Finite Group Databasebeta

← #15624898

Subgroups — #15624898

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082289C211yesmaximal, characteristic, complemented
2#13082280C211yesmaximal, characteristic, complemented
3#13079517C212yesmaximal, complemented
4#13079502C212yesmaximal, complemented
5#13079486C212yesmaximal, complemented
6#13079467C212yesmaximal, complemented
7#13079457C212yesmaximal, complemented
8#13079449C212yesmaximal, complemented
9#13079428C212yesmaximal, complemented
10#13079420C212yesmaximal, complemented
11#13078593C211yesmaximal, characteristic, complemented
12#13078590C211yesmaximal, characteristic, complemented
13#13078581C211yesmaximal, characteristic, complemented
14#13078575C211yesmaximal, characteristic, complemented
15#13078240C211yesmaximal, characteristic, complemented
16#13078238C211yesmaximal, characteristic, complemented
17#13078221C211yesmaximal, characteristic, complemented
18C2×#10622425C211yesmaximal, characteristic, complemented
19#13077916C211yesmaximal, characteristic, complemented
20#13077902C211yesmaximal, characteristic, complemented
21#13077892C211yesmaximal, characteristic, complemented
22#13077058C211yesmaximal, characteristic, complemented
23C11×#3013C211yesmaximal, characteristic, complemented
24C2×C11×2−1+4C2211yescharacteristic, complemented
25C2×#67042C2211yescharacteristic
26C2×#41×D11C2211yescharacteristic
27C2×C11×#137C2211yescharacteristic, complemented
28C2×C11×#135C2211yescharacteristic, complemented
29C11×#537C2211yescharacteristic
30#10623364C2211yescharacteristic
31#10623364C2212yescomplemented
32#10623361C2211yescharacteristic
33#10623360—22no—
34#10623360—21no—
35#10623359C2211yescharacteristic
36#10623359C2212yescomplemented
37#10623359C2211yescharacteristic, complemented
38#10623358C2211yescharacteristic, complemented
39#10623355—21no—
40#10623355—22no—
41C2×#67002C2211yescharacteristic, complemented
42#10623348—21no—
43#10623347C2211yescharacteristic
44#10623347C2212yescomplemented
45Q8×C22⋊D11—21no—
46C2×#66999C2212yescomplemented
47C2×#66999C2211yescharacteristic, complemented
48C22×#4325C2211yescharacteristic, complemented
49C2×M16×D11C2211yescharacteristic, complemented
50C22×#4313C2211yescharacteristic, complemented
51#10623164—21no—
52#10623161—21no—
53#10623160C2212yes—
54#10623158C2212yes—
55#10623141—22no—
56#10623140—21no—
57#10623140—22no—
58#10623138C2212yes—
59D11×#121C2212yes—
60#10623130—21no—
61C2×#66948C2211yescharacteristic
62#10623035C2211yescharacteristic
63C11×#452C2212yescomplemented
64C11×#451C2212yescomplemented
65C11×#449C2212yescomplemented
66C11×#448C2212yescomplemented
67C11×#417C2211yescharacteristic, complemented
68C2×C11×#103C2211yescharacteristic, complemented
69C11×#408C2211yescharacteristic, complemented
70#10622851C2212yescomplemented
71#10622851C2212yescomplemented
72#10622847C2211yescharacteristic, complemented
73#10622846C2211yescharacteristic, complemented
74#10622846C2211yescharacteristic, complemented
75#10622845C2211yescharacteristic, complemented
76#10622840C2212yescomplemented
77#10622840C2212yescomplemented
78#10622838C2211yescharacteristic, complemented
79#10622802C2211yescharacteristic, complemented
80#10622802C2212yescomplemented
81#10622802C2211yescharacteristic, complemented
82#10622801C2212yescomplemented
83#10622800C2212yescomplemented
84#10622800C2212yescomplemented
85#10622800C2212yescomplemented
86#10622787C2211yescharacteristic, complemented
87#10622787C2212yescomplemented
88#10622787C2211yescharacteristic, complemented
89#10622787C2211yescharacteristic, complemented
90#10622787C2211yescharacteristic, complemented
91#10622785C2212yescomplemented
92#10622784C2212yescomplemented
93#10622782C2212yescomplemented
94#10622782C2212yescomplemented
95#10622782C2212yescomplemented
96#10622772C2211yescharacteristic, complemented
97#10622772C2211yescharacteristic, complemented
