Finite Group Databasebeta

← #15622582

Subgroups — #15622582

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623047C211yesmaximal, characteristic, complemented
2#13078902C214yesmaximal, complemented
3#13078839C214yesmaximal, complemented
4#13078783C212yesmaximal, complemented
5#13078734C212yesmaximal, complemented
6#13078692C212yesmaximal, complemented
7#13078643C212yesmaximal, complemented
8#13078552C211yesmaximal, characteristic, complemented
9#13078525C211yesmaximal, characteristic, complemented
10#13078452C212yesmaximal, complemented
11#13078133C212yesmaximal, complemented
12#13077849C211yesmaximal, characteristic, complemented
13C2×#10622653C211yesmaximal, characteristic, complemented
14#13077473C212yesmaximal, complemented
15#13077455C212yesmaximal, complemented
16#13077274C211yesmaximal, characteristic, complemented
17C11×#3494C211yesmaximal, characteristic
18C23×Dic22C2211yescharacteristic
19C11×#555—21no—
20C11×#553—21no—
21C11×#553—21no—
22C11×#551—22no—
23C11×#547—21no—
24C11×#546—22no—
25C11×#544C2211yescharacteristic
26C11×#542C2212yes—
27C11×#540C2212yes—
28C11×#535C2211yescharacteristic
29C11×#532C2212yes—
30C11×#529C2212yes—
31C11×#525C2211yescharacteristic
32C2×C11×#121C2211yescharacteristic
33C11×#520C2211yescharacteristic
34C11×#518C2211yescharacteristic
35C2×C11×#117C2211yescharacteristic
36C2×#67004C2212yes—
37C22×#4324C2212yes—
38C2×#66979C2211yescharacteristic
39#10623047—22no—
40#10623047—21no—
41#10623047—21no—
42#10623047C2212yes—
43#10623047C2212yes—
44#10623047C2214yescomplemented
45C2×#66940—21no—
46C2×#66940—21no—
47C2×#66930—22no—
48C2×C4×Dic22C2212yescomplemented
49C2×C4×Dic22C2212yescomplemented
50#10622846C2212yes—
51#10622828C2212yes—
52#10622820C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622707C2214yescomplemented
55#10622704C2214yescomplemented
56#10622688C2214yescomplemented
57#10622688C2214yescomplemented
58#10622676C2214yescomplemented
59#10622676C2214yescomplemented
60#10622667C2214yescomplemented
61#10622667C2214yescomplemented
62#10622663C2212yescomplemented
63#10622663C2212yescomplemented
64#10622658C2212yescomplemented
65#10622657C2211yescharacteristic, complemented
66#10622656C2211yescharacteristic, complemented
67#10622653C2214yes—
68#10622653C2212yes—
69#10622653C2212yes—
70#10622653C2212yescomplemented
71#10622653C2212yescomplemented
72#10622648C2214yes—
73#10622648C2212yescomplemented
74#10622647C2212yes—
75#10622647C2211yescharacteristic, complemented
76#10622646C2212yes—
77#10622646C2211yescharacteristic, complemented
78#10622643C2214yescomplemented
79C4×#4326C2214yescomplemented
80#10622631C2214yescomplemented
81#10622631C2214yescomplemented
82#10622631C2214yescomplemented
83C4×#4324C2214yescomplemented
84C4×#4324C2214yescomplemented
85C4×#4324C2214yescomplemented
86#10622617C2212yes—
87#10622613C2214yescomplemented
88#10622612C2212yes—
89#10622611C2212yes—
90#10622610C2212yes—
91C2×#66874C2212yes—
92#10622577C2212yes—
93#10622539C2212yescomplemented
94#10622538C2212yescomplemented
95C2×C11×#41—22no—
