Finite Group Databasebeta

← #14791934

Subgroups — #14791934

Order 2816.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078237C211yesmaximal, characteristic, complemented
2C2×#10622854C211yesmaximal, characteristic, complemented
3#13077868C211yesmaximal, characteristic, complemented
4C22×#66901C211yesmaximal, characteristic, complemented
5#13076959C211yesmaximal, characteristic, complemented
6#13069837C211yesmaximal, characteristic, complemented
7#13069823C211yesmaximal, characteristic, complemented
8#13069658C211yesmaximal, characteristic, complemented
9#13069629C211yesmaximal, characteristic, complemented
10#13069080C211yesmaximal, characteristic, complemented
11#13069060C211yesmaximal, characteristic, complemented
12#13068992C211yesmaximal, characteristic, complemented
13#13068842C211yesmaximal, characteristic, complemented
14#13068570C211yesmaximal, characteristic, complemented
15C11×#3488C211yesmaximal, characteristic, complemented
16C2×C11×H(5,𝔽2)C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#550—21no—
19C11×#548—21no—
20C11×#546—21no—
21C11×#546—22no—
22D42×C11—22no—
23D42×C11—21no—
24C11×#537—21no—
25C11×#537C2211yescharacteristic
26C11×#535—21no—
27C11×#535C2211yescharacteristic
28C11×#525—21no—
29C11×#525C2211yescharacteristic
30C2×C11×#121—21no—
31C2×C11×#121C2211yescharacteristic
32C11×#520C2211yescharacteristic
33C2×#67002C2211yescharacteristic
34C2×#67002C2211yescharacteristic, complemented
35C2×#67002C2211yescharacteristic, complemented
36C2×#66993C2211yescharacteristic, complemented
37C2×#66992—22no—
38C2×#66983C2211yescharacteristic, complemented
39C22×C4×Dic11C2211yescharacteristic, complemented
40C22×#4318C2211yescharacteristic, complemented
41#10622854—24no—
42#10622851—21no—
43#10622851—21no—
44C2×#66901—24no—
45C2×#66901C2211yescharacteristic
46C2×#66901C2211yescharacteristic
47C2×#66901C2211yescharacteristic, complemented
48C2×#66901C2211yescharacteristic, complemented
49C2×#66901C2211yescharacteristic, complemented
50C2×#66901C2211yescharacteristic, complemented
51#10622845C2211yescharacteristic
52#10622845C2211yescharacteristic, complemented
53#10622845C2211yescharacteristic, complemented
54#10622840—21no—
55#10622834C2211yescharacteristic, complemented
56#10622830—21no—
57C2×#66897C2211yescharacteristic, complemented
58C2×#66897C2211yescharacteristic, complemented
59#10622820C2211yescharacteristic, complemented
60#10622662—21no—
61#10622661—21no—
62#10622652—21no—
63#10622651—21no—
64#10622614C2211yescharacteristic, complemented
65#10622608C2211yescharacteristic, complemented
66#10622601C2211yescharacteristic, complemented
67#10622589C2211yescharacteristic, complemented
68#10622570—22no—
69#10622170C2211yescharacteristic, complemented
70#10622170C2211yescharacteristic, complemented
71#10622168C2211yescharacteristic, complemented
72#10622168C2211yescharacteristic, complemented
73C11×H(5,𝔽2)—22no—
74C11×H(5,𝔽2)—22no—
75C11×H(5,𝔽2)—41no—
76C11×H(5,𝔽2)—41no—
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—22no—
82C2×C11×#41—22no—
83C2×C11×#41—41no—
84C2×C11×#41—41no—
85C2×C11×#41D411yescharacteristic, complemented
86C2×C11×#41D411yescharacteristic, complemented
