Finite Group Databasebeta

← D11×#3113 #15621970

Subgroups — D11×#3113 #15621970

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic
3#13078748C212yesmaximal, complemented
4#13078747C211yesmaximal, characteristic, complemented
5#13078746C211yesmaximal, characteristic, complemented
6#13078745C212yesmaximal, complemented
7#13078744C214yesmaximal, complemented
8#13078743C212yesmaximal, complemented
9#13078742C211yesmaximal, characteristic, complemented
10#13078741C212yesmaximal, complemented
11D11×#483C212yesmaximal
12D11×#475C212yesmaximal, complemented
13D11×#462C212yesmaximal, complemented
14D11×#451C212yesmaximal
15D11×#441C214yesmaximal, complemented
16D11×#432C211yesmaximal, characteristic
17C11×#3113C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2211yescharacteristic
19C11×#533C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q16×D11C2214yes—
23#10623259C2211yescharacteristic
24#10623259C2211yescharacteristic
25D11×C4⋊Q8C2211yescharacteristic
26D11×C4⋊Q8C2211yescharacteristic
27#10623219—21no—
28D11×#125—21no—
29D11×C22⋊Q8—21no—
30D11×C22⋊Q8C2212yes—
31#10623153—21no—
32#10623153C2212yes—
33#10623109—21no—
34#10623109C2212yes—
35C4×Q8×D11—21no—
36C4×Q8×D11—21no—
37C4×Q8×D11—21no—
38C4×Q8×D11—21no—
39C4×Q8×D11—21no—
40C4×Q8×D11C2212yes—
41C4×Q8×D11C2212yes—
42C4×Q8×D11C2212yes—
43C4×Q8×D11C2212yes—
44C4×Q8×D11C2212yes—
45D11×#117—21no—
46#10623048—21no—
47C2×C4⋊C4×D11—21no—
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×#66940—21no—
50C2×#66940C2211yescharacteristic
51C2×C42×D11—21no—
52C2×C42×D11C2211yescharacteristic
53#10623001C2211yescharacteristic
54C2×C4×Dic22—21no—
55C2×C4×Dic22C2211yescharacteristic
56C11×#483C2212yes—
57C11×#475C2212yescomplemented
58C11×#462C2212yescomplemented
59C11×#451C2212yes—
60C11×#441C2214yescomplemented
61C11×#432C2211yescharacteristic
62#10622841C2212yes—
63#10622799C2214yes—
64#10622797C2214yescomplemented
65#10622795C2214yescomplemented
66#10622707C2212yescomplemented
67#10622703C2212yescomplemented
68#10622663C2212yes—
69#10622656C2212yes—
70#10622644C2212yescomplemented
71#10622643C2214yescomplemented
72#10622643C2214yescomplemented
73#10622633C2212yescomplemented
74#10622584C2212yes—
75#10622539C2211yescharacteristic
76#10622475C2214yes—
77D11×#106C2214yes—
78#10622467C2214yescomplemented
79#10622466C2214yescomplemented
80#10622464C2212yescomplemented
81#10622462C2212yescomplemented
82#10622448C2212yes—
83D11×C4⋊C8C2212yes—
84#10622421C2214yes—
85#10622418C2214yes—
86D11×#103C2214yes—
87D11×#103C2214yes—
88#10622406C2214yescomplemented
89#10622404C2214yescomplemented
90#10622402C2214yescomplemented
91#10622402C2214yescomplemented
92#10622352C2212yes—
93D11×C22⋊C8C2212yes—
94#10622334C2212yes—
95#10622332C2212yes—
96#10622329C2214yescomplemented
97#10622318C2212yes—
98D11×#97C2212yes—
99C22×Q8×C11C2311yescharacteristic
100C2×Q8×D11—28no—
101C2×Q8×D11—21no—
102C2×Q8×D11—21no—
103C2×Q8×D11—21no—
104C2×Q8×D11C2312yes—
105C2×Q8×D11C2312yes—
