Finite Group Databasebeta

← #15624664

Subgroups — #15624664

Order 2816.

2208 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082281C211yesmaximal, characteristic, complemented
2#13081945C211yesmaximal, characteristic, complemented
3#13079525C212yesmaximal, complemented
4#13079515C212yesmaximal, complemented
5#13079467C212yesmaximal, complemented
6#13079465C212yesmaximal, complemented
7#13079455C212yesmaximal, complemented
8#13079428C212yesmaximal, complemented
9#13079406C212yesmaximal, complemented
10#13079379C212yesmaximal, complemented
11#13078581C211yesmaximal, characteristic, complemented
12#13078570C211yesmaximal, characteristic, complemented
13#13078552C211yesmaximal, characteristic, complemented
14#13078531C211yesmaximal, characteristic, complemented
15#13078305C211yesmaximal, characteristic, complemented
16#13078294C211yesmaximal, characteristic, complemented
17#13078260C211yesmaximal, characteristic, complemented
18#13078251C211yesmaximal, characteristic, complemented
19#13077889C211yesmaximal, characteristic, complemented
20#13077880C211yesmaximal, characteristic, complemented
21#13077858C211yesmaximal, characteristic, complemented
22#13077062C211yesmaximal, characteristic, complemented
23C2×C11×#449C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic, complemented
25C2×#67037C2211yescharacteristic
26C22×#4339C2211yescharacteristic
27C22×C11×SD16C2211yescharacteristic, complemented
28C22×C11×D8C2211yescharacteristic, complemented
29C2×C11×#121C2211yescharacteristic
30#10623364C2212yescomplemented
31#10623364C2212yescomplemented
32#10623363—21no—
33#10623363—21no—
34#10623361—21no—
35#10623359C2212yescomplemented
36#10623359C2212yescomplemented
37#10623356—21no—
38#10623347C2211yescharacteristic
39#10623347C2211yescharacteristic, complemented
40C2×#66995C2211yescharacteristic, complemented
41#10623336C2211yescharacteristic
42#10623336C2211yescharacteristic
43#10623336C2211yescharacteristic, complemented
44#10623335—22no—
45D4×C22⋊D11—22no—
46C2×#66985C2211yescharacteristic, complemented
47#10623322—22no—
48#10623322C2211yescharacteristic
49C2×#66979C2211yescharacteristic, complemented
50C2×#66954C2211yescharacteristic, complemented
51C2×#66954C2211yescharacteristic, complemented
52#10623143—21no—
53#10623140—21no—
54#10623139C2212yescomplemented
55#10623138C2212yescomplemented
56#10623137C2212yescomplemented
57D11×#121C2212yescomplemented
58#10623130—21no—
59#10623129—21no—
60#10623041C2211yescharacteristic
61#10623035C2211yescharacteristic
62#10623021—22no—
63C11×#449C2212yescomplemented
64C11×#449C2212yescomplemented
65C11×#449C2212yescomplemented
66C11×#449C2212yescomplemented
67C2×C11×#103C2211yescharacteristic, complemented
68C2×C11×#102C2211yescharacteristic, complemented
69C2×C11×C22⋊C8C2211yescharacteristic, complemented
70#10622852C2212yescomplemented
71#10622852C2212yescomplemented
72#10622851C2212yescomplemented
73#10622851C2212yescomplemented
74#10622838C2211yescharacteristic, complemented
75#10622828C2211yescharacteristic, complemented
76#10622828C2211yescharacteristic, complemented
77#10622828C2211yescharacteristic, complemented
78#10622820C2211yescharacteristic, complemented
79#10622787C2212yescomplemented
80#10622787C2212yescomplemented
81#10622786C2212yescomplemented
82#10622786C2212yescomplemented
83#10622784C2212yescomplemented
84#10622784C2212yescomplemented
85#10622782C2212yescomplemented
86#10622782C2212yescomplemented
87#10622772C2212yescomplemented
88#10622772C2212yescomplemented
89#10622771C2212yescomplemented
90#10622771C2212yescomplemented
91#10622770C2212yescomplemented
92#10622770C2212yescomplemented
93#10622769C2212yescomplemented
94#10622769C2212yescomplemented
95#10622726C2211yescharacteristic, complemented
96#10622726C2211yescharacteristic, complemented
97#10622723C2211yescharacteristic
98#10622723C2211yescharacteristic
99#10622719C2211yescharacteristic, complemented