87C2×C11×#41C2311yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C2×C11×#41C2311yescharacteristic
90C22×Q8×C11D411yescharacteristic, complemented
91C22×D4×C11—21no—
92C22×D4×C11—22no—
93C22×D4×C11—22no—
94C22×D4×C11—21no—
95C22×D4×C11—21no—
96C22×D4×C11D412yes—
97C22×D4×C11D411yescharacteristic, complemented
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100C23×C4×C11C2311yescharacteristic
101C22×C22⋊D11—21no—
102C22×C22⋊D11—22no—
103C23×Dic11—21no—
104C22×D44C2311yescharacteristic
105C11×#127—22no—
106C11×#127—21no—
107C11×#124—22no—
108C11×#124—21no—
109C11×#123—22no—
110C11×#123—21no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8D411yescharacteristic, complemented
115C11×C22⋊Q8D411yescharacteristic, complemented
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—21no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—22no—
128C11×#121—21no—
129C11×#121—21no—
130C11×#121D411yescharacteristic, complemented
131C11×#121D411yescharacteristic, complemented
132C11×#120—22no—
133C11×#120—22no—
134C11×#120—22no—
135C11×#120—21no—
136C11×#120—22no—
137C4×Q8×C11—21no—
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—21no—
141C4×D4×C11—22no—
142C4×D4×C11—21no—
143C4×D4×C11—21no—
144C11×#117—21no—
145C11×#117C2311yescharacteristic
146C2×C11×C4⋊C4—21no—
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C22⋊C4—22no—
149C2×C11×C22⋊C4D412yes—
150C2×C22⋊Dic11—22no—
151#67002—22no—
152#67002—22no—
153#67002—22no—
154#67002—41no—
155#67002—41no—
156#67002—41no—
157C2×#4325—21no—
158C2×#4325—21no—
159C2×#4325—21no—
160#66993—22no—
161#66993—41no—
162#66992—48no—
163C2×#4323—21no—
164C2×#4323—21no—
165C2×#4323—21no—
166#66983—21no—
167#66983—21no—
168#66983—21no—
169#66983—21no—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4—22no—
172C2×C4⋊Dic11C2311yescharacteristic
173C2×Dic11⋊C4—22no—
174C2×C4×Dic11—22no—
175C2×C4×Dic11—21no—
176C2×C4×Dic11—41no—
177C2×C4×Dic11C2311yescharacteristic
178C2×C4×Dic11C2311yescharacteristic
179C2×#4318—21no—
180C2×#4318—22no—
181C2×#4318—41no—
182C2×#4318C2311yescharacteristic
183C2×#4318C2311yescharacteristic
184C2×#4318C2311yescharacteristic
185C2×#4318C2311yescharacteristic
186C22×C11⋊C8—21no—
187#66901—22no—
188#66901—22no—
189#66901—22no—
190#66901—22no—
191#66901—41no—
192#66901D414yescomplemented
193#66899—21no—
194#66899—21no—
195#66899—21no—
196#66897—22no—
197#66897—41no—
198#66896—21no—
199#66896—21no—
200#66896—21no—
201C22⋊(C11⋊C8)—21no—
202C22⋊(C11⋊C8)—21no—
203#66873—21no—
204#66873—21no—
205#66872—21no—
206#66871—21no—
207#24464—111nomaximal, Sylow
208C24×C11—22no—
209C24×C11—21no—
210C24×C11C2×D411yescharacteristic
211C24×C11C2×D412yes—
212C23×D11—21no—
213C11×#41—21no—
214C11×#41—21no—
215C11×#41—22no—
216C11×#41—22no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—21no—
220C11×#41—21no—
221C11×#41—21no—
222C11×#41—21no—
223C11×#41—21no—
224C11×#41—21no—
225C11×#41—42no—
226C11×#41—42no—
227C11×#41—41no—
228C11×#41—41no—
229C11×#41—42no—
230C11×#41—42no—
231C11×#41—42no—
232C11×#41—42no—
233C11×#41—42no—
234C11×#41—42no—
235C11×#41C2×D412yes—
236C11×#41#4112yes—
237C2×Q8×C11—21no—
238C2×Q8×C11—22no—
239C2×Q8×C11—41no—
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2×D411yescharacteristic
