Finite Group Databasebeta

← #14720985

Subgroups — #14720985

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082653C211yesmaximal, characteristic
2#13077647C211yesmaximal, characteristic, complemented
3#13070975C211yesmaximal, characteristic, complemented
4#13067138C211yesmaximal, characteristic, complemented
5#13067135C211yesmaximal, characteristic, complemented
6#13067134C211yesmaximal, characteristic, complemented
7#13067126C211yesmaximal, characteristic, complemented
8#13067120C211yesmaximal, characteristic, complemented
9#13067117C211yesmaximal, characteristic, complemented
10#13067113C211yesmaximal, characteristic, complemented
11#13067104C211yesmaximal, characteristic, complemented
12#13067099C211yesmaximal, characteristic, complemented
13C2×#10622105C211yesmaximal, characteristic, complemented
14D11×#328C211yesmaximal, characteristic, complemented
15C11×#1501C211yesmaximal, characteristic, complemented
16C11×#525C2211yescharacteristic
17#10623362C411yescharacteristic, complemented
18#10623355C411yescharacteristic, complemented
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21#10623193—21no—
22#10623191—21no—
23#10623173C411yescharacteristic, complemented
24#10623163C411yescharacteristic, complemented
25D11×C22⋊Q8C2211yescharacteristic
26#10623153C2211yescharacteristic
27#10623142C411yescharacteristic, complemented
28#10623137C2211yescharacteristic
29#10623131C2211yescharacteristic
30#10623129C411yescharacteristic, complemented
31#10623122—21no—
32#10623118—21no—
33#10623095—21no—
34#10623087—21no—
35#10623077—21no—
36#10623070—21no—
37#10623064C411yescharacteristic, complemented
38#10623060C411yescharacteristic, complemented
39C2×(C22⋊D11)⋊C4—21no—
40C2×C11×C22⋊C8C2211yescharacteristic
41C4×C11×C22⋊C4C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43#10622820C2211yescharacteristic
44#10622724—21no—
45C8×C22⋊D11—21no—
46C22⋊C4×Dic11—21no—
47C4×(C2×D11)⋊C4—21no—
48C4×Dic11⋊C4—21no—
49#10622342—21no—
50#10622341—21no—
51#10622339C2211yescharacteristic
52D11×C22⋊C8C2211yescharacteristic
53#10622332C2211yescharacteristic
54#10622331C2211yescharacteristic
55#10622279C2211yescharacteristic
56D11×#95C2211yescharacteristic
57#10622262C2211yescharacteristic
58#10622261C2211yescharacteristic
59C11×#328C2211yescharacteristic
60C11×#328C2211yescharacteristic
61C11×#327C2211yescharacteristic
62C11×#327C2211yescharacteristic
63#10622176C2211yescharacteristic
64#10622176C2211yescharacteristic
65#10622175C2211yescharacteristic
66#10622175C2211yescharacteristic
67#10622105C2211yescharacteristic
68#10622105C2211yescharacteristic
69#10622105C2211yescharacteristic
70#10622105C2211yescharacteristic
71#10622090C2211yescharacteristic
72#10622090C2211yescharacteristic
73#10622090C2211yescharacteristic
74#10622090C2211yescharacteristic
75C2×C11×#41C2×C411yescharacteristic, complemented
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11D411yescharacteristic
78C23×Dic11—21no—
79C2×Q8×D11C2×C411yescharacteristic, complemented
80C2×#4341—21no—
81C2×#4341C2×C411yescharacteristic, complemented
82C22×C4×D11—21no—
83C22×C4×D11C2311yescharacteristic
