Finite Group Databasebeta

← #15622599

Subgroups — #15622599

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623047C211yesmaximal, characteristic, complemented
2#13078911C214yesmaximal, complemented
3#13078839C214yesmaximal, complemented
4#13078783C212yesmaximal, complemented
5#13078742C212yesmaximal, complemented
6#13078692C212yesmaximal, complemented
7#13078651C212yesmaximal, complemented
8#13078560C211yesmaximal, characteristic, complemented
9#13078525C211yesmaximal, characteristic
10#13078452C212yesmaximal, complemented
11#13078142C212yesmaximal, complemented
12#13077849C211yesmaximal, characteristic
13C2×#10622663C211yesmaximal, characteristic, complemented
14#13077482C212yesmaximal, complemented
15#13077455C212yesmaximal, complemented
16#13077274C211yesmaximal, characteristic, complemented
17C11×#3495C211yesmaximal, characteristic
18C23×Dic22C2211yescharacteristic
19C11×#556—21no—
20C11×#554—21no—
21C11×#552—22no—
22C11×#552—21no—
23C11×#552—21no—
24C11×#551—22no—
25C11×#544C2211yescharacteristic
26C11×#542C2212yes—
27C11×#541C2212yes—
28C11×#536C2211yescharacteristic
29C11×#533C2212yes—
30C11×#529C2212yes—
31C11×#525C2211yescharacteristic
32C2×C11×C22⋊Q8C2211yescharacteristic
33C11×#520C2211yescharacteristic
34C11×#519C2211yescharacteristic
35C2×C11×#117C2211yescharacteristic
36C2×#67004C2212yes—
37C22×#4326C2212yes—
38C2×#66979C2211yescharacteristic
39#10623047—21no—
40#10623047—22no—
41#10623047—21no—
42#10623047C2214yes—
43#10623047C2212yes—
44#10623047C2212yes—
45C2×#66940—21no—
46C2×#66940—21no—
47C2×#66930—22no—
48C2×C4×Dic22C2212yes—
49C2×C4×Dic22C2212yes—
50#10622846C2212yes—
51#10622838C2212yes—
52#10622820C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622707C2214yescomplemented
55#10622704C2214yescomplemented
56#10622703C2214yescomplemented
57#10622703C2214yescomplemented
58#10622676C2214yescomplemented
59#10622676C2214yescomplemented
60#10622667C2214yescomplemented
61#10622667C2214yescomplemented
62#10622663C2214yes—
63#10622663C2212yes—
64#10622663C2212yes—
65#10622663C2212yes—
66#10622663C2212yes—
67#10622658C2214yes—
68#10622658C2212yes—
69#10622657C2212yes—
70#10622657C2211yescharacteristic
71#10622656C2212yes—
72#10622656C2211yescharacteristic
73#10622653C2212yes—
74#10622653C2212yes—
75#10622648C2212yes—
76#10622647C2211yescharacteristic
77#10622646C2211yescharacteristic
78#10622643C2214yescomplemented
79#10622643C2214yescomplemented
80#10622643C2214yescomplemented
81C4×#4326C2214yescomplemented
82C4×#4326C2214yescomplemented
83C4×#4326C2214yescomplemented
84#10622631C2214yescomplemented
85C4×#4324C2214yescomplemented
86#10622617C2212yes—
87#10622613C2214yes—
88#10622612C2212yes—
89#10622611C2212yes—
90#10622610C2212yes—
91C2×#66874C2212yes—
92#10622577C2212yes—
93#10622539C2212yes—
94#10622538C2212yes—
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×Dic11—21no—
99C22×Dic22—21no—
100C22×Dic22—21no—
101C22×Dic22—21no—
102C22×Dic22—28no—
103C22×Dic22C2312yes—
104C22×Dic22C2312yes—
105C22×Dic22C2312yes—
