Finite Group Databasebeta

← #15630891

Subgroups — #15630891

Order 2816.

2162 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic, complemented
2#41×D44C211yesmaximal, characteristic
3#13080956C212yesmaximal, complemented
4#13080934C212yesmaximal, complemented
5#13080732C214yesmaximal, complemented
6#13080702C214yesmaximal, complemented
7#13080494C212yesmaximal, complemented
8#13080442C212yesmaximal, complemented
9#13079010C211yesmaximal, characteristic, complemented
10#13078542C212yesmaximal, complemented
11#13078431C211yesmaximal, characteristic, complemented
12#13078244C212yesmaximal, complemented
13#13078088C211yesmaximal, characteristic, complemented
14#13077872C212yesmaximal, complemented
15M16×D44C211yesmaximal, characteristic, complemented
16D11×#417C212yesmaximal, complemented
17C4×C11×#137C211yesmaximal, characteristic, complemented
18C2×#41×D11C2212yes—
19C2×C11×#137C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic, complemented
22C2×#66999C2212yescomplemented
23C2×#66995C2212yescomplemented
24C2×M16×D11C2212yescomplemented
25#10623110—21no—
26#10623110—21no—
27#10623110—22no—
28#10623110C2212yes—
29#10623110C2212yescomplemented
30#10623110C2214yescomplemented
31#10623108C2211yescharacteristic
32#10623107C2212yes—
33Q8×D44C2211yescharacteristic
34#10623086—21no—
35#10623086C2211yescharacteristic
36#10623085—22no—
37#10623085C2212yes—
38D4×D44—21no—
39D4×D44C2211yescharacteristic
40#10623055—22no—
41#10623055C2212yes—
42C2×#66949—22no—
43C2×C4⋊C4×D11C2212yescomplemented
44#10623008—21no—
45#10623008C2211yescharacteristic
46C2×C4×D44—21no—
47C2×C4×D44—21no—
48C2×C4×D44C2211yescharacteristic
49C2×#66923—21no—
50C2×#66922C2211yescharacteristic, complemented
51C11×#441C2212yescomplemented
52C11×#440C2212yescomplemented
53C4×C11×Q16C2212yescomplemented
54C4×C11×SD16C2212yescomplemented
55C11×#428C2211yescharacteristic, complemented
56C11×#419C2211yescharacteristic, complemented
57C11×#417C2211yescharacteristic
58C4×C11×M16C2211yescharacteristic, complemented
59#10622845C2212yes—
60#10622800C2214yescomplemented
61#10622799C2214yescomplemented
62#10622786C2214yescomplemented
63#10622782C2214yescomplemented
64#10622746C2212yescomplemented
65#10622746C2212yescomplemented
66#10622739C2212yescomplemented
67#10622644C2212yescomplemented
68#10622641C2214yescomplemented
69#10622640C2212yescomplemented
70#10622634C2212yescomplemented
71#10622633C2212yescomplemented
72#10622621C2212yescomplemented
73#10622620C2212yescomplemented
74#10622608C2212yescomplemented
75#10622579C2212yescomplemented
76#10622537C2211yescharacteristic, complemented
77#10622497C2214yescomplemented
78#10622495C2214yescomplemented
79#10622476C2214yescomplemented
80#10622475C2214yescomplemented
81#10622429C2214yescomplemented
82#10622426C2214yescomplemented
83#10622425C2214yescomplemented
84#10622420C2214yescomplemented
85#10622416C2214yescomplemented
86D11×#103C2214yescomplemented
87#10622384C2214yescomplemented
88D11×#102C2214yescomplemented
89#10622327C2214yescomplemented
90#10622319C2214yescomplemented
