Finite Group Databasebeta

← D11×#3499 #15662181

Subgroups — D11×#3499 #15662181

Order 2816.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×2−1+4C212yesmaximal, complemented
2#13082401C211yesmaximal, characteristic, complemented
3#13082400C214yesmaximal, complemented
4#13082399C213yesmaximal, complemented
5#13082398C216yesmaximal, complemented
6#13082397C212yesmaximal, complemented
7#13082396C213yesmaximal, complemented
8#13082395C2112yesmaximal, complemented
9D4×Q8×D11C214yesmaximal, complemented
10D11×#547C2112yesmaximal, complemented
11D11×#536C216yesmaximal, complemented
12D11×#532C213yesmaximal, complemented
13C2×D11×C4⋊Q8C213yesmaximal, complemented
14C4×#41×D11C211yesmaximal, characteristic, complemented
15C11×#3499C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2212yescomplemented
17D11×2−1+4—232no—
18C2×#67043C22112yescomplemented
19C2×#67043C2216yescomplemented
20C2×#67043C2212yescomplemented
21C2×#41×D11C2216yes—
22C2×#41×D11C22112yes—
23C2×#41×D11C2211yescharacteristic
24C2×#67040C2216yescomplemented
25C2×#67040C2214yescomplemented
26C22×Q8×D11C2216yes—
27C22×Q8×D11C2214yes—
28D4×Q8×C11C2214yescomplemented
29C11×#547C22112yescomplemented
30C11×#536C2216yescomplemented
31C11×#532C2213yescomplemented
32C2×C11×C4⋊Q8C2213yescomplemented
33C4×C11×#41C2211yescharacteristic, complemented
34#10623363C2216yescomplemented
35#41×Dic11C2211yescharacteristic, complemented
36#10623356C2216yescomplemented
37#10623355C22124yescomplemented
38#10623347C2216yescomplemented
39Q8×C22⋊D11C2218yescomplemented
40C2×#66997C2216yescomplemented
41#10623258C22112yescomplemented
42#10623257C22112yescomplemented
43#10623256C2213yescomplemented
44#10623255C22112yescomplemented
45D11×C4⋊Q8C2213yes—
46D11×C4⋊Q8C2216yes—
47D11×C4⋊Q8C22112yes—
48D11×C4⋊Q8C22112yescomplemented
49D11×C4⋊Q8C2216yescomplemented
50D11×C4⋊Q8C2216yescomplemented
51#10623247C2213yescomplemented
52D11×#127C2211yescharacteristic
53#10623206C22112yescomplemented
54D11×#124C2216yes—
55#10623199C2216yescomplemented
56#10623186C22148yescomplemented
57D11×#123C22124yes—
58#10623179C22124yescomplemented
59#10623163C22124yescomplemented
60#10623162C22124yescomplemented
61#10623159C22124yescomplemented
62D11×C22⋊Q8C22124yes—
63#10623142C22124yescomplemented
64D11×#121C22112yes—
65#10623127C22112yescomplemented
66Q8×D44C2214yescomplemented
67C4×#4343C2212yescomplemented
68C4×Q8×D11C2212yes—
69#10623086C22112yescomplemented
70#10623082C22112yescomplemented
71#10623079C22112yescomplemented
