Finite Group Databasebeta

← #14791994

Subgroups — #14791994

Order 2816.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 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
4C2×#10622849C211yesmaximal, characteristic, complemented
5#13074370C211yesmaximal, characteristic, complemented
6#13069842C211yesmaximal, characteristic, complemented
7#13069823C211yesmaximal, characteristic, complemented
8#13069658C211yesmaximal, characteristic, complemented
9#13069629C211yesmaximal, characteristic, complemented
10#13069080C211yesmaximal, characteristic, complemented
11#13069065C211yesmaximal, characteristic, complemented
12#13068992C211yesmaximal, characteristic, complemented
13#13068849C211yesmaximal, 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×#66983C2211yescharacteristic, complemented
38C2×#66979C2211yescharacteristic, complemented
39C22×#4318C2211yescharacteristic, complemented
40#10622854—24no—
41#10622851—21no—
42#10622851—21no—
43#10622849—24no—
44C2×#66901C2211yescharacteristic
45C2×#66901C2211yescharacteristic
46C2×#66901C2211yescharacteristic, complemented
47C2×#66901C2211yescharacteristic, complemented
48C2×#66901C2211yescharacteristic, complemented
49C2×#66901C2211yescharacteristic, complemented
50#10622845C2211yescharacteristic
51#10622845C2211yescharacteristic, complemented
52#10622845C2211yescharacteristic, complemented
53#10622840—21no—
54#10622836—22no—
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#10622590C2211yescharacteristic, complemented
68#10622574—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—
103C22×D44C2311yescharacteristic
104C11×#127—22no—
105C11×#127—21no—
106C11×#124—22no—
107C11×#124—21no—
108C11×#123—22no—
109C11×#123—21no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8D411yescharacteristic, complemented
114C11×C22⋊Q8D411yescharacteristic, complemented
115C11×#121—22no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—21no—
121C11×#121—21no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121—22no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121D411yescharacteristic, complemented
130C11×#121D411yescharacteristic, complemented
131C11×#120—22no—
132C11×#120—22no—
133C11×#120—22no—
134C11×#120—21no—
135C11×#120—22no—
136C4×Q8×C11—21no—
137C4×D4×C11—22no—
138C4×D4×C11—22no—
139C4×D4×C11—21no—
140C4×D4×C11—22no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C11×#117—21no—
144C11×#117C2311yescharacteristic
145C2×C11×C4⋊C4—21no—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4—22no—
148C2×C11×C22⋊C4D412yes—
149C2×C22⋊Dic11—21no—
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—
162C2×#4323—21no—
163C2×#4323—21no—
164C2×#4323—21no—
165#66983—21no—
166#66983—21no—
167#66983—21no—
168#66983—21no—
169C2×(C2×D11)⋊C4—21no—
170C2×(C2×D11)⋊C4—22no—
171#66979—22no—
172#66979—41no—
173C2×C4⋊Dic11—21no—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4×Dic11C2311yescharacteristic
176C2×C4×Dic11C2311yescharacteristic
177C2×#4318—21no—
178C2×#4318—22no—
179C2×#4318—41no—
180C2×#4318C2311yescharacteristic
181C2×#4318C2311yescharacteristic
182C2×#4318C2311yescharacteristic
183C2×#4318C2311yescharacteristic
184C22×C11⋊C8—21no—
185#66901—22no—
186#66901—22no—
