Finite Group Databasebeta

← #14722988

Subgroups — #14722988

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077733C211yesmaximal, characteristic
2#13077260C211yesmaximal, characteristic
3#13067407C211yesmaximal, characteristic, complemented
4#13067404C211yesmaximal, characteristic, complemented
5#13067402C211yesmaximal, characteristic, complemented
6#13067399C211yesmaximal, characteristic, complemented
7#13067397C211yesmaximal, characteristic, complemented
8#13067394C211yesmaximal, characteristic, complemented
9#13067392C211yesmaximal, characteristic, complemented
10#13067390C211yesmaximal, characteristic, complemented
11#13067384C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic, complemented
13#13067377C211yesmaximal, characteristic, complemented
14#13067374C211yesmaximal, characteristic, complemented
15C11×#2989C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17C11×#446—21no—
18C11×#436—21no—
19C11×#435—21no—
20C11×#435—21no—
21C11×#432C2211yescharacteristic
22C11×#432C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C11×#423C2211yescharacteristic
25C11×#423C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27#10622847C412yes—
28#10622637—21no—
29#10622625—21no—
30#10622624—21no—
31#10622624—21no—
32#10622613C412yes—
33#10622613C412yes—
34#10622612C412yes—
35#10622539C2211yescharacteristic
36#10622539C2211yescharacteristic
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622538C2211yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622537C2211yescharacteristic
43#10622537C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C4×#4318C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622118C2211yescharacteristic
48#10622118C2211yescharacteristic
49#10622118C2211yescharacteristic
50#10622118C2211yescharacteristic
51#10622118C2211yescharacteristic
52#10622118C2211yescharacteristic
53#10622117C2211yescharacteristic
54#10622117C2211yescharacteristic
55#10622117C2211yescharacteristic
56#10622117C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63C2×C11×#41C2×C411yescharacteristic
64C2×C11×M16—21no—
65C2×C11×M16—21no—
66C22×C8×C11—21no—
67C4×Q8×C11D411yescharacteristic
68C4×Q8×C11Q811yescharacteristic
69C4×D4×C11D411yescharacteristic
70C4×D4×C11D411yescharacteristic
71C4×D4×C11D411yescharacteristic
72C4×D4×C11Q811yescharacteristic
73C4×D4×C11Q811yescharacteristic
74C4×D4×C11Q811yescharacteristic
75C11×#117C2×C411yescharacteristic
76C11×#117C2×C411yescharacteristic
77C11×#117C2×C411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318C2×C412yes—
84C22×C11⋊C8—21no—
85C22×C11⋊C8C2×C412yes—
86C11×C4⋊C8—21no—
87C11×C4⋊C8—21no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8C2311yescharacteristic
90C11×C4⋊C8C2311yescharacteristic
91C11×C4⋊C8C2311yescharacteristic
92C11×C4⋊C8C2311yescharacteristic
93C11×C22⋊C8—21no—
94C11×C22⋊C8—21no—
95C11×C22⋊C8—21no—
96C11×#97—21no—
97C11×#97—21no—
98C4×C8×C11—21no—
99C22⋊(C11⋊C8)—21no—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)—21no—
102C22⋊(C11⋊C8)C2×C412yes—
103C22⋊(C11⋊C8)C2×C412yes—
