Finite Group Databasebeta

← #14721497

Subgroups — #14721497

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082444C211yesmaximal, characteristic
2#13077638C211yesmaximal, characteristic, complemented
3#13071553C211yesmaximal, characteristic, complemented
4#13067192C211yesmaximal, characteristic, complemented
5#13067190C211yesmaximal, characteristic, complemented
6#13067186C211yesmaximal, characteristic, complemented
7#13067182C211yesmaximal, characteristic, complemented
8#13067170C211yesmaximal, characteristic, complemented
9#13067108C211yesmaximal, characteristic, complemented
10#13067107C211yesmaximal, characteristic, complemented
11#13067101C211yesmaximal, characteristic, complemented
12#13067099C211yesmaximal, characteristic, complemented
13D11×#328C211yesmaximal, characteristic, complemented
14D11×#327C211yesmaximal, characteristic, complemented
15C11×#1516C211yesmaximal, characteristic, complemented
16C11×#525C2211yescharacteristic
17#10623362C411yescharacteristic, complemented
18#10623360C411yescharacteristic, complemented
19#10623322C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21#10623192—21no—
22#10623190—21no—
23#10623170C411yescharacteristic, complemented
24#10623164C411yescharacteristic, complemented
25D11×C22⋊Q8C2211yescharacteristic
26#10623155C2211yescharacteristic
27#10623145C411yescharacteristic, complemented
28#10623143C411yescharacteristic, complemented
29D11×#121C2211yescharacteristic
30#10623131C2211yescharacteristic
31#10623124—21no—
32#10623120—21no—
33#10623095—21no—
34#10623089—21no—
35#10623087—21no—
36#10623076—21no—
37#10623061C411yescharacteristic, complemented
38#10623060C411yescharacteristic, complemented
39C2×C11×C22⋊C8C2211yescharacteristic, complemented
40C11×#381C2211yescharacteristic, complemented
41C4×C22⋊Dic11C2211yescharacteristic, complemented
42C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
43C8×C22⋊D11—21no—
44C8×C22⋊D11—21no—
45#10622569—21no—
46#10622558—21no—
47(C22⋊D11)⋊C8—21no—
48(C22⋊D11)⋊C8—21no—
49D11×C22⋊C8C2211yescharacteristic
50D11×C22⋊C8C2211yescharacteristic
51#10622331C2211yescharacteristic, complemented
52#10622331C2211yescharacteristic, complemented
53#10622280C2211yescharacteristic
54#10622279—21no—
55D11×#95C2211yescharacteristic
56#10622265—21no—
57#10622264C2211yescharacteristic, complemented
58#10622261C2211yescharacteristic, complemented
59C11×#328C2211yescharacteristic, complemented
60C11×#328C2211yescharacteristic, complemented
61C11×#327C2211yescharacteristic
62C11×#327C2211yescharacteristic
63#10622176C2211yescharacteristic, complemented
64#10622176C2211yescharacteristic, complemented
65#10622175C2211yescharacteristic
66#10622175C2211yescharacteristic
67#10622108C2211yescharacteristic
68#10622108C2211yescharacteristic
69#10622105C2211yescharacteristic, complemented
70#10622105C2211yescharacteristic, complemented
71#10622090C2211yescharacteristic, complemented
72#10622090C2211yescharacteristic, complemented
73#10622089C2211yescharacteristic
74#10622089C2211yescharacteristic
75C2×C11×#41C2×C411yescharacteristic, complemented
