Finite Group Databasebeta

← #15630853

Subgroups — #15630853

Order 2816.

2172 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082174C211yesmaximal, characteristic, complemented
2#13080954C212yesmaximal, complemented
3#13080943C212yesmaximal, complemented
4#13080742C214yesmaximal, complemented
5#13080622C214yesmaximal, complemented
6#13080566C212yesmaximal, complemented
7#13080555C212yesmaximal, complemented
8#13078990C211yesmaximal, characteristic, complemented
9#13078552C212yesmaximal, complemented
10#13078421C211yesmaximal, characteristic, complemented
11#13078231C212yesmaximal, complemented
12#13078092C211yesmaximal, characteristic, complemented
13#13077858C212yesmaximal, complemented
14C4×#66995C211yesmaximal, characteristic, complemented
15D4×#4318C211yesmaximal, characteristic, complemented
16#13077135C212yesmaximal, complemented
17C2×C11×#550C211yesmaximal, characteristic, complemented
18C22×C11×#41C2212yes—
19C11×#550—21no—
20C11×#550—22no—
21C11×#550—21no—
22C11×#550C2214yes—
23C11×#550C2212yes—
24C11×#550C2212yes—
25C2×C11×#127—21no—
26C2×C11×#127C2211yescharacteristic
27C2×C11×#121—22no—
28C2×C11×#121C2212yes—
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×#66995C2211yescharacteristic
33#10623337—21no—
34C2×#66985C2212yes—
35#10623322C2212yes—
36C2×#66979C2212yes—
37C22×#4318C2212yes—
38#10623096C2212yescomplemented
39#10623094C2211yescharacteristic, complemented
40#10623088—21no—
41#10623086C2211yescharacteristic, complemented
42#10623074C2211yescharacteristic, complemented
43#10623073C2211yescharacteristic, complemented
44#10623072C2212yescomplemented
45#10623069—22no—
46C4×#4341—21no—
47#10623044—21no—
48#10623026—22no—
49C4×#4339C2211yescharacteristic
50#10623001C2211yescharacteristic
51#10622852C2214yescomplemented
52#10622852C2214yescomplemented
53#10622851C2214yescomplemented
54#10622851C2214yescomplemented
55#10622846C2214yescomplemented
56#10622846C2214yescomplemented
57#10622845C2214yescomplemented
58#10622845C2214yescomplemented
59#10622838C2212yes—
60#10622838C2211yescharacteristic
61#10622828C2212yes—
62#10622828C2212yes—
63#10622828C2212yes—
64#10622820C2212yes—
65#10622688C2212yescomplemented
66#10622688C2212yescomplemented
67#10622685C2212yescomplemented
68#10622685C2212yescomplemented
69#10622684C2214yescomplemented
70#10622683C2212yescomplemented
71#10622683C2212yescomplemented
72#10622655C2214yescomplemented
73#10622654C2214yescomplemented
74#10622652C2214yescomplemented
75#10622651C2214yescomplemented
76#10622648C2214yescomplemented
77#10622648C2214yescomplemented
78#10622647C2214yescomplemented
79#10622646C2214yescomplemented
80#10622643C2212yescomplemented
81C4×#4326C2212yescomplemented
82#10622639C2212yescomplemented
83C4×#4325C2212yescomplemented
84#10622635C2214yescomplemented
85#10622634C2212yescomplemented
86#10622633C2212yescomplemented
87#10622625C2212yescomplemented
88#10622624C2214yescomplemented
89D4×C11⋊C8C2212yescomplemented
90#10622579C2211yescharacteristic
91#10622577C2211yescharacteristic
