Finite Group Databasebeta

← #15617191

Subgroups — #15617191

Order 2816.

3178 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623281C211yesmaximal, characteristic
2C2×D11×#131C211yesmaximal, characteristic
3#13081815C211yesmaximal, characteristic
4#13077045C213yesmaximal, complemented
5#13077044C211yesmaximal, characteristic, complemented
6#13077043C213yesmaximal, complemented
7#13077042C211yesmaximal, characteristic, complemented
8#13077038C213yesmaximal, complemented
9#131×Dic11C211yesmaximal, characteristic, complemented
10C4×#66954C213yesmaximal, complemented
11#13077033C213yesmaximal, complemented
12#13077032C213yesmaximal, complemented
13C2×#10622302C213yesmaximal, complemented
14D11×#405C213yesmaximal, complemented
15C4×C11×#131C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C4×C11×#41C2211yescharacteristic
20#41×Dic11C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C2×#67001C2211yescharacteristic
23#10623281C4116yescomplemented
24D11×#131C4116yescomplemented
25C2×#66960C2213yes—
26C2×#66960C2213yes—
27C2×M16×D11C2213yes—
28C2×M16×D11C2213yes—
29C2×#66954C2213yes—
30C2×#66954C2213yes—
31C22×#4313C2213yes—
32C22×C8×D11C2213yes—
33#10623105C412yes—
34#10623103C412yes—
35#10623077C416yes—
36#10623076C416yes—
37#10623053C2213yes—
38D11×#117C2213yes—
39C4×#4339C2213yes—
40C2×#66925C2213yes—
41C11×#405C2213yescomplemented
42C11×#405C2213yescomplemented
43C4×C11×M16C2213yescomplemented
44C2×C4×C8×C11C2213yescomplemented
45#10622735C2213yescomplemented
46#10622735C2213yescomplemented
47M16×Dic11C2213yescomplemented
48M16×Dic11C2213yescomplemented
49#10622714C2213yescomplemented
50#10622714C2213yescomplemented
51C2×#66879C2213yescomplemented
52C2×C8×Dic11C2213yescomplemented
53#10622610C2213yescomplemented
54#10622610C2213yescomplemented
55C4×#4318C2213yescomplemented
56C2×#66867C2213yescomplemented
57#10622321C2216yes—
58#10622321C2216yescomplemented
59#10622320C2216yescomplemented
60D11×#97C2216yescomplemented
61#10622302C2213yes—
62#10622302C2211yescharacteristic
63#10622302C2213yes—
64#10622302C2213yes—
65#10622302C2213yescomplemented
66#10622302C2213yescomplemented
67#10622302C2213yescomplemented
68#10622302C2213yescomplemented
69#10622302C2216yescomplemented
70C4×#4313C2216yescomplemented
71C4×C8×D11C2216yescomplemented
72C2×C11×#41C2311yescharacteristic
73#41×D11C2×C418yes—
74#41×D11C2×C418yes—
75C2×#4343C2×C411yescharacteristic
76C2×Q8×D11C2×C411yescharacteristic
77C2×#4341C2×C413yes—
78C2×D4×D11C2×C413yes—
79C2×#4339C2313yes—
80C22×C4×D11C2313yes—
81C11×#131C2×C418yescomplemented
82C11×#131C2×C418yescomplemented
83C2×C11×M16C2313yes—
84C2×C11×M16C2313yes—
85C22×C8×C11C2313yes—
86C22×C8×C11C2313yes—
87C4×Q8×C11C2×C412yes—
88C4×D4×C11C2×C416yes—
89C11×#117C2313yes—
90C2×C42×C11C2313yes—
91#67001C2×C418yescomplemented
92#67001C2×C418yescomplemented
93Q8×Dic11C2×C412yes—
94D4×Dic11C2×C416yes—
95C4×C22⋊D11C2×C4112yes—
96C2×(C2×D11)⋊C4C2×C416yes—
97#66979C2313yes—
98C2×Dic11⋊C4C2×C416yes—
99C2×C4×Dic11C2313yes—
100C2×#4318C2313yes—