72C4×D4×D11C22112yes—
73C4×D4×D11C2216yes—
74D4×Dic22C22112yescomplemented
75C4×#4341C2216yescomplemented
76#10623057C2216yescomplemented
77#10623053C2213yescomplemented
78D11×#117C2213yes—
79#10623038C22124yescomplemented
80C2×C4⋊C4×D11C22112yes—
81C2×#66941C22112yescomplemented
82#10623008C2213yescomplemented
83C4×#4339C2213yescomplemented
84C2×C42×D11C2213yes—
85C2×#66922C2213yescomplemented
86C11×2−1+4—216no—
87C2×C11×#41C23112yes—
88C2×C11×#41C2316yes—
89C2×C11×#41C2311yescharacteristic
90C22×Q8×C11C2316yes—
91C22×Q8×C11C2314yes—
92#67043—216no—
93#67043—296no—
94#67043—248no—
95#41×D11—296no—
96#41×D11—248no—
97#41×D11D4116yescomplemented
98#67040—232no—
99#67040—248no—
100C2×#4343C2316yes—
101C2×#4343C23112yes—
102C2×#4343C2311yescharacteristic
103C2×Q8×D11—232no—
104C2×Q8×D11—248no—
105C2×Q8×D11C2316yes—
106C2×Q8×D11C23112yes—
107C2×Q8×D11C23112yes—
108C2×Q8×D11C23112yes—
109C2×Q8×D11C23112yes—
110C2×Q8×D11C2314yes—
111C2×Q8×D11C2311yescharacteristic
112C2×#4341C2316yes—
113C2×#4341C23112yes—
114C2×#4341C23112yes—
115C2×#4341C23124yes—
116C2×#4341C2313yes—
117C2×D4×D11C2314yes—
118C2×D4×D11C2312yes—
119C2×D4×D11C23112yes—
120C2×D4×D11C2313yes—
121C2×#4339C2316yes—
122C2×#4339C23124yes—
123C2×#4339C23112yes—
124C2×#4339C23112yes—
125C2×#4339C2313yes—
126C22×C4×D11C2316yes—
127C22×C4×D11C23112yes—
128C22×C4×D11C23112yes—
129C22×C4×D11C2313yes—
130C22×Dic22C2316yes—
131C22×Dic22C23112yes—
132C22×Dic22C23112yes—
133C11×C4⋊Q8C2313yes—
134C11×C4⋊Q8C2316yes—
135C11×C4⋊Q8C23112yes—
136C11×#127C2311yescharacteristic
137C11×#124C2316yes—
138C11×#123C23124yes—
139C11×C22⋊Q8C23124yes—
140C11×#121C23112yes—
141C4×Q8×C11C2312yes—
142C4×D4×C11C2316yes—
143C4×D4×C11C23112yes—
144C11×#117C2313yes—
145C2×C11×C4⋊C4C23112yes—
146C2×C42×C11C2313yes—
147#67000C2316yes—
148#66999C23124yes—
149Q8×Dic11C2312yes—
150#66997C2316yes—
151#66997C23112yes—
152#66997C23124yes—
153#66993C2314yes—
154#66993C2312yes—
155#66992C23124yes—
156#66991C23112yes—
157#66989C2316yes—
158#66988C23124yes—
159D4×Dic11C23112yes—
160D4×Dic11C2316yes—
161#66983C23112yes—
162#66982C23124yes—
163C4×C22⋊D11C23112yes—
164C4×C22⋊D11C23124yes—
165#66979C2313yes—
166C2×C4⋊Dic11C23112yes—
167#66977C23124yes—
168C2×Dic11⋊C4C23124yes—
169C2×C4×Dic11C2316yes—
170C2×C4×Dic11C2313yes—
171#66950C23124yes—
172#66949C23148yes—
173#66948C23112yes—
174#66947C23148yes—
175#66946C23112yes—
176#66946C2316yes—
177#66945C2316yes—
178C4⋊C4×D11C23112yes—
179C4⋊C4×D11C23124yes—
180C4⋊C4×D11C23124yes—