242C2×Q8×C11C2×D411yescharacteristic
243C2×D4×C11—21no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—22no—
248C2×D4×C11—21no—
249C2×D4×C11—21no—
250C2×D4×C11—21no—
251C2×D4×C11—21no—
252C2×D4×C11—21no—
253C2×D4×C11—22no—
254C2×D4×C11—22no—
255C2×D4×C11—22no—
256C2×D4×C11—21no—
257C2×D4×C11—22no—
258C2×D4×C11—21no—
259C2×D4×C11—21no—
260C2×D4×C11—21no—
261C2×D4×C11—21no—
262C2×D4×C11—21no—
263C2×D4×C11—21no—
264C2×D4×C11—21no—
265C2×D4×C11—41no—
266C2×D4×C11—42no—
267C2×D4×C11—42no—
268C2×D4×C11—42no—
269C2×D4×C11—42no—
270C2×D4×C11—44no—
271C2×D4×C11—44no—
272C2×D4×C11—42no—
273C2×D4×C11—42no—
274C2×D4×C11—44no—
275C2×D4×C11—84no—
276C2×D4×C11C2×D411yescharacteristic
277C2×D4×C11C2×D411yescharacteristic
278C2×D4×C11C2×D411yescharacteristic
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—22no—
285C22×C4×C11—21no—
286C22×C4×C11—22no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—42no—
292C22×C4×C11—42no—
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2×D412yes—
299C22×C4×C11C2411yescharacteristic
300C2×C22⋊D11—44no—
301C2×C22⋊D11—44no—
302C2×C22⋊D11—44no—
303C2×C22⋊D11—44no—
304C2×C22⋊D11—41no—
305C2×C22⋊D11—41no—
306C22×Dic11—24no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—42no—
311C22×Dic11—42no—
312C2×D44—21no—
313C2×D44—21no—
314C2×D44—21no—
315C2×D44—21no—
316C2×D44—21no—
317C2×D44—21no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—22no—
320C11×C4⋊C4—21no—
321C11×C4⋊C4—21no—
322C11×C4⋊C4—21no—
323C11×C4⋊C4—21no—
324C11×C4⋊C4C2×D411yescharacteristic
325C11×C4⋊C4C2×D411yescharacteristic
326C11×C22⋊C4—22no—
327C11×C22⋊C4—22no—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—22no—
330C11×C22⋊C4—22no—
331C11×C22⋊C4—21no—
332C11×C22⋊C4—21no—
333C11×C22⋊C4—21no—
334C11×C22⋊C4—21no—
335C11×C22⋊C4—22no—
336C11×C22⋊C4—22no—
337C11×C22⋊C4—21no—
338C42×C11—22no—
339C42×C11—21no—
340C22⋊Dic11—44no—
341#4325—42no—
342#4325—42no—
343#4325—42no—
344#4323—42no—
345#4323—42no—
346#4323—42no—
347(C2×D11)⋊C4—44no—
348(C2×D11)⋊C4—41no—
349(C2×D11)⋊C4—41no—
350C4⋊Dic11—21no—
351C4⋊Dic11—21no—
352Dic11⋊C4—44no—
353C4×Dic11—21no—
354C4×Dic11—21no—
355C4×Dic11—21no—
356C4×Dic11—42no—
357C4×Dic11C2×D412yescomplemented
358#4318—21no—
359#4318—21no—
360#4318—21no—
361#4318—21no—
362#4318—21no—
363#4318—21no—
364#4318—21no—
365#4318—42no—
366#4318C2×D412yescomplemented
367C2×C11⋊C8—21no—
368C2×C11⋊C8—21no—
369C2×C11⋊C8—21no—
370C2×C11⋊C8—21no—
371C2×C11⋊C8—42no—
372#3488D1111yescharacteristic, complemented
373#3055—111no—
374C2×#453—111no—
375#3006—111no—
376C22×#104—111no—
377#2856—111no—
378#2039—111no—
379#2037—111no—
380#2006—111no—
381#2002—111no—
382#1900—111no—
383#1896—111no—
384#1883—111no—
385#1859—111no—
386#1792—111no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—21no—
393C23×C11—21no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—41no—
397C23×C11—42no—
398C23×C11—44no—
399C23×C11—42no—
400C23×C11—42no—
401C23×C11—42no—
402C23×C11—81no—
403C23×C11—82no—
404C23×C11—82no—
405C23×C11#12011yescharacteristic
406C23×C11#12011yescharacteristic
407C23×C11C22×D411yescharacteristic
408C22×D11—42no—
409C22×D11—42no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413Q8×C11—21no—
