Finite Group Databasebeta

← #15622718

Subgroups — #15622718

Order 2816.

2074 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082368C211yesmaximal, characteristic, complemented
2#13078878C214yesmaximal, complemented
3#13078830C214yesmaximal, complemented
4#13078787C212yesmaximal, complemented
5#13078715C212yesmaximal, complemented
6#13078663C212yesmaximal, complemented
7#13078655C212yesmaximal, complemented
8#13078539C211yesmaximal, characteristic, complemented
9C2×#10622583C211yesmaximal, characteristic, complemented
10#13078467C212yesmaximal, complemented
11#13078166C212yesmaximal, complemented
12#13077876C211yesmaximal, characteristic, complemented
13#13077834C211yesmaximal, characteristic
14#13077489C212yesmaximal, complemented
15#13077455C212yesmaximal, complemented
16#13077274C211yesmaximal, characteristic, complemented
17C2×C11×#520C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C11×#520—21no—
20C11×#520—22no—
21C11×#520—21no—
22C11×#520C2214yes—
23C11×#520C2212yes—
24C11×#520C2212yes—
25C2×C4×Q8×C11C2212yes—
26C2×C4×D4×C11—22no—
27C2×C4×D4×C11C2212yes—
28C2×C11×#117—21no—
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4—21no—
31C22×C11×C4⋊C4C2211yescharacteristic
32C2×#67004C2212yes—
33C2×#67003C2212yes—
34#10623322C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36#10623065C2212yescomplemented
37#10623064—21no—
38#10623062—22no—
39#10623060—21no—
40#10623057C2211yescharacteristic, complemented
41#10623054C2211yescharacteristic, complemented
42#10623050C2211yescharacteristic, complemented
43#10623049C2212yescomplemented
44#10623047C2211yescharacteristic, complemented
45#10623044—21no—
46#10623042—21no—
47#10623026—22no—
48#10623010C2212yes—
49#10623001C2212yes—
50#10622852C2212yes—
51#10622852C2214yes—
52#10622851C2212yes—
53#10622846C2212yes—
54#10622845C2212yes—
55#10622841C2212yes—
56#10622841C2211yescharacteristic
57#10622840C2211yescharacteristic
58#10622831C2211yescharacteristic
59#10622831C2212yes—
60#10622830C2211yescharacteristic
61#10622820C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63#10622644C2214yescomplemented
64#10622643C2214yescomplemented
65C4×#4326C2214yescomplemented
66C4×#4326C2214yescomplemented
67#10622641C2214yescomplemented
68#10622639C2214yescomplemented
69#10622635C2214yescomplemented
70#10622634C2214yescomplemented
71#10622632C2214yescomplemented
72#10622631C2214yescomplemented
73#10622631C2214yescomplemented
74C4×#4324C2214yescomplemented
75#10622629C2214yescomplemented
76C4×#4323C2214yescomplemented
77#10622622C2214yescomplemented
78#10622620C2214yescomplemented
79#10622613C2214yescomplemented
80#10622612C2212yescomplemented
81#10622610C2212yescomplemented
82#10622584C2212yescomplemented
83#10622583C2212yes—
84#10622583C2212yes—
85#10622583C2212yes—
86#10622583C2214yescomplemented
87C2×#66874C2212yescomplemented
88#10622581C2212yes—
89#10622580C2212yescomplemented
90#10622579C2212yescomplemented
91#10622577C2212yescomplemented
92C2×#66871C2212yescomplemented
93#10622539C2212yes—
94#10622538C2212yes—
95C2×C11×#41—28no—
96C2×C11×#41—21no—
97C2×C11×#41—21no—
98C2×C11×#41C2312yes—
99C2×C11×#41C2312yes—
100C22×Q8×C11C2311yescharacteristic
101C22×D4×C11—21no—
102C22×D4×C11C2311yescharacteristic
103C23×C4×C11—21no—
104C23×C4×C11—21no—
105C23×C4×C11—22no—
