Finite Group Databasebeta

← #15624533

Subgroups — #15624533

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
3#13079450C214yesmaximal, complemented
4#13079439C212yesmaximal, complemented
5#13079421C212yesmaximal, complemented
6#13079401C214yesmaximal, complemented
7#13079390C212yesmaximal, complemented
8#13079372C212yesmaximal, complemented
9#13078564C211yesmaximal, characteristic, complemented
10#13078542C212yesmaximal, complemented
11#13078247C212yesmaximal, complemented
12#13078244C212yesmaximal, complemented
13#13077878C211yesmaximal, characteristic, complemented
14#13077874C211yesmaximal, characteristic, complemented
15#13077852C212yesmaximal, complemented
16D11×#407C211yesmaximal, characteristic, complemented
17C11×#3095C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2211yescharacteristic, complemented
19C22×#4339C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C2×#66999C2211yescharacteristic, complemented
24C2×#66995C2212yescomplemented
25C2×#66977C2211yescharacteristic
26C2×#66962C2212yescomplemented
27C2×M16×D11C2212yescomplemented
28D11×C22⋊Q8—21no—
29D11×C22⋊Q8—21no—
30D11×C22⋊Q8—21no—
31D11×C22⋊Q8—21no—
32D11×C22⋊Q8C2212yes—
33D11×C22⋊Q8C2212yes—
34D11×C22⋊Q8C2212yescomplemented
35D11×C22⋊Q8C2212yescomplemented
36#10623055—21no—
37#10623055—21no—
38#10623055—21no—
39#10623055—21no—
40#10623055C2212yes—
41#10623055C2212yes—
42#10623055C2212yes—
43#10623055C2212yes—
44C2×#66950C2211yescharacteristic
45C2×#66950C2211yescharacteristic
46C2×#66950C2211yescharacteristic, complemented
47C2×#66949—21no—
48C2×#66948C2211yescharacteristic
49C2×#66948C2211yescharacteristic
50C2×C4⋊C4×D11—21no—
51C2×C4⋊C4×D11C2211yescharacteristic, complemented
52C2×#66939—21no—
53C2×#66935—21no—
54C2×C22⋊C4×D11—21no—
55C2×#66931—21no—
56C2×C4×D44—21no—
57C2×C4×D44—21no—
58C11×#485C2214yescomplemented
59C11×#484C2212yescomplemented
60C11×#483C2212yescomplemented
61C11×#428C2212yescomplemented
62C11×#419C2212yescomplemented
63C11×#407C2211yescharacteristic
64#10622820C2211yescharacteristic
65#10622746C2212yescomplemented
66#10622739C2212yescomplemented
67#10622663C2212yescomplemented
68#10622660C2214yescomplemented
69#10622659C2212yescomplemented
70#10622617C2212yescomplemented
71#10622609C2214yescomplemented
72#10622608C2212yescomplemented
73#10622584C2212yescomplemented
74#10622583C2212yescomplemented
75#10622579C2212yescomplemented
76#10622500C2214yescomplemented
77#10622499C2214yescomplemented
78#10622497C2214yescomplemented
79#10622495C2214yescomplemented
80#10622481C2214yescomplemented
81#10622477C2214yescomplemented
82#10622476C2214yescomplemented
83#10622475C2214yescomplemented
84#10622429C2214yescomplemented
85#10622426C2214yescomplemented
86#10622425C2214yescomplemented
87#10622421C2214yescomplemented
88#10622421C2214yescomplemented
89#10622420C2214yescomplemented
90#10622419C2214yescomplemented
91#10622419C2214yescomplemented
92#10622352C2212yescomplemented
93#10622346C2214yescomplemented
94#10622344C2212yescomplemented
95#10622339C2212yes—
