Finite Group Databasebeta

← #15638463

Subgroups — #15638463

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082412C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊D11C211yesmaximal, characteristic
3#13080436C214yesmaximal, complemented
4#13080433C214yesmaximal, complemented
5#13080310C214yesmaximal, complemented
6SD16×C22⋊D11C214yesmaximal, complemented
7#13079555C212yesmaximal, complemented
8#13079374C211yesmaximal, characteristic, complemented
9#13079370C212yesmaximal, complemented
10#13079369C211yesmaximal, characteristic, complemented
11#13078619C212yesmaximal, complemented
12C2×#10622831C211yesmaximal, characteristic, complemented
13D11×#450C212yesmaximal, complemented
14#13077638C211yesmaximal, characteristic, complemented
15C2×C11×#450C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11—21no—
18C22×D4×D11C2211yescharacteristic
19C22×C11×SD16C2212yescomplemented
20C2×C11×C22⋊Q8C2211yescharacteristic, complemented
21C2×#67006—21no—
22Q8×C22⋊D11C2212yescomplemented
23C2×#66993C2211yescharacteristic
24C2×#66992—21no—
25D4×C22⋊D11—22no—
26D4×C22⋊D11—22no—
27D4×C22⋊D11C2214yes—
28D4×C22⋊D11C2214yes—
29C2×#66991C2211yescharacteristic
30C2×#66990—21no—
31C2×D4×Dic11C2211yescharacteristic
32C22×#4324C2212yescomplemented
33C2×#66983C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×#66977C2211yescharacteristic, complemented
36C2×SD16×D11C2214yescomplemented
37#10623167—22no—
38#10623166C2212yescomplemented
39#10623165—21no—
40#10623163C2212yescomplemented
41D11×C22⋊Q8C2212yescomplemented
42#10623154—21no—
43#10623153C2212yescomplemented
44#10623042—22no—
45#10623042C2212yescomplemented
46#10623017—21no—
47#10623014—21no—
48C11×#450C2212yes—
49C11×#450C2212yescomplemented
50C11×#450C2214yescomplemented
51C2×C11×#102C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53#10622840C2212yescomplemented
54#10622831C2212yes—
55#10622831C2212yescomplemented
56#10622831C2214yescomplemented
57C2×#66896C2212yescomplemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622788C2214yescomplemented
60#10622784C2214yescomplemented
61#10622783C2214yescomplemented
62#10622782C2214yescomplemented
63#10622776C2214yescomplemented
64#10622775C2214yescomplemented
65SD16×Dic11C2214yescomplemented
66#10622727C2214yescomplemented
67C8×C22⋊D11C2214yescomplemented
68#10622661C2214yescomplemented
69#10622659C2212yescomplemented
70#10622656C2212yescomplemented
71#10622581C2212yescomplemented
72#10622391C2214yescomplemented
73#10622390C2214yescomplemented
74#10622389C2214yescomplemented
75D11×#102C2214yescomplemented
76#10622375C2214yescomplemented
77#10622374C2214yescomplemented
78#10622373C2214yescomplemented
79#10622371C2214yescomplemented
80#10622351C2212yescomplemented
81#10622348C2212yescomplemented
82#10622344C2212yescomplemented
83(C22⋊D11)⋊C8C2214yescomplemented
84D11×C22⋊C8C2212yescomplemented
85#10622334C2212yescomplemented
86#10622331C2212yescomplemented
87C25×C11—21no—
88C24×D11—21no—
89C22×Q8×C11C2311yescharacteristic, complemented
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—21no—
93C22×D4×C11—44no—
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2312yes—
96C22×D4×C11C2312yes—
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—21no—
104C22×C22⋊D11—21no—
105C22×C22⋊D11—21no—
106C22×C22⋊D11—48no—