106C2×Q8×D11C2312yes—
107C22×C4×D11—21no—
108C22×C4×D11—21no—
109C22×C4×D11D411yescharacteristic
110C22×C4×D11D411yescharacteristic
111C22×C4×D11C2311yescharacteristic
112C22×Dic22—21no—
113C22×Dic22C2311yescharacteristic
114C2×C11×Q16C2314yes—
115C11×C4⋊Q8C2311yescharacteristic
116C11×C4⋊Q8C2311yescharacteristic
117C11×#125—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8C2312yes—
120C4×Q8×C11—21no—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2312yes—
125C4×Q8×C11C2312yes—
126C11×#117—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C42×C11—21no—
130C2×C42×C11C2311yescharacteristic
131#66999—21no—
132#66999C2312yes—
133Q8×Dic11—21no—
134Q8×Dic11—21no—
135Q8×Dic11—21no—
136Q8×Dic11C2312yes—
137Q8×Dic11C2312yes—
138Q8×Dic11C2312yes—
139#66997—21no—
140#66997C2312yes—
141C2×#4326C2314yes—
142C2×#4326C2314yes—
143#66979—21no—
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11C2311yescharacteristic
146#66977—21no—
147#66977C2312yes—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11—21no—
154C2×C4×Dic11D411yescharacteristic
155C2×C4×Dic11D411yescharacteristic
156C2×C4×Dic11C2311yescharacteristic
157Q16×D11—216no—
158C2×Dic44C2314yes—
159C2×C8×D11C2314yes—
160#66950—21no—
161#66950C2312yes—
162#66949—22no—
163#66949—22no—
164#66945—21no—
165#66945—21no—
166C4⋊C4×D11—21no—
167C4⋊C4×D11—21no—
168C4⋊C4×D11—21no—
169C4⋊C4×D11—22no—
170C4⋊C4×D11—22no—
171C4⋊C4×D11—22no—
172C4⋊C4×D11—22no—
173C4⋊C4×D11—21no—
174C4⋊C4×D11—21no—
175C4⋊C4×D11—22no—
176C4⋊C4×D11—22no—
177C4⋊C4×D11C2312yes—
178C4⋊C4×D11C2312yes—
179C4⋊C4×D11C2312yes—
180#66943—21no—
181#66943—21no—
182#66942—22no—
183#66942—22no—
184#66941—21no—
185#66941—21no—
186#66941—21no—
187#66941C2312yes—
188#66940—21no—
189#66940—22no—
190#66940—22no—
191#66940—22no—
192#66940—22no—
193#66940—21no—
194#66940—21no—
195#66940—22no—
196#66940—22no—
197#66940C2312yes—
198#66940C2312yes—
199#66940C2312yes—
200C22⋊C4×D11—22no—
201#66931—22no—
202#66931—22no—
203#66930—22no—
204#66925—22no—
205C42×D11—22no—
206C42×D11—22no—
207C42×D11—22no—
208C42×D11—22no—
209C42×D11—22no—
210C42×D11D411yescharacteristic
211C42×D11D411yescharacteristic
212C42×D11D411yescharacteristic
213C42×D11D411yescharacteristic
214C42×D11C2311yescharacteristic
215C42×D11C2311yescharacteristic
216C42×D11C2311yescharacteristic
217C42×D11C2311yescharacteristic
218#66923—21no—
219#66922C2311yescharacteristic
220#66922C2311yescharacteristic
221C4×Dic22—21no—
222C4×Dic22—21no—
223C4×Dic22—21no—
224C4×Dic22—22no—
225C4×Dic22—22no—
226C4×Dic22—22no—
227C4×Dic22—22no—
228C4×Dic22—22no—
229C4×Dic22—22no—
230C4×Dic22C2312yes—
231C4×Dic22C2312yes—
232C4×Dic22C2312yes—
233C11×#106C2314yes—
234C11×C4⋊C8C2312yes—
235C11×#103C2314yes—
236C11×#103C2314yes—
237C11×C22⋊C8C2312yes—
238C11×#97C2312yes—
239#66899C2314yes—
240#66899C2314yes—
241C22⋊(C11⋊C8)C2312yes—
242(C2×D11)⋊C8C2314yes—
243#66881C2314yes—
244#66880C2314yes—
245#66880C2314yes—
246#66879C2314yes—
