Finite Group Databasebeta

← #14722993

Subgroups — #14722993

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#13077730C211yesmaximal, characteristic
2#13077729C211yesmaximal, characteristic
3#13077255C211yesmaximal, characteristic
4#13067406C211yesmaximal, characteristic, complemented
5#13067401C211yesmaximal, characteristic, complemented
6#13067398C211yesmaximal, characteristic, complemented
7#13067394C211yesmaximal, characteristic, complemented
8#13067393C211yesmaximal, characteristic, complemented
9#13067392C211yesmaximal, characteristic, complemented
10#13067389C211yesmaximal, characteristic, complemented
11#13067382C211yesmaximal, characteristic, complemented
12#13067380C211yesmaximal, characteristic, complemented
13#13067376C211yesmaximal, characteristic, complemented
14#13067373C211yesmaximal, characteristic, complemented
15C11×#1574C211yesmaximal, characteristic, complemented
16C4×#4339C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#423C2211yescharacteristic
20#10622741—21no—
21#10622740—21no—
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622453C412yes—
26#10622452C412yes—
27#10622450C2211yescharacteristic
28#10622450C2211yescharacteristic
29#10622450C2211yescharacteristic
30#10622449—21no—
31#10622448C2211yescharacteristic
32#10622448C2211yescharacteristic
33#10622448C2211yescharacteristic
34#10622446C2211yescharacteristic
35D11×C4⋊C8C2211yescharacteristic
36#10622441—21no—
37#10622343—21no—
38#10622343—21no—
39#10622340C412yes—
40#10622333C412yes—
41#10622301—21no—
42C4×#4313C2211yescharacteristic
43#10622298C2211yescharacteristic
44#10622298C2211yescharacteristic
45C4×C8×D11C2211yescharacteristic
46#10622292—21no—
47C11×#335C2211yescharacteristic
48C11×#335C2211yescharacteristic
49C11×#334C2211yescharacteristic
50C11×#334C2211yescharacteristic
51#10622118C2211yescharacteristic
52#10622118C2211yescharacteristic
53#10622117C2211yescharacteristic
54#10622117C2211yescharacteristic
55#10622117C2211yescharacteristic
56#10622117C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622096C2211yescharacteristic
60#10622096C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622095C2211yescharacteristic
63C2×#4339C2×C411yescharacteristic
64C2×C11×M16—21no—
65C2×C42×C11C2311yescharacteristic
66C4×C22⋊D11D411yescharacteristic
67C4×C22⋊D11D411yescharacteristic
68C4×C22⋊D11Q811yescharacteristic
69C4×C22⋊D11Q811yescharacteristic
70#66979C2×C411yescharacteristic
71C22×C11⋊C8—21no—
72C2×#4313—21no—
73C2×#4313—21no—
74C2×#4313—21no—
75C2×#4313C2×C412yes—
76C2×C8×D11—21no—
77C2×C8×D11C2×C412yes—
78C4×D44D411yescharacteristic
79C4×D44Q811yescharacteristic
80#66925C2×C411yescharacteristic
81#66925C2×C411yescharacteristic
82C42×D11C2311yescharacteristic
83C42×D11C2311yescharacteristic
84C4×Dic22D411yescharacteristic
85C4×Dic22Q811yescharacteristic
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2×C412yes—
88C11×C4⋊C8C2311yescharacteristic
89C11×C4⋊C8C2311yescharacteristic
90C11×C4⋊C8C2311yescharacteristic
91C11×C4⋊C8C2311yescharacteristic
