Finite Group Databasebeta

← D11×#3504 #15662247

Subgroups — D11×#3504 #15662247

Order 2816.

6958 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082442C211yesmaximal, characteristic, complemented
2#13082441C214yesmaximal, complemented
3#13082440C213yesmaximal, complemented
4#13082439C216yesmaximal, complemented
5#13082438C212yesmaximal, complemented
6#13082437C213yesmaximal, complemented
7#13082436C2112yesmaximal, complemented
8D11×#557C214yesmaximal, complemented
9D11×#554C2112yesmaximal, complemented
10D11×#544C216yesmaximal, complemented
11D11×#533C213yesmaximal, complemented
12C2×D11×#125C213yesmaximal, complemented
13D11×#520C212yesmaximal
14C4×#41×D11C211yesmaximal, characteristic
15C11×#3504C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C11×#557C2214yescomplemented
18C11×#554C22112yescomplemented
19C11×#544C2216yescomplemented
20C11×#533C2213yescomplemented
21C2×C11×#125C2213yescomplemented
22C11×#520C2212yes—
23C4×C11×#41C2211yescharacteristic
24#10623358C2212yes—
25#41×Dic11C2211yescharacteristic
26#10623261C22112yescomplemented
27#10623260C22112yescomplemented
28#10623260C22112yescomplemented
29#10623259C2216yescomplemented
30D11×C4⋊Q8C22112yes—
31D11×C4⋊Q8C2216yes—
32#10623252C22112yescomplemented
33#10623221C22112yescomplemented
34#10623221C22112yescomplemented
35#10623220C22112yescomplemented
36#10623220C22112yescomplemented
37#10623219C2213yescomplemented
38#10623219C2213yescomplemented
39D11×#125C2213yes—
40D11×#125C22112yes—
41D11×#125C2216yes—
42D11×#125C22112yes—
43D11×#125C2211yescharacteristic
44D11×#125C22112yescomplemented
45D11×#125C2216yescomplemented
46D11×#125C2216yescomplemented
47#10623216C22112yescomplemented
48#10623216C22112yescomplemented
49#10623167C22124yescomplemented
50#10623167C22124yescomplemented
51#10623166C22124yescomplemented
52D11×C22⋊Q8C22112yes—
53D11×C22⋊Q8C22124yes—
54#10623154C22124yescomplemented
55#10623153C22112yescomplemented
56#10623110C22112yescomplemented
57#10623109C22112yescomplemented
58#10623105C2214yes—
59C4×#4343C2212yes—
60C4×Q8×D11C22112yes—
61C4×Q8×D11C2212yes—
62C4×Q8×D11C2214yes—
63#10623101C2214yescomplemented
64#10623100C2214yescomplemented
65#10623100C2214yescomplemented
66#10623098C22112yescomplemented
67#10623077C22112yes—
68C4×D4×D11C2216yes—
69C4×D4×D11C22112yes—
70#10623074C22112yescomplemented
71#10623070C22112yescomplemented
72#10623070C22112yescomplemented
73C4×#4341C2216yes—
74#10623054C2216yes—
75#10623053C2213yes—
76D11×#117C2216yes—
77D11×#117C2213yes—
78#10623050C2216yescomplemented
79#10623050C2216yescomplemented
80#10623048C2216yescomplemented
81#10623042C22124yescomplemented
82#10623035C2216yes—
