Finite Group Databasebeta

← #14721495

Subgroups — #14721495

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#13082451C211yesmaximal, characteristic
2#13077639C211yesmaximal, characteristic, complemented
3#13071549C211yesmaximal, characteristic, complemented
4#13067191C211yesmaximal, characteristic, complemented
5#13067186C211yesmaximal, characteristic, complemented
6#13067182C211yesmaximal, characteristic, complemented
7#13067171C211yesmaximal, characteristic, complemented
8#13067169C211yesmaximal, characteristic, complemented
9#13067106C211yesmaximal, characteristic, complemented
10#13067104C211yesmaximal, characteristic, complemented
11#13067103C211yesmaximal, characteristic, complemented
12#13067102C211yesmaximal, characteristic, complemented
13D11×#328C211yesmaximal, characteristic, complemented
14D11×#327C211yesmaximal, characteristic, complemented
15C11×#1521C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623240—21no—
18#10623236—21no—
19#10623226C411yescharacteristic, complemented
20#10623225C411yescharacteristic, complemented
21#10623208C411yescharacteristic, complemented
22#10623207C411yescharacteristic, complemented
23#10623196—21no—
24#10623184—21no—
25#10623158C2211yescharacteristic
26D11×C22⋊Q8C2211yescharacteristic
27#10623137C2211yescharacteristic
28D11×#121C2211yescharacteristic
29#10623112C411yescharacteristic, complemented
30#10623107C411yescharacteristic, complemented
31#10623091—21no—
32#10623089C411yescharacteristic, complemented
33#10623085C411yescharacteristic, complemented
34#10623076—21no—
35#10623061—21no—
36#10623058—21no—
37#10623010C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C11×#431C2211yescharacteristic, complemented
40C11×#383C2211yescharacteristic, complemented
41#10622545C2211yescharacteristic, complemented
42#10622538C2211yescharacteristic, complemented
43#10622447—21no—
44#10622447—21no—
45D11×C22⋊C8C2211yescharacteristic
46D11×C22⋊C8C2211yescharacteristic
47D11×C22⋊C8C2211yescharacteristic, complemented
48D11×C22⋊C8C2211yescharacteristic, complemented
49C8×D44—21no—
50C8×D44—21no—
51#10622282—21no—
52#10622280C2211yescharacteristic
53#10622279—21no—
54#10622279C2211yescharacteristic, complemented
55#10622278—21no—
56#10622277C2211yescharacteristic, complemented
57D11×#95C2211yescharacteristic
58#10622266—21no—
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×#4343C2×C411yescharacteristic, complemented
76C2×Q8×D11C2×C411yescharacteristic
77C2×#4341C2×C411yescharacteristic, complemented
78C2×D4×D11—21no—
79C2×D4×D11C2×C411yescharacteristic
80C22×D44D411yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11C2311yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C11×#126—21no—
85C11×#125C2×C411yescharacteristic, complemented
86C11×#124C2×C411yescharacteristic, complemented
87C11×#123—21no—
88C11×C22⋊Q8C2311yescharacteristic
89C11×#121C2311yescharacteristic
90C4×Q8×C11C2×C411yescharacteristic, complemented
91C4×D4×C11—21no—
92C4×D4×C11C2×C411yescharacteristic, complemented
93C11×#117—21no—
94C2×C42×C11C2311yescharacteristic
95#66999C2×C411yescharacteristic
96#66999C2×C411yescharacteristic, complemented
97#66992—21no—
98#66991C2×C411yescharacteristic
99#66991C2×C411yescharacteristic, complemented