247Dic11⋊C8C2314yes—
248#66874C2314yes—
249#66874C2314yes—
250#66872C2314yes—
251#66872C2314yes—
252C4⋊(C11⋊C8)C2312yes—
253#66867C2312yes—
254C2×#3113—111nomaximal, Sylow
255C23×D11C2×D411yescharacteristic
256C2×Q8×C11—24no—
257C2×Q8×C11—21no—
258C2×Q8×C11—21no—
259C2×Q8×C11C2412yes—
260C2×Q8×C11C2412yes—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11C2×D411yescharacteristic
269C22×Dic11C2×D411yescharacteristic
270C22×Dic11C2×D411yescharacteristic
271Q8×D11—28no—
272Q8×D11—28no—
273Q8×D11—24no—
274Q8×D11—24no—
275Q8×D11—28no—
276Q8×D11—24no—
277Q8×D11—44no—
278Q8×D11#4118yes—
279C2×C4×D11—28no—
280C2×C4×D11—24no—
281C2×C4×D11—24no—
282C2×C4×D11—24no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—22no—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×C4×D11—44no—
290C2×C4×D11C2×D411yescharacteristic
291C2×C4×D11C2×D411yescharacteristic
292C2×C4×D11C2×D411yescharacteristic
293C2×C4×D11C2×D411yescharacteristic
294C2×C4×D11C2×D411yescharacteristic
295C2×C4×D11C2×D411yescharacteristic
296C2×C4×D11C2×D411yescharacteristic
297C2×C4×D11C2×D411yescharacteristic
298C2×C4×D11C2×D411yescharacteristic
299C2×C4×D11C2×D411yescharacteristic
300C2×C4×D11C2411yescharacteristic
301C2×C4×D11C2411yescharacteristic
302C2×Dic22—28no—
303C2×Dic22—22no—
304C2×Dic22—22no—
305C2×Dic22—24no—
306C2×Dic22—22no—
307C2×Dic22—22no—
308C2×Dic22—21no—
309C2×Dic22—21no—
310C2×Dic22C2412yes—
311C2×Dic22C2412yes—
312C11×Q16—28no—
313C2×C8×C11C2414yes—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—21no—
317C11×C4⋊C4—21no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—22no—
320C11×C4⋊C4—21no—
321C11×C4⋊C4—21no—
322C11×C4⋊C4C2412yes—
323C11×C4⋊C4C2412yes—
324C11×C22⋊C4—22no—
325C42×C11—22no—
326C42×C11—22no—
327C42×C11—22no—
328C42×C11C2×D411yescharacteristic
329C42×C11C2×D411yescharacteristic
330C42×C11C2411yescharacteristic
331C42×C11C2411yescharacteristic
332C22⋊Dic11—22no—
333#4326—28no—
334#4326—28no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4—22no—
337C4⋊Dic11—22no—
338C4⋊Dic11—22no—
339C4⋊Dic11—22no—
340C4⋊Dic11—22no—
341C4⋊Dic11—21no—
342C4⋊Dic11—21no—
343C4⋊Dic11—21no—
344C4⋊Dic11—21no—
345C4⋊Dic11C2412yes—
346C4⋊Dic11C2412yes—
347Dic11⋊C4—22no—
348Dic11⋊C4—22no—
349Dic11⋊C4—22no—
350Dic11⋊C4—22no—
351Dic11⋊C4—22no—
352Dic11⋊C4—22no—
353Dic11⋊C4—22no—
354Dic11⋊C4—22no—
355Dic11⋊C4—22no—
356Dic11⋊C4—22no—
357Dic11⋊C4—22no—
358Dic11⋊C4—22no—
359Dic11⋊C4—22no—
360Dic11⋊C4—22no—
361C4×Dic11—22no—
362C4×Dic11—22no—
363C4×Dic11—22no—
364C4×Dic11—22no—
365C4×Dic11—22no—
366C4×Dic11—22no—
367C4×Dic11—22no—
368C4×Dic11—22no—
369C4×Dic11—22no—
370C4×Dic11C2×D411yescharacteristic
371C4×Dic11C2×D411yescharacteristic
372C4×Dic11C2×D411yescharacteristic
373C4×Dic11C2×D411yescharacteristic
374C4×Dic11C2×D411yescharacteristic
375C4×Dic11C2×D411yescharacteristic
376C4×Dic11C2×D411yescharacteristic
377C4×Dic11C2×D411yescharacteristic
378C4×Dic11C2×D411yescharacteristic
379C4×Dic11C2×D411yescharacteristic
