Finite Group Databasebeta

← #15632553

Subgroups — #15632553

Order 2816.

2088 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082174C211yesmaximal, characteristic, complemented
2#13081211C212yesmaximal, complemented
3#13081200C212yesmaximal, complemented
4#13081086C214yesmaximal, complemented
5#13081050C214yesmaximal, complemented
6#13080973C212yesmaximal, complemented
7#13080959C212yesmaximal, complemented
8#13079158C211yesmaximal, characteristic, complemented
9#13078552C212yesmaximal, complemented
10#13078539C212yesmaximal, complemented
11#13078425C211yesmaximal, characteristic, complemented
12#13078413C211yesmaximal, characteristic, complemented
13#13078231C212yesmaximal, complemented
14C4×#66985C211yesmaximal, characteristic, complemented
15D4×#4318C211yesmaximal, characteristic, complemented
16C2×#10622577C212yesmaximal, complemented
17C2×C11×#547C211yesmaximal, characteristic, complemented
18C22×C11×#41—21no—
19C11×#547—21no—
20C11×#547—22no—
21C11×#547—21no—
22C11×#547C2212yes—
23C11×#547C2212yes—
24C11×#547C2214yes—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#123—22no—
27C2×C11×C22⋊Q8—21no—
28C2×C11×#121C2212yes—
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C22×C11×C4⋊C4C2212yes—
32#10623337—21no—
33C2×#66985C2211yescharacteristic
34#10623322C2212yes—
35C2×#66979C2212yes—
36C22×#4318C2212yes—
37#10623096C2212yescomplemented
38#10623094C2211yescharacteristic, complemented
39#10623088—21no—
40#10623086C2211yescharacteristic, complemented
41#10623074C2211yescharacteristic, complemented
42#10623073C2211yescharacteristic, complemented
43#10623072C2212yescomplemented
44#10623069—22no—
45C4×#4341—21no—
46#10623044—21no—
47#10623026—22no—
48C4×#4339C2211yescharacteristic
49#10623001C2211yescharacteristic
50#10622828C2211yescharacteristic
51#10622828C2212yes—
52#10622820C2212yes—
53#10622707C2212yescomplemented
54#10622704C2212yescomplemented
55#10622700C2212yescomplemented
56#10622697C2212yescomplemented
57#10622693C2214yescomplemented
58#10622692C2212yescomplemented
59#10622691C2212yescomplemented
60#10622655C2214yescomplemented
61#10622654C2214yescomplemented
62#10622652C2214yescomplemented
63#10622651C2214yescomplemented
64#10622648C2214yescomplemented
65#10622648C2214yescomplemented
66#10622647C2214yescomplemented
67#10622646C2214yescomplemented
68#10622631C2212yescomplemented
69C4×#4324C2212yescomplemented
70#10622627C2212yescomplemented
71C4×#4323C2212yescomplemented
72#10622625C2212yescomplemented
73#10622624C2214yescomplemented
74D4×C11⋊C8C2212yescomplemented
75#10622622C2214yescomplemented
76#10622621C2212yescomplemented
77#10622620C2212yescomplemented
78#10622584C2214yescomplemented
79#10622583C2214yescomplemented
80#10622581C2214yescomplemented
81#10622580C2214yescomplemented
82#10622579C2211yescharacteristic
83#10622579C2212yes—
84#10622577C2212yes—
85#10622577C2212yes—
86#10622577C2212yes—
87#10622577C2212yes—
88#10622577C2211yescharacteristic
89#10622577C2214yescomplemented
90#10622577C2214yescomplemented
91C2×#66872C2214yescomplemented
92C2×#66871C2214yescomplemented
93#10622537C2211yescharacteristic
94C4×#4318C2211yescharacteristic
95C2×C11×#41—24no—
96C2×C11×#41—22no—
97C2×C11×#41—22no—
98C2×C11×#41—48no—
99C22×Q8×C11—21no—
100C22×D4×C11—22no—
101C22×D4×C11D411yescharacteristic
102C22×D4×C11C2311yescharacteristic
103C23×C4×C11—22no—
104C23×C4×C11—21no—
105C23×C4×C11C2312yes—
106C2×#4341—21no—
