Finite Group Databasebeta

← #15630952

Subgroups — #15630952

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2#13080899C212yesmaximal, complemented
3#13080847C212yesmaximal, complemented
4#13080682C214yesmaximal, complemented
5#13080652C214yesmaximal, complemented
6#13080555C212yesmaximal, complemented
7#13080533C212yesmaximal, complemented
8#13079009C211yesmaximal, characteristic, complemented
9#13078545C212yesmaximal, complemented
10#13078431C211yesmaximal, characteristic, complemented
11#13078248C212yesmaximal, complemented
12#13078084C211yesmaximal, characteristic, complemented
13#13077876C212yesmaximal, complemented
14C4×#67004C211yesmaximal, characteristic, complemented
15D4×#4318C211yesmaximal, characteristic, complemented
16#13077135C212yesmaximal, complemented
17D4×C11×#41C211yesmaximal, characteristic
18C22×C11×#41C2212yes—
19C11×#550C2211yescharacteristic
20D4×Q8×C11C2211yescharacteristic
21C11×#548C2212yes—
22C11×#547—21no—
23C11×#547C2211yescharacteristic
24C11×#546—22no—
25C11×#546C2212yes—
26D42×C11—21no—
27D42×C11C2211yescharacteristic
28C11×#532—21no—
29C11×#532C2211yescharacteristic
30C11×#525—22no—
31C11×#525C2212yes—
32C4×C11×#41C2211yescharacteristic
33C2×C4×D4×C11—21no—
34C2×C4×D4×C11C2211yescharacteristic
35C2×#67004C2211yescharacteristic
36C2×#67004C2212yescomplemented
37C2×#66989—21no—
38C2×#66979C2212yescomplemented
39C2×#66977C2212yescomplemented
40C22×#4318C2212yescomplemented
41#10623073—22no—
42#10623073—21no—
43#10623073—21no—
44#10623073C2212yes—
45#10623073C2214yescomplemented
46#10623073C2212yescomplemented
47C2×#66940—21no—
48C2×#66932—22no—
49C2×#66922C2211yescharacteristic, complemented
50C2×C4×Dic22C2211yescharacteristic, complemented
51#10622852C2214yescomplemented
52#10622852C2214yescomplemented
53#10622846C2214yescomplemented
54#10622846C2214yescomplemented
55#10622845C2212yes—
56#10622845C2211yescharacteristic
57#10622845C2212yescomplemented
58#10622845C2212yescomplemented
59#10622845C2212yescomplemented
60#10622841C2214yescomplemented
61#10622838C2214yescomplemented
62#10622831C2214yescomplemented
63#10622828C2214yescomplemented
64#10622820C2212yescomplemented
65#10622703C2212yescomplemented
66#10622694C2212yescomplemented
67#10622688C2212yescomplemented
68#10622683C2212yescomplemented
69#10622668C2214yescomplemented
70#10622667C2214yescomplemented
71#10622665C2214yescomplemented
72#10622664C2214yescomplemented
73#10622658C2214yescomplemented
74#10622658C2214yescomplemented
75#10622655C2214yescomplemented
76#10622654C2214yescomplemented
77#10622648C2214yescomplemented
78#10622648C2214yescomplemented
79#10622643C2212yescomplemented
80C4×#4326C2212yescomplemented
81#10622634C2212yescomplemented
82#10622633C2212yescomplemented
83#10622631C2212yescomplemented
84C4×#4324C2212yescomplemented
85#10622625C2212yes—
86#10622624C2214yescomplemented
87D4×C11⋊C8C2212yescomplemented
88#10622621C2212yescomplemented
89#10622620C2212yescomplemented
90#10622617C2211yescharacteristic, complemented
91#10622608C2211yescharacteristic, complemented
92#10622608C2212yescomplemented
