Finite Group Databasebeta

← #14761975

Subgroups — #14761975

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078959C211yesmaximal, characteristic
2#13077548C211yesmaximal, characteristic, complemented
3#13077326C211yesmaximal, characteristic
4#13069595C211yesmaximal, characteristic, complemented
5#13069446C211yesmaximal, characteristic
6#13069322C211yesmaximal, characteristic, complemented
7#13069321C211yesmaximal, characteristic, complemented
8#13069318C211yesmaximal, characteristic, complemented
9#13069317C211yesmaximal, characteristic, complemented
10#13068755C211yesmaximal, characteristic, complemented
11#13068462C211yesmaximal, characteristic, complemented
12#13068460C211yesmaximal, characteristic, complemented
13#13068458C211yesmaximal, characteristic, complemented
14#13068304C211yesmaximal, characteristic, complemented
15C11×#1765C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17#10623363C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19#10623048C2211yescharacteristic
20C2×C11×#104C2211yescharacteristic
21C11×#416C2211yescharacteristic
22C11×#405C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C2×#66901C2211yescharacteristic
25#10622847C2211yescharacteristic
26#10622846C2211yescharacteristic
27C2×#66889C2211yescharacteristic
28#10622742C2211yescharacteristic
29#10622741—22no—
30#10622732C2211yescharacteristic
31#10622731C2211yescharacteristic
32#10622731C2211yescharacteristic
33#10622726C2211yescharacteristic
34C8×C22⋊D11—22no—
35#10622714C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40#10622615C2211yescharacteristic
41#10622612C2211yescharacteristic
42#10622545C2211yescharacteristic
43C2×#66869C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622410C412yescomplemented
46#10622408C412yescomplemented
47#10622378C412yescomplemented
48#10622377C412yescomplemented
49#10622314—22no—
50C8×Dic22—22no—
51C11×#341C2211yescharacteristic
52C11×#339C2211yescharacteristic
53#10622196C2211yescharacteristic
54#10622196C2211yescharacteristic
55#10622193C2211yescharacteristic
56#10622190C2211yescharacteristic
57#10622170C2211yescharacteristic
58#10622161C2211yescharacteristic
59C2×C11×#41C2311yescharacteristic
60C2×#4339C2311yescharacteristic
61C11×#131—22no—
62C11×#131—22no—
63C2×C11×M16—21no—
64C2×C11×M16C2311yescharacteristic
65C2×C11×M16C2311yescharacteristic
66C22×C8×C11—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#117C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71#67000C2×C411yescharacteristic
72#66997C2×C411yescharacteristic
73#66993C2×C411yescharacteristic
74#66992—22no—
75#66989C2×C411yescharacteristic
76C4×C22⋊D11—22no—
77#66979C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C2×#4318C2311yescharacteristic
81C2×#4318C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66954—22no—
85#66954—22no—
86C2×#4313—21no—
87C2×C8×D11—21no—
88#66943C2×C412yes—
89#66941C2×C412yes—
90#66931—22no—
91C4×Dic22—22no—
92C11×#104—22no—
93C11×#103C2×C412yes—
94C11×#102C2×C412yes—
95C11×#97—21no—
96C11×#97—22no—
97C4×C8×C11—21no—
98#66901—22no—
99#66899C2×C412yes—
100#66896C2×C412yes—
101C11⋊#95—22no—
102C22⋊(C11⋊C8)—22no—
103#66889—22no—
104#66885C2×C412yes—
105(C2×D11)⋊C8—22no—
106#66880C2×C412yes—
107#66879—21no—
108#66879—22no—
109#66879C2×C412yes—
110#66879C2×C412yes—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113Dic11⋊C8—22no—
114C8×Dic11—21no—
115C8×Dic11—22no—
116C8×Dic11D412yes—
117C8×Dic11D412yes—
118#66874C2×C412yes—
119#66873C2×C412yes—
120#66869—22no—
121C4⋊(C11⋊C8)—22no—
122C4×C11⋊C8—22no—
123#21663—111nomaximal, Sylow
124C11×#41—21no—
125C11×#41—21no—
126C11×#41—21no—
127C11×#41—21no—
128C2×Q8×C11C22×C411yescharacteristic
129C2×D4×C11—21no—
130C2×D4×C11C22×C411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—22no—
135C2×C22⋊D11—21no—
136C22×Dic11—21no—
137C22×Dic11#4112yes—
138#4339—21no—
139#4339—21no—
140#4339—21no—
141#4339—21no—
142C2×D44C22×C411yescharacteristic
143C2×C4×D11—21no—