107C2×#4339C2311yescharacteristic
108C11×C4⋊Q8—21no—
109C11×C4⋊Q8—21no—
110C11×C4⋊Q8C2312yes—
111C11×C4⋊Q8C2312yes—
112C11×#123—24no—
113C11×#123—24no—
114C11×#123—24no—
115C11×#123—24no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—24no—
118C11×C22⋊Q8—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121C2314yes—
122C11×#121C2314yes—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C4×D4×C11D411yescharacteristic
126C4×D4×C11D412yes—
127C4×D4×C11D411yescharacteristic
128C4×D4×C11C2312yes—
129C4×D4×C11C2312yes—
130C4×D4×C11C2312yes—
131C4×D4×C11C2311yescharacteristic
132C4×D4×C11C2311yescharacteristic
133C2×C11×C4⋊C4—22no—
134C2×C11×C4⋊C4—22no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4D411yescharacteristic
138C2×C11×C4⋊C4C2314yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2314yes—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—22no—
144C2×C11×C22⋊C4D412yes—
145C2×C42×C11C2311yescharacteristic
146#67006—22no—
147C2×C22⋊Dic11—22no—
148#66992—22no—
149#66991—21no—
150#66989—21no—
151#66988—22no—
152D4×Dic11—21no—
153C2×#4324C2312yes—
154#66985—24no—
155C2×#4323C2312yes—
156#66983C2312yes—
157#66983C2312yes—
158#66982—22no—
159C4×C22⋊D11—21no—
160C4×C22⋊D11—21no—
161C4×C22⋊D11—22no—
162C4×C22⋊D11—22no—
163#66979—22no—
164#66979—22no—
165#66979C2312yes—
166#66979C2311yescharacteristic
167#66979C2312yes—
168#66979C2312yes—
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2312yes—
171#66977—21no—
172#66977—21no—
173#66977C2312yes—
174#66977C2312yes—
175C2×C4×Dic11—22no—
176C2×#4318—28no—
177C2×#4318C2311yescharacteristic
178C2×#4318C2312yes—
179C2×#4318C2314yes—
180C2×#4318C2311yescharacteristic
181C22×C11⋊C8C2314yes—
182#66951—22no—
183#66950—21no—
184#66945—21no—
185#66943—21no—
186#66942—22no—
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—
196C4×D44C2311yescharacteristic
197C4×D44C2311yescharacteristic
198#66925—21no—
199C42×D11—21no—
200#66923C2312yes—
201#66922C2311yescharacteristic
202#66922C2311yescharacteristic
203C4×Dic22—21no—
204C4×Dic22—21no—
205C4×Dic22C2311yescharacteristic
206C4×Dic22C2311yescharacteristic
207#66896C2314yes—
208#66896C2314yes—
209#66896C2312yes—
210#66896C2312yes—
211C22⋊(C11⋊C8)C2314yes—
212C22⋊(C11⋊C8)C2314yes—
213#66874C2312yes—
214#66874C2314yes—
215#66873C2312yes—
216#66873C2314yes—
217#66872C2312yes—
218#66872C2314yes—
219#66872C2314yes—
220#66872C2314yes—
221#66872C2314yes—
222#66871C2312yes—
223#66871C2314yes—
224#66871C2314yes—
225#66871C2314yes—
226#66871C2314yes—
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2312yes—
229#66867C2312yes—
230C4×C11⋊C8C2312yes—
231#61252—111nomaximal, Sylow
232C24×C11—21no—
233C24×C11C2×D412yes—
234C11×#41—416no—
235C11×#41—48no—
236C11×#41—48no—
237C2×Q8×C11—22no—
238C2×Q8×C11—22no—
239C2×Q8×C11—44no—
240C2×D4×C11—24no—
241C2×D4×C11—24no—
242C2×D4×C11—24no—
243C2×D4×C11—21no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—48no—
247C2×D4×C11C2×D412yes—
248C2×D4×C11C2×D411yescharacteristic
249C2×D4×C11C2×D411yescharacteristic
250C2×D4×C11C2412yes—
251C22×C4×C11—24no—
252C22×C4×C11—24no—
253C22×C4×C11—21no—
254C22×C4×C11—22no—
255C22×C4×C11—24no—
256C22×C4×C11—24no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—44no—
260C22×C4×C11—48no—
261C22×C4×C11C2×D412yes—
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2412yes—
267C22×C4×C11C2412yes—
268C22×C4×C11C2411yescharacteristic
269C2×C22⋊D11—22no—