380C4×Dic11C2411yescharacteristic
381C4×Dic11C2411yescharacteristic
382C2×C11⋊C8C2414yes—
383Dic44—28no—
384C8×D11—28no—
385C2×#533—111no—
386C22×C4×Q8—111no—
387#3113—112no—
388#3113—112no—
389#3113—112no—
390#3113—112no—
391#3113—114no—
392#3113—111no—
393#3113—111no—
394#3113—111no—
395#3113D1111yescharacteristic, direct product factor
396C2×#483—112no—
397C2×#475—112no—
398C2×#462—112no—
399C2×#451—112no—
400C2×#441—114no—
401C2×#432—111no—
402C23×C11C22×D411yescharacteristic
403C22×D11—22no—
404C22×D11—22no—
405C22×D11#13714yes—
406C22×D11C22×D411yescharacteristic
407C22×D11C22×D411yescharacteristic
408Q8×C11—24no—
409Q8×C11—22no—
410Q8×C11—24no—
411Q8×C11—42no—
412Q8×C11C2×#4114yes—
413C2×C4×C11—24no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—42no—
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C22×D411yescharacteristic
426C2×C4×C11C22×D411yescharacteristic
427C2×C4×C11C2511yescharacteristic
428C2×Dic11—24no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—42no—
437C2×Dic11C22×D411yescharacteristic
438C2×Dic11C22×D411yescharacteristic
439C2×Dic11C22×D411yescharacteristic
440C2×Dic11C22×D411yescharacteristic
441C2×Dic11C22×D411yescharacteristic
442C2×Dic11C22×D411yescharacteristic
443C4×D11—28no—
444C4×D11—28no—
445C4×D11—22no—
446C4×D11—22no—
447C4×D11—22no—
448C4×D11—22no—
449C4×D11—22no—
450C4×D11—22no—
451C4×D11—22no—
452C4×D11—22no—
453C4×D11—22no—
454C4×D11—22no—
455C4×D11—44no—
456C4×D11—44no—
457C4×D11—44no—
458C4×D11—44no—
459C4×D11#13714yes—
460C4×D11C2×#4114yes—
461Dic22—28no—
462Dic22—24no—
463Dic22—22no—
464Dic22—28no—
465Dic22—24no—
466Dic22—42no—
467Dic22—44no—
468Dic22—44no—
469Dic22C2×#4114yes—
470C8×C11—24no—
471C11⋊C8—24no—
472C23×Q8—111no—
473C22×Q16—114no—
474#533—111no—
475#533—111no—
476#533—112no—
477#533—112no—
478#533—111no—
479#533—221no—
480#533—221no—
481#533—221no—
482#533—221no—
483#533C2×D1111yescharacteristic
484C2×C4⋊Q8—111no—
485C2×C4⋊Q8—111no—
486C2×#125—221no—
487C2×C22⋊Q8—112no—
488C2×C22⋊Q8—221no—
489C2×C4×Q8—111no—
490C2×C4×Q8—112no—
491C2×C4×Q8—112no—
492C2×C4×Q8—112no—
493C2×C4×Q8—112no—
494C2×C4×Q8—112no—
495C2×C4×Q8—111no—
496C2×C4×Q8—111no—
497C2×C4×Q8—221no—
498C2×C4×Q8—221no—
499C2×C4×Q8—221no—
500C2×C4×Q8—221no—
501C2×C4×Q8—221no—
502C2×C4×Q8—221no—
503C2×C4×Q8—221no—
504C2×C4×Q8C2×D1111yescharacteristic
505C2×#117—221no—
506C22×C4⋊C4—111no—
507C22×C4⋊C4—221no—
508C22×C42—111no—
509C22×C42—221no—
510#483—112no—
511#483—112no—
512#483—114no—
513#483—114no—
514#483—112no—
515#483C2×D1112yes—
516#475—112no—
517#475—112no—
518#475—114no—
519#475—112no—
520#475—114no—
521#475C2×D1112yescomplemented
522#462—114no—
523#462—112no—
524#462—112no—
525#462—112no—
526#462—114no—
527#462C2×D1112yescomplemented
528#451—112no—
529#451—114no—
530#451—112no—
531#451—114no—
532#451—112no—
533#451C2×D1112yes—
534#441—114no—
535#441—114no—
536#441—114no—
537#441—114no—
538#441—114no—
539#441—114no—
540#441—114no—
541#441C2×D1114yescomplemented