414Q8×C11—21no—
415Q8×C11—21no—
416Q8×C11—21no—
417Q8×C11—21no—
418Q8×C11—42no—
419Q8×C11#12112yescomplemented
420D4×C11—22no—
421D4×C11—22no—
422D4×C11—21no—
423D4×C11—21no—
424D4×C11—21no—
425D4×C11—21no—
426D4×C11—21no—
427D4×C11—42no—
428D4×C11—42no—
429D4×C11—44no—
430D4×C11—42no—
431D4×C11—44no—
432D4×C11—41no—
433D4×C11—41no—
434D4×C11—41no—
435D4×C11—41no—
436D4×C11—44no—
437D4×C11—42no—
438D4×C11—41no—
439D4×C11—41no—
440D4×C11—41no—
441D4×C11—41no—
442D4×C11—81no—
443D4×C11—82no—
444D4×C11—82no—
445D4×C11—82no—
446D4×C11—82no—
447D4×C11#12112yescomplemented
448C2×C4×C11—21no—
449C2×C4×C11—21no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—21no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—22no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—22no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—42no—
467C2×C4×C11—42no—
468C2×C4×C11—42no—
469C2×C4×C11—44no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—42no—
475C2×C4×C11—82no—
476C2×C4×C11#12011yescharacteristic
477C2×C4×C11#12011yescharacteristic
478C2×C4×C11C22×D411yescharacteristic
479C2×C4×C11C22×D411yescharacteristic
480C2×C4×C11C22×D411yescharacteristic
481C2×C4×C11C2×#4111yescharacteristic
482C2×C4×C11H(5,𝔽2)11yescharacteristic
483C2×C4×C11H(5,𝔽2)11yescharacteristic
484C22⋊D11—88no—
485C22⋊D11—82no—
486C22⋊D11—82no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—48no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—42no—
495C2×Dic11—41no—
496D44—41no—
497D44—41no—
498D44—41no—
499D44—41no—
500C11⋊C8—22no—
501C11⋊C8—41no—
502C11⋊C8—41no—
503C11⋊C8—41no—
504C2×H(5,𝔽2)C2×D1111yescharacteristic
505C22×#41C2×D1111yescharacteristic
506C2×AGL(1,ℤ/8)—111no—
507C2×AGL(1,ℤ/8)—111no—
508C2×AGL(1,ℤ/8)—111no—
509C22×M16—111no—
510#550—21no—
511#548—21no—
512#546—21no—
513#546—22no—
514D42—22no—
515D42—21no—
516#537—21no—
517#537C2×D1111yescharacteristic
518#535—21no—
519#535C2×D1111yescharacteristic
520C2×#127—111no—
521#525—21no—
522#525C2×D1111yescharacteristic
523C2×#121—21no—
524C2×#121—111no—
525C2×#121—222no—
526C2×#121C2×D1111yescharacteristic
527#520C2×D1111yescharacteristic
528C22×C42—111no—
529#469—221no—
530#468—221no—
531#466—221no—
532#465—221no—
533#453—224no—
534#449—221no—
535#449—221no—
536#448—221no—
537#447—221no—
538#428—111no—
539C2×#104—111no—
540C2×#104—111no—
541C2×#104—111no—
542C2×#104—111no—
543C2×#104—111no—
544C2×#104—111no—
545C2×#104—224no—
546#418—111no—
547#417—111no—
548#417—111no—
549#417—111no—
550C2×#100—111no—
551C2×#100—111no—
552#407—111no—
553#390—111no—
554#390—111no—
555#390—222no—
556#384—111no—
557#343—111no—
558#343—111no—
559#339—111no—
560#339—111no—
561C22×C11—21no—
562C22×C11—21no—
563C22×C11—21no—
564C22×C11—21no—
565C22×C11—21no—
566C22×C11—22no—
567C22×C11—21no—
568C22×C11—21no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—41no—
572C22×C11—41no—
573C22×C11—41no—
574C22×C11—41no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—41no—
578C22×C11—41no—
579C22×C11—41no—
580C22×C11—42no—
581C22×C11—41no—
582C22×C11—84no—
583C22×C11—82no—
584C22×C11—82no—
585C22×C11—164no—
586C22×C11#45312yescomplemented
587C22×C11C2×#12011yescharacteristic
588C22×C11D4211yescharacteristic