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11D411yescharacteristic
78C2×Q8×D11C2×C411yescharacteristic
79C2×D4×D11—21no—
80C2×D4×D11C2×C411yescharacteristic
81C2×#4339C2×C411yescharacteristic, complemented
82C22×C4×D11—21no—
83C22×C4×D11C2311yescharacteristic
84C22×C8×C11—21no—
85C11×#123—21no—
86C11×C22⋊Q8C2×C411yescharacteristic, complemented
87C11×C22⋊Q8C2311yescharacteristic
88C11×#121C2×C411yescharacteristic, complemented
89C11×#121C2311yescharacteristic
90C11×#120—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C11×#117C2×C411yescharacteristic, complemented
94C2×C11×C22⋊C4—21no—
95#67006—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11D411yescharacteristic
98#67000C2×C411yescharacteristic, complemented
99#66999C2×C411yescharacteristic
100Q8×Dic11C2×C411yescharacteristic, complemented
101#66992—21no—
102#66992—21no—
103#66991—21no—
104#66991—21no—
105#66991—21no—
106#66991C2×C411yescharacteristic
107#66990—21no—
108#66990—21no—
109#66989—21no—
110#66989C2×C411yescharacteristic, complemented
111#66988—21no—
112#66988—21no—
113D4×Dic11—21no—
114D4×Dic11C2×C411yescharacteristic, complemented
115#66983C2×C411yescharacteristic, complemented
116#66983C2311yescharacteristic
117#66982—21no—
118#66982—21no—
119C4×C22⋊D11—21no—
120C4×C22⋊D11—21no—
121C4×C22⋊D11—21no—
122C4×C22⋊D11C2×C411yescharacteristic
123C4×C22⋊D11C2×C411yescharacteristic
124C4×C22⋊D11C2×C411yescharacteristic
125C4×C22⋊D11C2×C411yescharacteristic
126C4×C22⋊D11D411yescharacteristic
127C4×C22⋊D11D411yescharacteristic
128C4×C22⋊D11D411yescharacteristic
129C4×C22⋊D11D411yescharacteristic
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4D411yescharacteristic
133#66979C2×C411yescharacteristic, complemented
134#66977—21no—
135#66977C2×C411yescharacteristic, complemented
136#66977C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4D411yescharacteristic
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11C2311yescharacteristic
142C22×C11⋊C8—21no—
143C2×C8×D11—21no—
144C2×C8×D11—21no—
145#66951—21no—
146#66950C2×C411yescharacteristic
147#66949—21no—
148#66949—21no—
149#66948C2×C411yescharacteristic
150#66946—21no—
151#66946C2×C411yescharacteristic, complemented
152#66945—21no—
153#66945—21no—
154C4⋊C4×D11—21no—
155C4⋊C4×D11C2×C411yescharacteristic
156C4⋊C4×D11C2×C411yescharacteristic
157#66943C2×C411yescharacteristic, complemented
158#66943C2×C411yescharacteristic, complemented
159#66942—21no—
160#66940C2×C411yescharacteristic, complemented
161#66939—21no—
162#66938—21no—
163#66937—21no—
164#66937—21no—
165#66937—21no—
166#66936—21no—
167#66936—21no—
168#66936—21no—
169#66936—21no—
170(C22⋊D11)⋊C4—21no—
171(C22⋊D11)⋊C4—21no—
172C22⋊C4×D11—21no—
173C22⋊C4×D11—21no—
174C22⋊C4×D11—21no—
175#66932—21no—
176#66932—21no—
177#66932—21no—
178#66932—21no—
179#66931—21no—
180#66930—21no—
181#66929—21no—
182C4×D44—21no—
183#66925—21no—
184#66923—21no—
185C11×C22⋊C8—21no—
186C11×C22⋊C8C2311yescharacteristic
187C11×C22⋊C8C2311yescharacteristic
188C11×#95—21no—
189C11×#95C2311yescharacteristic
190C11×#95C2311yescharacteristic
191C11⋊#95—21no—
192C11⋊#95—21no—
193C11⋊#95—21no—
194C11⋊#95—21no—