100#10622719C2211yescharacteristic, complemented
101#10622648C2212yescomplemented
102#10622648C2212yescomplemented
103#10622647C2212yescomplemented
104#10622646C2212yescomplemented
105#10622577C2211yescharacteristic, complemented
106#10622577C2211yescharacteristic, complemented
107#10622429C2212yescomplemented
108#10622428C2212yescomplemented
109#10622427C2212yescomplemented
110#10622426C2212yescomplemented
111#10622425C2212yescomplemented
112#10622422C2212yescomplemented
113#10622420C2212yescomplemented
114#10622418C2212yescomplemented
115#10622397C2212yescomplemented
116#10622395C2212yescomplemented
117#10622393C2212yescomplemented
118#10622392C2212yescomplemented
119#10622391C2212yescomplemented
120#10622390C2212yescomplemented
121#10622388C2212yescomplemented
122#10622387C2212yescomplemented
123#10622350C2211yescharacteristic, complemented
124#10622350C2211yescharacteristic, complemented
125#10622349C2211yescharacteristic, complemented
126#10622348C2211yescharacteristic, complemented
127#10622340C2212yescomplemented
128#10622340C2212yescomplemented
129#10622339C2212yescomplemented
130D11×C22⋊C8C2212yescomplemented
131#10622336C2211yescharacteristic, complemented
132#10622336C2211yescharacteristic, complemented
133#10622335C2211yescharacteristic, complemented
134#10622334C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41—42no—
138C2×C11×#41—42no—
139C2×C11×#41C2312yes—
140C2×C11×#41C2312yes—
141C22×Q8×C11C2311yescharacteristic
142C22×D4×C11—21no—
143C22×D4×C11—21no—
144C22×D4×C11C2311yescharacteristic
145C22×D4×C11C2311yescharacteristic
146C23×C4×C11—21no—
147C23×C4×C11C2311yescharacteristic
148C22×C22⋊D11—22no—
149C22×C22⋊D11D412yes—
150#67037—42no—
151#67037—42no—
152C2×#4341—21no—
153C2×#4341C2312yes—
154C2×D4×D11—22no—
155C2×D4×D11—21no—
156C2×D4×D11C2312yes—
157C2×#4339—42no—
158C2×#4339—42no—
159C2×#4339D412yes—
160C2×#4339D411yescharacteristic
161C2×#4339D411yescharacteristic
162C2×#4339C2311yescharacteristic
163C2×#4339C2311yescharacteristic
164C2×#4339C2312yes—
165C2×#4339C2311yescharacteristic
166C22×D44D411yescharacteristic
167C22×C4×D11C2312yes—
168C22×Dic22D411yescharacteristic
169C2×C11×SD16—42no—
170C2×C11×SD16C2312yes—
171C2×C11×SD16C2312yes—
172C2×C11×D8—42no—
173C2×C11×D8C2312yes—
174C2×C11×D8C2312yes—
175C22×C8×C11C2311yescharacteristic
176C22×C8×C11C2311yescharacteristic
177C11×#121—21no—
178C11×#121—21no—
179C11×#121C2312yes—
180C11×#121C2312yes—
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4—21no—
183#67006—21no—
184#67006—22no—
185#67006—22no—
186#67006—22no—
187C2×C22⋊Dic11—21no—
188#67000—21no—
189#67000—21no—
190#66999C2312yes—
191#66999C2312yes—
192#66999C2312yes—
193#66999C2312yes—
194#66997—21no—
195#66997—21no—
196C2×#4326C2312yes—
197#66995—42no—
198C2×#4325C2312yes—
199#66993—22no—
200#66993—21no—
201#66993—21no—
202#66993—21no—
203#66992—22no—
204#66992—22no—
205#66992—22no—
206#66992—22no—
207#66992—22no—
208#66992—22no—
209#66991—22no—
210#66991C2312yes—
211#66991C2312yes—
212#66991C2312yes—
213#66991C2312yes—
214#66991C2312yes—
215#66991C2312yes—
216#66990—22no—
217#66990—22no—
218#66990—22no—
219#66990—22no—
220#66989—21no—
221#66989—21no—
222#66989—21no—
223#66988—22no—
224#66988—22no—
225D4×Dic11—22no—
226C2×#4324C2312yes—
227#66985—42no—
228C2×#4323C2312yes—
229#66983—22no—
230#66983—22no—
231#66983—22no—
232#66983C2311yescharacteristic
233#66983C2311yescharacteristic
234#66982—21no—
235#66982—22no—
236#66982—22no—
237C4×C22⋊D11—21no—
238C4×C22⋊D11—21no—
239C4×C22⋊D11—22no—
240C4×C22⋊D11—22no—
241C4×C22⋊D11—22no—
242C4×C22⋊D11—22no—
243C4×C22⋊D11—22no—
244#66979—21no—
245#66979—21no—
246#66979C2311yescharacteristic
247#66979C2311yescharacteristic
248#66979C2311yescharacteristic
249#66979C2311yescharacteristic
250#66979C2311yescharacteristic
251C2×C4⋊Dic11C2311yescharacteristic
252C2×C4⋊Dic11C2311yescharacteristic
253#66977—22no—
254#66977—22no—
255#66977C2311yescharacteristic