107C22×C22⋊D11D411yescharacteristic
108C23×Dic11—21no—
109C2×Q8×D11C2312yescomplemented
110C2×D4×D11—22no—
111C2×D4×D11—44no—
112C2×D4×D11C2314yes—
113C22×D44C2311yescharacteristic
114C22×C4×D11C2311yescharacteristic
115C22×Dic22C2311yescharacteristic, complemented
116C2×C11×SD16—44no—
117C2×C11×SD16C2314yes—
118C2×C11×SD16C2314yescomplemented
119C22×C8×C11C2312yescomplemented
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8C2312yes—
123C11×C22⋊Q8C2312yescomplemented
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4C2311yescharacteristic, complemented
126C2×C11×C22⋊C4—21no—
127#67006—24no—
128#67006—24no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11D411yescharacteristic
133#66999—22no—
134#66999C2312yescomplemented
135Q8×Dic11C2312yescomplemented
136#66997—22no—
137#66997C2312yescomplemented
138C2×#4325C2314yescomplemented
139#66993—22no—
140#66993C2314yes—
141#66992—24no—
142#66992—24no—
143#66991—22no—
144#66991C2314yes—
145#66990—24no—
146#66990—24no—
147D4×Dic11—22no—
148D4×Dic11C2314yes—
149C2×#4324—44no—
150C2×#4324C2314yes—
151C2×#4324C2314yescomplemented
152#66983—21no—
153#66983—21no—
154#66983C2312yes—
155#66983C2312yes—
156C4×C22⋊D11—22no—
157C4×C22⋊D11—22no—
158C4×C22⋊D11D412yes—
159C4×C22⋊D11D412yes—
160C4×C22⋊D11C2312yes—
161C4×C22⋊D11C2312yes—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4D411yescharacteristic
164C2×C4⋊Dic11C2311yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic, complemented
166#66977—21no—
167#66977—21no—
168#66977—22no—
169#66977—22no—
170#66977C2312yes—
171#66977C2312yescomplemented
172C2×Dic11⋊C4—21no—
173C2×Dic11⋊C4D411yescharacteristic
174C2×C4×Dic11C2311yescharacteristic
175C22×C11⋊C8C2312yescomplemented
176SD16×D11—48no—
177C2×#4314C2314yescomplemented
178C2×C8×D11C2314yescomplemented
179#66950—22no—
180#66950C2312yescomplemented
181#66949—22no—
182#66949—22no—
183#66949—22no—
184C4⋊C4×D11—22no—
185C4⋊C4×D11C2312yescomplemented
186#66942—22no—
187#66942—22no—
188#66942—22no—
189#66941—22no—
190#66941C2312yescomplemented
191#66940—22no—
192#66940C2312yescomplemented
193(C22⋊D11)⋊C4—22no—
194(C22⋊D11)⋊C4—22no—
195C22⋊C4×D11—22no—
196#66931—22no—
197#66931—22no—
198#66931—22no—
199#66931—22no—
200#66930—22no—
201C11×#102C2314yes—
202C11×#102C2314yescomplemented
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yescomplemented
205#66899C2314yescomplemented
206#66896C2314yes—
207#66896C2314yescomplemented
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yescomplemented
210#66885C2314yescomplemented
211(C2×D11)⋊C8C2314yescomplemented
212#66881C2314yescomplemented
213#66880C2314yescomplemented
214Dic11⋊C8C2314yescomplemented
215C8×Dic11C2314yescomplemented
216#66873C2314yescomplemented
217#66872C2314yescomplemented
218#61560—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11—22no—
222C24×C11—22no—
223C24×C11—44no—
224C24×C11—44no—
225C24×C11—82no—
226C24×C11C2×D411yescharacteristic
227C23×D11—21no—
228C23×D11—24no—
229C23×D11—44no—
230C23×D11—44no—
231C23×D11—82no—
232C23×D11C2×D411yescharacteristic
233C2×Q8×C11—21no—
234C2×Q8×C11—42no—
235C2×Q8×C11C2412yes—
236C2×D4×C11—24no—
237C2×D4×C11—24no—
238C2×D4×C11—24no—
239C2×D4×C11—21no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—42no—
244C2×D4×C11—42no—
245C2×D4×C11—42no—
246C2×D4×C11—44no—
