Finite Group Databasebeta

← #15662069

Subgroups — #15662069

Order 2816.

7190 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082716C216yesmaximal, complemented
2#13082714C212yesmaximal, complemented
3#13082634C211yesmaximal, characteristic, complemented
4#13082632C213yesmaximal, complemented
5#13082619C213yesmaximal, complemented
6#13082617C211yesmaximal, characteristic, complemented
7#13082460C213yesmaximal, complemented
8#13082458C213yesmaximal, complemented
9#13082425C211yesmaximal, characteristic, complemented
10#13082381C211yesmaximal, characteristic, complemented
11#13082327C216yesmaximal, complemented
12#13082269C212yesmaximal, complemented
13#13082240C213yesmaximal, complemented
14#13082238C211yesmaximal, characteristic, complemented
15#13082231C213yesmaximal, complemented
16#13082214C212yesmaximal, complemented
17#13082213C216yesmaximal, complemented
18#13082030C216yesmaximal, complemented
19#13081911C213yesmaximal, complemented
20#13081909C213yesmaximal, complemented
21C4×#67043C212yesmaximal, complemented
22C4×#41×D11C211yesmaximal, characteristic, complemented
23C11×#3483C211yesmaximal, characteristic, complemented
24C2×#67043C2212yes—
25C2×#41×D11C2211yescharacteristic
26Q82×C11C2211yescharacteristic, complemented
27C11×#555C2213yescomplemented
28C11×#555C2216yescomplemented
29C11×#550C2212yes—
30C11×#550C2211yescharacteristic, complemented
31C11×#550C2213yescomplemented
32C11×#532C2213yescomplemented
33C11×#532C2216yescomplemented
34C4×C11×#41C2211yescharacteristic
35C4×C11×#41C2213yescomplemented
36C4×C11×#41C2212yescomplemented
37#10623365C2212yes—
38#10623363C2213yescomplemented
39#10623363C22112yescomplemented
40#10623362C2212yes—
41#10623362C2212yescomplemented
42#10623359C2213yes—
43#10623359C2216yes—
44#10623358C2212yescomplemented
45#41×Dic11C2211yescharacteristic
46#41×Dic11C2216yescomplemented
47#10623355C2216yescomplemented
48#10623265C2213yescomplemented
49#10623264C2216yescomplemented
50#10623263C2216yescomplemented
51#10623260C2216yes—
52#10623259C2213yes—
53#10623259C2213yescomplemented
54#10623253C2213yescomplemented
55#10623252C2216yescomplemented
56#10623250C2216yescomplemented
57#10623249C2216yes—
58#10623249C2213yescomplemented
59#10623249C2213yescomplemented
60#10623247C2213yes—
61#10623247C2213yescomplemented
62#10623246C2216yes—
63#10623244C2216yescomplemented
64#10623212C22112yescomplemented
65#10623211C2216yes—
66#10623211C2216yescomplemented
67#10623209C22112yes—
68#10623202C22112yescomplemented
69#10623201C22112yescomplemented
70#10623200C22112yescomplemented
71#10623150C2216yescomplemented
72#10623149C2216yescomplemented
73#10623149C2216yescomplemented
74#10623147C2216yescomplemented
75#10623147C2216yescomplemented
76#10623146C22112yescomplemented
77#10623144C22112yes—
78#10623139C2216yes—
79#10623138C2216yes—
80#10623137C2216yes—
81#10623137C2216yes—
82#10623134C2216yescomplemented
83#10623132C22112yescomplemented
84#10623132C22112yescomplemented
85#10623131C2216yescomplemented
86#10623131C2216yescomplemented
87#10623130C2216yes—
88#10623130C2216yescomplemented
89#10623129C2216yes—
90#10623129C2216yescomplemented
91#10623115C2213yescomplemented
92#10623111C2211yescharacteristic
93#10623111C2213yescomplemented
94#10623109C2213yes—
95#10623109C2213yescomplemented
96#10623107C2212yes—
97Q8×D44C2211yescharacteristic, complemented
98C4×#4343C2211yescharacteristic
99C4×#4343C2211yescharacteristic
100#10623103C2212yes—
101#10623103C2212yescomplemented
102C4×Q8×D11C2211yescharacteristic
103C4×Q8×D11C2211yescharacteristic
104C4×Q8×D11C2212yescomplemented
105#10623101C2211yescharacteristic, complemented
106#10623100C2212yescomplemented
107#10623098C2213yescomplemented
108#10623090C2216yescomplemented
109#10623089C2216yescomplemented
110#10623088C2213yes—
111#10623088C2213yescomplemented
112#10623088C2216yescomplemented
113#10623088C2216yescomplemented
114#10623086C2213yescomplemented
115#10623083C2216yes—
116#10623082C2213yescomplemented
117#10623079C2213yes—