187#66901—22no—
188#66901—22no—
189#66901—41no—
190#66901D414yescomplemented
191#66899—21no—
192#66899—21no—
193#66899—21no—
194#66897—22no—
195#66897—41no—
196#66896—21no—
197#66896—21no—
198#66896—21no—
199C11⋊#95—22no—
200C22⋊(C11⋊C8)—21no—
201C22⋊(C11⋊C8)—21no—
202#66873—21no—
203#66873—21no—
204#66872—21no—
205#66871—21no—
206#24468—111nomaximal, Sylow
207C24×C11—22no—
208C24×C11—21no—
209C24×C11C2×D412yes—
210C24×C11C2×D411yescharacteristic
211C23×D11—21no—
212C11×#41—21no—
213C11×#41—21no—
214C11×#41—22no—
215C11×#41—22no—
216C11×#41—21no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—21no—
220C11×#41—21no—
221C11×#41—21no—
222C11×#41—21no—
223C11×#41—21no—
224C11×#41—42no—
225C11×#41—42no—
226C11×#41—41no—
227C11×#41—41no—
228C11×#41—42no—
229C11×#41—42no—
230C11×#41—42no—
231C11×#41—42no—
232C11×#41—42no—
233C11×#41—42no—
234C11×#41C2×D412yes—
235C11×#41#4112yes—
236C2×Q8×C11—21no—
237C2×Q8×C11—22no—
238C2×Q8×C11—41no—
239C2×Q8×C11C2×D411yescharacteristic
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2×D411yescharacteristic
242C2×D4×C11—21no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—21no—
248C2×D4×C11—21no—
249C2×D4×C11—21no—
250C2×D4×C11—21no—
251C2×D4×C11—21no—
252C2×D4×C11—22no—
253C2×D4×C11—22no—
254C2×D4×C11—22no—
255C2×D4×C11—21no—
256C2×D4×C11—22no—
257C2×D4×C11—21no—
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—41no—
265C2×D4×C11—42no—
266C2×D4×C11—42no—
267C2×D4×C11—42no—
268C2×D4×C11—42no—
269C2×D4×C11—44no—
270C2×D4×C11—44no—
271C2×D4×C11—42no—
272C2×D4×C11—42no—
273C2×D4×C11—82no—
274C2×D4×C11—84no—
275C2×D4×C11C2×D411yescharacteristic
276C2×D4×C11C2×D411yescharacteristic
277C2×D4×C11C2×D411yescharacteristic
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—22no—
284C22×C4×C11—21no—
285C22×C4×C11—22no—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—21no—
290C22×C4×C11—42no—
291C22×C4×C11—42no—
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D412yes—
298C22×C4×C11C2411yescharacteristic
299C2×C22⋊D11—44no—
300C2×C22⋊D11—41no—
301C2×C22⋊D11—41no—
302C2×C22⋊D11—82no—
303C2×C22⋊D11—82no—
304C2×C22⋊D11—82no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C2×D44—21no—
309C2×D44—21no—
310C2×D44—21no—
311C2×D44—21no—
312C2×D44—21no—
313C2×D44—21no—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—21no—
317C11×C4⋊C4—21no—
318C11×C4⋊C4—21no—
319C11×C4⋊C4—21no—
320C11×C4⋊C4C2×D411yescharacteristic
321C11×C4⋊C4C2×D411yescharacteristic
322C11×C22⋊C4—22no—
323C11×C22⋊C4—22no—
324C11×C22⋊C4—22no—
325C11×C22⋊C4—22no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—21no—
328C11×C22⋊C4—21no—
329C11×C22⋊C4—21no—
330C11×C22⋊C4—21no—
331C11×C22⋊C4—22no—
332C11×C22⋊C4—22no—
333C11×C22⋊C4—21no—
334C42×C11—22no—
335C42×C11—21no—
336C22⋊Dic11—42no—
337C22⋊Dic11—82no—
338#4325—42no—
339#4325—42no—
340#4325—42no—
341#4323—42no—
342#4323—42no—
343#4323—42no—
344(C2×D11)⋊C4—41no—
345(C2×D11)⋊C4—41no—
346(C2×D11)⋊C4—82no—
347C4⋊Dic11—21no—
348C4⋊Dic11—21no—
349C4⋊Dic11—42no—
350C4×Dic11—21no—
351C4×Dic11—21no—
352C4×Dic11—21no—
353C4×Dic11C2×D412yescomplemented
354#4318—21no—
355#4318—21no—
356#4318—21no—
357#4318—21no—
358#4318—21no—
359#4318—21no—
360#4318—21no—
361#4318—42no—
