Finite Group Databasebeta

← #14720649

Subgroups — #14720649

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082194C211yesmaximal, characteristic
2#13077572C211yesmaximal, characteristic
3#13077181C211yesmaximal, characteristic
4#13067071C211yesmaximal, characteristic, complemented
5#13067069C212yesmaximal, complemented
6#13067046C211yesmaximal, characteristic, complemented
7#13067043C212yesmaximal, complemented
8#13067017C212yesmaximal, complemented
9C2×#10622122C211yesmaximal, characteristic, complemented
10D11×Q8⋊C8C212yesmaximal, complemented
11C11×#1481C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66954—21no—
14#10623261C411yescharacteristic
15#10623258C411yescharacteristic
16#10623253C411yescharacteristic
17#10623252C411yescharacteristic
18#10623221—21no—
19#10623216—21no—
20#10623167—22no—
21#10623166C412yes—
22#10623163C412yes—
23#10623109—22no—
24#10623109C2212yes—
25C4×Q8×D11C2212yes—
26#10623053—21no—
27#10623048—21no—
28C4×#4339C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32#10622715—21no—
33#10622537C2211yescharacteristic
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622452—22no—
36#10622450C2212yes—
37#10622447—21no—
38D11×C4⋊C8C2212yes—
39#10622443—21no—
40(C22⋊D11)⋊C8—22no—
41#10622298C2212yes—
42C4×C8×D11C2212yes—
43C11×Q8⋊C8C2212yes—
44C11×Q8⋊C8C2212yes—
45Q8⋊(C11⋊C8)C2212yes—
46Q8⋊(C11⋊C8)C2212yes—
47#10622122C2211yescharacteristic
48#10622122C2211yescharacteristic
49#10622122C2211yescharacteristic
50#10622122C2211yescharacteristic
51#10622094C2212yes—
52#10622094C2212yes—
53C2×Q8×D11C2×C412yes—
54C2×#4339D411yescharacteristic
55C22×Dic22C2×C411yescharacteristic
56C22×C8×C11—21no—
57C11×C4⋊Q8C2×C411yescharacteristic
58C11×C4⋊Q8C2×C411yescharacteristic
59C11×#125—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8C2×C412yes—
62C4×Q8×C11—21no—
63C4×Q8×C11C2312yes—
64C11×#117—21no—
65C2×C42×C11C2311yescharacteristic
66#66999—22no—
67#66999C2×C412yes—
68Q8×Dic11C2×C412yes—
69#66997—22no—
70#66997C2×C412yes—
71C4×C22⋊D11C2×C412yes—
72C4×C22⋊D11D412yes—
73#66979D411yescharacteristic
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C2×#4318—21no—
78C22×C11⋊C8—21no—
79#66954—44no—
80C2×#4313—22no—
81C2×C8×D11—22no—
82C2×C8×D11—22no—
83#66950—22no—
84#66950C2×C412yes—
85#66949—22no—
86#66949—22no—
87#66949—22no—
88#66946—21no—
89#66946—21no—
90C4⋊C4×D11—22no—
91C4⋊C4×D11C2×C412yes—
92#66943—21no—
93#66943—21no—
94#66942—22no—
95#66942—22no—
96#66942—22no—
97#66941—21no—
98#66941—21no—
99#66941—22no—
100#66941C2×C412yes—
101#66940—21no—
102#66940—21no—
103#66940—22no—
104#66940C2×C412yes—
105(C22⋊D11)⋊C4—22no—
106(C22⋊D11)⋊C4—22no—
107#66931—22no—
108#66931—22no—
109C4×D44C2×C411yescharacteristic
110C4×D44D411yescharacteristic
111#66925—22no—
112#66925D412yes—
113C42×D11—22no—
114C42×D11C2312yes—
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—22no—
118C4×Dic22—22no—
119C4×Dic22C2×C411yescharacteristic
120C4×Dic22C2×C411yescharacteristic
121C4×Dic22C2×C411yescharacteristic
122C4×Dic22D411yescharacteristic
123C4×Dic22C2311yescharacteristic
124C4×Dic22C2311yescharacteristic
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8C2311yescharacteristic
128C11×C4⋊C8C2311yescharacteristic
129C11×C22⋊C8—21no—
130C4×C8×C11C2312yes—
131(C2×D11)⋊C8—22no—
132Dic11⋊C8—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2312yes—
138C4×C11⋊C8—21no—
139C4×C11⋊C8C2311yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141#17509—111nomaximal, Sylow
142C2×Q8×C11—21no—
143C2×Q8×C11C22×C412yes—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C2×C22⋊D11C22⋊C412yes—
148C22×Dic11—21no—
149C22×Dic11—21no—
150Q8×D11—24no—
151Q8×D11—42no—
152#4339SD1614yes—
153#4339Q1614yes—
154C2×D44C22⋊C411yescharacteristic
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11C22×C412yes—
158C2×C4×D11C2×D412yes—
159C2×C4×D11C2×D412yes—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—21no—
164C2×Dic22—41no—
165C2×Dic22C22⋊C411yescharacteristic
166C2×Dic22C22×C411yescharacteristic
167C2×Dic22C22×C411yescharacteristic
168C2×C8×C11—22no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—42no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C22×C412yes—