118#10623079C2213yescomplemented
119#10623079C2216yescomplemented
120#10623078C2216yes—
121#10623078C2216yes—
122#10623077C2216yes—
123#10623077C2216yescomplemented
124C4×D4×D11C2213yes—
125C4×D4×D11C2213yes—
126#10623073C2213yescomplemented
127#10623072C2216yescomplemented
128#10623069C2216yescomplemented
129#10623069C2216yescomplemented
130#10623069C22112yescomplemented
131D4×Dic22C2213yescomplemented
132C4×#4341C2213yes—
133C4×#4341C2216yes—
134C4×#4341C2213yes—
135C4×#4341C2216yescomplemented
136C4×#4341C2216yescomplemented
137#10623064C2216yescomplemented
138#10623064C2216yescomplemented
139#10623062C22112yescomplemented
140#10623061C2216yescomplemented
141#10623060C2216yescomplemented
142#10623059C2216yes—
143#10623059C2216yescomplemented
144#10623055C2213yes—
145#10623054C2216yes—
146#10623053C2213yes—
147D11×#117C2213yes—
148#10623048C2213yescomplemented
149#10623047C2216yescomplemented
150#10623010C2216yescomplemented
151C4×#4339C2216yes—
152C4×#4339C2213yes—
153C4×#4339C2216yescomplemented
154C4×#4339C2213yescomplemented
155C2×C42×D11C2213yes—
156#10623001C2213yescomplemented
157C2×C4×Dic22C2216yescomplemented
158C2×C11×#41C2311yescharacteristic
159C2×C11×#41C2312yes—
160C2×C11×#41C2313yes—
161C2×C11×#41C2316yes—
162#67043—216no—
163#41×D11—28no—
164C2×#4343C2311yescharacteristic
165C2×Q8×D11C2312yes—
166C2×Q8×D11C2311yescharacteristic
167C2×#4341C2316yes—
168C2×#4341C2313yes—
169C2×#4341C2316yes—
170C2×#4341C2316yes—
171C2×D4×D11C2313yes—
172C2×#4339C2313yes—
173C2×#4339C2316yes—
174C2×#4339C2313yes—
175C2×#4339C2316yes—
176C22×C4×D11C2313yes—
177C22×C4×D11C2313yes—
178C22×C4×D11C2313yes—
179C22×Dic22C2316yes—
180C11×C4⋊Q8C2316yes—
181C11×C4⋊Q8C2313yes—
182C11×#127C2316yes—
183C11×#127C2313yes—
184C11×#124C23112yes—
185C11×#124C2316yes—
186C11×#121C2316yes—
187C11×#121C2316yes—
188C11×#121C2316yes—
189C11×#121C2316yes—
190C11×#121C23112yes—
191C4×Q8×C11C2313yes—
192C4×Q8×C11C2312yes—
193C4×Q8×C11C2311yescharacteristic
194C4×Q8×C11C2311yescharacteristic
195C4×Q8×C11C2311yescharacteristic
196C4×D4×C11C2316yes—
197C4×D4×C11C2313yes—
198C4×D4×C11C2313yes—
199C4×D4×C11C2313yes—
200C4×D4×C11C2313yes—
201C4×D4×C11C2316yes—
202C4×D4×C11C2316yes—
203C4×D4×C11C2316yes—
204C11×#117C2316yes—
205C11×#117C2313yes—
206C11×#117C2313yes—
207C11×#117C2316yes—
208C2×C42×C11C2316yes—
209C2×C42×C11C2313yes—
210#67000C23112yes—
211#67000C2311yescharacteristic
212#66999C2316yes—
213#66999C2316yes—
214#66999C2313yes—
215#66999C2311yescharacteristic
216Q8×Dic11C2316yes—
217Q8×Dic11C2316yes—
218Q8×Dic11C2311yescharacteristic
219Q8×Dic11C2312yes—
220Q8×Dic11C2311yescharacteristic
221#66997C23112yes—
222#66997C2313yes—
223#66993C2316yes—
224#66993C23112yes—
225#66993C2313yes—
226#66992C23112yes—
227#66992C23112yes—
228#66992C2316yes—
229#66992C23112yes—
230#66992C23112yes—
231#66992C2316yes—
232#66992C23112yes—
233#66991C2313yes—
234#66991C2316yes—
235#66991C2316yes—
236#66991C2316yes—
237#66991C2316yes—
238#66991C2313yes—
239#66991C2316yes—
240#66990C2316yes—
241#66990C23112yes—
242#66989C2316yes—
243#66989C2316yes—
244#66989C23112yes—
245#66989C2313yes—
246#66988C2316yes—
247#66988C23112yes—
248#66988C23112yes—
249D4×Dic11C2313yes—
250D4×Dic11C2316yes—
251D4×Dic11C23112yes—
252D4×Dic11C2316yes—
253D4×Dic11C2316yes—
254D4×Dic11C2316yes—
255D4×Dic11C2316yes—
256D4×Dic11C23112yes—
257D4×Dic11C2313yes—
258#66983C2316yes—
259#66982C23112yes—
260C4×C22⋊D11C2316yes—
261C4×C22⋊D11C2316yes—
262C4×C22⋊D11C2316yes—
263C4×C22⋊D11C2316yes—
264C4×C22⋊D11C2316yes—
265C4×C22⋊D11C2316yes—
266C4×C22⋊D11C2316yes—
267C4×C22⋊D11C2316yes—
268C4×C22⋊D11C2316yes—
269C4×C22⋊D11C2316yes—
270C4×C22⋊D11C2316yes—
271C4×C22⋊D11C2316yes—
272C4×C22⋊D11C23112yes—
273#66979C2316yes—
274#66979C2316yes—
275#66979C2313yes—
276#66979C2313yes—
277#66979C2316yes—
278C2×C4⋊Dic11C2316yes—
279#66977C2316yes—
280#66977C2316yes—
281#66977C2316yes—
282C2×Dic11⋊C4C23112yes—
283C2×C4×Dic11C23112yes—
284C2×C4×Dic11C2313yes—
285C2×C4×Dic11C2313yes—
