Finite Group Databasebeta

← #14762901

Subgroups — #14762901

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#525C211yesmaximal, characteristic
2C2×#10622739C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4#13069058C212yesmaximal, complemented
5#13069056C212yesmaximal, complemented
6#13068919C211yesmaximal, characteristic, complemented
7#13068918C211yesmaximal, characteristic, complemented
8#13068916C211yesmaximal, characteristic, complemented
9#13068714C212yesmaximal, complemented
10#13068558C212yesmaximal, complemented
11C11×#1871C211yesmaximal, characteristic, complemented
12C2×#41×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic, complemented
15C11×#525C2211yescharacteristic
16#10623359C2211yescharacteristic
17#10623322C2211yescharacteristic
18C22×#4318C2211yescharacteristic, complemented
19#10623187—21no—
20D11×#123—21no—
21#10623158C411yescharacteristic, complemented
22#10623158C411yescharacteristic, complemented
23D11×C22⋊Q8C411yescharacteristic, complemented
24D11×C22⋊Q8C411yescharacteristic, complemented
25#10623137C411yescharacteristic, complemented
26#10623137C411yescharacteristic, complemented
27D11×#121C411yescharacteristic, complemented
28D11×#121C411yescharacteristic, complemented
29D11×#120—21no—
30#10623117—21no—
31#10623078—21no—
32#10623078—21no—
33C4×D4×D11—21no—
34C4×D4×D11—21no—
35#10623055C2211yescharacteristic
36D11×#117C2211yescharacteristic
37C2×C22⋊C4×D11—21no—
38C2×C42×D11C2212yescomplemented
39C2×C11×#104C2212yescomplemented
40C4×C11×C22⋊C4C2211yescharacteristic, complemented
41C2×#66901C2212yescomplemented
42C4×C22⋊Dic11C2211yescharacteristic, complemented
43C2×#66889C2212yescomplemented
44#10622739—21no—
45#10622739—21no—
46#10622739C2212yes—
47#10622739C2212yescomplemented
48C2×(C2×D11)⋊C8—21no—
49C2×(C2×D11)⋊C8—21no—
50C22⋊C4×Dic11—21no—
51C4×(C2×D11)⋊C4C2212yes—
52C2×#66869C2212yescomplemented
53#10622279—21no—
54D11×#95—21no—
55C11×#339C2212yescomplemented
56#10622193C2212yescomplemented
57#10622170C2212yescomplemented
58#10622161C2212yescomplemented
59C24×D11D411yescharacteristic
60C2×C11×#41C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11D411yescharacteristic
63#41×D11—42no—
64#41×D11—42no—
65C2×#4343C2×C411yescharacteristic, complemented
66C2×Q8×D11C2×C411yescharacteristic, complemented
67C2×#4341—21no—
68C2×#4341C2×C411yescharacteristic, complemented
69C2×D4×D11—21no—
70C2×D4×D11—21no—
71C2×D4×D11—21no—
72C2×D4×D11C2×C411yescharacteristic, complemented
73C2×#4339—21no—
74C2×#4339C2311yescharacteristic
75C22×C4×D11—22no—
76C22×C4×D11—21no—
77C22×C4×D11—42no—
78C22×C4×D11—42no—
79C22×C4×D11C2×C411yescharacteristic
80C22×C4×D11C2×C411yescharacteristic
81C22×C4×D11C2×C411yescharacteristic
82C22×C4×D11C2×C411yescharacteristic
83C22×C4×D11D411yescharacteristic
84C22×C4×D11D411yescharacteristic
85C22×C4×D11D411yescharacteristic
86C22×C4×D11D411yescharacteristic