96#10622339C2212yescomplemented
97D11×C22⋊C8C2212yes—
98D11×C22⋊C8C2212yescomplemented
99C24×D11D411yescharacteristic
100C22×Q8×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C22×C22⋊D11—21no—
103C23×Dic11D411yescharacteristic
104C2×Q8×D11—21no—
105C2×Q8×D11—21no—
106C2×Q8×D11—44no—
107C2×Q8×D11C2312yes—
108C2×Q8×D11C2312yes—
109C2×#4339—21no—
110C2×#4339—21no—
111C2×#4339—44no—
112C2×#4339C2312yes—
113C2×#4339C2312yes—
114C22×D44—21no—
115C22×D44—21no—
116C22×D44C2311yescharacteristic
117C22×C4×D11—21no—
118C22×C4×D11—21no—
119C22×C4×D11—21no—
120C22×C4×D11—44no—
121C22×C4×D11D411yescharacteristic
122C22×C4×D11D411yescharacteristic
123C22×C4×D11D411yescharacteristic
124C22×C4×D11D411yescharacteristic
125C22×C4×D11D411yescharacteristic
126C22×C4×D11D411yescharacteristic
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×Dic22—21no—
134C22×Dic22C2311yescharacteristic
135C22×Dic22C2311yescharacteristic
136C2×C11×M16C2312yes—
137C11×C22⋊Q8—21no—
138C11×C22⋊Q8—21no—
139C11×C22⋊Q8C2312yes—
140C11×C22⋊Q8C2312yes—
141C11×#117—21no—
142C11×#117—21no—
143C11×#117C2312yes—
144C11×#117C2312yes—
145C2×C11×C4⋊C4—21no—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C22⋊C4—21no—
150C2×C11×C22⋊C4—21no—
151C2×C42×C11—21no—
152C2×C22⋊Dic11—21no—
153#66999—21no—
154#66999—21no—
155#66999C2312yes—
156#66999C2312yes—
157C2×#4326C2314yescomplemented
158#66995—44no—
159C2×#4325C2314yescomplemented
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×C4⋊Dic11—21no—
167C2×C4⋊Dic11—21no—
168C2×C4⋊Dic11—21no—
169C2×C4⋊Dic11C2311yescharacteristic
170#66977—21no—
171#66977—21no—
172#66977C2312yes—
173#66977C2312yes—
174C2×Dic11⋊C4—21no—
175C2×Dic11⋊C4—21no—
176C2×Dic11⋊C4—21no—
177C2×#4318C2312yes—
178#66962—44no—
179M16×D11—44no—
180C2×Dic44C2314yescomplemented
181C2×#4314C2314yescomplemented
182C2×#4313C2314yes—
183C2×C8×D11C2314yes—
184#66950—21no—
185#66950—21no—
186#66950—21no—
187#66950—21no—
188#66950—21no—
189#66950—21no—
190#66950C2312yes—
191#66950C2312yes—
192#66950C2312yes—
193#66950C2312yes—
194#66950C2312yes—
195#66950C2312yes—
196#66949—22no—
197#66949—22no—
198#66949—22no—
199#66949—22no—
200#66948—21no—
201#66948—21no—
202#66948—21no—
203#66948—21no—
204#66948C2312yes—
205#66948C2312yes—
206#66948C2312yes—
207#66948C2312yes—
208C4⋊C4×D11—22no—
209C4⋊C4×D11—22no—
210C4⋊C4×D11—22no—
211C4⋊C4×D11—22no—
212C4⋊C4×D11—21no—
213C4⋊C4×D11—21no—
214C4⋊C4×D11C2312yes—
215C4⋊C4×D11C2312yes—
216#66939—22no—
217#66939—22no—
218#66939—22no—
219#66939—22no—
220#66935—22no—
221#66935—22no—
222#66935—22no—
223#66935—22no—
224C22⋊C4×D11—22no—
225C22⋊C4×D11—22no—
226C22⋊C4×D11—22no—
227C22⋊C4×D11—22no—
228#66931—22no—
229#66931—22no—
230#66931—22no—
231#66931—22no—
232C4×D44—22no—
233C4×D44—22no—
234C4×D44—22no—
235C4×D44—22no—
236C4×D44—22no—
237C4×D44—22no—
238C4×D44—22no—
239C4×D44—22no—
240C11×#107C2314yescomplemented
241C11×#106C2314yescomplemented
242C11×#103C2314yescomplemented
243C11×#103C2314yescomplemented
244C11×C22⋊C8C2312yes—
245C11×C22⋊C8C2312yes—
