Finite Group Databasebeta

← D11×#3548 #15661562

Subgroups — D11×#3548 #15661562

Order 2816.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083016C211yesmaximal, characteristic, complemented
2#13083015C214yesmaximal, complemented
3#13083014C212yesmaximal, complemented
4#13083013C214yesmaximal, complemented
5#13083012C214yesmaximal, complemented
6#13083011C218yesmaximal, complemented
7#13083010C214yesmaximal, complemented
8#13083009C214yesmaximal, complemented
9D11×#562C214yesmaximal, complemented
10D11×#554C214yesmaximal, complemented
11D11×#550C214yesmaximal, complemented
12D11×#547C214yesmaximal, complemented
13D11×#540C214yesmaximal, complemented
14D11×#537C218yesmaximal, complemented
15D11×#533C211yesmaximal, characteristic, complemented
16D11×#532C212yesmaximal, complemented
17C11×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D11C2214yes—
19C2×#41×D11C2218yes—
20C11×#562C2214yescomplemented
21C11×#554C2214yescomplemented
22C11×#550C2214yescomplemented
23C11×#547C2214yescomplemented
24C11×#540C2214yescomplemented
25C11×#537C2218yescomplemented
26C11×#533C2211yescharacteristic, complemented
27C11×#532C2212yescomplemented
28#10623365C2218yescomplemented
29#10623364C2218yescomplemented
30#10623364C2218yescomplemented
31#10623363C2214yescomplemented
32#10623355C2218yescomplemented
33#10623261C2214yescomplemented
34#10623259C2212yescomplemented
35#10623257C2214yescomplemented
36#10623256C2212yescomplemented
37D11×C4⋊Q8C2212yes—
38D11×C4⋊Q8C2212yes—
39#10623250C2214yescomplemented
40#10623249C2218yescomplemented
41#10623249C2214yescomplemented
42#10623247C2212yescomplemented
43D11×#127C2212yes—
44D11×#127C2214yes—
45#10623231C2214yescomplemented
46#10623229C2214yescomplemented
47#10623221C2218yescomplemented
48#10623219C2212yescomplemented
49D11×#125C2214yes—
50D11×#125C2212yes—
51#10623215C2218yescomplemented
52D11×#124C2214yes—
53#10623199C2214yescomplemented
54#10623198C22116yescomplemented
55#10623194C22116yescomplemented
56#10623186C22116yescomplemented
57D11×#123C22116yes—
58#10623178C22116yescomplemented
59#10623167C22116yescomplemented
60#10623166C2218yescomplemented
61#10623162C2218yescomplemented
62#10623160C2218yescomplemented
63#10623160C22116yescomplemented
64#10623160C2218yescomplemented
65D11×C22⋊Q8C22116yes—
66D11×C22⋊Q8C2218yes—
67D11×C22⋊Q8C2214yes—
68#10623153C2214yescomplemented
69#10623152C22116yescomplemented
70#10623150C2218yescomplemented
71#10623146C22116yescomplemented
72#10623142C2218yescomplemented
73#10623139C2218yescomplemented
74#10623139C22116yescomplemented
75#10623139C2218yescomplemented
76D11×#121C2214yes—
77D11×#121C2214yes—
78D11×#121C22116yes—
79D11×#121C22116yes—
80D11×#121C2218yes—
81#10623130C22116yescomplemented
82#10623130C2218yescomplemented
83#10623128C22116yescomplemented
84#10623128C22116yescomplemented
85#10623127C2214yescomplemented
86#10623127C2214yescomplemented
87#10623110C2214yescomplemented
88#10623109C2214yescomplemented
89#10623108C2214yescomplemented