84C22×Dic22C2×C411yescharacteristic, complemented
85C22×C8×C11—21no—
86C11×#123—21no—
87C11×C22⋊Q8C2×C411yescharacteristic, complemented
88C11×C22⋊Q8C2311yescharacteristic
89C11×#121C2×C411yescharacteristic, complemented
90C11×#121C2311yescharacteristic
91C11×#120—21no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C11×#117C2×C411yescharacteristic, complemented
95C2×C11×C22⋊C4—21no—
96C2×C42×C11—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11D411yescharacteristic
99#66999C2×C411yescharacteristic, complemented
100Q8×Dic11C2×C411yescharacteristic, complemented
101#66997C2×C411yescharacteristic, complemented
102#66992—21no—
103#66992—21no—
104#66991—21no—
105#66991C2×C411yescharacteristic, complemented
106#66990—21no—
107#66989—21no—
108#66989C2×C411yescharacteristic, complemented
109#66988—21no—
110#66988—21no—
111#66988—21no—
112D4×Dic11—21no—
113D4×Dic11—21no—
114D4×Dic11—21no—
115D4×Dic11C2×C411yescharacteristic, complemented
116#66982—21no—
117C4×C22⋊D11—21no—
118C4×C22⋊D11C2×C411yescharacteristic
119C4×C22⋊D11C2×C411yescharacteristic
120C4×C22⋊D11C2×C411yescharacteristic
121C4×C22⋊D11C2×C411yescharacteristic
122C4×C22⋊D11D411yescharacteristic
123C4×C22⋊D11D411yescharacteristic
124C4×C22⋊D11D411yescharacteristic
125C4×C22⋊D11D411yescharacteristic
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4D411yescharacteristic
128C2×C4⋊Dic11C2×C411yescharacteristic, complemented
129#66977—21no—
130#66977—21no—
131#66977—21no—
132#66977C2×C411yescharacteristic, complemented
133#66977C2×C411yescharacteristic, complemented
134#66977C2311yescharacteristic
135#66977C2311yescharacteristic
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4D411yescharacteristic
140C2×C4×Dic11—21no—
141C2×C4×Dic11—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11C2311yescharacteristic
144C2×#4318—21no—
145C2×#4313—21no—
146C2×C8×D11—21no—
147#66951—21no—
148#66950C2×C411yescharacteristic, complemented
149#66950C2×C411yescharacteristic, complemented
150#66949—21no—
151#66949—21no—
152#66945C2×C411yescharacteristic, complemented
153C4⋊C4×D11—21no—
154C4⋊C4×D11C2×C411yescharacteristic, complemented
155#66943—21no—
156#66943C2×C411yescharacteristic, complemented
157#66942—21no—
158#66941—21no—
159#66941C2×C411yescharacteristic, complemented
160#66940—21no—
161#66940C2×C411yescharacteristic, complemented
162#66940C2×C411yescharacteristic, complemented
163#66939—21no—
164#66938—21no—
165#66938—21no—
166#66936—21no—
167#66936—21no—
168#66936—21no—
169(C22⋊D11)⋊C4—28no—
170(C22⋊D11)⋊C4—21no—
171(C22⋊D11)⋊C4—21no—
172C22⋊C4×D11—21no—
173#66932—21no—
174#66932—21no—
175#66932—21no—
176#66931—21no—
177#66931—21no—
178#66931—21no—
179#66931—21no—
180#66931—21no—
181#66930—21no—
182#66930—21no—
183#66930—21no—
184#66929—21no—
185#66925—21no—
186#66923—21no—
187C4×Dic22—21no—
188C11×C22⋊C8—21no—
189C11×C22⋊C8C2311yescharacteristic
190C11×C22⋊C8C2311yescharacteristic
191C11×#95C2311yescharacteristic
192C11×#95C2311yescharacteristic
193C11⋊#95—21no—
194C11⋊#95—21no—
195C11⋊#95—21no—
196C11⋊#95C2311yescharacteristic
197C11⋊#95C2311yescharacteristic
198C22⋊(C11⋊C8)—21no—
199C22⋊(C11⋊C8)C2311yescharacteristic