144C2×Dic22—22no—
145C2×Dic22C22×C411yescharacteristic
146C11×M16—21no—
147C11×M16—21no—
148C11×M16—21no—
149C11×M16—21no—
150C11×M16—42no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—42no—
156C2×C8×C11C22×C412yes—
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11C2×D411yescharacteristic
159C2×C8×C11#4112yes—
160C2×C8×C11#4112yes—
161C11×C4⋊C4C22×C412yes—
162C11×C22⋊C4—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11#4112yes—
166C22⋊Dic11—22no—
167C22⋊Dic11—21no—
168(C2×D11)⋊C4—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11C22×C412yes—
171Dic11⋊C4—22no—
172Dic11⋊C4—22no—
173Dic11⋊C4—22no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11C22×C411yescharacteristic
177C4×Dic11C22×C411yescharacteristic
178C4×Dic11C2×D412yes—
179C4×Dic11#4112yes—
180#4318—21no—
181#4318—21no—
182#4318—21no—
183#4318—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8C22×C412yes—
191C2×C11⋊C8C2×D412yes—
192#4313—42no—
193C8×D11—42no—
194#3135—111no—
195#2960—111no—
196#2931—111no—
197#1995—111no—
198#1963—111no—
199#1937—111no—
200#1937—111no—
201#1937—111no—
202#1937—111no—
203#1838—111no—
204#1765—111no—
205#1765—111no—
206#1765—111no—
207#1765D1111yescharacteristic, complemented
208#1726—111no—
209C23×C11—21no—
210C23×C11C2×#4111yescharacteristic
211C22×D11—21no—
212Q8×C11—21no—
213Q8×C11—21no—
214D4×C11—21no—
215D4×C11—21no—
216D4×C11—41no—
217D4×C11—41no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C22⋊D11—44no—
231C22⋊D11—41no—
232C22⋊D11—41no—
233C2×Dic11—22no—
234C2×Dic11—21no—
235C2×Dic11—22no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11C4×D412yes—
239C2×Dic11C4×D412yes—
240D44—21no—
241D44—21no—
242C4×D11—41no—
243C4×D11—41no—
244Dic22—21no—
245Dic22—21no—
246Dic22—44no—
247C8×C11—22no—
248C8×C11—41no—
249C8×C11—41no—
250C8×C11#12412yes—
251C8×C11#12412yes—
252C11⋊C8—22no—
253C11⋊C8—22no—
254C11⋊C8—41no—
255C11⋊C8—41no—
256C2×#131—111no—
257C2×#131C2×D1111yescharacteristic
258#533—111no—
259#532—111no—
260#491—112no—
261#490—112no—
262#489—112no—
263#489—112no—
264#446—222no—
265C8×Q8—222no—
266#436—222no—
267C8×D4—222no—
268#424—111no—
269#424—111no—
270#423—111no—
271#423—111no—
272C2×#104—111no—
273C2×#104—111no—
274C2×#104—111no—
275C2×#104C2×D1111yescharacteristic
276#416—111no—
277#416—111no—
278#416—111no—
279#416C2×D1111yescharacteristic
280#408—111no—
281#408—111no—
282#405—111no—
283#405C2×D1111yescharacteristic
284C2×#97—111no—
285C2×#97—111no—
286C2×#97C2×D1111yescharacteristic
287C2×C4×C8—111no—
288C2×C4×C8—111no—
289C2×C4×C8—111no—
290#376—111no—
291#341—111no—
292#341—111no—
293#341—111no—
294#341C2×D1111yescharacteristic
295#339—111no—
296#339—111no—
297#339—111no—
298#339C2×D1111yescharacteristic
299C22×C11—22no—
300C22×C11—42no—
301C22×C11—41no—
302C22×C11C2×C4×D411yescharacteristic
303C22×C11#52911yescharacteristic
304C22×C11#52911yescharacteristic
305C2×D11—42no—
306C2×D11—41no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—41no—
310C4×C11C4×#4111yescharacteristic
311C4×C11C4×#4111yescharacteristic
312C4×C11C2×#12411yescharacteristic
313C4×C11#53211yescharacteristic
314Dic11—22no—
315Dic11—22no—
316Dic11—42no—
317Dic11—42no—
318Dic11—41no—
319C2×#41—111no—
320C2×#41C22×D1111yescharacteristic
321#131—22no—
322#131—22no—
323#131—222no—
324#131—222no—
325C2×M16—21no—
326C2×M16—111no—
327C2×M16—111no—
328C2×M16—221no—
329C2×M16C22×D1111yescharacteristic
330C2×M16C22×D1111yescharacteristic
331C22×C8—21no—
332C22×C8—111no—
333C22×C8—111no—
334C22×C8—221no—
335C22×C8C22×D1111yescharacteristic
336C22×C8C22×D1111yescharacteristic
337C4⋊Q8—112no—
338C4⋊Q8—111no—
339#127—111no—
340#125—112no—
341#124—111no—
342#124—111no—
343C22⋊Q8—222no—
344#121—222no—
345C4×Q8—222no—
346C4×D4—222no—
347#117—111no—
348#117C22×D1111yescharacteristic
349C2×C42—111no—
350C2×C42—111no—
351C2×C42C22×D1111yescharacteristic
352C4⋊C8—222no—
353C4⋊C8—222no—
354C4⋊C8—222no—
355C4⋊C8—222no—
356#104—22no—
357#104—222no—
358#104—222no—