286C2×C4×Dic11C2313yes—
287#66951C2316yes—
288#66951C23112yes—
289#66951C2312yes—
290#66950C2313yes—
291#66950C2316yes—
292#66950C2316yes—
293#66950C2313yes—
294#66949C2316yes—
295#66949C2316yes—
296#66948C2316yes—
297#66948C2313yes—
298#66948C2311yescharacteristic
299#66947C2316yes—
300#66947C2312yes—
301#66946C2313yes—
302#66946C2313yes—
303#66945C2316yes—
304#66945C2316yes—
305#66945C2313yes—
306#66945C2316yes—
307#66945C2313yes—
308C4⋊C4×D11C2313yes—
309C4⋊C4×D11C2313yes—
310C4⋊C4×D11C2316yes—
311#66943C2316yes—
312#66943C2316yes—
313#66943C2313yes—
314#66943C2311yescharacteristic
315#66942C2316yes—
316#66942C23112yes—
317#66942C2316yes—
318#66941C2313yes—
319#66941C2316yes—
320#66941C2313yes—
321#66940C2313yes—
322#66940C2316yes—
323#66940C2316yes—
324#66940C2316yes—
325#66940C2313yes—
326#66940C2316yes—
327#66939C2316yes—
328#66939C23112yes—
329#66938C2316yes—
330#66938C2316yes—
331#66938C23112yes—
332#66938C23112yes—
333#66937C2316yes—
334#66937C2316yes—
335#66937C23112yes—
336#66936C2316yes—
337#66936C2316yes—
338#66936C23112yes—
339#66936C23112yes—
340#66935C2316yes—
341(C22⋊D11)⋊C4C2316yes—
342(C22⋊D11)⋊C4C2316yes—
343(C22⋊D11)⋊C4C23112yes—
344(C22⋊D11)⋊C4C23112yes—
345(C22⋊D11)⋊C4C23112yes—
346C22⋊C4×D11C2316yes—
347#66932C2316yes—
348#66932C2316yes—
349#66932C23112yes—
350#66932C23112yes—
351#66932C23112yes—
352#66931C2316yes—
353#66931C2316yes—
354#66931C23112yes—
355#66930C23112yes—
356#66930C23112yes—
357#66930C2316yes—
358#66930C23112yes—
359#66929C23112yes—
360#66928C2316yes—
361C4×D44C2316yes—
362C4×D44C2313yes—
363C4×D44C2313yes—
364C4×D44C2312yes—
365C4×D44C2313yes—
366C4×D44C2316yes—
367C4×D44C2311yescharacteristic
368C4×D44C2316yes—
369#66925C2316yes—
370#66925C2316yes—
371#66925C2316yes—
372#66925C2312yes—
373#66925C2316yes—
374#66925C2316yes—
375C42×D11C2313yes—
376C42×D11C2313yes—
377C42×D11C2311yescharacteristic
378C42×D11C2313yes—
379C42×D11C2313yes—
380C42×D11C2313yes—
381C42×D11C2313yes—
382C42×D11C2313yes—
383C42×D11C2316yes—
384#66923C2316yes—
385#66923C2316yes—
386#66922C2313yes—
387#66922C2313yes—
388C4×Dic22C2316yes—
389C4×Dic22C2316yes—
390C4×Dic22C2316yes—
391C4×Dic22C2313yes—
392C4×Dic22C2313yes—
393C4×Dic22C2313yes—
394C4×Dic22C2316yes—
395C4×Dic22C2316yes—
396C4×Dic22C23112yes—
397C4×Dic22C2313yes—
398C4×Dic22C2316yes—
399C4×Dic22C2316yes—
400#62793—111nomaximal, Sylow
401C23×D11C2413yes—
402C11×#41—24no—
403C11×#41—28no—
404C11×#41—412no—
405C11×#41—46no—
406C2×Q8×C11C2411yescharacteristic
407C2×Q8×C11C2416yes—
408C2×Q8×C11C2411yescharacteristic
409C2×D4×C11C2413yes—
410C2×D4×C11C2416yes—
411C2×D4×C11C2413yes—
412C2×D4×C11C24112yes—
413C2×D4×C11C2416yes—
414C2×D4×C11C2416yes—
415C22×C4×C11C2416yes—
416C22×C4×C11C2413yes—
417C22×C4×C11C2413yes—
418C22×C4×C11C2413yes—
419C22×C4×C11C2416yes—
420C22×C4×C11C2416yes—
421C2×C22⋊D11C2416yes—
422C2×C22⋊D11C2416yes—
423C2×C22⋊D11C2416yes—
424C2×C22⋊D11C24112yes—
425C2×C22⋊D11C2416yes—
426C2×C22⋊D11C2416yes—
427C2×C22⋊D11C2416yes—
428C22×Dic11C2413yes—
429C22×Dic11C24112yes—
430C22×Dic11C24112yes—
431C22×Dic11C2413yes—
432C22×Dic11C2413yes—
433#4343—24no—
434Q8×D11—28no—
435Q8×D11#4118yescomplemented
436#4341—224no—
437#4341—212no—
438#4341—224no—
439#4341—412no—
440D4×D11—212no—
441#4339—224no—
442#4339—212no—
443#4339—46no—
444#4339—412no—
445C2×D44C2412yes—
446C2×D44C2411yescharacteristic
447C2×D44C2413yes—
448C2×D44C2416yes—
449C2×C4×D11—212no—
450C2×C4×D11—46no—
451C2×C4×D11—46no—
452C2×C4×D11C2411yescharacteristic
453C2×C4×D11C2411yescharacteristic
454C2×C4×D11C2411yescharacteristic
455C2×C4×D11C2412yes—
456C2×C4×D11C2413yes—
457C2×C4×D11C2413yes—
458C2×C4×D11C2413yes—
459C2×C4×D11C2413yes—
460C2×C4×D11C2416yes—
461C2×C4×D11C2413yes—
462C2×C4×D11C2413yes—
463C2×C4×D11C2413yes—
464C2×C4×D11C2413yes—
465C2×C4×D11C2416yes—
466C2×C4×D11C2413yes—
467C2×Dic22—224no—
468C2×Dic22C2416yes—
469C2×Dic22C2413yes—
470C2×Dic22C2416yes—
471C2×Dic22C2416yes—
472C2×Dic22C2413yes—
473C11×C4⋊C4C2413yes—
474C11×C4⋊C4C2416yes—