270C2×C22⋊D11—21no—
271C2×C22⋊D11—22no—
272C22×Dic11—22no—
273C22×Dic11—22no—
274#4341—44no—
275#4339—22no—
276#4339—22no—
277C2×D44C2411yescharacteristic
278C2×C4×D11—21no—
279C2×C4×D11—21no—
280C2×C4×D11—21no—
281C2×Dic22—21no—
282C2×Dic22—21no—
283C2×Dic22C2411yescharacteristic
284C11×C4⋊C4—21no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—24no—
287C11×C4⋊C4—24no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2×D411yescharacteristic
293C11×C4⋊C4C2412yes—
294C11×C4⋊C4C2414yes—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—24no—
298C11×C22⋊C4—24no—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C11×C22⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D411yescharacteristic
305C42×C11C2411yescharacteristic
306C42×C11C2411yescharacteristic
307C22⋊Dic11—22no—
308C22⋊Dic11—22no—
309C22⋊Dic11—22no—
310C22⋊Dic11—22no—
311C22⋊Dic11—22no—
312C22⋊Dic11—21no—
313#4324—24no—
314#4323—24no—
315(C2×D11)⋊C4—21no—
316(C2×D11)⋊C4—21no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319C4⋊Dic11—21no—
320C4⋊Dic11—21no—
321C4⋊Dic11—22no—
322C4⋊Dic11—22no—
323C4⋊Dic11C2411yescharacteristic
324C4⋊Dic11C2412yes—
325C4⋊Dic11C2411yescharacteristic
326C4⋊Dic11C2412yes—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—21no—
330Dic11⋊C4—21no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333C4×Dic11—22no—
334C4×Dic11—21no—
335C4×Dic11—21no—
336C4×Dic11—21no—
337C4×Dic11—22no—
338C4×Dic11—22no—
339#4318—28no—
340#4318—24no—
341#4318—22no—
342#4318#4114yescomplemented
343C2×C11⋊C8—28no—
344C2×C11⋊C8C2412yes—
345C2×C11⋊C8C2414yes—
346C2×C11⋊C8C2412yes—
347#3475—111no—
348C2×#547D1111yescharacteristic, complemented
349#3354—112no—
350#3353—112no—
351#3345—114no—
352#3343—114no—
353#3335—112no—
354#3334—112no—
355#3165—111no—
356#3094—112no—
357#3092—112no—
358#3079—111no—
359#3077—111no—
360#3055—112no—
361C4×AGL(1,ℤ/8)—111no—
362D4×M16—111no—
363C2×#428—112no—
364C23×C11—24no—
365C23×C11—24no—
366C23×C11—22no—
367C23×C11—42no—
368C23×C11—42no—
369C23×C11—42no—
370C23×C11—42no—
371C23×C11C22×D412yes—
372C23×C11C22×D411yescharacteristic
373C23×C11C22×D412yes—
374C22×D11—21no—
375Q8×C11—44no—
376Q8×C11—44no—
377D4×C11—24no—
378D4×C11—22no—
379D4×C11—22no—
380D4×C11—22no—
381D4×C11—48no—
382D4×C11—48no—
383D4×C11—42no—
384D4×C11AGL(1,ℤ/8)14yescomplemented
385C2×C4×C11—24no—
386C2×C4×C11—24no—
387C2×C4×C11—24no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—24no—
395C2×C4×C11—41no—
396C2×C4×C11—44no—
397C2×C4×C11—42no—
398C2×C4×C11—44no—
399C2×C4×C11—48no—
400C2×C4×C11—48no—
401C2×C4×C11—44no—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D412yes—
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C2×#4112yes—
410C2×C4×C112−1+412yes—
411C2×C4×C11C2511yescharacteristic
412C22⋊D11—42no—
413C22⋊D11—44no—
414C22⋊D11—82no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—21no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—44no—
421C2×Dic11—82no—
422D44—21no—
423D44—21no—
424C4×D11—42no—
425C4×D11—42no—
426C4×D11—81no—
427Dic22—21no—
428Dic22—21no—
429Dic22—42no—
430Dic22—81no—
431C11⋊C8—24no—
432C11⋊C8—22no—
433C11⋊C8C2×#4114yescomplemented
434C22×#41—21no—
435C2×AGL(1,ℤ/8)—111no—
436C22×M16—112no—
437#556—111no—
438#555—111no—
439#554—111no—
440#553—112no—
441#552—112no—
442#552—221no—
443#551—222no—
444#547—21no—
445#547—22no—
446#547—21no—
447#547—111no—
448#547C2×D1112yes—
449#547C2×D1114yes—
450#547C2×D1112yes—