200C22⋊(C11⋊C8)C2311yescharacteristic
201(C2×D11)⋊C8—21no—
202(C2×D11)⋊C8—21no—
203#66879—21no—
204Dic11⋊C8—21no—
205Dic11⋊C8—21no—
206C8×Dic11—21no—
207#17548—111nomaximal, Sylow
208C24×C11C2×D411yescharacteristic
209C23×D11C2×D411yescharacteristic
210C11×#41—81no—
211C2×Q8×C11C22×C411yescharacteristic
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11C22×C411yescharacteristic
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—81no—
220C22×C4×C11C22×C411yescharacteristic
221C22×C4×C11C22×C411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—24no—
227C2×C22⋊D11—21no—
228C2×C22⋊D11—21no—
229C2×C22⋊D11C22⋊C411yescharacteristic
230C2×C22⋊D11C22⋊C411yescharacteristic
231C2×C22⋊D11C22⋊C411yescharacteristic
232C2×C22⋊D11C22⋊C411yescharacteristic
233C22×Dic11—24no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—81no—
241C22×Dic11—81no—
242C22×Dic11C2×D411yescharacteristic
243C22×Dic11C2×D411yescharacteristic
244C22×Dic11C2×D411yescharacteristic
245Q8×D11—81no—
246#4341—44no—
247#4341—81no—
248C2×C4×D11—24no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—81no—
252C2×C4×D11—81no—
253C2×C4×D11—81no—
254C2×C4×D11C22×C411yescharacteristic
255C2×C4×D11C22×C411yescharacteristic
256C2×C4×D11C2×D411yescharacteristic
257C2×C4×D11C2×D411yescharacteristic
258C2×Dic22—21no—
259C2×Dic22—21no—
260C2×Dic22—21no—
261C2×Dic22—81no—
262C2×Dic22C22×C411yescharacteristic
263C2×Dic22C22×C411yescharacteristic
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—81no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4C22×C411yescharacteristic
270C11×C4⋊C4C22×C411yescharacteristic
271C11×C22⋊C4—24no—
272C11×C22⋊C4—21no—
273C11×C22⋊C4—21no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—21no—
276C11×C22⋊C4—21no—
277C42×C11—21no—
278C42×C11—81no—
279C22⋊Dic11—21no—
280C22⋊Dic11—21no—
281C22⋊Dic11—21no—
282C22⋊Dic11—21no—
283C22⋊Dic11—21no—
284C22⋊Dic11—21no—
285C22⋊Dic11—21no—
286C22⋊Dic11—21no—
287C22⋊Dic11C22⋊C411yescharacteristic
288C22⋊Dic11C22⋊C411yescharacteristic
289C22⋊Dic11C22⋊C411yescharacteristic
290C22⋊Dic11C22⋊C411yescharacteristic
291(C2×D11)⋊C4—24no—
292(C2×D11)⋊C4—21no—
293(C2×D11)⋊C4—21no—
294(C2×D11)⋊C4—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4C22⋊C411yescharacteristic
297(C2×D11)⋊C4C22⋊C411yescharacteristic
298(C2×D11)⋊C4C22⋊C411yescharacteristic
299(C2×D11)⋊C4C22⋊C411yescharacteristic
300C4⋊Dic11—21no—
301C4⋊Dic11—21no—
302C4⋊Dic11—21no—
303C4⋊Dic11—21no—
304C4⋊Dic11—21no—
305C4⋊Dic11C22×C411yescharacteristic
306C4⋊Dic11C22×C411yescharacteristic
307Dic11⋊C4—24no—
308Dic11⋊C4—21no—
309Dic11⋊C4—21no—
310Dic11⋊C4—21no—
311Dic11⋊C4—21no—
312Dic11⋊C4—21no—
313Dic11⋊C4—21no—
314Dic11⋊C4—21no—
315Dic11⋊C4—21no—
316Dic11⋊C4—21no—
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320Dic11⋊C4C22⋊C411yescharacteristic
321Dic11⋊C4C22⋊C411yescharacteristic
322Dic11⋊C4C22⋊C411yescharacteristic
323Dic11⋊C4C22⋊C411yescharacteristic
324C4×Dic11—24no—
325C4×Dic11—21no—
326C4×Dic11—21no—
327C4×Dic11—21no—
328C4×Dic11—21no—
329C4×Dic11—81no—
330C4×Dic11—81no—
331C4×Dic11C22×C411yescharacteristic
332C4×Dic11C22×C411yescharacteristic
