Finite Group Databasebeta

← D11×#3234 #15625872

Subgroups — D11×#3234 #15625872

Order 2816.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#532C211yesmaximal, characteristic
2C2×D11×#125C211yesmaximal, characteristic, complemented
3#13079808C211yesmaximal, characteristic, complemented
4#13079807C212yesmaximal, complemented
5#13079806C211yesmaximal, characteristic, complemented
6#13079805C212yesmaximal, complemented
7#13079804C214yesmaximal, complemented
8#13079803C212yesmaximal, complemented
9#13079802C211yesmaximal, characteristic, complemented
10#13079801C212yesmaximal, complemented
11D11×#501C212yesmaximal, complemented
12D11×#490C212yesmaximal, complemented
13D11×#481C212yesmaximal, complemented
14D11×#480C212yesmaximal, complemented
15D11×#478C214yesmaximal, complemented
16D11×#432C211yesmaximal, characteristic, complemented
17C11×#3234C211yesmaximal, characteristic, complemented
18C2×#41×D11—21no—
19C11×#532C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic, complemented
21#10623363—21no—
22#10623256C2211yescharacteristic
23D11×C4⋊Q8C2211yescharacteristic
24#10623247C2211yescharacteristic
25D11×#127C2211yescharacteristic
26D11×#125—21no—
27D11×#125—21no—
28D11×#125—21no—
29D11×#125—21no—
30D11×#125C2212yes—
31D11×#125C2212yes—
32D11×#125C2212yescomplemented
33D11×#125C2212yescomplemented
34D11×#124—21no—
35#10623199—21no—
36D11×#121—21no—
37D11×#121C2212yes—
38#10623127—21no—
39#10623127C2212yes—
40#10623079—21no—
41#10623079C2212yes—
42C4×D4×D11—21no—
43C4×D4×D11C2212yes—
44C2×C4⋊C4×D11—21no—
45C2×C4⋊C4×D11—21no—
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×#66943C2211yescharacteristic, complemented
49C2×#66943C2211yescharacteristic, complemented
50C2×#66942—21no—
51C2×#66942—21no—
52#10623008C2211yescharacteristic
53C2×C42×D11C2211yescharacteristic
54C2×#66923C2211yescharacteristic, complemented
55C11×#501C2212yescomplemented
56C11×#490C2212yescomplemented
57C11×#481C2212yescomplemented
58C11×#480C2212yescomplemented
59C11×#478C2214yescomplemented
60C11×#432C2211yescharacteristic, complemented
61#10622693C2212yescomplemented
62#10622684C2212yescomplemented
63#10622680C2212yescomplemented
64#10622679C2214yescomplemented
65#10622678C2212yescomplemented
66#10622647C2212yescomplemented
67#10622646C2212yescomplemented
68#10622622C2214yescomplemented
69#10622581C2212yescomplemented
70#10622580C2212yescomplemented
71#10622539C2211yescharacteristic, complemented
72#10622504C2214yescomplemented
73#10622495C2214yescomplemented
74D11×#107C2214yes—
75#10622489C2214yescomplemented
76#10622484C2214yescomplemented
77#10622476C2214yescomplemented
78D11×#106C2214yes—
79#10622469C2214yescomplemented
80#10622460C2214yescomplemented
81#10622448C2212yescomplemented
82D11×C4⋊C8C2212yes—
83#10622390C2214yescomplemented
84#10622387C2214yescomplemented