92C11×C22⋊C8—21no—
93C11×C22⋊C8C2×C412yes—
94C4×C8×C11—21no—
95C4×C8×C11C2311yescharacteristic
96C4×C8×C11C2311yescharacteristic
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)C2×C412yes—
99(C2×D11)⋊C8—21no—
100(C2×D11)⋊C8—21no—
101(C2×D11)⋊C8—21no—
102(C2×D11)⋊C8—21no—
103(C2×D11)⋊C8C2×C412yes—
104(C2×D11)⋊C8C2×C412yes—
105#66879—21no—
106#66879—21no—
107#66879—21no—
108#66879C2×C412yes—
109Dic11⋊C8—21no—
110Dic11⋊C8—21no—
111Dic11⋊C8—21no—
112Dic11⋊C8—21no—
113Dic11⋊C8C2×C412yes—
114Dic11⋊C8C2×C412yes—
115C8×Dic11—21no—
116C8×Dic11C2×C412yes—
117C4⋊(C11⋊C8)—21no—
118C4⋊(C11⋊C8)C2×C412yes—
119C4⋊(C11⋊C8)C2311yescharacteristic
120C4⋊(C11⋊C8)C2311yescharacteristic
121C4⋊(C11⋊C8)C2311yescharacteristic
122C4⋊(C11⋊C8)C2311yescharacteristic
123#66867—21no—
124C4×C11⋊C8C2311yescharacteristic
125C4×C11⋊C8C2311yescharacteristic
126#17825—111nomaximal, Sylow
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×Q811yescharacteristic
130C2×C22⋊D11C4⋊C411yescharacteristic
131C2×C22⋊D11C4⋊C411yescharacteristic
132#4339—42no—
133C2×D44C4⋊C411yescharacteristic
134C2×C4×D11C22×C411yescharacteristic
135C2×C4×D11C22×C411yescharacteristic
136C2×C4×D11C2×D411yescharacteristic
137C2×C4×D11C2×D411yescharacteristic
138C2×C4×D11C2×Q811yescharacteristic
139C2×C4×D11C2×Q811yescharacteristic
140C2×Dic22C4⋊C411yescharacteristic
141C11×M16—81no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C22×C412yes—
147C2×C8×C11C22×C412yes—
148C42×C11C22×C411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11C2×Q811yescharacteristic
151C42×C11C2411yescharacteristic
152C22⋊Dic11C4⋊C411yescharacteristic
153C22⋊Dic11C4⋊C411yescharacteristic
154(C2×D11)⋊C4C4⋊C411yescharacteristic
155(C2×D11)⋊C4C4⋊C411yescharacteristic
156(C2×D11)⋊C4C4⋊C411yescharacteristic
157(C2×D11)⋊C4C4⋊C411yescharacteristic
158C4⋊Dic11C4⋊C411yescharacteristic
159C4⋊Dic11C4⋊C411yescharacteristic
160Dic11⋊C4C4⋊C411yescharacteristic
161Dic11⋊C4C4⋊C411yescharacteristic
162Dic11⋊C4C4⋊C411yescharacteristic
163Dic11⋊C4C4⋊C411yescharacteristic
164C4×Dic11C22×C411yescharacteristic
165C4×Dic11C22×C411yescharacteristic
166C4×Dic11C2×D411yescharacteristic
167C4×Dic11C2×D411yescharacteristic
168C4×Dic11C2×Q811yescharacteristic
169C4×Dic11C2×Q811yescharacteristic
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—81no—
175C2×C11⋊C8C22×C412yes—
176C2×C11⋊C8C22×C412yes—
177#4313—42no—
178#4313—81no—
179#4313—81no—
180#4313—81no—
181C8×D11—42no—
182C8×D11—81no—
183#2989—111no—
184#2989—111no—
185#2922—111no—
186#1574—111no—
187#1574D1111yescharacteristic, complemented
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
199C22×D11C2×C4⋊C411yescharacteristic
200C22×D11C2×C4⋊C411yescharacteristic
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—41no—
205C2×C4×C11C2×C4⋊C411yescharacteristic
206C2×C4×C11C2×C4⋊C411yescharacteristic
207C2×C4×C11C2×C4⋊C411yescharacteristic
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×Q811yescharacteristic
211C22⋊D11—41no—
212C22⋊D11—41no—
213C2×Dic11C2×C4⋊C411yescharacteristic