90C4×Q8×D11C2214yes—
91#10623093C2218yescomplemented
92#10623086C2214yescomplemented
93#10623084C2218yescomplemented
94#10623084C2214yescomplemented
95#10623082C2214yescomplemented
96#10623079C2214yescomplemented
97#10623079C2214yescomplemented
98C4×D4×D11C2214yes—
99C4×D4×D11C2218yes—
100C4×D4×D11C2214yes—
101#10623074C2214yescomplemented
102#10623070C2218yescomplemented
103#10623066C2214yescomplemented
104D11×#117C2212yes—
105#10623048C2212yescomplemented
106#10623042C2218yescomplemented
107#10623041C2218yescomplemented
108#10623038C2218yescomplemented
109C2×C4⋊C4×D11C2218yes—
110#10623008C2212yescomplemented
111C2×C42×D11C2211yescharacteristic
112#10623001C2211yescharacteristic, complemented
113C2×C11×#41C2318yes—
114C2×C11×#41C2314yes—
115#41×D11—416no—
116#41×D11—432no—
117C2×#4343C2314yes—
118C2×#4343C2318yes—
119C2×Q8×D11C2314yes—
120C2×Q8×D11C2314yes—
121C2×#4341C2314yes—
122C2×#4341C2318yes—
123C2×#4341C23116yes—
124C2×#4341C2318yes—
125C2×D4×D11C2314yes—
126C2×D4×D11C2314yes—
127C2×D4×D11C23116yes—
128C2×D4×D11C2314yes—
129C2×D4×D11C2318yes—
130C2×#4339C2314yes—
131C2×#4339C23116yes—
132C2×#4339C2318yes—
133C2×#4339C2318yes—
134C22×C4×D11C2311yescharacteristic
135C22×C4×D11C2312yes—
136C22×C4×D11C2318yes—
137C22×C4×D11C23116yes—
138C11×C4⋊Q8C2312yes—
139C11×C4⋊Q8C2312yes—
140C11×#127C2312yes—
141C11×#127C2314yes—
142C11×#125C2312yes—
143C11×#125C2314yes—
144C11×#124C2314yes—
145C11×#123C23116yes—
146C11×C22⋊Q8C2314yes—
147C11×C22⋊Q8C2318yes—
148C11×C22⋊Q8C23116yes—
149C11×#121C2314yes—
150C11×#121C2314yes—
151C11×#121C23116yes—
152C11×#121C23116yes—
153C11×#121C2318yes—
154C4×Q8×C11C2314yes—
155C4×D4×C11C2318yes—
156C4×D4×C11C2314yes—
157C4×D4×C11C2314yes—
158C11×#117C2312yes—
159C2×C11×C4⋊C4C2318yes—
160C2×C42×C11C2311yescharacteristic
161#67000C2314yes—
162#66999C2318yes—
163#66999C2314yes—
164#66999C23116yes—
165Q8×Dic11C2314yes—
166#66997C2314yes—
167#66997C2314yes—
168#66993C2314yes—
169#66993C2318yes—
170#66993C2314yes—
171#66993C2314yes—
172#66993C23116yes—
173#66992C23116yes—
174#66992C23116yes—
175#66992C23116yes—
176#66992C23116yes—
177#66992C2318yes—
178#66992C2318yes—
179#66992C23116yes—
180#66991C2314yes—
181#66991C2314yes—
182#66991C2318yes—
183#66991C23116yes—
184#66991C23116yes—
185#66989C2314yes—
186#66988C23116yes—
187D4×Dic11C2314yes—
188D4×Dic11C2314yes—
189D4×Dic11C2318yes—
190#66983C2314yes—
191#66983C2314yes—
192#66983C2318yes—
193#66983C23116yes—
194#66983C23116yes—
195#66982C23116yes—
196C4×C22⋊D11C2318yes—
197C4×C22⋊D11C2318yes—
198C4×C22⋊D11C23116yes—
199#66979C2312yes—
200C2×C4⋊Dic11C2318yes—
201#66977C2314yes—
202#66977C23116yes—
203#66977C2318yes—
204C2×Dic11⋊C4C23116yes—
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2312yes—
207#66950C2314yes—
208#66950C2318yes—
209#66950C23116yes—
210#66949C23116yes—
211#66949C23116yes—
212#66949C2318yes—
213#66949C23116yes—
214#66948C2314yes—
215#66948C2314yes—
216#66948C2318yes—
217#66948C23116yes—
218#66948C23116yes—