85D11×#102C2214yes—
86D11×#102C2214yes—
87#10622379C2214yescomplemented
88#10622377C2214yescomplemented
89#10622377C2214yescomplemented
90#10622376C2214yescomplemented
91#10622349C2212yescomplemented
92#10622348C2212yescomplemented
93D11×C22⋊C8C2212yes—
94#10622332C2212yescomplemented
95#10622326C2212yescomplemented
96#10622318C2212yescomplemented
97D11×#97C2212yes—
98#10622315C2212yescomplemented
99C2×C11×#41—21no—
100#41×D11—48no—
101C2×#4343—21no—
102C2×Q8×D11—21no—
103C2×#4341—22no—
104C2×#4341—21no—
105C2×D4×D11—22no—
106C2×D4×D11—21no—
107C2×D4×D11—21no—
108C2×D4×D11C2312yes—
109C2×#4339—21no—
110C2×#4339—22no—
111C22×C4×D11—21no—
112C22×C4×D11—21no—
113C22×C4×D11—22no—
114C22×C4×D11D411yescharacteristic
115C22×C4×D11D411yescharacteristic
116C22×C4×D11C2311yescharacteristic
117C11×C4⋊Q8C2311yescharacteristic
118C11×#127C2311yescharacteristic
119C11×#125—21no—
120C11×#125—21no—
121C11×#125C2312yes—
122C11×#125C2312yes—
123C11×#124—21no—
124C11×#121—21no—
125C11×#121C2312yes—
126C4×D4×C11—21no—
127C4×D4×C11C2312yes—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C42×C11C2311yescharacteristic
133#67000—21no—
134#66997—21no—
135#66993—21no—
136#66993—21no—
137#66993C2312yes—
138#66992—22no—
139#66992—22no—
140#66991—21no—
141#66991C2312yes—
142#66989—21no—
143D4×Dic11—21no—
144D4×Dic11C2312yes—
145#66983—21no—
146#66983C2312yes—
147C4×C22⋊D11—22no—
148C4×C22⋊D11—22no—
149C2×C4⋊Dic11—21no—
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11C2311yescharacteristic
152C2×C4⋊Dic11C2311yescharacteristic
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4—21no—
159C2×C4×Dic11D411yescharacteristic
160C2×C4×Dic11D411yescharacteristic
161C2×C4×Dic11C2311yescharacteristic
162C2×C8×D11C2314yes—
163#66948—21no—
164#66948C2312yes—
165#66946—21no—
166#66946C2312yes—
167C4⋊C4×D11—21no—
168C4⋊C4×D11—22no—
169C4⋊C4×D11—22no—
170C4⋊C4×D11—22no—
171C4⋊C4×D11—22no—
172C4⋊C4×D11—22no—
173C4⋊C4×D11—22no—
174C4⋊C4×D11—22no—
175C4⋊C4×D11—22no—
176C4⋊C4×D11—21no—
177C4⋊C4×D11—21no—
178C4⋊C4×D11—21no—
179C4⋊C4×D11—21no—
180C4⋊C4×D11C2312yes—
181C4⋊C4×D11C2312yes—
182C4⋊C4×D11C2312yes—
183C4⋊C4×D11C2312yes—
184C4⋊C4×D11C2312yes—
185#66943—21no—
186#66943—21no—
187#66943—21no—
188#66943—21no—
189#66943C2312yes—
190#66943C2312yes—
191#66943C2312yes—
192#66943C2312yes—
193#66942—22no—
194#66942—22no—
195#66942—22no—
196#66942—22no—
197#66942—22no—
198#66942—22no—
199#66942—22no—
200#66942—22no—
201#66941—21no—
202#66941C2312yes—
203#66938—22no—
204#66938—22no—
205#66937—22no—
206#66937—22no—
207(C22⋊D11)⋊C4—22no—
208(C22⋊D11)⋊C4—22no—
209C22⋊C4×D11—22no—
210C22⋊C4×D11—22no—
211#66928—21no—
212#66927C2311yescharacteristic
213C4×D44—21no—
214C4×D44C2312yes—
215C42×D11D411yescharacteristic
216C42×D11D411yescharacteristic
217C42×D11D411yescharacteristic
218C42×D11D411yescharacteristic