451#546—221no—
452#533—111no—
453C2×C4⋊Q8C2×D1111yescharacteristic
454#529—222no—
455#529—221no—
456#525—112no—
457C2×#123—22no—
458C2×C22⋊Q8—21no—
459C2×#121C2×D1112yes—
460C4×#41—111no—
461C4×#41—221no—
462C2×C4×D4C2×D1111yescharacteristic
463C2×C4×D4C2×D1111yescharacteristic
464C2×#117—112no—
465C22×C4⋊C4C2×D1112yes—
466#501—114no—
467#500—112no—
468#498—112no—
469#484—114no—
470#483—114no—
471#482—114no—
472#482—114no—
473#481—114no—
474#481—114no—
475#480—114no—
476#480—114no—
477#478—114no—
478#477—112no—
479#476—112no—
480#476—112no—
481#475—112no—
482#474—112no—
483#474—112no—
484#469—114no—
485#468—114no—
486#466—114no—
487#465—114no—
488#442—112no—
489#440—112no—
490C4×SD16—112no—
491C4×D8—112no—
492#436—112no—
493#435—114no—
494C8×D4—112no—
495#428—112no—
496#428—112no—
497#428—114no—
498#428—114no—
499#428—112no—
500#428—112no—
501#428—111no—
502C2×#107—114no—
503C2×#106—114no—
504#423—111no—
505#418—112no—
506#418—111no—
507#417—112no—
508#417—111no—
509#407—112no—
510C4×M16—111no—
511C22×C11—21no—
512C22×C11—22no—
513C22×C11—22no—
514C22×C11—21no—
515C22×C11—22no—
516C22×C11—22no—
517C22×C11—22no—
518C22×C11—48no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—84no—
523C22×C11#54712yes—
524C22×C11C2×AGL(1,ℤ/8)14yes—
525C22×C11C23×D411yescharacteristic
526C2×D11—41no—
527C2×D11—41no—
528C2×D11—41no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—22no—
533C4×C11—21no—
534C4×C11—42no—
535C4×C11—44no—
536C4×C11#54712yes—
537C4×C11C2×AGL(1,ℤ/8)12yes—
538C4×C11C22×#4111yescharacteristic
539C4×C11C2×2−1+411yescharacteristic
540Dic11—42no—
541Dic11—41no—
542Dic11—41no—
543Dic11—42no—
544Dic11—41no—
545C2×#41—24no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—48no—
549C2×#41—111no—
550C2×#41—221no—
551C22×Q8—21no—
552C22×D4—22no—
553C22×D4C22⋊D1111yescharacteristic
554C22×D4C22×D1111yescharacteristic
555C23×C4—22no—
556C23×C4—21no—
557C23×C4C22×D1112yes—
558AGL(1,ℤ/8)—224no—
559C2×SD16—112no—
560C2×D8—112no—
561C2×M16—111no—
562C2×M16—112no—
563C2×M16—114no—
564C2×M16—111no—
565C2×M16—228no—
566C22×C8—114no—
567C4⋊Q8—21no—
568C4⋊Q8—21no—
569C4⋊Q8—111no—
570C4⋊Q8—111no—
571C4⋊Q8C22×D1112yes—
572C4⋊Q8C22×D1112yes—
573#126—222no—
574#126—222no—
575#126—222no—
576#125—112no—
577#125—222no—
578#125—221no—
579#124—221no—
580#124—222no—
581#123—24no—
582#123—24no—
583#123—24no—
584#123—24no—
585#123—222no—
586#123—222no—
587#123—222no—
588#123—222no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—24no—
592C22⋊Q8—112no—
593C22⋊Q8—112no—
594C22⋊Q8—221no—
595C22⋊Q8—221no—
596C22⋊Q8—221no—
597C22⋊Q8—222no—
598#121—22no—
599#121—22no—
600#121—112no—
601#121—112no—
602#121—222no—
603#121—221no—
604#121C22×D1114yes—
605#121C22×D1114yes—
606#120—222no—
607C4×Q8—111no—
608C4×Q8—111no—
609C4×Q8—221no—
610C4×Q8—221no—
611C4×Q8—221no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—111no—
615C4×D4—111no—
616C4×D4—221no—
617C4×D4—221no—
618C4×D4—221no—
619C4×D4—222no—
620C4×D4—222no—
621C4×D4—222no—
622C4×D4C22⋊D1111yescharacteristic
623C4×D4C22⋊D1111yescharacteristic
624C4×D4C22⋊D1112yes—
625C4×D4C22×D1112yes—
626C4×D4C22×D1112yes—
627C4×D4C22×D1111yescharacteristic
628C4×D4C22×D1112yes—
629C4×D4C22×D1111yescharacteristic
630#117—111no—
631#117—112no—
632#117—112no—
633#117—112no—
634#117—222no—
635#117—222no—
636#117—221no—
637#117—222no—
638#117—221no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4C22⋊D1111yescharacteristic