475C11×C4⋊C4C2413yes—
476C11×C4⋊C4C2413yes—
477C11×C4⋊C4C2411yescharacteristic
478C11×C4⋊C4C2412yes—
479C11×C4⋊C4C2416yes—
480C11×C22⋊C4C24112yes—
481C11×C22⋊C4C2416yes—
482C11×C22⋊C4C2416yes—
483C11×C22⋊C4C2416yes—
484C11×C22⋊C4C2416yes—
485C42×C11C2416yes—
486C42×C11C2416yes—
487C42×C11C2413yes—
488C42×C11C2411yescharacteristic
489C42×C11C2412yes—
490C42×C11C2413yes—
491C42×C11C2413yes—
492C22⋊Dic11C2416yes—
493C22⋊Dic11C2416yes—
494C22⋊Dic11C24112yes—
495C22⋊Dic11C2416yes—
496C22⋊Dic11C2416yes—
497C22⋊Dic11C2416yes—
498C22⋊Dic11C24112yes—
499C22⋊Dic11C2416yes—
500(C2×D11)⋊C4C2412yes—
501(C2×D11)⋊C4C2412yes—
502(C2×D11)⋊C4C2412yes—
503(C2×D11)⋊C4C2412yes—
504(C2×D11)⋊C4C2412yes—
505(C2×D11)⋊C4C2416yes—
506(C2×D11)⋊C4C2416yes—
507(C2×D11)⋊C4C2416yes—
508(C2×D11)⋊C4C2416yes—
509(C2×D11)⋊C4C2416yes—
510(C2×D11)⋊C4C2416yes—
511(C2×D11)⋊C4C2416yes—
512(C2×D11)⋊C4C24112yes—
513C4⋊Dic11C2412yes—
514C4⋊Dic11C2416yes—
515C4⋊Dic11C2411yescharacteristic
516C4⋊Dic11C2413yes—
517C4⋊Dic11C2416yes—
518C4⋊Dic11C2413yes—
519C4⋊Dic11C2413yes—
520C4⋊Dic11C2416yes—
521C4⋊Dic11C2416yes—
522C4⋊Dic11C2416yes—
523C4⋊Dic11C2416yes—
524Dic11⋊C4C2416yes—
525Dic11⋊C4C2412yes—
526Dic11⋊C4C2416yes—
527Dic11⋊C4C2412yes—
528Dic11⋊C4C2416yes—
529Dic11⋊C4C24112yes—
530Dic11⋊C4C2416yes—
531Dic11⋊C4C2416yes—
532Dic11⋊C4C2416yes—
533Dic11⋊C4C2416yes—
534Dic11⋊C4C2416yes—
535Dic11⋊C4C2416yes—
536Dic11⋊C4C2416yes—
537Dic11⋊C4C24112yes—
538C4×Dic11C2413yes—
539C4×Dic11C2416yes—
540C4×Dic11C2413yes—
541C4×Dic11C2413yes—
542C4×Dic11C2413yes—
543C4×Dic11C2413yes—
544C4×Dic11C2416yes—
545C4×Dic11C2416yes—
546C4×Dic11C24112yes—
547C4×Dic11C24112yes—
548C4×Dic11C2411yescharacteristic
549C4×Dic11C2411yescharacteristic
550C4×Dic11C2411yescharacteristic
551C4×Dic11C2413yes—
552C4×Dic11C2413yes—
553C4×Dic11C2413yes—
554C4×Dic11C2413yes—
555#3524—116no—
556#3524—112no—
557#3518—111no—
558#3518—113no—
559#3517—111no—
560#3517—113no—
561#3506—113no—
562#3506—113no—
563#3502—111no—
564#3497—111no—
565#3493—116no—
566#3487—112no—
567#3483—113no—
568#3483D1111yescharacteristic, complemented
569#3482—111no—
570#3482—113no—
571#3480—116no—
572#3480—112no—
573#3460—116no—
574#3444—113no—
575#3444—113no—
576C4×2−1+4—112no—
577C2×C4×#41—111no—
578C23×C11C2513yes—
579C23×C11C2516yes—
580C22×D11—26no—
581C22×D11—43no—
582C22×D11—43no—
583C22×D11C2513yes—
584C22×D11C2512yes—
585C22×D11C2511yescharacteristic
586Q8×C11—22no—
587Q8×C11—46no—
588Q8×C11C2×#4114yes—
589D4×C11—26no—
590D4×C11—212no—
591D4×C11—26no—
592D4×C11—412no—
593D4×C11—46no—
594D4×C11—46no—
595C2×C4×C11—212no—
596C2×C4×C11—26no—
597C2×C4×C11—26no—
598C2×C4×C11—26no—
599C2×C4×C11—212no—
600C2×C4×C11—46no—
601C2×C4×C11C2511yescharacteristic
602C2×C4×C11C2513yes—
603C2×C4×C11C2516yes—
604C2×C4×C11C2513yes—
605C2×C4×C11C2512yes—
606C2×C4×C11C2512yes—
607C2×C4×C11C2513yes—
608C2×C4×C11C2511yescharacteristic
609C2×C4×C11C2511yescharacteristic
610C22⋊D11—212no—
611C22⋊D11—212no—
612C22⋊D11—212no—
613C22⋊D11—46no—
614C22⋊D11—46no—
615C22⋊D11—46no—
616C22⋊D11—412no—
617C2×Dic11—224no—
618C2×Dic11—26no—
619C2×Dic11—43no—
620C2×Dic11—43no—
621C2×Dic11—412no—
622C2×Dic11C2511yescharacteristic
623C2×Dic11C2513yes—
624C2×Dic11C2511yescharacteristic
625C2×Dic11C2511yescharacteristic
626C2×Dic11C2512yes—
627C2×Dic11C2513yes—
628C2×Dic11C2516yes—
629C2×Dic11C2516yes—
630C2×Dic11C2513yes—
631D44—24no—
632D44—26no—
633D44—22no—
634D44—46no—
635C4×D11—22no—
636C4×D11—26no—
637C4×D11—212no—
638C4×D11—22no—
639C4×D11—22no—
640C4×D11—26no—
641C4×D11—26no—
642C4×D11—24no—
643C4×D11—26no—
644C4×D11—43no—
645C4×D11—43no—
646C4×D11—43no—
647C4×D11—43no—
648C4×D11—46no—
649C4×D11C2×#41112yes—
650Dic22—212no—
651Dic22—26no—
652Dic22—212no—
653Dic22—46no—
654Dic22C2×#41112yes—
655C2×2−1+4—112no—
656C22×#41—111no—
657#559—116no—
658#559—1112no—
659#559—116no—
660Q82—113no—
661Q82C2×D1111yescharacteristic, complemented
662#557—116no—
663#557—113no—
664#557—112no—
665#557—111no—
666#556—116no—
667#556—1112no—
668#556—113no—