362#4318C2×D412yescomplemented
363C2×C11⋊C8—21no—
364C2×C11⋊C8—21no—
365C2×C11⋊C8—21no—
366C2×C11⋊C8—21no—
367C2×C11⋊C8—42no—
368#3488D1111yescharacteristic, complemented
369#3055—111no—
370C2×#453—111no—
371#3006—111no—
372C2×#421—111no—
373#2619—111no—
374#2040—111no—
375#2037—111no—
376#2006—111no—
377#2002—111no—
378#1900—111no—
379#1897—111no—
380#1883—111no—
381#1860—111no—
382#1792—111no—
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—22no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—42no—
394C23×C11—42no—
395C23×C11—44no—
396C23×C11—42no—
397C23×C11—42no—
398C23×C11—81no—
399C23×C11—82no—
400C23×C11—82no—
401C23×C11#12011yescharacteristic
402C23×C11#12011yescharacteristic
403C23×C11C22×D411yescharacteristic
404C22×D11—42no—
405C22×D11—42no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409Q8×C11—21no—
410Q8×C11—21no—
411Q8×C11—21no—
412Q8×C11—21no—
413Q8×C11—21no—
414Q8×C11—42no—
415Q8×C11#12112yes—
416D4×C11—22no—
417D4×C11—22no—
418D4×C11—21no—
419D4×C11—21no—
420D4×C11—21no—
421D4×C11—21no—
422D4×C11—21no—
423D4×C11—42no—
424D4×C11—42no—
425D4×C11—44no—
426D4×C11—42no—
427D4×C11—44no—
428D4×C11—44no—
429D4×C11—42no—
430D4×C11—41no—
431D4×C11—41no—
432D4×C11—41no—
433D4×C11—41no—
434D4×C11—41no—
435D4×C11—41no—
436D4×C11—41no—
437D4×C11—41no—
438D4×C11—81no—
439D4×C11—82no—
440D4×C11—82no—
441D4×C11—82no—
442D4×C11—82no—
443D4×C11#12112yes—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—21no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—22no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—42no—
463C2×C4×C11—42no—
464C2×C4×C11—42no—
465C2×C4×C11—44no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—42no—
471C2×C4×C11—82no—
472C2×C4×C11#12011yescharacteristic
473C2×C4×C11#12011yescharacteristic
474C2×C4×C11C22×D411yescharacteristic
475C2×C4×C11C22×D411yescharacteristic
476C2×C4×C11C22×D411yescharacteristic
477C2×C4×C11C2×#4111yescharacteristic
478C2×C4×C11H(5,𝔽2)11yescharacteristic
479C2×C4×C11H(5,𝔽2)11yescharacteristic
480C22⋊D11—88no—
481C22⋊D11—82no—
482C22⋊D11—82no—
483C2×Dic11—22no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—42no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491D44—41no—
492D44—41no—
493D44—41no—
494D44—41no—
495C11⋊C8—22no—
496C11⋊C8—41no—
497C11⋊C8—41no—
498C11⋊C8—41no—
499C2×H(5,𝔽2)C2×D1111yescharacteristic
500C22×#41C2×D1111yescharacteristic
501C2×AGL(1,ℤ/8)—111no—
502C2×AGL(1,ℤ/8)—111no—
503C2×AGL(1,ℤ/8)—111no—
504C22×M16—111no—
505#550—21no—
506#548—21no—
507#546—21no—
508#546—22no—
509D42—22no—
510D42—21no—
511#537—21no—
512#537C2×D1111yescharacteristic
513#535—21no—
514#535C2×D1111yescharacteristic
515C2×#127—111no—
516#525—21no—
517#525C2×D1111yescharacteristic
518C2×#121—21no—
519C2×#121—111no—
520C2×#121C2×D1111yescharacteristic
521#520C2×D1111yescharacteristic
522C2×#117—111no—
523#469—221no—
524#468—221no—
525#466—221no—
526#465—221no—
527#453—224no—
528#449—221no—
529#449—221no—
530#448—221no—
531#447—221no—
532#428—111no—
533#421—224no—
534C2×#104—111no—
535C2×#104—111no—
536C2×#104—111no—
537C2×#104—111no—
538C2×#104—111no—
539C2×#104—111no—
540#418—111no—
541#417—111no—
542#417—111no—
543#417—111no—
544C2×#100—111no—
545C2×#100—111no—