91#10622307C2212yescomplemented
92#10622301C2212yescomplemented
93C8×D44C2212yes—
94#10622294C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97#41×D11—28no—
98#41×D11—44no—
99C2×#4343C2312yes—
100C2×Q8×D11C2312yes—
101C2×#4341—22no—
102C2×#4341C2312yes—
103C2×D4×D11—22no—
104C2×D4×D11C2312yes—
105C2×#4339—22no—
106C2×#4339C2312yes—
107C22×D44—21no—
108C22×D44D411yescharacteristic
109C22×C4×D11—22no—
110C22×C4×D11—22no—
111C22×C4×D11C2312yes—
112C22×Dic22—21no—
113C11×#137—24no—
114C2×C11×Q16C2312yes—
115C2×C11×SD16C2312yes—
116C2×C11×M16C2311yescharacteristic
117C2×C11×M16C2311yescharacteristic
118C4×Q8×C11—21no—
119C4×Q8×C11—21no—
120C4×Q8×C11C2311yescharacteristic
121C4×Q8×C11C2311yescharacteristic
122C4×Q8×C11C2312yes—
123C4×Q8×C11C2312yes—
124C4×D4×C11—21no—
125C4×D4×C11—21no—
126C4×D4×C11C2311yescharacteristic
127C4×D4×C11C2311yescharacteristic
128C11×#117—21no—
129C11×#117C2311yescharacteristic
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C42×C11—21no—
133C2×C42×C11—21no—
134C2×C42×C11C2311yescharacteristic
135#66999—22no—
136#66999—22no—
137#66999C2314yes—
138#66999C2314yes—
139C2×#4326C2314yes—
140#66995—44no—
141C2×#4325C2314yes—
142#66983—21no—
143#66983—21no—
144#66983—21no—
145#66983—22no—
146#66983—21no—
147C2×(C2×D11)⋊C4—22no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4D412yes—
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11—21no—
152C2×C4⋊Dic11D411yescharacteristic
153C2×C4⋊Dic11C2312yes—
154C2×Dic11⋊C4—22no—
155C2×Dic11⋊C4—22no—
156C2×#4318C2312yes—
157M16×D11—44no—
158C2×#4313C2314yes—
159C2×C8×D11C2314yes—
160#66950—22no—
161#66950—22no—
162#66950C2312yes—
163#66950C2312yes—
164#66949—24no—
165#66949—24no—
166#66949—24no—
167#66949—24no—
168#66948—22no—
169#66948—22no—
170#66948C2312yes—
171#66948C2312yes—
172C4⋊C4×D11—22no—
173C4⋊C4×D11—22no—
174C4⋊C4×D11C2314yes—
175C4⋊C4×D11C2314yes—
176#66939—22no—
177#66939—22no—
178#66939—22no—
179#66935—22no—
180#66935—22no—
181#66935—22no—
182#66928—22no—
183#66928C2312yes—
184#66927—21no—
185#66927C2311yescharacteristic
186C4×D44—21no—
187C4×D44—22no—
188C4×D44—22no—
189C4×D44—24no—
190C4×D44—22no—
191C4×D44—22no—
192C4×D44—21no—
193C4×D44—21no—
194C4×D44—22no—
195C4×D44—21no—
196C4×D44D411yescharacteristic
197C4×D44D411yescharacteristic
198C4×D44D412yes—
199C4×D44C2311yescharacteristic
200C4×D44C2311yescharacteristic
201C4×D44C2312yes—
202#66923—22no—
203#66923—22no—
204#66923—24no—
205#66922—21no—
206#66922—21no—
207#66922—21no—
208#66922C2311yescharacteristic
209#66922C2312yes—
210#66922C2312yes—
211C11×#107C2312yes—
212C11×#106C2312yes—
213C11×#103C2312yes—
214C11×#103C2312yes—
215C11×#103C2312yes—
216C11×#102C2312yes—
217C11×#97C2312yes—
218C4×C8×C11C2312yes—
219#66899C2314yes—
220#66896C2314yes—
221#66885C2314yes—
222#66885C2314yes—
223(C2×D11)⋊C8C2314yes—
224(C2×D11)⋊C8C2314yes—
225#66880C2314yes—
226#66880C2314yes—
227#66874C2314yes—
228#66873C2314yes—
229#66872C2314yes—
230#66871C2314yes—
231C4⋊(C11⋊C8)C2312yes—
232C4⋊(C11⋊C8)C2312yes—
233#61162—111nomaximal, Sylow
234C23×D11—22no—
235C23×D11C2×D412yes—