589C22×C11#54611yescharacteristic
590C2×D11—82no—
591C2×D11—82no—
592C2×D11—81no—
593C2×D11—81no—
594C2×D11—81no—
595C4×C11—21no—
596C4×C11—21no—
597C4×C11—22no—
598C4×C11—41no—
599C4×C11—41no—
600C4×C11—42no—
601C4×C11—41no—
602C4×C11—41no—
603C4×C11C2×#12111yescharacteristic
604C4×C11#53411yescharacteristic
605C4×C11D4211yescharacteristic
606C4×C11#54611yescharacteristic
607Dic11—24no—
608Dic11—42no—
609Dic11—81no—
610H(5,𝔽2)—22no—
611H(5,𝔽2)—22no—
612H(5,𝔽2)—41no—
613H(5,𝔽2)—41no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41—21no—
618C2×#41—22no—
619C2×#41—22no—
620C2×#41—41no—
621C2×#41—41no—
622C2×#41C22⋊D1111yescharacteristic, complemented
623C2×#41C22⋊D1111yescharacteristic, complemented
624C2×#41C22×D1111yescharacteristic
625C2×#41C22×D1111yescharacteristic
626C2×#41C22×D1111yescharacteristic
627C22×Q8C22⋊D1111yescharacteristic, complemented
628C22×D4—21no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—111no—
634C22×D4—221no—
635C22×D4—222no—
636C22×D4C22⋊D1112yes—
637C22×D4C22⋊D1111yescharacteristic, complemented
638C22×D4C22×D1111yescharacteristic
639C23×C4—21no—
640C23×C4—221no—
641C23×C4C22×D1111yescharacteristic
642AGL(1,ℤ/8)—222no—
643AGL(1,ℤ/8)—222no—
644AGL(1,ℤ/8)—222no—
645AGL(1,ℤ/8)—441no—
646AGL(1,ℤ/8)—441no—
647AGL(1,ℤ/8)—441no—
648C2×SD16—221no—
649C2×SD16—221no—
650C2×SD16—221no—
651C2×D8—221no—
652C2×D8—221no—
653C2×D8—221no—
654C2×M16—111no—
655C2×M16—111no—
656C2×M16—111no—
657C2×M16—111no—
658C2×M16—221no—
659C2×M16—222no—
660C2×M16—441no—
661C22×C8—221no—
662#127—22no—
663#127—21no—
664#127—222no—
665#127—441no—
666#124—22no—
667#124—21no—
668#123—22no—
669#123—21no—
670C22⋊Q8—22no—
671C22⋊Q8—21no—
672C22⋊Q8—21no—
673C22⋊Q8C22⋊D1111yescharacteristic, complemented
674C22⋊Q8C22⋊D1111yescharacteristic, complemented
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—21no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—221no—
690#121—221no—
691#121—221no—
692#121—221no—
693#121—448no—
694#121C22⋊D1111yescharacteristic, complemented
695#121C22⋊D1111yescharacteristic, complemented
696#120—22no—
697#120—22no—
698#120—22no—
699#120—21no—
700#120—22no—
701C4×Q8—21no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—21no—
705C4×D4—22no—
706C4×D4—21no—
707C4×D4—21no—
708#117—21no—
709#117C22×D1111yescharacteristic
710C2×C4⋊C4—21no—
711C2×C4⋊C4—111no—
712C2×C4⋊C4—222no—
713C2×C4⋊C4C22×D1111yescharacteristic
714C2×C22⋊C4—22no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—221no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4C22⋊D1112yes—
719C2×C42—111no—
720C2×C42—111no—
721C2×C42—222no—
722C2×C42—221no—
723C2×C42—441no—
724#107—221no—
725#106—221no—
726#104—114no—
727#104—222no—
728#104—222no—
729#104—222no—
730#104—222no—
731#104—441no—
732#103—221no—
733#103—221no—
734#103—221no—
735#102—221no—
736#102—221no—
737#102—221no—
738#102—221no—
739#102—221no—
740#100—222no—
741#100—441no—
742C22⋊C8—221no—
743C22⋊C8—221no—
744C2×C11—21no—
745C2×C11—21no—
746C2×C11—22no—
747C2×C11—41no—
748C2×C11—42no—
749C2×C11—81no—
750C2×C11—82no—
751C2×C11—81no—
752C2×C11#241011yescharacteristic
753C2×C11C2×#45311yescharacteristic
754C2×C11#301811yescharacteristic
755D11—161no—