96C2×C11×#41C2311yescharacteristic
97C22×D4×C11—21no—
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×Dic11—21no—
101C22×Dic22—21no—
102C22×Dic22—21no—
103C22×Dic22—21no—
104C22×Dic22—28no—
105C22×Dic22C2312yes—
106C22×Dic22C2312yes—
107C22×Dic22C2312yes—
108C11×C4⋊Q8—21no—
109C11×C4⋊Q8C2312yes—
110C11×#127C2312yes—
111C11×#126—22no—
112C11×#126—22no—
113C11×#125—21no—
114C11×#125C2312yes—
115C11×#124—22no—
116C11×#124—22no—
117C11×#124C2312yes—
118C11×#123—21no—
119C11×#123—22no—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8C2311yescharacteristic
126C11×C22⋊Q8C2311yescharacteristic
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—22no—
130C11×#121—21no—
131C11×#121—21no—
132C11×#121—22no—
133C11×#121—22no—
134C11×#121C2312yes—
135C11×#121C2312yes—
136C11×#121C2311yescharacteristic
137C11×#121C2311yescharacteristic
138C11×#120—21no—
139C11×#120—22no—
140C4×Q8×C11C2312yes—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11—21no—
145C4×D4×C11—21no—
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C4×D4×C11C2312yes—
149C4×D4×C11C2312yes—
150C4×D4×C11C2312yes—
151C11×#117—21no—
152C11×#117—22no—
153C11×#117D412yes—
154C11×#117D411yescharacteristic
155C11×#117D411yescharacteristic
156C11×#117C2311yescharacteristic
157C11×#117C2311yescharacteristic
158C11×#117C2311yescharacteristic
159C11×#117C2312yes—
160C2×C11×C4⋊C4—21no—
161C2×C11×C4⋊C4D411yescharacteristic
162C2×C11×C4⋊C4D411yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4—21no—
165C2×C11×C22⋊C4—22no—
166C2×C11×C22⋊C4D412yes—
167C2×C42×C11C2312yes—
168C2×C22⋊Dic11—21no—
169#67004—28no—
170C2×#4326C2314yes—
171C2×#4324—28no—
172C2×#4324C2314yes—
173C2×#4324C2314yes—
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—22no—
191#66940—22no—
192#66940—24no—
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#66899C2312yes—
207#66899C2312yes—
208#66896C2314yes—
209#66896C2314yes—
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#60582—111nomaximal, Sylow
232C24×C11—21no—
233C24×C11C2×D411yescharacteristic
234C11×#41—24no—
235C11×#41—84no—
236C2×Q8×C11—22no—
237C2×Q8×C11C2411yescharacteristic
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11—22no—
241C2×D4×C11—21no—
242C2×D4×C11—22no—
243C2×D4×C11—21no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—24no—
247C2×D4×C11—82no—
248C2×D4×C11C2412yes—
249C2×D4×C11C2411yescharacteristic
250C22×C4×C11—24no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C22×Dic11—28no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C2×Dic22—28no—
271C2×Dic22—28no—
272C2×Dic22—28no—
273C2×Dic22—28no—
274C2×Dic22—28no—
275C2×Dic22—22no—
276C2×Dic22—22no—
277C2×Dic22—22no—
278C2×Dic22—24no—
279C2×Dic22#4118yescomplemented
280C2×Dic22C2414yes—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2×D411yescharacteristic
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D411yescharacteristic
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2412yes—
295C11×C4⋊C4C2411yescharacteristic
296C11×C4⋊C4C2411yescharacteristic