87C22×C4×D11D411yescharacteristic
88C22×C4×D11D411yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C2×C11×M16—21no—
92C2×C11×M16—42no—
93C2×C11×M16C2312yes—
94C22×C8×C11—21no—
95C11×#123—21no—
96C11×C22⋊Q8C2×C411yescharacteristic, complemented
97C11×C22⋊Q8C2×C411yescharacteristic, complemented
98C11×#121C2×C411yescharacteristic, complemented
99C11×#121C2×C411yescharacteristic, complemented
100C11×#120—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C11×#117C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C42×C11C2312yes—
106#67006—21no—
107C2×C22⋊Dic11—21no—
108#66999C2×C411yescharacteristic
109#66999C2×C411yescharacteristic
110#66992—21no—
111#66992—21no—
112#66991C2×C411yescharacteristic
113#66991C2×C411yescharacteristic
114#66990—21no—
115#66990—21no—
116#66990—21no—
117#66988—21no—
118D4×Dic11—21no—
119D4×Dic11—21no—
120#66983C2×C411yescharacteristic, complemented
121#66983C2×C411yescharacteristic, complemented
122#66982—21no—
123C4×C22⋊D11—21no—
124C4×C22⋊D11—21no—
125C4×C22⋊D11—21no—
126C4×C22⋊D11—21no—
127C2×(C2×D11)⋊C4—22no—
128#66979C2311yescharacteristic
129#66977C2×C411yescharacteristic, complemented
130#66977C2×C411yescharacteristic, complemented
131C2×C4×Dic11—22no—
132C2×C4×Dic11C2312yes—
133C2×#4318—21no—
134C2×#4318—42no—
135C2×#4318C2312yes—
136C22×C11⋊C8—21no—
137#66950C2×C411yescharacteristic
138#66950C2×C411yescharacteristic
139#66949—21no—
140#66949—21no—
141#66948C2×C411yescharacteristic
142#66948C2×C411yescharacteristic
143#66947—21no—
144#66947—21no—
145#66946—21no—
146#66946—21no—
147#66945C2×C411yescharacteristic, complemented
148#66945C2×C411yescharacteristic, complemented
149C4⋊C4×D11—21no—
150C4⋊C4×D11—21no—
151C4⋊C4×D11C2×C411yescharacteristic, complemented
152C4⋊C4×D11C2×C411yescharacteristic, complemented
153#66939—21no—
154#66937—21no—
155#66937—21no—
156#66936—21no—
157#66936—21no—
158#66935—21no—
159#66935—21no—
160#66935—21no—
161(C22⋊D11)⋊C4—21no—
162(C22⋊D11)⋊C4—21no—
163(C22⋊D11)⋊C4—21no—
164(C22⋊D11)⋊C4—21no—
165C22⋊C4×D11—28no—
166C22⋊C4×D11—21no—
167C22⋊C4×D11—21no—
168C22⋊C4×D11—21no—
169C22⋊C4×D11—21no—
170C22⋊C4×D11—21no—
171#66931—21no—
172#66931—21no—
173#66930—21no—
174C4×D44—21no—
175C4×D44—21no—
176#66925—21no—
177C42×D11—21no—
178C42×D11—42no—
179C42×D11—42no—
180C11×#104—42no—
181C11×#95—21no—
182#66901—42no—
183C11⋊#95—21no—
184C11⋊#95—22no—
185#66889—42no—
186(C2×D11)⋊C8—22no—
187(C2×D11)⋊C8—22no—
188(C2×D11)⋊C8—22no—
189(C2×D11)⋊C8—22no—
190#66869—42no—
191#21773—111nomaximal, Sylow
192C24×C11C2×D411yescharacteristic
193C23×D11—24no—
194C23×D11—21no—
195C23×D11—42no—
196C23×D11—42no—
197C23×D11C22⋊C411yescharacteristic
198C23×D11C22⋊C411yescharacteristic
199C23×D11C22⋊C411yescharacteristic
200C23×D11C22⋊C411yescharacteristic
201C23×D11C2×D411yescharacteristic
202C23×D11C2×D411yescharacteristic
203C11×#41—22no—
204C11×#41—22no—
205C2×Q8×C11C22×C411yescharacteristic