669#556—113no—
670#556—116no—
671#556—116no—
672#555—113no—
673#555—1112no—
674#555—116no—
675#555—116no—
676#555C2×D1116yescomplemented
677#555C2×D1113yescomplemented
678#553—1112no—
679#553—1112no—
680#553—116no—
681#553—116no—
682#553—116no—
683#553—116no—
684#552—116no—
685#552—116no—
686#552—1112no—
687#550—112no—
688#550—116no—
689#550—113no—
690#550—113no—
691#550—116no—
692#550—116no—
693#550C2×D1112yes—
694#550C2×D1111yescharacteristic, complemented
695#550C2×D1113yescomplemented
696D4×Q8—111no—
697D4×Q8—113no—
698#548—112no—
699#548—112no—
700#548—116no—
701#548—116no—
702#548—112no—
703#548—116no—
704#547—116no—
705#547—113no—
706#547—113no—
707#544—116no—
708#542—116no—
709#542—1112no—
710#542—116no—
711#540—116no—
712#540—1112no—
713#540—116no—
714#538—1112no—
715#538—1112no—
716#537—116no—
717#535—116no—
718#535—116no—
719#533—113no—
720#533—113no—
721#533—113no—
722#533—113no—
723#533—113no—
724#533—113no—
725#532—113no—
726#532—1112no—
727#532—113no—
728#532—113no—
729#532—113no—
730#532—113no—
731#532—116no—
732#532C2×D1113yescomplemented
733#532C2×D1116yescomplemented
734#529—116no—
735#529—116no—
736#529—116no—
737#529—116no—
738#529—111no—
739#529—113no—
740#529—116no—
741#529—116no—
742#529—1112no—
743#529—113no—
744#529—116no—
745#529—113no—
746#529—116no—
747#529—116no—
748#529—116no—
749#529—116no—
750#525—116no—
751#525—113no—
752#525—116no—
753#525—116no—
754#525—116no—
755#525—116no—
756#525—113no—
757#520—112no—
758#520—116no—
759#520—116no—
760#520—116no—
761#519—112no—
762#519—112no—
763#519—116no—
764C4×#41—111no—
765C4×#41—116no—
766C4×#41—111no—
767C4×#41—111no—
768C4×#41—113no—
769C4×#41—113no—
770C4×#41—116no—
771C4×#41—116no—
772C4×#41—116no—
773C4×#41—113no—
774C4×#41—113no—
775C4×#41—116no—
776C4×#41—116no—
777C4×#41—113no—
778C4×#41C2×D1111yescharacteristic
779C4×#41C2×D1112yescomplemented
780C4×#41C2×D1113yescomplemented
781C2×C4×Q8—111no—
782C2×C4×Q8—111no—
783C2×C4×Q8—112no—
784C2×C4×Q8—116no—
785C2×C4×D4—113no—
786C2×C4×D4—113no—
787C2×#117—113no—
788C22×C42—113no—
789C22×C11—23no—
790C22×C11—26no—
791C22×C11—23no—
792C22×C11—26no—
793C22×C11—23no—
794C22×C11—26no—
795C22×C11C2611yescharacteristic
796C2×D11—21no—
797C2×D11—21no—
798C2×D11—23no—
799C2×D11—22no—
800C2×D11—23no—
801C2×D11—23no—
802C2×D11—22no—
803C2×D11—22no—
804C2×D11—412no—
805C2×D11C22×#4112yes—
806C4×C11—22no—
807C4×C11—21no—
808C4×C11—23no—
809C4×C11—26no—
810C4×C11—23no—
811C4×C11—22no—
812C4×C11C22×#4116yes—
813C4×C11#58512yes—
814C4×C11#58512yes—
815Dic11—26no—
816Dic11—21no—
817Dic11—26no—
818Dic11—22no—
819Dic11—23no—
820Dic11—21no—
821Dic11—21no—
822Dic11—23no—
823Dic11C22×#4116yes—
8242−1+4—2216no—
825C2×#41—111no—
826C2×#41—113no—
827C2×#41—116no—
828C2×#41—116no—
829C2×#41—116no—
830C2×#41—113no—
831C2×#41—116no—
832C2×#41—116no—
833C2×#41—113no—
834C2×#41—228no—
835C2×#41C22×D1111yescharacteristic
836C2×#41C22×D1112yes—
837C2×#41C22×D1116yes—
838C2×#41C22×D1113yes—
839C22×Q8—111no—
840C22×Q8—112no—
841C22×Q8—116no—
842C22×D4—113no—
843C23×C4—113no—
844C23×C4—113no—
845C23×C4—113no—
846C4⋊Q8—113no—
847C4⋊Q8—1112no—
848C4⋊Q8—113no—
849C4⋊Q8—113no—
850C4⋊Q8—116no—
851C4⋊Q8—113no—
852C4⋊Q8—113no—
853C4⋊Q8C22×D1113yes—
854C4⋊Q8C22×D1116yes—
855#127—113no—
856#127—1112no—
857#127—116no—
858#127C22×D1113yes—
859#127C22×D1116yes—
860#126—112no—
861#126—116no—
862#126—1112no—
863#126—116no—
864#126—116no—
865#126—1112no—
866#126—1112no—
867#126—1112no—
868#126—1112no—
869#125—113no—
870#125—111no—
871#125—116no—
872#125—116no—
873#125—116no—
874#125—1112no—
875#125—116no—
876#125—116no—
877#125—116no—
878#124—111no—
879#124—1112no—
880#124—113no—
881#124—116no—
882#124—116no—
883#124—1112no—
884#124—116no—
885#124—116no—
886#124—1112no—
887#124—1112no—
888#124—116no—
889#124C22×D1116yes—
890#124C22×D11112yes—
891#123—1112no—
892#123—116no—
893#123—1112no—
894#123—1112no—
895#123—112no—
896#123—116no—
897#123—116no—
898#123—116no—
899#123—1112no—
900#123—116no—
901#123—1112no—
