Finite Group Databasebeta

← #15624726

Subgroups — #15624726

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082289C211yesmaximal, characteristic, complemented
2D11×#537C211yesmaximal, characteristic, complemented
3#13079525C212yesmaximal, complemented
4#13079524C212yesmaximal, complemented
5#13079502C212yesmaximal, complemented
6#13079494C212yesmaximal, complemented
7#13079438C212yesmaximal, complemented
8#13079428C212yesmaximal, complemented
9#13079395C212yesmaximal, complemented
10#13079371C212yesmaximal, complemented
11#13078607C211yesmaximal, characteristic, complemented
12#13078601C211yesmaximal, characteristic, complemented
13#13078537C211yesmaximal, characteristic, complemented
14C2×#10622418C211yesmaximal, characteristic, complemented
15#13078305C211yesmaximal, characteristic, complemented
16#13078301C211yesmaximal, characteristic, complemented
17#13078277C211yesmaximal, characteristic, complemented
18#13078274C211yesmaximal, characteristic, complemented
19#13077931C211yesmaximal, characteristic, complemented
20#13077872C211yesmaximal, characteristic, complemented
21#13077830C211yesmaximal, characteristic, complemented
22#13077064C211yesmaximal, characteristic, complemented
23C11×#3013C211yesmaximal, characteristic, complemented
24C2×C11×2−1+4C2211yescharacteristic, complemented
25C2×#41×D11C2211yescharacteristic
26C2×#41×D11C2211yescharacteristic
27C2×C11×#137C2211yescharacteristic, complemented
28C2×C11×#135C2211yescharacteristic, complemented
29C11×#537C2211yescharacteristic
30#10623364C2211yescharacteristic
31#10623364C2211yescharacteristic
32#10623364C2211yescharacteristic, complemented
33#10623364C2212yescomplemented
34#10623360—22no—
35#10623360—21no—
36#10623359C2211yescharacteristic
37#10623359C2212yes—
38#10623358C2211yescharacteristic, complemented
39#10623355—22no—
40#10623355—21no—
41C2×#67003C2211yescharacteristic, complemented
42#10623348—21no—
43#10623347C2211yescharacteristic, complemented
44#10623347C2212yescomplemented
45Q8×C22⋊D11—21no—
46C2×#66999C2212yes—
47C2×#66999C2211yescharacteristic
48C2×#66995C2211yescharacteristic, complemented
49C2×#66960C2211yescharacteristic, complemented
50C2×#66954C2211yescharacteristic, complemented
51#10623160—21no—
52#10623160C2212yes—
53D11×C22⋊Q8—21no—
54D11×C22⋊Q8C2212yes—
55#10623139—21no—
56#10623139C2212yes—
57D11×#121—21no—
58D11×#121—22no—
59D11×#121C2212yes—
60#10623128—22no—
61#10623041C2211yescharacteristic
62C2×C4⋊C4×D11C2211yescharacteristic
63C11×#452C2212yescomplemented
64C11×#451C2212yescomplemented
65C11×#449C2212yescomplemented
66C11×#448C2212yescomplemented
67C11×#417C2211yescharacteristic, complemented
68C2×C11×#103C2211yescharacteristic, complemented
69C11×#408C2211yescharacteristic, complemented
70#10622852C2212yescomplemented
71#10622851C2212yescomplemented
72#10622847C2211yescharacteristic, complemented
73#10622846C2211yescharacteristic, complemented
74#10622845C2211yescharacteristic, complemented
75#10622845C2211yescharacteristic, complemented
76#10622841C2212yescomplemented
77#10622840C2212yescomplemented
78C2×#66899C2211yescharacteristic, complemented
79#10622802C2212yescomplemented
80#10622802C2212yescomplemented
81#10622801C2212yescomplemented
82#10622800C2211yescharacteristic, complemented
83#10622800C2212yescomplemented
84#10622799C2211yescharacteristic
85#10622799C2212yes—
86#10622787C2212yescomplemented
87#10622786C2211yescharacteristic, complemented
88#10622786C2212yescomplemented
89#10622785C2211yescharacteristic, complemented
90#10622784C2212yescomplemented
91#10622784C2212yescomplemented
92#10622784C2212yescomplemented
93#10622783C2211yescharacteristic
94#10622782C2211yescharacteristic
95#10622782C2212yes—
96#10622772C2212yescomplemented
97#10622771C2211yescharacteristic, complemented
98#10622769C2211yescharacteristic
99#10622746C2211yescharacteristic, complemented
100#10622739C2211yescharacteristic