83C2×C4⋊C4×D11C22112yes—
84C2×C4⋊C4×D11C2216yes—
85#10623031C2216yescomplemented
86C2×#66943C2216yescomplemented
87C2×#66942C22112yescomplemented
88C4×#4339C2213yes—
89C2×C42×D11C2213yes—
90#10623001C2213yescomplemented
91C2×#66923C2213yescomplemented
92C2×C11×#41C2311yescharacteristic
93#41×D11Q8116yescomplemented
94C2×#4343C2311yescharacteristic
95C2×Q8×D11C23112yes—
96C2×Q8×D11C2311yescharacteristic
97C2×#4341C2313yes—
98C2×D4×D11C2313yes—
99C2×#4339C2313yes—
100C22×C4×D11C2316yes—
101C22×C4×D11C23112yes—
102C22×C4×D11C2313yes—
103C11×C4⋊Q8C23112yes—
104C11×C4⋊Q8C2316yes—
105C11×#125C2313yes—
106C11×#125C2316yes—
107C11×#125C23112yes—
108C11×#125C2311yescharacteristic
109C11×#125C23112yes—
110C11×C22⋊Q8C23112yes—
111C11×C22⋊Q8C23124yes—
112C4×Q8×C11C23112yes—
113C4×Q8×C11C2312yes—
114C4×Q8×C11C2314yes—
115C4×D4×C11C2316yes—
116C4×D4×C11C23112yes—
117C11×#117C2316yes—
118C11×#117C2313yes—
119C2×C11×C4⋊C4C23112yes—
120C2×C11×C4⋊C4C2316yes—
121C2×C42×C11C2313yes—
122#66999C23112yes—
123#66999C23124yes—
124Q8×Dic11C23112yes—
125Q8×Dic11C2314yes—
126Q8×Dic11C2312yes—
127#66997C23124yes—
128#66997C23112yes—
129D4×Dic11C2316yes—
130D4×Dic11C23112yes—
131C4×C22⋊D11C23112yes—
132C4×C22⋊D11C23124yes—
133#66979C2316yes—
134#66979C2313yes—
135C2×C4⋊Dic11C2316yes—
136C2×C4⋊Dic11C23112yes—
137#66977C23112yes—
138#66977C23124yes—
139C2×Dic11⋊C4C23112yes—
140C2×Dic11⋊C4C23112yes—
141C2×Dic11⋊C4C23112yes—
142C2×C4×Dic11C2316yes—
143C2×C4×Dic11C2313yes—
144#66950C23112yes—
145#66950C23124yes—
146#66949C23124yes—
147#66949C23124yes—
148#66949C23112yes—
149#66949C23112yes—
150#66946C2316yes—
151#66946C23112yes—
152#66945C2316yes—
153#66945C2316yes—
154#66945C2316yes—
155C4⋊C4×D11C2312yes—
156C4⋊C4×D11C2316yes—
157C4⋊C4×D11C2316yes—
158C4⋊C4×D11C23112yes—
159C4⋊C4×D11C23124yes—
160C4⋊C4×D11C23112yes—
161C4⋊C4×D11C23112yes—
162C4⋊C4×D11C23112yes—
163C4⋊C4×D11C23124yes—
164C4⋊C4×D11C23112yes—
165C4⋊C4×D11C23124yes—
166C4⋊C4×D11C2314yes—
167#66943C23112yes—
168#66943C23112yes—
169#66943C2312yes—
170#66943C2316yes—
171#66943C23112yes—
172#66943C23112yes—
173#66943C23112yes—
174#66942C23124yes—
175#66942C23124yes—
176#66942C23124yes—
177#66942C23124yes—
178#66942C23112yes—
179#66942C23124yes—
180#66942C2314yes—
181#66941C2316yes—
182#66941C23112yes—
183#66941C2316yes—
184#66941C23112yes—
185#66941C23124yes—
186#66941C23112yes—
187#66940C2316yes—
188#66940C23112yes—
189#66940C23112yes—
190#66940C23112yes—
191#66940C23112yes—
192(C22⋊D11)⋊C4C23112yes—
193(C22⋊D11)⋊C4C23124yes—
194C22⋊C4×D11C23112yes—
195C22⋊C4×D11C2316yes—
196#66931C23112yes—
197#66931C23112yes—
198#66931C23124yes—
199#66931C23124yes—
200#66930C2316yes—