219C42×D11C2311yescharacteristic
220C42×D11C2311yescharacteristic
221C42×D11C2311yescharacteristic
222C42×D11C2311yescharacteristic
223#66923—21no—
224#66923—21no—
225#66923C2312yes—
226#66923C2312yes—
227#66922C2311yescharacteristic
228C11×#107C2314yes—
229C11×#106C2314yes—
230C11×C4⋊C8C2312yes—
231C11×#102C2314yes—
232C11×#102C2314yes—
233C11×C22⋊C8C2312yes—
234C11×#97C2312yes—
235#66896C2314yes—
236#66896C2314yes—
237C22⋊(C11⋊C8)C2312yes—
238#66885C2314yes—
239#66885C2314yes—
240(C2×D11)⋊C8C2314yes—
241#66882C2314yes—
242#66881C2314yes—
243#66879C2314yes—
244Dic11⋊C8C2314yes—
245#66873C2314yes—
246#66873C2314yes—
247#66872C2314yes—
248#66872C2314yes—
249#66871C2314yes—
250#66871C2314yes—
251C4⋊(C11⋊C8)C2312yes—
252#66867C2312yes—
253C2×#3234—111nomaximal, Sylow
254C23×D11—22no—
255C23×D11C2×D411yescharacteristic
256C11×#41—44no—
257C2×Q8×C11—21no—
258C2×D4×C11—22no—
259C2×D4×C11—21no—
260C2×D4×C11—21no—
261C2×D4×C11C2412yes—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—22no—
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C2×C22⋊D11—22no—
269C2×C22⋊D11—22no—
270C2×C22⋊D11—22no—
271C2×C22⋊D11—22no—
272C2×C22⋊D11—22no—
273C22×Dic11—22no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11C2×D411yescharacteristic
277C22×Dic11C2×D411yescharacteristic
278C22×Dic11C2×D411yescharacteristic
279#4343—44no—
280Q8×D11—44no—
281#4341—44no—
282#4341—48no—
283D4×D11—28no—
284D4×D11—44no—
285D4×D11—44no—
286D4×D11—48no—
287#4339—44no—
288#4339—48no—
289C2×D44—22no—
290C2×D44—21no—
291C2×D44—21no—
292C2×D44C2412yes—
293C2×C4×D11—24no—
294C2×C4×D11—22no—
295C2×C4×D11—24no—
296C2×C4×D11—22no—
297C2×C4×D11—22no—
298C2×C4×D11—22no—
299C2×C4×D11—22no—
300C2×C4×D11—22no—
301C2×C4×D11—22no—
302C2×C4×D11—42no—
303C2×C4×D11—44no—
304C2×C4×D11—48no—
305C2×C4×D11—44no—
306C2×C4×D11C2×D411yescharacteristic
307C2×C4×D11C2×D411yescharacteristic
308C2×C4×D11C2×D411yescharacteristic
309C2×C4×D11C2×D411yescharacteristic
310C2×C4×D11C2×D411yescharacteristic
311C2×C4×D11C2×D411yescharacteristic
312C2×C4×D11C2×D411yescharacteristic
313C2×C4×D11C2×D411yescharacteristic
314C2×C4×D11C2×D411yescharacteristic
315C2×C4×D11C2×D411yescharacteristic
316C2×C4×D11C2411yescharacteristic
317C2×C4×D11C2411yescharacteristic
318C2×Dic22—22no—
319C2×Dic22—21no—
320C2×C8×C11C2414yes—
321C11×C4⋊C4—21no—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—21no—
327C11×C4⋊C4—21no—
328C11×C4⋊C4C2412yes—
329C11×C4⋊C4C2412yes—
330C11×C4⋊C4C2412yes—
331C11×C22⋊C4—22no—
332C11×C22⋊C4—22no—
333C42×C11C2×D411yescharacteristic
334C42×C11C2×D411yescharacteristic
335C42×C11C2411yescharacteristic
336C42×C11C2411yescharacteristic
337C22⋊Dic11—22no—
338C22⋊Dic11—22no—
339(C2×D11)⋊C4—22no—
340(C2×D11)⋊C4—22no—
341(C2×D11)⋊C4—22no—
342(C2×D11)⋊C4—22no—
343C4⋊Dic11—22no—
344C4⋊Dic11—22no—