93#10622537C2211yescharacteristic, complemented
94C4×#4318C2211yescharacteristic, complemented
95C2×C11×#41—22no—
96C2×C11×#41—22no—
97C2×C11×#41—28no—
98C2×C11×#41—44no—
99C2×C11×#41C2312yes—
100C2×C11×#41C2312yes—
101C2×C11×#41C2312yes—
102C2×C11×#41C2311yescharacteristic
103C22×Q8×C11C2312yes—
104C22×D4×C11—22no—
105C22×D4×C11—21no—
106C22×D4×C11D411yescharacteristic
107C22×D4×C11C2312yes—
108C23×C4×C11—22no—
109C23×C4×C11C2312yes—
110C22×Dic22—21no—
111C22×Dic22C2311yescharacteristic
112C11×C4⋊Q8—21no—
113C11×C4⋊Q8C2311yescharacteristic
114C11×#127—21no—
115C11×#127C2311yescharacteristic
116C11×#124—22no—
117C11×#124C2312yes—
118C11×#123—22no—
119C11×#123—22no—
120C11×#123—22no—
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8—22no—
123C11×C22⋊Q8C2312yes—
124C11×C22⋊Q8C2312yes—
125C11×#121—22no—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—21no—
130C11×#121—22no—
131C11×#121—22no—
132C11×#121C2312yes—
133C11×#121C2312yes—
134C11×#120—22no—
135C11×#120—22no—
136C11×#120—22no—
137C4×Q8×C11C2311yescharacteristic
138C4×Q8×C11C2311yescharacteristic
139C4×D4×C11—21no—
140C4×D4×C11—22no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11—21no—
145C4×D4×C11—22no—
146C4×D4×C11—21no—
147C4×D4×C11—21no—
148C4×D4×C11D411yescharacteristic
149C4×D4×C11D412yes—
150C4×D4×C11D411yescharacteristic
151C4×D4×C11C2311yescharacteristic
152C4×D4×C11C2311yescharacteristic
153C4×D4×C11C2311yescharacteristic
154C4×D4×C11C2311yescharacteristic
155C4×D4×C11C2312yes—
156C11×#117—21no—
157C11×#117C2311yescharacteristic
158C2×C11×C4⋊C4—21no—
159C2×C11×C4⋊C4D411yescharacteristic
160C2×C11×C22⋊C4—22no—
161C2×C11×C22⋊C4D412yes—
162C2×C42×C11—21no—
163C2×C42×C11C2311yescharacteristic
164C2×C22⋊Dic11—22no—
165C2×C22⋊Dic11—22no—
166#67004—24no—
167#67004—44no—
168C2×#4326C2312yes—
169C2×#4326C2314yes—
170#66989—22no—
171#66989—22no—
172#66989—24no—
173C2×#4324C2312yes—
174C2×#4324C2314yes—
175#66979—22no—
176#66979—22no—
177#66979C2314yes—
178#66979C2314yes—
179C2×C4⋊Dic11—21no—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2312yes—
182#66977—22no—
183#66977—22no—
184#66977C2314yes—
185#66977C2314yes—
186C2×Dic11⋊C4—21no—
187C2×Dic11⋊C4—22no—
188C2×C4×Dic11—21no—
189C2×C4×Dic11—22no—
190C2×#4318—44no—
191C2×#4318C2311yescharacteristic
192C2×#4318C2311yescharacteristic
193C2×#4318C2312yes—
194C2×#4318C2314yes—
195C22×C11⋊C8C2314yes—
196#66940—22no—
197#66940—22no—
198#66940—24no—
199#66932—24no—
200#66932—24no—
201#66932—24no—
202#66932—24no—
203#66922—21no—
204#66922—21no—
205#66922C2312yes—
206#66922C2312yes—
207C4×Dic22—21no—
208C4×Dic22—21no—
209C4×Dic22C2312yes—
210C4×Dic22C2312yes—
211#66899C2312yes—
212#66899C2314yes—
213#66899C2314yes—
214#66899C2314yes—
215#66899C2314yes—
216#66896C2312yes—
217#66896C2314yes—
218#66896C2314yes—
219#66896C2314yes—
220#66896C2314yes—
221C22⋊(C11⋊C8)C2314yes—
222C22⋊(C11⋊C8)C2314yes—
223#66874C2312yes—
224#66874C2312yes—
225#66872C2314yes—
226#66872C2312yes—
227#66871C2314yes—
228#66871C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231#66867C2312yes—