333C4×Dic11C2×D411yescharacteristic
334C4×Dic11C2×D411yescharacteristic
335#4318—81no—
336C2×C11⋊C8—21no—
337C2×C11⋊C8—21no—
338#4313—81no—
339C8×D11—81no—
340#3520—111no—
341#2974—111no—
342#2275—111no—
343#1509—111no—
344#1508—111no—
345#1508—111no—
346#1506—111no—
347#1504—111no—
348#1504—111no—
349#1503—111no—
350#1501—111no—
351#1501D1111yescharacteristic, complemented
352#1500—111no—
353C2×#328—111no—
354C2×#328—111no—
355C23×C11—21no—
356C23×C11—21no—
357C23×C11—22no—
358C23×C11—21no—
359C23×C11—41no—
360C23×C11C2×C22⋊C411yescharacteristic
361C23×C11C2×C22⋊C411yescharacteristic
362C23×C11C22×D411yescharacteristic
363C22×D11—21no—
364C22×D11—21no—
365C22×D11—22no—
366C22×D11—41no—
367C22×D11C2×C22⋊C411yescharacteristic
368C22×D11C2×C22⋊C411yescharacteristic
369Q8×C11—41no—
370D4×C11—41no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—42no—
374D4×C11—81no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—81no—
391C2×C4×C11C2×C22⋊C411yescharacteristic
392C2×C4×C11C2×C22⋊C411yescharacteristic
393C2×C4×C11C23×C411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C22⋊D11—22no—
396C22⋊D11—22no—
397C22⋊D11—22no—
398C22⋊D11—42no—
399C22⋊D11—81no—
400C22⋊D11#10414yes—
401C2×Dic11—21no—
402C2×Dic11—21no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—21no—
409C2×Dic11—21no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417C2×Dic11—81no—
418C2×Dic11—81no—
419C2×Dic11—84no—
420C2×Dic11C2×C22⋊C411yescharacteristic
421C2×Dic11C2×C22⋊C411yescharacteristic
422C2×Dic11C2×C22⋊C411yescharacteristic
423C2×Dic11C2×C22⋊C411yescharacteristic
424C2×Dic11C2×C22⋊C411yescharacteristic
425C2×Dic11C2×C22⋊C411yescharacteristic
426C4×D11—41no—
427C4×D11—41no—
428C4×D11—41no—
429C4×D11—41no—
430C4×D11—42no—
431C4×D11—81no—
432C4×D11—84no—
433Dic22—42no—
434Dic22—41no—
435Dic22—41no—
436Dic22—81no—
437Dic22—81no—
438C8×C11—41no—
439C8×C11—41no—
440C11⋊C8—41no—
441C11⋊C8—41no—
442#556—111no—
443#554—221no—
444#552—111no—
445#552—111no—
446#551—221no—
447#551—221no—
448D4×Q8—111no—
449#548—111no—
450#548—111no—
451#547—111no—
452#547—111no—
453#546—221no—
454#542—221no—
455#539—221no—
456#539—221no—
457#533—111no—
458#529—111no—
459#525—111no—
460#525C2×D1111yescharacteristic
461C2×C22⋊Q8—111no—
462C2×C22⋊Q8—111no—
463#520—221no—
464C2×C4×D4—111no—
465C2×C4×D4—221no—
466#436—221no—
467#435—221no—
468#435—221no—
469C8×D4—221no—
470#432—111no—
471#431—111no—
472#407—111no—
473#407—111no—
474C2×C22⋊C8—111no—
475C2×C22⋊C8C2×D1111yescharacteristic
476C4×C4⋊C4—111no—
477C4×C4⋊C4—221no—
478C4×C22⋊C4—111no—
479C4×C22⋊C4—221no—
480C4×C22⋊C4—221no—
481C4×C22⋊C4C2×D1111yescharacteristic
482#376—111no—
483C2×#95—111no—
484C2×#95—111no—
485#328—111no—
486#328—111no—
487#328—111no—
488#328—111no—
489#328—111no—
490#328—111no—
491#328—111no—
492#328—111no—
493#328—111no—
494#328—111no—
495#328C2×D1111yescharacteristic
496#328C2×D1111yescharacteristic
497#327—111no—
498#327—111no—
499#327C2×D1111yescharacteristic
500#327C2×D1111yescharacteristic
501C22×C11—21no—
502C22×C11—21no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—41no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11C2×#10412yes—