92#10622577C2212yes—
93#10622537C2211yescharacteristic
94C4×#4318C2211yescharacteristic
95C2×C11×#41—22no—
96C2×C11×#41—22no—
97C2×C11×#41—28no—
98C2×C11×#41—44no—
99C2×C11×#41C2314yes—
100C2×C11×#41C2314yes—
101C22×Q8×C11C2311yescharacteristic
102C22×D4×C11—22no—
103C22×D4×C11—22no—
104C22×D4×C11—21no—
105C22×D4×C11—21no—
106C22×D4×C11D411yescharacteristic
107C22×D4×C11C2312yes—
108C23×C4×C11—22no—
109C23×C4×C11C2312yes—
110C2×#4341—21no—
111C2×#4339C2311yescharacteristic
112C11×#127—22no—
113C11×#127—22no—
114C11×#127—24no—
115C11×#127—21no—
116C11×#127—21no—
117C11×#127C2312yes—
118C11×#127C2312yes—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—24no—
122C11×#121—24no—
123C11×#121—24no—
124C11×#121—24no—
125C11×#121C2314yes—
126C11×#121C2314yes—
127C4×Q8×C11—21no—
128C4×Q8×C11—21no—
129C4×Q8×C11C2312yes—
130C4×Q8×C11C2312yes—
131C4×D4×C11—22no—
132C4×D4×C11—24no—
133C4×D4×C11—22no—
134C4×D4×C11D411yescharacteristic
135C4×D4×C11D412yes—
136C4×D4×C11D411yescharacteristic
137C4×D4×C11C2312yes—
138C4×D4×C11C2311yescharacteristic
139C4×D4×C11C2311yescharacteristic
140C2×C11×C4⋊C4—21no—
141C2×C11×C4⋊C4D411yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4—22no—
144C2×C11×C22⋊C4D412yes—
145C2×C42×C11—21no—
146C2×C42×C11C2311yescharacteristic
147#67006—22no—
148C2×C22⋊Dic11—22no—
149C2×#4326C2312yes—
150#66995—24no—
151C2×#4325C2312yes—
152#66992—22no—
153#66991—21no—
154#66989—21no—
155#66988—22no—
156D4×Dic11—21no—
157C2×#4324C2314yes—
158#66985—44no—
159C2×#4323C2314yes—
160#66983C2312yes—
161#66983C2312yes—
162#66982—22no—
163C4×C22⋊D11—21no—
164C4×C22⋊D11—21no—
165C4×C22⋊D11—22no—
166C4×C22⋊D11—22no—
167#66979—22no—
168#66979—22no—
169#66979C2312yes—
170#66979C2311yescharacteristic
171#66979C2312yes—
172#66979C2312yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2312yes—
175#66977—21no—
176#66977—21no—
177#66977C2312yes—
178#66977C2312yes—
179C2×C4×Dic11—22no—
180C2×#4318—44no—
181C2×#4318C2311yescharacteristic
182C2×#4318C2311yescharacteristic
183C2×#4318C2312yes—
184C2×#4318C2314yes—
185C22×C11⋊C8C2314yes—
186#66951—22no—
187#66950—21no—
188#66945—21no—
189#66943—21no—
190#66942—22no—
191#66940—21no—
192#66939—22no—
193#66938—22no—
194#66936—22no—
195(C22⋊D11)⋊C4—22no—
196#66932—22no—
197#66932—22no—
198#66931—22no—
199#66930—22no—
200C4×D44C2311yescharacteristic
201C4×D44C2311yescharacteristic
202#66925—21no—
203C42×D11—21no—
204#66923C2312yes—
205#66922C2311yescharacteristic
206#66922C2311yescharacteristic
207C4×Dic22—21no—
208C4×Dic22—21no—
209C4×Dic22C2311yescharacteristic
210C4×Dic22C2311yescharacteristic
211#66899C2312yes—
212#66899C2312yes—
213#66899C2314yes—
214#66899C2314yes—
215#66896C2314yes—
216#66896C2314yes—
217#66896C2314yes—
218#66896C2314yes—
219#66896C2314yes—
220#66896C2314yes—
221C22⋊(C11⋊C8)C2314yes—
222C22⋊(C11⋊C8)C2314yes—
223#66874C2312yes—
224#66873C2312yes—
225#66872C2314yes—
226#66872C2312yes—
227#66871C2314yes—
228#66871C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231#66867C2312yes—