98#10622769C2212yescomplemented
99#10622744C2211yescharacteristic, complemented
100#10622742C2211yescharacteristic
101#10622734C2211yescharacteristic, complemented
102C2×#66885C2211yescharacteristic, complemented
103#10622723C2211yescharacteristic
104#10622719C2211yescharacteristic, complemented
105#10622658C2212yescomplemented
106#10622657C2212yescomplemented
107#10622648C2212yescomplemented
108#10622646C2212yescomplemented
109#10622577C2211yescharacteristic, complemented
110C2×#66871C2211yescharacteristic, complemented
111#10622428C2212yescomplemented
112#10622428C2212yescomplemented
113#10622427C2212yescomplemented
114#10622425C2212yescomplemented
115#10622425C2212yescomplemented
116#10622425C2212yescomplemented
117#10622425C2212yescomplemented
118#10622425C2212yescomplemented
119#10622422C2212yescomplemented
120#10622422C2212yescomplemented
121#10622420C2212yescomplemented
122#10622418C2212yescomplemented
123#10622395C2212yescomplemented
124#10622392C2212yescomplemented
125#10622388C2212yescomplemented
126#10622387C2212yescomplemented
127#10622350C2212yescomplemented
128#10622350C2212yescomplemented
129#10622349C2212yescomplemented
130#10622348C2212yescomplemented
131#10622340C2212yescomplemented
132#10622340C2212yescomplemented
133#10622339C2212yescomplemented
134#10622339C2212yescomplemented
135C11×2−1+4—42no—
136C11×2−1+4—42no—
137C2×C11×#41—22no—
138C2×C11×#41—21no—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2311yescharacteristic
141C2×C11×#41C2312yes—
142C2×C11×#41C2311yescharacteristic
143C22×Q8×C11—21no—
144C22×Q8×C11C2311yescharacteristic
145C22×Q8×C11C2312yes—
146#67042—42no—
147#67042—42no—
148#41×D11—42no—
149#41×D11—42no—
150C2×#4343D411yescharacteristic
151C2×#4343C2312yes—
152C2×Q8×D11D411yescharacteristic
153C2×#4341D411yescharacteristic
154C2×#4341D412yes—
155C2×D4×D11—22no—
156C2×D4×D11—22no—
157C2×D4×D11D411yescharacteristic
158C2×D4×D11D412yes—
159C2×D4×D11C2312yes—
160C2×#4339—21no—
161C2×#4339C2311yescharacteristic
162C2×#4339C2312yes—
163C22×D44—21no—
164C22×D44—21no—
165C22×D44C2311yescharacteristic
166C22×C4×D11C2311yescharacteristic
167C22×C4×D11C2312yes—
168C11×#137—42no—
169C11×#135—42no—
170C2×C11×Q16C2312yes—
171C2×C11×Q16C2311yescharacteristic
172C2×C11×SD16C2312yes—
173C2×C11×SD16C2311yescharacteristic
174C2×C11×SD16C2311yescharacteristic
175C2×C11×D8C2311yescharacteristic
176C2×C11×M16C2311yescharacteristic
177C22×C8×C11C2311yescharacteristic
178C11×C22⋊Q8—21no—
179C11×C22⋊Q8C2312yes—
180C11×#121—21no—
181C11×#121—22no—
182C11×#121C2312yes—
183C2×C11×C4⋊C4C2311yescharacteristic
184#67002—42no—
185#67000—21no—
186#67000—21no—
187#67000—22no—
188#66999—21no—
189#66999—22no—
190#66999—21no—
191#66999—22no—
192#66999C2312yes—
193#66999C2312yes—
194#66999C2312yes—
195#66999C2312yes—
196#66999C2311yescharacteristic
197#66999C2311yescharacteristic
198#66999C2311yescharacteristic
199#66999C2312yes—
200#66999C2311yescharacteristic
201Q8×Dic11—21no—
202#66997—21no—
203#66997—22no—
204C2×#4325—42no—
205C2×#4325C2312yes—
206C2×#4325C2312yes—
207C2×#4325C2312yes—
208#66993—21no—
209#66993—22no—
210#66992—22no—
211#66992—22no—
212#66992—22no—
213#66992—22no—
214#66991C2312yes—
215#66991C2311yescharacteristic
216#66991C2311yescharacteristic
217#66991C2311yescharacteristic
218#66991C2311yescharacteristic
219#66990—21no—
220#66990—21no—
221#66990—22no—
222#66990—22no—
223#66990—22no—
224#66988—21no—
225#66988—22no—
226#66988—21no—
227D4×Dic11—22no—
228D4×Dic11—21no—
229C2×#4323C2312yes—
230#66983—21no—
231#66983—22no—
232#66983C2312yes—
233#66983C2312yes—
234#66982—22no—
235#66982—22no—
236#66982—22no—
237C4×C22⋊D11—22no—
238C4×C22⋊D11—21no—
239C4×C22⋊D11—22no—
240C4×C22⋊D11—21no—
241C4×C22⋊D11—22no—
242C4×C22⋊D11—21no—
243C4×C22⋊D11—21no—
244C2×(C2×D11)⋊C4—21no—
245C2×(C2×D11)⋊C4—22no—
246C2×(C2×D11)⋊C4—21no—
247#66979C2311yescharacteristic
248#66979C2311yescharacteristic
