Finite Group Databasebeta

← #15638490

Subgroups — #15638490

Order 2816.

2370 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082373C211yesmaximal, characteristic
2C2×#10623163C211yesmaximal, characteristic, complemented
3#13080479C214yesmaximal, complemented
4#13080476C214yesmaximal, complemented
5#13080310C214yesmaximal, complemented
6#13080309C214yesmaximal, complemented
7#13079539C212yesmaximal, complemented
8#13079375C212yesmaximal, complemented
9#13079369C211yesmaximal, characteristic, complemented
10#13078644C212yesmaximal, complemented
11C2×#10622351C211yesmaximal, characteristic, complemented
12C2×#10622653C211yesmaximal, characteristic, complemented
13D11×#448C212yesmaximal, complemented
14#13077638C211yesmaximal, characteristic, complemented
15C11×#3187C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic, complemented
17C2×#67037—21no—
18C23×Dic22C2211yescharacteristic, complemented
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20C2×C11×#121C2211yescharacteristic
21C2×#66997C2211yescharacteristic, complemented
22#10623335—21no—
23D4×C22⋊D11C2212yes—
24C22×#4324C2212yescomplemented
25C2×#66983C2211yescharacteristic
26C2×C4×C22⋊D11C2211yescharacteristic
27C2×SD16×D11C2214yescomplemented
28C22×#4314C2212yescomplemented
29#10623163—22no—
30#10623163—22no—
31#10623163C2214yescomplemented
32#10623163C2214yescomplemented
33#10623142C2212yes—
34#10623141—22no—
35#10623140C2212yes—
36#10623136—21no—
37D11×#121C2212yes—
38#10623128—21no—
39#10623127C2212yes—
40C2×#66950C2211yescharacteristic, complemented
41C2×#66949—21no—
42#10623038C2212yes—
43C2×#66941—21no—
44C2×#66940C2211yescharacteristic, complemented
45#10623021—22no—
46C2×(C22⋊D11)⋊C4—21no—
47C2×#66931—21no—
48C11×#483C2212yescomplemented
49C11×#481C2212yescomplemented
50C11×#465C2214yescomplemented
51C11×#450C2212yescomplemented
52C11×#448C2212yescomplemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54#10622840C2212yescomplemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
56#10622788C2214yescomplemented
57#10622783C2214yescomplemented
58#10622775C2214yescomplemented
59C8×C22⋊D11C2214yescomplemented
60C2×#66880C2212yescomplemented
61#10622661C2214yescomplemented
62#10622659C2212yescomplemented
63#10622656C2212yescomplemented
64#10622653C2212yescomplemented
65#10622653C2212yescomplemented
66#10622653C2214yescomplemented
67C2×#66874C2212yescomplemented
68#10622581C2212yescomplemented
69#10622477C2214yescomplemented
70#10622475C2214yescomplemented
71#10622467C2214yescomplemented
72#10622465C2214yescomplemented
73#10622431C2214yescomplemented
74#10622419C2214yescomplemented
75D11×#103C2214yescomplemented
76#10622405C2214yescomplemented
77#10622391C2214yescomplemented
78#10622389C2214yescomplemented
79#10622375C2214yescomplemented
80#10622371C2214yescomplemented
81#10622351C2212yescomplemented
82#10622351C2212yescomplemented
83#10622351C2214yescomplemented
84(C22⋊D11)⋊C8C2214yescomplemented
85D11×C22⋊C8C2212yescomplemented
86#10622331C2212yescomplemented
87C22×Q8×C11C2311yescharacteristic