514C22×C11C22×C22⋊C411yescharacteristic
515C22×C11#57711yescharacteristic
516C22×C11#57811yescharacteristic
517C2×D11—21no—
518C2×D11—21no—
519C2×D11—21no—
520C2×D11—21no—
521C2×D11—21no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11C2×#10412yes—
525C4×C11—21no—
526C4×C11—21no—
527C4×C11—21no—
528C4×C11—21no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11—41no—
532C4×C11—41no—
533C4×C11—41no—
534Dic11—21no—
535Dic11—21no—
536Dic11—21no—
537Dic11—21no—
538Dic11—21no—
539Dic11—42no—
540Dic11—42no—
541Dic11—41no—
542Dic11—41no—
543Dic11—41no—
544Dic11—41no—
545Dic11C2×#10412yes—
546C2×#41—111no—
547C2×#41—221no—
548C2×#41C4×D1111yescharacteristic, complemented
549C22×Q8—111no—
550C22×Q8—111no—
551C22×D4—111no—
552C23×C4—111no—
553C23×C4—221no—
554C23×C4—221no—
555C23×C4C22×D1111yescharacteristic
556C2×M16—221no—
557C2×M16—221no—
558C22×C8—21no—
559C22×C8—221no—
560C4⋊Q8—111no—
561C4⋊Q8—111no—
562C4⋊Q8—221no—
563#126—221no—
564#126—221no—
565#126—221no—
566#126—221no—
567#126—221no—
568#125—111no—
569#125—221no—
570#125—221no—
571#125—221no—
572#124—111no—
573#124—221no—
574#124—221no—
575#124—221no—
576#123—21no—
577#123—221no—
578#123—221no—
579#123—221no—
580#123—221no—
581#123—221no—
582#123—221no—
583#123—221no—
584#123—221no—
585C22⋊Q8—111no—
586C22⋊Q8—111no—
587C22⋊Q8—111no—
588C22⋊Q8—111no—
589C22⋊Q8—111no—
590C22⋊Q8—111no—
591C22⋊Q8—111no—
592C22⋊Q8—221no—
593C22⋊Q8—221no—
594C22⋊Q8—221no—
595C22⋊Q8—221no—
596C22⋊Q8—221no—
597C22⋊Q8—221no—
598C22⋊Q8—221no—
599C22⋊Q8—221no—
600C22⋊Q8—221no—
601C22⋊Q8—221no—
602C22⋊Q8C4×D1111yescharacteristic, complemented
603C22⋊Q8C22×D1111yescharacteristic
604#121—111no—
605#121—221no—
606#121—221no—
607#121—221no—
608#121C4×D1111yescharacteristic, complemented
609#121C22×D1111yescharacteristic
610#120—21no—
611#120—221no—
612C4×Q8—111no—
613C4×Q8—111no—
614C4×Q8—111no—
615C4×Q8—221no—
616C4×Q8—221no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—111no—
620C4×D4—111no—
621C4×D4—111no—
622C4×D4—111no—
623C4×D4—111no—
624C4×D4—111no—
625C4×D4—111no—
626C4×D4—111no—
627C4×D4—111no—
628C4×D4—221no—
629C4×D4—221no—
630C4×D4—228no—
631C4×D4—221no—
632C4×D4—221no—
633C4×D4—221no—
634C4×D4—221no—
635#117—111no—
636#117—221no—
637#117—221no—
638#117—221no—
639#117—221no—
640#117C4×D1111yescharacteristic, complemented
641C2×C4⋊C4—111no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—111no—
644C2×C4⋊C4—221no—
645C2×C4⋊C4—221no—
646C2×C4⋊C4—221no—
647C2×C4⋊C4—221no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—111no—
650C2×C22⋊C4—111no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C42—21no—
655C2×C42—111no—
656C2×C42—221no—
657C2×C42—221no—
658C2×C42—221no—
659C4⋊C8—221no—
660C4⋊C8—221no—
661C22⋊C8—21no—
662C22⋊C8—111no—
663C22⋊C8—111no—
664C22⋊C8—221no—
665C22⋊C8—221no—
666C22⋊C8—221no—
667C22⋊C8C22×D1111yescharacteristic
668C22⋊C8C22×D1111yescharacteristic
669#97—221no—
670C4×C8—221no—
671#95—111no—
672#95—111no—
673#95—221no—
674#95—221no—
675#95—221no—
676#95C22×D1111yescharacteristic
677#95C22×D1111yescharacteristic
678C2×C11—21no—
679C2×C11—21no—
680C2×C11—22no—
681C2×C11—41no—