249#66979C2312yes—
250C2×C4⋊Dic11C2311yescharacteristic
251C2×C4⋊Dic11C2312yes—
252#66977—21no—
253#66977—22no—
254C2×Dic11⋊C4—21no—
255C2×Dic11⋊C4—22no—
256C2×#4318C2311yescharacteristic
257C22×C11⋊C8C2311yescharacteristic
258M16×D11—42no—
259C2×#4313—42no—
260C2×#4313C2311yescharacteristic
261C2×#4313C2311yescharacteristic
262C2×#4313C2311yescharacteristic
263C2×#4313C2311yescharacteristic
264C2×#4313C2312yes—
265C2×C8×D11C2312yes—
266#66949—22no—
267#66948—22no—
268#66948—21no—
269#66948—21no—
270#66948C2312yes—
271#66948C2312yes—
272#66947—22no—
273#66946—21no—
274#66946—22no—
275#66945C2312yes—
276C4⋊C4×D11C2312yes—
277#66940—21no—
278#66938—22no—
279#66937—22no—
280#66937—22no—
281#66937—22no—
282#66935—22no—
283#66935—22no—
284(C22⋊D11)⋊C4—22no—
285C22⋊C4×D11—22no—
286C11×#103C2312yes—
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#102C2312yes—
290C11×C22⋊C8C2312yes—
291C11×C22⋊C8C2312yes—
292#66899C2312yes—
293#66899C2312yes—
294#66899C2311yescharacteristic
295#66899C2311yescharacteristic
296#66899C2312yes—
297#66899C2311yescharacteristic
298#66899C2311yescharacteristic
299#66896C2312yes—
300#66896C2311yescharacteristic
301#66896C2311yescharacteristic
302#66896C2311yescharacteristic
303#66896C2311yescharacteristic
304C22⋊(C11⋊C8)C2312yes—
305C22⋊(C11⋊C8)C2312yes—
306#66885C2312yes—
307#66885C2312yes—
308#66885C2312yes—
309#66885C2312yes—
310(C2×D11)⋊C8C2312yes—
311(C2×D11)⋊C8C2312yes—
312(C2×D11)⋊C8C2312yes—
313(C2×D11)⋊C8C2312yes—
314#66882C2312yes—
315#66882C2311yescharacteristic
316#66882C2311yescharacteristic
317#66881C2312yes—
318#66881C2311yescharacteristic
319#66881C2311yescharacteristic
320#66872C2312yes—
321#66871C2312yes—
322#66871C2312yes—
323#66871C2312yes—
324#60772—111nomaximal, Sylow
325C23×D11—21no—
326C23×D11—22no—
327C23×D11C2×D411yescharacteristic
328C23×D11C2×D412yes—
329C11×#41—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—22no—
333C11×#41—22no—
334C11×#41—22no—
335C11×#41—42no—
336C11×#41—42no—
337C11×#41—48no—
338C11×#41—44no—
339C2×Q8×C11—22no—
340C2×Q8×C11—21no—
341C2×Q8×C11—22no—
342C2×Q8×C11—22no—
343C2×Q8×C11—42no—
344C2×Q8×C11—42no—
345C2×Q8×C11—44no—
346C2×Q8×C11C2×D411yescharacteristic
347C2×Q8×C11C2411yescharacteristic
348C2×Q8×C11C2412yes—
349C2×Q8×C11C2411yescharacteristic
350C2×D4×C11—22no—
351C2×D4×C11—21no—
352C2×D4×C11—21no—
353C2×D4×C11—22no—
354C2×D4×C11C2×D412yes—
355C2×D4×C11C2×D411yescharacteristic
356C2×D4×C11C2411yescharacteristic
357C2×D4×C11C2411yescharacteristic
358C22×C4×C11—22no—
359C22×C4×C11—21no—
360C22×C4×C11—21no—
361C22×C4×C11—22no—
362C22×C4×C11—21no—
363C22×C4×C11—21no—
364C22×C4×C11C2412yes—
365C22×C4×C11C2411yescharacteristic
366C2×C22⋊D11—22no—
367C2×C22⋊D11—22no—
368C2×C22⋊D11—22no—
369C2×C22⋊D11—21no—
370C2×C22⋊D11—21no—
371C2×C22⋊D11—21no—
372C2×C22⋊D11—22no—
373C2×C22⋊D11—21no—
374C2×C22⋊D11C2×D412yes—
375C2×C22⋊D11C2×D412yes—
376C2×C22⋊D11C2×D412yes—
377C22×Dic11—22no—
378C22×Dic11—21no—
379C22×Dic11C2×D411yescharacteristic
380C22×Dic11C2×D412yes—
381#4343—42no—
382#4343—42no—
383#4343—42no—
384Q8×D11—42no—
385#4341—42no—
386#4341—44no—
387D4×D11—44no—
388D4×D11—42no—
389D4×D11—42no—
390D4×D11—42no—
391D4×D11—48no—
392D4×D11—84no—
393#4339—22no—
394#4339—22no—
395#4339—42no—
396#4339—42no—
397#4339—44no—
398C2×D44—22no—
399C2×D44—22no—
400C2×D44—22no—
401C2×D44—21no—
402C2×D44—22no—
403C2×D44—22no—
404C2×D44—44no—
405C2×D44—82no—
406C2×D44C2×D411yescharacteristic
407C2×D44C2×D412yes—
408C2×D44C2412yes—
409C2×C4×D11—22no—
410C2×C4×D11—22no—
411C2×C4×D11—22no—
412C2×C4×D11—22no—
413C2×C4×D11—42no—
414C2×C4×D11—42no—
415C2×C4×D11C2×D411yescharacteristic
416C2×C4×D11C2×D411yescharacteristic
417C2×C4×D11C2×D412yes—
418C2×C4×D11C2×D412yes—
419C2×C4×D11C2412yes—
420C2×C4×D11C2411yescharacteristic
421C2×C4×D11C2411yescharacteristic
422C2×Dic22C2×D411yescharacteristic
423C2×Dic22C2×D412yes—
424C11×Q16—41no—
425C11×Q16—42no—