297C11×C22⋊C4—21no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4—22no—
306C11×C22⋊C4—21no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—21no—
309C11×C22⋊C4C2×D412yes—
310C11×C22⋊C4C2×D412yes—
311C11×C22⋊C4C2×D412yes—
312C11×C22⋊C4C2×D412yes—
313C42×C11—22no—
314C42×C11—21no—
315C42×C11C2×D412yes—
316C42×C11C2×D412yes—
317C42×C11C2412yes—
318C42×C11C2412yes—
319C22⋊Dic11—22no—
320C22⋊Dic11—22no—
321#4326—28no—
322#4324—28no—
323#4324—28no—
324#4324—28no—
325C4⋊Dic11—21no—
326C4⋊Dic11—21no—
327C4⋊Dic11C2412yes—
328C4⋊Dic11C2412yes—
329Dic11⋊C4—24no—
330Dic11⋊C4—24no—
331Dic11⋊C4—24no—
332Dic11⋊C4—24no—
333C4×Dic11—24no—
334C4×Dic11—24no—
335C4×Dic11—24no—
336C4×Dic11—24no—
337C4×Dic11—22no—
338C4×Dic11—22no—
339#4318—24no—
340C2×C11⋊C8—24no—
341C2×C11⋊C8C2412yes—
342C2×C11⋊C8C2414yes—
343C2×C11⋊C8C2412yes—
344#3494D1111yescharacteristic
345C2×#519—111no—
346#3126—114no—
347#3121—114no—
348#3117—112no—
349#3112—112no—
350#3108—112no—
351#3103—112no—
352#3094—111no—
353#3091—111no—
354#3082—112no—
355#3043—112no—
356#3004—111no—
357C2×#448—111no—
358#2949—112no—
359#2947—112no—
360#2924—111no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—21no—
365C23×C11—41no—
366C23×C11—42no—
367C23×C11—81no—
368C23×C11—81no—
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372Q8×C11—22no—
373Q8×C11—82no—
374D4×C11—24no—
375D4×C11—22no—
376D4×C11—42no—
377D4×C11—44no—
378D4×C11—42no—
379D4×C11—42no—
380D4×C11—82no—
381D4×C11—82no—
382D4×C11—81no—
383D4×C11—82no—
384C2×C4×C11—22no—
385C2×C4×C11—24no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—21no—
393C2×C4×C11—22no—
394C2×C4×C11—42no—
395C2×C4×C11—42no—
396C2×C4×C11—82no—
397C2×C4×C11—82no—
398C2×C4×C11—82no—
399C2×C4×C11—81no—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D412yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C2×#4114yes—
408C2×C4×C11C2511yescharacteristic
409C2×Dic11—28no—
410C2×Dic11—28no—
411C2×Dic11—28no—
412C2×Dic11—24no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417Dic22—28no—
418Dic22—28no—
419Dic22—28no—
420Dic22—24no—
421Dic22C2×#4118yes—
422C11⋊C8—22no—
423C11⋊C8—22no—
424C11⋊C8—24no—
425C23×Q8—111no—
426C2×#137—112no—
427C22×SD16—112no—
428#555—21no—
429#553—21no—
430#553—21no—
431#551—22no—
432#547—21no—
433#546—22no—
434#544C2×D1111yescharacteristic
435#542C2×D1112yes—
436#540C2×D1112yes—
437#535C2×D1111yescharacteristic
438#532C2×D1112yes—
439#529C2×D1112yes—
440#525C2×D1111yescharacteristic
441C2×#121C2×D1111yescharacteristic
442#520C2×D1111yescharacteristic
443#519—112no—
444#519—114no—
445#519—112no—
446#519—222no—
447#519—221no—
448#519—221no—
449#518C2×D1111yescharacteristic
450C2×C4×Q8—112no—
451C2×C4×Q8—112no—
452C2×C4×Q8—221no—
453C2×C4×Q8—221no—
454C2×#117—111no—
455C2×#117—222no—
456C2×#117C2×D1111yescharacteristic
457#485—112no—
458#484—111no—
459#483—111no—
460#482—112no—
461#482—114no—
462#481—111no—
463#481—112no—
464#480—111no—
465#480—112no—
466#479—114no—
467#479—114no—
468#477—114no—
469#475—114no—
470#464—114no—
471#464—114no—
472#460—114no—
473#460—114no—