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11C22×C411yescharacteristic
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C22×C411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—21no—
221C2×C22⋊D11—21no—
222C2×C22⋊D11—21no—
223C2×C22⋊D11—21no—
224C2×C22⋊D11—21no—
225C2×C22⋊D11—21no—
226C2×C22⋊D11—21no—
227C22×Dic11—21no—
228C22×Dic11—22no—
229C22×Dic11—42no—
230C22×Dic11C22⋊C411yescharacteristic
231C22×Dic11C22⋊C411yescharacteristic
232C22×Dic11C22⋊C411yescharacteristic
233C22×Dic11C22⋊C411yescharacteristic
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236#4343—42no—
237Q8×D11—42no—
238#4341—42no—
239#4341—44no—
240D4×D11—42no—
241D4×D11—44no—
242D4×D11—44no—
243D4×D11—44no—
244#4339—22no—
245#4339—22no—
246#4339—42no—
247#4339—42no—
248C2×D44—21no—
249C2×D44—21no—
250C2×D44—21no—
251C2×D44C22×C411yescharacteristic
252C2×C4×D11—28no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—21no—
256C2×C4×D11—21no—
257C2×C4×D11—21no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—22no—
261C2×C4×D11—22no—
262C2×C4×D11—42no—
263C2×C4×D11—42no—
264C2×C4×D11—42no—
265C2×C4×D11—42no—
266C2×C4×D11—42no—
267C2×C4×D11—42no—
268C2×C4×D11—41no—
269C2×C4×D11—41no—
270C2×C4×D11—41no—
271C2×C4×D11—41no—
272C2×C4×D11—41no—
273C2×C4×D11—41no—
274C2×C4×D11—41no—
275C2×C4×D11—41no—
276C2×C4×D11—44no—
277C2×C4×D11—44no—
278C2×C4×D11—42no—
279C2×C4×D11—42no—
280C2×C4×D11C22⋊C411yescharacteristic
281C2×C4×D11C22⋊C411yescharacteristic
282C2×C4×D11C22⋊C411yescharacteristic
283C2×C4×D11C22⋊C411yescharacteristic
284C2×C4×D11C22⋊C411yescharacteristic
285C2×C4×D11C22⋊C411yescharacteristic
286C2×C4×D11C22⋊C411yescharacteristic
287C2×C4×D11C22⋊C411yescharacteristic
288C2×C4×D11C22×C411yescharacteristic
289C2×C4×D11C22×C411yescharacteristic
290C2×C4×D11C22×C411yescharacteristic
291C2×C4×D11C22×C411yescharacteristic
292C2×C4×D11C2×D411yescharacteristic
293C2×C4×D11C2×D411yescharacteristic
294C2×C4×D11C2×D411yescharacteristic
295C2×C4×D11C2×D411yescharacteristic
296C2×Dic22—21no—
297C2×Dic22C22×C411yescharacteristic
298C11×M16—22no—
299C11×M16—22no—
300C11×M16—42no—
301C2×C8×C11—22no—
302C2×C8×C11—42no—
303C11×C4⋊C4—21no—
304C11×C4⋊C4—21no—
305C11×C4⋊C4C22×C411yescharacteristic
306C11×C4⋊C4C22×C411yescharacteristic
307C11×C22⋊C4—24no—
308C11×C22⋊C4—21no—
309C11×C22⋊C4—21no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—21no—
313C42×C11—21no—
314C42×C11—22no—
315C42×C11—22no—
316C22⋊Dic11—24no—
317C22⋊Dic11—21no—
318C22⋊Dic11—21no—
319C22⋊Dic11—21no—
320C22⋊Dic11—21no—
321C22⋊Dic11—21no—
322(C2×D11)⋊C4—28no—
323(C2×D11)⋊C4—21no—
324(C2×D11)⋊C4—21no—
325(C2×D11)⋊C4—21no—
326(C2×D11)⋊C4—21no—
327(C2×D11)⋊C4—21no—
328(C2×D11)⋊C4—21no—
329(C2×D11)⋊C4—21no—
330(C2×D11)⋊C4—21no—
331(C2×D11)⋊C4—21no—
332(C2×D11)⋊C4—21no—
333C4⋊Dic11—21no—
334C4⋊Dic11—21no—
335C4⋊Dic11C22×C411yescharacteristic
336C4⋊Dic11C22×C411yescharacteristic