88C22×D4×C11—21no—
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—21no—
92C22×C22⋊D11—22no—
93C22×C22⋊D11D411yescharacteristic
94C23×Dic11—21no—
95C2×Q8×D11—22no—
96C2×Q8×D11—44no—
97C2×Q8×D11C2314yes—
98#67037—48no—
99C2×#4341—22no—
100C2×#4341—22no—
101C2×D4×D11—22no—
102C2×D4×D11—22no—
103C2×D4×D11C2312yes—
104C2×#4339—22no—
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×C4×D11C2311yescharacteristic
108C22×Dic22—21no—
109C22×Dic22—21no—
110C22×Dic22—21no—
111C22×Dic22—21no—
112C22×Dic22—44no—
113C22×Dic22C2311yescharacteristic
114C22×Dic22C2312yes—
115C22×Dic22C2312yes—
116C22×Dic22C2311yescharacteristic
117C2×C11×SD16C2314yes—
118C22×C8×C11C2312yes—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8C2312yes—
122C11×C22⋊Q8C2312yes—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121C2312yes—
126C11×#121C2312yes—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132#67006—22no—
133C2×C22⋊Dic11D411yescharacteristic
134#66997—22no—
135#66997C2314yes—
136C2×#4325C2314yes—
137#66993C2312yes—
138#66992—22no—
139#66992—22no—
140#66992—22no—
141#66991C2312yes—
142#66990—22no—
143#66990—22no—
144#66988—22no—
145D4×Dic11C2312yes—
146C2×#4324—44no—
147C2×#4324C2314yes—
148C2×#4324C2314yes—
149#66983—21no—
150#66983—21no—
151#66983C2312yes—
152#66983C2312yes—
153#66982—22no—
154C4×C22⋊D11D412yes—
155C4×C22⋊D11D412yes—
156C4×C22⋊D11C2312yes—
157C4×C22⋊D11C2312yes—
158C2×(C2×D11)⋊C4—21no—
159C2×(C2×D11)⋊C4—21no—
160C2×(C2×D11)⋊C4D411yescharacteristic
161C2×C4⋊Dic11—21no—
162C2×C4⋊Dic11C2311yescharacteristic
163C2×Dic11⋊C4—21no—
164C2×Dic11⋊C4—21no—
165C2×Dic11⋊C4—21no—
166C2×Dic11⋊C4D411yescharacteristic
167C2×C4×Dic11—21no—
168C2×C4×Dic11C2311yescharacteristic
169C22×C11⋊C8C2312yes—
170SD16×D11—48no—
171C2×#4314—44no—
172C2×#4314C2314yes—
173C2×#4314C2314yes—
174C2×C8×D11C2314yes—
175#66950—22no—
176#66950C2314yes—
177#66949—24no—
178#66949—24no—
179#66949—22no—
180#66948C2312yes—
181#66947—22no—
182#66946C2312yes—
183C4⋊C4×D11C2312yes—
184#66941—24no—
185#66941—24no—
186#66941C2312yes—
187#66940—22no—
188#66940C2314yes—
189#66938—22no—
190#66937—22no—
191#66937—22no—
192#66936—22no—
193#66935—22no—
194(C22⋊D11)⋊C4—24no—
195(C22⋊D11)⋊C4—24no—
196(C22⋊D11)⋊C4—22no—
197C22⋊C4×D11—22no—
198#66931—24no—
199#66931—24no—
200#66931—22no—
201C11×#106C2314yes—
202C11×#103C2314yes—
203C11×#102C2314yes—
204C11×C22⋊C8C2312yes—
205C11×C22⋊C8C2312yes—
206#66899C2314yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yes—
209(C2×D11)⋊C8C2314yes—
210#66880C2314yes—
211#66880C2314yes—
212Dic11⋊C8C2314yes—
213C8×Dic11C2314yes—
214#66874C2314yes—
215#66874C2314yes—
216#66873C2314yes—
217#66872C2314yes—
218#61562—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C23×D11—22no—
223C23×D11C2×D411yescharacteristic
224C2×Q8×C11—21no—
225C2×Q8×C11—42no—
226C2×Q8×C11C2412yes—
227C2×D4×C11—22no—
228C2×D4×C11—22no—
229C2×D4×C11—21no—
230C2×D4×C11—42no—
231C2×D4×C11—44no—
232C2×D4×C11C2412yes—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—42no—
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C2×C22⋊D11—22no—