232C4×C11⋊C8C2312yes—
233#61160—111nomaximal, Sylow
234C24×C11—22no—
235C24×C11C2×D412yes—
236C11×#41—28no—
237C11×#41—28no—
238C11×#41—44no—
239C11×#41—44no—
240C11×#41—48no—
241C11×#41—48no—
242C2×Q8×C11—21no—
243C2×Q8×C11—22no—
244C2×Q8×C11#4114yescomplemented
245C2×Q8×C11C2412yes—
246C2×D4×C11—24no—
247C2×D4×C11—24no—
248C2×D4×C11—24no—
249C2×D4×C11—24no—
250C2×D4×C11—22no—
251C2×D4×C11—22no—
252C2×D4×C11—22no—
253C2×D4×C11—22no—
254C2×D4×C11—22no—
255C2×D4×C11—24no—
256C2×D4×C11—24no—
257C2×D4×C11—42no—
258C2×D4×C11—48no—
259C2×D4×C11—44no—
260C2×D4×C11—82no—
261C2×D4×C11—84no—
262C2×D4×C11C2×D411yescharacteristic
263C2×D4×C11C2×D411yescharacteristic
264C2×D4×C11C2×D412yes—
265C2×D4×C11C2414yes—
266C22×C4×C11—21no—
267C22×C4×C11—24no—
268C22×C4×C11—24no—
269C22×C4×C11—21no—
270C22×C4×C11—24no—
271C22×C4×C11—24no—
272C22×C4×C11—48no—
273C22×C4×C11C2×D412yes—
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D412yes—
276C22×C4×C11C2×D412yes—
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2411yescharacteristic
281C2×C22⋊D11—22no—
282C2×C22⋊D11—21no—
283C2×C22⋊D11—22no—
284C22×Dic11—22no—
285C22×Dic11—22no—
286#4341—44no—
287#4339—22no—
288#4339—22no—
289C2×D44C2411yescharacteristic
290C2×C4×D11—21no—
291C2×C4×D11—21no—
292C2×C4×D11—21no—
293C2×Dic22—21no—
294C2×Dic22—21no—
295C2×Dic22C2411yescharacteristic
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—21no—
299C11×C4⋊C4C2×D411yescharacteristic
300C11×C4⋊C4C2×D412yes—
301C11×C4⋊C4C2×D411yescharacteristic
302C11×C4⋊C4C2412yes—
303C11×C22⋊C4—24no—
304C11×C22⋊C4—24no—
305C11×C22⋊C4C2×D412yes—
306C11×C22⋊C4C2×D412yes—
307C11×C22⋊C4C2×D412yes—
308C11×C22⋊C4C2×D412yes—
309C42×C11—22no—
310C42×C11—22no—
311C42×C11C2×D411yescharacteristic
312C42×C11C2×D411yescharacteristic
313C42×C11C2411yescharacteristic
314C42×C11C2411yescharacteristic
315C22⋊Dic11—22no—
316C22⋊Dic11—22no—
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319C22⋊Dic11—22no—
320C22⋊Dic11—21no—
321#4326—24no—
322#4325—24no—
323#4324—44no—
324#4323—44no—
325(C2×D11)⋊C4—21no—
326(C2×D11)⋊C4—21no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329C4⋊Dic11—21no—
330C4⋊Dic11—21no—
331C4⋊Dic11—22no—
332C4⋊Dic11—22no—
333C4⋊Dic11C2411yescharacteristic
334C4⋊Dic11C2412yes—
335C4⋊Dic11C2411yescharacteristic
336C4⋊Dic11C2412yes—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—21no—
340Dic11⋊C4—21no—
341Dic11⋊C4—22no—
342Dic11⋊C4—22no—
343C4×Dic11—22no—
344C4×Dic11—21no—
345C4×Dic11—21no—
346C4×Dic11—21no—
347C4×Dic11—22no—
348C4×Dic11—22no—
349#4318—22no—
350#4318—22no—
351#4318—24no—
352#4318—44no—
353C2×C11⋊C8—44no—
354C2×C11⋊C8C2412yes—
355C2×C11⋊C8C2412yes—
356C2×C11⋊C8C2414yes—
357#3475—111no—
358C2×#550D1111yescharacteristic, complemented
359#3333—112no—
360#3332—112no—
361#3317—114no—
362#3309—114no—
363#3305—112no—
364#3304—112no—
365#3138—111no—
366#3094—112no—
367#3078—111no—
368#3055—112no—
369#3038—111no—
370#3005—112no—
371C4×#137—111no—
372D4×M16—111no—
373#2896—112no—
374C23×C11—24no—