337Dic11⋊C4—21no—
338Dic11⋊C4—21no—
339Dic11⋊C4—21no—
340Dic11⋊C4—21no—
341Dic11⋊C4—21no—
342Dic11⋊C4—21no—
343C4×Dic11—21no—
344C4×Dic11—21no—
345C4×Dic11—21no—
346C4×Dic11—22no—
347C4×Dic11—22no—
348C4×Dic11—44no—
349#4318—22no—
350#4318—22no—
351#4318—42no—
352C2×C11⋊C8—22no—
353C2×C11⋊C8—42no—
354C2×#525—111no—
355C2×#407—111no—
356C2×C4×C22⋊C4—111no—
357#1896—112no—
358#1896—112no—
359#1871—111no—
360#1871—111no—
361#1871—111no—
362#1871D1111yescharacteristic, complemented
363#1826—112no—
364#1789—112no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—21no—
368C23×C11—41no—
369C23×C11C2×C22⋊C411yescharacteristic
370C23×C11C2×C22⋊C411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—21no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—416no—
391C22×D11—42no—
392C22×D11—42no—
393C22×D11—42no—
394C22×D11#10414yescomplemented
395C22×D11C2×C22⋊C411yescharacteristic
396C22×D11C2×C22⋊C411yescharacteristic
397C22×D11C2×C22⋊C411yescharacteristic
398C22×D11C2×C22⋊C411yescharacteristic
399Q8×C11—22no—
400D4×C11—22no—
401D4×C11—42no—
402D4×C11—42no—
403D4×C11—42no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—24no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—42no—
416C2×C4×C11—42no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11C2×C22⋊C411yescharacteristic
420C2×C4×C11C2×C22⋊C411yescharacteristic
421C2×C4×C11C23×C411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11H(5,𝔽2)12yes—
424C2×C4×C11H(5,𝔽2)12yes—
425C22⋊D11—42no—
426C22⋊D11—42no—
427C22⋊D11—42no—
428C22⋊D11—42no—
429C22⋊D11—42no—
430C22⋊D11—42no—
431C22⋊D11—42no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—24no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—42no—
443C2×Dic11—42no—
444C2×Dic11—42no—
445C2×Dic11C2×C22⋊C411yescharacteristic
446C2×Dic11C2×C22⋊C411yescharacteristic
447C2×Dic11C2×C22⋊C411yescharacteristic
448C2×Dic11C2×C22⋊C411yescharacteristic
449D44—22no—
450D44—42no—
451D44—42no—
452D44—42no—
453C4×D11—22no—
454C4×D11—22no—
455C4×D11—22no—
456C4×D11—22no—
457C4×D11—21no—
458C4×D11—21no—
459C4×D11—21no—
460C4×D11—21no—
461C4×D11—21no—
462C4×D11—21no—
463C4×D11—21no—
464C4×D11—21no—
465C4×D11—41no—
466C4×D11—41no—
467C4×D11—41no—
468C4×D11—41no—
469C4×D11—41no—
470C4×D11—41no—
471C4×D11—41no—
472C4×D11—41no—
473C4×D11—42no—
474C4×D11—416no—
475C4×D11—42no—
476C4×D11—42no—
477C4×D11—42no—
478C4×D11—41no—
479C4×D11—41no—
480Dic22—22no—
481Dic22—42no—
482C8×C11—42no—
483C11⋊C8—42no—
484C22×#41—111no—
485C24×C4—111no—
486C22×M16—111no—
487C22×M16C2×D1111yescharacteristic, complemented
488#525—111no—
489#525—111no—
490#525—111no—
491#525—111no—
492#525—111no—
493#525—111no—
494#525—111no—
495#525—221no—
496#525—221no—
497#525—221no—
498#525—221no—
499#525C2×D1111yescharacteristic
500C2×#123—221no—
501C2×C22⋊Q8—111no—
502C2×C22⋊Q8—111no—
503C2×#121—111no—
504C2×#121—111no—
505C2×#120—221no—