236C11×#41—22no—
237C11×#41#4114yes—
238C2×Q8×C11—21no—
239C2×Q8×C11—22no—
240C2×Q8×C11—22no—
241C2×Q8×C11C2412yes—
242C2×Q8×C11C2411yescharacteristic
243C2×D4×C11—21no—
244C2×D4×C11C2411yescharacteristic
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C2×C22⋊D11—22no—
254C2×C22⋊D11—22no—
255C2×C22⋊D11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11C2×D412yes—
259#4343—24no—
260#4343—42no—
261Q8×D11—24no—
262Q8×D11—42no—
263#4341—24no—
264#4341—42no—
265#4341—48no—
266D4×D11—24no—
267D4×D11—48no—
268D4×D11—42no—
269#4339—24no—
270#4339—24no—
271#4339—48no—
272C2×D44—24no—
273C2×D44—22no—
274C2×D44—22no—
275C2×D44—22no—
276C2×D44—21no—
277C2×D44—21no—
278C2×D44—44no—
279C2×D44C2×D411yescharacteristic
280C2×D44C2×D412yes—
281C2×D44C2×D411yescharacteristic
282C2×D44C2412yes—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—24no—
286C2×C4×D11—24no—
287C2×C4×D11—22no—
288C2×C4×D11—24no—
289C2×C4×D11—24no—
290C2×C4×D11—48no—
291C2×C4×D11—84no—
292C2×C4×D11C2×D412yes—
293C2×C4×D11C2×D412yes—
294C2×C4×D11C2412yes—
295C2×C4×D11C2412yes—
296C2×Dic22—22no—
297C2×Dic22—22no—
298C2×Dic22—22no—
299C2×Dic22—82no—
300C2×Dic22C2412yes—
301C11×Q16—24no—
302C11×SD16—24no—
303C11×M16—22no—
304C11×M16—22no—
305C2×C8×C11C2412yes—
306C2×C8×C11C2412yes—
307C11×C4⋊C4—21no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4—21no—
310C11×C4⋊C4—22no—
311C11×C4⋊C4—22no—
312C11×C4⋊C4C2411yescharacteristic
313C11×C4⋊C4C2411yescharacteristic
314C11×C4⋊C4C2412yes—
315C11×C22⋊C4—21no—
316C11×C22⋊C4—21no—
317C11×C22⋊C4—21no—
318C42×C11—21no—
319C42×C11—22no—
320C42×C11—22no—
321C42×C11—21no—
322C42×C11—21no—
323C42×C11C2×D411yescharacteristic
324C42×C11C2×D411yescharacteristic
325C42×C11C2411yescharacteristic
326C42×C11C2411yescharacteristic
327#4326—44no—
328#4325—44no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—22no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4—22no—
337(C2×D11)⋊C4C2×D412yes—
338(C2×D11)⋊C4C2×D412yes—
339(C2×D11)⋊C4C2×D412yes—
340(C2×D11)⋊C4C2×D412yes—
341C4⋊Dic11—22no—
342C4⋊Dic11—22no—
343C4⋊Dic11—22no—
344C4⋊Dic11—22no—
345C4⋊Dic11—22no—
346C4⋊Dic11—21no—
347C4⋊Dic11—21no—
348C4⋊Dic11C2×D411yescharacteristic
349C4⋊Dic11C2×D411yescharacteristic
350C4⋊Dic11C2×D412yes—
351C4⋊Dic11C2414yes—
352Dic11⋊C4—24no—
353Dic11⋊C4—24no—
354Dic11⋊C4—24no—
355Dic11⋊C4—24no—
356#4318—24no—
357C2×C11⋊C8C2414yes—
358#4313—44no—
359C8×D11—44no—
360C2×#554—111no—
361D4×#41—111no—
362#3333—112no—
363#3331—112no—
364#3316—114no—
365#3314—114no—
366#3299—112no—
367#3295—112no—
368#3141—111no—
369#3092—112no—
370#3079—111no—
371#3056—112no—
372#3037—111no—
373#3007—112no—
374C4×#137D1111yescharacteristic, complemented
375D4×M16—111no—
376C2×#417—112no—
377C23×C11—21no—
378C23×C11C22×D411yescharacteristic
379C22×D11—24no—
380C22×D11—24no—
381C22×D11—22no—
382C22×D11—42no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11—82no—
386C22×D11C22×D412yes—
387C22×D11C22×D412yes—
388Q8×C11—21no—
389Q8×C11—22no—
390Q8×C11—22no—
391Q8×C11—42no—
392Q8×C11C2×#4112yes—
393D4×C11—24no—