101#10622734C2211yescharacteristic, complemented
102#10622726C2211yescharacteristic, complemented
103C2×(C2×D11)⋊C8C2211yescharacteristic
104C2×#66881C2211yescharacteristic, complemented
105#10622658C2212yescomplemented
106#10622656C2212yescomplemented
107#10622648C2212yescomplemented
108#10622647C2212yescomplemented
109#10622577C2211yescharacteristic, complemented
110C2×#66872C2211yescharacteristic, complemented
111#10622429C2212yescomplemented
112#10622429C2212yescomplemented
113#10622426C2212yescomplemented
114#10622425C2212yescomplemented
115#10622422C2212yescomplemented
116#10622420C2212yescomplemented
117#10622420C2212yescomplemented
118#10622418C2212yes—
119#10622418C2212yes—
120#10622418C2212yes—
121#10622418C2212yescomplemented
122#10622418C2212yescomplemented
123#10622395C2212yescomplemented
124#10622391C2212yescomplemented
125#10622390C2212yescomplemented
126#10622387C2212yes—
127#10622350C2212yescomplemented
128#10622348C2212yescomplemented
129#10622340C2212yescomplemented
130#10622340C2212yescomplemented
131#10622339C2212yes—
132D11×C22⋊C8C2212yes—
133#10622336C2212yescomplemented
134#10622334C2212yescomplemented
135C11×2−1+4—42no—
136C11×2−1+4—42no—
137C2×C11×#41—21no—
138C2×C11×#41—22no—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2311yescharacteristic
141C2×C11×#41C2312yes—
142C2×C11×#41C2311yescharacteristic
143C22×Q8×C11—21no—
144C22×Q8×C11C2311yescharacteristic
145C22×Q8×C11C2312yes—
146#41×D11—42no—
147#41×D11—42no—
148#41×D11—42no—
149#41×D11—42no—
150C2×#4343D411yescharacteristic
151C2×#4343C2311yescharacteristic
152C2×Q8×D11D411yescharacteristic
153C2×Q8×D11C2311yescharacteristic
154C2×#4341—21no—
155C2×#4341D412yes—
156C2×#4341D411yescharacteristic
157C2×#4341C2311yescharacteristic
158C2×D4×D11—21no—
159C2×D4×D11—22no—
160C2×D4×D11D411yescharacteristic
161C2×D4×D11D412yes—
162C2×D4×D11C2311yescharacteristic
163C2×#4339—21no—
164C2×#4339C2311yescharacteristic
165C2×#4339C2312yes—
166C2×#4339C2311yescharacteristic
167C22×C4×D11—21no—
168C22×C4×D11—21no—
169C22×C4×D11C2311yescharacteristic
170C22×C4×D11C2312yes—
171C11×#137—42no—
172C11×#135—42no—
173C2×C11×Q16C2312yes—
174C2×C11×Q16C2311yescharacteristic
175C2×C11×SD16C2311yescharacteristic
176C2×C11×SD16C2312yes—
177C2×C11×SD16C2311yescharacteristic
178C2×C11×D8C2311yescharacteristic
179C2×C11×M16C2311yescharacteristic
180C22×C8×C11C2311yescharacteristic
181C11×C22⋊Q8—21no—
182C11×C22⋊Q8C2312yes—
183C11×#121—22no—
184C11×#121—21no—
185C11×#121C2312yes—
186C2×C11×C4⋊C4C2311yescharacteristic
187#67003—42no—
188#67000—21no—
189#67000—22no—
190#66999—21no—
191#66999—21no—
192#66999—22no—
193#66999—21no—
194#66999—22no—
195#66999C2311yescharacteristic
196#66999C2312yes—
197#66999C2312yes—
198#66999C2312yes—
199#66999C2312yes—
200#66999C2312yes—
201#66999C2311yescharacteristic
202#66999C2312yes—
203Q8×Dic11—21no—
204#66997—21no—
205#66997—22no—
206C2×#4326C2312yes—
207C2×#4326C2311yescharacteristic
208#66995—42no—
209C2×#4325C2312yes—
210C2×#4325C2311yescharacteristic
211#66992—22no—
212#66992—22no—
213#66992—22no—
214#66992—22no—
215#66992—22no—
216#66992—22no—
217#66992—22no—
218#66991—21no—
219#66991—22no—
220#66991C2311yescharacteristic
221#66991C2311yescharacteristic
222#66991C2312yes—
223#66991C2312yes—
224#66990—21no—
225#66990—22no—
226#66988—21no—
227#66988—22no—
228D4×Dic11—21no—
229D4×Dic11—22no—
230C2×#4324C2311yescharacteristic
231C2×#4323C2311yescharacteristic
232#66983—22no—
233#66983—21no—
234#66983—22no—
235#66983—21no—
236#66983C2312yes—
237#66982—22no—
238#66982—22no—
239#66982—22no—
240C4×C22⋊D11—21no—
241C4×C22⋊D11—22no—
242C4×C22⋊D11—21no—
243C4×C22⋊D11—22no—
244C2×(C2×D11)⋊C4—21no—
245C2×(C2×D11)⋊C4—22no—
246#66979C2311yescharacteristic
247#66979C2312yes—
248C2×C4⋊Dic11C2311yescharacteristic
249C2×C4⋊Dic11C2311yescharacteristic
250C2×C4⋊Dic11C2312yes—
251#66977—21no—
252#66977—22no—
253#66977—21no—