247C2×D4×C11—44no—
248C2×D4×C11—44no—
249C2×D4×C11C2412yes—
250C2×D4×C11C2412yes—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—42no—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—24no—
261C2×C22⋊D11—24no—
262C2×C22⋊D11—24no—
263C2×C22⋊D11—22no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—24no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—416no—
268C2×C22⋊D11—416no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—82no—
273C2×C22⋊D11SD1618yescomplemented
274C2×C22⋊D11C2×D412yes—
275C2×C22⋊D11C2×D412yes—
276C22×Dic11—24no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—44no—
281C22×Dic11C2×D411yescharacteristic
282C22×Dic11C2×D411yescharacteristic
283C22×Dic11C2×D411yescharacteristic
284Q8×D11—44no—
285D4×D11—28no—
286D4×D11—44no—
287D4×D11—48no—
288C2×D44—21no—
289C2×D44—42no—
290C2×D44C2412yes—
291C2×C4×D11—22no—
292C2×C4×D11—22no—
293C2×C4×D11—42no—
294C2×C4×D11C2×D412yes—
295C2×C4×D11C2412yes—
296C2×Dic22—22no—
297C2×Dic22—22no—
298C2×Dic22—21no—
299C2×Dic22—42no—
300C2×Dic22C2412yes—
301C11×SD16—28no—
302C11×SD16—44no—
303C2×C8×C11—42no—
304C2×C8×C11C2414yes—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—22no—
307C11×C4⋊C4—21no—
308C11×C4⋊C4C2412yes—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—22no—
311C22⋊Dic11—24no—
312C22⋊Dic11—24no—
313C22⋊Dic11—22no—
314C22⋊Dic11—22no—
315C22⋊Dic11C2×D412yes—
316C22⋊Dic11C2×D412yes—
317#4325—44no—
318#4324—28no—
319#4324—44no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4C2×D412yes—
325(C2×D11)⋊C4C2×D412yes—
326C4⋊Dic11—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11—21no—
329C4⋊Dic11—21no—
330C4⋊Dic11C2412yes—
331C4⋊Dic11C2412yes—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4C2×D412yes—
341Dic11⋊C4C2×D412yes—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11C2×D412yes—
345C4×Dic11C2412yes—
346C2×C11⋊C8—42no—
347C2×C11⋊C8C2414yes—
348#4314—44no—
349C8×D11—44no—
350#3501—111no—
351C2×D42—111no—
352#3295—114no—
353#3295—114no—
354D4×SD16—114no—
355D4×SD16—114no—
356#3208—112no—
357#3187—112no—
358#3187—111no—
359#3187—111no—
360#3101—112no—
361C2×#450—112no—
362C2×#450—111no—
363C2×#450D1111yescharacteristic, complemented
364#2972—111no—
365C23×C11—24no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—44no—
371C23×C11—44no—
372C23×C11—42no—
373C23×C11—42no—
374C23×C11—42no—
375C23×C11—42no—
376C23×C11—44no—
377C23×C11—44no—
378C23×C11—42no—
379C23×C11—82no—
380C23×C11—82no—
381C23×C11—816no—
382C23×C11C2×SD1614yescomplemented
383C23×C11C22×D411yescharacteristic
384C23×C11C22×D411yescharacteristic
385C23×C11C22×D411yescharacteristic
386C22×D11—22no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—48no—
390C22×D11—42no—
391C22×D11—42no—
392C22×D11—42no—
393C22×D11—48no—
394C22×D11—84no—
395C22×D11—816no—
396C22×D11C2×SD1614yescomplemented
397C22×D11C22×D412yes—
398Q8×C11—24no—
399Q8×C11—81no—
400D4×C11—24no—
401D4×C11—22no—
402D4×C11—22no—
403D4×C11—22no—
404D4×C11—44no—
405D4×C11—44no—
406D4×C11—42no—
407D4×C11H(5,𝔽2)14yes—
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—41no—
415C2×C4×C11—41no—
416C2×C4×C11—81no—
417C2×C4×C11—81no—
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C2511yescharacteristic
422C22⋊D11—48no—
423C22⋊D11—44no—
424C22⋊D11—44no—
425C22⋊D11—48no—
426C22⋊D11—48no—
