Finite Group Databasebeta

← #15631841

Subgroups — #15631841

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082480C211yesmaximal, characteristic, complemented
2#13082390C211yesmaximal, characteristic
3#13080947C212yesmaximal, complemented
4#13080840C212yesmaximal, complemented
5#13080746C212yesmaximal, complemented
6#13080735C212yesmaximal, complemented
7#13080641C212yesmaximal, complemented
8#13080630C212yesmaximal, complemented
9#13080548C212yesmaximal, complemented
10#13080433C212yesmaximal, complemented
11#13078988C211yesmaximal, characteristic, complemented
12#13078575C211yesmaximal, characteristic, complemented
13#13078572C211yesmaximal, characteristic, complemented
14#13078400C211yesmaximal, characteristic, complemented
15#13078257C211yesmaximal, characteristic, complemented
16#13078251C211yesmaximal, characteristic, complemented
17C2×#10622776C211yesmaximal, characteristic, complemented
18#13077892C211yesmaximal, characteristic, complemented
19#137×Dic11C211yesmaximal, characteristic, complemented
20#13077356C211yesmaximal, characteristic, complemented
21#13077142C211yesmaximal, characteristic, complemented
22#13077138C211yesmaximal, characteristic, complemented
23C11×#3009C211yesmaximal, characteristic, complemented
24C2×C11×H(5,𝔽2)C2211yescharacteristic
25C2×#67042C2211yescharacteristic
26C2×C11×#137C2211yescharacteristic
27C22×C11×SD16C2211yescharacteristic, complemented
28C11×#536C2211yescharacteristic, complemented
29#10623365C2212yes—
30#10623365C2212yes—
31#10623363—21no—
32#10623363C2211yescharacteristic
33#10623361—21no—
34#10623361C2211yescharacteristic
35#10623358C2211yescharacteristic, complemented
36#41×Dic11C2211yescharacteristic
37C2×#67001C2211yescharacteristic, complemented
38#10623347C2211yescharacteristic, complemented
39C2×Q8×Dic11C2211yescharacteristic, complemented
40C22×#4325C2211yescharacteristic, complemented
41#10623336—21no—
42#10623336C2211yescharacteristic
43C2×#66993—21no—
44C2×#66993C2211yescharacteristic
45D4×C22⋊D11—22no—
46D4×C22⋊D11—22no—
47D4×C22⋊D11C2212yes—
48D4×C22⋊D11C2212yes—
49C2×#66954C2211yescharacteristic, complemented
50#10623263—21no—
51#10623252—21no—
52#10623212—21no—
53#10623202—21no—
54#10623196—22no—
55#10623180—22no—
56#10623173C2212yescomplemented
57#10623172C2212yescomplemented
58#10623170C2212yescomplemented
59#10623166C2212yescomplemented
60#10623054C2211yescharacteristic, complemented
61#10623048C2211yescharacteristic, complemented
62C11×#452C2212yescomplemented
63C11×#452C2212yescomplemented
64C11×#450C2212yescomplemented
65C11×#450C2212yescomplemented
66C11×#418C2211yescharacteristic, complemented
67C11×#416C2211yescharacteristic
68C11×#408C2211yescharacteristic, complemented
69#10622846C2211yescharacteristic
70#10622846C2212yescomplemented
71#10622845C2211yescharacteristic
72#10622845C2212yescomplemented
73#10622838C2211yescharacteristic, complemented
74#10622828C2212yescomplemented
75#10622828C2211yescharacteristic, complemented
76C2×#66896C2211yescharacteristic, complemented
77C2×#66896C2212yescomplemented
78#10622800C2212yescomplemented
79#10622800C2212yescomplemented
80#10622797C2212yescomplemented
81Q16×Dic11C2212yescomplemented
82#10622787C2212yescomplemented
83#10622787C2212yescomplemented
84#10622784C2212yescomplemented
85#10622784C2212yescomplemented
86#10622782C2212yescomplemented
87#10622782C2212yescomplemented
88#10622777C2212yescomplemented
89#10622776C2212yescomplemented
90#10622776C2212yescomplemented
91#10622776C2212yescomplemented
92#10622776C2212yescomplemented
93SD16×Dic11C2212yescomplemented
94#10622744C2211yescharacteristic, complemented
95#10622742C2211yescharacteristic, complemented