394D4×C11—21no—
395D4×C11C2×#4112yes—
396C2×C4×C11—21no—
397C2×C4×C11—24no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—41no—
404C2×C4×C11—42no—
405C2×C4×C11—42no—
406C2×C4×C11—42no—
407C2×C4×C11—81no—
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C2×#4112yes—
414C2×C4×C11H(5,𝔽2)12yes—
415C2×C4×C11C2511yescharacteristic
416C22⋊D11—44no—
417C22⋊D11—44no—
418C22⋊D11—44no—
419C2×Dic11—24no—
420C2×Dic11—24no—
421C2×Dic11—22no—
422C2×Dic11—44no—
423C2×Dic11—44no—
424C2×Dic11C22×D412yes—
425C2×Dic11C22×D412yes—
426D44—24no—
427D44—22no—
428D44—22no—
429D44—22no—
430D44—44no—
431D44—44no—
432D44—42no—
433D44—81no—
434D44—82no—
435D44#13714yescomplemented
436C4×D11—24no—
437C4×D11—24no—
438C4×D11—22no—
439C4×D11—22no—
440C4×D11—22no—
441C4×D11—22no—
442C4×D11—44no—
443C4×D11—44no—
444C4×D11—44no—
445C4×D11—84no—
446C4×D11—84no—
447Dic22—22no—
448Dic22—22no—
449Dic22—44no—
450Dic22—82no—
451Dic22—82no—
452C8×C11—22no—
453C8×C11—22no—
454C11⋊C8—24no—
455C22×#41—112no—
456C2×#137—112no—
457C2×#137C2×D1111yescharacteristic
458C22×M16—112no—
459#554—112no—
460#554—112no—
461#554—114no—
462#554—221no—
463#554—222no—
464#554—221no—
465#550—111no—
466D4×Q8—111no—
467#548—112no—
468#547—111no—
469#547—221no—
470#546—112no—
471#546—222no—
472D42—111no—
473D42—221no—
474#532—111no—
475#532—221no—
476C2×C4⋊Q8—111no—
477C2×#125—221no—
478#525—112no—
479#525—222no—
480C2×C22⋊Q8—112no—
481C2×C22⋊Q8—222no—
482C4×#41C2×D1111yescharacteristic
483C2×C4×Q8C2×D1111yescharacteristic, complemented
484C2×C4×D4—111no—
485C2×C4×D4—221no—
486C2×C4×D4—221no—
487C22×C4⋊C4—112no—
488#489—114no—
489#487—112no—
490#486—112no—
491#484—114no—
492#483—114no—
493#481—114no—
494#480—114no—
495#477—112no—
496#476—112no—
497#475—112no—
498#474—112no—
499#470—114no—
500#468—114no—
501#467—114no—
502#465—114no—
503#464—114no—
504#462—112no—
505#460—112no—
506#452—114no—
507#452—114no—
508#451—114no—
509#450—114no—
510#441C2×D1112yescomplemented
511#440C2×D1112yescomplemented
512C4×Q16C2×D1112yescomplemented
513C4×SD16C2×D1112yescomplemented
514#436—112no—
515#435—114no—
516C8×D4—112no—
517#428—112no—
518#428C2×D1111yescharacteristic, complemented
519#423—111no—
520#419C2×D1111yescharacteristic, complemented
521#417—112no—
522#417—112no—
523#417—112no—
524#417—112no—
525#417—114no—
526#417—114no—
527#417C2×D1111yescharacteristic
528C2×#103—114no—
529C2×#102—114no—
530#407—112no—
531C4×M16C2×D1111yescharacteristic, complemented
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—22no—
535C22×C11—41no—
536C22×C11—41no—
537C22×C11#54612yes—
538C22×C11C23×D411yescharacteristic
539C2×D11—22no—
540C2×D11—22no—
541C2×D11—22no—
542C2×D11—22no—
543C2×D11—22no—
544C2×D11—48no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—88no—
549C2×D11C2×#13714yes—
550C4×C11—21no—
551C4×C11—21no—
552C4×C11—22no—
553C4×C11—21no—
554C4×C11—42no—
555C4×C11—41no—
556C4×C11—42no—
557C4×C11—41no—
558C4×C11#54612yes—
559C4×C11C2×#13712yes—
560C4×C11C22×#4111yescharacteristic
561C4×C11C2×H(5,𝔽2)11yescharacteristic
562Dic11—22no—
563Dic11—22no—
564Dic11—44no—