178C11×C22⋊C4—22no—
179C42×C11—22no—
180C42×C11C22×C411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11C22⋊C412yes—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4C22⋊C412yes—
188(C2×D11)⋊C4C22⋊C412yes—
189C4⋊Dic11—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22⋊C411yescharacteristic
193C4⋊Dic11C22⋊C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196Dic11⋊C4—22no—
197Dic11⋊C4—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—21no—
203Dic11⋊C4—21no—
204Dic11⋊C4—21no—
205Dic11⋊C4—21no—
206Dic11⋊C4C22⋊C412yes—
207Dic11⋊C4C22⋊C412yes—
208C4×Dic11—22no—
209C4×Dic11—22no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11C22×C412yes—
215C4×Dic11C2×D412yes—
216C4×Dic11C2×D412yes—
217#4318—42no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—42no—
222#4313—44no—
223C8×D11—44no—
224C8×D11—44no—
225Q8×#41—111no—
226C8×#41—111no—
227#2906—111no—
228#1493—112no—
229#1493—111no—
230#1487—111no—
231#1487—112no—
232#1481—112no—
233#1481D1111yescharacteristic, complemented
234C2×Q8⋊C8—111no—
235C2×Q8⋊C8—112no—
236C23×C11C2×C22⋊C411yescharacteristic
237C22×D11C2×C22⋊C412yes—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—81no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—41no—
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C2×SD1612yes—
250C2×C4×C11C2×Q1612yes—
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C22⋊D11#10318yes—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—42no—
260C2×Dic11—81no—
261C2×Dic11C2×C22⋊C412yes—
262C2×Dic11C2×C22⋊C412yes—
263C2×Dic11C2×C22⋊C412yes—
264D44#10314yes—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—42no—
268C4×D11—44no—
269C4×D11—82no—
270C4×D11C2×SD1614yes—
271C4×D11C2×Q1614yes—
272Dic22—21no—
273Dic22—21no—
274Dic22—21no—
275Dic22—44no—
276Dic22—42no—
277Dic22—82no—
278Dic22#10314yes—
279Dic22#13112yescomplemented
280C8×C11—42no—
281C8×C11—41no—
282C8×C11—41no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C11⋊C8—42no—
286C2×#131—221no—
287Q82—111no—
288#557—111no—
289#557—221no—
290#554—111no—
291#554—112no—
292#554—222no—
293#554—221no—
294D4×Q8—111no—
295D4×Q8—112no—
296#533—112no—
297#533—221no—
298#533—222no—
299#533C2×D1111yescharacteristic
300C4×#41—111no—
301C4×#41—221no—
302C2×C4×Q8—112no—
303C2×C4×Q8—111no—
304C8×Q8—221no—
305C8×D4—222no—
306C8×D4—221no—
307#431—112no—
308#431C2×D1111yescharacteristic
309#424—222no—
310#424—221no—
311#423—111no—
312#423—112no—
313C2×C4⋊C8—112no—
314C2×C4⋊C8C2×D1111yescharacteristic
315C2×C4×C8—111no—
316C2×C4×C8—112no—
317Q8⋊C8—112no—
318Q8⋊C8—112no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—112no—
324Q8⋊C8—112no—
325Q8⋊C8C2×D1112yes—
326Q8⋊C8C2×D1112yes—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11C2×#10312yes—
330C22×C11C22×C22⋊C411yescharacteristic
331C2×D11—22no—
332C2×D11—22no—
333C2×D11C2×#10314yes—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11C2×#10312yes—
340C4×C11C2×#13111yescharacteristic
341C4×C11#56811yescharacteristic
342C4×C11C22×SD1611yescharacteristic
343C4×C11C22×Q1611yescharacteristic
344Dic11—22no—
345Dic11—22no—
346Dic11—22no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350Dic11C2×#10314yes—
351C2×#41—111no—
352C22×Q8—112no—
353C22×Q8—111no—
354#131—444no—
355C2×M16—222no—
356C2×M16—221no—
357C22×C8—21no—
358C22×C8—222no—
359C22×C8—222no—
360C22×C8—221no—
361C4⋊Q8—112no—
362C4⋊Q8—112no—
363C4⋊Q8—222no—
364C4⋊Q8—221no—
365C4⋊Q8—221no—
366C4⋊Q8—222no—
367C4⋊Q8C4×D1111yescharacteristic
368C4⋊Q8C4×D1111yescharacteristic
369#125—21no—
370#125—222no—
371#125—222no—
372#125—221no—
373#125—222no—
374#125—221no—
375C22⋊Q8—21no—
376C22⋊Q8—112no—
377C22⋊Q8—112no—
378C22⋊Q8—222no—
379C22⋊Q8—222no—
380C22⋊Q8—222no—
381C22⋊Q8—222no—
382C22⋊Q8—222no—
383C22⋊Q8—222no—
384C22⋊Q8—222no—
385C22⋊Q8C4×D1112yes—
386C4×Q8—21no—
387C4×Q8—111no—
388C4×Q8—111no—
389C4×Q8—112no—
390C4×Q8—112no—
391C4×Q8—111no—
392C4×Q8—111no—
393C4×Q8—111no—
394C4×Q8—111no—
395C4×Q8—222no—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×Q8—221no—
399C4×Q8—221no—
400C4×Q8—221no—
401C4×Q8—221no—
402C4×Q8C22×D1112yes—
403C4×D4—112no—