232C4×C11⋊C8C2312yes—
233#61165—111nomaximal, Sylow
234C24×C11—22no—
235C24×C11C2×D412yes—
236C11×#41—22no—
237C11×#41—24no—
238C11×#41—24no—
239C11×#41—24no—
240C11×#41—24no—
241C11×#41—48no—
242C11×#41—42no—
243C11×#41—42no—
244C11×#41—48no—
245C11×#41#4114yes—
246C2×Q8×C11—22no—
247C2×Q8×C11—24no—
248C2×Q8×C11—42no—
249C2×Q8×C11C2412yes—
250C2×Q8×C11C2411yescharacteristic
251C2×D4×C11—21no—
252C2×D4×C11—24no—
253C2×D4×C11—22no—
254C2×D4×C11—22no—
255C2×D4×C11—22no—
256C2×D4×C11—22no—
257C2×D4×C11—22no—
258C2×D4×C11—21no—
259C2×D4×C11—22no—
260C2×D4×C11—21no—
261C2×D4×C11—42no—
262C2×D4×C11—42no—
263C2×D4×C11—48no—
264C2×D4×C11—44no—
265C2×D4×C11C2×D411yescharacteristic
266C2×D4×C11C2×D411yescharacteristic
267C2×D4×C11C2×D412yes—
268C2×D4×C11C2412yes—
269C2×D4×C11C2411yescharacteristic
270C22×C4×C11—21no—
271C22×C4×C11—24no—
272C22×C4×C11—24no—
273C22×C4×C11—22no—
274C22×C4×C11—21no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—22no—
278C22×C4×C11—21no—
279C22×C4×C11—48no—
280C22×C4×C11C2×D412yes—
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D412yes—
283C22×C4×C11C2×D412yes—
284C22×C4×C11C2×D411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—22no—
291C2×Dic22—21no—
292C2×Dic22—22no—
293C2×Dic22—22no—
294C2×Dic22—22no—
295C2×Dic22—22no—
296C2×Dic22—44no—
297C2×Dic22C2412yes—
298C11×C4⋊C4—21no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4—21no—
301C11×C4⋊C4—21no—
302C11×C4⋊C4—21no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4C2×D411yescharacteristic
305C11×C4⋊C4C2×D411yescharacteristic
306C11×C4⋊C4C2×D412yes—
307C11×C4⋊C4C2411yescharacteristic
308C11×C4⋊C4C2411yescharacteristic
309C11×C22⋊C4—22no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—22no—
314C11×C22⋊C4—21no—
315C11×C22⋊C4—21no—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—22no—
318C11×C22⋊C4C2×D412yes—
319C11×C22⋊C4C2×D412yes—
320C11×C22⋊C4C2×D412yes—
321C11×C22⋊C4C2×D412yes—
322C42×C11—21no—
323C42×C11—21no—
324C42×C11—21no—
325C42×C11C2×D411yescharacteristic
326C42×C11C2×D411yescharacteristic
327C42×C11C2411yescharacteristic
328C42×C11C2411yescharacteristic
329C22⋊Dic11—24no—
330C22⋊Dic11—24no—
331C22⋊Dic11—24no—
332C22⋊Dic11—24no—
333#4326—24no—
334#4326—44no—
335#4324—24no—
336#4324—44no—
337C4⋊Dic11—21no—
338C4⋊Dic11—22no—
339C4⋊Dic11—22no—
340C4⋊Dic11—22no—
341C4⋊Dic11C2412yes—
342C4⋊Dic11C2414yes—
343Dic11⋊C4—22no—
344Dic11⋊C4—22no—
345Dic11⋊C4—24no—
346Dic11⋊C4—24no—
347C4×Dic11—22no—
348C4×Dic11—22no—
349C4×Dic11—24no—
350C4×Dic11—24no—
351#4318—22no—
352#4318—22no—
353#4318—24no—
354#4318—44no—
355C2×C11⋊C8—44no—
356C2×C11⋊C8C2412yes—
357C2×C11⋊C8C2412yes—
358C2×C11⋊C8C2414yes—
359C2×#556—111no—
360D4×#41D1111yescharacteristic
361#3328—112no—
362#3324—112no—
363#3313—114no—
364#3311—114no—
365#3304—112no—
366#3302—112no—
367#3141—111no—
368#3093—112no—
369#3079—111no—
370#3056—112no—
371#3037—111no—
372#3007—112no—
373C4×#137—111no—
374D4×M16—111no—
375#2896—112no—
376C23×C11—21no—
377C23×C11—24no—
378C23×C11—22no—
379C23×C11—42no—
380C23×C11—42no—
381C23×C11—44no—