345C4⋊Dic11—22no—
346C4⋊Dic11—22no—
347C4⋊Dic11—21no—
348C4⋊Dic11—21no—
349C4⋊Dic11—21no—
350C4⋊Dic11C2412yes—
351C4⋊Dic11C2412yes—
352C4⋊Dic11C2412yes—
353Dic11⋊C4—22no—
354Dic11⋊C4—22no—
355Dic11⋊C4—22no—
356Dic11⋊C4—22no—
357Dic11⋊C4—22no—
358Dic11⋊C4—22no—
359Dic11⋊C4—22no—
360Dic11⋊C4—22no—
361Dic11⋊C4—22no—
362Dic11⋊C4—22no—
363Dic11⋊C4—22no—
364Dic11⋊C4—22no—
365Dic11⋊C4—22no—
366Dic11⋊C4—22no—
367C4×Dic11C2×D411yescharacteristic
368C4×Dic11C2×D411yescharacteristic
369C4×Dic11C2×D411yescharacteristic
370C4×Dic11C2×D411yescharacteristic
371C4×Dic11C2×D411yescharacteristic
372C4×Dic11C2×D411yescharacteristic
373C4×Dic11C2×D411yescharacteristic
374C4×Dic11C2×D411yescharacteristic
375C4×Dic11C2×D411yescharacteristic
376C4×Dic11C2×D411yescharacteristic
377C4×Dic11C2411yescharacteristic
378C4×Dic11C2411yescharacteristic
379C2×C11⋊C8C2414yes—
380C8×D11—28no—
381C2×#532—111no—
382C22×#125—111no—
383#3234—112no—
384#3234—112no—
385#3234—112no—
386#3234—112no—
387#3234—114no—
388#3234—111no—
389#3234—111no—
390#3234—111no—
391#3234D1111yescharacteristic, direct product factor
392C2×#501—112no—
393C2×#490—112no—
394C2×#481—112no—
395C2×#480—112no—
396C2×#478—114no—
397C2×#432—111no—
398C23×C11—22no—
399C23×C11C22×D411yescharacteristic
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—44no—
404C22×D11—44no—
405C22×D11—44no—
406C22×D11AGL(1,ℤ/8)14yes—
407C22×D11C22×D411yescharacteristic
408C22×D11C22×D411yescharacteristic
409Q8×C11—42no—
410D4×C11—24no—
411D4×C11—42no—
412D4×C11—42no—
413D4×C11—44no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—41no—
420C2×C4×C11—44no—
421C2×C4×C11—42no—
422C2×C4×C11—42no—
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C22×D411yescharacteristic
426C2×C4×C11C22×D411yescharacteristic
427C2×C4×C11C22×D411yescharacteristic
428C2×C4×C11C2511yescharacteristic
429C22⋊D11—44no—
430C22⋊D11—44no—
431C22⋊D11—44no—
432C22⋊D11—44no—
433C22⋊D11—44no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—41no—
440C2×Dic11—44no—
441C2×Dic11—42no—
442C2×Dic11—42no—
443C2×Dic11C22×D411yescharacteristic
444C2×Dic11C22×D411yescharacteristic
445C2×Dic11C22×D411yescharacteristic
446C2×Dic11C22×D411yescharacteristic
447C2×Dic11C22×D411yescharacteristic
448C2×Dic11C22×D411yescharacteristic
449D44—24no—
450D44—42no—
451D44—42no—
452D44—44no—
453C4×D11—22no—
454C4×D11—22no—
455C4×D11—22no—
456C4×D11—22no—
457C4×D11—22no—
458C4×D11—22no—
459C4×D11—22no—
460C4×D11—22no—
461C4×D11—22no—
462C4×D11—41no—
463C4×D11—41no—
464C4×D11—44no—
465C4×D11—44no—
466C4×D11—44no—
467C4×D11—44no—
468C4×D11—44no—
469C4×D11—44no—
470C4×D11—44no—
471C4×D112−1+414yes—
472Dic22—44no—
473Dic22—42no—
474C8×C11—24no—
475C11⋊C8—24no—
476C22×#41—221no—
477#532—111no—
478#532—111no—
479#532—112no—
480#532—112no—
481#532—111no—
482#532—221no—
483#532—221no—
484#532—221no—
