80#66950—22no—
81#66949—24no—
82#66946—22no—
83#66945—22no—
84C4⋊C4×D11—22no—
85C4⋊C4×D11—22no—
86#66943—22no—
87#66943—22no—
88#66942—24no—
89#66941—22no—
90#66941—22no—
91#66941—22no—
92#66940—22no—
93#66940—22no—
94C4×D44C2×C411yescharacteristic
95C4×D44D411yescharacteristic
96#66925D412yes—
97C42×D11C2312yes—
98#66923—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22C2×C412yes—
103C4×Dic22C2×C411yescharacteristic
104C4×Dic22D411yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2312yes—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C22⋊(C11⋊C8)—21no—
111(C2×D11)⋊C8—22no—
112Dic11⋊C8—22no—
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115C8×Dic11—22no—
116C4⋊(C11⋊C8)—21no—
117C4⋊(C11⋊C8)C2312yes—
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4⋊(C11⋊C8)C2311yescharacteristic
120C4×C11⋊C8—21no—
121#17722—111nomaximal, Sylow
122C2×Q8×C11—22no—
123C2×Q8×C11—82no—
124C2×Q8×C11C22×C414yes—
125C22×C4×C11—22no—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11C22⋊C412yes—
130Q8×D11—84no—
131#4339SD1614yes—
132#4339Q1614yes—
133C2×D44C22⋊C411yescharacteristic
134C2×C4×D11—24no—
135C2×C4×D11C22×C412yes—
136C2×C4×D11C2×D412yes—
137C2×C4×D11C2×D412yes—
138C2×Dic22—24no—
139C2×Dic22—21no—
140C2×Dic22C22⋊C411yescharacteristic
141C2×Dic22C22×C412yes—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—42no—
146C2×C8×C11—81no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C42×C11C22×C411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2411yescharacteristic
155C22⋊Dic11—22no—
156C22⋊Dic11C22⋊C412yes—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4C22⋊C412yes—
159(C2×D11)⋊C4C22⋊C412yes—
160C4⋊Dic11—24no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11C22⋊C411yescharacteristic
165C4⋊Dic11C22⋊C411yescharacteristic
166C4⋊Dic11C22×C412yes—
167Dic11⋊C4—24no—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—22no—
171Dic11⋊C4—22no—
172Dic11⋊C4C22⋊C412yes—
173Dic11⋊C4C22⋊C412yes—
174C4×Dic11—24no—
175C4×Dic11—22no—
176C4×Dic11C22×C412yes—
177C4×Dic11C2×D412yes—
178C4×Dic11C2×D412yes—
179#4318—42no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183#4313—44no—
184C8×D11—44no—
185C8×D11—82no—
186#3503—111no—
187#2988—111no—
188#2906—111no—
189#1550—111no—
190#1550—112no—
191#1548—112no—
192#1548—111no—
193#1542—111no—
194#1542—112no—
195C2×#333—112no—
196C2×#333D1111yescharacteristic, complemented
197C23×C11C2×C22⋊C411yescharacteristic
198C22×D11C2×C22⋊C412yes—
199Q8×C11—44no—
200Q8×C11—82no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—24no—
204C2×C4×C11—41no—
205C2×C4×C11—82no—
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×SD1612yes—
210C2×C4×C11C2×Q1612yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11#10318yes—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11C2×C22⋊C412yes—
218C2×Dic11C2×C22⋊C412yes—
219C2×Dic11C2×C22⋊C412yes—
220D44#10314yes—
221C4×D11—22no—
222C4×D11—22no—
223C4×D11—42no—
224C4×D11—84no—
225C4×D11C2×SD1614yes—
226C4×D11C2×Q1614yes—
227Dic22—41no—
228Dic22—41no—
229Dic22—42no—
230Dic22—84no—
231Dic22#10314yes—
232C8×C11—41no—
233C8×C11—41no—
234C8×C11—42no—
235C11⋊C8—42no—
236C11⋊C8—41no—
237C11⋊C8—41no—
238C2×#131—221no—
239Q82—221no—
240#557—112no—
241#554—222no—
242#554—221no—
243D4×Q8—114no—
244D4×Q8—112no—
245#544—221no—
246#544—222no—
247#533—112no—
248#533—111no—
249C2×C4⋊Q8—112no—
250C2×C4⋊Q8C2×D1111yescharacteristic
251#520—221no—
252C4×#41—111no—
253C8×Q8—221no—
254C8×D4—221no—
255C8×D4—222no—
256#431—111no—
257#431—112no—
258#424—222no—
259#424—221no—
260#423—111no—
261#423—112no—
262C2×C4⋊C8—112no—
263C2×C4⋊C8—112no—
264C2×C4⋊C8C2×D1111yescharacteristic
265C2×C4⋊C8C2×D1111yescharacteristic
266#333—112no—
267#333—112no—
268#333—111no—
269#333—112no—
270#333—111no—
271#333C2×D1112yes—
272#333C2×D1112yes—
273#332—111no—
274#332—112no—
275#332—111no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11C2×#10312yes—
279C22×C11C22×C22⋊C411yescharacteristic
280C2×D11—22no—
281C2×D11—22no—
282C2×D11C2×#10314yes—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—44no—
287C4×C11C2×#10312yes—
288C4×C11C22×SD1611yescharacteristic
289C4×C11C22×Q1611yescharacteristic
290C4×C11#57711yescharacteristic
291C4×C11#57811yescharacteristic
292Dic11—22no—
293Dic11—22no—
294Dic11—42no—
295Dic11—42no—
296Dic11C2×#10314yes—
297C2×#41—111no—
298C22×Q8—114no—
299C22×Q8C4×D1112yes—
300#131—444no—
301C2×M16—222no—