254#66977C2312yes—
255C2×Dic11⋊C4—21no—
256C2×Dic11⋊C4—21no—
257C2×Dic11⋊C4—22no—
258C2×#4318C2311yescharacteristic
259C22×C11⋊C8C2311yescharacteristic
260#66960—42no—
261#66954—42no—
262C2×#4313C2312yes—
263C2×#4313C2312yes—
264C2×C8×D11C2312yes—
265C2×C8×D11C2312yes—
266#66950—21no—
267#66950C2312yes—
268#66949—22no—
269#66949—22no—
270#66948—21no—
271#66948—22no—
272#66948C2312yes—
273C4⋊C4×D11—21no—
274C4⋊C4×D11—21no—
275C4⋊C4×D11—22no—
276C4⋊C4×D11C2312yes—
277C4⋊C4×D11C2312yes—
278#66937—22no—
279#66937—22no—
280#66937—22no—
281#66937—22no—
282C22⋊C4×D11—22no—
283C22⋊C4×D11—22no—
284#66931—22no—
285#66931—22no—
286C11×#103C2312yes—
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#102C2312yes—
290C11×C22⋊C8C2312yes—
291C11×C22⋊C8C2312yes—
292#66899C2311yescharacteristic
293#66899C2312yes—
294#66899C2312yes—
295#66899C2312yes—
296#66899C2311yescharacteristic
297#66899C2312yes—
298#66896C2311yescharacteristic
299#66896C2311yescharacteristic
300#66896C2312yes—
301#66896C2312yes—
302C22⋊(C11⋊C8)C2312yes—
303C22⋊(C11⋊C8)C2312yes—
304#66885C2311yescharacteristic
305#66885C2311yescharacteristic
306#66885C2312yes—
307(C2×D11)⋊C8C2311yescharacteristic
308(C2×D11)⋊C8C2311yescharacteristic
309(C2×D11)⋊C8C2311yescharacteristic
310(C2×D11)⋊C8C2311yescharacteristic
311(C2×D11)⋊C8C2312yes—
312(C2×D11)⋊C8C2312yes—
313#66882C2312yes—
314#66881C2312yes—
315#66881C2312yes—
316#66881C2312yes—
317#66880C2311yescharacteristic
318#66880C2311yescharacteristic
319#66880C2312yes—
320#66872C2312yes—
321#66872C2312yes—
322#66872C2312yes—
323#66871C2312yes—
324#60763—111nomaximal, Sylow
325C23×D11—21no—
326C23×D11C2×D411yescharacteristic
327C23×D11C2×D412yes—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—22no—
333C11×#41—22no—
334C11×#41—42no—
335C11×#41—42no—
336C11×#41—48no—
337C11×#41—44no—
338C2×Q8×C11—22no—
339C2×Q8×C11—21no—
340C2×Q8×C11—22no—
341C2×Q8×C11—22no—
342C2×Q8×C11—42no—
343C2×Q8×C11—42no—
344C2×Q8×C11—44no—
345C2×Q8×C11C2×D411yescharacteristic
346C2×Q8×C11C2411yescharacteristic
347C2×Q8×C11C2412yes—
348C2×Q8×C11C2411yescharacteristic
349C2×D4×C11—22no—
350C2×D4×C11—21no—
351C2×D4×C11—21no—
352C2×D4×C11—22no—
353C2×D4×C11C2×D411yescharacteristic
354C2×D4×C11C2×D412yes—
355C2×D4×C11C2411yescharacteristic
356C2×D4×C11C2411yescharacteristic
357C22×C4×C11—22no—
358C22×C4×C11—21no—
359C22×C4×C11—21no—
360C22×C4×C11—22no—
361C22×C4×C11—21no—
362C22×C4×C11—21no—
363C22×C4×C11C2412yes—
364C22×C4×C11C2411yescharacteristic
365C2×C22⋊D11—21no—
366C2×C22⋊D11—21no—
367C2×C22⋊D11—22no—
368C2×C22⋊D11—21no—
369C2×C22⋊D11—21no—
370C2×C22⋊D11—22no—
371C2×C22⋊D11—22no—
372C2×C22⋊D11—21no—
373C2×C22⋊D11C2×D412yes—
374C2×C22⋊D11C2×D412yes—
375C2×C22⋊D11C2×D412yes—
376C22×Dic11—21no—
377C22×Dic11—22no—
378C22×Dic11—21no—
379C22×Dic11—21no—
380C22×Dic11C2×D411yescharacteristic
381C22×Dic11C2×D412yes—
382#4343—42no—
383#4343—41no—
384#4343—41no—
385Q8×D11—42no—
386Q8×D11—41no—
387Q8×D11—41no—
388#4341—42no—
389#4341—41no—
390#4341—41no—
391#4341—44no—
392#4341—44no—
393D4×D11—44no—
394D4×D11—42no—
395D4×D11—41no—
396D4×D11—41no—
397D4×D11—44no—
398D4×D11—84no—
399#4339—22no—
400#4339—22no—
401#4339—22no—
402#4339—22no—
403#4339—42no—
404#4339—42no—
405#4339—44no—
406C2×D44—21no—
407C2×D44—22no—
408C2×D44C2×D411yescharacteristic
409C2×D44C2×D412yes—
410C2×D44C2411yescharacteristic
411C2×C4×D11—21no—
412C2×C4×D11—22no—
413C2×C4×D11—21no—
414C2×C4×D11—22no—
415C2×C4×D11—21no—
416C2×C4×D11—22no—
417C2×C4×D11—22no—
418C2×C4×D11—42no—
419C2×C4×D11—42no—
420C2×C4×D11—44no—
421C2×C4×D11—82no—
422C2×C4×D11C2×D411yescharacteristic
423C2×C4×D11C2×D411yescharacteristic
424C2×C4×D11C2×D412yes—
425C2×C4×D11C2×D412yes—
426C2×C4×D11C2411yescharacteristic
427C2×C4×D11C2411yescharacteristic
428C2×C4×D11C2412yes—
429C2×Dic22—21no—
430C2×Dic22C2×D411yescharacteristic
431C2×Dic22C2×D412yes—
432C2×Dic22C2411yescharacteristic