106C23×C4×C11C2311yescharacteristic
107C2×#4339C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C4×Q8×C11—22no—
110C4×Q8×C11—22no—
111C4×Q8×C11C2314yes—
112C4×Q8×C11C2314yes—
113C4×D4×C11—24no—
114C4×D4×C11—24no—
115C4×D4×C11—24no—
116C4×D4×C11—24no—
117C4×D4×C11—22no—
118C4×D4×C11—22no—
119C4×D4×C11C2314yes—
120C4×D4×C11C2314yes—
121C11×#117—22no—
122C11×#117—24no—
123C11×#117—22no—
124C11×#117D411yescharacteristic
125C11×#117D412yes—
126C11×#117D411yescharacteristic
127C11×#117C2311yescharacteristic
128C11×#117C2312yes—
129C11×#117C2311yescharacteristic
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—22no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—22no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4—24no—
137C2×C11×C4⋊C4D411yescharacteristic
138C2×C11×C4⋊C4D411yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C22⋊C4—22no—
143C2×C11×C22⋊C4D412yes—
144C2×C42×C11—22no—
145C2×C42×C11C2312yes—
146#67006—21no—
147C2×C22⋊Dic11—21no—
148#67004—28no—
149#67003—28no—
150C2×#4326C2312yes—
151C2×#4326C2314yes—
152C2×#4325C2312yes—
153C2×#4324C2312yes—
154C2×#4324C2314yes—
155C2×#4323C2312yes—
156#66983C2311yescharacteristic
157#66983C2311yescharacteristic
158#66982—22no—
159#66982—21no—
160C4×C22⋊D11—22no—
161C4×C22⋊D11—21no—
162C4×C22⋊D11—21no—
163#66979—22no—
164#66979C2311yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166#66977—22no—
167#66977—21no—
168#66977—21no—
169#66977C2311yescharacteristic
170#66977C2312yes—
171#66977C2311yescharacteristic
172#66977C2312yes—
173C2×Dic11⋊C4—21no—
174C2×#4318C2312yes—
175C22×C11⋊C8C2312yes—
176#66951—22no—
177#66950—21no—
178#66950—21no—
179#66949—22no—
180#66945—21no—
181C4⋊C4×D11—21no—
182#66943—21no—
183#66942—22no—
184#66942—22no—
185#66941—21no—
186#66940—21no—
187#66940—21no—
188#66939—22no—
189#66938—22no—
190#66936—22no—
191(C22⋊D11)⋊C4—22no—
192#66932—22no—
193#66932—22no—
194#66931—22no—
195#66930—22no—
196#66929—22no—
197#66928C2312yes—
198C4×D44C2312yes—
199#66925—22no—
200#66923—22no—
201#66923C2312yes—
202#66922C2312yes—
203#66922C2312yes—
204C4×Dic22—22no—
205C4×Dic22C2312yes—
206C4×Dic22C2312yes—
207C4×Dic22C2312yes—
208#66899C2312yes—
209#66899C2314yes—
210#66899C2312yes—
211#66896C2312yes—
212#66896C2314yes—
213#66896C2312yes—
214C22⋊(C11⋊C8)C2311yescharacteristic
215C22⋊(C11⋊C8)C2312yes—
216C22⋊(C11⋊C8)C2311yescharacteristic
217C22⋊(C11⋊C8)C2312yes—
218C22⋊(C11⋊C8)C2312yes—
219#66874C2314yes—
220#66874C2314yes—
221#66874C2314yes—
222#66873C2314yes—
223#66872C2314yes—
224#66871C2314yes—
225#66871C2314yes—
226#66871C2314yes—
227C4⋊(C11⋊C8)C2314yes—
228C4⋊(C11⋊C8)C2314yes—
229#66867C2314yes—
230C4×C11⋊C8C2314yes—
231#60589—111nomaximal, Sylow
232C24×C11—21no—
233C24×C11C2×D411yescharacteristic
234C11×#41—28no—
235C11×#41—28no—
236C11×#41—24no—
237C11×#41—24no—
238C11×#41—24no—
239C11×#41#4118yes—
240C2×Q8×C11—24no—
241C2×Q8×C11—21no—
242C2×Q8×C11C2412yes—
243C2×D4×C11—28no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—24no—
247C2×D4×C11—21no—
248C2×D4×C11C2412yes—
249C22×C4×C11—28no—
250C22×C4×C11—21no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—24no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—24no—
258C22×C4×C11—24no—
259C22×C4×C11—84no—
260C22×C4×C11—82no—
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D412yes—