219#66947C23116yes—
220#66947C23116yes—
221#66946C2314yes—
222#66946C2314yes—
223#66946C2318yes—
224#66945C2314yes—
225C4⋊C4×D11C2314yes—
226C4⋊C4×D11C2314yes—
227C4⋊C4×D11C2314yes—
228C4⋊C4×D11C2314yes—
229C4⋊C4×D11C2318yes—
230C4⋊C4×D11C2318yes—
231C4⋊C4×D11C23116yes—
232C4⋊C4×D11C23116yes—
233C4⋊C4×D11C2318yes—
234#66943C2314yes—
235#66943C2318yes—
236#66942C23116yes—
237#66942C2318yes—
238#66941C2314yes—
239#66941C2314yes—
240#66941C2314yes—
241#66941C2314yes—
242#66940C2314yes—
243#66940C2318yes—
244#66939C23116yes—
245#66938C2318yes—
246#66938C2318yes—
247#66937C23116yes—
248#66937C2318yes—
249#66937C2318yes—
250#66937C23116yes—
251#66937C23116yes—
252#66937C23116yes—
253#66937C23116yes—
254#66936C23116yes—
255#66936C23116yes—
256(C22⋊D11)⋊C4C2318yes—
257(C22⋊D11)⋊C4C2318yes—
258(C22⋊D11)⋊C4C23116yes—
259C22⋊C4×D11C2314yes—
260C22⋊C4×D11C23116yes—
261C22⋊C4×D11C2318yes—
262C22⋊C4×D11C2318yes—
263#66931C2318yes—
264#66931C23116yes—
265#66931C23116yes—
266#66931C23116yes—
267#66930C2314yes—
268#66928C2314yes—
269#66927C2312yes—
270#66927C2314yes—
271C4×D44C2314yes—
272C4×D44C2318yes—
273C4×D44C2314yes—
274#66925C2314yes—
275C42×D11C2312yes—
276C42×D11C2314yes—
277C42×D11C2312yes—
278C42×D11C2311yescharacteristic
279C42×D11C2311yescharacteristic
280C42×D11C2311yescharacteristic
281C42×D11C2311yescharacteristic
282#66923C2314yes—
283#66923C2312yes—
284#66922C2312yes—
285#66922C2312yes—
286C4×Dic22C2314yes—
287C4×Dic22C2318yes—
288C2×#3548—111nomaximal, Sylow
289C23×D11C2411yescharacteristic
290C23×D11C2418yes—
291C11×#41—48no—
292C11×#41—416no—
293C2×Q8×C11C2414yes—
294C2×Q8×C11C2414yes—
295C2×D4×C11C2414yes—
296C2×D4×C11C2414yes—
297C2×D4×C11C24116yes—
298C2×D4×C11C2414yes—
299C2×D4×C11C2418yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2418yes—
303C22×C4×C11C24116yes—
304C2×C22⋊D11C2418yes—
305C2×C22⋊D11C2418yes—
306C2×C22⋊D11C24116yes—
307C2×C22⋊D11C2418yes—
308C2×C22⋊D11C2418yes—
309C2×C22⋊D11C24116yes—
310C2×C22⋊D11C2418yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2418yes—
314C22×Dic11C24116yes—
315#4343—416no—
316#4343—48no—
317Q8×D11—216no—
318Q8×D11—48no—
319#4341—416no—
320#4341—432no—
321#4341—416no—
322#4341—48no—
323D4×D11—216no—
324D4×D11—216no—
325D4×D11—416no—
326D4×D11—48no—
327D4×D11—432no—
328#4339—416no—
329#4339—416no—
330#4339—48no—
331#4339—432no—
332C2×D44C2414yes—
333C2×D44C2414yes—
334C2×D44C2414yes—
335C2×D44C24116yes—
336C2×D44C2418yes—
337C2×C4×D11—232no—
338C2×C4×D11—28no—
339C2×C4×D11—24no—
340C2×C4×D11—432no—
341C2×C4×D11C2411yescharacteristic
342C2×C4×D11C2411yescharacteristic
343C2×C4×D11C2412yes—
344C2×C4×D11C2411yescharacteristic
345C2×C4×D11C2412yes—
346C2×C4×D11C2412yes—
347C2×C4×D11C2418yes—
348C2×C4×D11C2418yes—
349C2×C4×D11C2418yes—
350C2×C4×D11C2418yes—
351C2×C4×D11C24116yes—
352C2×C4×D11C24116yes—
353C2×C4×D11C2412yes—
354C2×C4×D11C2411yescharacteristic
355C2×Dic22C2414yes—
356C2×Dic22C2418yes—
357C2×Dic22C2414yes—
358C2×Dic22C2418yes—
359C11×C4⋊C4C2414yes—