100#66990—21no—
101D4×Dic11—21no—
102#66983—21no—
103#66983C2311yescharacteristic
104#66982—21no—
105#66982—21no—
106C4×C22⋊D11—21no—
107C4×C22⋊D11—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4D411yescharacteristic
113C2×(C2×D11)⋊C4D411yescharacteristic
114C2×C4⋊Dic11D411yescharacteristic
115#66977C2311yescharacteristic
116C2×Dic11⋊C4—21no—
117C2×C4×Dic11—21no—
118C2×C4×Dic11—21no—
119C2×C8×D11—21no—
120C2×C8×D11—21no—
121C2×C8×D11—21no—
122C2×C8×D11—21no—
123#66951—21no—
124#66951—21no—
125#66950—21no—
126#66950C2×C411yescharacteristic
127#66950C2×C411yescharacteristic, complemented
128#66949—21no—
129#66948—21no—
130#66948—21no—
131#66948C2×C411yescharacteristic
132#66948C2×C411yescharacteristic, complemented
133#66947—21no—
134#66947—21no—
135#66947—21no—
136#66947—21no—
137#66946—21no—
138#66946—21no—
139#66945—21no—
140#66945C2×C411yescharacteristic, complemented
141#66945C2×C411yescharacteristic, complemented
142C4⋊C4×D11—21no—
143C4⋊C4×D11C2×C411yescharacteristic
144C4⋊C4×D11C2×C411yescharacteristic
145#66943—21no—
146#66942—21no—
147#66939—21no—
148#66938—21no—
149#66937—21no—
150#66937—21no—
151#66937—21no—
152#66937—21no—
153#66936—21no—
154#66936—21no—
155#66935—21no—
156#66935—21no—
157#66935—21no—
158(C22⋊D11)⋊C4—21no—
159(C22⋊D11)⋊C4—21no—
160(C22⋊D11)⋊C4—21no—
161C22⋊C4×D11—21no—
162C22⋊C4×D11—21no—
163C22⋊C4×D11—21no—
164#66932—21no—
165#66931—21no—
166#66931—21no—
167#66929—21no—
168#66929—21no—
169#66928—21no—
170#66928C2×C411yescharacteristic, complemented
171C4×D44—21no—
172C4×D44C2×C411yescharacteristic
173C4×D44C2×C411yescharacteristic
174C4×D44C2×C411yescharacteristic
175C4×D44C2×C411yescharacteristic
176C4×D44C2×C411yescharacteristic, complemented
177C4×D44D411yescharacteristic
178C4×D44D411yescharacteristic
179C4×D44D411yescharacteristic
180C4×D44D411yescharacteristic
181#66925—21no—
182#66925—21no—
183#66923C2×C411yescharacteristic, complemented
184C4×Dic22C2×C411yescharacteristic, complemented
185C11×C4⋊C8—21no—
186C11×C22⋊C8C2311yescharacteristic
187C11×C22⋊C8C2311yescharacteristic
188C4×C8×C11—21no—
189C11×#95—21no—
190C11×#95—21no—
191C11×#95C2311yescharacteristic
192C11×#95C2311yescharacteristic
193C11⋊#95—21no—
194C11⋊#95—21no—
195C11⋊#95—21no—
196C11⋊#95C2311yescharacteristic
197C11⋊#95C2311yescharacteristic
198C22⋊(C11⋊C8)C2311yescharacteristic
199C22⋊(C11⋊C8)C2311yescharacteristic
200(C2×D11)⋊C8—21no—
201(C2×D11)⋊C8—21no—
202(C2×D11)⋊C8—21no—
203(C2×D11)⋊C8—21no—
204C4⋊(C11⋊C8)—21no—
205C4×C11⋊C8—21no—
206#17615—111nomaximal, Sylow
207C23×D11—21no—
208C23×D11C2×D411yescharacteristic
209C23×D11C2×D411yescharacteristic
210C2×Q8×C11C22×C411yescharacteristic
211C2×D4×C11—21no—
212C2×D4×C11C22×C411yescharacteristic
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2411yescharacteristic
219C2×C22⋊D11—21no—
220C2×C22⋊D11—21no—
221C2×C22⋊D11—21no—
222C2×C22⋊D11—21no—
223C2×C22⋊D11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229#4343—81no—
230Q8×D11—81no—
231#4341—81no—
232D4×D11—42no—
233D4×D11—42no—
234D4×D11—81no—
235C2×D44—21no—
236C2×D44—21no—
237C2×D44—21no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44C22⋊C411yescharacteristic
241C2×D44C22⋊C411yescharacteristic
242C2×D44C22⋊C411yescharacteristic