195C11⋊#95C2311yescharacteristic
196C11⋊#95C2311yescharacteristic
197C22⋊(C11⋊C8)—21no—
198C22⋊(C11⋊C8)C2311yescharacteristic
199C22⋊(C11⋊C8)C2311yescharacteristic
200(C2×D11)⋊C8—21no—
201(C2×D11)⋊C8—21no—
202Dic11⋊C8—21no—
203Dic11⋊C8—21no—
204C8×Dic11—21no—
205C8×Dic11—21no—
206#17615—111nomaximal, Sylow
207C24×C11C2×D411yescharacteristic
208C23×D11—21no—
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—21no—
227C2×C22⋊D11—21no—
228C2×C22⋊D11—21no—
229C2×C22⋊D11—21no—
230C2×C22⋊D11—21no—
231C2×C22⋊D11—22no—
232C2×C22⋊D11—22no—
233C2×C22⋊D11C22⋊C411yescharacteristic
234C2×C22⋊D11C22⋊C411yescharacteristic
235C2×C22⋊D11C22⋊C411yescharacteristic
236C2×C22⋊D11C22⋊C411yescharacteristic
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11C2×D411yescharacteristic
241C22×Dic11C2×D411yescharacteristic
242C22×Dic11C2×D411yescharacteristic
243Q8×D11—81no—
244D4×D11—42no—
245D4×D11—42no—
246D4×D11—81no—
247#4339—81no—
248C2×D44—21no—
249C2×D44C22×C411yescharacteristic
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—42no—
256C2×C4×D11—42no—
257C2×C4×D11—81no—
258C2×C4×D11—81no—
259C2×C4×D11C22×C411yescharacteristic
260C2×C4×D11C22×C411yescharacteristic
261C2×C4×D11C2×D411yescharacteristic
262C2×C4×D11C2×D411yescharacteristic
263C2×Dic22—21no—
264C2×Dic22C22×C411yescharacteristic
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—81no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4C22×C411yescharacteristic
271C11×C4⋊C4C22×C411yescharacteristic
272C11×C22⋊C4—21no—
273C11×C22⋊C4—21no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—21no—
276C11×C22⋊C4—21no—
277C11×C22⋊C4—81no—
278C42×C11—21no—
279C22⋊Dic11—21no—
280C22⋊Dic11—21no—
281C22⋊Dic11—21no—
282C22⋊Dic11—21no—
283C22⋊Dic11—21no—
284C22⋊Dic11—21no—
285C22⋊Dic11—21no—
286C22⋊Dic11—42no—
287C22⋊Dic11C22⋊C411yescharacteristic
288C22⋊Dic11C22⋊C411yescharacteristic
289C22⋊Dic11C22⋊C411yescharacteristic
290C22⋊Dic11C22⋊C411yescharacteristic
291(C2×D11)⋊C4—21no—
292(C2×D11)⋊C4—21no—
293(C2×D11)⋊C4—21no—
294(C2×D11)⋊C4—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297(C2×D11)⋊C4—21no—
298(C2×D11)⋊C4—21no—
299(C2×D11)⋊C4—42no—
300(C2×D11)⋊C4C22⋊C411yescharacteristic
301(C2×D11)⋊C4C22⋊C411yescharacteristic
302(C2×D11)⋊C4C22⋊C411yescharacteristic
303(C2×D11)⋊C4C22⋊C411yescharacteristic
304C4⋊Dic11—21no—
305C4⋊Dic11—21no—
306C4⋊Dic11—21no—
307C4⋊Dic11—21no—
308C4⋊Dic11C22×C411yescharacteristic
309C4⋊Dic11C22×C411yescharacteristic
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—81no—
319Dic11⋊C4C22⋊C411yescharacteristic
320Dic11⋊C4C22⋊C411yescharacteristic
321Dic11⋊C4C22⋊C411yescharacteristic
322Dic11⋊C4C22⋊C411yescharacteristic
323C4×Dic11—21no—
324C4×Dic11—21no—
325C4×Dic11—21no—
326C4×Dic11—42no—
327C4×Dic11—81no—
328C4×Dic11C22×C411yescharacteristic
329C4×Dic11C22×C411yescharacteristic
330C4×Dic11C2×D411yescharacteristic
331C4×Dic11C2×D411yescharacteristic
332C2×C11⋊C8—21no—
333C2×C11⋊C8—21no—
334C2×C11⋊C8—81no—
335C8×D11—81no—
336C8×D11—81no—
337#3505—111no—
338#2972—111no—
339#2353—111no—
340#1521—111no—
341#1521—111no—
342#1520—111no—
343#1519—111no—
344#1516—111no—