375C23×C11—24no—
376C23×C11—42no—
377C23×C11—42no—
378C23×C11—44no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11C22×D412yes—
382C23×C11C22×D412yes—
383C23×C11C22×D411yescharacteristic
384C22×D11—21no—
385Q8×C11—24no—
386Q8×C11—22no—
387Q8×C11C2×#4114yes—
388D4×C11—22no—
389D4×C11—22no—
390D4×C11—24no—
391D4×C11—24no—
392D4×C11—42no—
393D4×C11—48no—
394D4×C11—48no—
395D4×C11—44no—
396D4×C11—44no—
397D4×C11—44no—
398D4×C11—82no—
399D4×C11—82no—
400D4×C11—84no—
401D4×C11—84no—
402C2×C4×C11—24no—
403C2×C4×C11—24no—
404C2×C4×C11—22no—
405C2×C4×C11—24no—
406C2×C4×C11—24no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—41no—
414C2×C4×C11—48no—
415C2×C4×C11—48no—
416C2×C4×C11—42no—
417C2×C4×C11C22×D412yes—
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D412yes—
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C2×#4112yes—
425C2×C4×C11H(5,𝔽2)12yes—
426C2×C4×C11C2511yescharacteristic
427C22⋊D11—44no—
428C22⋊D11—42no—
429C22⋊D11—82no—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—21no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—44no—
436C2×Dic11—82no—
437D44—21no—
438D44—21no—
439C4×D11—42no—
440C4×D11—42no—
441C4×D11—81no—
442Dic22—21no—
443Dic22—21no—
444Dic22—42no—
445Dic22—81no—
446C11⋊C8—22no—
447C11⋊C8—22no—
448C11⋊C8—24no—
449C22×#41C2×D1112yes—
450C2×#137—111no—
451C2×AGL(1,ℤ/8)—112no—
452C22×M16—112no—
453#556—111no—
454#555—111no—
455#554—111no—
456#553—112no—
457#552—112no—
458#552—221no—
459#551—222no—
460#550—21no—
461#550—21no—
462#550—22no—
463#550C2×D1112yes—
464#550C2×D1112yes—
465#550C2×D1114yes—
466#547—111no—
467#546—221no—
468#533—111no—
469C2×#127—21no—
470C2×#127C2×D1111yescharacteristic
471#529—222no—
472#529—221no—
473#525—112no—
474C2×#121—22no—
475C2×#121C2×D1112yes—
476C4×#41—111no—
477C4×#41—221no—
478C2×C4×Q8C2×D1111yescharacteristic
479C2×C4×D4—21no—
480C2×C4×D4C2×D1111yescharacteristic
481C2×#117—112no—
482#490—114no—
483#486—112no—
484#486—112no—
485#482—114no—
486#482—114no—
487#481—114no—
488#480—114no—
489#479—114no—
490#477—112no—
491#475—112no—
492#469—114no—
493#468—114no—
494#466—114no—
495#465—114no—
496#460—112no—
497#460—112no—
498#459—112no—
499#459—112no—
500#452—114no—
501#452—114no—
502#449—114no—
503#449—114no—
504#441—112no—
505#440—112no—
506C4×Q16—112no—
507C4×SD16—112no—
508#436—112no—
509#435—114no—
510C8×D4—112no—
511#428—112no—
512#428—111no—
513#423—111no—
514#419—112no—
515#419—111no—
516#418—112no—
517#418—112no—
518#418—112no—
519#417—114no—
520#417—114no—
521#417—111no—
522#416—114no—
523#416—114no—
524#407—112no—
525C4×M16—111no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—22no—
529C22×C11—22no—
530C22×C11—22no—
531C22×C11—22no—
532C22×C11—22no—
533C22×C11—22no—
534C22×C11—44no—
535C22×C11—44no—
536C22×C11—44no—
537C22×C11—84no—
538C22×C11—88no—
539C22×C11#54612yes—
540C22×C11C23×D411yescharacteristic
541C2×D11—41no—
542C2×D11—41no—
543C2×D11—41no—
544C4×C11—21no—
545C4×C11—21no—
546C4×C11—22no—
547C4×C11—22no—
548C4×C11—24no—