565Dic11—42no—
566C2×#41—112no—
567C2×#41—112no—
568C2×#41—112no—
569C2×#41—222no—
570C2×#41—222no—
571C2×#41—228no—
572C2×#41—444no—
573C2×#41C22×D1111yescharacteristic
574C22×Q8—112no—
575C22×Q8—221no—
576C22×Q8C22×D1111yescharacteristic
577C22×D4—112no—
578C22×D4—111no—
579C22×D4—221no—
580C22×D4—222no—
581C23×C4—112no—
582C23×C4—222no—
583C23×C4—222no—
584#137—24no—
585#137—444no—
586C2×Q16—114no—
587C2×Q16C22×D1112yes—
588C2×SD16—114no—
589C2×SD16C22×D1112yes—
590C2×M16—112no—
591C2×M16—114no—
592C2×M16—444no—
593C2×M16C22×D1111yescharacteristic
594C2×M16C22×D1111yescharacteristic
595C22×C8—114no—
596C4⋊Q8—112no—
597C4⋊Q8—112no—
598C4⋊Q8—111no—
599C4⋊Q8—221no—
600C4⋊Q8—221no—
601C4⋊Q8—221no—
602#127—111no—
603#127—221no—
604#125—222no—
605#125—222no—
606#125—224no—
607#124—112no—
608#124—222no—
609#123—222no—
610#123—222no—
611#123—222no—
612C22⋊Q8—114no—
613C22⋊Q8—114no—
614C22⋊Q8—112no—
615C22⋊Q8—112no—
616C22⋊Q8—224no—
617C22⋊Q8—224no—
618C22⋊Q8—224no—
619C22⋊Q8—224no—
620C22⋊Q8—222no—
621C22⋊Q8—222no—
622C22⋊Q8—222no—
623C22⋊Q8—222no—
624#121—112no—
625#121—112no—
626#121—222no—
627#121—222no—
628#121—222no—
629#121—221no—
630#121—221no—
631#121—221no—
632#121—221no—
633#120—222no—
634#120—222no—
635#120—222no—
636C4×Q8—21no—
637C4×Q8—21no—
638C4×Q8C22×D1112yes—
639C4×Q8C22×D1112yes—
640C4×Q8C22×D1111yescharacteristic
641C4×Q8C22×D1111yescharacteristic
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—111no—
645C4×D4—112no—
646C4×D4—111no—
647C4×D4—111no—
648C4×D4—112no—
649C4×D4—111no—
650C4×D4—222no—
651C4×D4—221no—
652C4×D4—222no—
653C4×D4—222no—
654C4×D4—221no—
655C4×D4—222no—
656C4×D4—224no—
657C4×D4—222no—
658C4×D4—221no—
659C4×D4—221no—
660C4×D4C22×D1111yescharacteristic
661C4×D4C22×D1111yescharacteristic
662#117—21no—
663#117C22×D1111yescharacteristic
664C2×C4⋊C4—21no—
665C2×C4⋊C4—111no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4—114no—
668C2×C4⋊C4—114no—
669C2×C4⋊C4—222no—
670C2×C4⋊C4—222no—
671C2×C4⋊C4—221no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—221no—
675C2×C4⋊C4C22×D1111yescharacteristic
676C2×C22⋊C4—112no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42C22×D1111yescharacteristic
682#107—114no—
683#107C22×D1112yes—
684#106—114no—
685#106C22×D1112yes—
686C4⋊C8—112no—
687C4⋊C8—112no—
688#103—114no—
689#103—114no—
690#103—114no—
691#103—114no—
692#103C22×D1112yes—
693#103C22×D1112yes—
694#103C22×D1112yes—
695#102—114no—
696#102—114no—
697#102—114no—
698#102—114no—
699#102C22×D1112yes—
700C22⋊C8—114no—
701C22⋊C8—114no—
702#97C22×D1112yes—
703C4×C8C22×D1112yes—
704C2×C11—22no—
705C2×C11—42no—
706C2×C11C2×#54611yescharacteristic
707C2×C11C22×#13711yescharacteristic
708C2×C11#358511yescharacteristic
709D11—24no—
710D11—42no—
711D11—82no—
712C24—112no—
713C24—222no—
714#41—22no—
715#41—224no—
716#41—224no—
717#41—224no—
718#41—224no—
719#41—448no—
720#41—442no—
721#41—448no—
722#41—442no—
723#41#433914yes—
724C2×Q8—21no—
725C2×Q8—22no—
726C2×Q8—22no—
727C2×Q8—112no—
728C2×Q8—222no—
729C2×Q8—222no—
730C2×Q8—222no—
731C2×Q8—224no—