244C2×C22⋊D11—22no—
245C2×C22⋊D11—22no—
246C2×C22⋊D11—22no—
247C2×C22⋊D11—22no—
248C2×C22⋊D11—22no—
249C2×C22⋊D11—48no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11SD1618yescomplemented
252C2×C22⋊D11C2×D412yes—
253C2×C22⋊D11C2×D412yes—
254C22×Dic11—22no—
255C22×Dic11—21no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—44no—
261C22×Dic11C2×D411yescharacteristic
262C22×Dic11C2×D411yescharacteristic
263C22×Dic11C2×D411yescharacteristic
264Q8×D11—28no—
265Q8×D11—44no—
266Q8×D11—48no—
267#4341—48no—
268#4341—48no—
269D4×D11—44no—
270D4×D11—48no—
271D4×D11—48no—
272#4339—48no—
273C2×D44—22no—
274C2×D44—21no—
275C2×D44—42no—
276C2×D44C2412yes—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—24no—
280C2×C4×D11—42no—
281C2×C4×D11—44no—
282C2×C4×D11C2×D412yes—
283C2×C4×D11C2412yes—
284C2×Dic22—24no—
285C2×Dic22—24no—
286C2×Dic22—24no—
287C2×Dic22—24no—
288C2×Dic22—22no—
289C2×Dic22—21no—
290C2×Dic22—22no—
291C2×Dic22—22no—
292C2×Dic22—21no—
293C2×Dic22—42no—
294C2×Dic22—42no—
295C2×Dic22—42no—
296C2×Dic22—44no—
297C2×Dic22—44no—
298C2×Dic22—44no—
299C2×Dic22—44no—
300C2×Dic22C2412yes—
301C2×Dic22C2412yes—
302C11×SD16—44no—
303C2×C8×C11—42no—
304C2×C8×C11C2414yes—
305C11×C4⋊C4—21no—
306C11×C4⋊C4—22no—
307C11×C4⋊C4—22no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4C2412yes—
310C11×C4⋊C4C2412yes—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—22no—
314C11×C22⋊C4—22no—
315C22⋊Dic11—22no—
316C22⋊Dic11—22no—
317C22⋊Dic11C2×D412yes—
318C22⋊Dic11C2×D412yes—
319#4325—44no—
320#4324—28no—
321#4324—44no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4C2×D412yes—
328(C2×D11)⋊C4C2×D412yes—
329C4⋊Dic11—24no—
330C4⋊Dic11—21no—
331C4⋊Dic11C2412yes—
332Dic11⋊C4—24no—
333Dic11⋊C4—24no—
334Dic11⋊C4—22no—
335Dic11⋊C4—24no—
336Dic11⋊C4—22no—
337Dic11⋊C4C2×D412yes—
338Dic11⋊C4C2×D412yes—
339C4×Dic11—24no—
340C4×Dic11C2×D412yes—
341C4×Dic11C2412yes—
342C2×C11⋊C8—42no—
343C2×C11⋊C8C2414yes—
344#4314—28no—
345#4314—44no—
346C8×D11—44no—
347#3496—111no—
348C2×D4×Q8—111no—
349#3298—114no—
350#3298—114no—
351D4×SD16—114no—
352D4×SD16—114no—
353#3206—112no—
354#3187—112no—
355#3187—111no—
356#3187D1111yescharacteristic, complemented
357#3103—112no—
358C2×#448—112no—
359C2×#448—111no—
360C2×#448—111no—
361#2972—111no—
362C23×C11—22no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—42no—
366C23×C11—81no—
367C23×C11—81no—
368C23×C11C2×SD1614yescomplemented
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C22×D11—22no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—42no—
376C22×D11—44no—
377C22×D11—82no—
378C22×D11—82no—
379C22×D11—81no—
380C22×D11—81no—
381C22×D11C2×SD1614yescomplemented
382C22×D11C22×D412yes—
383Q8×C11—24no—
384Q8×C11—42no—
385D4×C11—24no—
386D4×C11—44no—
387D4×C11—44no—
388D4×C11—81no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—42no—
399C2×C4×C11—42no—
400C2×C4×C11—42no—
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C2511yescharacteristic
405C22⋊D11—44no—
406C22⋊D11—44no—
407C22⋊D11—44no—
408C22⋊D11—44no—