549C4×C11—21no—
550C4×C11—42no—
551C4×C11#54612yes—
552C4×C11#57512yes—
553C4×C11C22×#4111yescharacteristic
554C4×C11C2×H(5,𝔽2)11yescharacteristic
555Dic11—42no—
556Dic11—41no—
557Dic11—41no—
558Dic11—42no—
559Dic11—41no—
560C2×#41—22no—
561C2×#41—22no—
562C2×#41—28no—
563C2×#41—44no—
564C2×#41—111no—
565C2×#41—221no—
566C2×#41C22×D1114yes—
567C2×#41C22×D1114yes—
568C22×Q8C22×D1111yescharacteristic
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—21no—
572C22×D4—21no—
573C22×D4C22⋊D1111yescharacteristic
574C22×D4C22×D1112yes—
575C23×C4—22no—
576C23×C4C22×D1112yes—
577#137—224no—
578AGL(1,ℤ/8)—444no—
579C2×Q16—112no—
580C2×SD16—112no—
581C2×SD16—114no—
582C2×D8—114no—
583C2×M16—111no—
584C2×M16—112no—
585C2×M16—111no—
586C2×M16—114no—
587C2×M16—444no—
588C22×C8—114no—
589C4⋊Q8—111no—
590C4⋊Q8—111no—
591#127—22no—
592#127—22no—
593#127—24no—
594#127—21no—
595#127—21no—
596#127C22×D1112yes—
597#127C22×D1112yes—
598#126—222no—
599#126—222no—
600#126—222no—
601#125—112no—
602#125—222no—
603#125—221no—
604#124—221no—
605#124—222no—
606#123—222no—
607#123—222no—
608#123—222no—
609#123—222no—
610C22⋊Q8—112no—
611C22⋊Q8—112no—
612C22⋊Q8—221no—
613C22⋊Q8—221no—
614C22⋊Q8—221no—
615C22⋊Q8—222no—
616#121—22no—
617#121—22no—
618#121—24no—
619#121—24no—
620#121—24no—
621#121—24no—
622#121—112no—
623#121—112no—
624#121—222no—
625#121—221no—
626#121C22×D1114yes—
627#121C22×D1114yes—
628#120—222no—
629C4×Q8—21no—
630C4×Q8—21no—
631C4×Q8—111no—
632C4×Q8—111no—
633C4×Q8—221no—
634C4×Q8—221no—
635C4×Q8—221no—
636C4×Q8C22×D1112yes—
637C4×Q8C22×D1112yes—
638C4×D4—22no—
639C4×D4—22no—
640C4×D4—24no—
641C4×D4—111no—
642C4×D4—111no—
643C4×D4—221no—
644C4×D4—221no—
645C4×D4—221no—
646C4×D4—222no—
647C4×D4—222no—
648C4×D4—222no—
649C4×D4C22⋊D1111yescharacteristic
650C4×D4C22⋊D1111yescharacteristic
651C4×D4C22⋊D1112yes—
652C4×D4C22×D1111yescharacteristic
653C4×D4C22×D1112yes—
654C4×D4C22×D1111yescharacteristic
655#117—111no—
656#117—112no—
657#117—112no—
658#117—112no—
659#117—222no—
660#117—222no—
661#117—221no—
662#117—222no—
663#117—221no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—112no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4C22⋊D1111yescharacteristic
668C2×C4⋊C4C22×D1111yescharacteristic
669C2×C22⋊C4—22no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4C22⋊D1112yes—
672C2×C42—21no—
673C2×C42—222no—
674C2×C42—221no—
675C2×C42C22×D1111yescharacteristic
676#107—112no—
677#107—114no—
678#106—112no—
679#106—114no—
680C4⋊C8—112no—
681C4⋊C8—112no—
682#103—112no—
683#103—112no—
684#103—114no—
685#103—114no—
686#103—112no—
687#102—114no—
688#102—114no—
689#102—114no—
690#102—114no—
691#102—114no—
692#102—114no—
693#102—112no—
694C22⋊C8—114no—
695C22⋊C8—114no—
696#97—112no—
697C4×C8—112no—
698C2×C11—22no—
699C2×C11—42no—
700C2×C11—42no—
701C2×C11—84no—
702C2×C11C2×#54611yescharacteristic
703C2×C11C2×#57511yescharacteristic
704C2×C11#358511yescharacteristic
705D11—81no—
706C24—22no—
707C24C2×C22⋊D1112yes—
708#41—28no—
709#41—28no—
710#41—44no—