106C11×C4⋊Q8—21no—
107C11×C4⋊Q8C2312yes—
108C11×C4⋊Q8C2312yes—
109C11×#126—22no—
110C11×#126—22no—
111C11×#126—22no—
112C11×#126—22no—
113C11×#125—22no—
114C11×#125—22no—
115C11×#125—21no—
116C11×#125—22no—
117C11×#125C2312yes—
118C11×#124—22no—
119C11×#124C2312yes—
120C11×#123—21no—
121C11×#123—22no—
122C11×#123—22no—
123C11×#123—22no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8—21no—
128C11×C22⋊Q8—21no—
129C11×C22⋊Q8—22no—
130C11×C22⋊Q8—22no—
131C11×C22⋊Q8C2312yes—
132C11×C22⋊Q8C2312yes—
133C11×C22⋊Q8C2311yescharacteristic
134C11×C22⋊Q8C2311yescharacteristic
135C11×#121C2311yescharacteristic
136C11×#121C2311yescharacteristic
137C11×#120—21no—
138C4×Q8×C11—21no—
139C4×Q8×C11—21no—
140C4×Q8×C11—22no—
141C4×Q8×C11C2312yes—
142C4×Q8×C11C2312yes—
143C4×Q8×C11C2312yes—
144C4×D4×C11—21no—
145C4×D4×C11—21no—
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C4×D4×C11C2312yes—
149C11×#117—22no—
150C11×#117—21no—
151C11×#117—22no—
152C11×#117—22no—
153C11×#117D411yescharacteristic
154C11×#117D412yes—
155C11×#117D411yescharacteristic
156C11×#117C2311yescharacteristic
157C11×#117C2311yescharacteristic
158C11×#117C2311yescharacteristic
159C11×#117C2312yes—
160C2×C11×C4⋊C4—21no—
161C2×C11×C4⋊C4—21no—
162C2×C11×C4⋊C4D411yescharacteristic
163C2×C11×C4⋊C4D411yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4—21no—
166C2×C11×C22⋊C4D412yes—
167C2×C42×C11C2312yes—
168C2×C22⋊Dic11—21no—
169#67004—28no—
170C2×#4326—28no—
171C2×#4326C2314yes—
172C2×#4326C2314yes—
173C2×#4326C2314yes—
174C2×#4324C2314yes—
175#66979—21no—
176#66979—21no—
177#66979C2312yes—
178#66979C2312yes—
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2311yescharacteristic
181C2×Dic11⋊C4—22no—
182C2×Dic11⋊C4—22no—
183C2×C4×Dic11—22no—
184C2×C4×Dic11—22no—
185C2×C4×Dic11—21no—
186C2×#4318C2312yes—
187C22×C11⋊C8C2312yes—
188#66940—22no—
189#66940—22no—
190#66940—24no—
191#66940—22no—
192#66940—22no—
193#66940—24no—
194#66930—24no—
195#66930—24no—
196#66930—24no—
197#66930—24no—
198C4×Dic22—22no—
199C4×Dic22—22no—
200C4×Dic22—22no—
201C4×Dic22—22no—
202C4×Dic22C2314yes—
203C4×Dic22C2314yes—
204C4×Dic22C2314yes—
205C4×Dic22C2314yes—
206#66899C2314yes—
207#66899C2314yes—
208#66899C2312yes—
209#66899C2312yes—
210#66896C2312yes—
211#66896C2312yes—
212C22⋊(C11⋊C8)C2311yescharacteristic
213C22⋊(C11⋊C8)C2312yes—
214C22⋊(C11⋊C8)C2311yescharacteristic
215C22⋊(C11⋊C8)C2312yes—
216C22⋊(C11⋊C8)C2312yes—
217#66874C2314yes—
218#66874C2314yes—
219#66874C2314yes—
220#66874C2314yes—
221#66872C2314yes—
222#66872C2312yes—
223#66872C2312yes—
224#66871C2314yes—
225#66871C2312yes—
226#66871C2312yes—
227C4⋊(C11⋊C8)C2314yes—
228C4⋊(C11⋊C8)C2314yes—
229#66867C2314yes—
230C4×C11⋊C8C2314yes—
231#60583—111nomaximal, Sylow
232C24×C11C2×D411yescharacteristic
233C11×#41—24no—
234C2×Q8×C11—21no—
235C2×Q8×C11—22no—
236C2×Q8×C11—24no—
237C2×Q8×C11C2412yes—
238C2×Q8×C11C2411yescharacteristic
239C2×D4×C11—21no—
240C2×D4×C11—21no—
241C2×D4×C11—21no—
242C2×D4×C11C2411yescharacteristic