345#1516D1111yescharacteristic, complemented
346#1501—111no—
347#1501—111no—
348#1500—111no—
349#1500—111no—
350C2×#328—111no—
351C2×#327—111no—
352C23×C11—21no—
353C23×C11—21no—
354C23×C11—21no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11C2×C22⋊C411yescharacteristic
358C23×C11C2×C22⋊C411yescharacteristic
359C23×C11C22×D411yescharacteristic
360C22×D11—21no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—42no—
364C22×D11—81no—
365C22×D11—81no—
366C22×D11C2×C22⋊C411yescharacteristic
367C22×D11C2×C22⋊C411yescharacteristic
368C22×D11#13512yes—
369C22×D11#13512yes—
370Q8×C11—41no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—81no—
375D4×C11—81no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—41no—
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—41no—
391C2×C4×C11—81no—
392C2×C4×C11C2×C22⋊C411yescharacteristic
393C2×C4×C11C2×C22⋊C411yescharacteristic
394C2×C4×C11C23×C411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C22⋊D11—22no—
397C22⋊D11—22no—
398C22⋊D11—22no—
399C22⋊D11—22no—
400C22⋊D11—41no—
401C22⋊D11—41no—
402C22⋊D11—42no—
403C22⋊D11—81no—
404C22⋊D11—81no—
405C22⋊D11—81no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—22no—
409C2×Dic11—21no—
410C2×Dic11—21no—
411C2×Dic11—21no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—81no—
420C2×Dic11C2×C22⋊C411yescharacteristic
421C2×Dic11C2×C22⋊C411yescharacteristic
422C2×Dic11C2×C22⋊C411yescharacteristic
423C2×Dic11C2×C22⋊C411yescharacteristic
424C2×Dic11C2×C22⋊C411yescharacteristic
425C2×Dic11C2×C22⋊C411yescharacteristic
426D44—41no—
427D44—42no—
428C4×D11—41no—
429C4×D11—41no—
430C4×D11—41no—
431C4×D11—41no—
432C4×D11—42no—
433C4×D11—81no—
434C4×D11—81no—
435C4×D11—81no—
436C4×D11—81no—
437C4×D11—84no—
438Dic22—41no—
439Dic22—81no—
440C8×C11—41no—
441C8×C11—41no—
442C11⋊C8—41no—
443C11⋊C8—41no—
444#553—111no—
445#553—111no—
446#553—221no—
447#553—221no—
448#552—111no—
449#552—111no—
450#551—221no—
451#551—221no—
452#548—111no—
453#548—111no—
454#546—111no—
455#546—111no—
456#539—221no—
457#538—221no—
458#534—221no—
459#529—111no—
460#529—111no—
461#525—111no—
462#525C2×D1111yescharacteristic
463C2×C22⋊Q8—111no—
464C2×#121—111no—
465#518—221no—
466C2×C4×D4—111no—
467C8×D4—221no—
468C8×D4—221no—
469C8×D4—221no—
470C8×D4—221no—
471#431—111no—
472#431—111no—
473C2×C22⋊C8—111no—
474C2×C22⋊C8—111no—
475C2×C22⋊C8—111no—
476C2×C22⋊C8C2×D1111yescharacteristic, complemented
477#388—221no—
478#387—221no—
479#386—221no—
480#383—111no—
481#381C2×D1111yescharacteristic, complemented
482#380—111no—
483C4×C22⋊C4—111no—
484C4×C22⋊C4—221no—
485#376—111no—
486C2×#95—111no—
487#328—111no—
488#328—111no—
489#328—111no—
490#328—111no—
491#328—111no—
492#328—111no—
493#328C2×D1111yescharacteristic, complemented
494#328C2×D1111yescharacteristic, complemented
495#327—111no—
496#327—111no—
497#327—111no—
498#327—111no—
499#327—111no—
500#327—111no—
501#327C2×D1111yescharacteristic
502#327C2×D1111yescharacteristic
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11—41no—
514C22×C11—81no—
515C22×C11—81no—
516C22×C11C22×C22⋊C411yescharacteristic
517C22×C11C2×#13511yescharacteristic