360C11×C4⋊C4C2418yes—
361C11×C4⋊C4C2414yes—
362C11×C4⋊C4C2414yes—
363C11×C4⋊C4C2414yes—
364C11×C4⋊C4C24116yes—
365C11×C22⋊C4C2414yes—
366C11×C22⋊C4C24116yes—
367C11×C22⋊C4C2418yes—
368C11×C22⋊C4C2418yes—
369C42×C11C2412yes—
370C42×C11C2414yes—
371C42×C11C2411yescharacteristic
372C42×C11C2411yescharacteristic
373C22⋊Dic11C2414yes—
374C22⋊Dic11C24116yes—
375C22⋊Dic11C2418yes—
376C22⋊Dic11C2418yes—
377(C2×D11)⋊C4C2418yes—
378(C2×D11)⋊C4C2418yes—
379(C2×D11)⋊C4C2418yes—
380(C2×D11)⋊C4C24116yes—
381(C2×D11)⋊C4C2418yes—
382(C2×D11)⋊C4C2418yes—
383(C2×D11)⋊C4C24116yes—
384C4⋊Dic11C2414yes—
385C4⋊Dic11C2418yes—
386C4⋊Dic11C2414yes—
387C4⋊Dic11C2414yes—
388C4⋊Dic11C2414yes—
389C4⋊Dic11C24116yes—
390Dic11⋊C4C2418yes—
391Dic11⋊C4C2418yes—
392Dic11⋊C4C2418yes—
393Dic11⋊C4C24116yes—
394Dic11⋊C4C2418yes—
395Dic11⋊C4C2418yes—
396Dic11⋊C4C24116yes—
397Dic11⋊C4C2418yes—
398C4×Dic11C2412yes—
399C4×Dic11C2414yes—
400C4×Dic11C2411yescharacteristic
401C4×Dic11C2412yes—
402C4×Dic11C2411yescharacteristic
403C4×Dic11C2412yes—
404C4×Dic11C2412yes—
405C4×Dic11C2412yes—
406C4×Dic11C2418yes—
407#3548—114no—
408#3548—114no—
409#3548—114no—
410#3548—114no—
411#3548—114no—
412#3548—118no—
413#3548—111no—
414#3548—112no—
415#3548D1111yescharacteristic, direct product factor
416C2×#562—114no—
417C2×#554—114no—
418C2×#550—114no—
419C2×#547—114no—
420C2×#540—114no—
421C2×#537—118no—
422C2×#533—111no—
423C2×#532—112no—
424C23×C11C2511yescharacteristic
425C23×C11C2518yes—
426C22×D11—24no—
427C22×D11—216no—
428C22×D11—216no—
429C22×D11—22no—
430C22×D11—216no—
431C22×D11C2511yescharacteristic
432C22×D11C2518yes—
433C22×D11C2511yescharacteristic
434Q8×C11—28no—
435Q8×C11—44no—
436D4×C11—28no—
437D4×C11—28no—
438D4×C11—48no—
439D4×C11—44no—
440D4×C11—416no—
441C2×C4×C11—216no—
442C2×C4×C11—24no—
443C2×C4×C11—22no—
444C2×C4×C11—416no—
445C2×C4×C11C2512yes—
446C2×C4×C11C2511yescharacteristic
447C2×C4×C11C2518yes—
448C2×C4×C11C2518yes—
449C2×C4×C11C2512yes—
450C2×C4×C11C2511yescharacteristic
451C22⋊D11—216no—
452C22⋊D11—216no—
453C22⋊D11—416no—
454C22⋊D11—416no—
455C22⋊D11—48no—
456C22⋊D11—48no—
457C22⋊D11—48no—
458C2×Dic11—24no—
459C2×Dic11—216no—
460C2×Dic11—22no—
461C2×Dic11—416no—
462C2×Dic11C2511yescharacteristic
463C2×Dic11C2512yes—
464C2×Dic11C2518yes—
465C2×Dic11C2518yes—
466C2×Dic11C2512yes—
467C2×Dic11C2511yescharacteristic
468D44—28no—
469D44—28no—
470D44—48no—
471D44—44no—
472D44—416no—
473C4×D11—216no—
474C4×D11—24no—
475C4×D11—216no—
476C4×D11—22no—
477C4×D11—24no—
478C4×D11—216no—
479C4×D11—22no—
480C4×D11—216no—
481C4×D11—24no—
482C4×D11—22no—
483C4×D11—416no—
484C4×D11—416no—
485C4×D11H(5,𝔽2)18yes—
486C4×D112−1+414yes—
487Dic22—28no—
488Dic22—216no—
489Dic22—48no—
490Dic22—44no—
491C22×#41—114no—
492C22×#41—118no—
493#562—114no—
494#562—118no—
495#562—1116no—
496#562—1116no—
497#562—1116no—
498#562C2×D1114yescomplemented
499#554—114no—
500#554—118no—
501#554—118no—
502#554—1116no—
503#554—114no—
504#554—118no—
505#554—114no—
506#554—118no—