542#432—111no—
543#432—112no—
544#432—112no—
545#432—112no—
546#432C2×D1111yescharacteristic
547C2×#106—114no—
548C2×C4⋊C8—112no—
549C2×#103—114no—
550C2×#103—114no—
551C2×C22⋊C8—112no—
552C2×#97—112no—
553C22×C11—21no—
554C22×C11—21no—
555C22×C11C2×#13712yes—
556C22×C11C23×D411yescharacteristic
557C2×D11—21no—
558C2×D11—21no—
559C2×D11—28no—
560C2×D11#52512yes—
561C2×D11C2×#13712yes—
562C2×D11C2×#13712yes—
563C2×D11C2×#13712yes—
564C4×C11—24no—
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—21no—
569C4×C11—42no—
570C4×C11—42no—
571C4×C11—42no—
572C4×C11C2×#13712yes—
573C4×C11C22×#4112yes—
574Dic11—21no—
575Dic11—24no—
576Dic11—21no—
577Dic11—21no—
578Dic11—21no—
579Dic11—42no—
580Dic11—42no—
581Dic11—42no—
582Dic11#52512yes—
583Dic11C2×#13712yes—
584C22×Q8—112no—
585C22×Q8—112no—
586C22×Q8—112no—
587C22×Q8—111no—
588C22×Q8—221no—
589C22×Q8—221no—
590C22×Q8—221no—
591C22×Q8—221no—
592C22×Q8—228no—
593C22×Q8C22×D1111yescharacteristic
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—111no—
597C23×C4—221no—
598C23×C4—221no—
599C2×Q16—114no—
600C2×Q16—114no—
601C2×Q16—114no—
602C2×Q16—2216no—
603C2×Q16C22×D1114yes—
604C22×C8—114no—
605C4⋊Q8—112no—
606C4⋊Q8—112no—
607C4⋊Q8—111no—
608C4⋊Q8—111no—
609C4⋊Q8—221no—
610C4⋊Q8—221no—
611C4⋊Q8—221no—
612C4⋊Q8—221no—
613C4⋊Q8C22×D1111yescharacteristic
614C4⋊Q8C22×D1111yescharacteristic
615#125—21no—
616#125—222no—
617#125—222no—
618#125—221no—
619#125—221no—
620#125—221no—
621C22⋊Q8—21no—
622C22⋊Q8—112no—
623C22⋊Q8—112no—
624C22⋊Q8—112no—
625C22⋊Q8—222no—
626C22⋊Q8—222no—
627C22⋊Q8—222no—
628C22⋊Q8—222no—
629C22⋊Q8—221no—
630C22⋊Q8—221no—
631C22⋊Q8—221no—
632C22⋊Q8C22×D1112yes—
633C4×Q8—21no—
634C4×Q8—21no—
635C4×Q8—21no—
636C4×Q8—112no—
637C4×Q8—112no—
638C4×Q8—112no—
639C4×Q8—112no—
640C4×Q8—112no—
641C4×Q8—112no—
642C4×Q8—112no—
643C4×Q8—112no—
644C4×Q8—112no—
645C4×Q8—222no—
646C4×Q8—222no—
647C4×Q8—222no—
648C4×Q8—222no—
649C4×Q8—222no—
650C4×Q8—222no—
651C4×Q8—222no—
652C4×Q8—222no—
653C4×Q8—221no—
654C4×Q8—222no—
655C4×Q8—221no—
656C4×Q8—222no—
657C4×Q8—222no—
658C4×Q8—221no—
659C4×Q8—222no—
660C4×Q8—221no—
661C4×Q8—221no—
662C4×Q8—221no—
663C4×Q8—221no—
664C4×Q8—221no—
665C4×Q8—221no—
666C4×Q8C22×D1112yes—
667C4×Q8C22×D1112yes—
668C4×Q8C22×D1112yes—
669#117—21no—
670#117—222no—
671#117—222no—
672#117—221no—
673#117—221no—
674#117—221no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—111no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—221no—
681C2×C4⋊C4—221no—
682C2×C4⋊C4—222no—
683C2×C4⋊C4—222no—
684C2×C4⋊C4—222no—
685C2×C4⋊C4—222no—
686C2×C4⋊C4—221no—
687C2×C4⋊C4—221no—
688C2×C4⋊C4—222no—
689C2×C4⋊C4—222no—
690C2×C4⋊C4—221no—
691C2×C4⋊C4—221no—
692C2×C4⋊C4—221no—
693C2×C4⋊C4—221no—
694C2×C4⋊C4—221no—
695C2×C4⋊C4C22×D1111yescharacteristic
696C2×C22⋊C4—222no—
697C2×C42—21no—
698C2×C42—111no—
699C2×C42—111no—
700C2×C42—111no—
701C2×C42—111no—
702C2×C42—111no—
703C2×C42—111no—
704C2×C42—111no—
705C2×C42—111no—
706C2×C42—111no—