409C22⋊D11—82no—
410C22⋊D11—82no—
411C22⋊D11C2×SD1618yescomplemented
412C22⋊D11C2×SD1618yescomplemented
413C2×Dic11—24no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—44no—
420C2×Dic11—44no—
421C2×Dic11—42no—
422C2×Dic11—42no—
423C2×Dic11—44no—
424C2×Dic11C2×SD1614yescomplemented
425C2×Dic11C22×D412yes—
426C2×Dic11C22×D412yes—
427C2×Dic11C22×D412yes—
428D44—24no—
429D44—44no—
430D44—81no—
431C4×D11—24no—
432C4×D11—42no—
433C4×D11—48no—
434C4×D11—44no—
435C4×D11—44no—
436Dic22—24no—
437Dic22—22no—
438Dic22—22no—
439Dic22—22no—
440Dic22—48no—
441Dic22—44no—
442Dic22—44no—
443Dic22—42no—
444Dic22—44no—
445Dic22H(5,𝔽2)14yescomplemented
446C8×C11—24no—
447C11⋊C8—24no—
448C2×H(5,𝔽2)—221no—
449C23×Q8—111no—
450C23×Q8—111no—
451C22×SD16—112no—
452C22×SD16—114no—
453C22×SD16—112no—
454D4×Q8—114no—
455D4×Q8—114no—
456D4×Q8—222no—
457D4×Q8—222no—
458#547—112no—
459#547—112no—
460#546—222no—
461#546—222no—
462D42—112no—
463D42—112no—
464#537—221no—
465#534—221no—
466#534—221no—
467#532—112no—
468C2×C4⋊Q8—111no—
469C2×C4⋊Q8—221no—
470C2×C22⋊Q8—111no—
471C2×C22⋊Q8—221no—
472C2×C22⋊Q8—221no—
473C2×C22⋊Q8C2×D1111yescharacteristic, complemented
474C2×#121—111no—
475C2×#121—112no—
476C2×#121C2×D1111yescharacteristic
477C2×C4×Q8—111no—
478C2×C4×D4—111no—
479C2×C4×D4—221no—
480#492—114no—
481#487—114no—
482#483—112no—
483#483—114no—
484#483C2×D1112yescomplemented
485#481—112no—
486#481C2×D1112yescomplemented
487#475—114no—
488#465—114no—
489#465—114no—
490#465—114no—
491#465C2×D1114yescomplemented
492#461—114no—
493#461—114no—
494#460—114no—
495#450—112no—
496#450—114no—
497#450C2×D1112yescomplemented
498#448—112no—
499#448—114no—
500#448—112no—
501#448—112no—
502#448—114no—
503#448—114no—
504#448—112no—
505#448—112no—
506#448—114no—
507#448C2×D1112yescomplemented
508C4×SD16—114no—
509C4×SD16—114no—
510C8×D4—114no—
511C8×D4—114no—
512#431—112no—
513C2×#103—112no—
514C2×#103—112no—
515C2×#103—114no—
516C2×C22⋊C8—111no—
517C2×C22⋊C8—112no—
518C2×C22⋊C8C2×D1111yescharacteristic, complemented
519C22×C11—21no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—21no—
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—44no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—162no—
530C22×C11C22×SD1612yes—
531C22×C11C22×SD1612yes—
532C22×C11C22×SD1612yes—
533C22×C11C23×D411yescharacteristic
534C2×D11—22no—
535C2×D11—22no—
536C2×D11—44no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—164no—
541C2×D11—162no—
542C2×D11C22×SD1614yes—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—21no—
546C4×C11—42no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11C2×H(5,𝔽2)12yes—
550Dic11—22no—
551Dic11—24no—
552Dic11—22no—
553Dic11—42no—
554Dic11—42no—
555Dic11C22×SD1614yes—
556H(5,𝔽2)—448no—
557C2×#41—222no—
558C2×#41—222no—
559C2×#41—222no—
560C22×Q8—114no—
561C22×Q8—111no—
562C22×Q8—112no—
563C22×Q8—112no—
564C22×Q8—111no—
565C22×Q8—221no—
566C22×Q8—222no—
567C22×Q8—221no—
568C22×Q8—221no—
569C22×Q8—221no—
570C22×Q8—444no—
571C22×Q8—444no—
572C22×Q8C22×D1111yescharacteristic