246C22⋊(C11⋊C8)C2312yes—
247C22⋊(C11⋊C8)C2312yes—
248#66885C2314yescomplemented
249(C2×D11)⋊C8C2314yes—
250(C2×D11)⋊C8C2314yes—
251#66880C2314yescomplemented
252#66874C2314yescomplemented
253#66874C2314yescomplemented
254#66874C2314yescomplemented
255#66873C2314yescomplemented
256#66872C2314yescomplemented
257#66871C2314yescomplemented
258#60751—111nomaximal, Sylow
259C24×C11C2×D411yescharacteristic
260C23×D11—24no—
261C23×D11—21no—
262C23×D11—42no—
263C23×D11—42no—
264C23×D11C2×D411yescharacteristic
265C23×D11C2×D411yescharacteristic
266C23×D11C2×D411yescharacteristic
267C23×D11C2×D411yescharacteristic
268C23×D11C2×D411yescharacteristic
269C23×D11C2×D411yescharacteristic
270C2×Q8×C11—21no—
271C2×Q8×C11—24no—
272C2×Q8×C11C2412yes—
273C22×C4×C11—24no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C2×C22⋊D11—22no—
285C2×C22⋊D11—22no—
286C2×C22⋊D11—44no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—42no—
291C22×Dic11C2×D411yescharacteristic
292C22×Dic11C2×D411yescharacteristic
293C22×Dic11C2×D411yescharacteristic
294C22×Dic11C2×D411yescharacteristic
295C22×Dic11C2×D411yescharacteristic
296C22×Dic11C2×D411yescharacteristic
297Q8×D11—44no—
298Q8×D11—44no—
299Q8×D11—44no—
300Q8×D11—44no—
301#4339—24no—
302#4339—24no—
303#4339—42no—
304#4339—42no—
305#4339—44no—
306#4339—44no—
307C2×D44—22no—
308C2×D44—22no—
309C2×D44—22no—
310C2×D44—22no—
311C2×D44—21no—
312C2×D44—42no—
313C2×D44—44no—
314C2×D44—44no—
315C2×D44C2412yes—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—42no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—44no—
335C2×C4×D11—44no—
336C2×C4×D11—44no—
337C2×C4×D11C2×D411yescharacteristic
338C2×C4×D11C2×D411yescharacteristic
339C2×C4×D11C2×D411yescharacteristic
340C2×C4×D11C2×D411yescharacteristic
341C2×C4×D11C2×D411yescharacteristic
342C2×C4×D11C2×D411yescharacteristic
343C2×C4×D11C2×D411yescharacteristic
344C2×C4×D11C2×D411yescharacteristic
345C2×C4×D11C2×D411yescharacteristic
346C2×C4×D11C2×D411yescharacteristic
347C2×C4×D11C2×D411yescharacteristic
348C2×C4×D11C2×D411yescharacteristic
349C2×C4×D11C2411yescharacteristic
350C2×C4×D11C2411yescharacteristic
351C2×C4×D11C2411yescharacteristic
352C2×C4×D11C2411yescharacteristic
353C2×Dic22—22no—
354C2×Dic22—22no—
355C2×Dic22—21no—
356C2×Dic22—21no—
357C2×Dic22—24no—
358C2×Dic22—42no—
359C2×Dic22—44no—
360C2×Dic22C2412yes—
361C2×Dic22C2412yes—
362C11×M16—24no—
363C2×C8×C11C2414yes—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—22no—
366C11×C4⋊C4—21no—
367C11×C4⋊C4—21no—
368C11×C4⋊C4—21no—
369C11×C4⋊C4C2412yes—
370C11×C4⋊C4C2412yes—
371C11×C4⋊C4C2412yes—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—22no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—22no—
376C42×C11—22no—
377C42×C11—22no—
378C22⋊Dic11—22no—
379C22⋊Dic11—22no—
380#4326—44no—
381#4325—44no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—22no—
394C4⋊Dic11—22no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—22no—
399C4⋊Dic11—22no—
400C4⋊Dic11—21no—
401C4⋊Dic11C2412yes—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408#4318—24no—