433C11×Q16—41no—
434C11×Q16—42no—
435C11×SD16—41no—
436C11×SD16—41no—
437C11×SD16—42no—
438C11×D8—41no—
439C11×M16—22no—
440C2×C8×C11—22no—
441C2×C8×C11C2411yescharacteristic
442C2×C8×C11C2411yescharacteristic
443C2×C8×C11C2412yes—
444C11×C4⋊C4—21no—
445C11×C4⋊C4—22no—
446C11×C4⋊C4C2412yes—
447C11×C22⋊C4—22no—
448C11×C22⋊C4—22no—
449C22⋊Dic11—22no—
450C22⋊Dic11—21no—
451C22⋊Dic11—22no—
452C22⋊Dic11—21no—
453C22⋊Dic11—22no—
454C22⋊Dic11—22no—
455C22⋊Dic11—21no—
456#4326—42no—
457#4326—41no—
458#4325—42no—
459#4325—41no—
460#4324—41no—
461#4323—41no—
462(C2×D11)⋊C4—22no—
463(C2×D11)⋊C4—22no—
464(C2×D11)⋊C4—22no—
465(C2×D11)⋊C4—22no—
466(C2×D11)⋊C4—21no—
467(C2×D11)⋊C4—22no—
468(C2×D11)⋊C4—22no—
469(C2×D11)⋊C4—22no—
470(C2×D11)⋊C4—22no—
471(C2×D11)⋊C4—21no—
472(C2×D11)⋊C4—22no—
473C4⋊Dic11—22no—
474C4⋊Dic11—21no—
475C4⋊Dic11—22no—
476C4⋊Dic11—21no—
477C4⋊Dic11C2411yescharacteristic
478C4⋊Dic11C2412yes—
479C4⋊Dic11C2411yescharacteristic
480C4⋊Dic11C2412yes—
481Dic11⋊C4—22no—
482Dic11⋊C4—22no—
483Dic11⋊C4—22no—
484Dic11⋊C4—22no—
485Dic11⋊C4—21no—
486Dic11⋊C4—22no—
487Dic11⋊C4—22no—
488Dic11⋊C4—22no—
489Dic11⋊C4—21no—
490Dic11⋊C4—22no—
491Dic11⋊C4—22no—
492C4×Dic11—22no—
493C4×Dic11—21no—
494#4318—22no—
495C2×C11⋊C8—22no—
496C2×C11⋊C8C2412yes—
497C2×C11⋊C8C2411yescharacteristic
498C2×C11⋊C8C2411yescharacteristic
499#4313—42no—
500#4313—42no—
501C8×D11—42no—
502C8×D11—42no—
503#3489—111no—
504C2×#537—111no—
505#3204—112no—
506#3204—112no—
507#3201—112no—
508#3201—112no—
509#3195—112no—
510#3194—112no—
511#3190—112no—
512#3187—112no—
513#3099—111no—
514#3099—111no—
515#3092—111no—
516C2×#483—111no—
517#3063—111no—
518#3063—111no—
519#3060—111no—
520#3060—111no—
521#3013—111no—
522#3013D1111yescharacteristic, complemented
523#3007—111no—
524#3002—111no—
525#2880—111no—
526C23×C11—21no—
527C23×C11—21no—
528C23×C11C22×D412yes—
529C23×C11C22×D411yescharacteristic
530C22×D11—22no—
531C22×D11—22no—
532C22×D11—24no—
533C22×D11—21no—
534C22×D11—41no—
535C22×D11—42no—
536C22×D11—42no—
537C22×D11—42no—
538C22×D11—42no—
539C22×D11—42no—
540C22×D11C22×D412yes—
541C22×D11C22×D411yescharacteristic
542C22×D11C22×D411yescharacteristic
543Q8×C11—22no—
544Q8×C11—22no—
545Q8×C11—21no—
546Q8×C11—21no—
547Q8×C11—22no—
548Q8×C11—21no—
549Q8×C11—21no—
550Q8×C11—44no—
551Q8×C11—42no—
552D4×C11—24no—
553D4×C11—22no—
554D4×C11—21no—
555D4×C11—21no—
556D4×C11—21no—
557D4×C11—21no—
558D4×C11—44no—
559D4×C11—42no—
560D4×C11—42no—
561D4×C11—82no—
562C2×C4×C11—22no—
563C2×C4×C11—22no—
564C2×C4×C11—22no—
565C2×C4×C11—21no—
566C2×C4×C11—22no—
567C2×C4×C11—21no—
568C2×C4×C11—44no—
569C2×C4×C11—44no—
570C2×C4×C11—42no—
571C2×C4×C11—42no—
572C2×C4×C11—42no—
573C2×C4×C11—81no—
574C2×C4×C11C22×D412yes—
575C2×C4×C11C22×D411yescharacteristic
576C2×C4×C11H(5,𝔽2)12yes—
577C2×C4×C11H(5,𝔽2)12yes—
578C2×C4×C11C2511yescharacteristic
579C22⋊D11—24no—
580C22⋊D11—42no—
581C22⋊D11—42no—
582C22⋊D11—42no—
583C22⋊D11—42no—
584C22⋊D11—42no—
585C22⋊D11—42no—
586C22⋊D11—82no—
587C22⋊D11—81no—
588C22⋊D11—82no—
589C22⋊D11—82no—
590C2×Dic11—22no—
591C2×Dic11—21no—
592C2×Dic11—22no—
593C2×Dic11—21no—
594C2×Dic11—22no—
595C2×Dic11—21no—
596C2×Dic11—42no—
597C2×Dic11—42no—
598C2×Dic11—81no—
599C2×Dic11—81no—
600C2×Dic11—82no—
601C2×Dic11C22×D411yescharacteristic
602C2×Dic11C22×D411yescharacteristic
603C2×Dic11C22×D412yes—
604D44—22no—
605D44—21no—
606D44—21no—
607D44—42no—
608D44—42no—
609D44—82no—
610C4×D11—22no—
611C4×D11—22no—
612C4×D11—22no—
613C4×D11—22no—
614C4×D11—21no—
615C4×D11—21no—
616C4×D11—21no—
617C4×D11—21no—
618C4×D11—42no—
619C4×D11—42no—
620C4×D11—42no—
621C4×D11—42no—
622C4×D11—44no—
623C4×D11—42no—
624C4×D11—82no—
625Dic22—22no—
626Dic22—21no—
627Dic22—21no—
628Dic22—42no—
629Dic22—42no—
630C8×C11—21no—
631C8×C11—22no—
632C8×C11—21no—
633C11⋊C8—21no—
634C11⋊C8—22no—
635C11⋊C8—21no—
636C2×2−1+4C2×D1111yescharacteristic, complemented
637C22×#41—111no—