359#104—222no—
360#103—112no—
361#103—112no—
362#103—112no—
363#103C4×D1112yes—
364#102—112no—
365#102—112no—
366#102—112no—
367#102C4×D1112yes—
368C22⋊C8—222no—
369C22⋊C8—222no—
370#97—21no—
371#97—22no—
372#97—112no—
373#97—112no—
374#97—222no—
375#97—221no—
376C4×C8—21no—
377C4×C8—112no—
378C4×C8—112no—
379C4×C8—222no—
380C4×C8—221no—
381C4×C8—222no—
382#95—222no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—81no—
386C2×C11C4×#12411yescharacteristic
387C2×C11#295512yes—
388D11—81no—
389#41—21no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—221no—
394#41—221no—
395#41—221no—
396#41—221no—
397C2×Q8—111no—
398C2×Q8—222no—
399C2×Q8C2×C4×D1111yescharacteristic
400C2×D4—21no—
401C2×D4—111no—
402C2×D4—222no—
403C2×D4—221no—
404C2×D4C2×C4×D1111yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—112no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4C23×D1111yescharacteristic
411M16—21no—
412M16—21no—
413M16—21no—
414M16—21no—
415M16—42no—
416M16—221no—
417M16—221no—
418M16—221no—
419M16—221no—
420M16—442no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—42no—
426C2×C8—112no—
427C2×C8—112no—
428C2×C8—221no—
429C2×C8—221no—
430C2×C8—221no—
431C2×C8—221no—
432C2×C8—221no—
433C2×C8—221no—
434C2×C8—442no—
435C2×C8C2×C4×D1112yes—
436C2×C8#433912yes—
437C2×C8D4×D1111yescharacteristic
438C2×C8D4×D1111yescharacteristic
439C2×C8#434112yes—
440C4⋊C4—112no—
441C4⋊C4—222no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4C2×C4×D1112yes—
446C22⋊C4—21no—
447C22⋊C4—222no—
448C22⋊C4—222no—
449C22⋊C4—221no—
450C42—21no—
451C42—21no—
452C42—111no—
453C42—111no—
454C42—112no—
455C42—112no—
456C42—221no—
457C42—221no—
458C42#433912yes—
459C11#2166311yescharacteristic, complemented, Sylow
460C23—21no—
461C23—221no—
462C23#41×D1111yescharacteristic
463Q8—21no—
464Q8—21no—
465Q8—221no—
466Q8—221no—
467Q8—444no—
468D4—21no—
469D4—21no—
470D4—41no—
471D4—41no—
472D4—221no—
473D4—221no—
474D4—444no—
475D4—441no—
476D4—441no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—112no—
484C2×C4—112no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—221no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4C22×C4×D1111yescharacteristic
493C2×C4C2×#433911yescharacteristic
494C2×C4C2×#433911yescharacteristic
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4C2×#434111yescharacteristic
497C2×C4#41×D1111yescharacteristic
498C8—22no—
499C8—41no—
500C8—41no—
501C8—222no—
502C8—222no—
503C8—441no—
504C8—441no—
505C8#6693812yes—
506C8#6693812yes—
507C22—22no—
508C22—42no—
509C22—41no—
510C22—442no—
511C22—441no—
512C22#1062305911yescharacteristic
513C22#1062306911yescharacteristic
514C22C4×D4×D1111yescharacteristic
515C4—42no—
516C4—42no—
517C4—41no—
518C4—222no—
519C4—222no—
520C4—442no—
521C4—442no—
522C4—441no—
523C4C4×#433911yescharacteristic
524C4C2×#6693811yescharacteristic
525C4C4×#434111yescharacteristic
526C4#1062307911yescharacteristic
527C2—21no—
528C2—21no—
529C2—81no—
530C2—881no—
531C2C4×#6693811yescharacteristic
532C2#1307751612yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1765C2
socleC22×C11C2×C4×D4
prime radical#10623363C22
cosocleC22×C4×C11C24
hypercenter#1765D11
hypocenterC11#21663
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. #13077548C2semidirect
4. #13069595C2semidirect
6. #13069322C2semidirect
7. #13069321C2semidirect
8. #13069318C2semidirect
9. #13069317C2semidirect
10. #13068755C2semidirect
11. #13068462C2semidirect
12. #13068460C2semidirect
13. #13068458C2semidirect
14. #13068304C2semidirect
15. C11×#1765C2semidirect
45. #10622410C4semidirect
46. #10622408C4semidirect
47. #10622378C4semidirect
48. #10622377C4semidirect
207. #1765D11semidirect
459. C11#21663semidirect

Maximal subgroups

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

subgroupindex
#130789592
#130775482
#130773262
#130695952
#130694462
#130693222
#130693212
#130693182
#130693172
#130687552
#130684622
#130684602
#130684582
#130683042
C11×#17652
#2166311