506C2×C4×D4—221no—
507C2×C4×D4—221no—
508C2×#117—111no—
509C22×C22⋊C4—221no—
510C22×C42—112no—
511C2×#104—112no—
512C2×#104—112no—
513C2×#104—112no—
514C2×#104C2×D1112yescomplemented
515#407—112no—
516#407—112no—
517#407—221no—
518#407—221no—
519C2×C22⋊C8—221no—
520C2×C22⋊C8—221no—
521C4×C22⋊C4—111no—
522C4×C22⋊C4—112no—
523C4×C22⋊C4—221no—
524C4×C22⋊C4—221no—
525C4×C22⋊C4C2×D1111yescharacteristic, complemented
526C2×#95—221no—
527#339—112no—
528#339—112no—
529#339—112no—
530#339C2×D1112yescomplemented
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—44no—
539C22×C11—41no—
540C22×C11—41no—
541C22×C11—41no—
542C22×C11C2×#10412yes—
543C22×C11C22×C22⋊C411yescharacteristic
544C22×C11#53412yes—
545C2×D11—28no—
546C2×D11—21no—
547C2×D11—21no—
548C2×D11—21no—
549C2×D11—21no—
550C2×D11—21no—
551C2×D11—21no—
552C2×D11—21no—
553C2×D11—21no—
554C2×D11—21no—
555C2×D11—44no—
556C2×D11—44no—
557C2×D11—44no—
558C2×D11—44no—
559C2×D11—44no—
560C2×D11—41no—
561C2×D11—41no—
562C2×D11—41no—
563C2×D11—84no—
564C2×D11C2×#10412yes—
565C2×D11C2×#10412yes—
566C2×D11#42112yes—
567C4×C11—21no—
568C4×C11—21no—
569C4×C11—44no—
570C4×C11—41no—
571C4×C11—41no—
572C4×C11—41no—
573C4×C11#51812yes—
574C4×C11#53411yescharacteristic
575C4×C11#53411yescharacteristic
576Dic11—21no—
577Dic11—21no—
578Dic11—21no—
579Dic11—21no—
580Dic11—44no—
581Dic11—41no—
582Dic11—41no—
583Dic11—41no—
584C25—111no—
585C2×#41—111no—
586C2×#41—111no—
587C2×#41—111no—
588C2×#41—221no—
589C2×#41—221no—
590C2×#41—442no—
591C2×#41—442no—
592C2×#41C22×D1111yescharacteristic
593C22×Q8—111no—
594C22×D4—111no—
595C22×D4—221no—
596C22×D4—221no—
597C22×D4—221no—
598C23×C4—111no—
599C23×C4—111no—
600C23×C4—111no—
601C23×C4—111no—
602C23×C4—111no—
603C23×C4—111no—
604C23×C4—111no—
605C23×C4—111no—
606C23×C4—111no—
607C23×C4—111no—
608C23×C4—111no—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—221no—
612C23×C4—222no—
613C23×C4—442no—
614C23×C4—442no—
615C23×C4C22×D1111yescharacteristic
616C2×M16—21no—
617C2×M16—42no—
618C2×M16—112no—
619C2×M16—221no—
620C2×M16—442no—
621C2×M16C22×D1112yes—
622C22×C8—21no—
623C22×C8—221no—
624#123—21no—
625#123—221no—
626#123—221no—
627#123—221no—
628#123—221no—
629#123—221no—
630#123—221no—
631#123—221no—
632C22⋊Q8—111no—
633C22⋊Q8—111no—
634C22⋊Q8—111no—
635C22⋊Q8—111no—
636C22⋊Q8—111no—
637C22⋊Q8—111no—
638C22⋊Q8—221no—
639C22⋊Q8—221no—
640C22⋊Q8—221no—
641C22⋊Q8—221no—
642C22⋊Q8C4×D1111yescharacteristic, complemented
643C22⋊Q8C4×D1111yescharacteristic, complemented
644#121—111no—
645#121—111no—
646#121—111no—
647#121—111no—
648#121—111no—
649#121—111no—
650#121—221no—
651#121—221no—
652#121—221no—
653#121—221no—
654#121C4×D1111yescharacteristic, complemented
655#121C4×D1111yescharacteristic, complemented
656#120—21no—
657#120—221no—
658#120—221no—
659#120—221no—
660#120—221no—
661#120—221no—
662#120—221no—