382C23×C11—44no—
383C23×C11—82no—
384C23×C11C22×D412yes—
385C23×C11C22×D412yes—
386C23×C11C22×D411yescharacteristic
387Q8×C11—21no—
388Q8×C11—22no—
389Q8×C11—22no—
390Q8×C11—44no—
391Q8×C11C2×#4112yes—
392D4×C11—24no—
393D4×C11—22no—
394D4×C11—22no—
395D4×C11—22no—
396D4×C11—21no—
397D4×C11—22no—
398D4×C11—42no—
399D4×C11—44no—
400D4×C11—44no—
401D4×C11—44no—
402D4×C11—44no—
403D4×C11—44no—
404D4×C11—42no—
405D4×C11—81no—
406D4×C11—82no—
407D4×C11C2×#4112yes—
408C2×C4×C11—24no—
409C2×C4×C11—21no—
410C2×C4×C11—24no—
411C2×C4×C11—24no—
412C2×C4×C11—24no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11—41no—
422C2×C4×C11—44no—
423C2×C4×C11—44no—
424C2×C4×C11—44no—
425C2×C4×C11—44no—
426C2×C4×C11—42no—
427C2×C4×C11—81no—
428C2×C4×C11C22×D412yes—
429C2×C4×C11C22×D412yes—
430C2×C4×C11C22×D411yescharacteristic
431C2×C4×C11C22×D411yescharacteristic
432C2×C4×C11C22×D411yescharacteristic
433C2×C4×C11C22×D411yescharacteristic
434C2×C4×C11C22×D411yescharacteristic
435C2×C4×C11C2×#4112yes—
436C2×C4×C11H(5,𝔽2)12yes—
437C2×C4×C11C2511yescharacteristic
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—24no—
441C2×Dic11—44no—
442C2×Dic11—42no—
443C2×Dic11—42no—
444Dic22—22no—
445Dic22—22no—
446Dic22—44no—
447Dic22—42no—
448Dic22—44no—
449C11⋊C8—22no—
450C11⋊C8—22no—
451C11⋊C8—24no—
452C22×#41C2×D1112yes—
453C2×#137—111no—
454C2×#137—112no—
455C22×M16—112no—
456#556—112no—
457#556—112no—
458#556—114no—
459#556—221no—
460#556—222no—
461#556—221no—
462#550C2×D1111yescharacteristic
463D4×Q8C2×D1111yescharacteristic
464#548C2×D1112yes—
465#547—21no—
466#547C2×D1111yescharacteristic
467#546—22no—
468#546C2×D1112yes—
469D42—21no—
470D42C2×D1111yescharacteristic
471#532—21no—
472#532C2×D1111yescharacteristic
473C2×C4⋊Q8—111no—
474C2×#126—222no—
475C2×#124—221no—
476#525—22no—
477#525C2×D1112yes—
478C2×C22⋊Q8—112no—
479C4×#41C2×D1111yescharacteristic
480C2×C4×Q8—111no—
481C2×C4×Q8—221no—
482C2×C4×D4—21no—
483C2×C4×D4C2×D1111yescharacteristic
484C2×#117—112no—
485#489—114no—
486#487—112no—
487#486—112no—
488#485—114no—
489#485—114no—
490#482—114no—
491#482—114no—
492#477—112no—
493#476—112no—
494#475—112no—
495#474—112no—
496#470—114no—
497#468—114no—
498#467—114no—
499#465—114no—
500#464—114no—
501#462—112no—
502#460—112no—
503#452—114no—
504#452—114no—
505#451—114no—
506#450—114no—
507#441—112no—
508#440—112no—
509C4×Q16—112no—
510C4×SD16—112no—
511#436—112no—
512#435—114no—
513C8×D4—112no—
514#428—112no—
515#428—111no—
516#423—111no—
517#419—114no—
518#419—111no—
519#418—114no—
520#417—112no—
521#417—112no—
522#417—112no—
523#417—112no—
524#417—111no—
525#416—114no—
526#416—114no—
527#407—112no—
528C4×M16—111no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—22no—
532C22×C11—22no—
533C22×C11—22no—
534C22×C11—22no—
535C22×C11—22no—
536C22×C11—22no—
537C22×C11—22no—
538C22×C11—41no—
539C22×C11—41no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—84no—
544C22×C11—88no—
545C22×C11#54612yes—
546C22×C11C23×D411yescharacteristic
547C4×C11—21no—
548C4×C11—21no—
549C4×C11—22no—
550C4×C11—22no—