256#66977C2311yescharacteristic
257C2×C4×Dic11—21no—
258C2×#4318C2311yescharacteristic
259C2×#4318C2311yescharacteristic
260#66954—42no—
261#66954—42no—
262C2×#4313C2312yes—
263C2×#4313C2312yes—
264C2×C8×D11C2312yes—
265C2×C8×D11C2312yes—
266#66950—21no—
267#66950C2312yes—
268#66948—21no—
269#66948C2312yes—
270#66946—21no—
271#66945C2312yes—
272C4⋊C4×D11C2312yes—
273#66940—21no—
274#66938—22no—
275#66937—22no—
276#66937—22no—
277#66936—22no—
278#66935—22no—
279(C22⋊D11)⋊C4—22no—
280C22⋊C4×D11—22no—
281#66931—22no—
282C11×#103C2312yes—
283C11×#103C2312yes—
284C11×#102C2312yes—
285C11×#102C2312yes—
286C11×C22⋊C8C2311yescharacteristic
287C11×C22⋊C8C2311yescharacteristic
288C11×C22⋊C8C2311yescharacteristic
289C11×C22⋊C8C2311yescharacteristic
290#66899C2312yes—
291#66899C2312yes—
292#66896C2312yes—
293#66896C2312yes—
294#66896C2312yes—
295#66896C2312yes—
296#66896C2312yes—
297#66896C2312yes—
298C22⋊(C11⋊C8)C2312yes—
299C22⋊(C11⋊C8)C2312yes—
300#66885C2311yescharacteristic
301#66885C2311yescharacteristic
302#66885C2311yescharacteristic
303#66885C2311yescharacteristic
304(C2×D11)⋊C8C2312yes—
305(C2×D11)⋊C8C2312yes—
306(C2×D11)⋊C8C2312yes—
307(C2×D11)⋊C8C2312yes—
308#66882C2311yescharacteristic
309#66882C2311yescharacteristic
310#66882C2311yescharacteristic
311#66882C2311yescharacteristic
312#66881C2311yescharacteristic
313#66881C2311yescharacteristic
314#66881C2311yescharacteristic
315#66881C2311yescharacteristic
316#66880C2311yescharacteristic
317#66880C2311yescharacteristic
318#66880C2311yescharacteristic
319#66880C2311yescharacteristic
320#66872C2312yes—
321#66872C2312yes—
322#66871C2312yes—
323#66871C2312yes—
324#60760—111nomaximal, Sylow
325C24×C11—21no—
326C24×C11—21no—
327C24×C11C2×D411yescharacteristic
328C23×D11—22no—
329C23×D11C2×D412yes—
330C11×#41—42no—
331C11×#41—42no—
332C11×#41—42no—
333C11×#41—42no—
334C11×#41—44no—
335C11×#41—44no—
336C2×Q8×C11—21no—
337C2×Q8×C11—22no—
338C2×Q8×C11—22no—
339C2×Q8×C11C2412yes—
340C2×D4×C11—22no—
341C2×D4×C11—22no—
342C2×D4×C11—22no—
343C2×D4×C11—22no—
344C2×D4×C11—21no—
345C2×D4×C11—21no—
346C2×D4×C11—22no—
347C2×D4×C11—22no—
348C2×D4×C11—22no—
349C2×D4×C11—22no—
350C2×D4×C11—44no—
351C2×D4×C11—82no—
352C2×D4×C11C2412yes—
353C2×D4×C11C2412yes—
354C22×C4×C11—22no—
355C22×C4×C11—22no—
356C22×C4×C11—21no—
357C22×C4×C11—21no—
358C22×C4×C11—22no—
359C22×C4×C11—22no—
360C22×C4×C11—44no—
361C22×C4×C11C2×D411yescharacteristic
362C22×C4×C11C2×D411yescharacteristic
363C22×C4×C11C2×D411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2411yescharacteristic
366C22×C4×C11C2411yescharacteristic
367C2×C22⋊D11—22no—
368C2×C22⋊D11—21no—
369C2×C22⋊D11—21no—
370C2×C22⋊D11—21no—
371C2×C22⋊D11—22no—
372C2×C22⋊D11—22no—
373C2×C22⋊D11—22no—
374C2×C22⋊D11—22no—
375C2×C22⋊D11—22no—
376C2×C22⋊D11—22no—
377C2×C22⋊D11—22no—
378C2×C22⋊D11—44no—
379C2×C22⋊D11—48no—
380C2×C22⋊D11C2×D412yes—
381C2×C22⋊D11C2×D412yes—
382C2×C22⋊D11C2×D412yes—
383C2×C22⋊D11C2×D412yes—
384C22×Dic11—22no—
385C22×Dic11—21no—
386C22×Dic11—21no—
387C22×Dic11C2×D412yes—
388#4341—42no—
389#4341—42no—
390#4341—44no—
391D4×D11—42no—
392D4×D11—42no—
393D4×D11—44no—
394D4×D11—84no—
395#4339—22no—
396#4339—22no—
397#4339—22no—
398#4339—22no—
399#4339—22no—
400#4339—22no—
401#4339—42no—
402#4339—42no—
403#4339—42no—
404#4339—42no—
405#4339—44no—
406C2×D44—22no—
407C2×D44—42no—
408C2×D44C2×D411yescharacteristic
409C2×D44C2×D411yescharacteristic
410C2×D44C2×D412yes—
411C2×D44C2411yescharacteristic
412C2×C4×D11—22no—
413C2×C4×D11—21no—
414C2×C4×D11—42no—
415C2×C4×D11—42no—
416C2×C4×D11C2×D412yes—
417C2×C4×D11C2×D412yes—
418C2×C4×D11C2412yes—
419C2×C4×D11C2412yes—
420C2×Dic22—42no—
421C2×Dic22C2×D411yescharacteristic
422C2×Dic22C2×D411yescharacteristic
423C2×Dic22C2×D412yes—
424C2×Dic22C2411yescharacteristic
425C11×SD16—42no—
426C11×SD16—42no—
427C11×D8—42no—
428C11×D8—42no—
429C2×C8×C11—22no—
430C2×C8×C11—22no—
431C2×C8×C11C2411yescharacteristic