243C2×D44C22⋊C411yescharacteristic
244C2×D44C22×C411yescharacteristic
245C2×C4×D11—21no—
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—21no—
250C2×C4×D11—42no—
251C2×C4×D11—42no—
252C2×C4×D11—81no—
253C2×C4×D11—81no—
254C2×C4×D11—81no—
255C2×C4×D11C22×C411yescharacteristic
256C2×C4×D11C22×C411yescharacteristic
257C2×C4×D11C22×C411yescharacteristic
258C2×C4×D11C22×C411yescharacteristic
259C2×C4×D11C2×D411yescharacteristic
260C2×C4×D11C2×D411yescharacteristic
261C2×C4×D11C2×D411yescharacteristic
262C2×C4×D11C2×D411yescharacteristic
263C2×Dic22—21no—
264C2×Dic22C22×C411yescharacteristic
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4C22×C411yescharacteristic
272C11×C4⋊C4C22×C411yescharacteristic
273C11×C22⋊C4—21no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—21no—
276C11×C22⋊C4—21no—
277C11×C22⋊C4—21no—
278C42×C11—21no—
279C42×C11C22×C411yescharacteristic
280C42×C11C22×C411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C22⋊Dic11—21no—
284C22⋊Dic11—21no—
285C22⋊Dic11—21no—
286(C2×D11)⋊C4—21no—
287(C2×D11)⋊C4—21no—
288(C2×D11)⋊C4—21no—
289(C2×D11)⋊C4—21no—
290(C2×D11)⋊C4—21no—
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—42no—
299(C2×D11)⋊C4—42no—
300(C2×D11)⋊C4—81no—
301(C2×D11)⋊C4C22⋊C411yescharacteristic
302(C2×D11)⋊C4C22⋊C411yescharacteristic
303(C2×D11)⋊C4C22⋊C411yescharacteristic
304(C2×D11)⋊C4C22⋊C411yescharacteristic
305(C2×D11)⋊C4C22⋊C411yescharacteristic
306(C2×D11)⋊C4C22⋊C411yescharacteristic
307(C2×D11)⋊C4C22⋊C411yescharacteristic
308(C2×D11)⋊C4C22⋊C411yescharacteristic
309C4⋊Dic11—21no—
310C4⋊Dic11—21no—
311C4⋊Dic11C22⋊C411yescharacteristic
312C4⋊Dic11C22⋊C411yescharacteristic
313C4⋊Dic11C22⋊C411yescharacteristic
314C4⋊Dic11C22⋊C411yescharacteristic
315C4⋊Dic11C22×C411yescharacteristic
316C4⋊Dic11C22×C411yescharacteristic
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320Dic11⋊C4—21no—
321Dic11⋊C4—21no—
322Dic11⋊C4—21no—
323Dic11⋊C4—21no—
324Dic11⋊C4—21no—
325Dic11⋊C4—81no—
326C4×Dic11—21no—
327C4×Dic11—21no—
328C4×Dic11—21no—
329C4×Dic11—42no—
330C4×Dic11—81no—
331C2×C11⋊C8—21no—
332C2×C11⋊C8—21no—
333C8×D11—81no—
334C8×D11—81no—
335C8×D11—81no—
336C8×D11—81no—
337#3505—111no—
338#2972—111no—
339#2353—111no—
340#1521—111no—
341#1521D1111yescharacteristic, complemented
342#1520—111no—
343#1519—111no—
344#1516—111no—
345#1516—111no—
346#1501—111no—
347#1501—111no—
348#1500—111no—
349#1500—111no—
350C2×#328—111no—
351C2×#327—111no—
352C23×C11—21no—
353C23×C11C22×D411yescharacteristic
354C22×D11—21no—
355C22×D11—21no—
356C22×D11—21no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—42no—
362C22×D11—81no—
363C22×D11—81no—
364C22×D11C2×C22⋊C411yescharacteristic
365C22×D11C2×C22⋊C411yescharacteristic
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—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
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—81no—
388C2×C4×C11C2×C22⋊C411yescharacteristic
389C2×C4×C11C2×C22⋊C411yescharacteristic
390C2×C4×C11C2×C22⋊C411yescharacteristic
391C2×C4×C11C2×C22⋊C411yescharacteristic
392C2×C4×C11C23×C411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C22⋊D11—41no—
395C22⋊D11—41no—
396C22⋊D11—42no—
397C22⋊D11—81no—
398C22⋊D11—81no—
399C22⋊D11—81no—
400C2×Dic11—22no—