732C2×Q8—442no—
733C2×Q8—882no—
734C2×Q8C23×D1112yes—
735C2×Q8C23×D1111yescharacteristic
736C2×D4—21no—
737C2×D4—111no—
738C2×D4—112no—
739C2×D4—111no—
740C2×D4—112no—
741C2×D4—224no—
742C2×D4—222no—
743C2×D4—222no—
744C2×D4—222no—
745C2×D4—222no—
746C2×D4—224no—
747C2×D4—222no—
748C2×D4—222no—
749C2×D4—221no—
750C2×D4—221no—
751C2×D4—444no—
752C2×D4—442no—
753C2×D4—448no—
754C2×D4C23×D1111yescharacteristic
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—112no—
764C22×C4—112no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—224no—
768C22×C4—224no—
769C22×C4—222no—
770C22×C4—224no—
771C22×C4—224no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—448no—
775C22×C4—884no—
776C22×C4D4×D1111yescharacteristic
777C22×C4D4×D1111yescharacteristic
778C22×C4C23×D1111yescharacteristic
779Q16—24no—
780Q16—444no—
781SD16—24no—
782SD16—444no—
783M16—22no—
784M16—22no—
785M16—224no—
786M16—444no—
787C2×C8—114no—
788C2×C8—444no—
789C2×C8C23×D1112yes—
790C2×C8C23×D1112yes—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—111no—
797C4⋊C4—111no—
798C4⋊C4—112no—
799C4⋊C4—114no—
800C4⋊C4—224no—
801C4⋊C4—224no—
802C4⋊C4—222no—
803C4⋊C4—224no—
804C4⋊C4—224no—
805C4⋊C4—222no—
806C4⋊C4—222no—
807C4⋊C4—221no—
808C4⋊C4—222no—
809C4⋊C4—222no—
810C4⋊C4—221no—
811C4⋊C4C23×D1112yes—
812C4⋊C4C23×D1111yescharacteristic
813C4⋊C4C23×D1111yescharacteristic
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—112no—
818C22⋊C4—112no—
819C22⋊C4—112no—
820C22⋊C4—112no—
821C22⋊C4—222no—
822C22⋊C4—222no—
823C22⋊C4—222no—
824C22⋊C4—224no—
825C22⋊C4—224no—
826C22⋊C4—222no—
827C22⋊C4—222no—
828C22⋊C4—222no—
829C42—21no—
830C42—21no—
831C42—21no—
832C42—22no—
833C42—22no—
834C42D4×D1111yescharacteristic
835C42D4×D1111yescharacteristic
836C42C23×D1111yescharacteristic
837C42C23×D1111yescharacteristic
838C11#6116211yescharacteristic, complemented, Sylow
839C23—21no—
840C23—112no—
841C23—112no—
842C23—224no—
843C23—224no—
844C23—222no—
845C23—442no—
846C23—444no—
847C23—444no—
848C23—882no—
849C23C2×D4×D1111yescharacteristic
850Q8—21no—
851Q8—22no—
852Q8—22no—
853Q8—42no—
854Q8—222no—
855Q8—222no—
856Q8—444no—
857Q8—882no—
858Q8—882no—
859Q8C2×#433912yes—
860D4—24no—
861D4—21no—
862D4—114no—
863D4—224no—
864D4—222no—
865D4—222no—
866D4—222no—
867D4—444no—
868D4—444no—
869D4—444no—
870D4—444no—
871D4—444no—
872D4—442no—
873D4—881no—
874D4—882no—
875D4C2×#433912yes—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—81no—
888C2×C4—112no—
889C2×C4—112no—
890C2×C4—224no—
891C2×C4—224no—
892C2×C4—224no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—224no—
899C2×C4—444no—
900C2×C4—444no—
901C2×C4—444no—
902C2×C4—444no—
903C2×C4—444no—
904C2×C4—884no—
905C2×C4—884no—
906C2×C4C2×#433912yes—
907C2×C4C2×D4×D1111yescharacteristic
908C2×C4C2×D4×D1111yescharacteristic
909C2×C4C2×D4×D1111yescharacteristic
910C2×C4C2×D4×D1111yescharacteristic
911C2×C4C2×D4×D1111yescharacteristic
912C2×C4#6704212yes—
913C2×C4C24×D1111yescharacteristic
914C8—22no—
915C8—22no—
916C8—224no—
917C22—21no—
918C22—21no—
919C22—22no—
920C22—41no—
921C22—41no—
