Finite Group Databasebeta

← #15634362

Subgroups — #15634362

Order 2816.

1826 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4339C211yesmaximal, characteristic, complemented
2#13081570C214yesmaximal, complemented
3#13081561C214yesmaximal, complemented
4#13081526C212yesmaximal, complemented
5#13081515C212yesmaximal, complemented
6#13081491C212yesmaximal, complemented
7#13081479C212yesmaximal, complemented
8#13079165C212yesmaximal, complemented
9#13079158C211yesmaximal, characteristic, complemented
10#13078434C212yesmaximal, complemented
11#13078425C211yesmaximal, characteristic, complemented
12#13078413C211yesmaximal, characteristic, complemented
13#13078413C212yesmaximal, complemented
14Q8×#4318C211yesmaximal, characteristic, complemented
15C4×#66985C211yesmaximal, characteristic
16C4×#66985C212yesmaximal
17C2×C11×#554C211yesmaximal, characteristic, complemented
18C11×#554—21no—
19C11×#554—21no—
20C11×#554—22no—
21C11×#554C2212yes—
22C11×#554C2212yes—
23C11×#554C2214yes—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#125C2212yes—
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8—22no—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31C22×C11×C4⋊C4—21no—
32Q8×C22⋊D11—21no—
33C2×#66985C2211yescharacteristic
34#10623110C2211yescharacteristic, complemented
35#10623110C2212yescomplemented
36#10623109—22no—
37#10623109—21no—
38Q8×D44C2211yescharacteristic, complemented
39C4×Q8×D11—21no—
40#10623098C2211yescharacteristic, complemented
41#10623098C2212yescomplemented
42Q8×Dic22C2211yescharacteristic, complemented
43#10623042—21no—
44#10623042—22no—
45C4×#4339C2211yescharacteristic
46C4×#4339C2212yes—
47#10623001C2211yescharacteristic
48#10623001C2212yes—
49#10622828C2211yescharacteristic
50#10622828C2212yes—
51#10622707C2212yescomplemented
52#10622704C2212yescomplemented
53#10622700C2212yescomplemented
54#10622697C2212yescomplemented
55#10622693C2214yescomplemented
56#10622692C2212yescomplemented
57#10622691C2212yescomplemented
58#10622679C2214yescomplemented
59#10622679C2214yescomplemented
60#10622678C2214yescomplemented
61#10622678C2214yescomplemented
62#10622677C2214yescomplemented
63#10622677C2214yescomplemented
64#10622676C2214yescomplemented
65#10622676C2214yescomplemented
66#10622637C2212yescomplemented
67#10622637C2214yescomplemented
68Q8×C11⋊C8C2212yescomplemented
69#10622631C2214yes—
70#10622631C2212yes—
71C4×#4324C2212yes—
72C4×#4324C2214yes—
73#10622627C2214yes—
74#10622627C2212yes—
75C4×#4323C2212yes—
76C4×#4323C2214yes—
77#10622622C2214yes—
78#10622622C2214yes—
79#10622622C2214yes—
80#10622621C2212yes—
81#10622621C2214yes—
82#10622620C2212yes—
83#10622620C2214yes—
84#10622579C2212yes—
85#10622579C2211yescharacteristic
86#10622577C2212yes—
87#10622577C2212yes—
88#10622577C2211yescharacteristic
89#10622577C2212yes—
90#10622577C2212yes—
91#10622537C2211yescharacteristic
92#10622537C2212yes—
93C4×#4318C2211yescharacteristic
94C4×#4318C2212yes—
95C22×Q8×C11—21no—
96C22×Q8×C11D411yescharacteristic
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11—21no—
99C23×C4×C11—22no—
100C2×Q8×D11—21no—
101C2×#4339C2311yescharacteristic
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8C2312yes—