409C2×C11⋊C8C2414yes—
410Dic44—44no—
411#4314—44no—
412#4313—44no—
413C8×D11—44no—
414C2×#525—111no—
415C22×C22⋊Q8—111no—
416#3196—114no—
417#3195—112no—
418#3193—112no—
419#3190—114no—
420#3189—112no—
421#3187—112no—
422#3095—111no—
423#3095D1111yescharacteristic, complemented
424#3092—112no—
425#3056—112no—
426#3056—112no—
427#3007—111no—
428#3007—111no—
429#3004—112no—
430C2×#407—111no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—41no—
434C23×C11C22×D411yescharacteristic
435C23×C11C22×D411yescharacteristic
436C23×C11C22×D411yescharacteristic
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—41no—
449C22×D11—41no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—416no—
456C22×D11—42no—
457C22×D11—42no—
458C22×D11—42no—
459C22×D11#13714yescomplemented
460C22×D11C22×D411yescharacteristic
461C22×D11C22×D411yescharacteristic
462C22×D11C22×D411yescharacteristic
463C22×D11C22×D411yescharacteristic
464Q8×C11—24no—
465Q8×C11—42no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—42no—
476C2×C4×C11—42no—
477C2×C4×C11—42no—
478C2×C4×C11—42no—
479C2×C4×C11C22×D411yescharacteristic
480C2×C4×C11C22×D411yescharacteristic
481C2×C4×C11C22×D411yescharacteristic
482C2×C4×C11H(5,𝔽2)14yes—
483C2×C4×C11C2511yescharacteristic
484C22⋊D11—44no—
485C22⋊D11—44no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—42no—
496C2×Dic11—42no—
497C2×Dic11—42no—
498C2×Dic11C22×D411yescharacteristic
499C2×Dic11C22×D411yescharacteristic
500C2×Dic11C22×D411yescharacteristic
501C2×Dic11C22×D411yescharacteristic
502D44—22no—
503D44—22no—
504D44—42no—
505D44—44no—
506D44—44no—
507D44—44no—
508D44—44no—
509C4×D11—22no—
510C4×D11—22no—
511C4×D11—22no—
512C4×D11—22no—
513C4×D11—22no—
514C4×D11—22no—
515C4×D11—22no—
516C4×D11—22no—
517C4×D11—41no—
518C4×D11—41no—
519C4×D11—41no—
520C4×D11—41no—
521C4×D11—41no—
522C4×D11—41no—
523C4×D11—41no—
524C4×D11—41no—
525C4×D11—44no—
526C4×D11—44no—
527C4×D11—44no—
528C4×D11—44no—
529C4×D11—44no—
530C4×D11—44no—
531Dic22—24no—
532Dic22—22no—
533Dic22—22no—
534Dic22—44no—
535Dic22—44no—
536Dic22—42no—
537Dic22—42no—
538C8×C11—24no—
539C11⋊C8—24no—
540C22×#41—111no—
541C23×Q8—111no—
542C24×C4—111no—
543C2×#137—112no—
544C2×#137—112no—
545C22×M16—112no—
546#525—112no—
547#525—112no—
548#525—112no—
549#525—112no—
550#525—221no—
551#525—221no—
552#525—221no—
553#525—221no—
554C2×#123—221no—
555C2×C22⋊Q8—111no—
556C2×C22⋊Q8—111no—
557C2×C22⋊Q8—112no—
558C2×C22⋊Q8—112no—
559C2×C22⋊Q8—112no—
560C2×C22⋊Q8—112no—
561C2×C22⋊Q8—111no—
562C2×C22⋊Q8—111no—
563C2×C22⋊Q8—111no—
564C2×C22⋊Q8—221no—
565C2×C22⋊Q8—221no—
566C2×C22⋊Q8—221no—
567C2×C22⋊Q8—221no—
568C2×C22⋊Q8—221no—
569C2×C22⋊Q8—221no—
570C2×C22⋊Q8C2×D1111yescharacteristic
571C2×#121—111no—
572C2×#121—111no—
573C2×#120—221no—
574C2×C4×D4—221no—
575C2×C4×D4—221no—
576C2×#117C2×D1111yescharacteristic
577C22×C4⋊C4—111no—
578C22×C4⋊C4—221no—
579C22×C22⋊C4—221no—
580#485—114no—
581#485C2×D1114yescomplemented
582#484—112no—
583#484—114no—
584#484C2×D1112yescomplemented