507#554C2×D1114yescomplemented
508#550—118no—
509#550—118no—
510#550—114no—
511#550—118no—
512#550—1116no—
513#550—114no—
514#550—118no—
515#550—114no—
516#550C2×D1114yescomplemented
517#547—118no—
518#547—114no—
519#547—1116no—
520#547—118no—
521#547—118no—
522#547—114no—
523#547—114no—
524#547—118no—
525#547C2×D1114yescomplemented
526#540—114no—
527#540—114no—
528#540—1116no—
529#540—1116no—
530#540—118no—
531#540—118no—
532#540—114no—
533#540C2×D1114yescomplemented
534#537—118no—
535#537—118no—
536#537—118no—
537#537—1116no—
538#537—118no—
539#537—1116no—
540#537—1116no—
541#537—118no—
542#537—1116no—
543#537—118no—
544#537—118no—
545#537C2×D1118yescomplemented
546#533—112no—
547#533—112no—
548#533—114no—
549#533—114no—
550#533—112no—
551#533—111no—
552#533C2×D1111yescharacteristic, complemented
553#532—114no—
554#532—112no—
555#532—112no—
556#532—114no—
557#532—114no—
558#532—114no—
559#532—114no—
560#532—114no—
561#532—112no—
562#532C2×D1112yescomplemented
563C2×C4⋊Q8—112no—
564C2×C4⋊Q8—112no—
565C2×#127—112no—
566C2×#127—114no—
567C2×#125—112no—
568C2×#125—114no—
569C2×#124—114no—
570C2×#123—1116no—
571C2×C22⋊Q8—114no—
572C2×C22⋊Q8—118no—
573C2×C22⋊Q8—1116no—
574C2×#121—114no—
575C2×#121—114no—
576C2×#121—1116no—
577C2×#121—118no—
578C2×#121—1116no—
579C2×C4×Q8—114no—
580C2×C4×D4—114no—
581C2×C4×D4—114no—
582C2×C4×D4—118no—
583C2×#117—112no—
584C22×C4⋊C4—118no—
585C22×C42—111no—
586C22×C11—22no—
587C22×C11—28no—
588C22×C11—28no—
589C22×C11—21no—
590C22×C11—28no—
591C22×C11C2611yescharacteristic
592C2×D11—22no—
593C2×D11—28no—
594C2×D11—28no—
595C2×D11—21no—
596C2×D11—28no—
597C2×D11—44no—
598C2×D11—432no—
599C2×D11C2×H(5,𝔽2)14yes—
600C2×D11C2×2−1+412yes—
601C4×C11—28no—
602C4×C11—22no—
603C4×C11—28no—
604C4×C11—21no—
605C4×C11C2×H(5,𝔽2)14yes—
606C4×C11C2×2−1+412yes—
607Dic11—28no—
608Dic11—22no—
609Dic11—28no—
610Dic11—21no—
611Dic11C2×H(5,𝔽2)14yes—
612Dic11C2×2−1+412yes—
613C2×#41—114no—
614C2×#41—118no—
615C2×#41—118no—
616C2×#41—114no—
617C2×#41—1116no—
618C2×#41—118no—
619C2×#41—118no—
620C2×#41—114no—
621C2×#41—1116no—
622C2×#41—118no—
623C2×#41—4416no—
624C2×#41—4432no—
625C2×#41C22×D1114yes—
626C2×#41C22×D1118yes—
627C22×Q8—114no—
628C22×Q8—114no—
629C22×D4—114no—
630C22×D4—114no—
631C22×D4—118no—
632C22×D4—1116no—
633C22×D4—114no—
634C23×C4—118no—
635C23×C4—111no—
636C23×C4—112no—
637C23×C4—1116no—
638C4⋊Q8—114no—
639C4⋊Q8—114no—
640C4⋊Q8—114no—
641C4⋊Q8—114no—
642C4⋊Q8—114no—
643C4⋊Q8—114no—
644C4⋊Q8—112no—
645C4⋊Q8—112no—
646C4⋊Q8C22×D1112yes—
647C4⋊Q8C22×D1112yes—
648#127—114no—
649#127—114no—
650#127—114no—
651#127—1116no—
652#127—118no—
653#127—112no—
654#127—114no—
655#127C22×D1112yes—
656#127C22×D1114yes—
657#125—118no—
658#125—114no—
659#125—1116no—
660#125—118no—
661#125—112no—
662#125—114no—
663#125C22×D1112yes—
664#125C22×D1114yes—
665#124—114no—
666#124—114no—
667#124—118no—
668#124—118no—
669#124—114no—
670#124C22×D1114yes—
671#123—1116no—
672#123—1116no—
673#123—1116no—
674#123—1116no—