214C2×Dic11C2×C4⋊C411yescharacteristic
215C2×Dic11C2×C4⋊C411yescharacteristic
216C2×Dic11C2×C4⋊C411yescharacteristic
217C2×Dic11C2×C4⋊C411yescharacteristic
218C2×Dic11C2×C4⋊C411yescharacteristic
219D44—41no—
220C4×D11—22no—
221C4×D11—22no—
222C4×D11—21no—
223C4×D11—21no—
224C4×D11—21no—
225C4×D11—21no—
226C4×D11—41no—
227C4×D11—41no—
228Dic22—41no—
229C8×C11—22no—
230C8×C11—22no—
231C8×C11—41no—
232C8×C11—41no—
233C8×C11—41no—
234C8×C11—41no—
235C11⋊C8—22no—
236C11⋊C8—22no—
237C11⋊C8—41no—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C11⋊C8—41no—
241C4×#41—111no—
242#446—221no—
243#446—221no—
244#436—221no—
245#436—221no—
246#435—221no—
247#435—221no—
248#435—221no—
249#435—221no—
250#433—112no—
251#433—112no—
252#432—111no—
253#432—111no—
254#432—111no—
255#432—111no—
256#431—111no—
257#431—111no—
258#431—111no—
259#431—111no—
260#431C2×D1111yescharacteristic
261#431C2×D1111yescharacteristic
262#424—112no—
263#423—111no—
264#423—111no—
265#423—111no—
266#423C2×D1111yescharacteristic
267C2×C4⋊C8—111no—
268C2×C4⋊C8—111no—
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#335C2×D1111yescharacteristic
281#335C2×D1111yescharacteristic
282#334—111no—
283#334—111no—
284#334—111no—
285#334—111no—
286#334C2×D1111yescharacteristic
287#334C2×D1111yescharacteristic
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11C22×C4⋊C411yescharacteristic
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—21no—
296C2×D11—21no—
297C2×D11—21no—
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11#56812yes—
303C4×C11#57611yescharacteristic
304C4×C11#57811yescharacteristic
305Dic11—21no—
306Dic11—21no—
307Dic11—21no—
308Dic11—21no—
309Dic11—21no—
310Dic11—21no—
311C2×#41—111no—
312C2×M16—21no—
313C2×M16—112no—
314C2×M16—221no—
315C2×M16—221no—
316C2×M16—221no—
317C22×C8—112no—
318C22×C8—221no—
319C22×C8—221no—
320C4×Q8—111no—
321C4×Q8—111no—
322C4×D4—111no—
323C4×D4—111no—
324C4×D4—111no—
325C4×D4—111no—
326C4×D4—111no—
327C4×D4—111no—
328#117—111no—
329#117—111no—
330#117—111no—
331C2×C42—111no—
332C2×C42—111no—
333C2×C42C22×D1111yescharacteristic
334C4⋊C8—21no—
335C4⋊C8—112no—
336C4⋊C8—112no—
337C4⋊C8—112no—
338C4⋊C8—111no—
339C4⋊C8—111no—
340C4⋊C8—111no—
341C4⋊C8—111no—
342C4⋊C8—221no—
343C4⋊C8—221no—
344C4⋊C8—221no—
345C4⋊C8—221no—
346C4⋊C8—221no—
347C4⋊C8C4×D1112yes—
348C4⋊C8C22×D1111yescharacteristic
349C4⋊C8C22×D1111yescharacteristic
350C4⋊C8C22×D1111yescharacteristic
351C4⋊C8C22×D1111yescharacteristic
352C22⋊C8—21no—
353C22⋊C8—112no—
354C22⋊C8—112no—
355C22⋊C8—112no—
356C22⋊C8—221no—
357C22⋊C8—221no—
358C22⋊C8—221no—
359C22⋊C8—221no—
360C22⋊C8—221no—
361C22⋊C8C4×D1112yes—
362#97—112no—
363#97—221no—
364#97—221no—
365#97—221no—
366#97—221no—
367C4×C8—21no—
368C4×C8—112no—
369C4×C8—111no—
370C4×C8—111no—
371C4×C8—221no—
372C4×C8C22×D1111yescharacteristic
373C4×C8C22×D1111yescharacteristic
374C2×C11—41no—
375C2×C11#290511yescharacteristic
376C2×C11#291311yescharacteristic
377C2×C11#291611yescharacteristic
378D11—41no—
379D11—41no—
380#41—442no—
381C2×Q8—111no—