401C2×Dic11—21no—
402C2×Dic11—21no—
403C2×Dic11—21no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—81no—
412C2×Dic11C2×C22⋊C411yescharacteristic
413C2×Dic11C2×C22⋊C411yescharacteristic
414C2×Dic11C2×C22⋊C411yescharacteristic
415C2×Dic11C2×C22⋊C411yescharacteristic
416D44—22no—
417D44—22no—
418D44—22no—
419D44—22no—
420D44—41no—
421D44—42no—
422D44—81no—
423D44—81no—
424C4×D11—41no—
425C4×D11—41no—
426C4×D11—41no—
427C4×D11—41no—
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#529C2×D1111yescharacteristic
461#525—111no—
462#525—111no—
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#431C2×D1111yescharacteristic, complemented
473C2×C22⋊C8—111no—
474C2×C22⋊C8—111no—
475C2×C22⋊C8—111no—
476C2×C22⋊C8—111no—
477#388—221no—
478#387—221no—
479#386—221no—
480#383C2×D1111yescharacteristic, complemented
481#381—111no—
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—41no—
506C22×C11—41no—
507C22×C11—41no—
508C22×C11C22×C22⋊C411yescharacteristic
509C22×C11C2×#13511yescharacteristic
510C22×C11C2×#13511yescharacteristic
511C2×D11—21no—
512C2×D11—21no—
513C2×D11—21no—
514C2×D11—21no—
515C2×D11—21no—
516C2×D11—21no—
517C2×D11—21no—
518C2×D11—21no—
519C2×D11—21no—
520C2×D11—21no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—41no—
524C2×D11—41no—
525C2×D11—41no—
526C2×D11—81no—
527C2×D11—81no—
528C2×D11—162no—
529C2×D11#41612yes—
530C2×D11#41612yes—
531C4×C11—21no—
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—21no—
536C4×C11—21no—
537C4×C11—41no—
538C4×C11—41no—
539C4×C11—41no—
540C4×C11—81no—
541C4×C11—81no—
542Dic11—21no—
543Dic11—21no—
544Dic11—21no—
545Dic11—21no—
546Dic11—42no—
547Dic11—41no—
548Dic11—41no—
549Dic11—41no—
550Dic11—81no—
551C2×#41—111no—
552C2×#41—111no—
553C22×Q8—111no—
554C22×D4—111no—
555C22×D4—111no—
556C22×D4—221no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—221no—
560C22×C8—221no—
561C22×C8—221no—
562C22×C8—221no—
563C22×C8—221no—
564#126—21no—
565#126—221no—
566#126—221no—
567#126—221no—
568#126—221no—
569#126—221no—
570#125—111no—
571#125—221no—
572#125—221no—
573#125C4×D1111yescharacteristic, complemented
574#124—111no—
575#124—221no—
576#124—221no—
577#124C4×D1111yescharacteristic, complemented
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—111no—
593C22⋊Q8—221no—
594C22⋊Q8—221no—
595C22⋊Q8—221no—
596C22⋊Q8—221no—
597C22⋊Q8C22×D1111yescharacteristic
598#121—111no—
599#121—111no—
600#121—111no—
601#121—111no—
602#121—111no—
603#121—221no—
604#121—221no—
605#121—221no—
606#121—221no—
607#121—221no—
608#121—221no—
609#121—221no—
610#121—221no—
611#121C22×D1111yescharacteristic
612#120—221no—
613#120—221no—
614#120—221no—
615#120—221no—
616C4×Q8—111no—
617C4×Q8C4×D1111yescharacteristic, complemented
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—221no—
631C4×D4—221no—
632C4×D4—221no—
633C4×D4—221no—
634C4×D4—221no—
635C4×D4—221no—
636C4×D4—221no—
637C4×D4C4×D1111yescharacteristic, complemented
638#117—21no—
639#117—111no—
640#117—111no—
641#117—221no—
642#117—221no—
643#117—221no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—111no—
647C2×C4⋊C4—221no—
648C2×C4⋊C4—221no—
649C2×C22⋊C4—111no—
650C2×C22⋊C4—111no—
651C2×C22⋊C4—221no—
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—221no—