427C22⋊D11—84no—
428C22⋊D11C2×SD1618yescomplemented
429C22⋊D11C2×SD1618yescomplemented
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—42no—
436C2×Dic11—48no—
437C2×Dic11—81no—
438C2×Dic11—81no—
439C2×Dic11C2×SD1614yescomplemented
440C2×Dic11C22×D412yes—
441C2×Dic11C22×D412yes—
442C2×Dic11C22×D412yes—
443D44—24no—
444D44—42no—
445C4×D11—24no—
446C4×D11—42no—
447C4×D11—82no—
448C4×D11—82no—
449Dic22—24no—
450Dic22—82no—
451Dic22—82no—
452Dic22—81no—
453C8×C11—24no—
454C11⋊C8—24no—
455C23×D4—111no—
456C23×D4—221no—
457C23×D4C2×D1111yescharacteristic
458C22×SD16—112no—
459C22×SD16—114no—
460C22×SD16C2×D1112yescomplemented
461#554—112no—
462#554—112no—
463#554—222no—
464#554—222no—
465D4×Q8—112no—
466D4×Q8—112no—
467D42—114no—
468D42—114no—
469D42—222no—
470D42—222no—
471#544—221no—
472#543—221no—
473#543—221no—
474#533—112no—
475C2×#127—111no—
476C2×C22⋊Q8—111no—
477C2×C22⋊Q8—112no—
478C2×C22⋊Q8C2×D1111yescharacteristic, complemented
479C2×#121—111no—
480C2×#121—111no—
481C2×#121—221no—
482C2×#120—221no—
483C2×#120—221no—
484#518—221no—
485C2×C4×D4—111no—
486C2×C4×D4—111no—
487#492—114no—
488#486—114no—
489#483—112no—
490#483—112no—
491#481—112no—
492#481—114no—
493#481—112no—
494#476—114no—
495#465—114no—
496#465—114no—
497#465—114no—
498#465—114no—
499#461—114no—
500#460—114no—
501#460—114no—
502#450—112no—
503#450—112no—
504#450—114no—
505#450—114no—
506#450—112no—
507#450—114no—
508#450—112no—
509#450C2×D1112yes—
510#450C2×D1112yescomplemented
511#450C2×D1114yescomplemented
512#448—112no—
513#448—114no—
514#448—112no—
515C4×SD16—114no—
516C4×SD16—114no—
517C8×D4—114no—
518C8×D4—114no—
519#431—112no—
520C2×#102—112no—
521C2×#102—114no—
522C2×#102C2×D1112yescomplemented
523C2×C22⋊C8—111no—
524C2×C22⋊C8—112no—
525C2×C22⋊C8C2×D1111yescharacteristic, complemented
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—21no—
532C22×C11—24no—
533C22×C11—44no—
534C22×C11—48no—
535C22×C11—42no—
536C22×C11—42no—
537C22×C11—42no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—88no—
541C22×C11—88no—
542C22×C11—84no—
543C22×C11C22×SD1612yes—
544C22×C11C22×SD1612yes—
545C22×C11C22×SD1612yes—
546C22×C11C23×D411yescharacteristic
547C2×D11—22no—
548C2×D11—22no—
549C2×D11—44no—
550C2×D11—42no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—816no—
554C2×D11—84no—
555C2×D11C22×SD1614yes—
556C4×C11—21no—
557C4×C11—21no—
558C4×C11—21no—
559C4×C11—42no—
560C4×C11—42no—
561C4×C11C2×H(5,𝔽2)12yes—
562Dic11—22no—
563Dic11—22no—
564Dic11—42no—
565Dic11—42no—
566Dic11—42no—
567Dic11C22×SD1614yes—
568C25—21no—
569C25—221no—
570C22×Q8—112no—
571C22×Q8—111no—
572C22×Q8C22×D1111yescharacteristic, complemented
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—44no—
577C22×D4—111no—
578C22×D4—114no—
579C22×D4—111no—
580C22×D4—222no—
581C22×D4—221no—
582C22×D4—221no—
583C22×D4—221no—
584C22×D4—224no—
585C22×D4—224no—
586C22×D4—221no—
587C22×D4—221no—
588C22×D4—444no—
589C22×D4—448no—
590C22×D4C22×D1111yescharacteristic
591C22×D4C22×D1112yes—
592C22×D4C22×D1112yes—
593C22×D4C22×D1111yescharacteristic
594C23×C4—111no—
595C23×C4—221no—
596C23×C4C22×D1111yescharacteristic
597C2×SD16—44no—
598C2×SD16—114no—
599C2×SD16—114no—
600C2×SD16—114no—
601C2×SD16—114no—
602C2×SD16—448no—
603C2×SD16—444no—
604C2×SD16C22×D1114yes—
605C2×SD16C22×D1114yescomplemented