485#532—221no—
486#532C2×D1111yescharacteristic
487C2×C4⋊Q8—111no—
488C2×#127—111no—
489C2×#125—112no—
490C2×#125—112no—
491C2×#125—112no—
492C2×#125—112no—
493C2×#125—111no—
494C2×#125—111no—
495C2×#125—111no—
496C2×#125—221no—
497C2×#125—221no—
498C2×#125—221no—
499C2×#125—221no—
500C2×#125—221no—
501C2×#125—221no—
502C2×#125C2×D1111yescharacteristic, complemented
503C2×#124—221no—
504C2×#121—112no—
505C2×#121—221no—
506C2×C4×D4—112no—
507C2×C4×D4—221no—
508C22×C4⋊C4—111no—
509C22×C4⋊C4—111no—
510C22×C4⋊C4—221no—
511C22×C4⋊C4—221no—
512C22×C42—111no—
513#501—112no—
514#501—112no—
515#501—114no—
516#501—114no—
517#501—112no—
518#501C2×D1112yescomplemented
519#490—112no—
520#490—112no—
521#490—114no—
522#490—114no—
523#490—112no—
524#490C2×D1112yescomplemented
525#481—112no—
526#481—112no—
527#481—114no—
528#481—114no—
529#481—112no—
530#481C2×D1112yescomplemented
531#480—112no—
532#480—112no—
533#480—114no—
534#480—114no—
535#480—112no—
536#480C2×D1112yescomplemented
537#478—114no—
538#478—114no—
539#478—114no—
540#478—114no—
541#478—114no—
542#478—114no—
543#478—114no—
544#478C2×D1114yescomplemented
545#432—111no—
546#432—112no—
547#432—112no—
548#432—112no—
549#432C2×D1111yescharacteristic, complemented
550C2×#107—114no—
551C2×#106—114no—
552C2×C4⋊C8—112no—
553C2×#102—114no—
554C2×#102—114no—
555C2×C22⋊C8—112no—
556C2×#97—112no—
557C22×C11—21no—
558C22×C11—21no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11C2×AGL(1,ℤ/8)12yes—
563C22×C11C23×D411yescharacteristic
564C2×D11—21no—
565C2×D11—21no—
566C2×D11—28no—
567C2×D11—42no—
568C2×D11—42no—
569C2×D11—42no—
570C2×D11—88no—
571C2×D11#53612yes—
572C2×D11C2×AGL(1,ℤ/8)12yes—
573C2×D11C2×AGL(1,ℤ/8)12yes—
574C2×D11#57512yes—
575C4×C11—21no—
576C4×C11—21no—
577C4×C11—21no—
578C4×C11—21no—
579C4×C11—21no—
580C4×C11—42no—
581C4×C11—42no—
582C4×C11—42no—
583C4×C11C2×2−1+412yes—
584Dic11—21no—
585Dic11—21no—
586Dic11—21no—
587Dic11—21no—
588Dic11—21no—
589Dic11—42no—
590Dic11—42no—
591Dic11—42no—
592Dic11#53612yes—
593C2×#41—21no—
594C2×#41—222no—
595C2×#41—222no—
596C2×#41—221no—
597C2×#41—221no—
598C2×#41—221no—
599C2×#41—448no—
600C22×Q8—221no—
601C22×D4—112no—
602C22×D4—221no—
603C22×D4—221no—
604C22×D4—222no—
605C23×C4—111no—
606C23×C4—111no—
607C23×C4—111no—
608C23×C4—222no—
609C23×C4—221no—
610C23×C4—221no—
611C22×C8—114no—
612C4⋊Q8—112no—
613C4⋊Q8—111no—
614C4⋊Q8—221no—
615C4⋊Q8—221no—
616C4⋊Q8C22×D1111yescharacteristic
617#127—112no—
618#127—111no—
619#127—221no—
620#127—221no—
621#127C22×D1111yescharacteristic
622#125—21no—
623#125—21no—
624#125—112no—
625#125—112no—
626#125—112no—
627#125—112no—
628#125—112no—
629#125—112no—
630#125—222no—
631#125—222no—
632#125—222no—
633#125—222no—
634#125—222no—
635#125—222no—
636#125—222no—
637#125—222no—
638#125—221no—
639#125—221no—
640#125—221no—
641#125—221no—