546#407—111no—
547#394—222no—
548#392—222no—
549#390—111no—
550#390—111no—
551#382—111no—
552#343—111no—
553#343—111no—
554#339—111no—
555#339—111no—
556C22×C11—21no—
557C22×C11—21no—
558C22×C11—21no—
559C22×C11—21no—
560C22×C11—22no—
561C22×C11—21no—
562C22×C11—21no—
563C22×C11—21no—
564C22×C11—21no—
565C22×C11—41no—
566C22×C11—41no—
567C22×C11—41no—
568C22×C11—41no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—41no—
572C22×C11—41no—
573C22×C11—41no—
574C22×C11—42no—
575C22×C11—41no—
576C22×C11—81no—
577C22×C11—81no—
578C22×C11—82no—
579C22×C11—82no—
580C22×C11—84no—
581C22×C11—164no—
582C22×C11C2×#12011yescharacteristic
583C22×C11D4211yescharacteristic
584C22×C11#54611yescharacteristic
585C2×D11—82no—
586C2×D11—82no—
587C2×D11—81no—
588C2×D11—81no—
589C2×D11—81no—
590C4×C11—21no—
591C4×C11—21no—
592C4×C11—22no—
593C4×C11—41no—
594C4×C11—41no—
595C4×C11—42no—
596C4×C11—41no—
597C4×C11—41no—
598C4×C11C2×#12111yescharacteristic
599C4×C11#53411yescharacteristic
600C4×C11D4211yescharacteristic
601C4×C11#54611yescharacteristic
602Dic11—42no—
603Dic11—81no—
604Dic11—81no—
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41C22⋊D1111yescharacteristic, complemented
618C2×#41C22⋊D1111yescharacteristic, complemented
619C2×#41C22×D1111yescharacteristic
620C2×#41C22×D1111yescharacteristic
621C2×#41C22×D1111yescharacteristic
622C22×Q8C22⋊D1111yescharacteristic, complemented
623C22×D4—21no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—21no—
627C22×D4—21no—
628C22×D4—111no—
629C22×D4—221no—
630C22×D4—222no—
631C22×D4C22⋊D1112yes—
632C22×D4C22⋊D1111yescharacteristic, complemented
633C22×D4C22×D1111yescharacteristic
634C23×C4—21no—
635C23×C4C22×D1111yescharacteristic
636AGL(1,ℤ/8)—222no—
637AGL(1,ℤ/8)—222no—
638AGL(1,ℤ/8)—222no—
639AGL(1,ℤ/8)—441no—
640AGL(1,ℤ/8)—441no—
641AGL(1,ℤ/8)—441no—
642C2×SD16—221no—
643C2×SD16—221no—
644C2×SD16—221no—
645C2×D8—221no—
646C2×D8—221no—
647C2×D8—221no—
648C2×M16—111no—
649C2×M16—111no—
650C2×M16—111no—
651C2×M16—111no—
652C2×M16—221no—
653C2×M16—222no—
654C2×M16—441no—
655C22×C8—221no—
656#127—22no—
657#127—21no—
658#127—222no—
659#127—441no—
660#124—22no—
661#124—21no—
662#123—22no—
663#123—21no—
664C22⋊Q8—22no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8C22⋊D1111yescharacteristic, complemented
668C22⋊Q8C22⋊D1111yescharacteristic, complemented
669#121—22no—
670#121—22no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—22no—
681#121—21no—
682#121—21no—
683#121—221no—
684#121—221no—
685#121—221no—
686#121—221no—
687#121C22⋊D1111yescharacteristic, complemented
688#121C22⋊D1111yescharacteristic, complemented
689#120—22no—
690#120—22no—
691#120—22no—
692#120—21no—
693#120—22no—
694C4×Q8—21no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—22no—
699C4×D4—21no—
700C4×D4—21no—
701#117—21no—
702#117—222no—
703#117—441no—
704#117C22×D1111yescharacteristic
705C2×C4⋊C4—21no—
706C2×C4⋊C4—111no—
707C2×C4⋊C4—221no—
708C2×C4⋊C4C22×D1111yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—221no—
711C2×C22⋊C4—221no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4C22⋊D1112yes—
715C2×C42—111no—
716C2×C42—111no—
717#107—221no—
718#106—221no—
719#104—114no—
720#104—222no—
721#104—222no—