573C22×D4—21no—
574C22×D4—111no—
575C22×D4—112no—
576C22×D4—111no—
577C22×D4—222no—
578C22×D4—222no—
579C22×D4—222no—
580C22×D4—221no—
581C22×D4C22×D1111yescharacteristic
582C23×C4—111no—
583C23×C4—221no—
584C23×C4—221no—
585C23×C4C22×D1111yescharacteristic
586C2×SD16—114no—
587C2×SD16—114no—
588C2×SD16—114no—
589C2×SD16—114no—
590C2×SD16—114no—
591C2×SD16—444no—
592C2×SD16—448no—
593C2×SD16—444no—
594C2×SD16C22×D1114yes—
595C22×C8—112no—
596C22×C8—114no—
597C22×C8C22×D1112yes—
598C4⋊Q8—112no—
599C4⋊Q8—114no—
600C4⋊Q8—222no—
601C4⋊Q8—224no—
602C4⋊Q8—224no—
603#127—112no—
604#124—222no—
605#123—222no—
606#123—222no—
607#123—222no—
608#123—222no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—114no—
612C22⋊Q8—224no—
613C22⋊Q8—224no—
614C22⋊Q8—222no—
615C22⋊Q8—224no—
616C22⋊Q8—224no—
617C22⋊Q8—222no—
618C22⋊Q8—222no—
619C22⋊Q8C22×D1112yes—
620C22⋊Q8C22×D1112yes—
621#121—21no—
622#121—21no—
623#121—112no—
624#121—112no—
625#121—112no—
626#121—112no—
627#121—222no—
628#121—222no—
629#121—222no—
630#121—222no—
631#121—222no—
632#121—221no—
633#121—221no—
634#121C22×D1112yes—
635#121C22×D1112yes—
636#120—222no—
637#120—222no—
638#120—222no—
639#120—222no—
640C4×Q8—114no—
641C4×Q8—222no—
642C4×D4—112no—
643C4×D4—112no—
644C4×D4—112no—
645C4×D4—112no—
646C4×D4—112no—
647C4×D4—112no—
648C4×D4—222no—
649C4×D4—224no—
650C4×D4—224no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—221no—
656C2×C4⋊C4—221no—
657C2×C4⋊C4—221no—
658C2×C4⋊C4—221no—
659C2×C4⋊C4C22×D1111yescharacteristic
660C2×C4⋊C4C22×D1111yescharacteristic
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—111no—
664C2×C22⋊C4—111no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4—221no—
667C2×C22⋊C4—221no—
668C2×C42—111no—
669C2×C42—221no—
670#106—114no—
671#106C22×D1114yes—
672C4⋊C8—114no—
673#103—114no—
674#103—114no—
675#103—114no—
676#103—114no—
677#103—114no—
678#103C22×D1114yes—
679#102—114no—
680#102C22×D1114yes—
681C22⋊C8—112no—
682C22⋊C8—112no—
683C22⋊C8—114no—
684C22⋊C8C22×D1112yes—
685C22⋊C8C22×D1112yes—
686C4×C8—114no—
687C2×C11—22no—
688C2×C11—22no—
689C2×C11—22no—
690C2×C11—82no—
691C2×C11#348411yescharacteristic
692C2×C11C23×SD1611yescharacteristic
693C2×C11#358611yescharacteristic
694D11—24no—
695D11—82no—
696C24—21no—
697C24—111no—
698C24—222no—
699C24—221no—
700C24D4×D1111yescharacteristic
701#41—448no—
702#41—448no—
703#41—448no—
704C2×Q8—21no—
705C2×Q8—42no—
706C2×Q8—112no—
707C2×Q8—112no—
708C2×Q8—222no—
709C2×Q8—224no—
710C2×Q8—224no—
711C2×Q8—224no—
712C2×Q8—224no—
713C2×Q8—221no—
714C2×Q8—222no—
715C2×Q8—222no—
716C2×Q8—221no—
717C2×Q8—228no—
718C2×Q8—442no—
719C2×Q8—442no—
720C2×Q8—442no—
721C2×Q8—444no—
722C2×Q8—444no—
723C2×Q8—444no—
724C2×Q8—444no—
725C2×Q8—444no—
726C2×Q8—448no—
727C2×Q8C23×D1112yes—
728C2×D4—22no—
729C2×D4—22no—
730C2×D4—21no—
731C2×D4—42no—
732C2×D4—44no—
733C2×D4—118no—
734C2×D4—112no—
735C2×D4—112no—
736C2×D4—112no—
737C2×D4—222no—
738C2×D4—222no—
739C2×D4—222no—
740C2×D4—222no—
741C2×D4—222no—
742C2×D4—222no—
743C2×D4—222no—
744C2×D4—221no—
745C2×D4—442no—
746C2×D4—444no—