181C4⋊C4×D11C23124yes—
182C4⋊C4×D11C2316yes—
183#66941C23112yes—
184#66941C23124yes—
185#66941C23124yes—
186#66941C23124yes—
187#66940C2316yes—
188#66939C23124yes—
189#66938C23124yes—
190#66937C23124yes—
191#66936C23148yes—
192(C22⋊D11)⋊C4C23112yes—
193(C22⋊D11)⋊C4C23124yes—
194C22⋊C4×D11C2316yes—
195C22⋊C4×D11C23124yes—
196#66931C23148yes—
197#66930C2316yes—
198#66928C2316yes—
199#66927C2311yescharacteristic
200C4×D44C2316yes—
201C4×D44C23112yes—
202#66925C2316yes—
203C42×D11C2311yescharacteristic
204C42×D11C2313yes—
205C42×D11C2313yes—
206C42×D11C2316yes—
207C42×D11C2313yes—
208C42×D11C2316yes—
209#66922C2313yes—
210#66922C2316yes—
211#66922C23112yes—
212C4×Dic22C2316yes—
213C2×#3499—111nomaximal, Sylow
214C23×D11C2414yes—
215C23×D11C2413yes—
216C11×#41—248no—
217C11×#41—224no—
218C11×#41C2×D418yescomplemented
219C2×Q8×C11—216no—
220C2×Q8×C11—224no—
221C2×Q8×C11C2416yes—
222C2×Q8×C11C24112yes—
223C2×Q8×C11C2411yescharacteristic
224C2×D4×C11C2414yes—
225C2×D4×C11C24112yes—
226C2×D4×C11C2412yes—
227C2×D4×C11C2413yes—
228C22×C4×C11C2416yes—
229C22×C4×C11C24112yes—
230C22×C4×C11C24112yes—
231C22×C4×C11C2413yes—
232C2×C22⋊D11C2418yes—
233C2×C22⋊D11C24112yes—
234C2×C22⋊D11C2414yes—
235C2×C22⋊D11C24112yes—
236C2×C22⋊D11C2416yes—
237C22×Dic11C24112yes—
238C22×Dic11C2416yes—
239C22×Dic11C24112yes—
240C22×Dic11C2413yes—
241#4343—248no—
242#4343—224no—
243#4343C2×D418yescomplemented
244Q8×D11—248no—
245Q8×D11—224no—
246Q8×D11—248no—
247Q8×D11—248no—
248Q8×D11—248no—
249Q8×D11—216no—
250Q8×D11C2×D418yes—
251#4341—296no—
252#4341—248no—
253#4341—224no—
254#4341—248no—
255#4341C2×D4124yescomplemented
256D4×D11—28no—
257D4×D11—216no—
258D4×D11—248no—
259D4×D11C2×D4124yes—
260#4339—296no—
261#4339—248no—
262#4339—248no—
263#4339—224no—
264#4339C2×D4124yescomplemented
265C2×D44C2414yes—
266C2×D44C2412yes—
267C2×D44C24112yes—
268C2×D44C2413yes—
269C2×C4×D11—248no—
270C2×C4×D11—224no—
271C2×C4×D11—248no—
272C2×C4×D11C2×D4124yes—
273C2×C4×D11C2416yes—
274C2×C4×D11C2416yes—
275C2×C4×D11C2416yes—
276C2×C4×D11C24112yes—
277C2×C4×D11C24112yes—
278C2×C4×D11C24112yes—
279C2×C4×D11C24124yes—
280C2×C4×D11C2411yescharacteristic
281C2×C4×D11C2413yes—
282C2×C4×D11C2413yes—
283C2×C4×D11C2413yes—
284C2×C4×D11C2412yes—
285C2×Dic22—248no—
286C2×Dic22—248no—
287C2×Dic22—224no—
288C2×Dic22C2416yes—
289C2×Dic22C24112yes—
290C2×Dic22C24124yes—
291C2×Dic22C24112yes—
292C2×Dic22C2413yes—
293C11×C4⋊C4C2416yes—
294C11×C4⋊C4C24112yes—
295C11×C4⋊C4C24124yes—
296C11×C22⋊C4C2416yes—