638C22×#41—111no—
639C2×#137—111no—
640C2×#137C2×D1111yescharacteristic, complemented
641C2×#135—111no—
642C2×#135C2×D1111yescharacteristic, complemented
643C2×#131—111no—
644C2×#131—111no—
645D4×Q8—221no—
646#548—221no—
647#547—222no—
648#547—221no—
649#546—222no—
650#546—221no—
651#537—111no—
652#537—112no—
653#537—111no—
654#537—111no—
655#537—112no—
656#537—112no—
657#537—111no—
658#537—222no—
659#537—221no—
660#537—221no—
661#537C2×D1111yescharacteristic
662#536—112no—
663#536—111no—
664#525—111no—
665#525—112no—
666C2×C22⋊Q8—111no—
667C2×C22⋊Q8—112no—
668C2×C22⋊Q8—112no—
669C2×C22⋊Q8—221no—
670C2×#121—112no—
671C2×#121—222no—
672C2×#121—221no—
673#520—111no—
674C22×C4⋊C4—111no—
675#485—112no—
676#485—112no—
677#484—112no—
678#483—112no—
679#483—112no—
680#483—112no—
681#483—112no—
682#483—112no—
683#483—112no—
684#483—112no—
685#482—112no—
686#482—112no—
687#481—112no—
688#481—112no—
689#481—112no—
690#480—112no—
691#470—112no—
692#470—112no—
693#470—112no—
694#470—112no—
695#469—112no—
696#469—112no—
697#468—112no—
698#468—112no—
699#467—112no—
700#467—112no—
701#465—112no—
702#465—112no—
703#465—112no—
704#465—112no—
705#465—112no—
706#465—112no—
707#452—112no—
708#452—111no—
709#452—112no—
710#452—111no—
711#452—112no—
712#452C2×D1112yescomplemented
713#451—112no—
714#451—112no—
715#451—111no—
716#451C2×D1112yescomplemented
717#450—111no—
718#450—112no—
719#449—112no—
720#449—111no—
721#449—111no—
722#449C2×D1112yescomplemented
723#448—112no—
724#448—111no—
725#448C2×D1112yescomplemented
726#447—111no—
727#428—111no—
728#428—111no—
729C2×#106—111no—
730C2×#106—111no—
731#417—111no—
732#417—111no—
733#417—111no—
734#417C2×D1111yescharacteristic, complemented
735#416—111no—
736#416—111no—
737C2×#103—111no—
738C2×#103C2×D1111yescharacteristic, complemented
739#408—111no—
740#408—112no—
741#408—112no—
742#408C2×D1111yescharacteristic, complemented
743#407—111no—
744#407—112no—
745C2×C22⋊C8—111no—
746C2×C22⋊C8—112no—
747C22×C11—21no—
748C22×C11—21no—
749C22×C11—22no—
750C22×C11—22no—
751C22×C11—22no—
752C22×C11—41no—
753C22×C11—41no—
754C22×C11—41no—
755C22×C11—41no—
756C22×C11—41no—
757C22×C11—41no—
758C22×C11#53412yes—
759C22×C11C23×D411yescharacteristic
760C2×D11—21no—
761C2×D11—21no—
762C2×D11—21no—
763C2×D11—22no—
764C2×D11—21no—
765C2×D11—22no—
766C2×D11—21no—
767C2×D11—22no—
768C2×D11—44no—
769C2×D11—41no—
770C2×D11—41no—
771C2×D11—41no—
772C2×D11—84no—
773C2×D11—84no—
774C2×D11#57712yes—
775C4×C11—22no—
776C4×C11—42no—
777C4×C11—41no—
778C4×C11—41no—
779C4×C11—42no—
780C4×C11#53412yes—
781C4×C11C2×H(5,𝔽2)11yescharacteristic
782C4×C11C2×H(5,𝔽2)11yescharacteristic
783Dic11—22no—
784Dic11—21no—
785Dic11—21no—
786Dic11—42no—
787Dic11—41no—
788Dic11—41no—
789Dic11—42no—
790Dic11—41no—
7912−1+4—42no—
7922−1+4—42no—
793C2×#41—21no—
794C2×#41—22no—
795C2×#41—111no—
796C2×#41—112no—
797C2×#41—111no—
798C2×#41—111no—
799C2×#41—112no—
800C2×#41—111no—
801C2×#41—111no—
802C2×#41—111no—
803C2×#41—221no—
804C2×#41—221no—
805C2×#41—442no—
806C2×#41—442no—
807C2×#41—442no—
808C2×#41—442no—
809C2×#41C22×D1111yescharacteristic
810C2×#41C22×D1111yescharacteristic
811C2×#41C22×D1112yes—
812C2×#41C22×D1111yescharacteristic
813C22×Q8—21no—
814C22×Q8—111no—
815C22×Q8—111no—
816C22×Q8C22×D1111yescharacteristic
817C22×Q8C22×D1112yes—
818C22×D4—111no—
819C22×D4—112no—
820C22×D4—111no—
821C22×D4—221no—
822C22×D4—222no—
823C23×C4—111no—
824C23×C4—112no—
825C23×C4—221no—
826C23×C4—221no—
827#137—42no—
828#137—442no—
829#135—42no—
830#135—442no—
831C2×Q16—111no—
832C2×Q16—112no—
833C2×Q16C22×D1111yescharacteristic
834C2×Q16C22×D1112yes—
835C2×SD16—111no—
836C2×SD16—112no—
837C2×SD16—111no—
838C2×SD16C22×D1111yescharacteristic
839C2×SD16C22×D1111yescharacteristic
840C2×SD16C22×D1112yes—
841C2×D8—111no—
842C2×D8C22×D1111yescharacteristic
843#131—442no—
844#131—442no—
845C2×M16—111no—
846C2×M16—112no—
847C2×M16—112no—