585#483—112no—
586#483—114no—
587#483C2×D1112yescomplemented
588#481—114no—
589#480—114no—
590#470—114no—
591#470—114no—
592#468—114no—
593#468—114no—
594#467—114no—
595#467—114no—
596#465—114no—
597#465—114no—
598#452—114no—
599#452—114no—
600#451—112no—
601#451—114no—
602#451—114no—
603#451—112no—
604#450—112no—
605#450—112no—
606#448—114no—
607#448—114no—
608#428—112no—
609#428C2×D1112yescomplemented
610#419—112no—
611#419C2×D1112yescomplemented
612#417—112no—
613#417—112no—
614#407—111no—
615#407—112no—
616#407—112no—
617#407—112no—
618#407C2×D1111yescharacteristic
619C2×C22⋊C8—112no—
620C2×C22⋊C8—112no—
621C22×C11—21no—
622C22×C11—21no—
623C22×C11—21no—
624C22×C11—21no—
625C22×C11—21no—
626C22×C11—21no—
627C22×C11—21no—
628C22×C11—44no—
629C22×C11#53412yes—
630C22×C11C2×#13712yes—
631C22×C11C23×D411yescharacteristic
632C2×D11—28no—
633C2×D11—21no—
634C2×D11—21no—
635C2×D11—21no—
636C2×D11—21no—
637C2×D11—21no—
638C2×D11—21no—
639C2×D11—21no—
640C2×D11—21no—
641C2×D11—21no—
642C2×D11—44no—
643C2×D11—44no—
644C2×D11—44no—
645C2×D11—44no—
646C2×D11—44no—
647C2×D11—42no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—84no—
651C2×D11C2×#13712yes—
652C2×D11C2×#13712yes—
653C2×D11#57512yes—
654C4×C11—21no—
655C4×C11—21no—
656C4×C11—42no—
657C4×C11—42no—
658C4×C11—42no—
659C4×C11—42no—
660C4×C11#53412yes—
661C4×C11C2×H(5,𝔽2)12yes—
662Dic11—21no—
663Dic11—21no—
664Dic11—21no—
665Dic11—21no—
666Dic11—42no—
667Dic11—42no—
668Dic11—42no—
669C25—111no—
670C2×#41—112no—
671C2×#41—112no—
672C2×#41—221no—
673C2×#41—221no—
674C2×#41—444no—
675C22×Q8—112no—
676C22×Q8—112no—
677C22×Q8—111no—
678C22×Q8—111no—
679C22×Q8—221no—
680C22×Q8—221no—
681C22×Q8—221no—
682C22×Q8—444no—
683C22×Q8C22×D1111yescharacteristic
684C22×D4—111no—
685C22×D4—221no—
686C22×D4—221no—
687C22×D4—221no—
688C23×C4—111no—
689C23×C4—111no—
690C23×C4—111no—
691C23×C4—111no—
692C23×C4—111no—
693C23×C4—111no—
694C23×C4—111no—
695C23×C4—111no—
696C23×C4—111no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—111no—
701C23×C4—221no—
702C23×C4—221no—
703C23×C4—221no—
704C23×C4—444no—
705C23×C4C22×D1111yescharacteristic
706#137—444no—
707#137—444no—
708C2×Q16—114no—
709C2×Q16—114no—
710C2×SD16—114no—
711C2×SD16—114no—
712C2×M16—112no—
713C2×M16—114no—
714C2×M16—444no—
715C2×M16C22×D1112yes—
716C22×C8—114no—
717#123—222no—
718#123—222no—
719#123—222no—
720#123—222no—
721C22⋊Q8—21no—
722C22⋊Q8—21no—
723C22⋊Q8—112no—
724C22⋊Q8—112no—
725C22⋊Q8—112no—
726C22⋊Q8—112no—
727C22⋊Q8—112no—
728C22⋊Q8—112no—
729C22⋊Q8—112no—
730C22⋊Q8—112no—
731C22⋊Q8—112no—
732C22⋊Q8—112no—
733C22⋊Q8—222no—
734C22⋊Q8—222no—
735C22⋊Q8—222no—
736C22⋊Q8—222no—
737C22⋊Q8—222no—
738C22⋊Q8—222no—
739C22⋊Q8—222no—
740C22⋊Q8—222no—
741C22⋊Q8—221no—
742C22⋊Q8—221no—
743C22⋊Q8—221no—
744C22⋊Q8—221no—
745C22⋊Q8—221no—
746C22⋊Q8—221no—
747C22⋊Q8—221no—
748C22⋊Q8—221no—
749C22⋊Q8—221no—
750C22⋊Q8—221no—
751C22⋊Q8C22×D1112yes—
752C22⋊Q8C22×D1112yes—
753#121—112no—
754#121—112no—
755#121—112no—
756#121—112no—
757#121—221no—