606C22×C8—112no—
607C22×C8—114no—
608C22×C8C22×D1112yescomplemented
609C4⋊Q8—112no—
610C4⋊Q8—112no—
611C4⋊Q8—222no—
612C4⋊Q8—222no—
613#127—114no—
614#127—222no—
615#125—222no—
616#125—222no—
617#125—222no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—112no—
621C22⋊Q8—112no—
622C22⋊Q8—112no—
623C22⋊Q8—112no—
624C22⋊Q8—222no—
625C22⋊Q8—222no—
626C22⋊Q8—222no—
627C22⋊Q8—222no—
628C22⋊Q8—222no—
629C22⋊Q8—222no—
630C22⋊Q8—222no—
631C22⋊Q8—222no—
632C22⋊Q8—222no—
633C22⋊Q8—222no—
634C22⋊Q8—222no—
635C22⋊Q8—221no—
636C22⋊Q8—221no—
637C22⋊Q8C22×D1112yes—
638C22⋊Q8C22×D1112yescomplemented
639#121—114no—
640#121—112no—
641#121—112no—
642#121—224no—
643#121—224no—
644#121—222no—
645#121—221no—
646#121—221no—
647#120—224no—
648#120—224no—
649#120—224no—
650#120—224no—
651C4×Q8—112no—
652C4×Q8—112no—
653C4×Q8—222no—
654C4×D4—112no—
655C4×D4—112no—
656C4×D4—112no—
657C4×D4—112no—
658C4×D4—114no—
659C4×D4—222no—
660C4×D4—222no—
661C4×D4—222no—
662C4×D4—222no—
663C4×D4—222no—
664#117—222no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—111no—
667C2×C4⋊C4—111no—
668C2×C4⋊C4—111no—
669C2×C4⋊C4—112no—
670C2×C4⋊C4—222no—
671C2×C4⋊C4—221no—
672C2×C4⋊C4C22×D1111yescharacteristic, complemented
673C2×C22⋊C4—21no—
674C2×C22⋊C4—111no—
675C2×C22⋊C4—111no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—221no—
678C2×C22⋊C4—221no—
679C2×C22⋊C4—221no—
680C2×C22⋊C4—221no—
681C2×C42—111no—
682#106—114no—
683#106—114no—
684C4⋊C8—114no—
685#103—114no—
686#103—114no—
687#102—114no—
688#102—114no—
689#102—114no—
690#102—114no—
691#102C22×D1114yes—
692#102C22×D1114yescomplemented
693C22⋊C8—112no—
694C22⋊C8—112no—
695C22⋊C8—114no—
696C22⋊C8C22×D1112yes—
697C22⋊C8C22×D1112yescomplemented
698C4×C8—114no—
699C2×C11—22no—
700C2×C11—22no—
701C2×C11—22no—
702C2×C11—44no—
703C2×C11—82no—
704C2×C11#348411yescharacteristic
705C2×C11C23×SD1611yescharacteristic
706C2×C11#358511yescharacteristic
707D11—24no—
708D11—82no—
709C24—21no—
710C24—21no—
711C24—22no—
712C24—22no—
713C24—44no—
714C24—44no—
715C24—82no—
716C24—111no—
717C24—224no—
718C24—221no—
719C24—444no—
720C24—444no—
721C24—882no—
722C24D4×D1111yescharacteristic
723C2×Q8—21no—
724C2×Q8—42no—
725C2×Q8—112no—
726C2×Q8—222no—
727C2×Q8—222no—
728C2×Q8—221no—
729C2×Q8—442no—
730C2×Q8—444no—
731C2×Q8C23×D1112yes—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—21no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—21no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—118no—
746C2×D4—112no—
747C2×D4—112no—
748C2×D4—112no—
749C2×D4—224no—
750C2×D4—224no—
751C2×D4—224no—
752C2×D4—228no—
753C2×D4—224no—
754C2×D4—222no—
755C2×D4—222no—
756C2×D4—221no—
757C2×D4—442no—
758C2×D4—444no—
759C2×D4—444no—
760C2×D4—448no—
761C2×D4—4416no—
762C2×D4—4416no—
763C2×D4—444no—
764C2×D4—444no—
765C2×D4—444no—
766C2×D4—882no—
767C2×D4C23×D1112yes—
768C2×D4C23×D1112yes—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—42no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—224no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—442no—
784C22×C4—444no—
785C22×C4D4×D1111yescharacteristic
786C22×C4D4×D1111yescharacteristic
787C22×C4D4×D1111yescharacteristic
788C22×C4C23×D1111yescharacteristic
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791SD16—28no—
792SD16—44no—
793SD16—228no—
794SD16—444no—