432C2×C8×C11C2411yescharacteristic
433C2×C8×C11C2411yescharacteristic
434C2×C8×C11C2411yescharacteristic
435C11×C4⋊C4—21no—
436C11×C4⋊C4C2412yes—
437C11×C22⋊C4—22no—
438C11×C22⋊C4—22no—
439C22⋊Dic11—22no—
440C22⋊Dic11—22no—
441C22⋊Dic11—22no—
442C22⋊Dic11—22no—
443C22⋊Dic11—22no—
444C22⋊Dic11—22no—
445C22⋊Dic11—21no—
446C22⋊Dic11—21no—
447C22⋊Dic11—21no—
448C22⋊Dic11—21no—
449C22⋊Dic11—21no—
450C22⋊Dic11—21no—
451C22⋊Dic11—21no—
452#4326—42no—
453#4325—42no—
454#4324—42no—
455#4323—42no—
456(C2×D11)⋊C4—22no—
457(C2×D11)⋊C4—22no—
458(C2×D11)⋊C4—22no—
459(C2×D11)⋊C4—22no—
460(C2×D11)⋊C4—22no—
461(C2×D11)⋊C4—22no—
462(C2×D11)⋊C4—22no—
463(C2×D11)⋊C4—21no—
464(C2×D11)⋊C4—21no—
465C4⋊Dic11—22no—
466C4⋊Dic11—21no—
467C4⋊Dic11—21no—
468C4⋊Dic11C2411yescharacteristic
469C4⋊Dic11C2411yescharacteristic
470C4⋊Dic11C2411yescharacteristic
471C4⋊Dic11C2411yescharacteristic
472C4⋊Dic11C2411yescharacteristic
473C4⋊Dic11C2411yescharacteristic
474Dic11⋊C4—22no—
475Dic11⋊C4—22no—
476Dic11⋊C4—22no—
477Dic11⋊C4—22no—
478Dic11⋊C4—22no—
479Dic11⋊C4—21no—
480Dic11⋊C4—21no—
481C4×Dic11—22no—
482C4×Dic11—21no—
483C4×Dic11—21no—
484C4×Dic11—21no—
485C4×Dic11—21no—
486C4×Dic11—21no—
487#4318—22no—
488#4318—22no—
489C2×C11⋊C8C2412yes—
490C2×C11⋊C8C2412yes—
491#4313—42no—
492#4313—42no—
493C8×D11—42no—
494C8×D11—42no—
495#3488—111no—
496#3449—111no—
497#3204—112no—
498#3203—112no—
499#3198—112no—
500#3198—112no—
501#3197—112no—
502#3194—112no—
503#3191—112no—
504#3188—112no—
505#3097—111no—
506#3096—111no—
507#3094—111no—
508#3091—111no—
509#3063—111no—
510#3062—111no—
511#3058—111no—
512#3057—111no—
513#3009—111no—
514#3008—111no—
515#3005—111no—
516C2×#449D1111yescharacteristic, complemented
517#2880—111no—
518C23×C11—22no—
519C23×C11—22no—
520C23×C11—22no—
521C23×C11—41no—
522C23×C11—41no—
523C23×C11—42no—
524C23×C11—42no—
525C23×C11—81no—
526C23×C11—81no—
527C23×C11—81no—
528C23×C11—81no—
529C23×C11C22×D411yescharacteristic
530C23×C11C22×D411yescharacteristic
531C23×C11C22×D411yescharacteristic
532C22×D11—21no—
533C22×D11—42no—
534C22×D11—42no—
535C22×D11—42no—
536C22×D11—44no—
537C22×D11—82no—
538C22×D11—82no—
539C22×D11C22×D412yes—
540C22×D11C22×D412yes—
541Q8×C11—22no—
542Q8×C11—22no—
543Q8×C11—42no—
544D4×C11—22no—
545D4×C11—22no—
546D4×C11—22no—
547D4×C11—22no—
548D4×C11—44no—
549D4×C11—44no—
550D4×C11—44no—
551D4×C11—42no—
552D4×C11—42no—
553D4×C11—82no—
554C2×C4×C11—22no—
555C2×C4×C11—22no—
556C2×C4×C11—22no—
557C2×C4×C11—21no—
558C2×C4×C11—21no—
559C2×C4×C11—21no—
560C2×C4×C11—21no—
561C2×C4×C11—22no—
562C2×C4×C11—22no—
563C2×C4×C11—44no—
564C2×C4×C11—44no—
565C2×C4×C11—42no—
566C2×C4×C11—81no—
567C2×C4×C11C22×D411yescharacteristic
568C2×C4×C11C22×D411yescharacteristic
569C2×C4×C11C22×D411yescharacteristic
570C2×C4×C11H(5,𝔽2)12yes—
571C2×C4×C11H(5,𝔽2)12yes—
572C2×C4×C11C2511yescharacteristic
573C22⋊D11—24no—
574C22⋊D11—24no—
575C22⋊D11—42no—
576C22⋊D11—42no—
577C22⋊D11—44no—
578C22⋊D11—44no—
579C22⋊D11—42no—
580C22⋊D11—42no—
581C22⋊D11—82no—
582C22⋊D11—82no—
583C22⋊D11—82no—
584C22⋊D11—82no—
585C22⋊D11—82no—
586C22⋊D11—82no—
587C22⋊D11—81no—
588C2×Dic11—21no—
589C2×Dic11—21no—
590C2×Dic11—21no—
591C2×Dic11—21no—
592C2×Dic11—21no—
593C2×Dic11—21no—
594C2×Dic11—21no—
595C2×Dic11—42no—
596C2×Dic11—44no—
597C2×Dic11—81no—
598C2×Dic11—81no—
599C2×Dic11C22×D412yes—
600C2×Dic11C22×D412yes—
601D44—22no—
602D44—22no—
603D44—21no—
604D44—21no—
605D44—42no—
606D44—82no—
607C4×D11—22no—
608C4×D11—22no—
609C4×D11—22no—
610C4×D11—22no—
611C4×D11—42no—
612C4×D11—42no—
613C4×D11—42no—
614C4×D11—82no—
615Dic22—22no—
616Dic22—22no—
617Dic22—21no—
618Dic22—21no—
619Dic22—42no—
620C8×C11—21no—
621C8×C11—21no—
622C8×C11—21no—
623C8×C11—21no—
624C11⋊C8—22no—
625C11⋊C8—22no—
626C2×H(5,𝔽2)—111no—
627C22×#41—111no—
628C22×#41C2×D1111yescharacteristic, complemented
629C2×#137—111no—
630C2×AGL(1,ℤ/8)—111no—
631C22×SD16C2×D1111yescharacteristic, complemented