551C4×C11—22no—
552C4×C11—21no—
553C4×C11—41no—
554C4×C11—42no—
555C4×C11—41no—
556C4×C11#54612yes—
557C4×C11#57512yes—
558C4×C11C22×#4111yescharacteristic
559C4×C11C2×H(5,𝔽2)11yescharacteristic
560Dic11—42no—
561Dic11—42no—
562Dic11—44no—
563C2×#41—22no—
564C2×#41—22no—
565C2×#41—28no—
566C2×#41—44no—
567C2×#41C22×D1112yes—
568C2×#41C22×D1112yes—
569C2×#41C22×D1112yes—
570C2×#41C22×D1111yescharacteristic
571C22×Q8—111no—
572C22×Q8—221no—
573C22×Q8C22×D1112yes—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4C22⋊D1111yescharacteristic
577C22×D4C22×D1112yes—
578C23×C4—22no—
579C23×C4C22×D1112yes—
580#137—224no—
581#137—444no—
582C2×Q16—112no—
583C2×Q16—114no—
584C2×SD16—112no—
585C2×SD16—114no—
586C2×M16—111no—
587C2×M16—112no—
588C2×M16—111no—
589C2×M16—114no—
590C2×M16—444no—
591C22×C8—114no—
592C4⋊Q8—21no—
593C4⋊Q8—112no—
594C4⋊Q8—112no—
595C4⋊Q8—221no—
596C4⋊Q8—221no—
597C4⋊Q8C22×D1111yescharacteristic
598#127—21no—
599#127C22×D1111yescharacteristic
600#126—224no—
601#126—224no—
602#126—224no—
603#126—224no—
604#124—22no—
605#124—222no—
606#124—222no—
607#124—224no—
608#124C22×D1112yes—
609#123—22no—
610#123—22no—
611#123—22no—
612C22⋊Q8—22no—
613C22⋊Q8—22no—
614C22⋊Q8—114no—
615C22⋊Q8—114no—
616C22⋊Q8—222no—
617C22⋊Q8—222no—
618C22⋊Q8C22×D1112yes—
619C22⋊Q8C22×D1112yes—
620#121—22no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—22no—
626#121—22no—
627#121C22×D1112yes—
628#121C22×D1112yes—
629#120—22no—
630#120—22no—
631#120—22no—
632C4×Q8—112no—
633C4×Q8—112no—
634C4×Q8—222no—
635C4×Q8—222no—
636C4×Q8—224no—
637C4×Q8—221no—
638C4×Q8—221no—
639C4×Q8C22×D1111yescharacteristic
640C4×Q8C22×D1111yescharacteristic
641C4×D4—21no—
642C4×D4—22no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650C4×D4C22⋊D1111yescharacteristic
651C4×D4C22⋊D1112yes—
652C4×D4C22⋊D1111yescharacteristic
653C4×D4C22×D1111yescharacteristic
654C4×D4C22×D1111yescharacteristic
655C4×D4C22×D1111yescharacteristic
656C4×D4C22×D1112yes—
657C4×D4C22×D1111yescharacteristic
658#117—21no—
659#117—114no—
660#117—114no—
661#117—222no—
662#117—222no—
663#117C22×D1111yescharacteristic
664C2×C4⋊C4—21no—
665C2×C4⋊C4—111no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4—221no—
668C2×C4⋊C4—222no—
669C2×C4⋊C4—221no—
670C2×C4⋊C4C22⋊D1111yescharacteristic
671C2×C22⋊C4—22no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4C22⋊D1112yes—
675C2×C42—21no—
676C2×C42—222no—
677C2×C42—221no—
678C2×C42C22×D1111yescharacteristic
679#107—112no—
680#107—114no—
681#106—112no—
682#106—114no—
683C4⋊C8—112no—
684C4⋊C8—112no—
685#103—112no—
686#103—114no—
687#103—114no—
688#103—114no—
689#103—114no—
690#103—112no—
691#103—112no—
692#102—112no—
693#102—114no—
694#102—114no—
695#102—114no—
696#102—114no—
697C22⋊C8—114no—
698C22⋊C8—114no—
699#97—112no—
700C4×C8—112no—
701C2×C11—22no—
702C2×C11—42no—
703C2×C11—42no—
704C2×C11—42no—
705C2×C11—82no—
706C2×C11C2×#54611yescharacteristic
707C2×C11C2×#57511yescharacteristic
708C2×C11#358611yescharacteristic
709C24—22no—
710C24C2×C22⋊D1112yes—
711#41—22no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—24no—