518C22×C11C2×#13511yescharacteristic
519C2×D11—21no—
520C2×D11—21no—
521C2×D11—21no—
522C2×D11—21no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—41no—
526C2×D11—41no—
527C2×D11—41no—
528C2×D11—162no—
529C2×D11#41612yes—
530C2×D11#41612yes—
531C4×C11—21no—
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—41no—
536C4×C11—41no—
537C4×C11—41no—
538C4×C11—81no—
539C4×C11—81no—
540Dic11—21no—
541Dic11—21no—
542Dic11—21no—
543Dic11—21no—
544Dic11—21no—
545Dic11—21no—
546Dic11—42no—
547Dic11—41no—
548Dic11—41no—
549Dic11—41no—
550Dic11—81no—
551C2×#41—111no—
552C2×#41C4×D1111yescharacteristic, complemented
553C22×Q8—111no—
554C22×D4—111no—
555C22×D4—111no—
556C22×D4—221no—
557C23×C4—111no—
558C23×C4—221no—
559C23×C4C22×D1111yescharacteristic
560C22×C8—21no—
561C22×C8—221no—
562C22×C8—221no—
563C22×C8—221no—
564#126—221no—
565#126—221no—
566#126—221no—
567#126—221no—
568#126—221no—
569#126—221no—
570#125—111no—
571#125—111no—
572#125—221no—
573#125—221no—
574#124—111no—
575#124—111no—
576#124—221no—
577#124—221no—
578#123—21no—
579#123—221no—
580#123—221no—
581#123—221no—
582#123—221no—
583#123—221no—
584#123—221no—
585#123—221no—
586#123—221no—
587#123—221no—
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⋊Q8C4×D1111yescharacteristic, complemented
597C22⋊Q8C22×D1111yescharacteristic
598#121—111no—
599#121—111no—
600#121—111no—
601#121—111no—
602#121—221no—
603#121—221no—
604#121—221no—
605#121—221no—
606#121—221no—
607#121—221no—
608#121—221no—
609#121—221no—
610#121C4×D1111yescharacteristic, complemented
611#121C22×D1111yescharacteristic
612#120—21no—
613#120—221no—
614#120—221no—
615#120—221no—
616C4×Q8—111no—
617C4×Q8—111no—
618C4×D4—21no—
619C4×D4—21no—
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—111no—
629C4×D4—111no—
630C4×D4—221no—
631C4×D4—221no—
632C4×D4—221no—
633C4×D4—221no—
634C4×D4—221no—
635C4×D4—221no—
636C4×D4—221no—
637C4×D4—221no—
638#117—111no—
639#117—221no—
640#117—221no—
641#117—221no—
642#117—221no—
643#117C4×D1111yescharacteristic, complemented
644C2×C4⋊C4—111no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—111no—
647C2×C4⋊C4—221no—
648C2×C4⋊C4—221no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—111no—
651C2×C22⋊C4—111no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C22⋊C4—221no—
655C2×C22⋊C4—221no—
656C2×C22⋊C4—221no—
657C2×C22⋊C4—221no—
658C2×C42—111no—
659C2×C42—221no—
660C2×C42—221no—
661C4⋊C8—221no—
662C4⋊C8—221no—
663C22⋊C8—21no—
664C22⋊C8—111no—
665C22⋊C8—111no—
666C22⋊C8—221no—
667C22⋊C8—221no—
668C22⋊C8—221no—
669C22⋊C8C22×D1111yescharacteristic
670C22⋊C8C22×D1111yescharacteristic
671C4×C8—221no—
672C4×C8—221no—
673#95—21no—
674#95—111no—
675#95—111no—
676#95—221no—
677#95—221no—
678#95—221no—
679#95—221no—
680#95C22×D1111yescharacteristic
681#95C22×D1111yescharacteristic
682C2×C11—21no—
683C2×C11—21no—
684C2×C11—41no—
685C2×C11—41no—
686C2×C11—81no—
687C2×C11#288311yescharacteristic
688C2×C11C2×#41611yescharacteristic
689C2×C11#290111yescharacteristic
690D11—22no—
691D11—22no—
692D11—81no—
693C24—111no—
694C24—221no—
695C24D4×D1111yescharacteristic
696#41—81no—
697#41—881no—
698C2×Q8—111no—