922C22—114no—
923C22—222no—
924C22—222no—
925C22—222no—
926C22—222no—
927C22—222no—
928C22—448no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—888no—
933C22#1062308112yes—
934C22C22×D4×D1111yescharacteristic
935C4—21no—
936C4—21no—
937C4—22no—
938C4—21no—
939C4—42no—
940C4—41no—
941C4—42no—
942C4—41no—
943C4—222no—
944C4—222no—
945C4—444no—
946C4—442no—
947C4#1062308112yes—
948C4D11×#13712yes—
949C4C22×#433911yescharacteristic
950C4C2×#6704211yescharacteristic
951C2—22no—
952C2—42no—
953C2—224no—
954C2—442no—
955C2—882no—
956C2C2×#1062308111yescharacteristic
957C2C2×D11×#13711yescharacteristic
958C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×#137C2
socleC22×C11C23×D4
prime radical#41×D44C2
hypercenterC4×#137D11
hypocenterC11#61162
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
3. #13080956C2semidirect
4. #13080934C2semidirect
5. #13080732C2semidirect
6. #13080702C2semidirect
7. #13080494C2semidirect
8. #13080442C2semidirect
9. #13079010C2semidirect
10. #13078542C2semidirect
11. #13078431C2semidirect
12. #13078244C2semidirect
13. #13078088C2semidirect
14. #13077872C2semidirect
15. M16×D44C2semidirect
16. D11×#417C2semidirect
17. C4×C11×#137C2semidirect
21. C2×C4×Q8×C11C22semidirect
22. C2×#66999C22semidirect
23. C2×#66995C22semidirect
24. C2×M16×D11C22semidirect
29. #10623110C22semidirect
30. #10623110C22semidirect
43. C2×C4⋊C4×D11C22semidirect
50. C2×#66922C22semidirect
51. C11×#441C22semidirect
52. C11×#440C22semidirect
53. C4×C11×Q16C22semidirect
54. C4×C11×SD16C22semidirect
55. C11×#428C22semidirect
56. C11×#419C22semidirect
58. C4×C11×M16C22semidirect
60. #10622800C22semidirect
61. #10622799C22semidirect
62. #10622786C22semidirect
63. #10622782C22semidirect
64. #10622746C22semidirect
65. #10622746C22semidirect
66. #10622739C22semidirect
67. #10622644C22semidirect
68. #10622641C22semidirect
69. #10622640C22semidirect
70. #10622634C22semidirect
71. #10622633C22semidirect
72. #10622621C22semidirect
73. #10622620C22semidirect
74. #10622608C22semidirect
75. #10622579C22semidirect
76. #10622537C22semidirect
77. #10622497C22semidirect
78. #10622495C22semidirect
79. #10622476C22semidirect
80. #10622475C22semidirect
81. #10622429C22semidirect
82. #10622426C22semidirect
83. #10622425C22semidirect
84. #10622420C22semidirect
85. #10622416C22semidirect
86. D11×#103C22semidirect
87. #10622384C22semidirect
88. D11×#102C22semidirect
89. #10622327C22semidirect
90. #10622319C22semidirect
91. #10622307C22semidirect
92. #10622301C22semidirect
94. #10622294C22semidirect
374. C4×#137D11semidirect
435. D44#137semidirect
483. C2×C4×Q8C2×D11semidirect
510. #441C2×D11semidirect
511. #440C2×D11semidirect
512. C4×Q16C2×D11semidirect
513. C4×SD16C2×D11semidirect
518. #428C2×D11semidirect
520. #419C2×D11semidirect
531. C4×M16C2×D11semidirect
838. C11#61162semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
#41×D442
#130809562
#130809342
#130807322
#130807022
#130804942
#130804422
#130790102
#130785422
#130784312
#130782442
#130780882
#130778722
M16×D442
D11×#4172
C4×C11×#1372
#6116211