642#125—221no—
643#125—221no—
644#125C22×D1112yes—
645#125C22×D1112yes—
646#124—21no—
647#124—222no—
648#124—222no—
649#124—221no—
650#124—221no—
651#124—221no—
652#121—21no—
653#121—112no—
654#121—112no—
655#121—112no—
656#121—222no—
657#121—222no—
658#121—221no—
659#121—222no—
660#121—221no—
661#121—222no—
662#121—221no—
663#121C22×D1112yes—
664C4×D4—21no—
665C4×D4—112no—
666C4×D4—112no—
667C4×D4—112no—
668C4×D4—222no—
669C4×D4—222no—
670C4×D4—221no—
671C4×D4—222no—
672C4×D4—222no—
673C4×D4—221no—
674C4×D4—221no—
675C4×D4C22×D1112yes—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—111no—
679C2×C4⋊C4—111no—
680C2×C4⋊C4—112no—
681C2×C4⋊C4—112no—
682C2×C4⋊C4—112no—
683C2×C4⋊C4—112no—
684C2×C4⋊C4—112no—
685C2×C4⋊C4—221no—
686C2×C4⋊C4—221no—
687C2×C4⋊C4—221no—
688C2×C4⋊C4—221no—
689C2×C4⋊C4—222no—
690C2×C4⋊C4—222no—
691C2×C4⋊C4—222no—
692C2×C4⋊C4—222no—
693C2×C4⋊C4—222no—
694C2×C4⋊C4—222no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4—222no—
697C2×C4⋊C4—221no—
698C2×C4⋊C4—221no—
699C2×C4⋊C4—221no—
700C2×C4⋊C4—221no—
701C2×C4⋊C4—221no—
702C2×C4⋊C4—221no—
703C2×C4⋊C4—221no—
704C2×C4⋊C4—221no—
705C2×C4⋊C4—221no—
706C2×C4⋊C4C22×D1111yescharacteristic
707C2×C4⋊C4C22×D1111yescharacteristic
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
710C2×C42—111no—
711C2×C42—111no—
712C2×C42—111no—
713C2×C42—111no—
714C2×C42—111no—
715C2×C42—111no—
716C2×C42—111no—
717C2×C42—111no—
718C2×C42—111no—
719C2×C42—111no—
720C2×C42—111no—
721C2×C42C22×D1111yescharacteristic
722#107—114no—
723#107—114no—
724#107—114no—
725#107C22×D1114yes—
726#106—114no—
727#106—114no—
728#106—114no—
729#106C22×D1114yes—
730C4⋊C8—114no—
731C4⋊C8—112no—
732C4⋊C8C22×D1112yes—
733#102—114no—
734#102—114no—
735#102—114no—
736#102—114no—
737#102—114no—
738#102—114no—
739#102C22×D1114yes—
740#102C22×D1114yes—
741C22⋊C8—112no—
742C22⋊C8—114no—
743C22⋊C8C22×D1112yes—
744#97—114no—
745#97—112no—
746#97C22×D1112yes—
747C2×C11—22no—
748C2×C11—82no—
749C2×C11C2×#53611yescharacteristic
750C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
751C2×C11C2×#57511yescharacteristic
752D11—22no—
753D11—82no—
754D11#323414yesdirect product factor
755C24—111no—
756C24—222no—
757#41—44no—
758#41—444no—
759#41—448no—
760#41—444no—
761#41—448no—
762#41—444no—
763C2×Q8—21no—
764C2×Q8—222no—
765C2×Q8—221no—
766C2×Q8—444no—
767C2×D4—22no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—112no—
771C2×D4—222no—
772C2×D4—228no—
773C2×D4—222no—
774C2×D4—222no—
775C2×D4—222no—
776C2×D4—222no—
777C2×D4—222no—
778C2×D4—221no—
779C2×D4—221no—
780C2×D4—444no—
781C2×D4—444no—
782C2×D4—448no—
783C2×D4C23×D1112yes—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—111no—
788C22×C4—111no—
789C22×C4—111no—
790C22×C4—111no—
791C22×C4—111no—
792C22×C4—111no—
793C22×C4—111no—
794C22×C4—111no—
795C22×C4—111no—