902#123—1112no—
903C22⋊Q8—111no—
904C22⋊Q8—116no—
905C22⋊Q8—116no—
906C22⋊Q8—113no—
907C22⋊Q8—116no—
908C22⋊Q8—116no—
909C22⋊Q8—116no—
910C22⋊Q8—113no—
911C22⋊Q8—116no—
912C22⋊Q8—113no—
913C22⋊Q8—116no—
914C22⋊Q8—116no—
915C22⋊Q8—116no—
916C22⋊Q8—116no—
917C22⋊Q8—116no—
918C22⋊Q8—1112no—
919#121—113no—
920#121—116no—
921#121—116no—
922#121—116no—
923#121—116no—
924#121—116no—
925#121—113no—
926#121—116no—
927#121—1112no—
928#121—1112no—
929#121—116no—
930#121—1112no—
931#121—1112no—
932#121—1112no—
933#121—116no—
934#121—111no—
935#121—113no—
936#121—116no—
937#121—116no—
938#121—116no—
939#121—1112no—
940#121C22×D1116yes—
941#121C22×D1116yes—
942#121C22×D1116yes—
943#121C22×D1116yes—
944#121C22×D11112yes—
945#120—1112no—
946#120—116no—
947#120—116no—
948C4×Q8—111no—
949C4×Q8—111no—
950C4×Q8—112no—
951C4×Q8—116no—
952C4×Q8—116no—
953C4×Q8—113no—
954C4×Q8—113no—
955C4×Q8—116no—
956C4×Q8—116no—
957C4×Q8—116no—
958C4×Q8—116no—
959C4×Q8—113no—
960C4×Q8—116no—
961C4×Q8—116no—
962C4×Q8—113no—
963C4×Q8—116no—
964C4×Q8—116no—
965C4×Q8—1112no—
966C4×Q8—113no—
967C4×Q8—116no—
968C4×Q8—113no—
969C4×Q8—116no—
970C4×Q8—116no—
971C4×Q8C22×D1111yescharacteristic
972C4×Q8C22×D1111yescharacteristic
973C4×Q8C22×D1111yescharacteristic
974C4×Q8C22×D1112yes—
975C4×Q8C22×D1113yes—
976C4×D4—113no—
977C4×D4—113no—
978C4×D4—116no—
979C4×D4—116no—
980C4×D4—1112no—
981C4×D4—1112no—
982C4×D4—116no—
983C4×D4—116no—
984C4×D4—116no—
985C4×D4—116no—
986C4×D4—116no—
987C4×D4—116no—
988C4×D4—116no—
989C4×D4—116no—
990C4×D4—116no—
991C4×D4—116no—
992C4×D4—1112no—
993C4×D4—116no—
994C4×D4—116no—
995C4×D4—116no—
996C4×D4—116no—
997C4×D4—116no—
998C4×D4—113no—
999C4×D4—113no—
1000C4×D4—116no—
1001C4×D4—116no—
1002C4×D4—1112no—
1003C4×D4—1112no—
1004C4×D4—1112no—
1005C4×D4—113no—
1006C4×D4—113no—
1007C4×D4—112no—
1008C4×D4—111no—
1009C4×D4—116no—
1010C4×D4—116no—
1011C4×D4—116no—
1012C4×D4—113no—
1013C4×D4C22×D1113yes—
1014C4×D4C22×D1113yes—
1015C4×D4C22×D1116yes—
1016C4×D4C22×D1113yes—
1017C4×D4C22×D1116yes—
1018C4×D4C22×D1116yes—
1019C4×D4C22×D1116yes—
1020C4×D4C22×D1113yes—
1021#117—113no—
1022#117—116no—
1023#117—116no—
1024#117—116no—
1025#117—113no—
1026#117—113no—
1027#117—113no—
1028#117—116no—
1029#117—116no—
1030#117—116no—
1031#117—116no—
1032#117—1112no—
1033#117—1112no—
1034#117—1112no—
1035#117—116no—
1036#117—112no—
1037#117—116no—
1038#117—116no—
1039#117—116no—
1040#117—116no—
1041#117C22×D1113yes—
1042#117C22×D1116yes—
1043#117C22×D1113yes—
1044#117C22×D1116yes—
1045C2×C4⋊C4—1112no—
1046C2×C4⋊C4—116no—
1047C2×C4⋊C4—113no—
1048C2×C4⋊C4—113no—
1049C2×C4⋊C4—116no—
1050C2×C22⋊C4—116no—
1051C2×C42—1112no—
1052C2×C42—113no—
1053C2×C42—113no—
1054C2×C42—113no—
1055C2×C42—113no—
1056C2×C42—113no—
1057C2×C42—113no—
1058C2×C42—116no—
1059C2×C42—113no—
1060C2×C42—113no—
1061C2×C42—113no—
1062C2×C42—113no—
1063C2×C42—111no—
1064C2×C42C22×D1116yes—
1065C2×C42C22×D1113yes—
1066C2×C11—43no—
1067C2×C11—46no—
1068C2×C11C23×#4111yescharacteristic
1069C2×C11C2×#58511yescharacteristic
1070C2×C11C2×#58511yescharacteristic
1071D11—22no—
1072D11—42no—
1073D11—43no—
1074C24—113no—
1075#41—24no—
1076#41—28no—
1077#41—412no—
1078#41—46no—
1079#41—2224no—
1080#41—2212no—
1081#41—2224no—
1082#41—2212no—
1083#41—2224no—
1084#41—224no—
1085#41—4412no—
1086#41—446no—
1087#41—4412no—
1088C2×Q8—118no—
1089C2×Q8—113no—
1090C2×Q8—116no—
1091C2×Q8—116no—
1092C2×Q8—113no—
1093C2×Q8—116no—
1094C2×Q8—2224no—
1095C2×Q8—228no—
1096C2×Q8C23×D1111yescharacteristic
1097C2×Q8C23×D1116yes—
1098C2×Q8C23×D1111yescharacteristic
1099C2×D4—116no—
1100C2×D4—116no—
1101C2×D4—116no—
1102C2×D4—1112no—
1103C2×D4—116no—
1104C2×D4—116no—
1105C2×D4—116no—
1106C2×D4—112no—
1107C2×D4—113no—
1108C2×D4—111no—
1109C2×D4—116no—
1110C2×D4—2212no—
1111C2×D4C23×D1113yes—
1112C2×D4C23×D1116yes—
1113C2×D4C23×D1113yes—
1114C2×D4C23×D11112yes—
1115C2×D4C23×D1116yes—
1116C2×D4C23×D1116yes—
1117C22×C4—113no—
1118C22×C4—113no—
1119C22×C4—1112no—
1120C22×C4—113no—
1121C22×C4—113no—