426C11×SD16—41no—
427C11×SD16—41no—
428C11×SD16—42no—
429C11×D8—41no—
430C11×M16—22no—
431C2×C8×C11—22no—
432C2×C8×C11C2411yescharacteristic
433C2×C8×C11C2412yes—
434C2×C8×C11C2411yescharacteristic
435C11×C4⋊C4—21no—
436C11×C4⋊C4—22no—
437C11×C4⋊C4C2412yes—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—22no—
440C22⋊Dic11—21no—
441C22⋊Dic11—21no—
442C22⋊Dic11—22no—
443C22⋊Dic11—21no—
444C22⋊Dic11—21no—
445C22⋊Dic11—21no—
446C22⋊Dic11—22no—
447C22⋊Dic11—21no—
448#4325—42no—
449#4325—42no—
450#4325—42no—
451#4323—42no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—21no—
456(C2×D11)⋊C4—21no—
457(C2×D11)⋊C4—22no—
458(C2×D11)⋊C4—21no—
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—22no—
465(C2×D11)⋊C4—22no—
466C4⋊Dic11—22no—
467C4⋊Dic11—21no—
468C4⋊Dic11C2412yes—
469C4⋊Dic11C2411yescharacteristic
470C4⋊Dic11C2411yescharacteristic
471C4⋊Dic11C2411yescharacteristic
472C4⋊Dic11C2411yescharacteristic
473Dic11⋊C4—21no—
474Dic11⋊C4—22no—
475Dic11⋊C4—21no—
476Dic11⋊C4—22no—
477Dic11⋊C4—21no—
478Dic11⋊C4—22no—
479Dic11⋊C4—22no—
480Dic11⋊C4—22no—
481Dic11⋊C4—22no—
482Dic11⋊C4—21no—
483C4×Dic11—22no—
484C4×Dic11—21no—
485C4×Dic11—22no—
486C4×Dic11—21no—
487#4318—22no—
488C2×C11⋊C8—22no—
489C2×C11⋊C8C2411yescharacteristic
490C2×C11⋊C8C2411yescharacteristic
491C2×C11⋊C8C2412yes—
492#4313—41no—
493#4313—41no—
494#4313—41no—
495#4313—41no—
496#4313—42no—
497C8×D11—42no—
498#3489—111no—
499#3488—111no—
500#3203—112no—
501#3201—112no—
502#3200—112no—
503#3198—112no—
504#3197—112no—
505#3196—112no—
506#3194—112no—
507#3193—112no—
508#3098—111no—
509#3098—111no—
510#3097—111no—
511#3096—111no—
512#3056—111no—
513#3055—111no—
514#3054—111no—
515C2×#468—111no—
516#3013D1111yescharacteristic, complemented
517#3012—111no—
518#3010—111no—
519#3009—111no—
520#2879—111no—
521C23×C11—21no—
522C23×C11—21no—
523C23×C11C22×D412yes—
524C23×C11C22×D411yescharacteristic
525C22×D11—22no—
526C22×D11—22no—
527C22×D11—42no—
528C22×D11—41no—
529C22×D11—42no—
530C22×D11—42no—
531C22×D11—41no—
532C22×D11—44no—
533C22×D11—42no—
534C22×D11—82no—
535C22×D11—82no—
536C22×D11—81no—
537C22×D11—81no—
538C22×D11C22×D412yes—
539C22×D11C22×D411yescharacteristic
540C22×D11C22×D411yescharacteristic
541Q8×C11—22no—
542Q8×C11—22no—
543Q8×C11—21no—
544Q8×C11—21no—
545Q8×C11—22no—
546Q8×C11—21no—
547Q8×C11—21no—
548Q8×C11—44no—
549Q8×C11—42no—
550D4×C11—24no—
551D4×C11—22no—
552D4×C11—21no—
553D4×C11—21no—
554D4×C11—21no—
555D4×C11—21no—
556D4×C11—44no—
557D4×C11—42no—
558D4×C11—42no—
559D4×C11—82no—
560C2×C4×C11—22no—
561C2×C4×C11—22no—
562C2×C4×C11—22no—
563C2×C4×C11—22no—
564C2×C4×C11—21no—
565C2×C4×C11—21no—
566C2×C4×C11—44no—
567C2×C4×C11—44no—
568C2×C4×C11—42no—
569C2×C4×C11—42no—
570C2×C4×C11—42no—
571C2×C4×C11—81no—
572C2×C4×C11C22×D412yes—
573C2×C4×C11C22×D411yescharacteristic
574C2×C4×C11H(5,𝔽2)12yes—
575C2×C4×C11H(5,𝔽2)12yes—
576C2×C4×C11C2511yescharacteristic
577C22⋊D11—24no—
578C22⋊D11—42no—
579C22⋊D11—42no—
580C22⋊D11—44no—
581C22⋊D11—42no—
582C22⋊D11—42no—
583C22⋊D11—82no—
584C22⋊D11—81no—
585C22⋊D11—81no—
586C22⋊D11—82no—
587C22⋊D11—82no—
588C2×Dic11—22no—
589C2×Dic11—21no—
590C2×Dic11—21no—
591C2×Dic11—22no—
592C2×Dic11—21no—
593C2×Dic11—21no—
594C2×Dic11—42no—
595C2×Dic11—81no—
596C2×Dic11—82no—
597C2×Dic11C22×D412yes—
598C2×Dic11C22×D411yescharacteristic
599C2×Dic11C22×D411yescharacteristic
600D44—22no—
601D44—22no—
602D44—22no—
603D44—42no—
604D44—44no—
605D44—44no—
606D44—42no—
607D44—82no—
608C4×D11—22no—
609C4×D11—22no—
610C4×D11—21no—
611C4×D11—21no—
612C4×D11—21no—
613C4×D11—21no—
614C4×D11—22no—
615C4×D11—22no—
616C4×D11—42no—
617C4×D11—42no—
618C4×D11—44no—
619C4×D11—82no—
620Dic22—22no—
621Dic22—42no—
622C8×C11—22no—
623C8×C11—21no—
624C8×C11—21no—
625C11⋊C8—22no—
626C11⋊C8—21no—
627C11⋊C8—21no—
628C2×2−1+4C2×D1111yescharacteristic, complemented
629C2×H(5,𝔽2)—111no—
630C22×#41—111no—