756C24—22no—
757C24—21no—
758C24—221no—
759C24C2×C22⋊D1111yescharacteristic
760C24C2×C22⋊D1112yes—
761#41—21no—
762#41—21no—
763#41—22no—
764#41—22no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—42no—
774#41—42no—
775#41—41no—
776#41—41no—
777#41—42no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41D4×D1112yes—
784#41#434112yes—
785C2×Q8—21no—
786C2×Q8—22no—
787C2×Q8—41no—
788C2×Q8C2×C22⋊D1111yescharacteristic
789C2×Q8C2×C22⋊D1111yescharacteristic
790C2×Q8C2×C22⋊D1111yescharacteristic
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—21no—
805C2×D4—22no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—41no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—44no—
823C2×D4—84no—
824C2×D4—221no—
825C2×D4—221no—
826C2×D4—221no—
827C2×D4—221no—
828C2×D4—221no—
829C2×D4—221no—
830C2×D4—444no—
831C2×D4—444no—
832C2×D4—444no—
833C2×D4—444no—
834C2×D4—441no—
835C2×D4—441no—
836C2×D4C2×C22⋊D1111yescharacteristic
837C2×D4C2×C22⋊D1111yescharacteristic
838C2×D4C2×C22⋊D1111yescharacteristic
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—221no—
854C22×C4—224no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—442no—
858C22×C4—442no—
859C22×C4C2×C22⋊D1111yescharacteristic
860C22×C4C2×C22⋊D1111yescharacteristic
861C22×C4C2×C22⋊D1111yescharacteristic
862C22×C4C2×C22⋊D1111yescharacteristic
863C22×C4C2×C22⋊D1111yescharacteristic
864C22×C4C2×C22⋊D1112yes—
865C22×C4C23×D1111yescharacteristic
866SD16—442no—
867SD16—442no—
868SD16—442no—
869D8—442no—
870D8—442no—
871D8—442no—
872M16—112no—
873M16—221no—
874M16—221no—
875M16—221no—
876M16—221no—
877M16—221no—
878M16—221no—
879M16—221no—
880M16—442no—
881C2×C8—221no—
882C2×C8—221no—
883C2×C8—221no—
884C2×C8—221no—
885C2×C8—442no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—221no—
893C4⋊C4—221no—
894C4⋊C4—444no—
895C4⋊C4C2×C22⋊D1111yescharacteristic
896C4⋊C4C2×C22⋊D1111yescharacteristic
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—21no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—21no—
909C22⋊C4—444no—
910C22⋊C4—444no—
911C22⋊C4—441no—
912C22⋊C4—441no—
913C42—22no—
914C42—21no—
915C42—112no—
916C42—221no—
917C42—221no—
918C42—221no—
919C42—442no—
920C11#2446411yescharacteristic, complemented, Sylow
921C23—21no—
922C23—21no—
923C23—22no—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—81no—
937C23—82no—
938C23—82no—
939C23—442no—
940C23—442no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23#6700611yescharacteristic
945C23#6700611yescharacteristic
946C23C22×C22⋊D1111yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#6699212yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—44no—
971D4—42no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—81no—
977D4—82no—
978D4—82no—
979D4—82no—
980D4—82no—
981D4—441no—
982D4—441no—
983D4—441no—
984D4—441no—
985D4—888no—
986D4—882no—
987D4—882no—
988D4#6699212yescomplemented
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—44no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—42no—
1016C2×C4—82no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—448no—
1022C2×C4—441no—
1023C2×C4—441no—
1024C2×C4—442no—
1025C2×C4—441no—
1026C2×C4#6700611yescharacteristic
1027C2×C4#6700611yescharacteristic