758#121—221no—
759#121—221no—
760#121—221no—
761#120—222no—
762#120—222no—
763#120—222no—
764#120—222no—
765C4×D4—222no—
766C4×D4—222no—
767C4×D4—222no—
768C4×D4—222no—
769C4×D4—222no—
770C4×D4—222no—
771C4×D4—222no—
772C4×D4—222no—
773#117—21no—
774#117—21no—
775#117C22×D1112yes—
776#117C22×D1112yes—
777C2×C4⋊C4—21no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—221no—
782C2×C4⋊C4—221no—
783C2×C4⋊C4—222no—
784C2×C4⋊C4—222no—
785C2×C4⋊C4—222no—
786C2×C4⋊C4—222no—
787C2×C4⋊C4—221no—
788C2×C4⋊C4—221no—
789C2×C4⋊C4—221no—
790C2×C4⋊C4—221no—
791C2×C4⋊C4—221no—
792C2×C4⋊C4—221no—
793C2×C4⋊C4C22×D1111yescharacteristic
794C2×C4⋊C4C22×D1111yescharacteristic
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C22⋊C4—21no—
797C2×C22⋊C4—21no—
798C2×C22⋊C4—222no—
799C2×C22⋊C4—222no—
800C2×C22⋊C4—222no—
801C2×C22⋊C4—222no—
802C2×C22⋊C4—221no—
803C2×C22⋊C4—221no—
804C2×C22⋊C4—221no—
805C2×C22⋊C4—221no—
806C2×C22⋊C4—221no—
807C2×C22⋊C4—221no—
808C2×C22⋊C4—221no—
809C2×C42—21no—
810#107—114no—
811#107C22×D1114yescomplemented
812#106—114no—
813#106C22×D1114yescomplemented
814#103—114no—
815#103—114no—
816#103—114no—
817#103—114no—
818#103C22×D1114yescomplemented
819#103C22×D1114yescomplemented
820#102—114no—
821#102—114no—
822C22⋊C8—112no—
823C22⋊C8—112no—
824C22⋊C8—114no—
825C22⋊C8—114no—
826C22⋊C8C22×D1112yes—
827C22⋊C8C22×D1112yes—
828C2×C11—22no—
829C2×C11—22no—
830C2×C11—41no—
831C2×C11C2×#53411yescharacteristic
832C2×C11C22×#13711yescharacteristic
833C2×C11C2×#57511yescharacteristic
834D11—22no—
835D11—22no—
836D11—22no—
837D11—41no—
838D11—82no—
839C24—111no—
840C24—111no—
841C24—111no—
842C24—111no—
843C24—111no—
844C24—111no—
845C24—224no—
846C24—221no—
847C24—442no—
848C24—442no—
849C24D4×D1111yescharacteristic
850#41—224no—
851#41—224no—
852#41—442no—
853#41—442no—
854#41—444no—
855#41—444no—
856C2×Q8—21no—
857C2×Q8—24no—
858C2×Q8—112no—
859C2×Q8—112no—
860C2×Q8—222no—
861C2×Q8—222no—
862C2×Q8—221no—
863C2×Q8—221no—
864C2×Q8—224no—
865C2×Q8—442no—
866C2×Q8—444no—
867C2×Q8—444no—
868C2×Q8—444no—
869C2×Q8—444no—
870C2×Q8—444no—
871C2×Q8C23×D1112yes—
872C2×D4—112no—
873C2×D4—222no—
874C2×D4—222no—
875C2×D4—222no—
876C2×D4—222no—
877C2×D4—222no—
878C2×D4—222no—
879C2×D4—221no—
880C2×D4—442no—
881C2×D4—444no—
882C2×D4—444no—
883C2×D4—444no—
884C22×C4—24no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—111no—
890C22×C4—111no—
891C22×C4—111no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—111no—
898C22×C4—111no—
899C22×C4—111no—
900C22×C4—111no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—111no—
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—222no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—222no—
915C22×C4—224no—
916C22×C4—224no—
917C22×C4—221no—
918C22×C4—221no—
919C22×C4—221no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—442no—
923C22×C4—442no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4—442no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—444no—
933C22×C4—444no—
934C22×C4—444no—
935C22×C4—442no—