711#41—44no—
712#41—48no—
713#41—48no—
714#41—222no—
715#41—222no—
716#41—444no—
717C2×Q8—22no—
718C2×Q8—21no—
719C2×Q8—111no—
720C2×Q8—221no—
721C2×Q8—221no—
722C2×Q8#434114yescomplemented
723C2×Q8C23×D1112yes—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—24no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—42no—
736C2×D4—48no—
737C2×D4—44no—
738C2×D4—82no—
739C2×D4—84no—
740C2×D4—111no—
741C2×D4—221no—
742C2×D4—222no—
743C2×D4—222no—
744C2×D4C2×C22⋊D1111yescharacteristic
745C2×D4C2×C22⋊D1111yescharacteristic
746C2×D4C2×C22⋊D1112yes—
747C2×D4C23×D1114yes—
748C22×C4—21no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—21no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—48no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4C2×C22⋊D1111yescharacteristic
761C22×C4C2×C22⋊D1112yes—
762C22×C4C2×C22⋊D1112yes—
763C22×C4C2×C22⋊D1112yes—
764C22×C4C2×C22⋊D1111yescharacteristic
765C22×C4C23×D1112yes—
766C22×C4C23×D1112yes—
767C22×C4C23×D1111yescharacteristic
768Q16—224no—
769SD16—224no—
770SD16—444no—
771D8—444no—
772M16—222no—
773M16—222no—
774M16—224no—
775M16—444no—
776C2×C8—112no—
777C2×C8—112no—
778C2×C8—114no—
779C2×C8—444no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—111no—
784C4⋊C4—112no—
785C4⋊C4—111no—
786C4⋊C4—112no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—221no—
790C4⋊C4—221no—
791C4⋊C4—221no—
792C4⋊C4—222no—
793C4⋊C4—222no—
794C4⋊C4—222no—
795C4⋊C4—222no—
796C4⋊C4—221no—
797C4⋊C4C2×C22⋊D1111yescharacteristic
798C4⋊C4C2×C22⋊D1111yescharacteristic
799C4⋊C4C2×C22⋊D1112yes—
800C4⋊C4C23×D1112yes—
801C22⋊C4—24no—
802C22⋊C4—24no—
803C22⋊C4—221no—
804C22⋊C4—222no—
805C22⋊C4—222no—
806C22⋊C4—222no—
807C22⋊C4—222no—
808C22⋊C4—222no—
809C22⋊C4—221no—
810C22⋊C4—221no—
811C22⋊C4—222no—
812C22⋊C4—222no—
813C22⋊C4C2×C22⋊D1112yes—
814C22⋊C4C2×C22⋊D1112yes—
815C22⋊C4C2×C22⋊D1112yes—
816C22⋊C4C2×C22⋊D1112yes—
817C42—22no—
818C42—22no—
819C42—221no—
820C42—222no—
821C42—222no—
822C42—222no—
823C42—221no—
824C42—221no—
825C42C2×C22⋊D1111yescharacteristic
826C42C2×C22⋊D1111yescharacteristic
827C42C23×D1111yescharacteristic
828C42C23×D1111yescharacteristic
829C11#6116011yescharacteristic, complemented, Sylow
830C23—24no—
831C23—24no—
832C23—42no—
833C23—42no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—221no—
838C23C22×C22⋊D1112yes—
839C23C22×C22⋊D1112yes—
840C23C22×C22⋊D1111yescharacteristic
841Q8—24no—
842Q8—22no—
843Q8—221no—
844Q8—221no—
845Q8—442no—
846Q8—881no—
847Q8C2×#434114yes—
848D4—22no—
849D4—22no—
850D4—24no—
851D4—24no—
852D4—42no—
853D4—48no—
854D4—48no—
855D4—44no—
856D4—44no—
857D4—44no—
858D4—82no—
859D4—82no—
860D4—84no—
861D4—84no—
862D4—221no—
863D4—221no—
864D4—444no—
865D4—442no—
866D4—882no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—41no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—42no—
882C2×C4—221no—
883C2×C4—221no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—221no—
887C2×C4—444no—
888C2×C4—442no—
889C2×C4—442no—
890C2×C4—881no—
891C2×C4—882no—