663#120—221no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—221no—
667C4×D4—221no—
668C4×D4—221no—
669C4×D4—221no—
670C4×D4—221no—
671C4×D4—221no—
672C4×D4—221no—
673C4×D4—221no—
674C4×D4—221no—
675C4×D4—221no—
676C4×D4—221no—
677C4×D4—221no—
678C4×D4—221no—
679C4×D4—221no—
680#117—111no—
681#117—111no—
682#117—111no—
683#117—221no—
684#117—221no—
685#117C22×D1111yescharacteristic
686C2×C4⋊C4—111no—
687C2×C4⋊C4—111no—
688C2×C4⋊C4—221no—
689C2×C4⋊C4—221no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—221no—
692C2×C22⋊C4—221no—
693C2×C22⋊C4—221no—
694C2×C22⋊C4—221no—
695C2×C22⋊C4—221no—
696C2×C22⋊C4—228no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—221no—
699C2×C42—112no—
700C2×C42—221no—
701C2×C42—222no—
702C2×C42—442no—
703C2×C42—442no—
704C2×C42C22×D1112yes—
705#104—42no—
706#104—442no—
707#104—442no—
708#104—442no—
709C22⋊C8—222no—
710C22⋊C8—222no—
711C22⋊C8—222no—
712C22⋊C8—222no—
713#95—21no—
714#95—222no—
715#95—221no—
716C2×C11—22no—
717C2×C11—22no—
718C2×C11—41no—
719C2×C11—81no—
720C2×C11#230811yescharacteristic
721C2×C11C22×#10411yescharacteristic
722C2×C11C2×#42111yescharacteristic
723D11—22no—
724D11—22no—
725D11—22no—
726D11—41no—
727D11—81no—
728C24—111no—
729C24—111no—
730C24—111no—
731C24—111no—
732C24—111no—
733C24—111no—
734C24—224no—
735C24—221no—
736C24—442no—
737C24—442no—
738C24D4×D1111yescharacteristic
739#41—22no—
740#41—22no—
741#41—222no—
742#41—222no—
743#41—442no—
744#41—442no—
745#41—442no—
746#41—444no—
747#41—442no—
748C2×Q8—111no—
749C2×Q8—221no—
750C2×Q8—442no—
751C2×Q8C2×C4×D1111yescharacteristic
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—111no—
756C2×D4—221no—
757C2×D4—221no—
758C2×D4—221no—
759C2×D4—221no—
760C2×D4—221no—
761C2×D4—221no—
762C2×D4—221no—
763C2×D4—221no—
764C2×D4—221no—
765C2×D4—221no—
766C2×D4—442no—
767C2×D4—444no—
768C2×D4—444no—
769C2×D4—444no—
770C2×D4C2×C4×D1111yescharacteristic
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—111no—
776C22×C4—111no—
777C22×C4—111no—
778C22×C4—111no—
779C22×C4—111no—
780C22×C4—111no—
781C22×C4—111no—
782C22×C4—111no—
783C22×C4—111no—
784C22×C4—111no—
785C22×C4—111no—
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—111no—
795C22×C4—111no—
796C22×C4—111no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—228no—
802C22×C4—221no—
803C22×C4—222no—
804C22×C4—222no—
805C22×C4—222no—
806C22×C4—222no—
807C22×C4—222no—
808C22×C4—221no—
809C22×C4—442no—
810C22×C4—442no—
811C22×C4—442no—
812C22×C4—442no—
813C22×C4—441no—
814C22×C4—441no—
815C22×C4—441no—
816C22×C4—441no—
817C22×C4—441no—
818C22×C4—441no—
819C22×C4—441no—
820C22×C4—441no—
821C22×C4—442no—
822C22×C4—442no—
823C22×C4—442no—
824C22×C4—442no—
825C22×C4—444no—
826C22×C4—444no—
827C22×C4—442no—
828C22×C4C2×C4×D1111yescharacteristic
829C22×C4C2×C4×D1111yescharacteristic
830C22×C4D4×D1111yescharacteristic
831C22×C4D4×D1111yescharacteristic
832C22×C4D4×D1111yescharacteristic