936C22×C4D4×D1111yescharacteristic
937C22×C4D4×D1111yescharacteristic
938C22×C4D4×D1111yescharacteristic
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942Q16—444no—
943Q16—444no—
944SD16—444no—
945SD16—444no—
946M16—24no—
947M16—224no—
948M16—444no—
949C2×C8—114no—
950C2×C8—444no—
951C2×C8C23×D1114yes—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—112no—
958C4⋊C4—222no—
959C4⋊C4—222no—
960C4⋊C4—222no—
961C4⋊C4—222no—
962C4⋊C4—222no—
963C4⋊C4—222no—
964C4⋊C4—222no—
965C4⋊C4—222no—
966C4⋊C4—222no—
967C4⋊C4—222no—
968C4⋊C4—221no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4C23×D1112yes—
972C4⋊C4C23×D1112yes—
973C4⋊C4C23×D1112yes—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—222no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C22⋊C4—222no—
985C22⋊C4—222no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—222no—
990C22⋊C4—222no—
991C22⋊C4—222no—
992C42—22no—
993C42—22no—
994C11#6075111yescharacteristic, complemented, Sylow
995C23—22no—
996C23—22no—
997C23—41no—
998C23—111no—
999C23—111no—
1000C23—111no—
1001C23—114no—
1002C23—111no—
1003C23—222no—
1004C23—222no—
1005C23—222no—
1006C23—222no—
1007C23—222no—
1008C23—222no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—441no—
1015C23—441no—
1016C23—441no—
1017C23—441no—
1018C23—441no—
1019C23—441no—
1020C23—441no—
1021C23—442no—
1022C23—442no—
1023C23—4416no—
1024C23—442no—
1025C23C2×D4×D1111yescharacteristic
1026C23C2×D4×D1111yescharacteristic
1027C23C2×D4×D1111yescharacteristic
1028Q8—24no—
1029Q8—42no—
1030Q8—224no—
1031Q8—222no—
1032Q8—222no—
1033Q8—442no—
1034Q8—444no—
1035Q8—444no—
1036Q8—442no—
1037D4—222no—
1038D4—222no—
1039D4—442no—
1040D4—444no—
1041D4—444no—
1042D4—444no—
1043D4—444no—
1044D4—444no—
1045D4—444no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—111no—
1060C2×C4—111no—
1061C2×C4—111no—
1062C2×C4—111no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—444no—
1085C2×C4—444no—
1086C2×C4—444no—
1087C2×C4—444no—
1088C2×C4—444no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—442no—
1094C2×C4—442no—
1095C2×C4—442no—
1096C2×C4—444no—
1097C2×C4C2×D4×D1111yescharacteristic
1098C2×C4C2×D4×D1111yescharacteristic
1099C2×C4C2×D4×D1111yescharacteristic
1100C2×C4#6704214yes—
1101C2×C4C24×D1111yescharacteristic
1102C8—24no—
1103C8—224no—
1104C22—21no—
1105C22—21no—
1106C22—21no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—44no—
1112C22—112no—
1113C22—112no—
1114C22—112no—
1115C22—228no—
1116C22—221no—
1117C22—221no—
1118C22—221no—
1119C22—221no—
1120C22—221no—
1121C22—221no—
1122C22—221no—
1123C22—221no—
1124C22—221no—
1125C22—444no—
1126C22—444no—
1127C22—444no—
1128C22—444no—
1129C22—444no—
1130C22—442no—
1131C22—442no—
1132C22—442no—
1133C22—884no—
1134C22#1062318412yes—
1135C22D11×#13712yes—
1136C22C22×D4×D1111yescharacteristic
1137C4—21no—
1138C4—21no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—221no—
1144C4—221no—
1145C4—221no—
1146C4—221no—
1147C4—442no—
1148C4—442no—
1149C4—442no—
1150C4#1062318412yes—
1151C4C2×#6704212yes—