201#66930C23112yes—
202C4×D44C2316yes—
203C4×D44C23112yes—
204#66925C2316yes—
205#66925C23112yes—
206C42×D11C2313yes—
207C42×D11C23112yes—
208C42×D11C2311yescharacteristic
209C42×D11C2313yes—
210C42×D11C2313yes—
211C42×D11C2316yes—
212C42×D11C2316yes—
213#66923C2313yes—
214#66923C2316yes—
215#66923C23112yes—
216#66923C2311yescharacteristic
217#66923C23112yes—
218#66922C2316yes—
219#66922C23112yes—
220C4×Dic22C23112yes—
221C4×Dic22C23112yes—
222C4×Dic22C23112yes—
223C4×Dic22C2316yes—
224C4×Dic22C23112yes—
225C2×#3504—111nomaximal, Sylow
226C23×D11C2413yes—
227C11×#41C2×Q818yescomplemented
228C2×Q8×C11C24112yes—
229C2×Q8×C11C2411yescharacteristic
230C2×D4×C11C2413yes—
231C22×C4×C11C2416yes—
232C22×C4×C11C24112yes—
233C22×C4×C11C2413yes—
234C2×C22⋊D11C2416yes—
235C22×Dic11C2416yes—
236C22×Dic11C24112yes—
237C22×Dic11C2413yes—
238#4343C2×Q818yescomplemented
239Q8×D11—424no—
240Q8×D11C2×Q818yes—
241#4341C2×Q8124yescomplemented
242D4×D11C2×Q8124yes—
243#4339C2×Q8124yescomplemented
244C2×D44C2413yes—
245C2×C4×D11—412no—
246C2×C4×D11—424no—
247C2×C4×D11C2×Q8124yes—
248C2×C4×D11C2412yes—
249C2×C4×D11C2414yes—
250C2×C4×D11C2416yes—
251C2×C4×D11C24112yes—
252C2×C4×D11C2416yes—
253C2×C4×D11C2416yes—
254C2×C4×D11C24124yes—
255C2×C4×D11C2413yes—
256C2×C4×D11C2411yescharacteristic
257C2×C4×D11C2413yes—
258C2×C4×D11C2413yes—
259C2×Dic22C24112yes—
260C2×Dic22C24112yes—
261C2×Dic22C24112yes—
262C2×Dic22C2413yes—
263C11×C4⋊C4C2414yes—
264C11×C4⋊C4C2416yes—
265C11×C4⋊C4C24112yes—
266C11×C4⋊C4C24112yes—
267C11×C4⋊C4C24112yes—
268C11×C4⋊C4C2412yes—
269C11×C4⋊C4C24124yes—
270C11×C4⋊C4C2416yes—
271C11×C22⋊C4C24112yes—
272C11×C22⋊C4C2416yes—
273C42×C11C24112yes—
274C42×C11C2416yes—
275C42×C11C2413yes—
276C42×C11C2411yescharacteristic
277C22⋊Dic11C24112yes—
278C22⋊Dic11C2416yes—
279(C2×D11)⋊C4C24112yes—
280(C2×D11)⋊C4C24112yes—
281(C2×D11)⋊C4C24112yes—
282C4⋊Dic11C2414yes—
283C4⋊Dic11C2416yes—
284C4⋊Dic11C24112yes—
285C4⋊Dic11C24112yes—
286C4⋊Dic11C24112yes—
287C4⋊Dic11C2412yes—
288C4⋊Dic11C2416yes—
289C4⋊Dic11C24124yes—
290Dic11⋊C4C2414yes—
291Dic11⋊C4C2414yes—
292Dic11⋊C4C24112yes—
293Dic11⋊C4C24112yes—
294Dic11⋊C4C24112yes—
295Dic11⋊C4C24112yes—
296Dic11⋊C4C24112yes—
297Dic11⋊C4C24124yes—
298Dic11⋊C4C24124yes—
299Dic11⋊C4C24124yes—
300Dic11⋊C4C2414yes—
301Dic11⋊C4C24112yes—
302C4×Dic11C2416yes—
303C4×Dic11C24112yes—
304C4×Dic11C2416yes—
305C4×Dic11C24112yes—
306C4×Dic11C2412yes—
307C4×Dic11C2411yescharacteristic
308C4×Dic11C2413yes—
309C4×Dic11C2416yes—
310C4×Dic11C2416yes—
311C4×Dic11C24112yes—
312#3504—114no—
313#3504—1112no—
314#3504—116no—
315#3504—113no—
316#3504—113no—
317#3504—112no—
318#3504—111no—