659C2×C42—221no—
660C2×C42C22×D1111yescharacteristic
661C4⋊C8—21no—
662C4⋊C8—221no—
663C22⋊C8—111no—
664C22⋊C8—111no—
665C22⋊C8—221no—
666C22⋊C8—221no—
667C22⋊C8—221no—
668C22⋊C8—221no—
669C22⋊C8C22×D1111yescharacteristic
670C22⋊C8C22×D1111yescharacteristic
671C4×C8—21no—
672C4×C8—221no—
673#95—21no—
674#95—21no—
675#95—111no—
676#95—111no—
677#95—221no—
678#95—221no—
679#95—221no—
680#95C22×D1111yescharacteristic
681#95C22×D1111yescharacteristic
682C2×C11—21no—
683C2×C11—21no—
684C2×C11—81no—
685C2×C11#288311yescharacteristic
686C2×C11C2×#41611yescharacteristic
687C2×C11#290111yescharacteristic
688D11—22no—
689D11—22no—
690D11—41no—
691D11—41no—
692D11—81no—
693C24—111no—
694C24—111no—
695C24—221no—
696#41—881no—
697#41—881no—
698C2×Q8—111no—
699C2×Q8—221no—
700C2×Q8—881no—
701C2×Q8C2×C4×D1111yescharacteristic
702C2×D4—21no—
703C2×D4—111no—
704C2×D4—111no—
705C2×D4—111no—
706C2×D4—111no—
707C2×D4—111no—
708C2×D4—222no—
709C2×D4—222no—
710C2×D4—221no—
711C2×D4—221no—
712C2×D4—221no—
713C2×D4—221no—
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—111no—
726C22×C4—111no—
727C22×C4—111no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—111no—
731C22×C4—111no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—111no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—442no—
744C22×C4—442no—
745C22×C4—881no—
746C22×C4—881no—
747C22×C4—881no—
748C22×C4D4×D1111yescharacteristic
749C22×C4D4×D1111yescharacteristic
750C22×C4C23×D1111yescharacteristic
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—221no—
754C2×C8—221no—
755C2×C8—881no—
756C2×C8—881no—
757C2×C8—881no—
758C2×C8—881no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—111no—
764C4⋊C4—111no—
765C4⋊C4—111no—
766C4⋊C4—111no—
767C4⋊C4—111no—
768C4⋊C4—111no—
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—111no—
788C22⋊C4—111no—
789C22⋊C4—111no—
790C22⋊C4—111no—
791C22⋊C4—111no—
792C22⋊C4—111no—
793C22⋊C4—111no—
794C22⋊C4—111no—
795C22⋊C4—221no—
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—442no—
811C22⋊C4—442no—
812C22⋊C4—881no—
813C42—21no—
814C42—221no—
815C42—221no—
816C42—221no—
817C42—442no—
818C42—881no—
819C42C2×C4×D1111yescharacteristic
820C42C2×C4×D1111yescharacteristic
821C42D4×D1111yescharacteristic
822C42D4×D1111yescharacteristic
823C11#1761511yescharacteristic, complemented, Sylow
824C23—21no—
825C23—111no—
826C23—111no—
827C23—112no—
828C23—112no—
829C23—111no—
830C23—111no—
831C23—221no—
832C23—221no—
833C23—221no—
834C23—441no—
835C23—441no—
836C23—441no—
837C23—441no—
838C23—442no—
839C23—881no—
840C23—881no—
841C23C2×D4×D1111yescharacteristic
842Q8—41no—
843Q8—441no—
844Q8—881no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—222no—
849D4—222no—
850D4—222no—
851D4—222no—
852D4—441no—
853D4—442no—
854D4—442no—
855D4—441no—
856D4—441no—
857D4—881no—
858D4—881no—
859D4—881no—
860D4—881no—
861D4—881no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
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—81no—
876C2×C4—111no—
877C2×C4—111no—
878C2×C4—111no—
879C2×C4—111no—
880C2×C4—222no—
881C2×C4—221no—
882C2×C4—221no—
883C2×C4—221no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—442no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—881no—