297C11×C22⋊C4C24124yes—
298C42×C11C2416yes—
299C42×C11C2411yescharacteristic
300C42×C11C2413yes—
301C22⋊Dic11C2416yes—
302C22⋊Dic11C24124yes—
303(C2×D11)⋊C4C24112yes—
304(C2×D11)⋊C4C24124yes—
305(C2×D11)⋊C4C24124yes—
306C4⋊Dic11C2416yes—
307C4⋊Dic11C24112yes—
308C4⋊Dic11C24124yes—
309Dic11⋊C4C24112yes—
310Dic11⋊C4C24148yes—
311Dic11⋊C4C24124yes—
312C4×Dic11C2416yes—
313C4×Dic11C2412yes—
314C4×Dic11C2411yescharacteristic
315C4×Dic11C2413yes—
316C4×Dic11C2416yes—
317C4×Dic11C2416yes—
318C4×Dic11C2416yes—
319C22×2−1+4—112no—
320#3499—112no—
321#3499—114no—
322#3499—1112no—
323#3499—116no—
324#3499—113no—
325#3499—113no—
326#3499—111no—
327#3499D1111yescharacteristic, direct product factor
328C2×D4×Q8—114no—
329C2×#547—1112no—
330C2×#536—116no—
331C2×#532—113no—
332C22×C4⋊Q8—113no—
333C2×C4×#41—111no—
334C23×C11C2514yes—
335C23×C11C2513yes—
336C22×D11—212no—
337C22×D11—28no—
338C22×D11—216no—
339C22×D11C22×D4112yes—
340C22×D11C2514yes—
341C22×D11C2513yes—
342C22×D11C2511yescharacteristic
343Q8×C11—224no—
344Q8×C11—212no—
345Q8×C11C22×D414yes—
346D4×C11—224no—
347D4×C11—24no—
348D4×C11—28no—
349D4×C11C22×D4112yes—
350C2×C4×C11—224no—
351C2×C4×C11—224no—
352C2×C4×C11—212no—
353C2×C4×C11C22×D4112yes—
354C2×C4×C11C2516yes—
355C2×C4×C11C25112yes—
356C2×C4×C11C2511yescharacteristic
357C2×C4×C11C2513yes—
358C2×C4×C11C2512yes—
359C22⋊D11—224no—
360C22⋊D11—224no—
361C22⋊D11—28no—
362C22⋊D11—216no—
363C22⋊D11C22×D4124yes—
364C2×Dic11—224no—
365C2×Dic11—224no—
366C2×Dic11—212no—
367C2×Dic11C22×D4112yes—
368C2×Dic11C2516yes—
369C2×Dic11C25112yes—
370C2×Dic11C2511yescharacteristic
371C2×Dic11C2513yes—
372C2×Dic11C2512yes—
373D44—224no—
374D44—24no—
375D44—28no—
376D44C22×D4112yes—
377C4×D11—224no—
378C4×D11—248no—
379C4×D11—212no—
380C4×D11—224no—
381C4×D11—212no—
382C4×D11—224no—
383C4×D11—212no—
384C4×D11C22×D4112yes—
385C4×D11C22×D414yes—
386C4×D11C22×D4112yes—
387C4×D11C22×D4112yes—
388C4×D112−1+418yescomplemented
389Dic22—224no—
390Dic22—212no—
391Dic22—224no—
392Dic22—248no—
393Dic22C22×D4112yes—
394C2×2−1+4—116no—
395C2×2−1+4—1112no—
396C2×2−1+4—112no—
397C2×2−1+4—114no—
398C2×2−1+4—116no—
399C2×2−1+4—2232no—
400C2×2−1+4C2×D1112yescomplemented
401C22×#41—111no—
402C22×#41—116no—
403C22×#41—1112no—
404C23×Q8—116no—
405C23×Q8—114no—
406D4×Q8—118no—
407D4×Q8—1112no—
408D4×Q8—1124no—
409D4×Q8—114no—
410D4×Q8—1112no—
411D4×Q8C2×D1114yescomplemented
412#547—1124no—
413#547—1112no—
414#547—1148no—
415#547—1124no—
416#547—1124no—
417#547—1112no—