101C2×#4318C2313yes—
102C22×C11⋊C8C2313yes—
103C22×C11⋊C8C2313yes—
104#66960C2×C4124yescomplemented
105#66960C2×C4124yescomplemented
106M16×D11C2×C4124yescomplemented
107M16×D11C2×C4124yescomplemented
108#66954C2×C4124yescomplemented
109#66954C2×C4124yescomplemented
110C2×#4313C2×C4124yescomplemented
111C2×#4313C2311yescharacteristic
112C2×#4313C2313yes—
113C2×#4313C2313yes—
114C2×#4313C2313yes—
115C2×#4313C2316yes—
116C2×C8×D11C2×C4124yescomplemented
117C2×C8×D11C2311yescharacteristic
118C2×C8×D11C2313yes—
119C2×C8×D11C2313yes—
120C2×C8×D11C2313yes—
121C2×C8×D11C2316yes—
122#66946C2×C416yes—
123#66945C2×C416yes—
124C4⋊C4×D11C2×C416yes—
125#66940C2×C416yes—
126(C22⋊D11)⋊C4C2×C4112yes—
127C22⋊C4×D11C2×C416yes—
128#66930C2×C416yes—
129C4×D44C2×C416yes—
130#66925C2×C416yes—
131#66925C2×C416yes—
132#66925C2311yescharacteristic
133#66925C2313yes—
134#66925C2313yes—
135#66925C2313yes—
136C42×D11C2316yes—
137C4×Dic22C2×C416yes—
138C11×#97C2316yes—
139C4×C8×C11C2313yes—
140C4×C8×C11C2313yes—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2313yes—
143#66879C2313yes—
144#66879C2316yes—
145#66879C2313yes—
146#66879C2313yes—
147#66879C2311yescharacteristic
148C8×Dic11C2313yes—
149C8×Dic11C2316yes—
150C8×Dic11C2313yes—
151C8×Dic11C2313yes—
152C8×Dic11C2311yescharacteristic
153#66867C2311yescharacteristic
154#66867C2313yes—
155#66867C2313yes—
156#66867C2313yes—
157C4×C11⋊C8C2316yes—
158#60058—111nomaximal, Sylow
159C23×D11C22×C413yes—
160C11×#41C22×C414yes—
161C11×#41C22×C414yes—
162C2×Q8×C11C22×C411yescharacteristic
163C2×D4×C11C22×C413yes—
164C22×C4×C11C22×C416yes—
165C22×C4×C11C2413yes—
166C2×C22⋊D11C22×C416yes—
167C22×Dic11C22×C416yes—
168C22×Dic11C22×C413yes—
169#4343C4218yes—
170Q8×D11C4218yes—
171#4341C42124yes—
172D4×D11C42124yes—
173#4339C22×C4112yes—
174#4339C22×C4112yes—
175C2×D44C22×C413yes—
176C2×C4×D11C22×C4112yes—
177C2×C4×D11C22×C4112yes—
178C2×C4×D11C22×C4112yes—
179C2×C4×D11C22×C413yes—
180C2×C4×D11C22×C413yes—
181C2×C4×D11C2413yes—
182C2×C4×D11C2411yescharacteristic
183C2×Dic22C22×C413yes—
184C11×M16C22×C4112yes—
185C11×M16C22×C4112yes—
186C2×C8×C11C22×C4112yes—
187C2×C8×C11C22×C4112yes—
188C2×C8×C11C2413yes—
189C2×C8×C11C2413yes—
190C2×C8×C11C2411yescharacteristic
191C2×C8×C11C2411yescharacteristic
192C11×C4⋊C4C22×C416yes—
193C11×C22⋊C4C22×C416yes—
194C42×C11C22×C416yes—
195C42×C11C2413yes—
196C42×C11C2411yescharacteristic
197C22⋊Dic11C22×C416yes—
198(C2×D11)⋊C4C22×C412yes—
199(C2×D11)⋊C4C22×C416yes—
200(C2×D11)⋊C4C22×C416yes—
201(C2×D11)⋊C4C22×C416yes—
202C4⋊Dic11C22×C416yes—
203Dic11⋊C4C22×C416yes—
204Dic11⋊C4C22×C412yes—
205Dic11⋊C4C22×C416yes—
206Dic11⋊C4C22×C416yes—
207C4×Dic11C22×C4112yes—
208C4×Dic11C22×C416yes—
209C4×Dic11C2413yes—
210C4×Dic11C2411yescharacteristic
211#4318C22×C4112yes—
212#4318C22×C4112yes—
213C2×C11⋊C8C22×C4112yes—
214C2×C11⋊C8C22×C4112yes—
215C2×C11⋊C8C2413yes—
216C2×C11⋊C8C2413yes—
217C2×C11⋊C8C2411yescharacteristic
218C2×C11⋊C8C2411yescharacteristic
219#4313C22×C414yes—
220#4313C22×C4112yes—