682C2×C11—81no—
683C2×C11#288311yescharacteristic
684C2×C11#289811yescharacteristic
685C2×C11C22×#10411yescharacteristic
686D11—22no—
687D11—41no—
688C24—111no—
689C24D4×D1111yescharacteristic
690#41—81no—
691#41—444no—
692#41—881no—
693C2×Q8—111no—
694C2×Q8—111no—
695C2×Q8—221no—
696C2×Q8—221no—
697C2×Q8—221no—
698C2×Q8—881no—
699C2×Q8—881no—
700C2×Q8C2×C4×D1111yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—111no—
705C2×D4—111no—
706C2×D4—111no—
707C2×D4—111no—
708C2×D4—224no—
709C2×D4—221no—
710C2×D4—221no—
711C2×D4C2×C4×D1111yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—81no—
716C22×C4—111no—
717C22×C4—111no—
718C22×C4—111no—
719C22×C4—111no—
720C22×C4—111no—
721C22×C4—111no—
722C22×C4—111no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—224no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—224no—
732C22×C4—221no—
733C22×C4—881no—
734C22×C4—881no—
735C22×C4—881no—
736C22×C4—881no—
737C22×C4—881no—
738C22×C4C2×C4×D1111yescharacteristic
739C22×C4C2×C4×D1111yescharacteristic
740C22×C4D4×D1111yescharacteristic
741C22×C4D4×D1111yescharacteristic
742C22×C4D4×D1111yescharacteristic
743C22×C4C23×D1111yescharacteristic
744M16—881no—
745M16—881no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—81no—
749C2×C8—221no—
750C2×C8—221no—
751C2×C8—881no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—111no—
755C4⋊C4—111no—
756C4⋊C4—111no—
757C4⋊C4—111no—
758C4⋊C4—111no—
759C4⋊C4—111no—
760C4⋊C4—221no—
761C4⋊C4—221no—
762C4⋊C4—221no—
763C4⋊C4—221no—
764C4⋊C4—221no—
765C4⋊C4—221no—
766C4⋊C4—221no—
767C4⋊C4—221no—
768C4⋊C4—221no—
769C4⋊C4—221no—
770C4⋊C4—221no—
771C4⋊C4—221no—
772C4⋊C4—224no—
773C4⋊C4—221no—
774C4⋊C4—221no—
775C4⋊C4—221no—
776C4⋊C4—221no—
777C4⋊C4—221no—
778C4⋊C4C2×C4×D1111yescharacteristic
779C4⋊C4C2×C4×D1111yescharacteristic
780C22⋊C4—24no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—111no—
787C22⋊C4—111no—
788C22⋊C4—111no—
789C22⋊C4—111no—
790C22⋊C4—111no—
791C22⋊C4—111no—
792C22⋊C4—111no—
793C22⋊C4—111no—
794C22⋊C4—221no—
795C22⋊C4—221no—
796C22⋊C4—221no—
797C22⋊C4—221no—
798C22⋊C4—224no—
799C22⋊C4—221no—
800C22⋊C4—221no—
801C22⋊C4—221no—
802C22⋊C4—221no—
803C22⋊C4—221no—
804C22⋊C4—221no—
805C22⋊C4—221no—
806C22⋊C4—221no—
807C42—21no—
808C42—81no—
809C42—111no—
810C42—111no—
811C42—111no—
812C42—111no—
813C42—221no—
814C42—221no—
815C42—221no—
816C42—221no—
817C42—224no—
818C42—881no—
819C42—881no—
820C11#1754811yescharacteristic, complemented, Sylow
821C23—21no—
822C23—21no—
823C23—22no—
824C23—21no—
825C23—41no—
826C23—111no—
827C23—111no—
828C23—222no—
829C23—221no—
830C23—221no—
831C23—441no—
832C23C22⋊C4×D1111yescharacteristic
833C23C22⋊C4×D1111yescharacteristic
834C23C2×D4×D1111yescharacteristic
835Q8—41no—
836Q8—441no—
837Q8—441no—
838Q8—442no—
839Q8—881no—
840Q8—881no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—42no—
845D4—81no—
846D4—114no—
847D4—222no—
848D4—222no—
849D4—222no—
850D4—442no—
851D4—881no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—81no—
868C2×C4—111no—
869C2×C4—111no—
870C2×C4—111no—
871C2×C4—111no—
872C2×C4—111no—
873C2×C4—111no—
874C2×C4—222no—
875C2×C4—221no—