747C2×D4—448no—
748C2×D4—448no—
749C2×D4—448no—
750C2×D4—444no—
751C2×D4C23×D1112yes—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—111no—
757C22×C4—111no—
758C22×C4—111no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—224no—
764C22×C4—222no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—442no—
771C22×C4—444no—
772C22×C4—444no—
773C22×C4D4×D1111yescharacteristic
774C22×C4D4×D1111yescharacteristic
775C22×C4D4×D1111yescharacteristic
776C22×C4C23×D1111yescharacteristic
777C22×C4C23×D1111yescharacteristic
778C22×C4C23×D1111yescharacteristic
779SD16—44no—
780SD16—228no—
781SD16—228no—
782SD16—444no—
783SD16—444no—
784SD16—444no—
785C2×C8—42no—
786C2×C8—114no—
787C2×C8—444no—
788C2×C8—442no—
789C2×C8C23×D1114yes—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—112no—
795C4⋊C4—112no—
796C4⋊C4—112no—
797C4⋊C4—222no—
798C4⋊C4—224no—
799C4⋊C4—224no—
800C4⋊C4—224no—
801C4⋊C4—224no—
802C4⋊C4—222no—
803C4⋊C4—221no—
804C4⋊C4C23×D1112yes—
805C4⋊C4C23×D1112yes—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—112no—
811C22⋊C4—112no—
812C22⋊C4—112no—
813C22⋊C4—112no—
814C22⋊C4—222no—
815C22⋊C4—222no—
816C22⋊C4—224no—
817C22⋊C4—222no—
818C22⋊C4—222no—
819C22⋊C4—222no—
820C22⋊C4—222no—
821C42—112no—
822C42—112no—
823C42—224no—
824C11#6156211yescharacteristic, complemented, Sylow
825C23—22no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—81no—
830C23—81no—
831C23—112no—
832C23—114no—
833C23—222no—
834C23—441no—
835C23—441no—
836C23—444no—
837C23—442no—
838C23—881no—
839C23—881no—
840C23—882no—
841C23—882no—
842C23SD16×D1114yescomplemented
843C23C2×D4×D1111yescharacteristic
844C23C2×D4×D1111yescharacteristic
845C23C2×D4×D1111yescharacteristic
846Q8—24no—
847Q8—42no—
848Q8—114no—
849Q8—224no—
850Q8—222no—
851Q8—222no—
852Q8—222no—
853Q8—444no—
854Q8—444no—
855Q8—442no—
856Q8—444no—
857Q8—448no—
858D4—24no—
859D4—44no—
860D4—44no—
861D4—81no—
862D4—118no—
863D4—118no—
864D4—224no—
865D4—444no—
866D4—444no—
867D4—444no—
868D4—444no—
869D4—444no—
870D4—881no—
871D4—882no—
872D4—882no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—114no—
886C2×C4—112no—
887C2×C4—112no—
888C2×C4—112no—
889C2×C4—224no—
890C2×C4—222no—
891C2×C4—224no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—442no—
895C2×C4—444no—
896C2×C4—448no—
897C2×C4—444no—
898C2×C4—444no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—444no—
902C2×C4—444no—
903C2×C4—442no—
904C2×C4—442no—
905C2×C4C2×D4×D1111yescharacteristic
906C2×C4C2×D4×D1111yescharacteristic
907C2×C4C2×D4×D1111yescharacteristic
908C2×C4C24×D1111yescharacteristic
909C8—24no—
910C8—224no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—44no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—114no—
922C22—162no—
923C22—222no—
924C22—222no—
925C22—444no—
926C22—442no—
927C22—442no—
928C22—442no—
929C22—1762no—
930C22—1764no—
931C22C2×SD16×D1112yes—
932C22C2×SD16×D1112yes—
933C22C2×SD16×D1112yes—
934C22C22×D4×D1111yescharacteristic
935C4—21no—
936C4—21no—
937C4—21no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—114no—