1152C2—22no—
1153C2—22no—
1154C2—41no—
1155C2—222no—
1156C2—222no—
1157C2—222no—
1158C2—441no—
1159C2—882no—
1160C2C2×#1062318411yescharacteristic
1161C2C2×D11×#13711yescharacteristic
1162C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3095C2
socleC22×C11C23×D4
prime radicalC2×#10623055C2
hypercenter#3095D11
hypocenterC11#60751
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
2. C2×D11×C22⋊Q8C2semidirect
3. #13079450C2semidirect
4. #13079439C2semidirect
5. #13079421C2semidirect
6. #13079401C2semidirect
7. #13079390C2semidirect
8. #13079372C2semidirect
9. #13078564C2semidirect
10. #13078542C2semidirect
11. #13078247C2semidirect
12. #13078244C2semidirect
13. #13077878C2semidirect
14. #13077874C2semidirect
15. #13077852C2semidirect
16. D11×#407C2semidirect
17. C11×#3095C2semidirect
18. C22×Q8×D11C22semidirect
23. C2×#66999C22semidirect
24. C2×#66995C22semidirect
26. C2×#66962C22semidirect
27. C2×M16×D11C22semidirect
34. D11×C22⋊Q8C22semidirect
35. D11×C22⋊Q8C22semidirect
46. C2×#66950C22semidirect
51. C2×C4⋊C4×D11C22semidirect
58. C11×#485C22semidirect
59. C11×#484C22semidirect
60. C11×#483C22semidirect
61. C11×#428C22semidirect
62. C11×#419C22semidirect
65. #10622746C22semidirect
66. #10622739C22semidirect
67. #10622663C22semidirect
68. #10622660C22semidirect
69. #10622659C22semidirect
70. #10622617C22semidirect
71. #10622609C22semidirect
72. #10622608C22semidirect
73. #10622584C22semidirect
74. #10622583C22semidirect
75. #10622579C22semidirect
76. #10622500C22semidirect
77. #10622499C22semidirect
78. #10622497C22semidirect
79. #10622495C22semidirect
80. #10622481C22semidirect
81. #10622477C22semidirect
82. #10622476C22semidirect
83. #10622475C22semidirect
84. #10622429C22semidirect
85. #10622426C22semidirect
86. #10622425C22semidirect
87. #10622421C22semidirect
88. #10622421C22semidirect
89. #10622420C22semidirect
90. #10622419C22semidirect
91. #10622419C22semidirect
92. #10622352C22semidirect
93. #10622346C22semidirect
94. #10622344C22semidirect
96. #10622339C22semidirect
98. D11×C22⋊C8C22semidirect
157. C2×#4326C23semidirect
159. C2×#4325C23semidirect
180. C2×Dic44C23semidirect
181. C2×#4314C23semidirect
240. C11×#107C23semidirect
241. C11×#106C23semidirect
242. C11×#103C23semidirect
243. C11×#103C23semidirect
248. #66885C23semidirect
251. #66880C23semidirect
252. #66874C23semidirect
253. #66874C23semidirect
254. #66874C23semidirect
255. #66873C23semidirect
256. #66872C23semidirect
257. #66871C23semidirect
423. #3095D11semidirect
459. C22×D11#137semidirect
581. #485C2×D11semidirect
584. #484C2×D11semidirect
587. #483C2×D11semidirect
609. #428C2×D11semidirect
611. #419C2×D11semidirect
811. #107C22×D11semidirect
813. #106C22×D11semidirect
818. #103C22×D11semidirect
819. #103C22×D11semidirect
994. C11#60751semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×D11×C22⋊Q82
#130794502
#130794392
#130794212
#130794012
#130793902
#130793722
#130785642
#130785422
#130782472
#130782442
#130778782
#130778742
#130778522
D11×#4072
C11×#30952
#6075111