418#547—1112no—
419#547—1124no—
420#547C2×D11112yescomplemented
421#536—116no—
422#536—116no—
423#536—1112no—
424#536—1112no—
425#536—1124no—
426#536—1124no—
427#536—116no—
428#536C2×D1116yescomplemented
429#532—116no—
430#532—113no—
431#532—113no—
432#532—116no—
433#532—1112no—
434#532—1112no—
435#532—113no—
436#532C2×D1113yescomplemented
437C2×C4⋊Q8—116no—
438C2×C4⋊Q8—113no—
439C2×C4⋊Q8—116no—
440C2×C4⋊Q8—1112no—
441C2×C4⋊Q8—116no—
442C2×C4⋊Q8—116no—
443C2×C4⋊Q8—1112no—
444C2×C4⋊Q8—1112no—
445C2×C4⋊Q8—113no—
446C2×C4⋊Q8C2×D1113yescomplemented
447C2×#127—111no—
448C2×#124—116no—
449C2×#123—1124no—
450C2×C22⋊Q8—1124no—
451C2×#121—1112no—
452C4×#41—111no—
453C4×#41—112no—
454C4×#41—116no—
455C4×#41—113no—
456C4×#41—113no—
457C4×#41C2×D1111yescharacteristic, complemented
458C2×C4×Q8—112no—
459C2×C4×D4—116no—
460C2×C4×D4—1112no—
461C2×#117—113no—
462C22×C4⋊C4—1112no—
463C22×C42—113no—
464C22×C11—26no—
465C22×C11—24no—
466C22×C11—28no—
467C22×C11C23×D416yes—
468C22×C11C2611yescharacteristic
469C2×D11—26no—
470C2×D11—224no—
471C2×D11—24no—
472C2×D11—28no—
473C2×D11—416no—
474C2×D11C23×D416yes—
475C2×D11C23×D412yes—
476C2×D11C2×2−1+414yes—
477C4×C11—212no—
478C4×C11—26no—
479C4×C11C23×D416yes—
480C4×C11C23×D412yes—
481C4×C11C2×2−1+414yescomplemented
482Dic11—212no—
483Dic11—26no—
484Dic11C23×D412yes—
485Dic11C23×D416yes—
486Dic11C2×2−1+414yescomplemented
4872−1+4—216no—
4882−1+4—2232no—
4892−1+4—2248no—
4902−1+4—2296no—
4912−1+4—2248no—
4922−1+4—2216no—
493C2×#41—1116no—
494C2×#41—111no—
495C2×#41—116no—
496C2×#41—1112no—
497C2×#41—113no—
498C2×#41—1112no—
499C2×#41—116no—
500C2×#41—1112no—
501C2×#41—1124no—
502C2×#41—113no—
503C2×#41—1112no—
504C2×#41—116no—
505C2×#41—1112no—
506C2×#41—1124no—
507C2×#41—2248no—
508C2×#41—2296no—
509C2×#41C22×D1116yes—
510C2×#41C22×D11112yes—
511C2×#41C22×D1111yescharacteristic
512C22×Q8—111no—
513C22×Q8—1112no—
514C22×Q8—116no—
515C22×Q8—1112no—
516C22×Q8—1112no—
517C22×Q8—1112no—
518C22×Q8—114no—
519C22×Q8—1112no—
520C22×Q8—116no—
521C22×Q8—1112no—
522C22×Q8—2248no—
523C22×Q8—2232no—
524C22×Q8C22×D1116yes—
525C22×Q8C22×D1114yes—
526C22×D4—113no—
527C22×D4—114no—
528C22×D4—1112no—
529C22×D4—112no—
530C23×C4—113no—
531C23×C4—116no—
532C23×C4—1112no—
533C23×C4—1112no—
534C4⋊Q8—116no—
535C4⋊Q8—1112no—
536C4⋊Q8—1124no—
537C4⋊Q8—1112no—
538C4⋊Q8—1124no—
539C4⋊Q8—1124no—
540C4⋊Q8—1124no—
541C4⋊Q8—113no—
542C4⋊Q8—116no—
543C4⋊Q8—1112no—
544C4⋊Q8C22×D1113yes—
545C4⋊Q8C22×D1116yes—
546C4⋊Q8C22×D11112yes—
547#127—112no—