382C2×D4—111no—
383C2×D4—111no—
384C2×D4—111no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—111no—
390C22×C4—111no—
391C22×C4C2×C4×D1111yescharacteristic
392C22×C4D4×D1111yescharacteristic
393C22×C4Q8×D1111yescharacteristic
394M16—81no—
395M16—442no—
396M16—881no—
397M16—881no—
398M16—881no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—112no—
404C2×C8—112no—
405C2×C8—221no—
406C2×C8—221no—
407C2×C8—221no—
408C2×C8—221no—
409C2×C8—442no—
410C2×C8—881no—
411C2×C8—881no—
412C2×C8C2×C4×D1112yes—
413C2×C8C2×C4×D1112yes—
414C4⋊C4—111no—
415C4⋊C4—111no—
416C4⋊C4—111no—
417C4⋊C4—111no—
418C4⋊C4—111no—
419C4⋊C4—111no—
420C22⋊C4—111no—
421C22⋊C4—111no—
422C22⋊C4—111no—
423C22⋊C4—111no—
424C22⋊C4—111no—
425C22⋊C4—111no—
426C42—111no—
427C42—111no—
428C42—111no—
429C42—111no—
430C42—111no—
431C42—111no—
432C42C2×C4×D1111yescharacteristic
433C42D4×D1111yescharacteristic
434C42Q8×D1111yescharacteristic
435C42C23×D1111yescharacteristic
436C11#1782511yescharacteristic, complemented, Sylow
437C23—111no—
438C23—111no—
439C23C4⋊C4×D1111yescharacteristic
440Q8—441no—
441D4—441no—
442D4—441no—
443D4—441no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—41no—
448C2×C4—111no—
449C2×C4—111no—
450C2×C4—111no—
451C2×C4—111no—
452C2×C4—111no—
453C2×C4—111no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4C4⋊C4×D1111yescharacteristic
463C2×C4C4⋊C4×D1111yescharacteristic
464C2×C4C4⋊C4×D1111yescharacteristic
465C2×C4C22×C4×D1111yescharacteristic
466C2×C4C2×D4×D1111yescharacteristic
467C2×C4C2×Q8×D1111yescharacteristic
468C8—22no—
469C8—22no—
470C8—41no—
471C8—41no—
472C8—41no—
473C8—41no—
474C8—222no—
475C8—222no—
476C8—441no—
477C8—441no—
478C8—441no—
479C8—441no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—221no—
484C22—221no—
485C22—221no—
486C22—221no—
487C22—221no—
488C22—221no—
489C22C2×C4⋊C4×D1111yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—221no—
495C4—221no—
496C4—221no—
497C4—221no—
498C4—221no—
499C4—221no—
500C4#1062328112yes—
501C4#1062330511yescharacteristic
502C4#1062331011yescharacteristic
503C2—41no—
504C2—441no—
505C2—441no—
506C2#1307717711yescharacteristic
507C2#1307721511yescharacteristic
508C2#1307722411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1574C2
socleC22×C11C22×C4⋊C4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1574D11
hypocenterC11#17825
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
4. #13067406C2semidirect
5. #13067401C2semidirect
6. #13067398C2semidirect
7. #13067394C2semidirect
8. #13067393C2semidirect
9. #13067392C2semidirect
10. #13067389C2semidirect
11. #13067382C2semidirect
12. #13067380C2semidirect
13. #13067376C2semidirect
14. #13067373C2semidirect
15. C11×#1574C2semidirect
187. #1574D11semidirect
436. C11#17825semidirect

Maximal subgroups

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

subgroupindex
#130777302
#130777292
#130772552
#130674062
#130674012
#130673982
#130673942
#130673932
#130673922
#130673892
#130673822
#130673802
#130673762
#130673732
C11×#15742
#1782511