833C22×C4C23×D1111yescharacteristic
834M16—22no—
835M16—22no—
836M16—42no—
837M16—222no—
838M16—222no—
839M16—442no—
840C2×C8—22no—
841C2×C8—42no—
842C2×C8—222no—
843C2×C8—442no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—111no—
847C4⋊C4—111no—
848C4⋊C4—221no—
849C4⋊C4—221no—
850C4⋊C4—221no—
851C4⋊C4—221no—
852C4⋊C4—221no—
853C4⋊C4—221no—
854C4⋊C4—221no—
855C4⋊C4—221no—
856C4⋊C4C2×C4×D1111yescharacteristic
857C4⋊C4C2×C4×D1111yescharacteristic
858C22⋊C4—24no—
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—221no—
865C22⋊C4—221no—
866C22⋊C4—221no—
867C22⋊C4—221no—
868C22⋊C4—221no—
869C22⋊C4—221no—
870C22⋊C4—221no—
871C22⋊C4—221no—
872C22⋊C4—228no—
873C22⋊C4—221no—
874C22⋊C4—221no—
875C22⋊C4—224no—
876C22⋊C4—221no—
877C22⋊C4—221no—
878C22⋊C4—221no—
879C22⋊C4—221no—
880C22⋊C4—221no—
881C42—21no—
882C42—22no—
883C42—22no—
884C42—221no—
885C42—221no—
886C42—221no—
887C42—222no—
888C42—222no—
889C42—444no—
890C11#2177311yescharacteristic, complemented, Sylow
891C23—22no—
892C23—22no—
893C23—21no—
894C23—41no—
895C23—111no—
896C23—111no—
897C23—111no—
898C23—114no—
899C23—111no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23—222no—
908C23—222no—
909C23—222no—
910C23—221no—
911C23—441no—
912C23—441no—
913C23—441no—
914C23—441no—
915C23—441no—
916C23—441no—
917C23—441no—
918C23—442no—
919C23—4416no—
920C23—442no—
921C23—442no—
922C23C22⋊C4×D1111yescharacteristic
923C23C22⋊C4×D1111yescharacteristic
924C23C2×D4×D1111yescharacteristic
925Q8—22no—
926Q8—222no—
927Q8—442no—
928D4—22no—
929D4—42no—
930D4—42no—
931D4—42no—
932D4—222no—
933D4—442no—
934D4—442no—
935D4—442no—
936D4—442no—
937D4—442no—
938D4—442no—
939D4—442no—
940D4—442no—
941D4—442no—
942D4—442no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—24no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—111no—
959C2×C4—111no—
960C2×C4—111no—
961C2×C4—111no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—221no—
969C2×C4—221no—
970C2×C4—221no—
971C2×C4—221no—
972C2×C4—221no—
973C2×C4—221no—
974C2×C4—221no—
975C2×C4—221no—
976C2×C4—224no—
977C2×C4—221no—
978C2×C4—221no—
979C2×C4—221no—
980C2×C4—441no—
981C2×C4—441no—
982C2×C4—441no—
983C2×C4—441no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4—441no—
987C2×C4—441no—
988C2×C4—442no—
989C2×C4—442no—
990C2×C4—442no—
991C2×C4—4416no—
992C2×C4—442no—
993C2×C4—441no—
994C2×C4—441no—
995C2×C4—441no—
996C2×C4—441no—
997C2×C4—442no—
998C2×C4—442no—
999C2×C4—442no—
1000C2×C4—441no—
1001C2×C4—441no—
1002C2×C4C22⋊C4×D1111yescharacteristic
1003C2×C4C22⋊C4×D1111yescharacteristic
1004C2×C4C22×C4×D1111yescharacteristic
1005C2×C4C2×D4×D1111yescharacteristic
1006C2×C4#6703712yes—
1007C2×C4#6704212yes—
1008C8—42no—
1009C8—442no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—44no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—112no—
1022C22—112no—
1023C22—112no—
1024C22—228no—
1025C22—221no—