104C22⋊(C11⋊C8)C2×C412yes—
105C22⋊(C11⋊C8)C2×C412yes—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)—21no—
109C4⋊(C11⋊C8)C2×C412yes—
110C4⋊(C11⋊C8)C2×C412yes—
111C4⋊(C11⋊C8)C2×C412yes—
112C4⋊(C11⋊C8)C2×C412yes—
113C4⋊(C11⋊C8)C2311yescharacteristic
114C4⋊(C11⋊C8)C2311yescharacteristic
115C4⋊(C11⋊C8)C2311yescharacteristic
116C4⋊(C11⋊C8)C2311yescharacteristic
117#66867—21no—
118#66867—21no—
119#66867C2×C412yes—
120C4×C11⋊C8—21no—
121C4×C11⋊C8C2×C412yes—
122C4×C11⋊C8C2311yescharacteristic
123C4×C11⋊C8C2311yescharacteristic
124C4×C11⋊C8C2311yescharacteristic
125C4×C11⋊C8C2311yescharacteristic
126#17825—111nomaximal, Sylow
127C11×#41—42no—
128C2×Q8×C11C4⋊C411yescharacteristic
129C2×D4×C11C4⋊C411yescharacteristic
130C2×D4×C11C4⋊C411yescharacteristic
131C2×D4×C11C4⋊C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×Q811yescharacteristic
139C22×C4×C11C2×Q811yescharacteristic
140C22×C4×C11C2×Q811yescharacteristic
141C11×M16—81no—
142C11×M16—81no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—81no—
148C11×C4⋊C4C4⋊C411yescharacteristic
149C11×C4⋊C4C4⋊C411yescharacteristic
150C11×C4⋊C4C4⋊C411yescharacteristic
151C11×C4⋊C4C4⋊C411yescharacteristic
152C11×C4⋊C4C4⋊C411yescharacteristic
153C11×C4⋊C4C4⋊C411yescharacteristic
154C11×C22⋊C4C4⋊C411yescharacteristic
155C11×C22⋊C4C4⋊C411yescharacteristic
156C11×C22⋊C4C4⋊C411yescharacteristic
157C11×C22⋊C4C4⋊C411yescharacteristic
158C11×C22⋊C4C4⋊C411yescharacteristic
159C11×C22⋊C4C4⋊C411yescharacteristic
160C42×C11C22×C411yescharacteristic
161C42×C11C22×C411yescharacteristic
162C42×C11C22×C411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2×Q811yescharacteristic
167C42×C11C2×Q811yescharacteristic
168C42×C11C2×Q811yescharacteristic
169C42×C11C2411yescharacteristic
170#4318—42no—
171#4318—81no—
172#4318—81no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—42no—
178C2×C11⋊C8—81no—
179C2×C11⋊C8C22×C412yes—
180C2×C11⋊C8C22×C412yes—
181C2×C11⋊C8C22×C412yes—
182C2×C11⋊C8C22×C412yes—
183#2989—111no—
184#2989D1111yescharacteristic
185#2922—111no—
186#1574—111no—
187#1574—111no—
188#1573—111no—
189#1573—111no—
190#1572—111no—
191#1572—111no—
192#1571—111no—
193#1571—111no—
194#1569—111no—
195#1569—111no—
196#1568—111no—
197#1567—111no—
198C23×C11C2×C4⋊C411yescharacteristic
199C23×C11C2×C4⋊C411yescharacteristic
200C23×C11C2×C4⋊C411yescharacteristic
201Q8×C11—41no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—41no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11C2×C4⋊C411yescharacteristic
218C2×C4×C11C2×C4⋊C411yescharacteristic
219C2×C4×C11C2×C4⋊C411yescharacteristic
220C2×C4×C11C2×C4⋊C411yescharacteristic
221C2×C4×C11C2×C4⋊C411yescharacteristic
222C2×C4×C11C2×C4⋊C411yescharacteristic
223C2×C4×C11C2×C4⋊C411yescharacteristic
224C2×C4×C11C2×C4⋊C411yescharacteristic
225C2×C4×C11C2×C4⋊C411yescharacteristic
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×Q811yescharacteristic
229C8×C11—41no—
230C8×C11—41no—
231C8×C11—41no—
232C8×C11—41no—
233C11⋊C8—22no—
234C11⋊C8—22no—
235C11⋊C8—22no—
236C11⋊C8—22no—