404C4×D4—112no—
405C4×D4—111no—
406C4×D4—111no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4—221no—
410C4×D4—221no—
411#117—21no—
412#117—111no—
413#117—112no—
414#117—222no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—221no—
419C2×C42—112no—
420C2×C42—222no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8—112no—
426C4⋊C8—222no—
427C4⋊C8—222no—
428C4⋊C8—222no—
429C4⋊C8—221no—
430C4⋊C8C22×D1111yescharacteristic
431C4⋊C8C22×D1111yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—222no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—222no—
437C4×C8—221no—
438C4×C8C22×D1112yes—
439C2×C11—22no—
440C2×C11#288011yescharacteristic
441C2×C11C22×#10311yescharacteristic
442C2×C11#290111yescharacteristic
443D11—24no—
444#41—114no—
445#41—114no—
446C2×Q8—21no—
447C2×Q8—111no—
448C2×Q8—111no—
449C2×Q8—111no—
450C2×Q8—222no—
451C2×Q8—222no—
452C2×Q8—222no—
453C2×Q8—221no—
454C2×Q8—224no—
455C2×Q8—441no—
456C2×Q8—442no—
457C2×Q8C2×C4×D1112yes—
458C2×D4—112no—
459C2×D4—111no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—112no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4C2×C4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470M16—444no—
471M16—442no—
472C2×C8—22no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—42no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—222no—
479C2×C8—444no—
480C2×C8—444no—
481C2×C8—442no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—111no—
490C4⋊C4—111no—
491C4⋊C4—111no—
492C4⋊C4—111no—
493C4⋊C4—222no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4C2×C4×D1112yes—
507C22⋊C4—22no—
508C22⋊C4—112no—
509C22⋊C4—112no—
510C22⋊C4—112no—
511C22⋊C4—222no—
512C22⋊C4—222no—
513C42—22no—
514C42—112no—
515C42—112no—
516C42—112no—
517C42—222no—
518C42—222no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42—221no—
523C42C2×C4×D1111yescharacteristic
524C42D4×D1111yescharacteristic
525C42D4×D1111yescharacteristic
526C42C23×D1111yescharacteristic
527C11#1750911yescharacteristic, complemented, Sylow
528C23—112no—
529C23C22⋊C4×D1111yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—81no—
533Q8—114no—
534Q8—112no—
535Q8—221no—
536Q8—221no—
537Q8—221no—
538Q8—442no—
539Q8—444no—
540Q8—882no—
541D4—118no—
542D4—114no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—112no—
549C2×C4—114no—
550C2×C4—114no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—221no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—442no—
560C2×C4—444no—
561C2×C4—442no—
562C2×C4—882no—
563C2×C4—881no—
564C2×C4C22⋊C4×D1111yescharacteristic
565C2×C4C22⋊C4×D1111yescharacteristic
566C2×C4C22⋊C4×D1111yescharacteristic
567C2×C4SD16×D1112yes—
568C2×C4Q16×D1112yes—
569C2×C4C22×C4×D1111yescharacteristic
570C2×C4C2×D4×D1111yescharacteristic
571C2×C4C2×D4×D1111yescharacteristic
572C8—42no—
573C8—41no—
574C8—41no—
575C8—222no—
576C8—441no—
577C8—442no—
578C22—21no—
579C22—21no—
580C22—114no—
581C22—222no—
582C22—222no—
583C22D11×#10312yes—
584C22C2×C22⋊C4×D1111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—42no—
589C4—42no—
590C4—114no—
591C4—222no—
592C4—222no—
593C4—222no—
594C4—441no—
595C4—441no—
596C4—441no—
597C4D11×#10312yes—
598C4D11×#13111yescharacteristic
599C4#1062328111yescharacteristic
600C4C2×SD16×D1111yescharacteristic
601C4C2×Q16×D1111yescharacteristic
602C2—22no—
603C2—224no—
604C2#1307706411yescharacteristic
605C2C2×D11×#10311yescharacteristic
606C2#1307716211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1481C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#4339D4
cosocleC42×C11C24
hypercenter#1481D11
hypocenterC11#17509
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
4. #13067071C2semidirect
5. #13067069C2semidirect
6. #13067046C2semidirect
7. #13067043C2semidirect
8. #13067017C2semidirect
9. C2×#10622122C2semidirect
10. D11×Q8⋊C8C2semidirect
11. C11×#1481C2semidirect
233. #1481D11semidirect
279. Dic22#131semidirect
527. C11#17509semidirect

Maximal subgroups

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

subgroupindex
#130821942
#130775722
#130771812
#130670712
#130670692
#130670462
#130670432
#130670172
C2×#106221222
D11×Q8⋊C82
C11×#14812
#1750911