795SD16—444no—
796SD16—444no—
797C2×C8—42no—
798C2×C8—114no—
799C2×C8—444no—
800C2×C8—442no—
801C2×C8C23×D1114yes—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—21no—
805C4⋊C4—112no—
806C4⋊C4—112no—
807C4⋊C4—112no—
808C4⋊C4—112no—
809C4⋊C4—222no—
810C4⋊C4—222no—
811C4⋊C4—222no—
812C4⋊C4—222no—
813C4⋊C4—222no—
814C4⋊C4—222no—
815C4⋊C4—222no—
816C4⋊C4—222no—
817C4⋊C4—221no—
818C4⋊C4—221no—
819C4⋊C4—222no—
820C4⋊C4—222no—
821C4⋊C4C23×D1112yes—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—112no—
825C22⋊C4—112no—
826C22⋊C4—112no—
827C22⋊C4—112no—
828C22⋊C4—222no—
829C22⋊C4—222no—
830C22⋊C4—224no—
831C22⋊C4—224no—
832C22⋊C4—222no—
833C22⋊C4—222no—
834C22⋊C4—222no—
835C22⋊C4—222no—
836C42—112no—
837C42—112no—
838C42—222no—
839C42—222no—
840C11#6156011yescharacteristic, complemented, Sylow
841C23—24no—
842C23—22no—
843C23—22no—
844C23—41no—
845C23—41no—
846C23—44no—
847C23—44no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—44no—
853C23—44no—
854C23—42no—
855C23—82no—
856C23—82no—
857C23—816no—
858C23—112no—
859C23—114no—
860C23—222no—
861C23—441no—
862C23—441no—
863C23—448no—
864C23—442no—
865C23—442no—
866C23—448no—
867C23—442no—
868C23—884no—
869C23—8816no—
870C23SD16×D1114yescomplemented
871C23C2×D4×D1111yescharacteristic
872C23C2×D4×D1111yescharacteristic
873C23C2×D4×D1111yescharacteristic
874Q8—24no—
875Q8—81no—
876Q8—224no—
877Q8—881no—
878Q8—882no—
879Q8—882no—
880D4—24no—
881D4—22no—
882D4—22no—
883D4—22no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—118no—
888D4—118no—
889D4—224no—
890D4—442no—
891D4—448no—
892D4—448no—
893D4—448no—
894D4—444no—
895D4—444no—
896D4—884no—
897D4#6703714yes—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4—114no—
909C2×C4—112no—
910C2×C4—112no—
911C2×C4—112no—
912C2×C4—224no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—442no—
917C2×C4—448no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—442no—
921C2×C4—882no—
922C2×C4—882no—
923C2×C4—881no—
924C2×C4—881no—
925C2×C4C2×D4×D1111yescharacteristic
926C2×C4C2×D4×D1111yescharacteristic
927C2×C4C2×D4×D1111yescharacteristic
928C2×C4C24×D1111yescharacteristic
929C8—24no—
930C8—224no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—21no—
937C22—24no—
938C22—44no—
939C22—48no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—88no—
946C22—88no—
947C22—84no—
948C22—114no—
949C22—222no—
950C22—222no—
951C22—444no—
952C22—442no—
953C22—442no—
954C22—442no—
955C22—884no—
956C22—8816no—
957C22C2×SD16×D1112yes—
958C22C2×SD16×D1112yes—
959C22C2×SD16×D1112yes—
960C22C22×D4×D1111yescharacteristic
961C4—21no—
962C4—21no—
963C4—21no—
964C4—42no—
965C4—42no—
966C4—114no—
967C4—222no—
968C4—222no—
969C4—442no—
970C4—442no—
971C4—442no—
972C4C2×#6703712yes—
973C2—22no—
974C2—22no—
975C2—22no—
976C2—44no—
977C2—82no—
978C2—224no—
979C2—882no—
980C2#1308224511yescharacteristic
981C2C22×SD16×D1111yescharacteristic
982C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC22×C11C23×D4
prime radicalC2×D4×C22⋊D11C2
hypercenterC2×#450D11
hypocenterC11#61560
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. #13082412C2semidirect
3. #13080436C2semidirect
4. #13080433C2semidirect
5. #13080310C2semidirect
6. SD16×C22⋊D11C2semidirect
7. #13079555C2semidirect
8. #13079374C2semidirect
9. #13079370C2semidirect