319#3504D1111yescharacteristic, direct product factor
320C2×#557—114no—
321C2×#554—1112no—
322C2×#544—116no—
323C2×#533—113no—
324C22×#125—113no—
325C2×#520—112no—
326C2×C4×#41—111no—
327C23×C11C2513yes—
328C22×D11—212no—
329C22×D11C22×Q8112yes—
330C22×D11C2513yes—
331C22×D11C2511yescharacteristic
332Q8×C11—412no—
333Q8×C11C22×Q814yes—
334D4×C11C22×Q8112yes—
335C2×C4×C11—46no—
336C2×C4×C11—412no—
337C2×C4×C11C22×Q8112yes—
338C2×C4×C11C2512yes—
339C2×C4×C11C2514yes—
340C2×C4×C11C2516yes—
341C2×C4×C11C25112yes—
342C2×C4×C11C2513yes—
343C2×C4×C11C2511yescharacteristic
344C22⋊D11C22×Q8124yes—
345C2×Dic11—46no—
346C2×Dic11—412no—
347C2×Dic11C22×Q8112yes—
348C2×Dic11C2512yes—
349C2×Dic11C2514yes—
350C2×Dic11C2516yes—
351C2×Dic11C25112yes—
352C2×Dic11C2513yes—
353C2×Dic11C2511yescharacteristic
354D44C22×Q8112yes—
355C4×D11—24no—
356C4×D11—224no—
357C4×D11—212no—
358C4×D11—28no—
359C4×D11—46no—
360C4×D11—424no—
361C4×D11—46no—
362C4×D11C22×Q814yes—
363C4×D11C22×Q8112yes—
364C4×D11C22×Q8112yes—
365C4×D11C22×Q8112yes—
366Dic22—412no—
367Dic22—412no—
368Dic22—412no—
369Dic22C22×Q8112yes—
370C22×#41—111no—
371#557—1112no—
372#557—1112no—
373#557—1112no—
374#557—1112no—
375#557—114no—
376#557—114no—
377#557—114no—
378#557C2×D1114yescomplemented
379#554—1112no—
380#554—1112no—
381#554—1112no—
382#554—1124no—
383#554—1124no—
384#554—1124no—
385#554—1112no—
386#554—1112no—
387#554—1112no—
388#554—1112no—
389#554—1124no—
390#554C2×D11112yescomplemented
391#544—1112no—
392#544—1112no—
393#544—1112no—
394#544—1112no—
395#544—1124no—
396#544—116no—
397#544—116no—
398#544—116no—
399#544C2×D1116yescomplemented
400#533—116no—
401#533—113no—
402#533—113no—
403#533—1112no—
404#533—1112no—
405#533—116no—
406#533—113no—
407#533C2×D1113yescomplemented
408C2×C4⋊Q8—116no—
409C2×C4⋊Q8—1112no—
410C2×#125—113no—
411C2×#125—116no—
412C2×#125—1112no—
413C2×#125—1112no—
414C2×#125—116no—
415C2×#125—116no—
416C2×#125—111no—
417C2×#125—1112no—
418C2×#125—1112no—
419C2×#125—116no—
420C2×#125—113no—
421C2×#125C2×D1113yescomplemented
422C2×C22⋊Q8—1112no—
423C2×C22⋊Q8—1124no—
424#520—112no—
425#520—114no—
426#520—1112no—
427#520—116no—
428#520—116no—
429#520C2×D1112yes—
430C4×#41—111no—
431C4×#41—112no—
432C4×#41—116no—
433C4×#41—113no—
434C4×#41—113no—
435C4×#41C2×D1111yescharacteristic
436C2×C4×Q8—112no—
437C2×C4×Q8—114no—
438C2×C4×Q8—1112no—
439C2×C4×D4—116no—
440C2×C4×D4—1112no—
441C2×#117—113no—
442C2×#117—116no—
443C22×C4⋊C4—116no—
444C22×C4⋊C4—1112no—
445C22×C42—113no—
446C22×C11—26no—
447C22×C11C23×Q816yes—
448C22×C11C2611yescharacteristic
449C2×D11—26no—
450C2×D11—224no—
451C2×D11C23×Q816yes—
452C2×D11C23×Q812yes—
453C2×D11#58514yes—