631C2×#137C2×D1111yescharacteristic, complemented
632C2×AGL(1,ℤ/8)—111no—
633C2×#135C2×D1111yescharacteristic, complemented
634C22×SD16—111no—
635C22×M16—111no—
636C22×M16—111no—
637#550—221no—
638D4×Q8—221no—
639#548—221no—
640#548—221no—
641#547—222no—
642#547—221no—
643#546—222no—
644#546—221no—
645#546—222no—
646#546—221no—
647D42—222no—
648D42—221no—
649#537—111no—
650#537—112no—
651#537—112no—
652#537C2×D1111yescharacteristic
653#536—111no—
654#536—112no—
655#535—111no—
656#535—112no—
657#525—112no—
658#525—111no—
659#525—111no—
660#525—112no—
661C2×C22⋊Q8—112no—
662C2×C22⋊Q8—111no—
663C2×#121—112no—
664C2×#121—111no—
665#520—111no—
666#520—111no—
667#485—112no—
668#485—112no—
669#485—112no—
670#485—112no—
671#484—112no—
672#484—112no—
673#484—112no—
674#483—112no—
675#482—112no—
676#482—112no—
677#482—112no—
678#482—112no—
679#481—112no—
680#480—112no—
681#480—112no—
682#480—112no—
683#470—111no—
684#470—112no—
685#470—111no—
686#469—111no—
687#469—111no—
688#469—112no—
689#468—111no—
690#468—112no—
691#468—111no—
692#468—111no—
693#468—111no—
694#468—112no—
695#468—112no—
696#468—112no—
697#468—112no—
698#468—112no—
699#467—112no—
700#466—112no—
701#465—112no—
702#465—112no—
703#452—112no—
704#452—112no—
705#452—112no—
706#452C2×D1112yescomplemented
707#451C2×D1112yescomplemented
708#450—112no—
709#450—112no—
710#450—112no—
711#449—112no—
712#449—112no—
713#449—112no—
714#449C2×D1112yescomplemented
715#448—112no—
716#448—112no—
717#448C2×D1112yescomplemented
718#447—112no—
719#428—111no—
720#428—111no—
721#427—111no—
722C2×#107—111no—
723#419—111no—
724#418—111no—
725#417—111no—
726#417C2×D1111yescharacteristic, complemented
727#416—111no—
728#416—111no—
729C2×#103C2×D1111yescharacteristic, complemented
730C2×#102—111no—
731#408—111no—
732#408—111no—
733#408—111no—
734#408—112no—
735#408—112no—
736#408C2×D1111yescharacteristic, complemented
737#407—112no—
738#407—112no—
739C22×C11—21no—
740C22×C11—21no—
741C22×C11—22no—
742C22×C11—22no—
743C22×C11—22no—
744C22×C11—41no—
745C22×C11—41no—
746C22×C11—41no—
747C22×C11—41no—
748C22×C11—41no—
749C22×C11—41no—
750C22×C11#53412yes—
751C22×C11C23×D411yescharacteristic
752C2×D11—21no—
753C2×D11—22no—
754C2×D11—21no—
755C2×D11—21no—
756C2×D11—22no—
757C2×D11—21no—
758C2×D11—21no—
759C2×D11—21no—
760C2×D11—22no—
761C2×D11—42no—
762C2×D11—42no—
763C2×D11—42no—
764C2×D11—82no—
765C2×D11—84no—
766C2×D11—164no—
767C2×D11—162no—
768C4×C11—22no—
769C4×C11—42no—
770C4×C11—42no—
771C4×C11—41no—
772C4×C11—41no—
773C4×C11#53412yes—
774C4×C11C2×H(5,𝔽2)11yescharacteristic
775C4×C11C2×H(5,𝔽2)11yescharacteristic
776Dic11—22no—
777Dic11—21no—
778Dic11—21no—
779Dic11—41no—
780Dic11—42no—
781Dic11—41no—
782Dic11—41no—
783Dic11—41no—
7842−1+4—42no—
7852−1+4—42no—
786H(5,𝔽2)—442no—
787H(5,𝔽2)—442no—
788C2×#41—22no—
789C2×#41—21no—
790C2×#41—111no—
791C2×#41—112no—
792C2×#41—111no—
793C2×#41—111no—
794C2×#41—112no—
795C2×#41—112no—
796C2×#41—221no—
797C2×#41—442no—
798C2×#41—442no—
799C2×#41C22×D1111yescharacteristic
800C2×#41C22×D1111yescharacteristic
801C2×#41C22×D1112yes—
802C2×#41C22×D1111yescharacteristic
803C22×Q8—21no—
804C22×Q8—111no—
805C22×Q8C22×D1111yescharacteristic
806C22×Q8C22×D1112yes—
807C22×D4—111no—
808C22×D4—112no—
809C22×D4—112no—
810C22×D4—111no—
811C22×D4—221no—
812C22×D4—221no—
813C22×D4—222no—
814C22×D4—222no—
815C23×C4—111no—
816C23×C4—112no—
817#137—42no—
818AGL(1,ℤ/8)—442no—
819#135—42no—
820C2×Q16C22×D1111yescharacteristic
821C2×Q16C22×D1112yes—
822C2×SD16—112no—
823C2×SD16—112no—
824C2×SD16—112no—
825C2×SD16—442no—
826C2×SD16C22×D1111yescharacteristic
827C2×SD16C22×D1111yescharacteristic
828C2×SD16C22×D1112yes—
829C2×D8—112no—
830C2×D8C22×D1111yescharacteristic
831C2×M16—111no—
832C2×M16—111no—
833C2×M16—111no—
834C2×M16—112no—
835C2×M16—111no—
836C2×M16—111no—
837C2×M16—442no—
838C2×M16—442no—
839C2×M16C22×D1111yescharacteristic
840C22×C8—111no—
841C22×C8—112no—