10. #13079369C2semidirect
11. #13078619C2semidirect
12. C2×#10622831C2semidirect
13. D11×#450C2semidirect
14. #13077638C2semidirect
15. C2×C11×#450C2semidirect
19. C22×C11×SD16C22semidirect
20. C2×C11×C22⋊Q8C22semidirect
22. Q8×C22⋊D11C22semidirect
32. C22×#4324C22semidirect
35. C2×#66977C22semidirect
36. C2×SD16×D11C22semidirect
38. #10623166C22semidirect
40. #10623163C22semidirect
41. D11×C22⋊Q8C22semidirect
43. #10623153C22semidirect
45. #10623042C22semidirect
49. C11×#450C22semidirect
50. C11×#450C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. #10622840C22semidirect
55. #10622831C22semidirect
56. #10622831C22semidirect
57. C2×#66896C22semidirect
58. C2×C22⋊(C11⋊C8)C22semidirect
59. #10622788C22semidirect
60. #10622784C22semidirect
61. #10622783C22semidirect
62. #10622782C22semidirect
63. #10622776C22semidirect
64. #10622775C22semidirect
65. SD16×Dic11C22semidirect
66. #10622727C22semidirect
67. C8×C22⋊D11C22semidirect
68. #10622661C22semidirect
69. #10622659C22semidirect
70. #10622656C22semidirect
71. #10622581C22semidirect
72. #10622391C22semidirect
73. #10622390C22semidirect
74. #10622389C22semidirect
75. D11×#102C22semidirect
76. #10622375C22semidirect
77. #10622374C22semidirect
78. #10622373C22semidirect
79. #10622371C22semidirect
80. #10622351C22semidirect
81. #10622348C22semidirect
82. #10622344C22semidirect
83. (C22⋊D11)⋊C8C22semidirect
84. D11×C22⋊C8C22semidirect
85. #10622334C22semidirect
86. #10622331C22semidirect
89. C22×Q8×C11C23semidirect
109. C2×Q8×D11C23semidirect
115. C22×Dic22C23semidirect
118. C2×C11×SD16C23semidirect
119. C22×C8×C11C23semidirect
123. C11×C22⋊Q8C23semidirect
125. C2×C11×C4⋊C4C23semidirect
134. #66999C23semidirect
135. Q8×Dic11C23semidirect
137. #66997C23semidirect
138. C2×#4325C23semidirect
151. C2×#4324C23semidirect
165. C2×C4⋊Dic11C23semidirect
171. #66977C23semidirect
175. C22×C11⋊C8C23semidirect
177. C2×#4314C23semidirect
178. C2×C8×D11C23semidirect
180. #66950C23semidirect
185. C4⋊C4×D11C23semidirect
190. #66941C23semidirect
192. #66940C23semidirect
202. C11×#102C23semidirect
204. C11×C22⋊C8C23semidirect
205. #66899C23semidirect
207. #66896C23semidirect
209. C22⋊(C11⋊C8)C23semidirect
210. #66885C23semidirect
211. (C2×D11)⋊C8C23semidirect
212. #66881C23semidirect
213. #66880C23semidirect
214. Dic11⋊C8C23semidirect
215. C8×Dic11C23semidirect
216. #66873C23semidirect
217. #66872C23semidirect
273. C2×C22⋊D11SD16semidirect
363. C2×#450D11semidirect
382. C23×C11C2×SD16semidirect
396. C22×D11C2×SD16semidirect
428. C22⋊D11C2×SD16semidirect
429. C22⋊D11C2×SD16semidirect
439. C2×Dic11C2×SD16semidirect
460. C22×SD16C2×D11semidirect
478. C2×C22⋊Q8C2×D11semidirect
510. #450C2×D11semidirect
511. #450C2×D11semidirect
522. C2×#102C2×D11semidirect
525. C2×C22⋊C8C2×D11semidirect
572. C22×Q8C22×D11semidirect
605. C2×SD16C22×D11semidirect
608. C22×C8C22×D11semidirect
638. C22⋊Q8C22×D11semidirect
672. C2×C4⋊C4C22×D11semidirect
692. #102C22×D11semidirect
697. C22⋊C8C22×D11semidirect
840. C11#61560semidirect
870. C23SD16×D11semidirect

Maximal subgroups

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

subgroupindex
#130824122
C2×D4×C22⋊D112
#130804362
#130804332
#130803102
SD16×C22⋊D112
#130795552
#130793742
#130793702
#130793692
#130786192
C2×#106228312
D11×#4502
#130776382
C2×C11×#4502
#6156011