707C2×C42—111no—
708C2×C42—111no—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—222no—
713C2×C42—222no—
714C2×C42—221no—
715C2×C42—221no—
716C2×C42—221no—
717C2×C42C22×D1111yescharacteristic
718#106—114no—
719#106—114no—
720#106—114no—
721#106C22×D1114yes—
722C4⋊C8—114no—
723C4⋊C8—112no—
724C4⋊C8C22×D1112yes—
725#103—114no—
726#103—114no—
727#103—114no—
728#103—114no—
729#103—114no—
730#103—114no—
731#103C22×D1114yes—
732#103C22×D1114yes—
733C22⋊C8—112no—
734C22⋊C8—114no—
735C22⋊C8C22×D1112yes—
736#97—114no—
737#97—112no—
738#97C22×D1112yes—
739C2×C11—22no—
740C2×C11C2×#52511yescharacteristic
741C2×C11C22×#13711yescharacteristic
742C2×C11C22×#13711yescharacteristic
743D11—22no—
744D11#311314yesdirect product factor
745C24—111no—
746C2×Q8—24no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—118no—
750C2×Q8—112no—
751C2×Q8—112no—
752C2×Q8—222no—
753C2×Q8—222no—
754C2×Q8—222no—
755C2×Q8—222no—
756C2×Q8—224no—
757C2×Q8—228no—
758C2×Q8—224no—
759C2×Q8—228no—
760C2×Q8—224no—
761C2×Q8—228no—
762C2×Q8—228no—
763C2×Q8—224no—
764C2×Q8—221no—
765C2×Q8—221no—
766C2×Q8—444no—
767C2×Q8C23×D1112yes—
768C2×Q8C23×D1112yes—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—111no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—111no—
776C22×C4—111no—
777C22×C4—111no—
778C22×C4—111no—
779C22×C4—111no—
780C22×C4—111no—
781C22×C4—111no—
782C22×C4—111no—
783C22×C4—111no—
784C22×C4—111no—
785C22×C4—111no—
786C22×C4—224no—
787C22×C4—224no—
788C22×C4—222no—
789C22×C4—222no—
790C22×C4—224no—
791C22×C4—228no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4—222no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—444no—
799C22×C4D4×D1111yescharacteristic
800C22×C4D4×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802Q16—28no—
803Q16—228no—
804Q16—228no—
805Q16—228no—
806C2×C8—114no—
807C2×C8—228no—
808C2×C8C23×D1114yes—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—112no—
818C4⋊C4—112no—
819C4⋊C4—222no—
820C4⋊C4—222no—
821C4⋊C4—222no—
822C4⋊C4—222no—
823C4⋊C4—222no—
824C4⋊C4—222no—
825C4⋊C4—222no—
826C4⋊C4—222no—
827C4⋊C4—222no—
828C4⋊C4—222no—
829C4⋊C4—222no—
830C4⋊C4—222no—
831C4⋊C4—222no—
832C4⋊C4—222no—
833C4⋊C4—221no—
834C4⋊C4—222no—
835C4⋊C4—222no—
836C4⋊C4—221no—
837C4⋊C4—221no—
838C4⋊C4—222no—
839C4⋊C4—222no—
840C4⋊C4—221no—
841C4⋊C4C23×D1112yes—
842C4⋊C4C23×D1112yes—
843C22⋊C4—22no—
844C22⋊C4—222no—
845C22⋊C4—222no—
846C22⋊C4—222no—
847C42—22no—
848C42—22no—
849C42—22no—
850C42—111no—
851C42—111no—
852C42—111no—
853C42—111no—
854C42—111no—
855C42—111no—
856C42—111no—
857C42—111no—
858C42—111no—
859C42—111no—
860C42—111no—
861C42—111no—
862C42—222no—
863C42—222no—
864C42—222no—
865C42—222no—
866C42—222no—
867C42—222no—
868C42—222no—
869C42—222no—
870C42—222no—
871C42D4×D1111yescharacteristic
872C42D4×D1111yescharacteristic
873C42C23×D1111yescharacteristic
874C42C23×D1111yescharacteristic
875C11C2×#311311yescharacteristic, complemented, Sylow
876C23—111no—
877C23—114no—