632C22×D8C2×D1111yescharacteristic, complemented
633C2×#131—111no—
634C2×#131—111no—
635#550—221no—
636#548—221no—
637#546—222no—
638#546—221no—
639D42—221no—
640D42—222no—
641#537—112no—
642#537—112no—
643#537—112no—
644#537—111no—
645#536—111no—
646#536—111no—
647#536—221no—
648#535—111no—
649#535—111no—
650#535—111no—
651#535—112no—
652#535—221no—
653#534—222no—
654#532—221no—
655#532—221no—
656#525—112no—
657#525—112no—
658#525—111no—
659#525—112no—
660#525—222no—
661C2×#121—112no—
662C2×#121C2×D1111yescharacteristic
663#520—111no—
664C2×#117—111no—
665#485—112no—
666#485—112no—
667#485—111no—
668#485—111no—
669#484—112no—
670#484—111no—
671#483—112no—
672#483—111no—
673#482—112no—
674#482—112no—
675#482—112no—
676#482—112no—
677#482—111no—
678#482—111no—
679#481—112no—
680#481—112no—
681#481—111no—
682#480—112no—
683#480—112no—
684#480—111no—
685#470—112no—
686#469—112no—
687#469—112no—
688#469—112no—
689#468—112no—
690#468—112no—
691#468—112no—
692#468—112no—
693#467—112no—
694#466—112no—
695#466—112no—
696#466—112no—
697#465—112no—
698#465—112no—
699#465—112no—
700#465—112no—
701#452—112no—
702#452—112no—
703#452—112no—
704#452—112no—
705#450—112no—
706#450—112no—
707#449—112no—
708#449—112no—
709#449—112no—
710#449—112no—
711#449C2×D1112yescomplemented
712#449C2×D1112yescomplemented
713#449C2×D1112yescomplemented
714#449C2×D1112yescomplemented
715#447—112no—
716#447—112no—
717#428—111no—
718#428—111no—
719#427—111no—
720#427—111no—
721#419—111no—
722#418—111no—
723#418—111no—
724#418—111no—
725#416—111no—
726#416—111no—
727C2×#103C2×D1111yescharacteristic, complemented
728C2×#102C2×D1111yescharacteristic, complemented
729#408—111no—
730#408—111no—
731#408—112no—
732#408—112no—
733#407—111no—
734#407—112no—
735C2×C22⋊C8—112no—
736C2×C22⋊C8C2×D1111yescharacteristic, complemented
737C22×C11—21no—
738C22×C11—21no—
739C22×C11—21no—
740C22×C11—21no—
741C22×C11—21no—
742C22×C11—21no—
743C22×C11—21no—
744C22×C11—21no—
745C22×C11—42no—
746C22×C11—42no—
747C22×C11—42no—
748C22×C11—42no—
749C22×C11—42no—
750C22×C11—42no—
751C22×C11—82no—
752C22×C11—84no—
753C22×C11—162no—
754C22×C11#53412yes—
755C22×C11C23×D411yescharacteristic
756C2×D11—22no—
757C2×D11—22no—
758C2×D11—22no—
759C2×D11—22no—
760C2×D11—22no—
761C2×D11—22no—
762C2×D11—41no—
763C2×D11—41no—
764C2×D11—41no—
765C2×D11—84no—
766C2×D11—164no—
767C4×C11—21no—
768C4×C11—21no—
769C4×C11—42no—
770C4×C11—42no—
771C4×C11#53412yes—
772C4×C11C2×H(5,𝔽2)11yescharacteristic
773C4×C11C2×H(5,𝔽2)11yescharacteristic
774Dic11—22no—
775Dic11—22no—
776Dic11—41no—
777Dic11—41no—
778Dic11—41no—
779Dic11—41no—
780Dic11—41no—
781Dic11—41no—
782Dic11—41no—
783H(5,𝔽2)—442no—
784H(5,𝔽2)—442no—
785C2×#41—21no—
786C2×#41—21no—
787C2×#41—42no—
788C2×#41—42no—
789C2×#41—112no—
790C2×#41—111no—
791C2×#41—111no—
792C2×#41—111no—
793C2×#41—111no—
794C2×#41—112no—
795C2×#41—112no—
796C2×#41—111no—
797C2×#41—221no—
798C2×#41—442no—
799C2×#41—442no—
800C2×#41C22×D1112yes—
801C2×#41C22×D1112yes—
802C22×Q8—111no—
803C22×Q8C22×D1111yescharacteristic
804C22×D4—21no—
805C22×D4—21no—
806C22×D4—112no—
807C22×D4—112no—
808C22×D4—111no—
809C22×D4—221no—
810C22×D4—222no—
811C22×D4—222no—
812C22×D4C22×D1111yescharacteristic
813C22×D4C22×D1111yescharacteristic
814C23×C4—21no—
815C23×C4—112no—
816C23×C4C22×D1111yescharacteristic
817#137—442no—
818AGL(1,ℤ/8)—442no—
819C2×Q16—112no—
820C2×SD16—42no—
821C2×SD16—112no—
822C2×SD16—112no—
823C2×SD16C22×D1112yes—
824C2×SD16C22×D1112yes—
825C2×D8—42no—
826C2×D8—112no—
827C2×D8C22×D1112yes—
828C2×D8C22×D1112yes—
829#131—442no—
830#131—442no—
831C2×M16—111no—
832C2×M16—111no—
833C2×M16—112no—
834C2×M16—112no—
835C22×C8—112no—
836C22×C8—112no—
837C22×C8C22×D1111yescharacteristic
838C22×C8C22×D1111yescharacteristic
839C4⋊Q8—221no—
840C4⋊Q8—221no—
841#127—221no—
842#127—221no—
843#127—222no—
844#127—221no—
845#124—222no—
846#124—221no—
847#124—221no—
848#124—221no—
849#124—221no—