842C22×C8C22×D1111yescharacteristic
843C4⋊Q8—221no—
844C4⋊Q8—222no—
845#127—222no—
846#127—221no—
847#124—222no—
848#124—221no—
849#124—222no—
850#124—221no—
851#123—222no—
852#123—222no—
853#123—222no—
854#123—222no—
855#123—221no—
856#123—221no—
857#123—222no—
858C22⋊Q8—21no—
859C22⋊Q8—111no—
860C22⋊Q8—112no—
861C22⋊Q8—112no—
862C22⋊Q8—112no—
863C22⋊Q8—112no—
864C22⋊Q8—111no—
865C22⋊Q8—112no—
866C22⋊Q8—111no—
867C22⋊Q8—111no—
868C22⋊Q8—222no—
869C22⋊Q8—221no—
870C22⋊Q8—222no—
871C22⋊Q8—221no—
872C22⋊Q8—222no—
873C22⋊Q8—221no—
874C22⋊Q8—222no—
875C22⋊Q8C22×D1112yes—
876#121—22no—
877#121—21no—
878#121—111no—
879#121—111no—
880#121—111no—
881#121—112no—
882#121—111no—
883#121—112no—
884#121—112no—
885#121—112no—
886#121—112no—
887#121—222no—
888#121—222no—
889#121—222no—
890#121—221no—
891#121—221no—
892#121—222no—
893#121—221no—
894#121—222no—
895#121—222no—
896#121—222no—
897#121—222no—
898#121—222no—
899#121C22×D1112yes—
900#120—222no—
901#120—222no—
902#120—222no—
903#120—221no—
904#120—221no—
905#120—222no—
906#120—222no—
907C4×Q8—221no—
908C4×Q8—221no—
909C4×D4—222no—
910C4×D4—222no—
911C4×D4—221no—
912C4×D4—221no—
913C4×D4—221no—
914C4×D4—222no—
915C4×D4—221no—
916C4×D4—221no—
917C4×D4—222no—
918C4×D4—222no—
919C4×D4—222no—
920C4×D4—221no—
921#117—111no—
922#117—111no—
923#117—112no—
924#117—112no—
925C2×C4⋊C4—111no—
926C2×C4⋊C4—112no—
927C2×C4⋊C4—112no—
928C2×C4⋊C4—221no—
929C2×C4⋊C4—222no—
930C2×C4⋊C4C22×D1111yescharacteristic
931C2×C22⋊C4—222no—
932C2×C22⋊C4—221no—
933C2×C22⋊C4—221no—
934C2×C22⋊C4—222no—
935#107—111no—
936#107—111no—
937#107—112no—
938#107—112no—
939#107—112no—
940#107—112no—
941#106—111no—
942#106—111no—
943#106—112no—
944#106—112no—
945#103—111no—
946#103—111no—
947#103—111no—
948#103—111no—
949#103—112no—
950#103—112no—
951#103—112no—
952#103C22×D1112yes—
953#103C22×D1112yes—
954#103C22×D1112yes—
955#102—111no—
956#102—111no—
957#102—111no—
958#102—111no—
959#102—112no—
960#102—112no—
961#102—112no—
962#102—112no—
963#102—112no—
964#102C22×D1112yes—
965C22⋊C8—112no—
966C22⋊C8—112no—
967C22⋊C8—112no—
968C22⋊C8—112no—
969C22⋊C8—112no—
970C22⋊C8—112no—
971C22⋊C8C22×D1112yes—
972C22⋊C8C22×D1112yes—
973C2×C11—22no—
974C2×C11—42no—
975C2×C11—81no—
976C2×C11—81no—
977C2×C11C2×#53411yescharacteristic
978C2×C11#358511yescharacteristic
979C2×C11#358611yescharacteristic
980D11—41no—
981D11—41no—
982D11—42no—
983D11—82no—
984C24—111no—
985C24—112no—
986C24—222no—
987C24—221no—
988#41—22no—
989#41—22no—
990#41—22no—
991#41—22no—
992#41—22no—
993#41—22no—
994#41—42no—
995#41—42no—
996#41—48no—
997#41—44no—
998#41—222no—
999#41—222no—
1000#41—442no—
1001#41—442no—
1002#41—444no—
1003#41—444no—
1004#41—442no—
1005#41—442no—
1006#41—442no—
1007#41—442no—
1008C2×Q8—22no—
1009C2×Q8—21no—
1010C2×Q8—22no—
1011C2×Q8—22no—
1012C2×Q8—42no—
1013C2×Q8—42no—
1014C2×Q8—44no—
1015C2×Q8—111no—
1016C2×Q8—112no—
1017C2×Q8—442no—
1018C2×Q8D4×D1111yescharacteristic
1019C2×Q8C23×D1111yescharacteristic
1020C2×Q8C23×D1112yes—
1021C2×Q8C23×D1111yescharacteristic
1022C2×D4—21no—
1023C2×D4—22no—
1024C2×D4—21no—
1025C2×D4—22no—
1026C2×D4—112no—
1027C2×D4—112no—
1028C2×D4—112no—
1029C2×D4—111no—
1030C2×D4—112no—
1031C2×D4—112no—
1032C2×D4—222no—
1033C2×D4—222no—
1034C2×D4—222no—
1035C2×D4—222no—
1036C2×D4—221no—
1037C2×D4—221no—
1038C2×D4—221no—
1039C2×D4—222no—
1040C2×D4—221no—
1041C2×D4—222no—
1042C2×D4—222no—
1043C2×D4—221no—
1044C2×D4—222no—
1045C2×D4—222no—
1046C2×D4—444no—
1047C2×D4—442no—
1048C2×D4—442no—
1049C2×D4—442no—
1050C2×D4—444no—
1051C2×D4—448no—
1052C2×D4—882no—
1053C2×D4—884no—
1054C2×D4D4×D1112yes—
1055C2×D4D4×D1111yescharacteristic
1056C2×D4C23×D1111yescharacteristic
1057C2×D4C23×D1111yescharacteristic
1058C22×C4—22no—
1059C22×C4—21no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—22no—
1063C22×C4—21no—
1064C22×C4—111no—
1065C22×C4—112no—
1066C22×C4—111no—
1067C22×C4—111no—
1068C22×C4—112no—