722#104—222no—
723#104—222no—
724#104—441no—
725#103—221no—
726#103—221no—
727#103—221no—
728#102—221no—
729#102—221no—
730#102—221no—
731#102—221no—
732#102—221no—
733#100—222no—
734#100—441no—
735C22⋊C8—221no—
736C22⋊C8—221no—
737#95—222no—
738C2×C11—21no—
739C2×C11—21no—
740C2×C11—41no—
741C2×C11—41no—
742C2×C11—42no—
743C2×C11—81no—
744C2×C11—82no—
745C2×C11—81no—
746C2×C11#241011yescharacteristic
747C2×C11#301911yescharacteristic
748C2×C11#302111yescharacteristic
749D11—161no—
750C24—22no—
751C24—21no—
752C24—221no—
753C24C2×C22⋊D1112yes—
754C24C2×C22⋊D1111yescharacteristic
755#41—21no—
756#41—21no—
757#41—22no—
758#41—22no—
759#41—21no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—42no—
768#41—42no—
769#41—41no—
770#41—41no—
771#41—42no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41D4×D1112yes—
778#41#434112yes—
779C2×Q8—21no—
780C2×Q8—22no—
781C2×Q8—41no—
782C2×Q8C2×C22⋊D1111yescharacteristic
783C2×Q8C2×C22⋊D1111yescharacteristic
784C2×Q8C2×C22⋊D1111yescharacteristic
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—21no—
799C2×D4—22no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—41no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—82no—
817C2×D4—84no—
818C2×D4—221no—
819C2×D4—221no—
820C2×D4—221no—
821C2×D4—221no—
822C2×D4—221no—
823C2×D4—221no—
824C2×D4—444no—
825C2×D4—441no—
826C2×D4—441no—
827C2×D4—882no—
828C2×D4—882no—
829C2×D4—882no—
830C2×D4C2×C22⋊D1111yescharacteristic
831C2×D4C2×C22⋊D1111yescharacteristic
832C2×D4C2×C22⋊D1111yescharacteristic
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4C2×C22⋊D1111yescharacteristic
851C22×C4C2×C22⋊D1111yescharacteristic
852C22×C4C2×C22⋊D1111yescharacteristic
853C22×C4C2×C22⋊D1111yescharacteristic
854C22×C4C2×C22⋊D1111yescharacteristic
855C22×C4C2×C22⋊D1112yes—
856C22×C4C23×D1111yescharacteristic
857SD16—442no—
858SD16—442no—
859SD16—442no—
860D8—442no—
861D8—442no—
862D8—442no—
863M16—112no—
864M16—221no—
865M16—221no—
866M16—221no—
867M16—221no—
868M16—221no—
869M16—221no—
870M16—221no—
871M16—442no—
872C2×C8—221no—
873C2×C8—221no—
874C2×C8—221no—
875C2×C8—221no—
876C2×C8—442no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—221no—
884C4⋊C4—221no—
885C4⋊C4—442no—
886C4⋊C4C2×C22⋊D1111yescharacteristic
887C4⋊C4C2×C22⋊D1111yescharacteristic
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—21no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—21no—
900C22⋊C4—442no—
901C22⋊C4—441no—
902C22⋊C4—441no—
903C22⋊C4—882no—
904C22⋊C4—882no—
905C42—22no—
906C42—21no—
907C42—112no—
908C42—221no—
909C42—221no—
910C42—221no—
911C11#2446811yescharacteristic, complemented, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—81no—
928C23—82no—
929C23—82no—
930C23—442no—
931C23—442no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23#6700611yescharacteristic
936C23#6700611yescharacteristic
937C23C22×C22⋊D1111yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#6699212yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—81no—
968D4—82no—
969D4—82no—
970D4—82no—
971D4—82no—
972D4—441no—
973D4—441no—
974D4—441no—
975D4—441no—
976D4—888no—
977D4—882no—
978D4—882no—
979D4#6699212yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—44no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—42no—