850#124—221no—
851#123—222no—
852#123—222no—
853#123—222no—
854#123—222no—
855#123—222no—
856#123—221no—
857C22⋊Q8—112no—
858C22⋊Q8—112no—
859C22⋊Q8—112no—
860C22⋊Q8—112no—
861C22⋊Q8—111no—
862C22⋊Q8—111no—
863C22⋊Q8—112no—
864C22⋊Q8—222no—
865C22⋊Q8—221no—
866C22⋊Q8—222no—
867C22⋊Q8—222no—
868#121—21no—
869#121—21no—
870#121—112no—
871#121—112no—
872#121—112no—
873#121—112no—
874#121—112no—
875#121—112no—
876#121—111no—
877#121—111no—
878#121—112no—
879#121—222no—
880#121—222no—
881#121—221no—
882#121—222no—
883#121—222no—
884#121—222no—
885#121—222no—
886#121—222no—
887#121—222no—
888#121—222no—
889#121—222no—
890#121—222no—
891#121—222no—
892#121C22×D1112yes—
893#121C22×D1112yes—
894#120—222no—
895#120—222no—
896#120—222no—
897#120—222no—
898#120—222no—
899#120—222no—
900#120—222no—
901#120—222no—
902#120—221no—
903C4×Q8—221no—
904C4×D4—222no—
905C4×D4—221no—
906C4×D4—222no—
907C4×D4—222no—
908C4×D4—222no—
909C4×D4—222no—
910C4×D4—222no—
911C4×D4—222no—
912C4×D4—221no—
913C4×D4—221no—
914#117—111no—
915#117—111no—
916#117—111no—
917#117—111no—
918#117—111no—
919#117—112no—
920#117—221no—
921#117—221no—
922C2×C4⋊C4—111no—
923C2×C4⋊C4—111no—
924C2×C4⋊C4—112no—
925C2×C4⋊C4C22×D1111yescharacteristic
926C2×C22⋊C4—21no—
927C2×C22⋊C4—222no—
928C2×C22⋊C4—221no—
929C2×C42—221no—
930#107—111no—
931#107—111no—
932#107—111no—
933#107—111no—
934#107—112no—
935#107—112no—
936#106—111no—
937#106—111no—
938#106—111no—
939#106—111no—
940#106—112no—
941#106—112no—
942#103—112no—
943#103—112no—
944#103—111no—
945#103—111no—
946#103—111no—
947#103—111no—
948#103C22×D1112yes—
949#103C22×D1112yes—
950#102—112no—
951#102—112no—
952#102—112no—
953#102—112no—
954#102—112no—
955#102—112no—
956#102—111no—
957#102—111no—
958#102—111no—
959#102—111no—
960#102C22×D1112yes—
961#102C22×D1112yes—
962C22⋊C8—112no—
963C22⋊C8—112no—
964C22⋊C8—112no—
965C22⋊C8—112no—
966C22⋊C8—112no—
967C22⋊C8—112no—
968C22⋊C8C22×D1111yescharacteristic
969C22⋊C8C22×D1111yescharacteristic
970C22⋊C8C22×D1111yescharacteristic
971C22⋊C8C22×D1111yescharacteristic
972C2×C11—22no—
973C2×C11—41no—
974C2×C11—41no—
975C2×C11—82no—
976C2×C11—82no—
977C2×C11C2×#53411yescharacteristic
978C2×C11#358411yescharacteristic
979C2×C11#358511yescharacteristic
980D11—42no—
981D11—42no—
982D11—81no—
983C24—21no—
984C24—21no—
985C24—112no—
986C24—222no—
987C24D4×D1111yescharacteristic
988#41—42no—
989#41—42no—
990#41—42no—
991#41—42no—
992#41—44no—
993#41—44no—
994#41—222no—
995#41—222no—
996#41—222no—
997#41—222no—
998#41—222no—
999#41—222no—
1000#41—442no—
1001#41—442no—
1002#41—444no—
1003#41—442no—
1004#41—442no—
1005#41—442no—
1006#41—442no—
1007#41—444no—
1008C2×Q8—21no—
1009C2×Q8—22no—
1010C2×Q8—22no—
1011C2×Q8—111no—
1012C2×Q8—111no—
1013C2×Q8—112no—
1014C2×Q8—111no—
1015C2×Q8—442no—
1016C2×Q8C23×D1112yes—
1017C2×D4—22no—
1018C2×D4—22no—
1019C2×D4—22no—
1020C2×D4—22no—
1021C2×D4—21no—
1022C2×D4—21no—
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—22no—
1026C2×D4—22no—
1027C2×D4—44no—
1028C2×D4—82no—
1029C2×D4—112no—
1030C2×D4—112no—
1031C2×D4—112no—
1032C2×D4—112no—
1033C2×D4—111no—
1034C2×D4—111no—
1035C2×D4—112no—
1036C2×D4—111no—
1037C2×D4—222no—
1038C2×D4—222no—
1039C2×D4—222no—
1040C2×D4—221no—
1041C2×D4—221no—
1042C2×D4—222no—
1043C2×D4—222no—
1044C2×D4—222no—
1045C2×D4—222no—
1046C2×D4—222no—
1047C2×D4—222no—
1048C2×D4—221no—
1049C2×D4—442no—
1050C2×D4—442no—
1051C2×D4—442no—
1052C2×D4—444no—
1053C2×D4—444no—
1054C2×D4—448no—
1055C2×D4—884no—
1056C2×D4C23×D1112yes—
1057C2×D4C23×D1112yes—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—22no—
1063C22×C4—22no—
1064C22×C4—44no—
1065C22×C4—112no—
1066C22×C4—112no—
1067C22×C4—112no—
1068C22×C4—112no—
1069C22×C4—112no—
1070C22×C4—222no—
1071C22×C4—222no—
1072C22×C4—221no—
1073C22×C4—221no—
1074C22×C4—221no—
1075C22×C4—442no—
1076C22×C4—442no—
1077C22×C4D4×D1111yescharacteristic
1078C22×C4D4×D1111yescharacteristic