105C11×C4⋊Q8C2312yes—
106C11×#125—22no—
107C11×#125—22no—
108C11×#125C2314yes—
109C11×#125C2314yes—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—24no—
113C11×C22⋊Q8—24no—
114C11×C22⋊Q8—24no—
115C11×C22⋊Q8—24no—
116C11×C22⋊Q8—24no—
117C4×Q8×C11D411yescharacteristic
118C4×Q8×C11D412yes—
119C4×Q8×C11D411yescharacteristic
120C4×Q8×C11C2311yescharacteristic
121C4×Q8×C11C2311yescharacteristic
122C4×Q8×C11C2312yes—
123C4×D4×C11—22no—
124C4×D4×C11—21no—
125C4×D4×C11—22no—
126C4×D4×C11—21no—
127C4×D4×C11C2312yes—
128C4×D4×C11C2314yes—
129C4×D4×C11C2314yes—
130C4×D4×C11C2312yes—
131C2×C11×C4⋊C4—22no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—22no—
134C2×C11×C4⋊C4—22no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4—24no—
137C2×C11×C4⋊C4D411yescharacteristic
138C2×C11×C4⋊C4D412yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—22no—
143C2×C42×C11C2312yes—
144C2×C42×C11C2311yescharacteristic
145#66999—21no—
146#66999—22no—
147Q8×Dic11—21no—
148#66997—21no—
149#66997—22no—
150C2×#4324C2312yes—
151#66985Q818yescomplemented
152C2×#4323C2312yes—
153C4×C22⋊D11—21no—
154C4×C22⋊D11—22no—
155C4×C22⋊D11—21no—
156C4×C22⋊D11—22no—
157#66979C2312yes—
158#66979C2311yescharacteristic
159#66977—21no—
160#66977—22no—
161#66977—21no—
162#66977—22no—
163C2×#4318C2311yescharacteristic
164C2×#4318C2312yes—
165C2×#4318C2311yescharacteristic
166#66950—21no—
167#66950—22no—
168#66949—22no—
169#66949—22no—
170#66949—22no—
171C4⋊C4×D11—21no—
172C4⋊C4×D11—22no—
173#66942—22no—
174#66942—22no—
175#66942—22no—
176#66941—21no—
177#66941—22no—
178#66940—21no—
179#66940—22no—
180C4×D44C2311yescharacteristic
181C4×D44C2312yes—
182C4×D44C2312yes—
183C4×D44C2311yescharacteristic
184#66925—22no—
185#66925—21no—
186C42×D11—22no—
187C42×D11—21no—
188#66923C2312yes—
189#66923C2312yes—
190#66923C2312yes—
191#66922C2312yes—
192#66922C2311yescharacteristic
193#66922C2311yescharacteristic
194#66922C2312yes—
195C4×Dic22—22no—
196C4×Dic22—21no—
197C4×Dic22—22no—
198C4×Dic22—21no—
199C4×Dic22C2311yescharacteristic
200C4×Dic22C2312yes—
201C4×Dic22C2312yes—
202C4×Dic22C2311yescharacteristic
203#66896C2312yes—
204#66896C2314yes—
205#66896C2314yes—
206#66896C2312yes—
207#66874C2312yes—
208#66874C2314yes—
209#66873C2312yes—
210#66873C2314yes—
211#66872C2314yes—
212#66872C2314yes—
213#66872C2314yes—
214#66872C2312yes—
215#66872C2314yes—
216#66871C2314yes—
217#66871C2314yes—
218#66871C2314yes—
219#66871C2312yes—
220#66871C2314yes—
221C4⋊(C11⋊C8)C2312yes—
222C4⋊(C11⋊C8)C2314yes—
223C4⋊(C11⋊C8)C2314yes—
224C4⋊(C11⋊C8)C2312yes—
225#66867C2314yes—
226#66867C2312yes—
227C4×C11⋊C8C2314yes—
228C4×C11⋊C8C2312yes—
229#61367—111nomaximal, Sylow
230C24×C11—21no—
231C2×Q8×C11—22no—
232C2×Q8×C11—22no—
233C2×Q8×C11—42no—
234C2×Q8×C11—82no—
235C2×Q8×C11C2×D411yescharacteristic
236C2×Q8×C11C2×D411yescharacteristic
237C2×Q8×C11C2×D412yes—
238C2×D4×C11—21no—
239C2×D4×C11—22no—
240C2×D4×C11C2×Q814yescomplemented
241C2×D4×C11C2412yes—
242C22×C4×C11—21no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—24no—
247C22×C4×C11—24no—
248C22×C4×C11—44no—
249C22×C4×C11—84no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—21no—
256Q8×D11—44no—
257#4339—22no—