1026C22—221no—
1027C22—221no—
1028C22—221no—
1029C22—221no—
1030C22—221no—
1031C22—221no—
1032C22—221no—
1033C22—221no—
1034C22—444no—
1035C22—444no—
1036C22—444no—
1037C22—444no—
1038C22—444no—
1039C22—441no—
1040C22—441no—
1041C22—441no—
1042C22—884no—
1043C22D11×#10412yes—
1044C22C2×C22⋊C4×D1111yescharacteristic
1045C22#1062313612yes—
1046C4—21no—
1047C4—21no—
1048C4—44no—
1049C4—41no—
1050C4—41no—
1051C4—41no—
1052C4—221no—
1053C4—221no—
1054C4—221no—
1055C4—221no—
1056C4—444no—
1057C4—441no—
1058C4—441no—
1059C4—441no—
1060C4#1062307612yes—
1061C4#1062312011yescharacteristic
1062C4#1062318411yescharacteristic
1063C2—22no—
1064C2—22no—
1065C2—41no—
1066C2—81no—
1067C2—222no—
1068C2—222no—
1069C2—222no—
1070C2—441no—
1071C2—881no—
1072C2#1307119011yescharacteristic
1073C2C2×D11×#10411yescharacteristic
1074C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1871C2
socleC22×C11C22×C22⋊C4
prime radicalD11×#525C2
cosocleC22×C4×C11C24
hypercenter#1871D11
hypocenterC11#21773
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×#10622739C2semidirect
3. C4×C22⋊C4×D11C2semidirect
4. #13069058C2semidirect
5. #13069056C2semidirect
6. #13068919C2semidirect
7. #13068918C2semidirect
8. #13068916C2semidirect
9. #13068714C2semidirect
10. #13068558C2semidirect
11. C11×#1871C2semidirect
14. C22×C11×M16C22semidirect
18. C22×#4318C22semidirect
21. #10623158C4semidirect
22. #10623158C4semidirect
23. D11×C22⋊Q8C4semidirect
24. D11×C22⋊Q8C4semidirect
25. #10623137C4semidirect
26. #10623137C4semidirect
27. D11×#121C4semidirect
28. D11×#121C4semidirect
38. C2×C42×D11C22semidirect
39. C2×C11×#104C22semidirect
40. C4×C11×C22⋊C4C22semidirect
41. C2×#66901C22semidirect
42. C4×C22⋊Dic11C22semidirect
43. C2×#66889C22semidirect
47. #10622739C22semidirect
52. C2×#66869C22semidirect
55. C11×#339C22semidirect
56. #10622193C22semidirect
57. #10622170C22semidirect
58. #10622161C22semidirect
65. C2×#4343C2×C4semidirect
66. C2×Q8×D11C2×C4semidirect
68. C2×#4341C2×C4semidirect
72. C2×D4×D11C2×C4semidirect
96. C11×C22⋊Q8C2×C4semidirect
97. C11×C22⋊Q8C2×C4semidirect
98. C11×#121C2×C4semidirect
99. C11×#121C2×C4semidirect
120. #66983C2×C4semidirect
121. #66983C2×C4semidirect
129. #66977C2×C4semidirect
130. #66977C2×C4semidirect
147. #66945C2×C4semidirect
148. #66945C2×C4semidirect
151. C4⋊C4×D11C2×C4semidirect
152. C4⋊C4×D11C2×C4semidirect
362. #1871D11semidirect
394. C22×D11#104semidirect
487. C22×M16C2×D11semidirect
514. C2×#104C2×D11semidirect
525. C4×C22⋊C4C2×D11semidirect
530. #339C2×D11semidirect
642. C22⋊Q8C4×D11semidirect
643. C22⋊Q8C4×D11semidirect
654. #121C4×D11semidirect
655. #121C4×D11semidirect
890. C11#21773semidirect

Maximal subgroups

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

subgroupindex
D11×#5252
C2×#106227392
C4×C22⋊C4×D112
#130690582
#130690562
#130689192
#130689182
#130689162
#130687142
#130685582
C11×#18712
#2177311