848C2×M16C22×D1111yescharacteristic
849C22×C8—111no—
850C22×C8—112no—
851C22×C8—112no—
852C22×C8C22×D1111yescharacteristic
853C4⋊Q8—221no—
854C4⋊Q8—222no—
855#124—221no—
856#124—222no—
857#123—222no—
858#123—222no—
859#123—222no—
860#123—221no—
861#123—222no—
862C22⋊Q8—21no—
863C22⋊Q8—112no—
864C22⋊Q8—111no—
865C22⋊Q8—112no—
866C22⋊Q8—112no—
867C22⋊Q8—112no—
868C22⋊Q8—112no—
869C22⋊Q8—111no—
870C22⋊Q8—112no—
871C22⋊Q8—112no—
872C22⋊Q8—112no—
873C22⋊Q8—222no—
874C22⋊Q8—222no—
875C22⋊Q8—222no—
876C22⋊Q8—222no—
877C22⋊Q8—221no—
878C22⋊Q8—221no—
879C22⋊Q8—221no—
880C22⋊Q8—222no—
881C22⋊Q8—221no—
882C22⋊Q8—222no—
883C22⋊Q8—221no—
884C22⋊Q8—222no—
885C22⋊Q8—221no—
886C22⋊Q8C22×D1112yes—
887#121—21no—
888#121—22no—
889#121—112no—
890#121—111no—
891#121—111no—
892#121—112no—
893#121—112no—
894#121—112no—
895#121—222no—
896#121—222no—
897#121—222no—
898#121—222no—
899#121—221no—
900#121—222no—
901#121—222no—
902#121—221no—
903#121—221no—
904#121—222no—
905#121—222no—
906#121—222no—
907#121—222no—
908#121—222no—
909#121—222no—
910#121—222no—
911#121—222no—
912#121—221no—
913#121—222no—
914#121C22×D1112yes—
915#120—221no—
916#120—222no—
917C4×Q8—221no—
918C4×D4—221no—
919C4×D4—222no—
920C4×D4—221no—
921C4×D4—222no—
922C4×D4—222no—
923C4×D4—221no—
924#117—111no—
925#117—112no—
926C2×C4⋊C4—111no—
927C2×C4⋊C4—111no—
928C2×C4⋊C4—112no—
929C2×C4⋊C4—112no—
930C2×C4⋊C4—112no—
931C2×C4⋊C4—221no—
932C2×C4⋊C4—221no—
933C2×C4⋊C4—222no—
934C2×C4⋊C4—221no—
935C2×C4⋊C4—221no—
936C2×C4⋊C4—222no—
937C2×C4⋊C4C22×D1111yescharacteristic
938C2×C22⋊C4—222no—
939C2×C22⋊C4—222no—
940C2×C22⋊C4—221no—
941C2×C22⋊C4—222no—
942#107—112no—
943#107—112no—
944#106—112no—
945#106—112no—
946#106—112no—
947#106—112no—
948#106—112no—
949#106—112no—
950#103—112no—
951#103—112no—
952#103—111no—
953#103—111no—
954#103—112no—
955#103—112no—
956#103—111no—
957#103—111no—
958#103—112no—
959#103C22×D1112yes—
960#103C22×D1112yes—
961#103C22×D1112yes—
962#102—111no—
963#102—111no—
964#102—112no—
965#102—112no—
966#102—111no—
967#102—111no—
968#102—112no—
969#102C22×D1112yes—
970C22⋊C8—112no—
971C22⋊C8—112no—
972C22⋊C8—111no—
973C22⋊C8—111no—
974C22⋊C8—112no—
975C22⋊C8—111no—
976C22⋊C8—111no—
977C22⋊C8—112no—
978C22⋊C8C22×D1112yes—
979C22⋊C8C22×D1112yes—
980C2×C11—22no—
981C2×C11—42no—
982C2×C11—81no—
983C2×C11—81no—
984C2×C11C2×#53411yescharacteristic
985C2×C11C2×#57711yescharacteristic
986C2×C11#358611yescharacteristic
987D11—22no—
988D11—41no—
989D11—42no—
990D11—81no—
991C24—111no—
992C24—112no—
993C24—221no—
994#41—22no—
995#41—22no—
996#41—22no—
997#41—22no—
998#41—22no—
999#41—22no—
1000#41—42no—
1001#41—42no—
1002#41—48no—
1003#41—44no—
1004#41—222no—
1005#41—222no—
1006#41—222no—
1007#41—222no—
1008#41—442no—
1009#41—442no—
1010#41—444no—
1011#41—444no—
1012#41—442no—
1013#41—441no—
1014#41—441no—
1015#41—444no—
1016#41—442no—
1017#41—441no—
1018#41—441no—
1019C2×Q8—22no—
1020C2×Q8—21no—
1021C2×Q8—22no—
1022C2×Q8—22no—
1023C2×Q8—42no—
1024C2×Q8—42no—
1025C2×Q8—44no—
1026C2×Q8—111no—
1027C2×Q8—112no—
1028C2×Q8—111no—
1029C2×Q8—221no—
1030C2×Q8—442no—
1031C2×Q8—441no—
1032C2×Q8—441no—
1033C2×Q8D4×D1111yescharacteristic
1034C2×Q8C23×D1111yescharacteristic
1035C2×Q8C23×D1112yes—
1036C2×Q8C23×D1111yescharacteristic
1037C2×D4—22no—
1038C2×D4—21no—
1039C2×D4—21no—
1040C2×D4—22no—
1041C2×D4—112no—
1042C2×D4—112no—
1043C2×D4—112no—
1044C2×D4—111no—
1045C2×D4—112no—
1046C2×D4—111no—
1047C2×D4—221no—
1048C2×D4—222no—
1049C2×D4—221no—
1050C2×D4—221no—
1051C2×D4—221no—
1052C2×D4—221no—
1053C2×D4—222no—
1054C2×D4—221no—
1055C2×D4—222no—
1056C2×D4—222no—
1057C2×D4—442no—
1058C2×D4—441no—
1059C2×D4—441no—
1060C2×D4—444no—
1061C2×D4—444no—
1062C2×D4—884no—
1063C2×D4D4×D1112yes—
1064C2×D4D4×D1111yescharacteristic
1065C2×D4C23×D1111yescharacteristic
1066C2×D4C23×D1111yescharacteristic
1067C22×C4—22no—
1068C22×C4—21no—
1069C22×C4—21no—
1070C22×C4—22no—
1071C22×C4—21no—