258#4339C2×Q814yes—
259C2×D44C2411yescharacteristic
260C2×C4×D11—21no—
261C2×C4×D11—22no—
262C2×C4×D11—21no—
263C2×C4×D11—21no—
264C2×C4×D11—22no—
265C2×Dic22—22no—
266C2×Dic22—21no—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22C2411yescharacteristic
270C11×C4⋊C4—24no—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—24no—
275C11×C4⋊C4—24no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4C2×D411yescharacteristic
279C11×C4⋊C4C2×D412yes—
280C11×C4⋊C4C2×D411yescharacteristic
281C11×C4⋊C4C2×D412yes—
282C11×C4⋊C4C2×D412yes—
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D412yes—
285C11×C4⋊C4C2412yes—
286C11×C4⋊C4C2414yes—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—24no—
291C42×C11C2×D412yes—
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D412yes—
294C42×C11C2×D411yescharacteristic
295C42×C11C2411yescharacteristic
296C42×C11C2412yes—
297C42×C11C2412yes—
298C42×C11C2411yescharacteristic
299C22⋊Dic11—22no—
300C22⋊Dic11—21no—
301#4324C2×Q818yescomplemented
302#4323C2×Q818yescomplemented
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—21no—
307C4⋊Dic11—22no—
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11—22no—
311C4⋊Dic11C2412yes—
312C4⋊Dic11C2411yescharacteristic
313C4⋊Dic11C2412yes—
314C4⋊Dic11C2411yescharacteristic
315Dic11⋊C4—22no—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—22no—
321Dic11⋊C4—21no—
322Dic11⋊C4—22no—
323Dic11⋊C4—22no—
324Dic11⋊C4—21no—
325C4×Dic11—21no—
326C4×Dic11—22no—
327C4×Dic11—21no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11—21no—
331#4318—22no—
332#4318—24no—
333#4318C2×Q814yescomplemented
334C2×C11⋊C8C2414yes—
335C2×C11⋊C8C2412yes—
336C2×C11⋊C8C2412yes—
337Q8×#41—111no—
338C2×#554D1111yescharacteristic, complemented
339#3389—114no—
340#3388—114no—
341#3385—112no—
342#3384—112no—
343#3381—112no—
344#3380—112no—
345#3166—112no—
346#3165—111no—
347#3080—112no—
348#3079—111no—
349#3077—111no—
350#3077—112no—
351Q8×M16—111no—
352C4×AGL(1,ℤ/8)—111no—
353C4×AGL(1,ℤ/8)—112no—
354C23×C11—24no—
355C23×C11—22no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11C22×D411yescharacteristic
359C22×D11—21no—
360Q8×C11—22no—
361Q8×C11—22no—
362Q8×C11—42no—
363Q8×C11—82no—
364Q8×C11—82no—
365D4×C11—24no—
366D4×C11—22no—
367D4×C11C22×Q814yes—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—24no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11—41no—
374C2×C4×C11—44no—
375C2×C4×C11—42no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11—84no—
379C2×C4×C11—84no—
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D412yes—
382C2×C4×C11C22×D412yes—
383C2×C4×C11C22×D412yes—
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×Q812yes—
390C2×C4×C112−1+412yes—
391C2×C4×C11C2511yescharacteristic
392C22⋊D11—24no—
393C2×Dic11—21no—
394C2×Dic11—22no—
395C2×Dic11—21no—
396C2×Dic11—21no—
397C2×Dic11—22no—
398D44—21no—
399D44C22×Q812yes—
400C4×D11—24no—
401C4×D11—44no—
402C4×D11—42no—
403C4×D11—82no—
404C4×D11—81no—
405Dic22—21no—
406Dic22—44no—
407Dic22—42no—
408Dic22—82no—
409Dic22—81no—
410Dic22C22×Q812yes—
411C11⋊C8—24no—
412C11⋊C8—22no—
413C11⋊C8C22×Q814yes—
414C2×AGL(1,ℤ/8)—111no—
415Q82—111no—
416#557—111no—
417#557—112no—
418#554—21no—