942C4—222no—
943C4—222no—
944C4—224no—
945C4—442no—
946C4—442no—
947C4D11×H(5,𝔽2)12yes—
948C2—22no—
949C2—22no—
950C2—22no—
951C2—82no—
952C2—224no—
953C2—882no—
954C2#1308224811yescharacteristic
955C2C22×SD16×D1111yescharacteristic
956C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3187C2
socleC22×C11C23×D4
prime radical#13082373C2
hypercenter#3187D11
hypocenterC11#61562
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3187

Complements

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

NH ≅ G/Ntype
2. C2×#10623163C2semidirect
3. #13080479C2semidirect
4. #13080476C2semidirect
5. #13080310C2semidirect
6. #13080309C2semidirect
7. #13079539C2semidirect
8. #13079375C2semidirect
9. #13079369C2semidirect
10. #13078644C2semidirect
11. C2×#10622351C2semidirect
12. C2×#10622653C2semidirect
13. D11×#448C2semidirect
14. #13077638C2semidirect
15. C11×#3187C2semidirect
16. C22×Q8×D11C22semidirect
18. C23×Dic22C22semidirect
19. C2×C11×C22⋊Q8C22semidirect
21. C2×#66997C22semidirect
24. C22×#4324C22semidirect
27. C2×SD16×D11C22semidirect
28. C22×#4314C22semidirect
31. #10623163C22semidirect
32. #10623163C22semidirect
40. C2×#66950C22semidirect
44. C2×#66940C22semidirect
48. C11×#483C22semidirect
49. C11×#481C22semidirect
50. C11×#465C22semidirect
51. C11×#450C22semidirect
52. C11×#448C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. #10622840C22semidirect
55. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622788C22semidirect
57. #10622783C22semidirect
58. #10622775C22semidirect
59. C8×C22⋊D11C22semidirect
60. C2×#66880C22semidirect
61. #10622661C22semidirect
62. #10622659C22semidirect
63. #10622656C22semidirect
64. #10622653C22semidirect
65. #10622653C22semidirect
66. #10622653C22semidirect
67. C2×#66874C22semidirect
68. #10622581C22semidirect
69. #10622477C22semidirect
70. #10622475C22semidirect
71. #10622467C22semidirect
72. #10622465C22semidirect
73. #10622431C22semidirect
74. #10622419C22semidirect
75. D11×#103C22semidirect
76. #10622405C22semidirect
77. #10622391C22semidirect
78. #10622389C22semidirect
79. #10622375C22semidirect
80. #10622371C22semidirect
81. #10622351C22semidirect
82. #10622351C22semidirect
83. #10622351C22semidirect
84. (C22⋊D11)⋊C8C22semidirect
85. D11×C22⋊C8C22semidirect
86. #10622331C22semidirect
251. C2×C22⋊D11SD16semidirect
356. #3187D11semidirect
368. C23×C11C2×SD16semidirect
381. C22×D11C2×SD16semidirect
411. C22⋊D11C2×SD16semidirect
412. C22⋊D11C2×SD16semidirect
424. C2×Dic11C2×SD16semidirect
445. Dic22H(5,𝔽2)semidirect
473. C2×C22⋊Q8C2×D11semidirect
484. #483C2×D11semidirect
486. #481C2×D11semidirect
491. #465C2×D11semidirect
497. #450C2×D11semidirect
507. #448C2×D11semidirect
518. C2×C22⋊C8C2×D11semidirect
824. C11#61562semidirect
842. C23SD16×D11semidirect

Maximal subgroups

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

subgroupindex
#130823732
C2×#106231632
#130804792
#130804762
#130803102
#130803092
#130795392
#130793752
#130793692
#130786442
C2×#106223512
C2×#106226532
D11×#4482
#130776382
C11×#31872
#6156211