1122C22×C4—1112no—
1123C22×C4—111no—
1124C22×C4—111no—
1125C22×C4—113no—
1126C22×C4—113no—
1127C22×C4—113no—
1128C22×C4—116no—
1129C22×C4—111no—
1130C22×C4—112no—
1131C22×C4—113no—
1132C22×C4—113no—
1133C22×C4—113no—
1134C22×C4—113no—
1135C22×C4—113no—
1136C22×C4—116no—
1137C22×C4—2212no—
1138C22×C4—446no—
1139C22×C4—446no—
1140C22×C4C23×D1113yes—
1141C22×C4C23×D1113yes—
1142C22×C4C23×D1116yes—
1143C22×C4C23×D1116yes—
1144C22×C4C23×D1113yes—
1145C22×C4C23×D1116yes—
1146C4⋊C4—116no—
1147C4⋊C4—113no—
1148C4⋊C4—116no—
1149C4⋊C4—116no—
1150C4⋊C4—116no—
1151C4⋊C4—1112no—
1152C4⋊C4—116no—
1153C4⋊C4—116no—
1154C4⋊C4—113no—
1155C4⋊C4—113no—
1156C4⋊C4—116no—
1157C4⋊C4—116no—
1158C4⋊C4—111no—
1159C4⋊C4—116no—
1160C4⋊C4—112no—
1161C4⋊C4—112no—
1162C4⋊C4—116no—
1163C4⋊C4—112no—
1164C4⋊C4—116no—
1165C4⋊C4—116no—
1166C4⋊C4—1112no—
1167C4⋊C4—116no—
1168C4⋊C4—116no—
1169C4⋊C4—116no—
1170C4⋊C4—116no—
1171C4⋊C4C23×D1113yes—
1172C4⋊C4C23×D1113yes—
1173C4⋊C4C23×D1116yes—
1174C4⋊C4C23×D1113yes—
1175C4⋊C4C23×D1111yescharacteristic
1176C4⋊C4C23×D1112yes—
1177C4⋊C4C23×D1116yes—
1178C22⋊C4—116no—
1179C22⋊C4—116no—
1180C22⋊C4—116no—
1181C22⋊C4—116no—
1182C22⋊C4—116no—
1183C22⋊C4—1112no—
1184C22⋊C4—116no—
1185C22⋊C4—1112no—
1186C22⋊C4—116no—
1187C22⋊C4—116no—
1188C22⋊C4—112no—
1189C22⋊C4—116no—
1190C22⋊C4—112no—
1191C22⋊C4—116no—
1192C22⋊C4—112no—
1193C22⋊C4—112no—
1194C22⋊C4—112no—
1195C22⋊C4—116no—
1196C22⋊C4—116no—
1197C22⋊C4—1112no—
1198C22⋊C4—116no—
1199C22⋊C4C23×D1116yes—
1200C22⋊C4C23×D11112yes—
1201C22⋊C4C23×D1116yes—
1202C22⋊C4C23×D1116yes—
1203C22⋊C4C23×D1116yes—
1204C42—111no—
1205C42—111no—
1206C42—113no—
1207C42—113no—
1208C42—113no—
1209C42—113no—
1210C42—113no—
1211C42—113no—
1212C42—113no—
1213C42—113no—
1214C42—1112no—
1215C42—116no—
1216C42—1112no—
1217C42—116no—
1218C42—111no—
1219C42—113no—
1220C42—116no—
1221C42C23×D1113yes—
1222C42C23×D1113yes—
1223C42C23×D1116yes—
1224C42C23×D1116yes—
1225C42C23×D1113yes—
1226C42C23×D1111yescharacteristic
1227C42C23×D1112yes—
1228C11#6279311yescharacteristic, complemented, Sylow
1229C23—111no—
1230C23—113no—
1231C23—112no—
1232C23—226no—
1233C23—443no—
1234C23—443no—
1235C23C24×D1113yes—
1236C23C24×D1116yes—
1237Q8—22no—
1238Q8—46no—
1239Q8—1112no—
1240Q8—2212no—
1241Q8—2212no—
1242Q8—226no—
1243Q8—446no—
1244Q8#41×D1114yes—
1245D4—26no—
1246D4—212no—
1247D4—26no—
1248D4—46no—
1249D4—412no—
1250D4—46no—
1251D4—224no—
1252D4—2212no—
1253D4—2212no—
1254D4—2212no—
1255D4—226no—
1256D4—222no—
1257D4—446no—
1258D4—446no—
1259D4—446no—
1260D4—446no—
1261D4—4412no—
1262C2×C4—26no—
1263C2×C4—212no—
1264C2×C4—26no—
1265C2×C4—26no—
1266C2×C4—212no—
1267C2×C4—46no—
1268C2×C4—113no—
1269C2×C4—1112no—
1270C2×C4—111no—
1271C2×C4—111no—
1272C2×C4—111no—
1273C2×C4—113no—
1274C2×C4—112no—
1275C2×C4—116no—
1276C2×C4—113no—
1277C2×C4—116no—
1278C2×C4—226no—
1279C2×C4—222no—
1280C2×C4—226no—
1281C2×C4—2224no—
1282C2×C4—226no—
1283C2×C4—2212no—
1284C2×C4—222no—
1285C2×C4—226no—
1286C2×C4—222no—
1287C2×C4—226no—
1288C2×C4—224no—
1289C2×C4—443no—
1290C2×C4—443no—
1291C2×C4—443no—
1292C2×C4—443no—
1293C2×C4—446no—
1294C2×C4—443no—
1295C2×C4—443no—
1296C2×C4—4412no—
1297C2×C4C24×D1111yescharacteristic
1298C2×C4C24×D1113yes—
1299C2×C4C24×D1116yes—
1300C2×C4C24×D1113yes—
1301C2×C4C24×D1112yes—
1302C2×C4C24×D1112yes—
1303C2×C4C24×D1113yes—
1304C2×C4C24×D1111yescharacteristic
1305C2×C4C24×D1111yescharacteristic
1306C22—26no—
1307C22—23no—
1308C22—23no—
1309C22—26no—
1310C22—23no—
1311C22—26no—
1312C22—112no—
1313C22—221no—
1314C22—221no—
1315C22—222no—
1316C22—223no—
1317C22—223no—
1318C22—222no—
1319C22—223no—
1320C22—222no—
1321C22—4412no—
1322C22C25×D1111yescharacteristic
1323C4—21no—
1324C4—22no—
1325C4—23no—
1326C4—26no—
1327C4—23no—
1328C4—22no—
1329C4—116no—
1330C4—221no—
1331C4—226no—
1332C4—221no—
1333C4—223no—
1334C4—222no—
1335C4—221no—
1336C4—223no—
1337C4—226no—
1338C4C2×#41×D1116yes—
1339C4#1062345312yes—
1340C4#1062345512yes—
1341C2—43no—
1342C2—46no—
1343C2—222no—
1344C2—443no—