419#554—22no—
420#554—21no—
421#554—111no—
422#554—112no—
423#554—221no—
424#554—222no—
425#554C2×D1112yes—
426#554C2×D1112yes—
427#554C2×D1114yes—
428D4×Q8—111no—
429D4×Q8—221no—
430#533—111no—
431#533—112no—
432#533—222no—
433#533—221no—
434C2×C4⋊Q8C2×D1111yescharacteristic
435C2×#125C2×D1112yes—
436C2×C22⋊Q8—21no—
437C2×C22⋊Q8—22no—
438C4×#41—111no—
439C4×#41—112no—
440C2×C4×Q8—221no—
441C2×C4×Q8C2×D1111yescharacteristic
442C2×C4×D4C2×D1112yes—
443C2×C4×D4C2×D1111yescharacteristic
444C22×C4⋊C4—21no—
445#501—114no—
446#501—114no—
447#501—114no—
448#500—112no—
449#499—114no—
450#499—114no—
451#498—112no—
452#479—114no—
453#479—114no—
454#478—114no—
455#478—114no—
456#478—114no—
457#478—114no—
458#478—114no—
459#477—112no—
460#476—112no—
461#476—112no—
462#476—114no—
463#475—112no—
464#474—112no—
465#474—112no—
466#474—114no—
467#446—112no—
468#446—114no—
469C8×Q8—112no—
470#442—114no—
471#442—112no—
472#440—114no—
473#440—112no—
474C4×SD16—112no—
475C4×SD16—114no—
476C4×D8—112no—
477C4×D8—114no—
478#428—112no—
479#428—112no—
480#428—112no—
481#428—112no—
482#428—111no—
483#423—111no—
484#423—112no—
485#418—112no—
486#418—111no—
487#417—112no—
488#417—111no—
489C4×M16—111no—
490C4×M16—112no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—24no—
494C22×C11—48no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11D4×Q812yes—
498C22×C11C23×D411yescharacteristic
499C2×D11—22no—
500C2×D11—41no—
501C2×D11—41no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—22no—
508C4×C11—22no—
509C4×C11—44no—
510C4×C11—42no—
511C4×C11D4×Q812yes—
512C4×C11#57512yes—
513C4×C11C23×Q811yescharacteristic
514C4×C11C2×2−1+411yescharacteristic
515Dic11—22no—
516Dic11—41no—
517Dic11—42no—
518Dic11—41no—
519Dic11—42no—
520C2×#41—111no—
521C22×Q8—21no—
522C22×Q8—221no—
523C22×Q8C22⋊D1111yescharacteristic
524C22×D4C22×D1111yescharacteristic
525C23×C4—21no—
526C23×C4—22no—
527AGL(1,ℤ/8)—118no—
528C2×SD16—112no—
529C2×D8—112no—
530C2×M16—111no—
531C2×M16—111no—
532C2×M16—112no—
533C4⋊Q8—21no—
534C4⋊Q8—21no—
535C4⋊Q8—111no—
536C4⋊Q8—112no—
537C4⋊Q8—112no—
538C4⋊Q8—111no—
539C4⋊Q8—221no—
540C4⋊Q8—222no—
541C4⋊Q8—221no—
542C4⋊Q8—222no—
543C4⋊Q8C22×D1112yes—
544C4⋊Q8C22×D1112yes—
545#125—22no—
546#125—22no—
547#125—112no—
548#125—112no—
549#125—112no—
550#125—222no—
551#125—222no—
552#125—222no—
553#125C22×D1114yes—
554#125C22×D1114yes—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8—24no—
558C22⋊Q8—24no—
559C22⋊Q8—24no—
560C22⋊Q8—24no—
561C22⋊Q8—24no—
562C22⋊Q8—221no—
563C22⋊Q8—222no—
564C22⋊Q8—221no—
565C22⋊Q8—222no—
566C22⋊Q8—221no—
567C22⋊Q8—222no—
568C22⋊Q8—221no—
569C22⋊Q8—222no—
570C22⋊Q8—222no—
571C22⋊Q8—222no—
572C22⋊Q8—222no—
573C4×Q8—112no—
574C4×Q8—111no—
575C4×Q8—111no—
576C4×Q8—112no—
577C4×Q8—221no—
578C4×Q8—221no—
579C4×Q8—222no—
580C4×Q8—222no—
581C4×Q8—221no—
582C4×Q8—222no—
583C4×Q8—221no—
584C4×Q8C22⋊D1111yescharacteristic
585C4×Q8C22⋊D1112yes—
586C4×Q8C22⋊D1111yescharacteristic
587C4×Q8C22×D1111yescharacteristic
588C4×Q8C22×D1111yescharacteristic
589C4×Q8C22×D1112yes—
590C4×D4—22no—
591C4×D4—21no—
592C4×D4—22no—
593C4×D4—21no—
594C4×D4—111no—
595C4×D4—112no—
596C4×D4—112no—
597C4×D4—111no—
598C4×D4—221no—