454C4×C11—22no—
455C4×C11—212no—
456C4×C11—26no—
457C4×C11—24no—
458C4×C11C23×Q812yes—
459C4×C11C23×Q816yes—
460Dic11—24no—
461Dic11—26no—
462Dic11—212no—
463Dic11—22no—
464Dic11C23×Q816yes—
465Dic11C23×Q812yes—
466C2×#41—1116no—
467C2×#41—111no—
468C2×#41—113no—
469C2×#41—113no—
470C2×#41C22×D1111yescharacteristic
471C22×Q8—111no—
472C22×Q8—1112no—
473C22×D4—113no—
474C23×C4—113no—
475C23×C4—1112no—
476C23×C4—116no—
477C4⋊Q8—1112no—
478C4⋊Q8—1124no—
479C4⋊Q8—1112no—
480C4⋊Q8—116no—
481C4⋊Q8—116no—
482C4⋊Q8—1124no—
483C4⋊Q8—1112no—
484C4⋊Q8—1112no—
485C4⋊Q8—116no—
486C4⋊Q8—1112no—
487C4⋊Q8C22×D1116yes—
488C4⋊Q8C22×D11112yes—
489#125—1112no—
490#125—116no—
491#125—1124no—
492#125—1112no—
493#125—1124no—
494#125—1124no—
495#125—1112no—
496#125—1112no—
497#125—114no—
498#125—112no—
499#125—1124no—
500#125—1124no—
501#125—1112no—
502#125—1112no—
503#125—113no—
504#125—116no—
505#125—1112no—
506#125—111no—
507#125—1112no—
508#125C22×D1113yes—
509#125C22×D1116yes—
510#125C22×D11112yes—
511#125C22×D1111yescharacteristic
512#125C22×D11112yes—
513C22⋊Q8—1112no—
514C22⋊Q8—1124no—
515C22⋊Q8—1112no—
516C22⋊Q8—1124no—
517C22⋊Q8—1112no—
518C22⋊Q8—1112no—
519C22⋊Q8—1112no—
520C22⋊Q8—1124no—
521C22⋊Q8—1124no—
522C22⋊Q8—1124no—
523C22⋊Q8—1112no—
524C22⋊Q8—1112no—
525C22⋊Q8—1124no—
526C22⋊Q8—1124no—
527C22⋊Q8C22×D11112yes—
528C22⋊Q8C22×D11124yes—
529C4×Q8—112no—
530C4×Q8—114no—
531C4×Q8—1112no—
532C4×Q8—116no—
533C4×Q8—1112no—
534C4×Q8—1112no—
535C4×Q8—1112no—
536C4×Q8—1112no—
537C4×Q8—116no—
538C4×Q8—1112no—
539C4×Q8—1112no—
540C4×Q8—1112no—
541C4×Q8—1112no—
542C4×Q8C22×D1112yes—
543C4×Q8C22×D1114yes—
544C4×Q8C22×D11112yes—
545C4×D4—116no—
546C4×D4—1112no—
547C4×D4—1112no—
548C4×D4—1124no—
549C4×D4—116no—
550C4×D4—1112no—
551C4×D4—1112no—
552C4×D4—1124no—
553C4×D4—116no—
554C4×D4—1112no—
555C4×D4C22×D1116yes—
556C4×D4C22×D11112yes—
557#117—113no—
558#117—116no—
559#117—116no—
560#117—116no—
561#117—116no—
562#117—116no—
563#117—1112no—
564#117—116no—
565#117—1112no—
566#117C22×D1113yes—
567#117C22×D1116yes—
568C2×C4⋊C4—1112no—
569C2×C4⋊C4—116no—
570C2×C4⋊C4—1112no—
571C2×C4⋊C4—1112no—
572C2×C4⋊C4—1112no—
573C2×C4⋊C4—116no—
574C2×C4⋊C4—1112no—
575C2×C4⋊C4—1112no—
576C2×C4⋊C4—1112no—
577C2×C4⋊C4—1112no—
578C2×C4⋊C4—1124no—
579C2×C4⋊C4—1124no—
580C2×C4⋊C4—1124no—
581C2×C4⋊C4—112no—
582C2×C4⋊C4—116no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—1112no—
585C2×C4⋊C4C22×D1116yes—
586C2×C4⋊C4C22×D11112yes—
587C2×C22⋊C4—1112no—
588C2×C22⋊C4—116no—
589C2×C42—116no—
590C2×C42—113no—
591C2×C42—113no—
592C2×C42—1112no—
593C2×C42—116no—
594C2×C42—116no—
595C2×C42—113no—
596C2×C42—113no—
597C2×C42—111no—