1079C22×C4D4×D1111yescharacteristic
1080C22×C4C23×D1111yescharacteristic
1081C22×C4C23×D1111yescharacteristic
1082C22×C4C23×D1111yescharacteristic
1083Q16—442no—
1084SD16—42no—
1085SD16—42no—
1086SD16—442no—
1087SD16—442no—
1088D8—42no—
1089D8—42no—
1090D8—442no—
1091M16—222no—
1092M16—222no—
1093M16—442no—
1094M16—442no—
1095C2×C8—22no—
1096C2×C8—22no—
1097C2×C8—112no—
1098C2×C8—112no—
1099C2×C8—442no—
1100C2×C8—442no—
1101C2×C8C23×D1111yescharacteristic
1102C2×C8C23×D1111yescharacteristic
1103C2×C8C23×D1111yescharacteristic
1104C2×C8C23×D1111yescharacteristic
1105C4⋊C4—21no—
1106C4⋊C4—111no—
1107C4⋊C4—111no—
1108C4⋊C4—111no—
1109C4⋊C4—111no—
1110C4⋊C4—111no—
1111C4⋊C4—111no—
1112C4⋊C4—222no—
1113C4⋊C4—222no—
1114C4⋊C4—222no—
1115C4⋊C4—222no—
1116C4⋊C4—222no—
1117C4⋊C4—222no—
1118C4⋊C4—221no—
1119C4⋊C4—221no—
1120C4⋊C4—221no—
1121C4⋊C4—221no—
1122C4⋊C4C23×D1112yes—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—222no—
1126C22⋊C4—222no—
1127C22⋊C4—222no—
1128C22⋊C4—222no—
1129C22⋊C4—222no—
1130C22⋊C4—222no—
1131C22⋊C4—222no—
1132C22⋊C4—222no—
1133C22⋊C4—222no—
1134C22⋊C4—222no—
1135C22⋊C4—222no—
1136C22⋊C4—222no—
1137C22⋊C4—222no—
1138C22⋊C4—221no—
1139C22⋊C4—221no—
1140C22⋊C4—221no—
1141C22⋊C4—221no—
1142C22⋊C4—221no—
1143C22⋊C4—221no—
1144C22⋊C4—221no—
1145C22⋊C4—221no—
1146C22⋊C4—221no—
1147C42—222no—
1148C42—221no—
1149C42—221no—
1150C42—221no—
1151C42—221no—
1152C42—221no—
1153C11#6076011yescharacteristic, complemented, Sylow
1154C23—22no—
1155C23—22no—
1156C23—22no—
1157C23—41no—
1158C23—41no—
1159C23—42no—
1160C23—42no—
1161C23—81no—
1162C23—81no—
1163C23—81no—
1164C23—81no—
1165C23—112no—
1166C23—112no—
1167C23—221no—
1168C23—442no—
1169C23—442no—
1170C23—442no—
1171C23—444no—
1172C23—882no—
1173C23—882no—
1174C23C2×D4×D1111yescharacteristic
1175C23C2×D4×D1111yescharacteristic
1176C23C2×D4×D1111yescharacteristic
1177Q8—22no—
1178Q8—22no—
1179Q8—42no—
1180Q8—222no—
1181Q8—222no—
1182Q8—221no—
1183Q8—221no—
1184Q8—442no—
1185D4—22no—
1186D4—22no—
1187D4—22no—
1188D4—22no—
1189D4—44no—
1190D4—44no—
1191D4—44no—
1192D4—42no—
1193D4—42no—
1194D4—82no—
1195D4—224no—
1196D4—224no—
1197D4—222no—
1198D4—222no—
1199D4—221no—
1200D4—221no—
1201D4—442no—
1202D4—442no—
1203D4—442no—
1204D4—444no—
1205D4—442no—
1206D4—444no—
1207D4—442no—
1208D4—882no—
1209D4—881no—
1210D4—882no—
1211D4—882no—
1212D4—882no—
1213D4—882no—
1214D4—882no—
1215D4—882no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—44no—
1226C2×C4—44no—
1227C2×C4—42no—
1228C2×C4—81no—
1229C2×C4—112no—
1230C2×C4—112no—
1231C2×C4—222no—
1232C2×C4—222no—
1233C2×C4—222no—
1234C2×C4—222no—
1235C2×C4—221no—
1236C2×C4—221no—
1237C2×C4—221no—
1238C2×C4—221no—
1239C2×C4—221no—
1240C2×C4—221no—
1241C2×C4—221no—
1242C2×C4—442no—
1243C2×C4—442no—
1244C2×C4—442no—
1245C2×C4—444no—
1246C2×C4—442no—
1247C2×C4—882no—
1248C2×C4—881no—
1249C2×C4—881no—
1250C2×C4C2×D4×D1111yescharacteristic
1251C2×C4C2×D4×D1111yescharacteristic
1252C2×C4C2×D4×D1111yescharacteristic
1253C2×C4#6703712yes—
1254C2×C4#6703712yes—
1255C2×C4C24×D1111yescharacteristic
1256C8—21no—
1257C8—21no—
1258C8—21no—
1259C8—21no—
1260C8—222no—
1261C8—222no—
1262C22—21no—
1263C22—21no—
1264C22—21no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—82no—
1277C22—84no—
1278C22—162no—
1279C22—222no—
1280C22—222no—
1281C22—222no—
1282C22—222no—
1283C22—222no—
1284C22—222no—
1285C22—441no—
1286C22—441no—
1287C22—441no—
1288C22—884no—
1289C22—1764no—
1290C22#1062312012yes—
1291C22C22×D4×D1111yescharacteristic
1292C4—21no—
1293C4—21no—
1294C4—42no—
1295C4—42no—
1296C4—222no—
1297C4—222no—
1298C4—441no—
1299C4—441no—
1300C4—441no—
1301C4—441no—
1302C4—441no—
1303C4—441no—
1304C4—441no—
1305C4#1062312012yes—
1306C4C2×#6703711yescharacteristic
1307C4C2×#6703711yescharacteristic
1308C2—22no—
1309C2—41no—
1310C2—41no—
1311C2—82no—
1312C2—82no—
1313C2—442no—
1314C2—442no—
1315C2—881no—
1316C2C2×#1062312011yescharacteristic