1072C22×C4—21no—
1073C22×C4—111no—
1074C22×C4—112no—
1075C22×C4—111no—
1076C22×C4—111no—
1077C22×C4—111no—
1078C22×C4—111no—
1079C22×C4—112no—
1080C22×C4—112no—
1081C22×C4—112no—
1082C22×C4—221no—
1083C22×C4—222no—
1084C22×C4—221no—
1085C22×C4—222no—
1086C22×C4—221no—
1087C22×C4—222no—
1088C22×C4—222no—
1089C22×C4—222no—
1090C22×C4—221no—
1091C22×C4—221no—
1092C22×C4—221no—
1093C22×C4—442no—
1094C22×C4—442no—
1095C22×C4—444no—
1096C22×C4—882no—
1097C22×C4C23×D1112yes—
1098C22×C4C23×D1111yescharacteristic
1099Q16—41no—
1100Q16—42no—
1101Q16—441no—
1102Q16—442no—
1103SD16—41no—
1104SD16—41no—
1105SD16—42no—
1106SD16—441no—
1107SD16—441no—
1108SD16—442no—
1109D8—41no—
1110D8—441no—
1111M16—22no—
1112M16—222no—
1113M16—442no—
1114M16—442no—
1115C2×C8—22no—
1116C2×C8—112no—
1117C2×C8—111no—
1118C2×C8—111no—
1119C2×C8—222no—
1120C2×C8—442no—
1121C2×C8—442no—
1122C2×C8C23×D1112yes—
1123C2×C8C23×D1111yescharacteristic
1124C2×C8C23×D1111yescharacteristic
1125C4⋊C4—21no—
1126C4⋊C4—22no—
1127C4⋊C4—111no—
1128C4⋊C4—112no—
1129C4⋊C4—111no—
1130C4⋊C4—112no—
1131C4⋊C4—222no—
1132C4⋊C4—222no—
1133C4⋊C4—222no—
1134C4⋊C4—221no—
1135C4⋊C4—222no—
1136C4⋊C4—222no—
1137C4⋊C4—222no—
1138C4⋊C4—222no—
1139C4⋊C4—222no—
1140C4⋊C4—222no—
1141C4⋊C4—221no—
1142C4⋊C4—221no—
1143C4⋊C4—222no—
1144C4⋊C4—221no—
1145C4⋊C4—222no—
1146C4⋊C4C23×D1112yes—
1147C22⋊C4—22no—
1148C22⋊C4—22no—
1149C22⋊C4—222no—
1150C22⋊C4—222no—
1151C22⋊C4—221no—
1152C22⋊C4—222no—
1153C22⋊C4—222no—
1154C22⋊C4—222no—
1155C22⋊C4—222no—
1156C22⋊C4—222no—
1157C22⋊C4—222no—
1158C22⋊C4—221no—
1159C22⋊C4—222no—
1160C22⋊C4—221no—
1161C22⋊C4—222no—
1162C22⋊C4—221no—
1163C22⋊C4—222no—
1164C22⋊C4—222no—
1165C22⋊C4—221no—
1166C22⋊C4—222no—
1167C42—222no—
1168C42—221no—
1169C11#6076311yescharacteristic, complemented, Sylow
1170C23—21no—
1171C23—21no—
1172C23—111no—
1173C23—112no—
1174C23—111no—
1175C23—222no—
1176C23—224no—
1177C23—222no—
1178C23—221no—
1179C23—441no—
1180C23—442no—
1181C23—442no—
1182C23—442no—
1183C23—442no—
1184C23—442no—
1185C23C2×D4×D1112yes—
1186C23C2×D4×D1111yescharacteristic
1187Q8—22no—
1188Q8—22no—
1189Q8—21no—
1190Q8—21no—
1191Q8—22no—
1192Q8—21no—
1193Q8—21no—
1194Q8—44no—
1195Q8—42no—
1196Q8—222no—
1197Q8—221no—
1198Q8—221no—
1199Q8—442no—
1200Q8—442no—
1201D4—24no—
1202D4—22no—
1203D4—21no—
1204D4—21no—
1205D4—21no—
1206D4—21no—
1207D4—44no—
1208D4—42no—
1209D4—42no—
1210D4—82no—
1211D4—224no—
1212D4—222no—
1213D4—221no—
1214D4—221no—
1215D4—442no—
1216D4—442no—
1217D4—442no—
1218D4—442no—
1219D4—442no—
1220D4—442no—
1221D4—442no—
1222D4—442no—
1223D4—882no—
1224D4—882no—
1225D4—882no—
1226D4—881no—
1227D4—882no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—44no—
1235C2×C4—44no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—81no—
1240C2×C4—112no—
1241C2×C4—111no—
1242C2×C4—111no—
1243C2×C4—222no—
1244C2×C4—222no—
1245C2×C4—222no—
1246C2×C4—222no—
1247C2×C4—222no—
1248C2×C4—221no—
1249C2×C4—221no—
1250C2×C4—221no—
1251C2×C4—221no—
1252C2×C4—221no—
1253C2×C4—222no—
1254C2×C4—221no—
1255C2×C4—222no—
1256C2×C4—221no—
1257C2×C4—442no—
1258C2×C4—442no—
1259C2×C4—442no—
1260C2×C4—444no—
1261C2×C4—442no—
1262C2×C4—442no—
1263C2×C4—442no—
1264C2×C4—442no—
1265C2×C4—882no—
1266C2×C4—881no—
1267C2×C4—881no—
1268C2×C4—882no—
1269C2×C4C2×D4×D1112yes—
1270C2×C4C2×D4×D1111yescharacteristic
1271C2×C4#6703712yes—
1272C2×C4#6703712yes—
1273C2×C4C24×D1111yescharacteristic
1274C8—21no—
1275C8—21no—
1276C8—22no—
1277C8—221no—
1278C8—221no—
1279C8—222no—
1280C22—21no—
1281C22—21no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—112no—
1292C22—221no—
1293C22—221no—
1294C22—221no—
1295C22—222no—
1296C22—221no—
1297C22—222no—
1298C22—221no—
1299C22—222no—
1300C22—444no—
1301C22—441no—
1302C22—441no—
1303C22—441no—
1304C22—884no—
1305C22—884no—
1306C22#1062312012yes—
1307C22C22×D4×D1111yescharacteristic
1308C4—22no—
1309C4—42no—
1310C4—41no—