796C22×C4—111no—
797C22×C4—111no—
798C22×C4—111no—
799C22×C4—111no—
800C22×C4—111no—
801C22×C4—111no—
802C22×C4—224no—
803C22×C4—222no—
804C22×C4—224no—
805C22×C4—222no—
806C22×C4—222no—
807C22×C4—222no—
808C22×C4—222no—
809C22×C4—222no—
810C22×C4—222no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—222no—
814C22×C4—442no—
815C22×C4—448no—
816C22×C4—444no—
817C22×C4—444no—
818C22×C4D4×D1111yescharacteristic
819C22×C4D4×D1111yescharacteristic
820C22×C4C23×D1111yescharacteristic
821C2×C8—114no—
822C2×C8—228no—
823C2×C8C23×D1114yes—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—112no—
832C4⋊C4—112no—
833C4⋊C4—112no—
834C4⋊C4—222no—
835C4⋊C4—222no—
836C4⋊C4—222no—
837C4⋊C4—222no—
838C4⋊C4—222no—
839C4⋊C4—222no—
840C4⋊C4—222no—
841C4⋊C4—222no—
842C4⋊C4—222no—
843C4⋊C4—222no—
844C4⋊C4—222no—
845C4⋊C4—222no—
846C4⋊C4—222no—
847C4⋊C4—222no—
848C4⋊C4—221no—
849C4⋊C4—221no—
850C4⋊C4—222no—
851C4⋊C4—222no—
852C4⋊C4—222no—
853C4⋊C4—222no—
854C4⋊C4—221no—
855C4⋊C4C23×D1112yes—
856C4⋊C4C23×D1112yes—
857C4⋊C4C23×D1112yes—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—222no—
861C22⋊C4—222no—
862C22⋊C4—222no—
863C22⋊C4—222no—
864C22⋊C4—222no—
865C22⋊C4—222no—
866C42—111no—
867C42—111no—
868C42—111no—
869C42—111no—
870C42—111no—
871C42—111no—
872C42—111no—
873C42—111no—
874C42—111no—
875C42—111no—
876C42—111no—
877C42—111no—
878C42D4×D1111yescharacteristic
879C42D4×D1111yescharacteristic
880C42C23×D1111yescharacteristic
881C42C23×D1111yescharacteristic
882C11C2×#323411yescharacteristic, complemented, Sylow
883C23—22no—
884C23—111no—
885C23—114no—
886C23—111no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—444no—
891C23—444no—
892C23—444no—
893C23C2×D4×D1111yescharacteristic
894Q8—42no—
895Q8—442no—
896Q8—444no—
897D4—24no—
898D4—42no—
899D4—42no—
900D4—44no—
901D4—224no—
902D4—442no—
903D4—442no—
904D4—444no—
905D4—444no—
906D4—444no—
907D4—444no—
908D4—444no—
909D4—444no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—41no—
916C2×C4—44no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—111no—
920C2×C4—114no—
921C2×C4—111no—
922C2×C4—111no—
923C2×C4—111no—
924C2×C4—111no—
925C2×C4—111no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—444no—
943C2×C4—444no—
944C2×C4—444no—
945C2×C4—444no—
946C2×C4—444no—
947C2×C4—444no—
948C2×C4—444no—
949C2×C4—441no—
950C2×C4—444no—
951C2×C4—442no—
952C2×C4—442no—
953C2×C4C2×D4×D1111yescharacteristic
954C2×C4C2×D4×D1111yescharacteristic
955C2×C4C2×D4×D1111yescharacteristic
956C2×C4C2×D4×D1111yescharacteristic
957C2×C4C2×D4×D1111yescharacteristic
958C2×C4C24×D1111yescharacteristic
959C8—24no—
960C8—224no—
961C22—21no—
962C22—21no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—112no—
967C22—112no—
968C22—112no—
969C22—112no—
970C22—228no—
971C22—221no—
972C22—221no—
973C22—442no—
974C22—442no—