675#123—1116no—
676#123—1116no—
677#123—1116no—
678#123C22×D11116yes—
679C22⋊Q8—114no—
680C22⋊Q8—118no—
681C22⋊Q8—1116no—
682C22⋊Q8—114no—
683C22⋊Q8—118no—
684C22⋊Q8—1116no—
685C22⋊Q8—118no—
686C22⋊Q8—114no—
687C22⋊Q8—1116no—
688C22⋊Q8—118no—
689C22⋊Q8—1116no—
690C22⋊Q8—1116no—
691C22⋊Q8—1116no—
692C22⋊Q8—118no—
693C22⋊Q8—1116no—
694C22⋊Q8—1116no—
695C22⋊Q8—1116no—
696C22⋊Q8C22×D1114yes—
697C22⋊Q8C22×D1118yes—
698C22⋊Q8C22×D11116yes—
699#121—114no—
700#121—118no—
701#121—114no—
702#121—118no—
703#121—1116no—
704#121—1116no—
705#121—1116no—
706#121—118no—
707#121—1116no—
708#121—1116no—
709#121—1116no—
710#121—1116no—
711#121—114no—
712#121—114no—
713#121—1116no—
714#121—118no—
715#121—1116no—
716#121—114no—
717#121—114no—
718#121—1116no—
719#121—118no—
720#121—1116no—
721#121—118no—
722#121—118no—
723#121—1116no—
724#121—1116no—
725#121—1116no—
726#121—1116no—
727#121—1116no—
728#121C22×D1114yes—
729#121C22×D1114yes—
730#121C22×D11116yes—
731#121C22×D1118yes—
732#121C22×D11116yes—
733C4×Q8—114no—
734C4×Q8—118no—
735C4×Q8—114no—
736C4×Q8—118no—
737C4×Q8—114no—
738C4×Q8C22×D1114yes—
739C4×D4—114no—
740C4×D4—114no—
741C4×D4—118no—
742C4×D4—118no—
743C4×D4—118no—
744C4×D4—1116no—
745C4×D4—114no—
746C4×D4—114no—
747C4×D4—118no—
748C4×D4—118no—
749C4×D4—118no—
750C4×D4—1116no—
751C4×D4—114no—
752C4×D4—114no—
753C4×D4—118no—
754C4×D4C22×D1114yes—
755C4×D4C22×D1114yes—
756C4×D4C22×D1118yes—
757#117—112no—
758#117—114no—
759#117—114no—
760#117—114no—
761#117C22×D1112yes—
762C2×C4⋊C4—1116no—
763C2×C4⋊C4—118no—
764C2×C4⋊C4—114no—
765C2×C4⋊C4—114no—
766C2×C4⋊C4—1116no—
767C2×C4⋊C4—1116no—
768C2×C4⋊C4—118no—
769C2×C4⋊C4—118no—
770C2×C4⋊C4—114no—
771C2×C4⋊C4—114no—
772C2×C4⋊C4—118no—
773C2×C4⋊C4C22×D1118yes—
774C2×C22⋊C4—114no—
775C2×C22⋊C4—1116no—
776C2×C22⋊C4—118no—
777C2×C22⋊C4—118no—
778C2×C42—112no—
779C2×C42—111no—
780C2×C42—114no—
781C2×C42—111no—
782C2×C42—112no—
783C2×C42—111no—
784C2×C42—111no—
785C2×C42—112no—
786C2×C42—111no—
787C2×C42C22×D1111yescharacteristic
788C2×C11—41no—
789C2×C11—48no—
790C2×C11C22×H(5,𝔽2)12yes—
791C2×C11C22×2−1+411yescharacteristic
792D11—41no—
793D11—48no—
794D11#354814yesdirect product factor
795C24—111no—
796C24—118no—
797#41—48no—
798#41—416no—
799#41—4416no—
800#41—448no—
801#41—4416no—
802#41—4432no—
803#41—4416no—
804#41—448no—
805#41—448no—
806#41—4416no—
807#41—4432no—
808#41—4416no—
809C2×Q8—118no—
810C2×Q8—114no—
811C2×Q8—118no—
812C2×Q8—114no—
813C2×Q8—2216no—
814C2×Q8—448no—
815C2×Q8C23×D1114yes—
816C2×Q8C23×D1114yes—
817C2×D4—118no—
818C2×D4—118no—
819C2×D4—118no—
820C2×D4—118no—
821C2×D4—1116no—
822C2×D4—1116no—
823C2×D4—118no—
824C2×D4—114no—
825C2×D4—114no—
826C2×D4—118no—
827C2×D4—1116no—
828C2×D4—114no—
829C2×D4—2216no—
830C2×D4—2216no—
831C2×D4—4416no—
832C2×D4—448no—
833C2×D4—4432no—
834C2×D4C23×D1114yes—
835C2×D4C23×D1114yes—
836C2×D4C23×D1118yes—
837C2×D4C23×D11116yes—
838C2×D4C23×D1114yes—
839C22×C4—111no—
840C22×C4—112no—
841C22×C4—111no—
842C22×C4—112no—
843C22×C4—118no—