1345C2—442no—
1346C2C22×#41×D1111yescharacteristic
1347C2C2×#1062345511yescharacteristic
1348C2C2×#1062345311yescharacteristic
subgroupG/H
centerC2×C4C24×D11
commutator, socle, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC11×#3483C2
hypercenter#3483D11
hypocenterC11#62793
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #3483

Complements

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

NH ≅ G/Ntype
1. #13082716C2semidirect
2. #13082714C2semidirect
3. #13082634C2semidirect
4. #13082632C2semidirect
5. #13082619C2semidirect
6. #13082617C2semidirect
7. #13082460C2semidirect
8. #13082458C2semidirect
9. #13082425C2semidirect
10. #13082381C2semidirect
11. #13082327C2semidirect
12. #13082269C2semidirect
13. #13082240C2semidirect
14. #13082238C2semidirect
15. #13082231C2semidirect
16. #13082214C2semidirect
17. #13082213C2semidirect
18. #13082030C2semidirect
19. #13081911C2semidirect
20. #13081909C2semidirect
21. C4×#67043C2semidirect
22. C4×#41×D11C2semidirect
23. C11×#3483C2semidirect
26. Q82×C11C22semidirect
27. C11×#555C22semidirect
28. C11×#555C22semidirect
30. C11×#550C22semidirect
31. C11×#550C22semidirect
32. C11×#532C22semidirect
33. C11×#532C22semidirect
35. C4×C11×#41C22semidirect
36. C4×C11×#41C22semidirect
38. #10623363C22semidirect
39. #10623363C22semidirect
41. #10623362C22semidirect
44. #10623358C22semidirect
46. #41×Dic11C22semidirect
47. #10623355C22semidirect
48. #10623265C22semidirect
49. #10623264C22semidirect
50. #10623263C22semidirect
53. #10623259C22semidirect
54. #10623253C22semidirect
55. #10623252C22semidirect
56. #10623250C22semidirect
58. #10623249C22semidirect
59. #10623249C22semidirect
61. #10623247C22semidirect
63. #10623244C22semidirect
64. #10623212C22semidirect
66. #10623211C22semidirect
68. #10623202C22semidirect
69. #10623201C22semidirect
70. #10623200C22semidirect
71. #10623150C22semidirect
72. #10623149C22semidirect
73. #10623149C22semidirect
74. #10623147C22semidirect
75. #10623147C22semidirect
76. #10623146C22semidirect
82. #10623134C22semidirect
83. #10623132C22semidirect
84. #10623132C22semidirect
85. #10623131C22semidirect
86. #10623131C22semidirect
88. #10623130C22semidirect
90. #10623129C22semidirect
91. #10623115C22semidirect
93. #10623111C22semidirect
95. #10623109C22semidirect
97. Q8×D44C22semidirect
101. #10623103C22semidirect
104. C4×Q8×D11C22semidirect
105. #10623101C22semidirect
106. #10623100C22semidirect
107. #10623098C22semidirect
108. #10623090C22semidirect
109. #10623089C22semidirect
111. #10623088C22semidirect
112. #10623088C22semidirect
113. #10623088C22semidirect
114. #10623086C22semidirect
116. #10623082C22semidirect
118. #10623079C22semidirect
119. #10623079C22semidirect
123. #10623077C22semidirect
126. #10623073C22semidirect
127. #10623072C22semidirect
128. #10623069C22semidirect
129. #10623069C22semidirect
130. #10623069C22semidirect
131. D4×Dic22C22semidirect
135. C4×#4341C22semidirect
136. C4×#4341C22semidirect
137. #10623064C22semidirect
138. #10623064C22semidirect
139. #10623062C22semidirect
140. #10623061C22semidirect
141. #10623060C22semidirect
143. #10623059C22semidirect
148. #10623048C22semidirect
149. #10623047C22semidirect
150. #10623010C22semidirect
153. C4×#4339C22semidirect
154. C4×#4339C22semidirect
156. #10623001C22semidirect
157. C2×C4×Dic22C22semidirect
435. Q8×D11#41semidirect
568. #3483D11semidirect
661. Q82C2×D11semidirect
676. #555C2×D11semidirect
677. #555C2×D11semidirect
694. #550C2×D11semidirect
695. #550C2×D11semidirect
732. #532C2×D11semidirect
733. #532C2×D11semidirect
779. C4×#41C2×D11semidirect
780. C4×#41C2×D11semidirect
1228. C11#62793semidirect

Maximal subgroups

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

subgroupindex
#130827162
#130827142
#130826342
#130826322
#130826192
#130826172
#130824602
#130824582
#130824252
#130823812
#130823272
#130822692
#130822402
#130822382
#130822312
#130822142
#130822132
#130820302
#130819112
#130819092
C4×#670432
C4×#41×D112
C11×#34832
#6279311