901C2×C4—881no—
902C2×C4—881no—
903C2×C4—881no—
904C2×C4—884no—
905C2×C4—881no—
906C2×C4C22⋊C4×D1111yescharacteristic
907C2×C4C22⋊C4×D1111yescharacteristic
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—41no—
919C22—41no—
920C22—41no—
921C22—112no—
922C22—112no—
923C22—221no—
924C22—221no—
925C22—221no—
926C22—221no—
927C22—221no—
928C22—221no—
929C22—221no—
930C22—221no—
931C22—221no—
932C22—221no—
933C22—442no—
934C22—442no—
935C22—441no—
936C22—441no—
937C22—441no—
938C22—881no—
939C22—881no—
940C22—1762no—
941C22C2×C22⋊C4×D1111yescharacteristic
942C22D11×#13511yescharacteristic
943C22D11×#13511yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—21no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—81no—
954C4—81no—
955C4—221no—
956C4—221no—
957C4—221no—
958C4—221no—
959C4—442no—
960C4—441no—
961C4—441no—
962C4—441no—
963C4—881no—
964C2—21no—
965C2—21no—
966C2—81no—
967C2—222no—
968C2—222no—
969C2—441no—
970C2—441no—
971C2—881no—
972C2#1307707511yescharacteristic
973C2D11×#41611yescharacteristic
974C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1521C2
socleC22×C11C22×C22⋊C4
prime radical#13082451C2
cosocleC22×C4×C11C24
hypercenter#1521D11
hypocenterC11#17615
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #13077639C2semidirect
3. #13071549C2semidirect
4. #13067191C2semidirect
5. #13067186C2semidirect
6. #13067182C2semidirect
7. #13067171C2semidirect
8. #13067169C2semidirect
9. #13067106C2semidirect
10. #13067104C2semidirect
11. #13067103C2semidirect
12. #13067102C2semidirect
13. D11×#328C2semidirect
14. D11×#327C2semidirect
15. C11×#1521C2semidirect
19. #10623226C4semidirect
20. #10623225C4semidirect
21. #10623208C4semidirect
22. #10623207C4semidirect
29. #10623112C4semidirect
30. #10623107C4semidirect
32. #10623089C4semidirect
33. #10623085C4semidirect
39. C11×#431C22semidirect
40. C11×#383C22semidirect
41. #10622545C22semidirect
42. #10622538C22semidirect
47. D11×C22⋊C8C22semidirect
48. D11×C22⋊C8C22semidirect
54. #10622279C22semidirect
56. #10622277C22semidirect
59. C11×#328C22semidirect
60. C11×#328C22semidirect
63. #10622176C22semidirect
64. #10622176C22semidirect
69. #10622105C22semidirect
70. #10622105C22semidirect
71. #10622090C22semidirect
72. #10622090C22semidirect
75. C2×#4343C2×C4semidirect
77. C2×#4341C2×C4semidirect
85. C11×#125C2×C4semidirect
86. C11×#124C2×C4semidirect
90. C4×Q8×C11C2×C4semidirect
92. C4×D4×C11C2×C4semidirect
96. #66999C2×C4semidirect
99. #66991C2×C4semidirect
127. #66950C2×C4semidirect
132. #66948C2×C4semidirect
140. #66945C2×C4semidirect
141. #66945C2×C4semidirect
170. #66928C2×C4semidirect
176. C4×D44C2×C4semidirect
183. #66923C2×C4semidirect
184. C4×Dic22C2×C4semidirect
341. #1521D11semidirect
472. #431C2×D11semidirect
480. #383C2×D11semidirect
493. #328C2×D11semidirect
494. #328C2×D11semidirect
573. #125C4×D11semidirect
577. #124C4×D11semidirect
617. C4×Q8C4×D11semidirect
637. C4×D4C4×D11semidirect
823. C11#17615semidirect

Maximal subgroups

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

subgroupindex
#130824512
#130776392
#130715492
#130671912
#130671862
#130671822
#130671712
#130671692
#130671062
#130671042
#130671032
#130671022
D11×#3282
D11×#3272
C11×#15212
#1761511