1028C2×C4C2×D4×D1111yescharacteristic
1029C2×C4C2×#434111yescharacteristic
1030C2×C4#6703711yescharacteristic
1031C2×C4#6703711yescharacteristic
1032C2×C4C22×C22⋊D1111yescharacteristic
1033C2×C4C22×C22⋊D1111yescharacteristic
1034C8—222no—
1035C8—441no—
1036C8—441no—
1037C8—441no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—164no—
1063C22—882no—
1064C22—882no—
1065C22—881no—
1066C22—881no—
1067C22—881no—
1068C22#1062285412yescomplemented
1069C22D4×C22⋊D1111yescharacteristic
1070C22#1062333711yescharacteristic
1071C22C2×#6700611yescharacteristic
1072C4—21no—
1073C4—21no—
1074C4—22no—
1075C4—41no—
1076C4—41no—
1077C4—42no—
1078C4—41no—
1079C4—41no—
1080C4—224no—
1081C4—442no—
1082C4—881no—
1083C4D4×C22⋊D1111yescharacteristic
1084C4C2×#6699211yescharacteristic
1085C4#1062333511yescharacteristic
1086C4#1062333711yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—1761no—
1096C2#1307199011yescharacteristic
1097C2C2×#1062285411yescharacteristic
1098C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3488C2
socleC22×C11C2×#120
hypercenter#3488D11
hypocenterC11#24464
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #13078237C2semidirect
2. C2×#10622854C2semidirect
3. #13077868C2semidirect
4. C22×#66901C2semidirect
5. #13076959C2semidirect
6. #13069837C2semidirect
7. #13069823C2semidirect
8. #13069658C2semidirect
9. #13069629C2semidirect
10. #13069080C2semidirect
11. #13069060C2semidirect
12. #13068992C2semidirect
13. #13068842C2semidirect
14. #13068570C2semidirect
15. C11×#3488C2semidirect
34. C2×#67002C22semidirect
35. C2×#67002C22semidirect
36. C2×#66993C22semidirect
38. C2×#66983C22semidirect
39. C22×C4×Dic11C22semidirect
40. C22×#4318C22semidirect
47. C2×#66901C22semidirect
48. C2×#66901C22semidirect
49. C2×#66901C22semidirect
50. C2×#66901C22semidirect
52. #10622845C22semidirect
53. #10622845C22semidirect
55. #10622834C22semidirect
57. C2×#66897C22semidirect
58. C2×#66897C22semidirect
59. #10622820C22semidirect
64. #10622614C22semidirect
65. #10622608C22semidirect
66. #10622601C22semidirect
67. #10622589C22semidirect
69. #10622170C22semidirect
70. #10622170C22semidirect
71. #10622168C22semidirect
72. #10622168C22semidirect
85. C2×C11×#41D4semidirect
86. C2×C11×#41D4semidirect
90. C22×Q8×C11D4semidirect
97. C22×D4×C11D4semidirect
114. C11×C22⋊Q8D4semidirect
115. C11×C22⋊Q8D4semidirect
130. C11×#121D4semidirect
131. C11×#121D4semidirect
192. #66901D4semidirect
357. C4×Dic11C2×D4semidirect
366. #4318C2×D4semidirect
372. #3488D11semidirect
419. Q8×C11#121semidirect
447. D4×C11#121semidirect
586. C22×C11#453semidirect
622. C2×#41C22⋊D11semidirect
623. C2×#41C22⋊D11semidirect
627. C22×Q8C22⋊D11semidirect
637. C22×D4C22⋊D11semidirect
673. C22⋊Q8C22⋊D11semidirect
674. C22⋊Q8C22⋊D11semidirect
694. #121C22⋊D11semidirect
695. #121C22⋊D11semidirect
920. C11#24464semidirect
953. Q8#66992semidirect
988. D4#66992semidirect
1068. C22#10622854semidirect

Maximal subgroups

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

subgroupindex
#130782372
C2×#106228542
#130778682
C22×#669012
#130769592
#130698372
#130698232
#130696582
#130696292
#130690802
#130690602
#130689922
#130688422
#130685702
C11×#34882
#2446411