599C4×D4—222no—
600C4×D4—221no—
601C4×D4—222no—
602C4×D4C22×D1112yes—
603C4×D4C22×D1114yes—
604C4×D4C22×D1114yes—
605C4×D4C22×D1112yes—
606#117—111no—
607#117—112no—
608#117—222no—
609#117—221no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—221no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4C22⋊D1111yescharacteristic
619C2×C4⋊C4C22⋊D1112yes—
620C2×C4⋊C4C22×D1111yescharacteristic
621C2×C4⋊C4C22×D1112yes—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—22no—
624C2×C42—222no—
625C2×C42—221no—
626C2×C42C22×D1112yes—
627C2×C42C22×D1111yescharacteristic
628#107—112no—
629#107—114no—
630#107—114no—
631#107—114no—
632#107—114no—
633#106—114no—
634#106—112no—
635#106—114no—
636#106—114no—
637#106—114no—
638C4⋊C8—112no—
639C4⋊C8—114no—
640C4⋊C8—112no—
641C4⋊C8—114no—
642#103—114no—
643#103—112no—
644#102—114no—
645#102—112no—
646#102—112no—
647#102—114no—
648#102—114no—
649#102—112no—
650#97—112no—
651#97—114no—
652C4×C8—112no—
653C4×C8—114no—
654C2×C11—22no—
655C2×C11—44no—
656C2×C11C2×D4×Q811yescharacteristic
657C2×C11C2×#57511yescharacteristic
658C2×C11#358511yescharacteristic
659D11—42no—
660C24—21no—
661#41—114no—
662#41—222no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—42no—
666C2×Q8—82no—
667C2×Q8—111no—
668C2×Q8—222no—
669C2×Q8—221no—
670C2×Q8—221no—
671C2×Q8—222no—
672C2×Q8—444no—
673C2×Q8C2×C22⋊D1111yescharacteristic
674C2×Q8C2×C22⋊D1111yescharacteristic
675C2×Q8C2×C22⋊D1112yes—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—111no—
679C2×D4—221no—
680C2×D4Q8×D1114yescomplemented
681C2×D4C23×D1112yes—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—44no—
689C22×C4—84no—
690C22×C4—221no—
691C22×C4—222no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—222no—
695C22×C4C2×C22⋊D1111yescharacteristic
696C22×C4C2×C22⋊D1112yes—
697C22×C4C2×C22⋊D1111yescharacteristic
698C22×C4C2×C22⋊D1112yes—
699C22×C4C23×D1111yescharacteristic
700SD16—118no—
701D8—118no—
702M16—114no—
703M16—222no—
704M16—224no—
705C2×C8—112no—
706C2×C8—112no—
707C2×C8—114no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—111no—
717C4⋊C4—112no—
718C4⋊C4—112no—
719C4⋊C4—111no—
720C4⋊C4—222no—
721C4⋊C4—222no—
722C4⋊C4—222no—
723C4⋊C4—222no—
724C4⋊C4—221no—
725C4⋊C4—222no—
726C4⋊C4—221no—
727C4⋊C4—221no—
728C4⋊C4—222no—
729C4⋊C4—222no—
730C4⋊C4—222no—
731C4⋊C4—222no—
732C4⋊C4—221no—
733C4⋊C4—222no—
734C4⋊C4C2×C22⋊D1111yescharacteristic
735C4⋊C4C2×C22⋊D1112yes—
736C4⋊C4C2×C22⋊D1111yescharacteristic
737C4⋊C4C2×C22⋊D1112yes—
738C4⋊C4C2×C22⋊D1112yes—
739C4⋊C4C2×C22⋊D1112yes—
740C4⋊C4C2×C22⋊D1112yes—
741C4⋊C4C23×D1112yes—
742C4⋊C4C23×D1114yes—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—221no—
748C22⋊C4—222no—
749C22⋊C4—222no—
750C22⋊C4—221no—
751C22⋊C4—221no—
752C22⋊C4—222no—
753C42—222no—
754C42—221no—
755C42—221no—
756C42—222no—
757C42—222no—
758C42—221no—
759C42C2×C22⋊D1112yes—
760C42C2×C22⋊D1111yescharacteristic
761C42C2×C22⋊D1112yes—
762C42C2×C22⋊D1111yescharacteristic
763C42C23×D1112yes—
764C42C23×D1111yescharacteristic
765C42C23×D1111yescharacteristic
766C42C23×D1112yes—
767C11#6136711yescharacteristic, complemented, Sylow
768C23—24no—
769C23—22no—
770C23—42no—
771C23—42no—
772C23—221no—