237C11⋊C8—41no—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C11⋊C8—41no—
241C4×#41C2×D1111yescharacteristic
242#446—21no—
243#446—221no—
244#436—21no—
245#436—221no—
246#435—21no—
247#435—21no—
248#435—221no—
249#435—221no—
250#433—112no—
251#433—112no—
252#432—111no—
253#432—111no—
254#432C2×D1111yescharacteristic
255#432C2×D1111yescharacteristic
256#431—111no—
257#431—111no—
258#431—111no—
259#431—111no—
260#431—111no—
261#431C2×D1111yescharacteristic
262#424—112no—
263#423—111no—
264#423—111no—
265#423C2×D1111yescharacteristic
266#423C2×D1111yescharacteristic
267C2×C4⋊C8—111no—
268C2×C4⋊C8C2×D1111yescharacteristic
269#408—112no—
270C4×M16—111no—
271C2×C4×C8—111no—
272#335—111no—
273#335—111no—
274#335—111no—
275#335—111no—
276#335—111no—
277#335—111no—
278#335—111no—
279#335—111no—
280#335—111no—
281#335—111no—
282#334—111no—
283#334—111no—
284#334—111no—
285#334—111no—
286#334—111no—
287#334—111no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11C22×C4⋊C411yescharacteristic
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11#56812yes—
309C4×C11#57611yescharacteristic
310C4×C11#57811yescharacteristic
311C2×#41C4×D1111yescharacteristic
312C2×M16—21no—
313C2×M16—21no—
314C2×M16—112no—
315C2×M16—221no—
316C2×M16—221no—
317C22×C8—21no—
318C22×C8—112no—
319C22×C8—221no—
320C4×Q8Dic2211yescharacteristic
321C4×Q8C22⋊D1111yescharacteristic
322C4×D4Dic2211yescharacteristic
323C4×D4Dic2211yescharacteristic
324C4×D4Dic2211yescharacteristic
325C4×D4C22⋊D1111yescharacteristic
326C4×D4C22⋊D1111yescharacteristic
327C4×D4C22⋊D1111yescharacteristic
328#117C4×D1111yescharacteristic
329#117C4×D1111yescharacteristic
330#117C4×D1111yescharacteristic
331C2×C42C22×D1111yescharacteristic
332C2×C42C22×D1111yescharacteristic
333C2×C42C22×D1111yescharacteristic
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337C4⋊C8—112no—
338C4⋊C8—112no—
339C4⋊C8—112no—
340C4⋊C8—112no—
341C4⋊C8—111no—
342C4⋊C8—111no—
343C4⋊C8—111no—
344C4⋊C8—111no—
345C4⋊C8—221no—
346C4⋊C8—221no—
347C4⋊C8—221no—
348C4⋊C8C22×D1111yescharacteristic
349C4⋊C8C22×D1111yescharacteristic
350C4⋊C8C22×D1111yescharacteristic
351C4⋊C8C22×D1111yescharacteristic
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—112no—
356C22⋊C8—112no—
357C22⋊C8—112no—
358C22⋊C8—112no—
359C22⋊C8—221no—
360C22⋊C8—221no—
361C22⋊C8—221no—
362#97—21no—
363#97—21no—
364#97—112no—
365#97—221no—
366#97—221no—
367C4×C8—21no—
368C4×C8—112no—
369C4×C8—111no—
370C4×C8—111no—
371C4×C8—111no—
372C4×C8—111no—
373C4×C8—221no—
374C2×C11—41no—
375C2×C11—41no—
376C2×C11—41no—
377C2×C11#290511yescharacteristic
378C2×C11#291311yescharacteristic
379C2×C11#291611yescharacteristic
380#41—42no—
381C2×Q8Dic11⋊C411yescharacteristic
382C2×D4Dic11⋊C411yescharacteristic
383C2×D4Dic11⋊C411yescharacteristic
384C2×D4Dic11⋊C411yescharacteristic
385C22×C4C2×Dic2211yescharacteristic
386C22×C4C2×Dic2211yescharacteristic
387C22×C4C2×Dic2211yescharacteristic
388C22×C4C2×C4×D1111yescharacteristic
389C22×C4C2×C4×D1111yescharacteristic
390C22×C4C2×C4×D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394M16—81no—