243C22×C4×C11—24no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—22no—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×Dic11—28no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C2×Dic22—28no—
263C2×Dic22—28no—
264C2×Dic22—28no—
265C2×Dic22—28no—
266C2×Dic22—28no—
267C2×Dic22—22no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×Dic22—24no—
271C2×Dic22#4118yes—
272C2×Dic22C2414yes—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4C2×D411yescharacteristic
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D412yes—
289C11×C4⋊C4C2×D411yescharacteristic
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2412yes—
293C11×C4⋊C4C2411yescharacteristic
294C11×C4⋊C4C2411yescharacteristic
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—21no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4C2×D412yes—
306C11×C22⋊C4C2×D412yes—
307C11×C22⋊C4C2×D412yes—
308C11×C22⋊C4C2×D412yes—
309C42×C11—22no—
310C42×C11—22no—
311C42×C11—22no—
312C42×C11—21no—
313C42×C11C2×D412yes—
314C42×C11C2×D412yes—
315C42×C11C2412yes—
316C42×C11C2412yes—
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319#4326—28no—
320#4326—28no—
321#4326—28no—
322#4324—28no—
323C4⋊Dic11—21no—
324C4⋊Dic11—21no—
325C4⋊Dic11C2412yes—
326C4⋊Dic11C2412yes—
327Dic11⋊C4—24no—
328Dic11⋊C4—24no—
329Dic11⋊C4—24no—
330Dic11⋊C4—24no—
331C4×Dic11—24no—
332C4×Dic11—24no—
333C4×Dic11—24no—
334C4×Dic11—24no—
335C4×Dic11—22no—
336C4×Dic11—22no—
337#4318—24no—
338C2×C11⋊C8—24no—
339C2×C11⋊C8C2412yes—
340C2×C11⋊C8C2414yes—
341C2×C11⋊C8C2412yes—
342#3495D1111yescharacteristic
343C2×#519—111no—
344#3127—114no—
345#3121—114no—
346#3117—112no—
347#3113—112no—
348#3108—112no—
349#3104—112no—
350#3095—111no—
351#3091—111no—
352#3082—112no—
353#3044—112no—
354#3004—111no—
355C2×#451—111no—
356#2950—112no—
357#2947—112no—
358#2924—111no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—21no—
362C23×C11—41no—
363C23×C11C22×D411yescharacteristic
364C23×C11C22×D411yescharacteristic
365C23×C11C22×D411yescharacteristic
366Q8×C11—24no—
367Q8×C11—22no—
368Q8×C11—42no—
369Q8×C11—82no—
370D4×C11—22no—
371D4×C11—42no—
372D4×C11—42no—
373D4×C11—81no—
374C2×C4×C11—22no—
375C2×C4×C11—24no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—22no—
383C2×C4×C11—21no—
384C2×C4×C11—22no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11—82no—
389C2×C4×C11—81no—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D412yes—
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C2×#4114yes—
398C2×C4×C11C2511yescharacteristic
399C2×Dic11—28no—
400C2×Dic11—28no—
401C2×Dic11—28no—
402C2×Dic11—24no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—42no—
406C2×Dic11—42no—
407Dic22—28no—
408Dic22—28no—
409Dic22—28no—
410Dic22—24no—
411Dic22C2×#4118yes—
412C11⋊C8—22no—
413C11⋊C8—22no—
414C11⋊C8—24no—
415C23×Q8—111no—
416C2×#137—112no—
417C22×Q16—112no—
418#556—21no—
419#554—21no—
420#552—22no—
421#552—21no—
422#552—21no—
423#551—22no—
424#544C2×D1111yescharacteristic
425#542C2×D1112yes—
426#541C2×D1112yes—
427#536C2×D1111yescharacteristic