773C23C22×C22⋊D1111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—42no—
777Q8—82no—
778Q8—82no—
779Q8—112no—
780Q8—221no—
781Q8—444no—
782Q8—442no—
783Q8—882no—
784Q8—881no—
785D4—24no—
786D4—22no—
787D4—112no—
788D4—224no—
789D4—221no—
790D4C2×Q8×D1114yes—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—84no—
802C2×C4—84no—
803C2×C4—221no—
804C2×C4—224no—
805C2×C4—222no—
806C2×C4—221no—
807C2×C4—222no—
808C2×C4—221no—
809C2×C4—444no—
810C2×C4—442no—
811C2×C4—882no—
812C2×C4—881no—
813C2×C4C2×Q8×D1112yes—
814C2×C4#6704012yes—
815C2×C4C22×C22⋊D1112yes—
816C2×C4C22×C22⋊D1111yescharacteristic
817C2×C4C22×C22⋊D1112yes—
818C2×C4C22×C22⋊D1112yes—
819C2×C4C22×C22⋊D1111yescharacteristic
820C2×C4C22×C22⋊D1111yescharacteristic
821C2×C4C22×C22⋊D1112yes—
822C2×C4C22×C22⋊D1111yescharacteristic
823C2×C4C22×C22⋊D1111yescharacteristic
824C2×C4C24×D1111yescharacteristic
825C8—114no—
826C8—222no—
827C8—224no—
828C22—21no—
829C22—21no—
830C22—24no—
831C22—48no—
832C22—42no—
833C22—42no—
834C22—222no—
835C22—441no—
836C22—441no—
837C22Q8×C22⋊D1112yes—
838C22C23×C22⋊D1111yescharacteristic
839C4—22no—
840C4—22no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—22no—
846C4—44no—
847C4—42no—
848C4—222no—
849C4—442no—
850C4—441no—
851C4—442no—
852C4—441no—
853C4Q8×C22⋊D1112yes—
854C4#1062335312yes—
855C4C22×Q8×D1111yescharacteristic
856C4C2×#6704011yescharacteristic
857C2—22no—
858C2—44no—
859C2—442no—
860C2C2×Q8×C22⋊D1111yescharacteristic
861C2C2×#1062335311yescharacteristic
862C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC22×C11C23×D4
prime radicalC2×#66985C22
hypercenterC2×#554D11
hypocenterC11#61367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. Q8×#4339C2semidirect
2. #13081570C2semidirect
3. #13081561C2semidirect
4. #13081526C2semidirect
5. #13081515C2semidirect
6. #13081491C2semidirect
7. #13081479C2semidirect
8. #13079165C2semidirect
9. #13079158C2semidirect
10. #13078434C2semidirect
11. #13078425C2semidirect
12. #13078413C2semidirect
13. #13078413C2semidirect
14. Q8×#4318C2semidirect
17. C2×C11×#554C2semidirect
34. #10623110C22semidirect
35. #10623110C22semidirect
38. Q8×D44C22semidirect
40. #10623098C22semidirect
41. #10623098C22semidirect
42. Q8×Dic22C22semidirect
51. #10622707C22semidirect
52. #10622704C22semidirect
53. #10622700C22semidirect
54. #10622697C22semidirect
55. #10622693C22semidirect
56. #10622692C22semidirect
57. #10622691C22semidirect
58. #10622679C22semidirect
59. #10622679C22semidirect
60. #10622678C22semidirect
61. #10622678C22semidirect
62. #10622677C22semidirect
63. #10622677C22semidirect
64. #10622676C22semidirect
65. #10622676C22semidirect
66. #10622637C22semidirect
67. #10622637C22semidirect
68. Q8×C11⋊C8C22semidirect
151. #66985Q8semidirect
240. C2×D4×C11C2×Q8semidirect
301. #4324C2×Q8semidirect
302. #4323C2×Q8semidirect
333. #4318C2×Q8semidirect
338. C2×#554D11semidirect
680. C2×D4Q8×D11semidirect
767. C11#61367semidirect

Maximal subgroups

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

subgroupindex
Q8×#43392
#130815702
#130815612
#130815262
#130815152
#130814912
#130814792
#130791652
#130791582
#130784342
#130784252
#130784132
Q8×#43182
C4×#669852
C2×C11×#5542
#6136711