474#451—112no—
475#451—112no—
476#448—112no—
477#448—112no—
478#448—112no—
479#448—114no—
480#448—112no—
481#441—114no—
482#440—114no—
483#440—114no—
484#440—114no—
485C4×Q16—114no—
486C4×SD16—114no—
487C4×SD16—114no—
488C4×SD16—114no—
489#433—114no—
490#432—112no—
491#431—112no—
492#428—112no—
493#427—112no—
494#424—112no—
495#419—112no—
496#418—112no—
497#416—112no—
498C2×#103—112no—
499#407—111no—
500C2×C22⋊C8—111no—
501#405—112no—
502C22×C11—21no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—44no—
510C22×C11—42no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11—42no—
514C22×C11—41no—
515C22×C11—42no—
516C22×C11—162no—
517C22×C11#52512yes—
518C22×C11#57712yes—
519C22×C11C23×D411yescharacteristic
520C4×C11—22no—
521C4×C11—22no—
522C4×C11—21no—
523C4×C11—21no—
524C4×C11—22no—
525C4×C11—22no—
526C4×C11—41no—
527C4×C11—41no—
528C4×C11—42no—
529C4×C11—41no—
530C4×C11#52512yes—
531C4×C11C22×#4112yes—
532Dic11—28no—
533Dic11—42no—
534Dic11—42no—
535C2×#41—22no—
536C2×#41C22×D1111yescharacteristic
537C22×Q8—112no—
538C22×Q8—112no—
539C22×Q8—112no—
540C22×Q8—228no—
541C22×Q8—221no—
542C22×Q8—221no—
543C22×Q8—221no—
544C22×D4—21no—
545C22×D4C22×D1111yescharacteristic
546C23×C4—221no—
547C23×C4C22×D1111yescharacteristic
548#137—228no—
549C2×Q16—114no—
550C2×SD16—114no—
551C2×SD16—114no—
552C2×SD16—114no—
553C2×SD16—228no—
554C2×M16—112no—
555C22×C8—112no—
556C4⋊Q8—21no—
557C4⋊Q8C22×D1112yes—
558#127C22×D1112yes—
559#126—22no—
560#126—22no—
561#125—21no—
562#125C22×D1112yes—
563#124—22no—
564#124—22no—
565#124C22×D1112yes—
566#123—21no—
567#123—22no—
568#123—22no—
569#123—22no—
570#123—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8C22×D1111yescharacteristic
574C22⋊Q8C22×D1111yescharacteristic
575#121—21no—
576#121—21no—
577#121—22no—
578#121—21no—
579#121—21no—
580#121—22no—
581#121—22no—
582#121C22×D1112yes—
583#121C22×D1112yes—
584#121C22×D1111yescharacteristic
585#121C22×D1111yescharacteristic
586#120—21no—
587#120—22no—
588C4×Q8—114no—
589C4×Q8—114no—
590C4×Q8—114no—
591C4×Q8—114no—
592C4×Q8—222no—
593C4×Q8—222no—
594C4×Q8—222no—
595C4×Q8—222no—
596C4×Q8—224no—
597C4×Q8—224no—
598C4×Q8—222no—
599C4×Q8—222no—
600C4×Q8—222no—
601C4×Q8—222no—
602C4×Q8C22×D1112yes—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—22no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4C22×D1112yes—
611C4×D4C22×D1112yes—
612C4×D4C22×D1112yes—
613#117—21no—
614#117—22no—
615#117—112no—
616#117—112no—
617#117—221no—
618#117—221no—
619#117—224no—
620#117—224no—
621#117—224no—
622#117—224no—
623#117C22⋊D1112yes—
624#117C22⋊D1111yescharacteristic
625#117C22⋊D1111yescharacteristic
626#117C22×D1111yescharacteristic
627#117C22×D1111yescharacteristic
628#117C22×D1111yescharacteristic
629#117C22×D1112yes—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—222no—
634C2×C4⋊C4—222no—
635C2×C4⋊C4C22⋊D1111yescharacteristic
636C2×C4⋊C4C22⋊D1111yescharacteristic
637C2×C4⋊C4C22×D1111yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—221no—
641C2×C22⋊C4C22⋊D1112yes—
642C2×C42—221no—