395M16—81no—
396M16—442no—
397M16—881no—
398M16—881no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—81no—
404C2×C8—112no—
405C2×C8—112no—
406C2×C8—112no—
407C2×C8—112no—
408C2×C8—221no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—442no—
413C2×C8—881no—
414C4⋊C4Dic11⋊C411yescharacteristic
415C4⋊C4Dic11⋊C411yescharacteristic
416C4⋊C4Dic11⋊C411yescharacteristic
417C4⋊C4Dic11⋊C411yescharacteristic
418C4⋊C4Dic11⋊C411yescharacteristic
419C4⋊C4Dic11⋊C411yescharacteristic
420C22⋊C4Dic11⋊C411yescharacteristic
421C22⋊C4Dic11⋊C411yescharacteristic
422C22⋊C4Dic11⋊C411yescharacteristic
423C22⋊C4Dic11⋊C411yescharacteristic
424C22⋊C4Dic11⋊C411yescharacteristic
425C22⋊C4Dic11⋊C411yescharacteristic
426C42C2×Dic2211yescharacteristic
427C42C2×Dic2211yescharacteristic
428C42C2×Dic2211yescharacteristic
429C42C2×C4×D1111yescharacteristic
430C42C2×C4×D1111yescharacteristic
431C42C2×C4×D1111yescharacteristic
432C42C2×C22⋊D1111yescharacteristic
433C42C2×C22⋊D1111yescharacteristic
434C42C2×C22⋊D1111yescharacteristic
435C42C23×D1111yescharacteristic
436C11#1782511yescharacteristic, complemented, Sylow
437C23C2×Dic11⋊C411yescharacteristic
438C23C2×Dic11⋊C411yescharacteristic
439C23C2×Dic11⋊C411yescharacteristic
440Q8—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4C2×Dic11⋊C411yescharacteristic
457C2×C4C2×Dic11⋊C411yescharacteristic
458C2×C4C2×Dic11⋊C411yescharacteristic
459C2×C4C2×Dic11⋊C411yescharacteristic
460C2×C4C2×Dic11⋊C411yescharacteristic
461C2×C4C2×Dic11⋊C411yescharacteristic
462C2×C4C2×Dic11⋊C411yescharacteristic
463C2×C4C2×Dic11⋊C411yescharacteristic
464C2×C4C2×Dic11⋊C411yescharacteristic
465C2×C4C22×Dic2211yescharacteristic
466C2×C4C22×C4×D1111yescharacteristic
467C2×C4C22×C22⋊D1111yescharacteristic
468C8—41no—
469C8—41no—
470C8—41no—
471C8—41no—
472C8—222no—
473C8—222no—
474C8—222no—
475C8—222no—
476C8—441no—
477C8—441no—
478C8—441no—
479C8—441no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22C22×Dic11⋊C411yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4#1062327612yes—
501C4#1062336611yescharacteristic
502C4#1062336911yescharacteristic
503C2—41no—
504C2—41no—
505C2—41no—
506C2#1307717911yescharacteristic
507C2#1307721411yescharacteristic
508C2#1307722511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2989C2
socleC22×C11C22×C4⋊C4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#2989D11
hypocenterC11#17825
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
3. #13067407C2semidirect
4. #13067404C2semidirect
5. #13067402C2semidirect
6. #13067399C2semidirect
7. #13067397C2semidirect
8. #13067394C2semidirect
9. #13067392C2semidirect
10. #13067390C2semidirect
11. #13067384C2semidirect
12. #13067381C2semidirect
13. #13067377C2semidirect
14. #13067374C2semidirect
436. C11#17825semidirect

Maximal subgroups

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

subgroupindex
#130777332
#130772602
#130674072
#130674042
#130674022
#130673992
#130673972
#130673942
#130673922
#130673902
#130673842
#130673812
#130673772
#130673742
C11×#29892
#1782511