892C2×C4C2×#434112yes—
893C2×C4#6703712yes—
894C2×C4C22×C22⋊D1111yescharacteristic
895C2×C4C22×C22⋊D1112yes—
896C2×C4C22×C22⋊D1111yescharacteristic
897C2×C4C22×C22⋊D1111yescharacteristic
898C2×C4C22×C22⋊D1112yes—
899C2×C4C22×C22⋊D1111yescharacteristic
900C2×C4C22×C22⋊D1111yescharacteristic
901C2×C4C24×D1111yescharacteristic
902C8—222no—
903C8—222no—
904C8—224no—
905C22—21no—
906C22—21no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—84no—
917C22—88no—
918C22—441no—
919C22—441no—
920C22—441no—
921C22#1062333712yes—
922C22C23×C22⋊D1111yescharacteristic
923C4—21no—
924C4—21no—
925C4—22no—
926C4—22no—
927C4—24no—
928C4—21no—
929C4—42no—
930C4—441no—
931C4—442no—
932C4—441no—
933C4—441no—
934C4—442no—
935C4#1062333712yes—
936C4#1062335312yes—
937C4C22×#434111yescharacteristic
938C4C2×#6703711yescharacteristic
939C2—22no—
940C2—42no—
941C2—42no—
942C2—84no—
943C2—881no—
944C2C2×#1062333711yescharacteristic
945C2C2×#1062335311yescharacteristic
946C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC22×C11C23×D4
hypercenterC2×#550D11
hypocenterC11#61160
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13082174C2semidirect
2. #13080954C2semidirect
3. #13080943C2semidirect
4. #13080742C2semidirect
5. #13080622C2semidirect
6. #13080566C2semidirect
7. #13080555C2semidirect
8. #13078990C2semidirect
9. #13078552C2semidirect
10. #13078421C2semidirect
11. #13078231C2semidirect
12. #13078092C2semidirect
13. #13077858C2semidirect
14. C4×#66995C2semidirect
15. D4×#4318C2semidirect
16. #13077135C2semidirect
17. C2×C11×#550C2semidirect
38. #10623096C22semidirect
39. #10623094C22semidirect
41. #10623086C22semidirect
42. #10623074C22semidirect
43. #10623073C22semidirect
44. #10623072C22semidirect
51. #10622852C22semidirect
52. #10622852C22semidirect
53. #10622851C22semidirect
54. #10622851C22semidirect
55. #10622846C22semidirect
56. #10622846C22semidirect
57. #10622845C22semidirect
58. #10622845C22semidirect
65. #10622688C22semidirect
66. #10622688C22semidirect
67. #10622685C22semidirect
68. #10622685C22semidirect
69. #10622684C22semidirect
70. #10622683C22semidirect
71. #10622683C22semidirect
72. #10622655C22semidirect
73. #10622654C22semidirect
74. #10622652C22semidirect
75. #10622651C22semidirect
76. #10622648C22semidirect
77. #10622648C22semidirect
78. #10622647C22semidirect
79. #10622646C22semidirect
80. #10622643C22semidirect
81. C4×#4326C22semidirect
82. #10622639C22semidirect
83. C4×#4325C22semidirect
84. #10622635C22semidirect
85. #10622634C22semidirect
86. #10622633C22semidirect
87. #10622625C22semidirect
88. #10622624C22semidirect
89. D4×C11⋊C8C22semidirect
244. C2×Q8×C11#41semidirect
358. C2×#550D11semidirect
722. C2×Q8#4341semidirect
829. C11#61160semidirect

Maximal subgroups

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

subgroupindex
#130821742
#130809542
#130809432
#130807422
#130806222
#130805662
#130805552
#130789902
#130785522
#130784212
#130782312
#130780922
#130778582
C4×#669952
D4×#43182
#130771352
C2×C11×#5502
#6116011