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2411yescharacteristic
269C2×C22⋊D11—21no—
270C2×C22⋊D11—21no—
271C2×C22⋊D11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274#4339—24no—
275C2×D44C2411yescharacteristic
276C2×C4×D11—21no—
277C2×C4×D11—22no—
278C2×Dic22—21no—
279C2×Dic22—22no—
280C2×Dic22—24no—
281C2×Dic22C2411yescharacteristic
282C2×Dic22C2412yes—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—24no—
286C11×C4⋊C4—24no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2×D411yescharacteristic
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2×D411yescharacteristic
294C11×C4⋊C4C2414yes—
295C11×C22⋊C4—24no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4C2×D412yes—
298C11×C22⋊C4C2×D412yes—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C42×C11—24no—
302C42×C11—24no—
303C42×C11C2×D412yes—
304C42×C11C2×D412yes—
305C42×C11C2412yes—
306C42×C11C2412yes—
307C22⋊Dic11—21no—
308C22⋊Dic11—21no—
309C22⋊Dic11—22no—
310C22⋊Dic11—21no—
311C22⋊Dic11—22no—
312#4326—24no—
313#4326—28no—
314#4325—24no—
315#4324—24no—
316#4324—28no—
317#4323—24no—
318(C2×D11)⋊C4—21no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—21no—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11—21no—
327C4⋊Dic11C2411yescharacteristic
328C4⋊Dic11C2412yes—
329C4⋊Dic11C2411yescharacteristic
330Dic11⋊C4—21no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337Dic11⋊C4—21no—
338Dic11⋊C4—22no—
339C4×Dic11—22no—
340C4×Dic11—22no—
341C4×Dic11—22no—
342C4×Dic11—21no—
343#4318—24no—
344C2×C11⋊C8—24no—
345C2×C11⋊C8C2412yes—
346C2×C11⋊C8C2414yes—
347C2×C11⋊C8C2412yes—
348#3495—111no—
349C2×#520D1111yescharacteristic, complemented
350#3124—114no—
351#3120—114no—
352#3117—112no—
353#3110—112no—
354#3105—112no—
355#3104—112no—
356#3092—111no—
357C2×#484—111no—
358#3083—112no—
359#3046—112no—
360#3007—111no—
361#3002—111no—
362#2951—112no—
363#2947—112no—
364#2924—111no—
365C23×C11—24no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—41no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11C22×D411yescharacteristic
373C23×C11C22×D411yescharacteristic
374C23×C11C22×D411yescharacteristic
375C22×D11—21no—
376Q8×C11—24no—
377Q8×C11—22no—
378Q8×C11C2×#4114yes—
379D4×C11—28no—
380D4×C11—24no—
381D4×C11—28no—
382D4×C11—22no—
383D4×C11C2×#4114yes—
384C2×C4×C11—24no—
385C2×C4×C11—28no—
386C2×C4×C11—22no—
387C2×C4×C11—24no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—28no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—24no—
395C2×C4×C11—42no—
396C2×C4×C11—44no—
397C2×C4×C11—84no—
398C2×C4×C11—84no—
399C2×C4×C11—82no—
400C2×C4×C11—82no—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D412yes—
406C2×C4×C11C22×D412yes—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C2×#4114yes—
409C2×C4×C11C2511yescharacteristic
410C22⋊D11—42no—
411C22⋊D11—42no—
412C22⋊D11—81no—
413C2×Dic11—21no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—42no—
419C2×Dic11—81no—
420D44—22no—
421C4×D11—42no—
422C4×D11—82no—
423Dic22—24no—
424Dic22—22no—
425Dic22—42no—
426Dic22—82no—
427C11⋊C8—22no—
428C11⋊C8—22no—
429C11⋊C8—24no—
430C22×#41C2×D1111yescharacteristic
431C2×#137—112no—
432C2×#135—112no—
433#556—221no—
434#554—221no—
435#552—221no—
436#552—222no—
437#552—221no—
438#551—222no—
439#544—111no—
440#542—112no—
441#541—112no—