548#127—114no—
549#127—111no—
550#127C22×D1111yescharacteristic
551#124—116no—
552#124—116no—
553#124—1124no—
554#124—116no—
555#124C22×D1116yes—
556#123—1124no—
557#123—1124no—
558#123—1148no—
559#123—1148no—
560#123—1124no—
561#123C22×D11124yes—
562C22⋊Q8—1124no—
563C22⋊Q8—1124no—
564C22⋊Q8—1148no—
565C22⋊Q8—1124no—
566C22⋊Q8—1148no—
567C22⋊Q8C22×D11124yes—
568#121—1112no—
569#121—1124no—
570#121—1112no—
571#121—1112no—
572#121—1124no—
573#121C22×D11112yes—
574C4×Q8—112no—
575C4×Q8—116no—
576C4×Q8—116no—
577C4×Q8C22×D1112yes—
578C4×D4—116no—
579C4×D4—1112no—
580C4×D4—1112no—
581C4×D4—1124no—
582C4×D4—116no—
583C4×D4—1112no—
584C4×D4—1112no—
585C4×D4—1124no—
586C4×D4—116no—
587C4×D4—1112no—
588C4×D4C22×D1116yes—
589C4×D4C22×D11112yes—
590#117—113no—
591#117—116no—
592#117—116no—
593#117—116no—
594#117C22×D1113yes—
595C2×C4⋊C4—1124no—
596C2×C4⋊C4—1112no—
597C2×C4⋊C4—1112no—
598C2×C4⋊C4—1124no—
599C2×C4⋊C4—1124no—
600C2×C4⋊C4—1124no—
601C2×C4⋊C4—116no—
602C2×C4⋊C4C22×D11112yes—
603C2×C22⋊C4—116no—
604C2×C22⋊C4—1124no—
605C2×C42—116no—
606C2×C42—113no—
607C2×C42—113no—
608C2×C42—116no—
609C2×C42—116no—
610C2×C42—113no—
611C2×C42—113no—
612C2×C42—111no—
613C2×C42C22×D1113yes—
614C2×C11—26no—
615C2×C11—44no—
616C2×C11C24×D411yescharacteristic
617C2×C11C22×2−1+412yes—
618D11—26no—
619D11—44no—
620D11#349914yesdirect product factor
621C24—113no—
622C24—114no—
623#41—248no—
624#41—224no—
625#41—118no—
626#41—1124no—
627#41—1124no—
628#41—2248no—
629#41—2296no—
630#41—2248no—
631#41—2248no—
632#41—2224no—
633#41—2224no—
634#41—2296no—
635#41—2248no—
636#41—2248no—
637#41—2224no—
638#41D4×D1118yescomplemented
639C2×Q8—216no—
640C2×Q8—224no—
641C2×Q8—118no—
642C2×Q8—113no—
643C2×Q8—1124no—
644C2×Q8—1112no—
645C2×Q8—1112no—
646C2×Q8—116no—
647C2×Q8—2248no—
648C2×Q8—2248no—
649C2×Q8—2224no—
650C2×Q8—2248no—
651C2×Q8—2248no—
652C2×Q8—2248no—
653C2×Q8—2248no—
654C2×Q8—2216no—
655C2×Q8—2224no—
656C2×Q8C23×D11112yes—
657C2×Q8C23×D1116yes—
658C2×Q8C23×D1111yescharacteristic
659C2×D4—116no—
660C2×D4—1124no—
661C2×D4—118no—
662C2×D4—1112no—
663C2×D4—1112no—
664C2×D4—114no—
665C2×D4—113no—
666C2×D4—114no—
667C2×D4—1112no—
668C2×D4—112no—
669C2×D4—228no—
670C2×D4—2216no—
671C2×D4—2248no—
672C2×D4C23×D1114yes—
673C2×D4C23×D11112yes—
674C2×D4C23×D1112yes—
675C2×D4C23×D1113yes—
676C22×C4—113no—
677C22×C4—1124no—
678C22×C4—112no—
679C22×C4—111no—
680C22×C4—113no—
681C22×C4—113no—
682C22×C4—113no—
683C22×C4—116no—
684C22×C4—1112no—
685C22×C4—1112no—
686C22×C4—116no—