221#4313C22×C4112yes—
222#4313C22×C4112yes—
223#4313C22×C4124yes—
224C8×D11C22×C414yes—
225C8×D11C22×C4112yes—
226C8×D11C22×C4112yes—
227C8×D11C22×C4112yes—
228C8×D11C22×C4124yes—
229C2×#568—111no—
230C22×#131—111no—
231#3428—111no—
232#2875—113no—
233#2875—113no—
234#2875—111no—
235#2875—111no—
236C4×#131—113no—
237C4×#131—113no—
238C4×#131—111no—
239C4×#131D1111yescharacteristic, complemented
240#2873—113no—
241#2873—113no—
242C2×#405—113no—
243C2×#405—113no—
244C23×C11C23×C413yes—
245C22×D11—46no—
246C22×D11C2×C42112yes—
247C22×D11C23×C411yescharacteristic
248C22×D11C23×C413yes—
249Q8×C11C2×C4214yes—
250D4×C11C2×C42112yes—
251C2×C4×C11—46no—
252C2×C4×C11C23×C416yes—
253C2×C4×C11C23×C412yes—
254C2×C4×C11C23×C416yes—
255C2×C4×C11C23×C416yes—
256C2×C4×C11C23×C413yes—
257C2×C4×C11C2511yescharacteristic
258C22⋊D11C2×C42124yes—
259C2×Dic11—46no—
260C2×Dic11C2×C42112yes—
261C2×Dic11C23×C412yes—
262C2×Dic11C23×C416yes—
263C2×Dic11C23×C413yes—
264C2×Dic11C23×C411yescharacteristic
265D44C2×C42112yes—
266C4×D11—412no—
267C4×D11C2×C42112yes—
268C4×D11C2×C42112yes—
269C4×D11C23×C412yes—
270C4×D11C23×C416yes—
271C4×D11C23×C416yes—
272C4×D11C23×C412yes—
273Dic22C2×C42112yes—
274C8×C11C23×C412yes—
275C8×C11C23×C416yes—
276C8×C11C23×C416yes—
277C8×C11C23×C412yes—
278C11⋊C8C23×C412yes—
279C11⋊C8C23×C416yes—
280C11⋊C8C23×C416yes—
281C11⋊C8C23×C412yes—
282C22×#41—111no—
283#568—1116no—
284C2×#131—111no—
285C2×#131—111no—
286C2×#131—1116no—
287C2×#131—113no—
288C2×#131—113no—
289C2×#131—113no—
290C2×#131—113no—
291C2×#131C2×D1111yescharacteristic
292C2×#131C2×D1111yescharacteristic
293C22×M16—113no—
294C22×M16—113no—
295C22×M16—113no—
296C23×C8—113no—
297#520—112no—
298#520—116no—
299#519—112no—
300#518—116no—
301C4×#41—111no—
302C4×#41—113no—
303C4×#41—113no—
304C4×#41C2×D1111yescharacteristic
305C2×#117—113no—
306C2×#117—113no—
307#405—113no—
308#405—113no—
309#405—113no—
310#405—113no—
311#405—113no—
312#405—113no—
313#405—116no—
314#405—116no—
315#405—113no—
316#405—111no—
317#405—113no—
318#405—113no—
319#405—113no—
320#405—113no—
321#405—113no—
322#405—113no—
323#405—116no—
324#405C2×D1113yescomplemented
325#405C2×D1113yescomplemented
326C4×M16—113no—
327C4×M16—113no—
328C4×M16—113no—
329C4×M16—116no—
330C4×M16—116no—
331C4×M16C2×D1113yescomplemented
332C2×#97—113no—
333C2×#97—113no—
334C2×#97—116no—
335C2×C4×C8—113no—
336C2×C4×C8—116no—
337C2×C4×C8C2×D1113yescomplemented
338C22×C11—26no—
339C22×C11C22×C4216yes—
340C22×C11C24×C411yescharacteristic
341C2×D11—22no—
342C2×D11—26no—
343C2×D11—412no—
344C2×D11C22×C4212yes—
345C2×D11C22×C4216yes—
346C4×C11—22no—
347C4×C11—26no—
348C4×C11C22×C4216yes—
349C4×C11C24×C411yescharacteristic
350C4×C11C24×C411yescharacteristic
351Dic11—26no—
352Dic11—22no—
353Dic11C22×C4216yes—
354Dic11C22×C4212yes—
355C2×#41—118no—
356C2×#41—118no—
357C2×#41—111no—
358C2×#41—113no—
359C2×#41—113no—
360C2×#41C22×D1111yescharacteristic
361C22×Q8—111no—
362C22×D4—113no—
363C23×C4—113no—
364#131—118no—
365#131—118no—
366#131—1124no—
367#131—1124no—