844C22×C4—1116no—
845C22×C4—111no—
846C22×C4—112no—
847C22×C4—111no—
848C22×C4—111no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—118no—
852C22×C4—118no—
853C22×C4—118no—
854C22×C4—118no—
855C22×C4—1116no—
856C22×C4—1116no—
857C22×C4—2232no—
858C22×C4—228no—
859C22×C4—224no—
860C22×C4—4432no—
861C22×C4C23×D1111yescharacteristic
862C22×C4C23×D1112yes—
863C22×C4C23×D1118yes—
864C22×C4C23×D11116yes—
865C4⋊C4—118no—
866C4⋊C4—114no—
867C4⋊C4—118no—
868C4⋊C4—114no—
869C4⋊C4—1116no—
870C4⋊C4—1116no—
871C4⋊C4—1116no—
872C4⋊C4—118no—
873C4⋊C4—114no—
874C4⋊C4—118no—
875C4⋊C4—114no—
876C4⋊C4—118no—
877C4⋊C4—118no—
878C4⋊C4—118no—
879C4⋊C4C23×D1114yes—
880C4⋊C4C23×D1114yes—
881C4⋊C4C23×D11116yes—
882C4⋊C4C23×D1114yes—
883C4⋊C4C23×D1114yes—
884C4⋊C4C23×D1118yes—
885C22⋊C4—114no—
886C22⋊C4—1116no—
887C22⋊C4—118no—
888C22⋊C4—118no—
889C22⋊C4—118no—
890C22⋊C4—1116no—
891C22⋊C4—1116no—
892C22⋊C4—118no—
893C22⋊C4—118no—
894C22⋊C4—118no—
895C22⋊C4—118no—
896C22⋊C4C23×D1114yes—
897C22⋊C4C23×D11116yes—
898C22⋊C4C23×D1118yes—
899C22⋊C4C23×D1118yes—
900C42—111no—
901C42—112no—
902C42—112no—
903C42—112no—
904C42—112no—
905C42—112no—
906C42—111no—
907C42—118no—
908C42—114no—
909C42C23×D1111yescharacteristic
910C42C23×D1112yes—
911C42C23×D1111yescharacteristic
912C42C23×D1114yes—
913C11C2×#354811yescharacteristic, complemented, Sylow
914C23—111no—
915C23—111no—
916C23—118no—
917C23—224no—
918C23—2216no—
919C23—222no—
920C23—2216no—
921C23—2216no—
922C23C24×D1111yescharacteristic
923C23C24×D1118yes—
924Q8—28no—
925Q8—44no—
926Q8—2216no—
927Q8—228no—
928Q8—448no—
929Q8—444no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—2216no—
936D4—2216no—
937D4—228no—
938D4—228no—
939D4—448no—
940D4—444no—
941D4—4416no—
942D4—448no—
943D4—448no—
944D4—448no—
945D4—4416no—
946D4—4416no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—111no—
952C2×C4—112no—
953C2×C4—118no—
954C2×C4—114no—
955C2×C4—111no—
956C2×C4—112no—
957C2×C4—118no—
958C2×C4—118no—
959C2×C4—2216no—
960C2×C4—224no—
961C2×C4—222no—
962C2×C4—2216no—
963C2×C4—224no—
964C2×C4—222no—
965C2×C4—2216no—
966C2×C4—2216no—
967C2×C4—224no—
968C2×C4—222no—
969C2×C4—2216no—
970C2×C4—224no—
971C2×C4—222no—
972C2×C4—4416no—
973C2×C4—4416no—
974C2×C4—4416no—
975C2×C4C24×D1111yescharacteristic
976C2×C4C24×D1112yes—
977C2×C4C24×D1118yes—
978C2×C4C24×D1118yes—
979C2×C4C24×D1112yes—
980C2×C4C24×D1111yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—114no—
987C22—112no—
988C22—222no—
989C22—228no—
990C22—228no—
991C22—221no—
992C22—228no—
993C22—444no—
994C22—4432no—
995C22C25×D1111yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—114no—
1001C4—112no—
1002C4—228no—
1003C4—222no—
1004C4—228no—
1005C4—221no—
1006C4D11×H(5,𝔽2)14yes—
1007C4D11×2−1+412yes—
1008C2—41no—
1009C2—48no—
1010C2—114no—
1011C2—441no—
1012C2—448no—
1013C2C2×D11×H(5,𝔽2)12yes—
1014C2C2×D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D11
commutator, socle, cosocleC22×C11C26
FittingC11×#3548C2
hypercenter#3548D11