1007C2×C4—82no—
1008C2×C4—222no—
1009C2×C4—441no—
1010C2×C4—441no—
1011C2×C4—441no—
1012C2×C4—441no—
1013C2×C4—442no—
1014C2×C4—441no—
1015C2×C4—441no—
1016C2×C4#6700611yescharacteristic
1017C2×C4#6700611yescharacteristic
1018C2×C4C2×D4×D1111yescharacteristic
1019C2×C4C2×#434111yescharacteristic
1020C2×C4#6703711yescharacteristic
1021C2×C4#6703711yescharacteristic
1022C2×C4C22×C22⋊D1111yescharacteristic
1023C2×C4C22×C22⋊D1111yescharacteristic
1024C8—222no—
1025C8—441no—
1026C8—441no—
1027C8—441no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—84no—
1053C22—164no—
1054C22—882no—
1055C22—882no—
1056C22—881no—
1057C22—881no—
1058C22—881no—
1059C22D4×C22⋊D1111yescharacteristic
1060C22#1062333711yescharacteristic
1061C22C2×#6700611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—41no—
1066C4—41no—
1067C4—42no—
1068C4—41no—
1069C4—41no—
1070C4—442no—
1071C4—881no—
1072C4—881no—
1073C4D4×C22⋊D1111yescharacteristic
1074C4C2×#6699211yescharacteristic
1075C4#1062333511yescharacteristic
1076C4#1062333711yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—1761no—
1086C2#1307199011yescharacteristic
1087C2#1307797311yescharacteristic
1088C2#1307798811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3488C2
socleC22×C11C2×#120
hypercenter#3488D11
hypocenterC11#24468
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. C2×#10622849C2semidirect
5. #13074370C2semidirect
6. #13069842C2semidirect
7. #13069823C2semidirect
8. #13069658C2semidirect
9. #13069629C2semidirect
10. #13069080C2semidirect
11. #13069065C2semidirect
12. #13068992C2semidirect
13. #13068849C2semidirect
14. #13068570C2semidirect
15. C11×#3488C2semidirect
34. C2×#67002C22semidirect
35. C2×#67002C22semidirect
36. C2×#66993C22semidirect
37. C2×#66983C22semidirect
38. C2×#66979C22semidirect
39. C22×#4318C22semidirect
46. C2×#66901C22semidirect
47. C2×#66901C22semidirect
48. C2×#66901C22semidirect
49. C2×#66901C22semidirect
51. #10622845C22semidirect
52. #10622845C22semidirect
55. #10622834C22semidirect
57. C2×#66897C22semidirect
58. C2×#66897C22semidirect
59. #10622820C22semidirect
64. #10622614C22semidirect
65. #10622608C22semidirect
66. #10622601C22semidirect
67. #10622590C22semidirect
69. #10622170C22semidirect
70. #10622170C22semidirect
71. #10622168C22semidirect
72. #10622168C22semidirect
85. C2×C11×#41D4semidirect
86. C2×C11×#41D4semidirect
90. C22×Q8×C11D4semidirect
97. C22×D4×C11D4semidirect
113. C11×C22⋊Q8D4semidirect
114. C11×C22⋊Q8D4semidirect
129. C11×#121D4semidirect
130. C11×#121D4semidirect
190. #66901D4semidirect
353. C4×Dic11C2×D4semidirect
362. #4318C2×D4semidirect
368. #3488D11semidirect
617. C2×#41C22⋊D11semidirect
618. C2×#41C22⋊D11semidirect
622. C22×Q8C22⋊D11semidirect
632. C22×D4C22⋊D11semidirect
667. C22⋊Q8C22⋊D11semidirect
668. C22⋊Q8C22⋊D11semidirect
687. #121C22⋊D11semidirect
688. #121C22⋊D11semidirect
911. C11#24468semidirect

Maximal subgroups

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

subgroupindex
#130782372
C2×#106228542
#130778682
C2×#106228492
#130743702
#130698422
#130698232
#130696582
#130696292
#130690802
#130690652
#130689922
#130688492
#130685702
C11×#34882
#2446811