428#533C2×D1112yes—
429#529C2×D1112yes—
430#525C2×D1111yescharacteristic
431C2×C22⋊Q8C2×D1111yescharacteristic
432#520C2×D1111yescharacteristic
433#519—112no—
434#519—114no—
435#519—112no—
436#519—222no—
437#519—221no—
438#519—221no—
439#519C2×D1111yescharacteristic
440C2×C4×Q8—112no—
441C2×C4×Q8—112no—
442C2×C4×Q8—221no—
443C2×C4×Q8—221no—
444C2×#117—111no—
445C2×#117—222no—
446C2×#117C2×D1111yescharacteristic
447#485—112no—
448#485—114no—
449#484—111no—
450#484—112no—
451#483—111no—
452#483—112no—
453#482—112no—
454#481—111no—
455#480—111no—
456#479—114no—
457#479—114no—
458#477—114no—
459#475—114no—
460#464—114no—
461#464—114no—
462#462—114no—
463#462—114no—
464#451—112no—
465#451—112no—
466#451—112no—
467#451—114no—
468#451—112no—
469#448—112no—
470#448—112no—
471#441—114no—
472#441—114no—
473#441—114no—
474#440—114no—
475C4×Q16—114no—
476C4×Q16—114no—
477C4×Q16—114no—
478C4×SD16—114no—
479#433—114no—
480#432—112no—
481#431—112no—
482#428—112no—
483#427—112no—
484#424—112no—
485#419—112no—
486#419—112no—
487#416—112no—
488C2×#103—112no—
489#407—111no—
490C2×C22⋊C8—111no—
491#405—112no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—21no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—44no—
500C22×C11—41no—
501C22×C11—41no—
502C22×C11—41no—
503C22×C11#52512yes—
504C22×C11#57812yes—
505C22×C11C23×D411yescharacteristic
506C4×C11—22no—
507C4×C11—22no—
508C4×C11—21no—
509C4×C11—21no—
510C4×C11—22no—
511C4×C11—22no—
512C4×C11—42no—
513C4×C11—41no—
514C4×C11—41no—
515C4×C11—42no—
516C4×C11—41no—
517C4×C11#52512yes—
518C4×C11C22×#4112yes—
519Dic11—28no—
520Dic11—42no—
521Dic11—42no—
522C2×#41C22×D1111yescharacteristic
523C22×Q8—112no—
524C22×Q8—112no—
525C22×Q8—112no—
526C22×Q8—228no—
527C22×Q8—221no—
528C22×Q8—221no—
529C22×Q8—221no—
530C22×Q8C22×D1111yescharacteristic
531C23×C4—221no—
532C23×C4C22×D1111yescharacteristic
533#137—228no—
534C2×Q16—114no—
535C2×Q16—114no—
536C2×Q16—114no—
537C2×Q16—228no—
538C2×SD16—114no—
539C2×M16—112no—
540C22×C8—112no—
541C4⋊Q8—21no—
542C4⋊Q8C22×D1112yes—
543C4⋊Q8C22×D1112yes—
544#126—22no—
545#126—22no—
546#126—22no—
547#126—22no—
548#125—22no—
549#125—22no—
550#125—21no—
551#125—22no—
552#125C22×D1112yes—
553#124—22no—
554#124C22×D1112yes—
555#123—21no—
556#123—22no—
557#123—22no—
558#123—22no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—22no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8C22×D1112yes—
567C22⋊Q8C22×D1112yes—
568C22⋊Q8C22×D1111yescharacteristic
569C22⋊Q8C22×D1111yescharacteristic
570#121C22×D1111yescharacteristic
571#121C22×D1111yescharacteristic
572#120—21no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—22no—
576C4×Q8—114no—
577C4×Q8—114no—
578C4×Q8—114no—
579C4×Q8—114no—
580C4×Q8—222no—
581C4×Q8—222no—
582C4×Q8—222no—
583C4×Q8—224no—
584C4×Q8—222no—
585C4×Q8—224no—
586C4×Q8—222no—
587C4×Q8—222no—
588C4×Q8—222no—
589C4×Q8—222no—
590C4×Q8C22×D1112yes—
591C4×Q8C22×D1112yes—
592C4×Q8C22×D1112yes—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4C22×D1112yes—