975C22—442no—
976C22—888no—
977C22D11×AGL(1,ℤ/8)12yes—
978C22C22×D4×D1111yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—112no—
988C4—221no—
989C4—221no—
990C4—221no—
991C4—221no—
992C4—221no—
993C4—442no—
994C4—442no—
995C4—442no—
996C4D11×2−1+412yes—
997C2—22no—
998C2—82no—
999C2—114no—
1000C2—222no—
1001C2—882no—
1002C2D11×#53611yescharacteristic
1003C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1004C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3234C2
socleC22×C11C23×D4
prime radicalD11×#532C2
hypercenter#3234D11
hypocenterC11C2×#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3234

Complements

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

NH ≅ G/Ntype
2. C2×D11×#125C2semidirect
3. #13079808C2semidirect
4. #13079807C2semidirect
5. #13079806C2semidirect
6. #13079805C2semidirect
7. #13079804C2semidirect
8. #13079803C2semidirect
9. #13079802C2semidirect
10. #13079801C2semidirect
11. D11×#501C2semidirect
12. D11×#490C2semidirect
13. D11×#481C2semidirect
14. D11×#480C2semidirect
15. D11×#478C2semidirect
16. D11×#432C2semidirect
17. C11×#3234C2semidirect
20. C2×C11×#125C22semidirect
32. D11×#125C22semidirect
33. D11×#125C22semidirect
48. C2×#66943C22semidirect
49. C2×#66943C22semidirect
54. C2×#66923C22semidirect
55. C11×#501C22semidirect
56. C11×#490C22semidirect
57. C11×#481C22semidirect
58. C11×#480C22semidirect
59. C11×#478C22semidirect
60. C11×#432C22semidirect
61. #10622693C22semidirect
62. #10622684C22semidirect
63. #10622680C22semidirect
64. #10622679C22semidirect
65. #10622678C22semidirect
66. #10622647C22semidirect
67. #10622646C22semidirect
68. #10622622C22semidirect
69. #10622581C22semidirect
70. #10622580C22semidirect
71. #10622539C22semidirect
72. #10622504C22semidirect
73. #10622495C22semidirect
75. #10622489C22semidirect
76. #10622484C22semidirect
77. #10622476C22semidirect
79. #10622469C22semidirect
80. #10622460C22semidirect
81. #10622448C22semidirect
83. #10622390C22semidirect
84. #10622387C22semidirect
87. #10622379C22semidirect
88. #10622377C22semidirect
89. #10622377C22semidirect
90. #10622376C22semidirect
91. #10622349C22semidirect
92. #10622348C22semidirect
94. #10622332C22semidirect
95. #10622326C22semidirect
96. #10622318C22semidirect
98. #10622315C22semidirect
391. #3234D11direct (N × H)
502. C2×#125C2×D11semidirect
518. #501C2×D11semidirect
524. #490C2×D11semidirect
530. #481C2×D11semidirect
536. #480C2×D11semidirect
544. #478C2×D11semidirect
549. #432C2×D11semidirect
754. D11#3234direct (N × H)
882. C11C2×#3234semidirect

Maximal subgroups

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

subgroupindex
D11×#5322
C2×D11×#1252
#130798082
#130798072
#130798062
#130798052
#130798042
#130798032
#130798022
#130798012
D11×#5012
D11×#4902
D11×#4812
D11×#4802
D11×#4782
D11×#4322
C11×#32342
C2×#323411