1069C22×C4—111no—
1070C22×C4—111no—
1071C22×C4—112no—
1072C22×C4—112no—
1073C22×C4—222no—
1074C22×C4—222no—
1075C22×C4—222no—
1076C22×C4—222no—
1077C22×C4—222no—
1078C22×C4—221no—
1079C22×C4—442no—
1080C22×C4—442no—
1081C22×C4C23×D1112yes—
1082C22×C4C23×D1111yescharacteristic
1083Q16—41no—
1084Q16—42no—
1085SD16—41no—
1086SD16—41no—
1087SD16—42no—
1088SD16—442no—
1089SD16—442no—
1090SD16—442no—
1091D8—41no—
1092D8—442no—
1093M16—22no—
1094M16—222no—
1095M16—441no—
1096M16—441no—
1097M16—441no—
1098M16—441no—
1099M16—442no—
1100C2×C8—22no—
1101C2×C8—111no—
1102C2×C8—111no—
1103C2×C8—112no—
1104C2×C8—222no—
1105C2×C8—442no—
1106C2×C8C23×D1112yes—
1107C2×C8C23×D1111yescharacteristic
1108C2×C8C23×D1111yescharacteristic
1109C4⋊C4—21no—
1110C4⋊C4—22no—
1111C4⋊C4—111no—
1112C4⋊C4—111no—
1113C4⋊C4—112no—
1114C4⋊C4—111no—
1115C4⋊C4—111no—
1116C4⋊C4—222no—
1117C4⋊C4—222no—
1118C4⋊C4—221no—
1119C4⋊C4—222no—
1120C4⋊C4—222no—
1121C4⋊C4—222no—
1122C4⋊C4—221no—
1123C4⋊C4—221no—
1124C4⋊C4—222no—
1125C4⋊C4—221no—
1126C4⋊C4—222no—
1127C4⋊C4—221no—
1128C4⋊C4C23×D1112yes—
1129C22⋊C4—22no—
1130C22⋊C4—22no—
1131C22⋊C4—222no—
1132C22⋊C4—222no—
1133C22⋊C4—222no—
1134C22⋊C4—221no—
1135C22⋊C4—222no—
1136C22⋊C4—222no—
1137C22⋊C4—222no—
1138C22⋊C4—222no—
1139C22⋊C4—221no—
1140C22⋊C4—221no—
1141C22⋊C4—222no—
1142C22⋊C4—221no—
1143C22⋊C4—221no—
1144C22⋊C4—221no—
1145C22⋊C4—221no—
1146C22⋊C4—222no—
1147C22⋊C4—221no—
1148C22⋊C4—221no—
1149C22⋊C4—222no—
1150C22⋊C4—221no—
1151C22⋊C4—222no—
1152C22⋊C4—222no—
1153C42—222no—
1154C42—221no—
1155C42—222no—
1156C42—221no—
1157C11#6077211yescharacteristic, complemented, Sylow
1158C23—21no—
1159C23—21no—
1160C23—111no—
1161C23—112no—
1162C23—111no—
1163C23—222no—
1164C23—222no—
1165C23—442no—
1166C23—441no—
1167C23—442no—
1168C23—441no—
1169C23—442no—
1170C23—444no—
1171C23—442no—
1172C23—881no—
1173C23—881no—
1174C23—882no—
1175C23—882no—
1176C23C2×D4×D1112yes—
1177C23C2×D4×D1111yescharacteristic
1178Q8—22no—
1179Q8—22no—
1180Q8—21no—
1181Q8—21no—
1182Q8—22no—
1183Q8—21no—
1184Q8—21no—
1185Q8—44no—
1186Q8—42no—
1187Q8—222no—
1188Q8—442no—
1189D4—24no—
1190D4—22no—
1191D4—21no—
1192D4—21no—
1193D4—21no—
1194D4—21no—
1195D4—44no—
1196D4—42no—
1197D4—42no—
1198D4—82no—
1199D4—224no—
1200D4—222no—
1201D4—222no—
1202D4—222no—
1203D4—442no—
1204D4—444no—
1205D4—444no—
1206D4—442no—
1207D4—442no—
1208D4—444no—
1209D4—442no—
1210D4—442no—
1211D4—442no—
1212D4—882no—
1213D4—882no—
1214D4—882no—
1215D4—882no—
1216D4—881no—
1217D4—881no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—81no—
1230C2×C4—112no—
1231C2×C4—111no—
1232C2×C4—111no—
1233C2×C4—222no—
1234C2×C4—222no—
1235C2×C4—222no—
1236C2×C4—221no—
1237C2×C4—221no—
1238C2×C4—221no—
1239C2×C4—221no—
1240C2×C4—222no—
1241C2×C4—222no—
1242C2×C4—221no—
1243C2×C4—221no—
1244C2×C4—222no—
1245C2×C4—221no—
1246C2×C4—221no—
1247C2×C4—442no—
1248C2×C4—442no—
1249C2×C4—444no—
1250C2×C4—442no—
1251C2×C4—882no—
1252C2×C4—881no—
1253C2×C4—882no—
1254C2×C4C2×D4×D1112yes—
1255C2×C4C2×D4×D1111yescharacteristic
1256C2×C4#6703712yes—
1257C2×C4#6703712yes—
1258C2×C4C24×D1111yescharacteristic
1259C8—21no—
1260C8—21no—
1261C8—22no—
1262C8—221no—
1263C8—221no—
1264C8—222no—
1265C22—21no—
1266C22—21no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—222no—
1277C22—221no—
1278C22—221no—
1279C22—221no—
1280C22—221no—
1281C22—222no—
1282C22—221no—
1283C22—221no—
1284C22—222no—
1285C22—442no—
1286C22—442no—
1287C22—442no—
1288C22—882no—
1289C22—884no—
1290C22—1762no—
1291C22—1764no—
1292C22#1062312012yes—
1293C22C22×D4×D1111yescharacteristic
1294C4—22no—
1295C4—42no—
1296C4—42no—
1297C4—41no—
1298C4—41no—
1299C4—221no—
1300C4—221no—
1301C4—222no—
1302C4—441no—
1303C4—442no—
1304C4—441no—
1305C4—441no—
1306C4—441no—
1307C4#1062312012yes—
1308C4C2×#6703711yescharacteristic
1309C4C2×#6703711yescharacteristic
1310C2—22no—
1311C2—42no—
1312C2—81no—
1313C2—81no—