598#117—22no—
599#117—21no—
600#117—22no—
601#117—22no—
602#117—112no—
603#117—112no—
604#117—221no—
605#117—221no—
606#117—224no—
607#117—224no—
608#117—224no—
609#117—224no—
610#117C22⋊D1111yescharacteristic
611#117C22⋊D1112yes—
612#117C22⋊D1111yescharacteristic
613#117C22×D1111yescharacteristic
614#117C22×D1111yescharacteristic
615#117C22×D1111yescharacteristic
616#117C22×D1112yes—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—111no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—222no—
622C2×C4⋊C4—222no—
623C2×C4⋊C4C22⋊D1111yescharacteristic
624C2×C4⋊C4C22⋊D1111yescharacteristic
625C2×C4⋊C4C22×D1111yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4C22⋊D1112yes—
629C2×C42—221no—
630C2×C42—222no—
631C2×C42—222no—
632C2×C42C22×D1112yes—
633#107—112no—
634#107—112no—
635#107—114no—
636#106—112no—
637#106—112no—
638#106—114no—
639C4⋊C8—114no—
640C4⋊C8—114no—
641#103—112no—
642#103—112no—
643#103—114no—
644#103—114no—
645#103—114no—
646#103—114no—
647#103—114no—
648#103—114no—
649#102—112no—
650#102—112no—
651C22⋊C8—111no—
652C22⋊C8—111no—
653C22⋊C8—112no—
654C22⋊C8—112no—
655C22⋊C8—112no—
656#97—114no—
657C4×C8—114no—
658C2×C11—22no—
659C2×C11—22no—
660C2×C11—41no—
661C2×C11—81no—
662C2×C11C2×#52511yescharacteristic
663C2×C11C2×#57811yescharacteristic
664C2×C11#358611yescharacteristic
665C24C2×C22⋊D1111yescharacteristic
666#41—24no—
667C2×Q8—21no—
668C2×Q8—22no—
669C2×Q8—24no—
670C2×Q8—118no—
671C2×Q8—114no—
672C2×Q8—228no—
673C2×Q8—228no—
674C2×Q8—228no—
675C2×Q8—228no—
676C2×Q8—228no—
677C2×Q8—224no—
678C2×Q8—222no—
679C2×Q8—222no—
680C2×Q8—222no—
681C2×Q8C23×D1112yes—
682C2×Q8C23×D1111yescharacteristic
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4C23×D1111yescharacteristic
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—228no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4C2×C22⋊D1112yes—
699C22×C4C2×C22⋊D1111yescharacteristic
700C22×C4C2×C22⋊D1111yescharacteristic
701C22×C4C2×C22⋊D1111yescharacteristic
702C22×C4C2×C22⋊D1112yes—
703C22×C4C23×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705C22×C4C23×D1111yescharacteristic
706Q16—228no—
707Q16—228no—
708Q16—228no—
709SD16—228no—
710M16—224no—
711C2×C8—112no—
712C2×C8—114no—
713C2×C8—112no—
714C2×C8—224no—
715C4⋊C4—21no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—22no—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—21no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—22no—
728C4⋊C4—112no—
729C4⋊C4—112no—
730C4⋊C4—221no—
731C4⋊C4—221no—
732C4⋊C4—224no—
733C4⋊C4—224no—
734C4⋊C4—224no—
735C4⋊C4—224no—
736C4⋊C4C2×C22⋊D1111yescharacteristic
737C4⋊C4C2×C22⋊D1111yescharacteristic
738C4⋊C4C2×C22⋊D1112yes—
739C4⋊C4C2×C22⋊D1111yescharacteristic
740C4⋊C4C2×C22⋊D1111yescharacteristic
741C4⋊C4C2×C22⋊D1112yes—
742C4⋊C4C23×D1112yes—
743C4⋊C4C23×D1111yescharacteristic
744C4⋊C4C23×D1111yescharacteristic
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—21no—
754C22⋊C4—22no—
755C22⋊C4—222no—
756C22⋊C4—222no—
757C22⋊C4C2×C22⋊D1112yes—