368#131—1124no—
369#131—1124no—
370#131C4×D1118yescomplemented
371#131C4×D1118yescomplemented
372C2×M16—113no—
373C2×M16—113no—
374C2×M16—1124no—
375C2×M16—1124no—
376C2×M16—1124no—
377C2×M16—113no—
378C2×M16—111no—
379C2×M16—116no—
380C2×M16—113no—
381C2×M16—113no—
382C2×M16C22×D1113yes—
383C2×M16C22×D1113yes—
384C22×C8—113no—
385C22×C8—113no—
386C22×C8—1124no—
387C22×C8—113no—
388C22×C8—113no—
389C22×C8—116no—
390C22×C8—111no—
391C22×C8—113no—
392C22×C8C22×D1113yes—
393C22×C8C22×D1113yes—
394C4×Q8—112no—
395C4×Q8—116no—
396C4×Q8—116no—
397C4×Q8C4×D1112yes—
398C4×D4—116no—
399C4×D4—1112no—
400C4×D4—116no—
401C4×D4—1112no—
402C4×D4—116no—
403C4×D4C4×D1116yes—
404#117—113no—
405#117—116no—
406#117—116no—
407#117—116no—
408#117—116no—
409#117—113no—
410#117—111no—
411#117—113no—
412#117—113no—
413#117C22×D1113yes—
414C2×C4⋊C4—116no—
415C2×C4⋊C4—116no—
416C2×C22⋊C4—116no—
417C2×C22⋊C4—116no—
418C2×C42—113no—
419C2×C42—116no—
420C2×C42C22×D1113yes—
421#97—113no—
422#97—111no—
423#97—113no—
424#97—116no—
425#97—113no—
426#97—113no—
427#97—111no—
428#97—113no—
429#97—113no—
430#97C22×D1116yes—
431C4×C8—113no—
432C4×C8—116no—
433C4×C8—113no—
434C4×C8—113no—
435C4×C8—111no—
436C4×C8—116no—
437C4×C8C22×D1113yes—
438C4×C8C22×D1113yes—
439C4×C8C22×D1113yes—
440C4×C8C22×D1111yescharacteristic
441C2×C11—26no—
442C2×C11C23×C4211yescharacteristic
443C2×C11#357312yes—
444D11—22no—
445D11—26no—
446C24—113no—
447#41—118no—
448#41—1124no—
449#41—1112no—
450#41—1112no—
451#41C2×C4×D1114yes—
452#41C2×C4×D1114yes—
453C2×Q8—118no—
454C2×Q8—113no—
455C2×Q8C2×C4×D1111yescharacteristic
456C2×D4—116no—
457C2×D4—1124no—
458C2×D4—113no—
459C2×D4C2×C4×D1113yes—
460C22×C4—113no—
461C22×C4—113no—
462C22×C4—113no—
463C22×C4—1112no—
464C22×C4—1112no—
465C22×C4—113no—
466C22×C4—111no—
467C22×C4—116no—
468C22×C4—1112no—
469C22×C4C2×C4×D1116yes—
470C22×C4C23×D1113yes—
471M16—1112no—
472M16—1112no—
473M16—1112no—
474M16—114no—
475M16—1124no—
476M16—1112no—
477M16—1112no—
478M16C2×C4×D11112yes—
479M16C2×C4×D11112yes—
480C2×C8—1112no—
481C2×C8—1112no—
482C2×C8—111no—
483C2×C8—113no—
484C2×C8—113no—
485C2×C8—111no—
486C2×C8—114no—
487C2×C8—1112no—
488C2×C8—1112no—
489C2×C8—1112no—
490C2×C8—1124no—
491C2×C8C2×C4×D11112yes—
492C2×C8C2×C4×D11112yes—
493C2×C8C23×D1113yes—
494C2×C8C23×D1113yes—
495C2×C8C23×D1111yescharacteristic
496C2×C8C23×D1111yescharacteristic
497C4⋊C4—116no—
498C4⋊C4—112no—
499C4⋊C4—116no—
500C4⋊C4—116no—
501C4⋊C4—116no—
502C4⋊C4C2×C4×D1116yes—
503C22⋊C4—116no—
504C22⋊C4—116no—
505C22⋊C4—112no—
506C22⋊C4—116no—
507C22⋊C4—116no—
508C22⋊C4C2×C4×D1116yes—
509C42—1112no—
510C42—116no—
511C42—111no—
512C42—113no—
513C42C2×C4×D1116yes—
514C42C23×D1113yes—
515C42C23×D1111yescharacteristic
516C11#6005811yescharacteristic, complemented, Sylow
517C23—111no—
518C23—113no—
519C23—1112no—
520C23—446no—
521C23C22×C4×D1113yes—
522Q8—1112no—
523Q8C42×D1114yes—
524D4—1124no—
525D4—1112no—
526D4C42×D11112yes—
527C2×C4—46no—
528C2×C4—1112no—
529C2×C4—113no—
530C2×C4—111no—
531C2×C4—1112no—