687C22×C4—116no—
688C22×C4—116no—
689C22×C4—1112no—
690C22×C4—1124no—
691C22×C4—1112no—
692C22×C4—1112no—
693C22×C4—2248no—
694C22×C4—2224no—
695C22×C4—2248no—
696C22×C4C23×D1116yes—
697C22×C4C23×D11112yes—
698C22×C4C23×D11112yes—
699C22×C4C23×D1113yes—
700C4⋊C4—1124no—
701C4⋊C4—1112no—
702C4⋊C4—1148no—
703C4⋊C4—1124no—
704C4⋊C4—1112no—
705C4⋊C4—116no—
706C4⋊C4C23×D11112yes—
707C4⋊C4C23×D11124yes—
708C4⋊C4C23×D1116yes—
709C22⋊C4—116no—
710C22⋊C4—1124no—
711C22⋊C4—1112no—
712C22⋊C4—1124no—
713C22⋊C4—1124no—
714C22⋊C4C23×D1116yes—
715C22⋊C4C23×D11124yes—
716C42—111no—
717C42—112no—
718C42—116no—
719C42—113no—
720C42—116no—
721C42—116no—
722C42—116no—
723C42C23×D1111yescharacteristic
724C42C23×D1113yes—
725C42C23×D1116yes—
726C11C2×#349911yescharacteristic, complemented, Sylow
727C23—111no—
728C23—1112no—
729C23—113no—
730C23—114no—
731C23—2212no—
732C23—228no—
733C23—2216no—
734C23C24×D1114yes—
735C23C24×D1113yes—
736Q8—224no—
737Q8—212no—
738Q8—1112no—
739Q8—2224no—
740Q8—2248no—
741Q8—2224no—
742Q8—2212no—
743Q8C2×D4×D1114yes—
744D4—224no—
745D4—24no—
746D4—28no—
747D4—1124no—
748D4—1112no—
749D4—2224no—
750D4—228no—
751D4—2216no—
752D4—2224no—
753D4—2224no—
754D4—224no—
755D4—228no—
756D4C2×D4×D11112yes—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—212no—
760C2×C4—1112no—
761C2×C4—112no—
762C2×C4—111no—
763C2×C4—113no—
764C2×C4—114no—
765C2×C4—1112no—
766C2×C4—1112no—
767C2×C4—1112no—
768C2×C4—118no—
769C2×C4—116no—
770C2×C4—1112no—
771C2×C4—2224no—
772C2×C4—2212no—
773C2×C4—2224no—
774C2×C4—2248no—
775C2×C4—2212no—
776C2×C4—2224no—
777C2×C4—2212no—
778C2×C4—2224no—
779C2×C4—2224no—
780C2×C4—2212no—
781C2×C4C2×D4×D11112yes—
782C2×C4C24×D1116yes—
783C2×C4C24×D11112yes—
784C2×C4C24×D1111yescharacteristic
785C2×C4C24×D1113yes—
786C2×C4C24×D1112yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—112no—
791C22—114no—
792C22—116no—
793C22—2224no—
794C22—226no—
795C22—224no—
796C22—228no—
797C22—4416no—
798C22C22×D4×D1116yes—
799C22C25×D1111yescharacteristic
800C4—212no—
801C4—26no—
802C4—112no—
803C4—116no—
804C4—114no—
805C4—2212no—
806C4—226no—
807C4C22×D4×D1116yes—
808C4C22×D4×D1112yes—
809C4D11×2−1+414yescomplemented
810C2—26no—
811C2—44no—
812C2—114no—
813C2—226no—
814C2—444no—
815C2C23×D4×D1111yescharacteristic
816C2C2×D11×2−1+412yes—
subgroupG/H
center, FrattiniC22C25×D11
commutator, socle, cosocleC22×C11C26
FittingC11×#3499C2
hypercenter#3499D11
hypocenterC11C2×#3499
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×D11×2−1+4C2semidirect