878C23—111no—
879C23—222no—
880C23—222no—
881C23C2×D4×D1111yescharacteristic
882Q8—24no—
883Q8—22no—
884Q8—24no—
885Q8—42no—
886Q8—114no—
887Q8—228no—
888Q8—228no—
889Q8—224no—
890Q8—222no—
891Q8—224no—
892Q8—444no—
893Q8—444no—
894Q8—442no—
895Q8#41×D1114yes—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—42no—
905C2×C4—111no—
906C2×C4—111no—
907C2×C4—114no—
908C2×C4—114no—
909C2×C4—111no—
910C2×C4—111no—
911C2×C4—111no—
912C2×C4—111no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—228no—
922C2×C4—228no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—224no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—444no—
934C2×C4—444no—
935C2×C4—444no—
936C2×C4—444no—
937C2×C4—442no—
938C2×C4C2×D4×D1111yescharacteristic
939C2×C4C2×D4×D1111yescharacteristic
940C2×C4C2×D4×D1111yescharacteristic
941C2×C4C2×D4×D1111yescharacteristic
942C2×C4C2×D4×D1111yescharacteristic
943C2×C4C24×D1111yescharacteristic
944C8—24no—
945C8—224no—
946C22—21no—
947C22—21no—
948C22—112no—
949C22—112no—
950C22—112no—
951C22—112no—
952C22—228no—
953C22—221no—
954C22—221no—
955C22D11×#13712yes—
956C22C22×D4×D1111yescharacteristic
957C4—21no—
958C4—21no—
959C4—21no—
960C4—24no—
961C4—21no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—112no—
966C4—112no—
967C4—221no—
968C4—221no—
969C4—221no—
970C4—221no—
971C4—224no—
972C4—442no—
973C4—442no—
974C4—442no—
975C4D11×#13712yes—
976C4C2×#41×D1112yes—
977C2—22no—
978C2—114no—
979C2—222no—
980C2D11×#52511yescharacteristic
981C2C2×D11×#13711yescharacteristic
982C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3113C2
socleC22×C11C23×D4
prime radicalC23×D11C2×D4
hypercenter#3113D11
hypocenterC11C2×#3113
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
3. #13078748C2semidirect
4. #13078747C2semidirect
5. #13078746C2semidirect
6. #13078745C2semidirect
7. #13078744C2semidirect
8. #13078743C2semidirect
9. #13078742C2semidirect
10. #13078741C2semidirect
12. D11×#475C2semidirect
13. D11×#462C2semidirect
15. D11×#441C2semidirect
17. C11×#3113C2semidirect
57. C11×#475C22semidirect
58. C11×#462C22semidirect
60. C11×#441C22semidirect
64. #10622797C22semidirect
65. #10622795C22semidirect
66. #10622707C22semidirect
67. #10622703C22semidirect
70. #10622644C22semidirect
71. #10622643C22semidirect
72. #10622643C22semidirect
73. #10622633C22semidirect
78. #10622467C22semidirect
79. #10622466C22semidirect
80. #10622464C22semidirect
81. #10622462C22semidirect
88. #10622406C22semidirect
89. #10622404C22semidirect
90. #10622402C22semidirect
91. #10622402C22semidirect
96. #10622329C22semidirect
395. #3113D11direct (N × H)
521. #475C2×D11semidirect
527. #462C2×D11semidirect
541. #441C2×D11semidirect
744. D11#3113direct (N × H)
875. C11C2×#3113semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
C2×C4×Q8×D112
#130787482
#130787472
#130787462
#130787452
#130787442
#130787432
#130787422
#130787412
D11×#4832
D11×#4752
D11×#4622
D11×#4512
D11×#4412
D11×#4322
C11×#31132
C2×#311311