699C2×Q8—221no—
700C2×Q8—881no—
701C2×Q8C2×C4×D1111yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—111no—
706C2×D4—111no—
707C2×D4—111no—
708C2×D4—111no—
709C2×D4—111no—
710C2×D4—221no—
711C2×D4—221no—
712C2×D4—222no—
713C2×D4—222no—
714C2×D4—221no—
715C2×D4—221no—
716C2×D4—221no—
717C2×D4—221no—
718C2×D4—442no—
719C2×D4—442no—
720C2×D4—881no—
721C2×D4C2×C4×D1111yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—81no—
726C22×C4—111no—
727C22×C4—111no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—111no—
731C22×C4—111no—
732C22×C4—111no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—442no—
742C22×C4—442no—
743C22×C4—881no—
744C22×C4—881no—
745C22×C4C2×C4×D1111yescharacteristic
746C22×C4C2×C4×D1111yescharacteristic
747C22×C4D4×D1111yescharacteristic
748C22×C4D4×D1111yescharacteristic
749C22×C4D4×D1111yescharacteristic
750C22×C4C23×D1111yescharacteristic
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—81no—
754C2×C8—221no—
755C2×C8—221no—
756C2×C8—881no—
757C2×C8—881no—
758C2×C8—881no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—111no—
762C4⋊C4—111no—
763C4⋊C4—111no—
764C4⋊C4—111no—
765C4⋊C4—111no—
766C4⋊C4—111no—
767C4⋊C4—221no—
768C4⋊C4—221no—
769C4⋊C4—221no—
770C4⋊C4—221no—
771C4⋊C4—221no—
772C4⋊C4—221no—
773C4⋊C4—221no—
774C4⋊C4—221no—
775C4⋊C4—221no—
776C4⋊C4—221no—
777C4⋊C4—221no—
778C4⋊C4—221no—
779C4⋊C4—881no—
780C4⋊C4C2×C4×D1111yescharacteristic
781C4⋊C4C2×C4×D1111yescharacteristic
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—81no—
788C22⋊C4—111no—
789C22⋊C4—111no—
790C22⋊C4—111no—
791C22⋊C4—111no—
792C22⋊C4—111no—
793C22⋊C4—111no—
794C22⋊C4—111no—
795C22⋊C4—111no—
796C22⋊C4—221no—
797C22⋊C4—221no—
798C22⋊C4—221no—
799C22⋊C4—221no—
800C22⋊C4—221no—
801C22⋊C4—221no—
802C22⋊C4—221no—
803C22⋊C4—221no—
804C22⋊C4—221no—
805C22⋊C4—221no—
806C22⋊C4—221no—
807C22⋊C4—221no—
808C22⋊C4—221no—
809C22⋊C4—221no—
810C22⋊C4—221no—
811C22⋊C4—442no—
812C22⋊C4—442no—
813C42—21no—
814C42—111no—
815C42—111no—
816C42—111no—
817C42—111no—
818C42—221no—
819C42—221no—
820C42—221no—
821C42—442no—
822C42—881no—
823C11#1761511yescharacteristic, complemented, Sylow
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—111no—
830C23—111no—
831C23—112no—
832C23—112no—
833C23—221no—
834C23—441no—
835C23—441no—
836C23—442no—
837C23—881no—
838C23—881no—
839C23C22⋊C4×D1111yescharacteristic
840C23C22⋊C4×D1111yescharacteristic
841C23C2×D4×D1111yescharacteristic
842Q8—41no—
843Q8—441no—
844Q8—881no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—81no—
849D4—81no—
850D4—222no—
851D4—222no—
852D4—222no—
853D4—222no—
854D4—441no—
855D4—442no—
856D4—442no—
857D4—441no—
858D4—441no—
859D4—881no—
860D4—881no—
861D4—881no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—81no—
878C2×C4—111no—
879C2×C4—111no—
880C2×C4—111no—
881C2×C4—111no—
882C2×C4—111no—
883C2×C4—111no—
884C2×C4—221no—
885C2×C4—221no—
886C2×C4—222no—
887C2×C4—221no—
888C2×C4—221no—
889C2×C4—221no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—442no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—881no—
903C2×C4—881no—
904C2×C4—881no—
905C2×C4—881no—