302C2×M16—221no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—222no—
306C22×C8—222no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—114no—
310C4⋊Q8—111no—
311C4⋊Q8—111no—
312C4⋊Q8—222no—
313C4⋊Q8—222no—
314C4⋊Q8—222no—
315C4⋊Q8—224no—
316C4⋊Q8C4×D1112yes—
317C4⋊Q8C22×D1112yes—
318#125—222no—
319#125—224no—
320#125—222no—
321#125—221no—
322C22⋊Q8—114no—
323C22⋊Q8—112no—
324C22⋊Q8—224no—
325C22⋊Q8—224no—
326C22⋊Q8—224no—
327C22⋊Q8—222no—
328C22⋊Q8—221no—
329C4×Q8—111no—
330C4×Q8—111no—
331C4×Q8—114no—
332C4×Q8—112no—
333C4×Q8—222no—
334C4×Q8—222no—
335C4×Q8—221no—
336C4×D4—112no—
337C4×D4—112no—
338C4×D4—111no—
339C4×D4—111no—
340C4×D4—222no—
341C4×D4—224no—
342#117—111no—
343#117—112no—
344#117—222no—
345#117—221no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C42—112no—
351C2×C42C22×D1111yescharacteristic
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—111no—
355C4⋊C8—112no—
356C4⋊C8—111no—
357C4⋊C8—222no—
358C4⋊C8—222no—
359C4⋊C8—222no—
360C4⋊C8—221no—
361C4⋊C8C22×D1111yescharacteristic
362C4⋊C8C22×D1112yes—
363C4⋊C8C22×D1111yescharacteristic
364C22⋊C8—222no—
365C22⋊C8—221no—
366C4×C8—222no—
367C4×C8—221no—
368C2×C11—22no—
369C2×C11#288811yescharacteristic
370C2×C11C22×#10311yescharacteristic
371C2×C11#289811yescharacteristic
372D11—24no—
373#41—114no—
374#41—114no—
375C2×Q8—22no—
376C2×Q8—82no—
377C2×Q8—111no—
378C2×Q8—112no—
379C2×Q8—224no—
380C2×Q8—221no—
381C2×Q8—884no—
382C2×Q8C2×C4×D1114yes—
383C2×D4—112no—
384C2×D4—111no—
385C22×C4—22no—
386C22×C4—112no—
387C22×C4—112no—
388C22×C4—112no—
389C22×C4—224no—
390C22×C4C2×C4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4D4×D1111yescharacteristic
393M16—444no—
394M16—442no—
395C2×C8—22no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—42no—
399C2×C8—81no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—222no—
403C2×C8—444no—
404C2×C8—882no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—112no—
410C4⋊C4—111no—
411C4⋊C4—112no—
412C4⋊C4—111no—
413C4⋊C4—112no—
414C4⋊C4—224no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4—224no—
418C4⋊C4—222no—
419C4⋊C4—222no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C22⋊C4—112no—
424C22⋊C4—112no—
425C22⋊C4—112no—
426C22⋊C4—224no—
427C22⋊C4—222no—
428C42—112no—
429C42—112no—
430C42—112no—
431C42—224no—
432C42—222no—
433C42C2×C4×D1111yescharacteristic
434C42D4×D1111yescharacteristic
435C42D4×D1111yescharacteristic
436C42C23×D1111yescharacteristic
437C11#1772211yescharacteristic, complemented, Sylow
438C23—112no—
439C23C22⋊C4×D1111yescharacteristic
440Q8—44no—
441Q8—82no—
442Q8—114no—
443Q8—442no—
444Q8—441no—
445Q8—441no—
446Q8—884no—
447D4—118no—
448D4—114no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—24no—
452C2×C4—41no—
453C2×C4—82no—
454C2×C4—112no—
455C2×C4—114no—
456C2×C4—114no—
457C2×C4—112no—
458C2×C4—112no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—442no—
464C2×C4—884no—
465C2×C4C22⋊C4×D1111yescharacteristic
466C2×C4C22⋊C4×D1111yescharacteristic
467C2×C4C22⋊C4×D1111yescharacteristic
468C2×C4SD16×D1112yes—
469C2×C4Q16×D1112yes—
470C2×C4C22×C4×D1111yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C8—41no—
474C8—41no—
475C8—42no—
476C8—442no—
477C8—441no—
478C8—441no—
479C22—21no—
480C22—21no—
481C22—114no—
482C22—222no—
483C22—222no—
484C22D11×#10312yes—
485C22C2×C22⋊C4×D1111yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—44no—
490C4—114no—
491C4—222no—
492C4—222no—
493C4—442no—
494C4—442no—
495C4D11×#10312yes—
496C4C2×SD16×D1111yescharacteristic
497C4#1062329311yescharacteristic
498C4C2×Q16×D1111yescharacteristic
499C4#1062329711yescharacteristic
500C2—22no—
501C2—224no—
502C2#1307709211yescharacteristic
503C2C2×D11×#10311yescharacteristic
504C2#1307714411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×#333C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#4339D4
cosocleC42×C11C24
hypercenterC2×#333D11
hypocenterC11#17722
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
4. #13067304C2semidirect
5. #13067303C2semidirect
6. #13067297C2semidirect
7. #13067295C2semidirect
8. #13067274C2semidirect
9. #13067270C2semidirect
10. D11×#333C2semidirect
11. C2×C11×#333C2semidirect
196. C2×#333D11semidirect
437. C11#17722semidirect

Maximal subgroups

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

subgroupindex
#130824322
#130777252
#130771812
#130673042
#130673032
#130672972
#130672952
#130672742
#130672702
D11×#3332
C2×C11×#3332
#1772211