598C2×C42C22×D1113yes—
599C2×C11—26no—
600C2×C11C24×Q811yescharacteristic
601C2×C11C2×#58512yes—
602D11—26no—
603D11#350414yesdirect product factor
604C24—113no—
605#41—118no—
606#41—1124no—
607#41—1124no—
608#41Q8×D1118yescomplemented
609C2×Q8—118no—
610C2×Q8—113no—
611C2×Q8—1112no—
612C2×Q8—1112no—
613C2×Q8—1112no—
614C2×Q8—4424no—
615C2×Q8C23×D11112yes—
616C2×Q8C23×D1111yescharacteristic
617C2×D4—116no—
618C2×D4—1124no—
619C2×D4—113no—
620C2×D4C23×D1113yes—
621C22×C4—113no—
622C22×C4—1124no—
623C22×C4—113no—
624C22×C4—111no—
625C22×C4—113no—
626C22×C4—113no—
627C22×C4—116no—
628C22×C4—1112no—
629C22×C4—112no—
630C22×C4—114no—
631C22×C4—116no—
632C22×C4—1112no—
633C22×C4—116no—
634C22×C4—116no—
635C22×C4—1124no—
636C22×C4—4412no—
637C22×C4—4424no—
638C22×C4C23×D1116yes—
639C22×C4C23×D11112yes—
640C22×C4C23×D1113yes—
641C4⋊C4—1112no—
642C4⋊C4—116no—
643C4⋊C4—1112no—
644C4⋊C4—1112no—
645C4⋊C4—1112no—
646C4⋊C4—1124no—
647C4⋊C4—1112no—
648C4⋊C4—1124no—
649C4⋊C4—1124no—
650C4⋊C4—1124no—
651C4⋊C4—114no—
652C4⋊C4—112no—
653C4⋊C4—1112no—
654C4⋊C4—116no—
655C4⋊C4—114no—
656C4⋊C4—114no—
657C4⋊C4—114no—
658C4⋊C4—1112no—
659C4⋊C4—1112no—
660C4⋊C4—1112no—
661C4⋊C4C23×D1116yes—
662C4⋊C4C23×D11112yes—
663C4⋊C4C23×D11112yes—
664C4⋊C4C23×D11124yes—
665C4⋊C4C23×D1112yes—
666C4⋊C4C23×D1116yes—
667C4⋊C4C23×D1114yes—
668C4⋊C4C23×D11112yes—
669C22⋊C4—1112no—
670C22⋊C4—116no—
671C22⋊C4—1112no—
672C22⋊C4—1112no—
673C22⋊C4—1112no—
674C22⋊C4C23×D11112yes—
675C22⋊C4C23×D1116yes—
676C42—112no—
677C42—111no—
678C42—116no—
679C42—113no—
680C42—116no—
681C42—116no—
682C42—116no—
683C42—1112no—
684C42—1112no—
685C42—1112no—
686C42C23×D1111yescharacteristic
687C42C23×D1113yes—
688C42C23×D1116yes—
689C42C23×D11112yes—
690C11C2×#350411yescharacteristic, complemented, Sylow
691C23—111no—
692C23—1112no—
693C23—113no—
694C23—2212no—
695C23C24×D1113yes—
696Q8—412no—
697Q8—1112no—
698Q8—4412no—
699Q8—4412no—
700Q8—4412no—
701Q8C2×Q8×D1114yes—
702D4—1124no—
703D4—1112no—
704D4C2×Q8×D11112yes—
705C2×C4—46no—
706C2×C4—412no—
707C2×C4—1112no—
708C2×C4—113no—
709C2×C4—111no—
710C2×C4—114no—
711C2×C4—1112no—
712C2×C4—1112no—
713C2×C4—1112no—
714C2×C4—112no—
715C2×C4—114no—
716C2×C4—116no—
717C2×C4—1112no—
718C2×C4—224no—
719C2×C4—2224no—
720C2×C4—2212no—
721C2×C4—228no—
722C2×C4—446no—
723C2×C4—4424no—
724C2×C4—446no—
725C2×C4—446no—
726C2×C4—4412no—
727C2×C4C2×Q8×D11112yes—
728C2×C4C24×D1112yes—
729C2×C4C24×D1114yes—
730C2×C4C24×D1116yes—
731C2×C4C24×D11112yes—
732C2×C4C24×D1113yes—
733C2×C4C24×D1111yescharacteristic
734C22—26no—
735C22—112no—
736C22—114no—
737C22—116no—
738C22—2224no—
739C22—226no—
740C22C22×Q8×D1116yes—