1311C4—41no—
1312C4—42no—
1313C4—221no—
1314C4—221no—
1315C4—222no—
1316C4—442no—
1317C4—441no—
1318C4—441no—
1319C4—442no—
1320C4—441no—
1321C4#1062312012yes—
1322C4C2×#6703711yescharacteristic
1323C4C2×#6703711yescharacteristic
1324C2—22no—
1325C2—42no—
1326C2—81no—
1327C2—81no—
1328C2—222no—
1329C2—441no—
1330C2—442no—
1331C2—881no—
1332C2C2×#1062312011yescharacteristic
1333C2D11×#57711yescharacteristic
1334C2#1308340111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3013C2
socleC22×C11C23×D4
hypercenter#3013D11
hypocenterC11#60763
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3013

Complements

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

NH ≅ G/Ntype
1. #13082289C2semidirect
2. D11×#537C2semidirect
3. #13079525C2semidirect
4. #13079524C2semidirect
5. #13079502C2semidirect
6. #13079494C2semidirect
7. #13079438C2semidirect
8. #13079428C2semidirect
9. #13079395C2semidirect
10. #13079371C2semidirect
11. #13078607C2semidirect
12. #13078601C2semidirect
13. #13078537C2semidirect
14. C2×#10622418C2semidirect
15. #13078305C2semidirect
16. #13078301C2semidirect
17. #13078277C2semidirect
18. #13078274C2semidirect
19. #13077931C2semidirect
20. #13077872C2semidirect
21. #13077830C2semidirect
22. #13077064C2semidirect
23. C11×#3013C2semidirect
24. C2×C11×2−1+4C22semidirect
27. C2×C11×#137C22semidirect
28. C2×C11×#135C22semidirect
32. #10623364C22semidirect
33. #10623364C22semidirect
38. #10623358C22semidirect
41. C2×#67003C22semidirect
43. #10623347C22semidirect
44. #10623347C22semidirect
48. C2×#66995C22semidirect
49. C2×#66960C22semidirect
50. C2×#66954C22semidirect
63. C11×#452C22semidirect
64. C11×#451C22semidirect
65. C11×#449C22semidirect
66. C11×#448C22semidirect
67. C11×#417C22semidirect
68. C2×C11×#103C22semidirect
69. C11×#408C22semidirect
70. #10622852C22semidirect
71. #10622851C22semidirect
72. #10622847C22semidirect
73. #10622846C22semidirect
74. #10622845C22semidirect
75. #10622845C22semidirect
76. #10622841C22semidirect
77. #10622840C22semidirect
78. C2×#66899C22semidirect
79. #10622802C22semidirect
80. #10622802C22semidirect
81. #10622801C22semidirect
82. #10622800C22semidirect
83. #10622800C22semidirect
86. #10622787C22semidirect
87. #10622786C22semidirect
88. #10622786C22semidirect
89. #10622785C22semidirect
90. #10622784C22semidirect
91. #10622784C22semidirect
92. #10622784C22semidirect
96. #10622772C22semidirect
97. #10622771C22semidirect
99. #10622746C22semidirect
101. #10622734C22semidirect
102. #10622726C22semidirect
104. C2×#66881C22semidirect
105. #10622658C22semidirect
106. #10622656C22semidirect
107. #10622648C22semidirect
108. #10622647C22semidirect
109. #10622577C22semidirect
110. C2×#66872C22semidirect
111. #10622429C22semidirect
112. #10622429C22semidirect
113. #10622426C22semidirect
114. #10622425C22semidirect
115. #10622422C22semidirect
116. #10622420C22semidirect
117. #10622420C22semidirect
121. #10622418C22semidirect
122. #10622418C22semidirect
123. #10622395C22semidirect
124. #10622391C22semidirect
125. #10622390C22semidirect
127. #10622350C22semidirect
128. #10622348C22semidirect
129. #10622340C22semidirect
130. #10622340C22semidirect
133. #10622336C22semidirect
134. #10622334C22semidirect
522. #3013D11semidirect
636. C2×2−1+4C2×D11semidirect
640. C2×#137C2×D11semidirect
642. C2×#135C2×D11semidirect
712. #452C2×D11semidirect
716. #451C2×D11semidirect
722. #449C2×D11semidirect
725. #448C2×D11semidirect
734. #417C2×D11semidirect
738. C2×#103C2×D11semidirect
742. #408C2×D11semidirect
1169. C11#60763semidirect

Maximal subgroups

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

subgroupindex
#130822892
D11×#5372
#130795252
#130795242
#130795022
#130794942
#130794382
#130794282
#130793952
#130793712
#130786072
#130786012
#130785372
C2×#106224182
#130783052
#130783012
#130782772
#130782742
#130779312
#130778722
#130778302
#130770642
C11×#30132
#6076311