643C2×C42—222no—
644C2×C42—222no—
645C2×C42C22×D1112yes—
646#107—112no—
647#107—112no—
648#107—114no—
649#106—112no—
650#106—112no—
651#106—114no—
652C4⋊C8—114no—
653C4⋊C8—114no—
654#103—112no—
655#103—112no—
656#103—114no—
657#103—114no—
658#103—114no—
659#103—114no—
660#102—112no—
661#102—112no—
662#102—114no—
663#102—114no—
664C22⋊C8—111no—
665C22⋊C8—111no—
666C22⋊C8—112no—
667C22⋊C8—112no—
668C22⋊C8—112no—
669#97—114no—
670C4×C8—114no—
671C2×C11—22no—
672C2×C11—22no—
673C2×C11—41no—
674C2×C11—81no—
675C2×C11—82no—
676C2×C11C2×#52511yescharacteristic
677C2×C11C2×#57711yescharacteristic
678C2×C11#358611yescharacteristic
679C24—21no—
680C24C2×C22⋊D1111yescharacteristic
681#41—24no—
682#41—84no—
683C2×Q8—22no—
684C2×Q8—118no—
685C2×Q8—114no—
686C2×Q8—228no—
687C2×Q8—228no—
688C2×Q8—228no—
689C2×Q8—228no—
690C2×Q8—228no—
691C2×Q8—224no—
692C2×Q8—222no—
693C2×Q8—222no—
694C2×Q8—222no—
695C2×Q8C23×D1111yescharacteristic
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—22no—
701C2×D4—24no—
702C2×D4—21no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—82no—
706C2×D4C23×D1112yes—
707C2×D4C23×D1111yescharacteristic
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—228no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4C2×C22⋊D1112yes—
721C22×C4C2×C22⋊D1111yescharacteristic
722C22×C4C2×C22⋊D1111yescharacteristic
723C22×C4C2×C22⋊D1111yescharacteristic
724C22×C4C2×C22⋊D1112yes—
725C22×C4C23×D1111yescharacteristic
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1111yescharacteristic
728Q16—228no—
729SD16—228no—
730SD16—228no—
731SD16—228no—
732M16—224no—
733C2×C8—112no—
734C2×C8—114no—
735C2×C8—112no—
736C2×C8—224no—
737C4⋊C4—21no—
738C4⋊C4—22no—
739C4⋊C4—21no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—21no—
744C4⋊C4—112no—
745C4⋊C4—112no—
746C4⋊C4—221no—
747C4⋊C4—221no—
748C4⋊C4—224no—
749C4⋊C4—224no—
750C4⋊C4—224no—
751C4⋊C4—224no—
752C4⋊C4C2×C22⋊D1111yescharacteristic
753C4⋊C4C2×C22⋊D1111yescharacteristic
754C4⋊C4C2×C22⋊D1111yescharacteristic
755C4⋊C4C2×C22⋊D1111yescharacteristic
756C4⋊C4C2×C22⋊D1112yes—
757C4⋊C4C2×C22⋊D1112yes—
758C4⋊C4C23×D1112yes—
759C4⋊C4C23×D1111yescharacteristic
760C4⋊C4C23×D1111yescharacteristic
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—21no—
771C22⋊C4—22no—
772C22⋊C4—21no—
773C22⋊C4—222no—
774C22⋊C4—222no—
775C22⋊C4C2×C22⋊D1112yes—
776C22⋊C4C2×C22⋊D1112yes—
777C22⋊C4C2×C22⋊D1112yes—
778C22⋊C4C2×C22⋊D1112yes—
779C42—22no—
780C42—21no—
781C42—222no—
782C42—222no—
783C42—224no—
784C42—224no—
785C42—224no—
786C42—224no—
787C42C2×C22⋊D1112yes—
788C42C2×C22⋊D1112yes—
789C42C23×D1112yes—
790C42C23×D1112yes—
791C11#6058211yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—21no—
796C23—41no—
797C23—42no—
798C23—81no—
799C23—81no—
800C23C22×C22⋊D1111yescharacteristic
801C23C22×C22⋊D1111yescharacteristic
802C23C22×C22⋊D1111yescharacteristic
803Q8—22no—
804Q8—82no—
805Q8—118no—
806Q8—228no—
807Q8—228no—
808Q8—228no—
809Q8—224no—
810D4—24no—
811D4—22no—
812D4—42no—
813D4—44no—
814D4—42no—
815D4—42no—
816D4—82no—