758C22⋊C4C2×C22⋊D1112yes—
759C22⋊C4C2×C22⋊D1112yes—
760C22⋊C4C2×C22⋊D1112yes—
761C42—22no—
762C42—22no—
763C42—22no—
764C42—21no—
765C42—222no—
766C42—222no—
767C42—224no—
768C42—224no—
769C42—224no—
770C42—224no—
771C42C2×C22⋊D1112yes—
772C42C2×C22⋊D1112yes—
773C42C23×D1112yes—
774C42C23×D1112yes—
775C11#6058311yescharacteristic, complemented, Sylow
776C23—22no—
777C23—22no—
778C23—21no—
779C23—41no—
780C23C22×C22⋊D1111yescharacteristic
781C23C22×C22⋊D1111yescharacteristic
782C23C22×C22⋊D1111yescharacteristic
783Q8—24no—
784Q8—22no—
785Q8—42no—
786Q8—82no—
787Q8—118no—
788Q8—228no—
789Q8—228no—
790Q8—228no—
791Q8—224no—
792D4—22no—
793D4—42no—
794D4—42no—
795D4—81no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—82no—
811C2×C4—81no—
812C2×C4—228no—
813C2×C4—228no—
814C2×C4—228no—
815C2×C4—224no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—442no—
819C2×C4—442no—
820C2×C4#41×D1114yes—
821C2×C4C22×C22⋊D1112yes—
822C2×C4C22×C22⋊D1112yes—
823C2×C4C22×C22⋊D1112yes—
824C2×C4C22×C22⋊D1112yes—
825C2×C4C22×C22⋊D1111yescharacteristic
826C2×C4C22×C22⋊D1111yescharacteristic
827C2×C4C22×C22⋊D1111yescharacteristic
828C2×C4C24×D1111yescharacteristic
829C8—222no—
830C8—222no—
831C8—224no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—44no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22#1062335912yes—
844C22#1062336912yes—
845C22C23×C22⋊D1111yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—22no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—228no—
858C4—442no—
859C4—442no—
860C4#1062335912yes—
861C4C2×#41×D1112yes—
862C2—22no—
863C2—22no—
864C2—41no—
865C2—81no—
866C2C2×#1062335911yescharacteristic
867C2C2×#1062336911yescharacteristic
868C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3495C2
socleC22×C11C23×D4
prime radicalC11×#525C22
hypercenter#3495D11
hypocenterC11#60583
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. C2×#10623047C2semidirect
2. #13078911C2semidirect
3. #13078839C2semidirect
4. #13078783C2semidirect
5. #13078742C2semidirect
6. #13078692C2semidirect
7. #13078651C2semidirect
8. #13078560C2semidirect
10. #13078452C2semidirect
11. #13078142C2semidirect
13. C2×#10622663C2semidirect
14. #13077482C2semidirect
15. #13077455C2semidirect
16. #13077274C2semidirect
54. #10622707C22semidirect
55. #10622704C22semidirect
56. #10622703C22semidirect
57. #10622703C22semidirect
58. #10622676C22semidirect
59. #10622676C22semidirect
60. #10622667C22semidirect
61. #10622667C22semidirect
78. #10622643C22semidirect
79. #10622643C22semidirect
80. #10622643C22semidirect
81. C4×#4326C22semidirect
82. C4×#4326C22semidirect
83. C4×#4326C22semidirect
84. #10622631C22semidirect
85. C4×#4324C22semidirect
775. C11#60583semidirect

Maximal subgroups

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

subgroupindex
C2×#106230472
#130789112
#130788392
#130787832
#130787422
#130786922
#130786512
#130785602
#130785252
#130784522
#130781422
#130778492
C2×#106226632
#130774822
#130774552
#130772742
C11×#34952
#6058311