1317C2#1308338511yescharacteristic
1318C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#449C2
socleC22×C11C23×D4
hypercenterC2×#449D11
hypocenterC11#60760
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #13082281C2semidirect
2. #13081945C2semidirect
3. #13079525C2semidirect
4. #13079515C2semidirect
5. #13079467C2semidirect
6. #13079465C2semidirect
7. #13079455C2semidirect
8. #13079428C2semidirect
9. #13079406C2semidirect
10. #13079379C2semidirect
11. #13078581C2semidirect
12. #13078570C2semidirect
13. #13078552C2semidirect
14. #13078531C2semidirect
15. #13078305C2semidirect
16. #13078294C2semidirect
17. #13078260C2semidirect
18. #13078251C2semidirect
19. #13077889C2semidirect
20. #13077880C2semidirect
21. #13077858C2semidirect
22. #13077062C2semidirect
23. C2×C11×#449C2semidirect
24. C22×C11×#41C22semidirect
27. C22×C11×SD16C22semidirect
28. C22×C11×D8C22semidirect
30. #10623364C22semidirect
31. #10623364C22semidirect
35. #10623359C22semidirect
36. #10623359C22semidirect
39. #10623347C22semidirect
40. C2×#66995C22semidirect
43. #10623336C22semidirect
46. C2×#66985C22semidirect
49. C2×#66979C22semidirect
50. C2×#66954C22semidirect
51. C2×#66954C22semidirect
54. #10623139C22semidirect
55. #10623138C22semidirect
56. #10623137C22semidirect
57. D11×#121C22semidirect
63. C11×#449C22semidirect
64. C11×#449C22semidirect
65. C11×#449C22semidirect
66. C11×#449C22semidirect
67. C2×C11×#103C22semidirect
68. C2×C11×#102C22semidirect
69. C2×C11×C22⋊C8C22semidirect
70. #10622852C22semidirect
71. #10622852C22semidirect
72. #10622851C22semidirect
73. #10622851C22semidirect
74. #10622838C22semidirect
75. #10622828C22semidirect
76. #10622828C22semidirect
77. #10622828C22semidirect
78. #10622820C22semidirect
79. #10622787C22semidirect
80. #10622787C22semidirect
81. #10622786C22semidirect
82. #10622786C22semidirect
83. #10622784C22semidirect
84. #10622784C22semidirect
85. #10622782C22semidirect
86. #10622782C22semidirect
87. #10622772C22semidirect
88. #10622772C22semidirect
89. #10622771C22semidirect
90. #10622771C22semidirect
91. #10622770C22semidirect
92. #10622770C22semidirect
93. #10622769C22semidirect
94. #10622769C22semidirect
95. #10622726C22semidirect
96. #10622726C22semidirect
99. #10622719C22semidirect
100. #10622719C22semidirect
101. #10622648C22semidirect
102. #10622648C22semidirect
103. #10622647C22semidirect
104. #10622646C22semidirect
105. #10622577C22semidirect
106. #10622577C22semidirect
107. #10622429C22semidirect
108. #10622428C22semidirect
109. #10622427C22semidirect
110. #10622426C22semidirect
111. #10622425C22semidirect
112. #10622422C22semidirect
113. #10622420C22semidirect
114. #10622418C22semidirect
115. #10622397C22semidirect
116. #10622395C22semidirect
117. #10622393C22semidirect
118. #10622392C22semidirect
119. #10622391C22semidirect
120. #10622390C22semidirect
121. #10622388C22semidirect
122. #10622387C22semidirect
123. #10622350C22semidirect
124. #10622350C22semidirect
125. #10622349C22semidirect
126. #10622348C22semidirect
127. #10622340C22semidirect
128. #10622340C22semidirect
129. #10622339C22semidirect
130. D11×C22⋊C8C22semidirect
131. #10622336C22semidirect
132. #10622336C22semidirect
133. #10622335C22semidirect
134. #10622334C22semidirect
516. C2×#449D11semidirect
628. C22×#41C2×D11semidirect
631. C22×SD16C2×D11semidirect
632. C22×D8C2×D11semidirect
711. #449C2×D11semidirect
712. #449C2×D11semidirect
713. #449C2×D11semidirect
714. #449C2×D11semidirect
727. C2×#103C2×D11semidirect
728. C2×#102C2×D11semidirect
736. C2×C22⋊C8C2×D11semidirect
1153. C11#60760semidirect

Maximal subgroups

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

subgroupindex
#130822812
#130819452
#130795252
#130795152
#130794672
#130794652
#130794552
#130794282
#130794062
#130793792
#130785812
#130785702
#130785522
#130785312
#130783052
#130782942
#130782602
#130782512
#130778892
#130778802
#130778582
#130770622
C2×C11×#4492
#6076011