646C2×C4⋊C4C22×D1111yescharacteristic
647C2×C4⋊C4C22×D1112yes—
648C2×C4⋊C4C22×D1114yes—
649C2×C4⋊C4C22×D1114yes—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—222no—
653C2×C22⋊C4C22⋊D1112yes—
654C2×C42—222no—
655C2×C42—221no—
656C2×C42C22×D1111yescharacteristic
657#107—112no—
658#107—114no—
659#107—114no—
660#107—114no—
661#107—114no—
662#106—112no—
663#106—114no—
664#106—114no—
665#106—114no—
666#106—114no—
667C4⋊C8—112no—
668C4⋊C8—112no—
669#103—112no—
670#103—114no—
671#102—112no—
672#102—112no—
673#102—114no—
674#102—114no—
675#102—112no—
676#102—114no—
677C22⋊C8—114no—
678C22⋊C8—114no—
679#97—112no—
680C4×C8—112no—
681C2×C11—22no—
682C2×C11—24no—
683C2×C11—42no—
684C2×C11—82no—
685C2×C11C2×#54711yescharacteristic
686C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
687C2×C11#358611yescharacteristic
688D11—81no—
689C24—21no—
690C24C2×C22⋊D1112yes—
691#41—416no—
692#41—48no—
693#41—48no—
694#41—222no—
695#41—222no—
696#41—444no—
697C2×Q8—22no—
698C2×Q8—22no—
699C2×Q8—44no—
700C2×Q8—111no—
701C2×Q8—221no—
702C2×Q8—221no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—24no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—21no—
709C2×D4—48no—
710C2×D4—111no—
711C2×D4—221no—
712C2×D4—222no—
713C2×D4—222no—
714C2×D4C2×C22⋊D1112yes—
715C2×D4C2×C22⋊D1111yescharacteristic
716C2×D4C2×C22⋊D1111yescharacteristic
717C2×D4C23×D1112yes—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—21no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4C2×C22⋊D1112yes—
734C22×C4C2×C22⋊D1111yescharacteristic
735C22×C4C2×C22⋊D1112yes—
736C22×C4C2×C22⋊D1112yes—
737C22×C4C2×C22⋊D1111yescharacteristic
738C22×C4C23×D1112yes—
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741SD16—224no—
742D8—224no—
743M16—114no—
744M16—228no—
745M16—224no—
746M16—222no—
747C2×C8—112no—
748C2×C8—112no—
749C2×C8—114no—
750C2×C8—228no—
751C4⋊C4—21no—
752C4⋊C4—22no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—111no—
758C4⋊C4—112no—
759C4⋊C4—111no—
760C4⋊C4—112no—
761C4⋊C4—222no—
762C4⋊C4—222no—
763C4⋊C4—221no—
764C4⋊C4—221no—
765C4⋊C4—221no—
766C4⋊C4—222no—
767C4⋊C4—222no—
768C4⋊C4—222no—
769C4⋊C4—222no—
770C4⋊C4—221no—
771C4⋊C4C2×C22⋊D1111yescharacteristic
772C4⋊C4C2×C22⋊D1111yescharacteristic
773C4⋊C4C2×C22⋊D1112yes—
774C4⋊C4C23×D1112yes—
775C4⋊C4C23×D1114yes—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—221no—
781C22⋊C4—222no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—222no—
786C22⋊C4—221no—
787C22⋊C4—221no—
788C22⋊C4—222no—
789C22⋊C4—222no—
790C22⋊C4C2×C22⋊D1112yes—
791C22⋊C4C2×C22⋊D1112yes—
792C22⋊C4C2×C22⋊D1112yes—
793C22⋊C4C2×C22⋊D1112yes—
794C42—221no—
795C42—222no—
796C42—222no—
797C42—222no—
798C42—221no—
799C42—221no—
800C42C2×C22⋊D1111yescharacteristic
801C42C2×C22⋊D1111yescharacteristic
802C42C23×D1111yescharacteristic
803C42C23×D1111yescharacteristic
804C11#6125211yescharacteristic, complemented, Sylow
805C23—24no—
806C23—24no—
807C23—22no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—221no—
813C23C22×C22⋊D1112yes—
814C23C22×C22⋊D1112yes—
815C23C22×C22⋊D1111yescharacteristic
816Q8—44no—
817Q8—44no—
818Q8—221no—
819Q8—221no—
820Q8—442no—
821Q8—881no—
822D4—24no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—48no—
827D4—48no—
828D4—42no—
829D4—221no—
830D4—221no—
831D4—444no—
832D4—442no—
833D4—882no—
834D4#6698514yescomplemented