716#41—48no—
717#41—42no—
718#41—42no—
719#41—48no—
720#41#434114yes—
721C2×Q8—22no—
722C2×Q8—24no—
723C2×Q8—42no—
724C2×Q8—112no—
725C2×Q8—221no—
726C2×Q8—222no—
727C2×Q8—222no—
728C2×Q8—222no—
729C2×Q8—222no—
730C2×Q8—444no—
731C2×Q8C23×D1112yes—
732C2×Q8C23×D1111yescharacteristic
733C2×D4—21no—
734C2×D4—24no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—21no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4C2×C22⋊D1111yescharacteristic
748C2×D4C2×C22⋊D1111yescharacteristic
749C2×D4C2×C22⋊D1112yes—
750C2×D4C23×D1112yes—
751C2×D4C23×D1111yescharacteristic
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—48no—
762C22×C4—221no—
763C22×C4—222no—
764C22×C4—221no—
765C22×C4C2×C22⋊D1111yescharacteristic
766C22×C4C2×C22⋊D1112yes—
767C22×C4C2×C22⋊D1112yes—
768C22×C4C2×C22⋊D1112yes—
769C22×C4C2×C22⋊D1111yescharacteristic
770C22×C4C23×D1112yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1111yescharacteristic
773Q16—224no—
774Q16—444no—
775SD16—224no—
776SD16—444no—
777M16—222no—
778M16—222no—
779M16—224no—
780M16—444no—
781C2×C8—112no—
782C2×C8—112no—
783C2×C8—114no—
784C2×C8—444no—
785C4⋊C4—21no—
786C4⋊C4—22no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—22no—
791C4⋊C4—112no—
792C4⋊C4—114no—
793C4⋊C4—221no—
794C4⋊C4—222no—
795C4⋊C4—222no—
796C4⋊C4—222no—
797C4⋊C4—224no—
798C4⋊C4—224no—
799C4⋊C4—222no—
800C4⋊C4—222no—
801C4⋊C4C2×C22⋊D1111yescharacteristic
802C4⋊C4C2×C22⋊D1111yescharacteristic
803C4⋊C4C2×C22⋊D1112yes—
804C4⋊C4C23×D1111yescharacteristic
805C4⋊C4C23×D1111yescharacteristic
806C22⋊C4—22no—
807C22⋊C4—21no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—22no—
814C22⋊C4—22no—
815C22⋊C4—224no—
816C22⋊C4—224no—
817C22⋊C4—224no—
818C22⋊C4—224no—
819C22⋊C4C2×C22⋊D1112yes—
820C22⋊C4C2×C22⋊D1112yes—
821C22⋊C4C2×C22⋊D1112yes—
822C22⋊C4C2×C22⋊D1112yes—
823C42—21no—
824C42—21no—
825C42—21no—
826C42—224no—
827C42—224no—
828C42—222no—
829C42—222no—
830C42C2×C22⋊D1111yescharacteristic
831C42C2×C22⋊D1111yescharacteristic
832C42C23×D1111yescharacteristic
833C42C23×D1111yescharacteristic
834C11#6116511yescharacteristic, complemented, Sylow
835C23—21no—
836C23—24no—
837C23—22no—
838C23—42no—
839C23—42no—
840C23—44no—
841C23—44no—
842C23—82no—
843C23C22×C22⋊D1112yes—
844C23C22×C22⋊D1112yes—
845C23C22×C22⋊D1111yescharacteristic
846Q8—21no—
847Q8—22no—
848Q8—22no—
849Q8—44no—
850Q8—222no—
851Q8—222no—
852Q8—444no—
853Q8—442no—
854Q8—444no—
855Q8C2×#434112yes—
856D4—24no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—21no—
861D4—22no—
862D4—42no—
863D4—44no—
864D4—44no—
865D4—44no—
866D4—44no—
867D4—44no—
868D4—42no—
869D4—81no—
870D4—82no—
871D4C2×#434112yes—
872C2×C4—24no—
873C2×C4—21no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—41no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—42no—
891C2×C4—81no—
892C2×C4—222no—
893C2×C4—224no—
894C2×C4—222no—
895C2×C4—444no—
896C2×C4—442no—
897C2×C4—442no—
898C2×C4C2×#434112yes—
899C2×C4#6703712yes—
900C2×C4C22×C22⋊D1111yescharacteristic
901C2×C4C22×C22⋊D1111yescharacteristic
902C2×C4C22×C22⋊D1112yes—