hypocenterC11C2×#3548
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #13083016C2semidirect
2. #13083015C2semidirect
3. #13083014C2semidirect
4. #13083013C2semidirect
5. #13083012C2semidirect
6. #13083011C2semidirect
7. #13083010C2semidirect
8. #13083009C2semidirect
9. D11×#562C2semidirect
10. D11×#554C2semidirect
11. D11×#550C2semidirect
12. D11×#547C2semidirect
13. D11×#540C2semidirect
14. D11×#537C2semidirect
15. D11×#533C2semidirect
16. D11×#532C2semidirect
17. C11×#3548C2semidirect
20. C11×#562C22semidirect
21. C11×#554C22semidirect
22. C11×#550C22semidirect
23. C11×#547C22semidirect
24. C11×#540C22semidirect
25. C11×#537C22semidirect
26. C11×#533C22semidirect
27. C11×#532C22semidirect
28. #10623365C22semidirect
29. #10623364C22semidirect
30. #10623364C22semidirect
31. #10623363C22semidirect
32. #10623355C22semidirect
33. #10623261C22semidirect
34. #10623259C22semidirect
35. #10623257C22semidirect
36. #10623256C22semidirect
39. #10623250C22semidirect
40. #10623249C22semidirect
41. #10623249C22semidirect
42. #10623247C22semidirect
45. #10623231C22semidirect
46. #10623229C22semidirect
47. #10623221C22semidirect
48. #10623219C22semidirect
51. #10623215C22semidirect
53. #10623199C22semidirect
54. #10623198C22semidirect
55. #10623194C22semidirect
56. #10623186C22semidirect
58. #10623178C22semidirect
59. #10623167C22semidirect
60. #10623166C22semidirect
61. #10623162C22semidirect
62. #10623160C22semidirect
63. #10623160C22semidirect
64. #10623160C22semidirect
68. #10623153C22semidirect
69. #10623152C22semidirect
70. #10623150C22semidirect
71. #10623146C22semidirect
72. #10623142C22semidirect
73. #10623139C22semidirect
74. #10623139C22semidirect
75. #10623139C22semidirect
81. #10623130C22semidirect
82. #10623130C22semidirect
83. #10623128C22semidirect
84. #10623128C22semidirect
85. #10623127C22semidirect
86. #10623127C22semidirect
87. #10623110C22semidirect
88. #10623109C22semidirect
89. #10623108C22semidirect
91. #10623093C22semidirect
92. #10623086C22semidirect
93. #10623084C22semidirect
94. #10623084C22semidirect
95. #10623082C22semidirect
96. #10623079C22semidirect
97. #10623079C22semidirect
101. #10623074C22semidirect
102. #10623070C22semidirect
103. #10623066C22semidirect
105. #10623048C22semidirect
106. #10623042C22semidirect
107. #10623041C22semidirect
108. #10623038C22semidirect
110. #10623008C22semidirect
112. #10623001C22semidirect
415. #3548D11direct (N × H)
498. #562C2×D11semidirect
507. #554C2×D11semidirect
516. #550C2×D11semidirect
525. #547C2×D11semidirect
533. #540C2×D11semidirect
545. #537C2×D11semidirect
552. #533C2×D11semidirect
562. #532C2×D11semidirect
794. D11#3548direct (N × H)
913. C11C2×#3548semidirect

Maximal subgroups

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

subgroupindex
#130830162
#130830152
#130830142
#130830132
#130830122
#130830112
#130830102
#130830092
D11×#5622
D11×#5542
D11×#5502
D11×#5472
D11×#5402
D11×#5372
D11×#5332
D11×#5322
C11×#35482
C2×#354811