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—41no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—48no—
850C2×C4—48no—
851C2×C4—44no—
852C2×C4—221no—
853C2×C4—221no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—221no—
857C2×C4—444no—
858C2×C4—442no—
859C2×C4—442no—
860C2×C4—881no—
861C2×C4—882no—
862C2×C4#41×D1112yes—
863C2×C4#6704312yes—
864C2×C4C22×C22⋊D1112yes—
865C2×C4C22×C22⋊D1111yescharacteristic
866C2×C4C22×C22⋊D1111yescharacteristic
867C2×C4C22×C22⋊D1111yescharacteristic
868C2×C4C22×C22⋊D1112yes—
869C2×C4C22×C22⋊D1111yescharacteristic
870C2×C4C22×C22⋊D1111yescharacteristic
871C2×C4C24×D1111yescharacteristic
872C8—114no—
873C8—224no—
874C8—222no—
875C22—21no—
876C22—22no—
877C22—21no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—48no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—84no—
887C22—441no—
888C22—441no—
889C22—441no—
890C22C2×#6698514yes—
891C22#1062335512yes—
892C22C23×C22⋊D1111yescharacteristic
893C4—21no—
894C4—21no—
895C4—21no—
896C4—22no—
897C4—22no—
898C4—42no—
899C4—44no—
900C4—441no—
901C4—442no—
902C4—441no—
903C4—442no—
904C4—441no—
905C4C2×#6698512yes—
906C4#1062335512yes—
907C4C2×#41×D1111yescharacteristic
908C4C2×#6704311yescharacteristic
909C2—22no—
910C2—24no—
911C2—42no—
912C2—82no—
913C2—881no—
914C2C2×#1062335511yescharacteristic
915C2C22×#6698511yescharacteristic
916C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC22×C11C23×D4
hypercenterC2×#547D11
hypocenterC11#61252
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13082174C2semidirect
2. #13081211C2semidirect
3. #13081200C2semidirect
4. #13081086C2semidirect
5. #13081050C2semidirect
6. #13080973C2semidirect
7. #13080959C2semidirect
8. #13079158C2semidirect
9. #13078552C2semidirect
10. #13078539C2semidirect
11. #13078425C2semidirect
12. #13078413C2semidirect
13. #13078231C2semidirect
14. C4×#66985C2semidirect
15. D4×#4318C2semidirect
16. C2×#10622577C2semidirect
17. C2×C11×#547C2semidirect
37. #10623096C22semidirect
38. #10623094C22semidirect
40. #10623086C22semidirect
41. #10623074C22semidirect
42. #10623073C22semidirect
43. #10623072C22semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
55. #10622700C22semidirect
56. #10622697C22semidirect
57. #10622693C22semidirect
58. #10622692C22semidirect
59. #10622691C22semidirect
60. #10622655C22semidirect
61. #10622654C22semidirect
62. #10622652C22semidirect
63. #10622651C22semidirect
64. #10622648C22semidirect
65. #10622648C22semidirect
66. #10622647C22semidirect
67. #10622646C22semidirect
68. #10622631C22semidirect
69. C4×#4324C22semidirect
70. #10622627C22semidirect
71. C4×#4323C22semidirect
72. #10622625C22semidirect
73. #10622624C22semidirect
74. D4×C11⋊C8C22semidirect
75. #10622622C22semidirect
76. #10622621C22semidirect
77. #10622620C22semidirect
78. #10622584C22semidirect
79. #10622583C22semidirect
80. #10622581C22semidirect
81. #10622580C22semidirect
89. #10622577C22semidirect
90. #10622577C22semidirect
91. C2×#66872C22semidirect
92. C2×#66871C22semidirect
342. #4318#41semidirect
348. C2×#547D11semidirect
384. D4×C11AGL(1,ℤ/8)semidirect
433. C11⋊C8C2×#41semidirect
804. C11#61252semidirect
834. D4#66985semidirect

Maximal subgroups

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

subgroupindex
#130821742
#130812112
#130812002
#130810862
#130810502
#130809732
#130809592
#130791582
#130785522
#130785392
#130784252
#130784132
#130782312
C4×#669852
D4×#43182
C2×#106225772
C2×C11×#5472
#6125211