906C2×C4—884no—
907C2×C4—881no—
908C2×C4C22⋊C4×D1111yescharacteristic
909C2×C4C22⋊C4×D1111yescharacteristic
910C2×C4C22×C4×D1111yescharacteristic
911C2×C4C2×D4×D1111yescharacteristic
912C8—41no—
913C8—41no—
914C8—441no—
915C8—441no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—112no—
930C22—112no—
931C22—221no—
932C22—221no—
933C22—221no—
934C22—221no—
935C22—442no—
936C22—442no—
937C22—441no—
938C22—441no—
939C22—441no—
940C22—1762no—
941C22C2×C22⋊C4×D1111yescharacteristic
942C22D11×#13511yescharacteristic
943C22D11×#13511yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C4—221no—
954C4—221no—
955C4—221no—
956C4—221no—
957C4—221no—
958C4—221no—
959C4—442no—
960C4—441no—
961C4—441no—
962C4—441no—
963C4—881no—
964C2—21no—
965C2—21no—
966C2—41no—
967C2—41no—
968C2—81no—
969C2—222no—
970C2—222no—
971C2—881no—
972C2#1307707411yescharacteristic
973C2D11×#41611yescharacteristic
974C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1516C2
socleC22×C11C22×C22⋊C4
prime radical#13082444C2
cosocleC22×C4×C11C24
hypercenter#1516D11
hypocenterC11#17615
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #13077638C2semidirect
3. #13071553C2semidirect
4. #13067192C2semidirect
5. #13067190C2semidirect
6. #13067186C2semidirect
7. #13067182C2semidirect
8. #13067170C2semidirect
9. #13067108C2semidirect
10. #13067107C2semidirect
11. #13067101C2semidirect
12. #13067099C2semidirect
13. D11×#328C2semidirect
14. D11×#327C2semidirect
15. C11×#1516C2semidirect
17. #10623362C4semidirect
18. #10623360C4semidirect
23. #10623170C4semidirect
24. #10623164C4semidirect
27. #10623145C4semidirect
28. #10623143C4semidirect
37. #10623061C4semidirect
38. #10623060C4semidirect
39. C2×C11×C22⋊C8C22semidirect
40. C11×#381C22semidirect
41. C4×C22⋊Dic11C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
51. #10622331C22semidirect
52. #10622331C22semidirect
57. #10622264C22semidirect
58. #10622261C22semidirect
59. C11×#328C22semidirect
60. C11×#328C22semidirect
63. #10622176C22semidirect
64. #10622176C22semidirect
69. #10622105C22semidirect
70. #10622105C22semidirect
71. #10622090C22semidirect
72. #10622090C22semidirect
75. C2×C11×#41C2×C4semidirect
81. C2×#4339C2×C4semidirect
86. C11×C22⋊Q8C2×C4semidirect
88. C11×#121C2×C4semidirect
93. C11×#117C2×C4semidirect
98. #67000C2×C4semidirect
100. Q8×Dic11C2×C4semidirect
110. #66989C2×C4semidirect
114. D4×Dic11C2×C4semidirect
115. #66983C2×C4semidirect
133. #66979C2×C4semidirect
135. #66977C2×C4semidirect
151. #66946C2×C4semidirect
157. #66943C2×C4semidirect
158. #66943C2×C4semidirect
160. #66940C2×C4semidirect
345. #1516D11semidirect
476. C2×C22⋊C8C2×D11semidirect
481. #381C2×D11semidirect
493. #328C2×D11semidirect
494. #328C2×D11semidirect
552. C2×#41C4×D11semidirect
596. C22⋊Q8C4×D11semidirect
610. #121C4×D11semidirect
643. #117C4×D11semidirect
823. C11#17615semidirect

Maximal subgroups

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

subgroupindex
#130824442
#130776382
#130715532
#130671922
#130671902
#130671862
#130671822
#130671702
#130671082
#130671072
#130671012
#130670992
D11×#3282
D11×#3272
C11×#15162
#1761511