817D4—82no—
818D4—81no—
819D4—82no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—82no—
833C2×C4—82no—
834C2×C4—82no—
835C2×C4—81no—
836C2×C4—228no—
837C2×C4—228no—
838C2×C4—228no—
839C2×C4—224no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—442no—
843C2×C4—442no—
844C2×C4#41×D1114yes—
845C2×C4C22×C22⋊D1112yes—
846C2×C4C22×C22⋊D1112yes—
847C2×C4C22×C22⋊D1112yes—
848C2×C4C22×C22⋊D1112yes—
849C2×C4C22×C22⋊D1111yescharacteristic
850C2×C4C22×C22⋊D1111yescharacteristic
851C2×C4C22×C22⋊D1111yescharacteristic
852C2×C4C24×D1111yescharacteristic
853C8—222no—
854C8—222no—
855C8—224no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—44no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—41no—
869C22—42no—
870C22—162no—
871C22#1062335912yes—
872C22#1062336712yes—
873C22C23×C22⋊D1111yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—21no—
879C4—21no—
880C4—41no—
881C4—42no—
882C4—41no—
883C4—41no—
884C4—228no—
885C4—442no—
886C4—442no—
887C4#1062335912yes—
888C4C2×#41×D1112yes—
889C2—22no—
890C2—22no—
891C2—41no—
892C2—82no—
893C2—81no—
894C2C2×#1062335911yescharacteristic
895C2C2×#1062336711yescharacteristic
896C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3494C2
socleC22×C11C23×D4
hypercenter#3494D11
hypocenterC11#60582
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3494

Complements

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

NH ≅ G/Ntype
1. C2×#10623047C2semidirect
2. #13078902C2semidirect
3. #13078839C2semidirect
4. #13078783C2semidirect
5. #13078734C2semidirect
6. #13078692C2semidirect
7. #13078643C2semidirect
8. #13078552C2semidirect
9. #13078525C2semidirect
10. #13078452C2semidirect
11. #13078133C2semidirect
12. #13077849C2semidirect
13. C2×#10622653C2semidirect
14. #13077473C2semidirect
15. #13077455C2semidirect
16. #13077274C2semidirect
44. #10623047C22semidirect
48. C2×C4×Dic22C22semidirect
49. C2×C4×Dic22C22semidirect
54. #10622707C22semidirect
55. #10622704C22semidirect
56. #10622688C22semidirect
57. #10622688C22semidirect
58. #10622676C22semidirect
59. #10622676C22semidirect
60. #10622667C22semidirect
61. #10622667C22semidirect
62. #10622663C22semidirect
63. #10622663C22semidirect
64. #10622658C22semidirect
65. #10622657C22semidirect
66. #10622656C22semidirect
70. #10622653C22semidirect
71. #10622653C22semidirect
73. #10622648C22semidirect
75. #10622647C22semidirect
77. #10622646C22semidirect
78. #10622643C22semidirect
79. C4×#4326C22semidirect
80. #10622631C22semidirect
81. #10622631C22semidirect
82. #10622631C22semidirect
83. C4×#4324C22semidirect
84. C4×#4324C22semidirect
85. C4×#4324C22semidirect
87. #10622613C22semidirect
93. #10622539C22semidirect
94. #10622538C22semidirect
279. C2×Dic22#41semidirect
791. C11#60582semidirect

Maximal subgroups

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

subgroupindex
C2×#106230472
#130789022
#130788392
#130787832
#130787342
#130786922
#130786432
#130785522
#130785252
#130784522
#130781332
#130778492
C2×#106226532
#130774732
#130774552
#130772742
C11×#34942
#6058211