442#536—111no—
443#533—112no—
444#529—112no—
445#525—111no—
446C2×C22⋊Q8—111no—
447#520—22no—
448#520—21no—
449#520—21no—
450#520—111no—
451#520C2×D1112yes—
452#520C2×D1114yes—
453#520C2×D1112yes—
454#519—111no—
455C2×C4×Q8C2×D1112yes—
456C2×C4×D4—22no—
457C2×C4×D4C2×D1112yes—
458C2×#117—21no—
459C2×#117C2×D1111yescharacteristic
460C22×C4⋊C4—21no—
461C22×C4⋊C4C2×D1111yescharacteristic
462#484—112no—
463#484—112no—
464#484—114no—
465#484—112no—
466#483—112no—
467#481—112no—
468#480—112no—
469#479—114no—
470#478—114no—
471#477—114no—
472#474—114no—
473#464—114no—
474#463—114no—
475#462—114no—
476#461—114no—
477#452—112no—
478#452—114no—
479#451—111no—
480#451—112no—
481#450—112no—
482#450—111no—
483#449—112no—
484#448—111no—
485#447—111no—
486#441—114no—
487#440—114no—
488#440—114no—
489#440—114no—
490C4×Q16—114no—
491C4×Q16—114no—
492C4×SD16—114no—
493C4×D8—114no—
494#433—114no—
495#432—112no—
496#431—112no—
497#428—112no—
498C2×#107—112no—
499#424—112no—
500#417—112no—
501#417—112no—
502#416—112no—
503C2×#103—112no—
504#407—111no—
505C2×C22⋊C8—111no—
506#405—112no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—24no—
514C22×C11—21no—
515C22×C11—44no—
516C22×C11—48no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11#52512yes—
520C22×C11#57812yes—
521C22×C11C23×D411yescharacteristic
522C2×D11—41no—
523C2×D11—41no—
524C2×D11—41no—
525C4×C11—22no—
526C4×C11—22no—
527C4×C11—21no—
528C4×C11—24no—
529C4×C11—21no—
530C4×C11—22no—
531C4×C11—22no—
532C4×C11—44no—
533C4×C11#52512yes—
534C4×C11C22×#4112yes—
535Dic11—41no—
536Dic11—42no—
537Dic11—42no—
538Dic11—41no—
539Dic11—41no—
540C2×#41—28no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—111no—
544C2×#41C22×D1112yes—
545C2×#41C22×D1112yes—
546C22×Q8—111no—
547C22×Q8C22×D1111yescharacteristic
548C22×D4—21no—
549C22×D4C22×D1111yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—22no—
553C23×C4C22×D1111yescharacteristic
554#137—228no—
555#135—228no—
556C2×Q16—112no—
557C2×Q16—114no—
558C2×SD16—112no—
559C2×SD16—112no—
560C2×SD16—114no—
561C2×D8—112no—
562C2×M16—112no—
563C22×C8—112no—
564C4⋊Q8—112no—
565C4⋊Q8—112no—
566C4⋊Q8—221no—
567#126—222no—
568#126—222no—
569#126—222no—
570#126—222no—
571#125—112no—
572#125—222no—
573#125—222no—
574#125—221no—
575#125—222no—
576#124—112no—
577#124—222no—
578#123—221no—
579#123—222no—
580#123—222no—
581#123—222no—
582C22⋊Q8—112no—
583C22⋊Q8—112no—
584C22⋊Q8—111no—
585C22⋊Q8—111no—
586C22⋊Q8—221no—
587C22⋊Q8—221no—
588C22⋊Q8—222no—
589C22⋊Q8—221no—
590C22⋊Q8—221no—
591C22⋊Q8—222no—
592C22⋊Q8—222no—
593#121—111no—
594#121—111no—
595#120—221no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—112no—
599C4×Q8—112no—
600C4×Q8—112no—
601C4×Q8—221no—
602C4×Q8—221no—
603C4×Q8—222no—
604C4×Q8C22×D1114yes—
605C4×Q8C22×D1114yes—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—24no—
609C4×D4—24no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—112no—
613C4×D4—221no—
614C4×D4—221no—
615C4×D4—222no—
616C4×D4—222no—
617C4×D4C22×D1114yes—
618C4×D4C22×D1114yes—
619#117—22no—
620#117—22no—
621#117—24no—
622#117—111no—
623#117—222no—
624#117—221no—
625#117—222no—
626#117—222no—
627#117C22⋊D1111yescharacteristic
628#117C22⋊D1112yes—
629#117C22⋊D1111yescharacteristic
630#117C22×D1111yescharacteristic
631#117C22×D1111yescharacteristic