532C2×C4—1112no—
533C2×C4—112no—
534C2×C4—116no—
535C2×C4—116no—
536C2×C4—112no—
537C2×C4—116no—
538C2×C4—112no—
539C2×C4—4412no—
540C2×C4—446no—
541C2×C4C22×C4×D1116yes—
542C2×C4C22×C4×D1112yes—
543C2×C4C22×C4×D1113yes—
544C2×C4C22×C4×D1116yes—
545C2×C4C22×C4×D1116yes—
546C2×C4C24×D1111yescharacteristic
547C8—112no—
548C8—116no—
549C8—112no—
550C8—116no—
551C8C22×C4×D1112yes—
552C8C22×C4×D1116yes—
553C8C22×C4×D1116yes—
554C8C22×C4×D1112yes—
555C22—26no—
556C22—112no—
557C22—116no—
558C22—226no—
559C22—222no—
560C22—4412no—
561C22C2×C42×D1116yes—
562C22C23×C4×D1111yescharacteristic
563C4—22no—
564C4—26no—
565C4—112no—
566C4—116no—
567C4—226no—
568C4—222no—
569C4C2×C42×D1116yes—
570C4C23×C4×D1111yescharacteristic
571C4C23×C4×D1111yescharacteristic
572C2—26no—
573C2—222no—
574C2—226no—
575C2C22×C42×D1111yescharacteristic
576C2#1308332712yes—
subgroupG/H
centerC2×C8C23×D11
commutatorC2×C11C23×C42
FrattiniC2×C4C24×D11
FittingC4×C11×#131C2
socleC22×C11C24×C4
prime radicalC2×#41×D11C22
cosocleC2×C4×C11C25
hypercenterC4×#131D11
hypocenterC11#60058
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
4. #13077045C2semidirect
5. #13077044C2semidirect
6. #13077043C2semidirect
7. #13077042C2semidirect
8. #13077038C2semidirect
9. #131×Dic11C2semidirect
10. C4×#66954C2semidirect
11. #13077033C2semidirect
12. #13077032C2semidirect
13. C2×#10622302C2semidirect
14. D11×#405C2semidirect
15. C4×C11×#131C2semidirect
23. #10623281C4semidirect
24. D11×#131C4semidirect
41. C11×#405C22semidirect
42. C11×#405C22semidirect
43. C4×C11×M16C22semidirect
44. C2×C4×C8×C11C22semidirect
45. #10622735C22semidirect
46. #10622735C22semidirect
47. M16×Dic11C22semidirect
48. M16×Dic11C22semidirect
49. #10622714C22semidirect
50. #10622714C22semidirect
51. C2×#66879C22semidirect
52. C2×C8×Dic11C22semidirect
53. #10622610C22semidirect
54. #10622610C22semidirect
55. C4×#4318C22semidirect
56. C2×#66867C22semidirect
58. #10622321C22semidirect
59. #10622320C22semidirect
60. D11×#97C22semidirect
65. #10622302C22semidirect
66. #10622302C22semidirect
67. #10622302C22semidirect
68. #10622302C22semidirect
69. #10622302C22semidirect
70. C4×#4313C22semidirect
71. C4×C8×D11C22semidirect
81. C11×#131C2×C4semidirect
82. C11×#131C2×C4semidirect
91. #67001C2×C4semidirect
92. #67001C2×C4semidirect
104. #66960C2×C4semidirect
105. #66960C2×C4semidirect
106. M16×D11C2×C4semidirect
107. M16×D11C2×C4semidirect
108. #66954C2×C4semidirect
109. #66954C2×C4semidirect
110. C2×#4313C2×C4semidirect
116. C2×C8×D11C2×C4semidirect
239. C4×#131D11semidirect
324. #405C2×D11semidirect
325. #405C2×D11semidirect
331. C4×M16C2×D11semidirect
337. C2×C4×C8C2×D11semidirect
370. #131C4×D11semidirect
371. #131C4×D11semidirect
516. C11#60058semidirect

Maximal subgroups

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

subgroupindex
C2×#106232812
C2×D11×#1312
#130818152
#130770452
#130770442
#130770432
#130770422
#130770382
#131×Dic112
C4×#669542
#130770332
#130770322
C2×#106223022
D11×#4052
C4×C11×#1312
#6005811