876C2×C4—221no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—221no—
880C2×C4—221no—
881C2×C4—221no—
882C2×C4—221no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—442no—
888C2×C4—442no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—442no—
895C2×C4—881no—
896C2×C4—884no—
897C2×C4—881no—
898C2×C4—881no—
899C2×C4—884no—
900C2×C4C22⋊C4×D1111yescharacteristic
901C2×C4C22⋊C4×D1111yescharacteristic
902C2×C4C22×C4×D1111yescharacteristic
903C2×C4C2×D4×D1111yescharacteristic
904C8—41no—
905C8—41no—
906C8—441no—
907C8—441no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—112no—
921C22—221no—
922C22—221no—
923C22—221no—
924C22—221no—
925C22—221no—
926C22—442no—
927C22—442no—
928C22D11×#10412yes—
929C22C2×C22⋊C4×D1111yescharacteristic
930C22#1062330111yescharacteristic
931C22#1062330211yescharacteristic
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—42no—
937C4—42no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—112no—
942C4—221no—
943C4—221no—
944C4—221no—
945C4—221no—
946C4—221no—
947C4—442no—
948C4—442no—
949C4—441no—
950C4—441no—
951C4—441no—
952C4—441no—
953C2—21no—
954C2—21no—
955C2—22no—
956C2—41no—
957C2—81no—
958C2—222no—
959C2—441no—
960C2#1307707411yescharacteristic
961C2#1307714511yescharacteristic
962C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1501C2
socleC22×C11C22×C22⋊C4
prime radical#13082653C2
cosocleC22×C4×C11C24
hypercenter#1501D11
hypocenterC11#17548
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #13077647C2semidirect
3. #13070975C2semidirect
4. #13067138C2semidirect
5. #13067135C2semidirect
6. #13067134C2semidirect
7. #13067126C2semidirect
8. #13067120C2semidirect
9. #13067117C2semidirect
10. #13067113C2semidirect
11. #13067104C2semidirect
12. #13067099C2semidirect
13. C2×#10622105C2semidirect
14. D11×#328C2semidirect
15. C11×#1501C2semidirect
17. #10623362C4semidirect
18. #10623355C4semidirect
23. #10623173C4semidirect
24. #10623163C4semidirect
27. #10623142C4semidirect
30. #10623129C4semidirect
37. #10623064C4semidirect
38. #10623060C4semidirect
75. C2×C11×#41C2×C4semidirect
79. C2×Q8×D11C2×C4semidirect
81. C2×#4341C2×C4semidirect
84. C22×Dic22C2×C4semidirect
87. C11×C22⋊Q8C2×C4semidirect
89. C11×#121C2×C4semidirect
94. C11×#117C2×C4semidirect
99. #66999C2×C4semidirect
100. Q8×Dic11C2×C4semidirect
101. #66997C2×C4semidirect
105. #66991C2×C4semidirect
108. #66989C2×C4semidirect
115. D4×Dic11C2×C4semidirect
128. C2×C4⋊Dic11C2×C4semidirect
132. #66977C2×C4semidirect
133. #66977C2×C4semidirect
148. #66950C2×C4semidirect
149. #66950C2×C4semidirect
152. #66945C2×C4semidirect
154. C4⋊C4×D11C2×C4semidirect
156. #66943C2×C4semidirect
159. #66941C2×C4semidirect
161. #66940C2×C4semidirect
162. #66940C2×C4semidirect
351. #1501D11semidirect
548. C2×#41C4×D11semidirect
602. C22⋊Q8C4×D11semidirect
608. #121C4×D11semidirect
640. #117C4×D11semidirect
820. C11#17548semidirect

Maximal subgroups

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

subgroupindex
#130826532
#130776472
#130709752
#130671382
#130671352
#130671342
#130671262
#130671202
#130671172
#130671132
#130671042
#130670992
C2×#106221052
D11×#3282
C11×#15012
#1754811