632#117C22×D1112yes—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—24no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—221no—
642C2×C4⋊C4—221no—
643C2×C4⋊C4C22⋊D1111yescharacteristic
644C2×C4⋊C4C22⋊D1111yescharacteristic
645C2×C4⋊C4C22×D1112yes—
646C2×C4⋊C4C22×D1112yes—
647C2×C4⋊C4C22×D1112yes—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4C22⋊D1112yes—
651C2×C42—22no—
652C2×C42C22×D1112yes—
653#107—114no—
654#107—114no—
655#107—114no—
656#106—114no—
657C4⋊C8—114no—
658C4⋊C8—114no—
659#103—112no—
660#103—112no—
661#103—114no—
662#103—114no—
663#103—114no—
664#103—114no—
665#102—112no—
666#102—112no—
667#102—114no—
668#102—114no—
669C22⋊C8—111no—
670C22⋊C8—111no—
671C22⋊C8—112no—
672C22⋊C8—112no—
673C22⋊C8—112no—
674#97—114no—
675C4×C8—114no—
676C2×C11—22no—
677C2×C11—22no—
678C2×C11—41no—
679C2×C11—44no—
680C2×C11C2×#52511yescharacteristic
681C2×C11C2×#57811yescharacteristic
682C2×C11#358511yescharacteristic
683D11—81no—
684C24—21no—
685C24C2×C22⋊D1111yescharacteristic
686#41—28no—
687#41—28no—
688#41—24no—
689#41—24no—
690#41—24no—
691#41—224no—
692#41#433918yes—
693C2×Q8—24no—
694C2×Q8—21no—
695C2×Q8—112no—
696C2×Q8—111no—
697C2×Q8—221no—
698C2×Q8—222no—
699C2×Q8—224no—
700C2×Q8C23×D1112yes—
701C2×D4—28no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—24no—
705C2×D4—21no—
706C2×D4—111no—
707C2×D4—221no—
708C2×D4—221no—
709C2×D4—221no—
710C2×D4C23×D1112yes—
711C22×C4—28no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—84no—
722C22×C4—82no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—222no—
727C22×C4C2×C22⋊D1112yes—
728C22×C4C2×C22⋊D1111yescharacteristic
729C22×C4C2×C22⋊D1111yescharacteristic
730C22×C4C2×C22⋊D1111yescharacteristic
731C22×C4C2×C22⋊D1112yes—
732C22×C4C23×D1111yescharacteristic
733C22×C4C23×D1111yescharacteristic
734C22×C4C23×D1111yescharacteristic
735Q16—224no—
736Q16—228no—
737SD16—224no—
738SD16—224no—
739SD16—228no—
740D8—224no—
741M16—224no—
742C2×C8—112no—
743C2×C8—114no—
744C2×C8—112no—
745C2×C8—224no—
746C4⋊C4—22no—
747C4⋊C4—22no—
748C4⋊C4—24no—
749C4⋊C4—24no—
750C4⋊C4—22no—
751C4⋊C4—111no—
752C4⋊C4—112no—
753C4⋊C4—111no—
754C4⋊C4—221no—
755C4⋊C4—222no—
756C4⋊C4—222no—
757C4⋊C4—222no—
758C4⋊C4—222no—
759C4⋊C4—222no—
760C4⋊C4—222no—
761C4⋊C4—222no—
762C4⋊C4—222no—
763C4⋊C4—221no—
764C4⋊C4—221no—
765C4⋊C4—222no—
766C4⋊C4—222no—
767C4⋊C4C2×C22⋊D1111yescharacteristic
768C4⋊C4C2×C22⋊D1112yes—
769C4⋊C4C2×C22⋊D1111yescharacteristic
770C4⋊C4C2×C22⋊D1111yescharacteristic
771C4⋊C4C2×C22⋊D1111yescharacteristic
772C4⋊C4C2×C22⋊D1112yes—
773C4⋊C4C23×D1114yes—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—222no—
777C22⋊C4—222no—
778C22⋊C4—221no—
779C22⋊C4—221no—
780C22⋊C4—221no—
781C22⋊C4—221no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—221no—
785C22⋊C4—222no—
786C22⋊C4C2×C22⋊D1112yes—
787C22⋊C4C2×C22⋊D1112yes—
788C22⋊C4C2×C22⋊D1112yes—
789C22⋊C4C2×C22⋊D1112yes—
790C42—24no—
791C42—24no—
792C42—221no—
793C42—222no—
794C42—222no—
795C42—222no—
796C42C2×C22⋊D1112yes—
797C42C2×C22⋊D1112yes—
798C42C23×D1112yes—
799C42C23×D1112yes—
800C11#6058911yescharacteristic, complemented, Sylow
801C23—24no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—41no—
806C23—42no—
807C23—42no—
808C23—221no—
809C23C22×C22⋊D1111yescharacteristic
810C23C22×C22⋊D1111yescharacteristic