2. #13082401C2semidirect
3. #13082400C2semidirect
4. #13082399C2semidirect
5. #13082398C2semidirect
6. #13082397C2semidirect
7. #13082396C2semidirect
8. #13082395C2semidirect
9. D4×Q8×D11C2semidirect
10. D11×#547C2semidirect
11. D11×#536C2semidirect
12. D11×#532C2semidirect
13. C2×D11×C4⋊Q8C2semidirect
14. C4×#41×D11C2semidirect
15. C11×#3499C2semidirect
16. C2×C11×2−1+4C22semidirect
18. C2×#67043C22semidirect
19. C2×#67043C22semidirect
20. C2×#67043C22semidirect
24. C2×#67040C22semidirect
25. C2×#67040C22semidirect
28. D4×Q8×C11C22semidirect
29. C11×#547C22semidirect
30. C11×#536C22semidirect
31. C11×#532C22semidirect
32. C2×C11×C4⋊Q8C22semidirect
33. C4×C11×#41C22semidirect
34. #10623363C22semidirect
35. #41×Dic11C22semidirect
36. #10623356C22semidirect
37. #10623355C22semidirect
38. #10623347C22semidirect
39. Q8×C22⋊D11C22semidirect
40. C2×#66997C22semidirect
41. #10623258C22semidirect
42. #10623257C22semidirect
43. #10623256C22semidirect
44. #10623255C22semidirect
48. D11×C4⋊Q8C22semidirect
49. D11×C4⋊Q8C22semidirect
50. D11×C4⋊Q8C22semidirect
51. #10623247C22semidirect
53. #10623206C22semidirect
55. #10623199C22semidirect
56. #10623186C22semidirect
58. #10623179C22semidirect
59. #10623163C22semidirect
60. #10623162C22semidirect
61. #10623159C22semidirect
63. #10623142C22semidirect
65. #10623127C22semidirect
66. Q8×D44C22semidirect
67. C4×#4343C22semidirect
69. #10623086C22semidirect
70. #10623082C22semidirect
71. #10623079C22semidirect
74. D4×Dic22C22semidirect
75. C4×#4341C22semidirect
76. #10623057C22semidirect
77. #10623053C22semidirect
79. #10623038C22semidirect
81. C2×#66941C22semidirect
82. #10623008C22semidirect
83. C4×#4339C22semidirect
85. C2×#66922C22semidirect
97. #41×D11D4semidirect
218. C11×#41C2×D4semidirect
243. #4343C2×D4semidirect
255. #4341C2×D4semidirect
264. #4339C2×D4semidirect
327. #3499D11direct (N × H)
388. C4×D112−1+4semidirect
400. C2×2−1+4C2×D11semidirect
411. D4×Q8C2×D11semidirect
420. #547C2×D11semidirect
428. #536C2×D11semidirect
436. #532C2×D11semidirect
446. C2×C4⋊Q8C2×D11semidirect
457. C4×#41C2×D11semidirect
481. C4×C11C2×2−1+4semidirect
486. Dic11C2×2−1+4semidirect
620. D11#3499direct (N × H)
638. #41D4×D11semidirect
726. C11C2×#3499semidirect
809. C4D11×2−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×D11×2−1+42
#130824012
#130824002
#130823992
#130823982
#130823972
#130823962
#130823952
D4×Q8×D112
D11×#5472
D11×#5362
D11×#5322
C2×D11×C4⋊Q82
C4×#41×D112
C11×#34992
C2×#349911