1314C2—441no—
1315C2—442no—
1316C2—441no—
1317C2—882no—
1318C2C2×#1062312011yescharacteristic
1319C2#1308339411yescharacteristic
1320C2#1308340111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3013C2
socleC22×C11C23×D4
hypercenter#3013D11
hypocenterC11#60772
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. #13082280C2semidirect
3. #13079517C2semidirect
4. #13079502C2semidirect
5. #13079486C2semidirect
6. #13079467C2semidirect
7. #13079457C2semidirect
8. #13079449C2semidirect
9. #13079428C2semidirect
10. #13079420C2semidirect
11. #13078593C2semidirect
12. #13078590C2semidirect
13. #13078581C2semidirect
14. #13078575C2semidirect
15. #13078240C2semidirect
16. #13078238C2semidirect
17. #13078221C2semidirect
18. C2×#10622425C2semidirect
19. #13077916C2semidirect
20. #13077902C2semidirect
21. #13077892C2semidirect
22. #13077058C2semidirect
23. C11×#3013C2semidirect
24. C2×C11×2−1+4C22semidirect
27. C2×C11×#137C22semidirect
28. C2×C11×#135C22semidirect
31. #10623364C22semidirect
36. #10623359C22semidirect
37. #10623359C22semidirect
38. #10623358C22semidirect
41. C2×#67002C22semidirect
44. #10623347C22semidirect
46. C2×#66999C22semidirect
47. C2×#66999C22semidirect
48. C22×#4325C22semidirect
49. C2×M16×D11C22semidirect
50. C22×#4313C22semidirect
63. C11×#452C22semidirect
64. C11×#451C22semidirect
65. C11×#449C22semidirect
66. C11×#448C22semidirect
67. C11×#417C22semidirect
68. C2×C11×#103C22semidirect
69. C11×#408C22semidirect
70. #10622851C22semidirect
71. #10622851C22semidirect
72. #10622847C22semidirect
73. #10622846C22semidirect
74. #10622846C22semidirect
75. #10622845C22semidirect
76. #10622840C22semidirect
77. #10622840C22semidirect
78. #10622838C22semidirect
79. #10622802C22semidirect
80. #10622802C22semidirect
81. #10622802C22semidirect
82. #10622801C22semidirect
83. #10622800C22semidirect
84. #10622800C22semidirect
85. #10622800C22semidirect
86. #10622787C22semidirect
87. #10622787C22semidirect
88. #10622787C22semidirect
89. #10622787C22semidirect
90. #10622787C22semidirect
91. #10622785C22semidirect
92. #10622784C22semidirect
93. #10622782C22semidirect
94. #10622782C22semidirect
95. #10622782C22semidirect
96. #10622772C22semidirect
97. #10622772C22semidirect
98. #10622769C22semidirect
99. #10622744C22semidirect
101. #10622734C22semidirect
102. C2×#66885C22semidirect
104. #10622719C22semidirect
105. #10622658C22semidirect
106. #10622657C22semidirect
107. #10622648C22semidirect
108. #10622646C22semidirect
109. #10622577C22semidirect
110. C2×#66871C22semidirect
111. #10622428C22semidirect
112. #10622428C22semidirect
113. #10622427C22semidirect
114. #10622425C22semidirect
115. #10622425C22semidirect
116. #10622425C22semidirect
117. #10622425C22semidirect
118. #10622425C22semidirect
119. #10622422C22semidirect
120. #10622422C22semidirect
121. #10622420C22semidirect
122. #10622418C22semidirect
123. #10622395C22semidirect
124. #10622392C22semidirect
125. #10622388C22semidirect
126. #10622387C22semidirect
127. #10622350C22semidirect
128. #10622350C22semidirect
129. #10622349C22semidirect
130. #10622348C22semidirect
131. #10622340C22semidirect
132. #10622340C22semidirect
133. #10622339C22semidirect
134. #10622339C22semidirect
516. #3013D11semidirect
628. C2×2−1+4C2×D11semidirect
631. C2×#137C2×D11semidirect
633. C2×#135C2×D11semidirect
706. #452C2×D11semidirect
707. #451C2×D11semidirect
714. #449C2×D11semidirect
717. #448C2×D11semidirect
726. #417C2×D11semidirect
729. C2×#103C2×D11semidirect
736. #408C2×D11semidirect
1157. C11#60772semidirect

Maximal subgroups

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

subgroupindex
#130822892
#130822802
#130795172
#130795022
#130794862
#130794672
#130794572
#130794492
#130794282
#130794202
#130785932
#130785902
#130785812
#130785752
#130782402
#130782382
#130782212
C2×#106224252
#130779162
#130779022
#130778922
#130770582
C11×#30132
#6077211