811C23C22×C22⋊D1111yescharacteristic
812Q8—24no—
813Q8—22no—
814Q8—224no—
815Q8—222no—
816Q8—442no—
817Q8—882no—
818Q8C2×#433914yes—
819D4—28no—
820D4—24no—
821D4—28no—
822D4—22no—
823D4—222no—
824D4—442no—
825D4—442no—
826D4—881no—
827D4C2×#433914yes—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—28no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—84no—
842C2×C4—84no—
843C2×C4—82no—
844C2×C4—82no—
845C2×C4—221no—
846C2×C4—221no—
847C2×C4—222no—
848C2×C4—221no—
849C2×C4—222no—
850C2×C4—442no—
851C2×C4—442no—
852C2×C4—882no—
853C2×C4—881no—
854C2×C4C2×#433914yes—
855C2×C4C22×C22⋊D1112yes—
856C2×C4C22×C22⋊D1112yes—
857C2×C4C22×C22⋊D1112yes—
858C2×C4C22×C22⋊D1111yescharacteristic
859C2×C4C22×C22⋊D1112yes—
860C2×C4C22×C22⋊D1111yescharacteristic
861C2×C4C22×C22⋊D1111yescharacteristic
862C2×C4C24×D1111yescharacteristic
863C8—222no—
864C8—222no—
865C8—224no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—24no—
872C22—21no—
873C22—21no—
874C22—44no—
875C22—48no—
876C22—42no—
877C22—42no—
878C22—441no—
879C22—441no—
880C22—441no—
881C22#1062332212yes—
882C22#1062336912yes—
883C22C23×C22⋊D1111yescharacteristic
884C4—21no—
885C4—24no—
886C4—21no—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—44no—
892C4—441no—
893C4—442no—
894C4—442no—
895C4—441no—
896C4—441no—
897C4#1062332212yes—
898C4C22×#433912yes—
899C2—22no—
900C2—22no—
901C2—41no—
902C2—44no—
903C2—881no—
904C2C2×#1062332211yescharacteristic
905C2C2×#1062336911yescharacteristic
906C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#520C2
socleC22×C11C23×D4
prime radical#13077834C2
hypercenterC2×#520D11
hypocenterC11#60589
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13082368C2semidirect
2. #13078878C2semidirect
3. #13078830C2semidirect
4. #13078787C2semidirect
5. #13078715C2semidirect
6. #13078663C2semidirect
7. #13078655C2semidirect
8. #13078539C2semidirect
9. C2×#10622583C2semidirect
10. #13078467C2semidirect
11. #13078166C2semidirect
12. #13077876C2semidirect
14. #13077489C2semidirect
15. #13077455C2semidirect
16. #13077274C2semidirect
17. C2×C11×#520C2semidirect
36. #10623065C22semidirect
40. #10623057C22semidirect
41. #10623054C22semidirect
42. #10623050C22semidirect
43. #10623049C22semidirect
44. #10623047C22semidirect
63. #10622644C22semidirect
64. #10622643C22semidirect
65. C4×#4326C22semidirect
66. C4×#4326C22semidirect
67. #10622641C22semidirect
68. #10622639C22semidirect
69. #10622635C22semidirect
70. #10622634C22semidirect
71. #10622632C22semidirect
72. #10622631C22semidirect
73. #10622631C22semidirect
74. C4×#4324C22semidirect
75. #10622629C22semidirect
76. C4×#4323C22semidirect
77. #10622622C22semidirect
78. #10622620C22semidirect
79. #10622613C22semidirect
80. #10622612C22semidirect
81. #10622610C22semidirect
82. #10622584C22semidirect
86. #10622583C22semidirect
87. C2×#66874C22semidirect
89. #10622580C22semidirect
90. #10622579C22semidirect
91. #10622577C22semidirect
92. C2×#66871C22semidirect
349. C2×#520D11semidirect
800. C11#60589semidirect

Maximal subgroups

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

subgroupindex
#130823682
#130788782
#130788302
#130787872
#130787152
#130786632
#130786552
#130785392
C2×#106225832
#130784672
#130781662
#130778762
#130778342
#130774892
#130774552
#130772742
C2×C11×#5202
#6058911