741C22C25×D1111yescharacteristic
742C4—22no—
743C4—212no—
744C4—26no—
745C4—24no—
746C4—112no—
747C4—116no—
748C4—222no—
749C4—2212no—
750C4—226no—
751C4—224no—
752C4C22×Q8×D1112yes—
753C4C22×Q8×D1116yes—
754C2—26no—
755C2—114no—
756C2—226no—
757C2C23×Q8×D1111yescharacteristic
758C2D11×#58512yes—
subgroupG/H
center, FrattiniC22C25×D11
commutator, socle, cosocleC22×C11C26
FittingC11×#3504C2
prime radicalC2×#41×D11C22
hypercenter#3504D11
hypocenterC11C2×#3504
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #13082442C2semidirect
2. #13082441C2semidirect
3. #13082440C2semidirect
4. #13082439C2semidirect
5. #13082438C2semidirect
6. #13082437C2semidirect
7. #13082436C2semidirect
8. D11×#557C2semidirect
9. D11×#554C2semidirect
10. D11×#544C2semidirect
11. D11×#533C2semidirect
12. C2×D11×#125C2semidirect
15. C11×#3504C2semidirect
17. C11×#557C22semidirect
18. C11×#554C22semidirect
19. C11×#544C22semidirect
20. C11×#533C22semidirect
21. C2×C11×#125C22semidirect
26. #10623261C22semidirect
27. #10623260C22semidirect
28. #10623260C22semidirect
29. #10623259C22semidirect
32. #10623252C22semidirect
33. #10623221C22semidirect
34. #10623221C22semidirect
35. #10623220C22semidirect
36. #10623220C22semidirect
37. #10623219C22semidirect
38. #10623219C22semidirect
44. D11×#125C22semidirect
45. D11×#125C22semidirect
46. D11×#125C22semidirect
47. #10623216C22semidirect
48. #10623216C22semidirect
49. #10623167C22semidirect
50. #10623167C22semidirect
51. #10623166C22semidirect
54. #10623154C22semidirect
55. #10623153C22semidirect
56. #10623110C22semidirect
57. #10623109C22semidirect
63. #10623101C22semidirect
64. #10623100C22semidirect
65. #10623100C22semidirect
66. #10623098C22semidirect
70. #10623074C22semidirect
71. #10623070C22semidirect
72. #10623070C22semidirect
78. #10623050C22semidirect
79. #10623050C22semidirect
80. #10623048C22semidirect
81. #10623042C22semidirect
85. #10623031C22semidirect
86. C2×#66943C22semidirect
87. C2×#66942C22semidirect
90. #10623001C22semidirect
91. C2×#66923C22semidirect
93. #41×D11Q8semidirect
227. C11×#41C2×Q8semidirect
238. #4343C2×Q8semidirect
241. #4341C2×Q8semidirect
243. #4339C2×Q8semidirect
319. #3504D11direct (N × H)
378. #557C2×D11semidirect
390. #554C2×D11semidirect
399. #544C2×D11semidirect
407. #533C2×D11semidirect
421. C2×#125C2×D11semidirect
603. D11#3504direct (N × H)
608. #41Q8×D11semidirect
690. C11C2×#3504semidirect

Maximal subgroups

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

subgroupindex
#130824422
#130824412
#130824402
#130824392
#130824382
#130824372
#130824362
D11×#5572
D11×#5542
D11×#5442
D11×#5332
C2×D11×#1252
D11×#5202
C4×#41×D112
C11×#35042
C2×#350411