903C2×C4C22×C22⋊D1112yes—
904C2×C4C22×C22⋊D1111yescharacteristic
905C2×C4C22×C22⋊D1111yescharacteristic
906C2×C4C22×C22⋊D1111yescharacteristic
907C2×C4C24×D1111yescharacteristic
908C8—222no—
909C8—222no—
910C8—224no—
911C22—21no—
912C22—21no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—41no—
921C22—41no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—84no—
926C22—88no—
927C22#1062333712yes—
928C22C23×C22⋊D1111yescharacteristic
929C4—21no—
930C4—21no—
931C4—22no—
932C4—22no—
933C4—22no—
934C4—21no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—442no—
939C4—442no—
940C4—444no—
941C4#1062333712yes—
942C4#1062335312yes—
943C4C22×#434111yescharacteristic
944C4C2×#6703711yescharacteristic
945C2—22no—
946C2—42no—
947C2—42no—
948C2—42no—
949C2—82no—
950C2C2×#1062333711yescharacteristic
951C2C2×#1062335311yescharacteristic
952C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalD4×C11×#41C2
socleC22×C11C23×D4
hypercenterD4×#41D11
hypocenterC11#61165
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. #13080899C2semidirect
3. #13080847C2semidirect
4. #13080682C2semidirect
5. #13080652C2semidirect
6. #13080555C2semidirect
7. #13080533C2semidirect
8. #13079009C2semidirect
9. #13078545C2semidirect
10. #13078431C2semidirect
11. #13078248C2semidirect
12. #13078084C2semidirect
13. #13077876C2semidirect
14. C4×#67004C2semidirect
15. D4×#4318C2semidirect
16. #13077135C2semidirect
36. C2×#67004C22semidirect
38. C2×#66979C22semidirect
39. C2×#66977C22semidirect
40. C22×#4318C22semidirect
45. #10623073C22semidirect
46. #10623073C22semidirect
49. C2×#66922C22semidirect
50. C2×C4×Dic22C22semidirect
51. #10622852C22semidirect
52. #10622852C22semidirect
53. #10622846C22semidirect
54. #10622846C22semidirect
57. #10622845C22semidirect
58. #10622845C22semidirect
59. #10622845C22semidirect
60. #10622841C22semidirect
61. #10622838C22semidirect
62. #10622831C22semidirect
63. #10622828C22semidirect
64. #10622820C22semidirect
65. #10622703C22semidirect
66. #10622694C22semidirect
67. #10622688C22semidirect
68. #10622683C22semidirect
69. #10622668C22semidirect
70. #10622667C22semidirect
71. #10622665C22semidirect
72. #10622664C22semidirect
73. #10622658C22semidirect
74. #10622658C22semidirect
75. #10622655C22semidirect
76. #10622654C22semidirect
77. #10622648C22semidirect
78. #10622648C22semidirect
79. #10622643C22semidirect
80. C4×#4326C22semidirect
81. #10622634C22semidirect
82. #10622633C22semidirect
83. #10622631C22semidirect
84. C4×#4324C22semidirect
86. #10622624C22semidirect
87. D4×C11⋊C8C22semidirect
88. #10622621C22semidirect
89. #10622620C22semidirect
90. #10622617C22semidirect
91. #10622608C22semidirect
92. #10622608C22semidirect
93. #10622537C22semidirect
94. C4×#4318C22semidirect
834. C11#61165semidirect

Maximal subgroups

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

subgroupindex
C2×#106230732
#130808992
#130808472
#130806822
#130806522
#130805552
#130805332
#130790092
#130785452
#130784312
#130782482
#130780842
#130778762
C4×#670042
D4×#43182
#130771352
D4×C11×#412
#6116511