96#10622734C2211yescharacteristic, complemented
97M16×Dic11C2211yescharacteristic, complemented
98C2×#66885C2211yescharacteristic, complemented
99#10622719C2211yescharacteristic, complemented
100C2×Dic11⋊C8C2211yescharacteristic, complemented
101#10622662C2212yescomplemented
102#10622662C2212yescomplemented
103#10622661C2212yescomplemented
104#10622661C2212yescomplemented
105#10622614C2211yescharacteristic, complemented
106#10622611C2211yescharacteristic, complemented
107#10622417C2212yescomplemented
108#10622416C2212yescomplemented
109#10622412C2211yescharacteristic, complemented
110#10622409C2211yescharacteristic, complemented
111#10622407C2211yescharacteristic, complemented
112#10622404C2211yescharacteristic, complemented
113#10622397C2212yescomplemented
114#10622392C2212yescomplemented
115#10622390C2212yescomplemented
116#10622387C2212yescomplemented
117#10622383C2212yescomplemented
118D11×#102C2212yescomplemented
119#10622379C2211yescharacteristic, complemented
120#10622377C2212yescomplemented
121#10622377C2212yescomplemented
122#10622376C2211yescharacteristic, complemented
123#10622374C2211yescharacteristic, complemented
124#10622373C2212yescomplemented
125#10622373C2212yescomplemented
126#10622372C2211yescharacteristic, complemented
127#10622350C2212yescomplemented
128#10622350C2212yescomplemented
129#10622349C2212yescomplemented
130#10622348C2212yescomplemented
131#10622343C2212yescomplemented
132#10622342C2212yescomplemented
133#10622341C2212yescomplemented
134(C22⋊D11)⋊C8C2212yescomplemented
135C11×H(5,𝔽2)—24no—
136C11×H(5,𝔽2)—42no—
137C2×C11×#41—21no—
138C2×C11×#41C2312yes—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2311yescharacteristic
141C22×Q8×C11C2311yescharacteristic
142C22×D4×C11—22no—
143C22×D4×C11—21no—
144C22×D4×C11C2311yescharacteristic
145C22×D4×C11C2312yes—
146C22×C22⋊D11—22no—
147C22×C22⋊D11—22no—
148C22×C22⋊D11—21no—
149C22×C22⋊D11—21no—
150#67042—24no—
151#67042—42no—
152C2×#4343C2312yes—
153C2×D4×D11—22no—
154C2×D4×D11C2312yes—
155C2×#4339—21no—
156C2×#4339C2311yescharacteristic
157C22×D44—21no—
158C22×D44C2311yescharacteristic
159C11×#137—24no—
160C2×C11×Q16C2312yes—
161C2×C11×SD16—42no—
162C2×C11×SD16C2312yes—
163C2×C11×SD16C2312yes—
164C2×C11×SD16C2312yes—
165C2×C11×M16C2311yescharacteristic
166C22×C8×C11C2311yescharacteristic
167C11×C4⋊Q8—21no—
168C11×#124—21no—
169C11×#123—22no—
170C11×C22⋊Q8C2312yes—
171C11×C22⋊Q8C2312yes—
172C11×#117C2311yescharacteristic
173#67006—22no—
174#67006—22no—
175#67006—22no—
176#67001—42no—
177#67000—21no—
178#67000—21no—
179#67000D411yescharacteristic
180#66999C2312yes—
181#66999C2312yes—
182Q8×Dic11—21no—
183Q8×Dic11—21no—
184Q8×Dic11—21no—
185Q8×Dic11C2312yes—
186Q8×Dic11C2312yes—
187Q8×Dic11C2311yescharacteristic
188Q8×Dic11C2311yescharacteristic
189#66997—21no—
190#66997D411yescharacteristic
191C2×#4325—42no—
192C2×#4325C2312yes—
193C2×#4325C2312yes—
194#66993—21no—
195#66993—22no—
196#66993—22no—
197#66993—21no—
198#66993—21no—
199#66993—21no—
200#66993D411yescharacteristic
201#66993C2312yes—
202#66993C2312yes—
203#66992—22no—
204#66992—22no—
205#66992D412yes—
206#66992D412yes—
207#66991—22no—
208#66991—22no—
209#66991C2312yes—
210#66991C2312yes—
211#66990—22no—
212#66990—22no—
213#66990—22no—
214#66989—21no—
215#66989D411yescharacteristic
216D4×Dic11—22no—
217D4×Dic11—21no—
218D4×Dic11—21no—
219D4×Dic11—21no—
220D4×Dic11C2311yescharacteristic
221D4×Dic11C2311yescharacteristic
222#66983—22no—
223#66983—22no—
224#66983C2312yes—
225#66983C2312yes—
226#66982—22no—
227C4×C22⋊D11—22no—
228C4×C22⋊D11—22no—
229C4×C22⋊D11C2312yes—
230C4×C22⋊D11C2312yes—
231#66979—21no—
232#66979C2311yescharacteristic
233#66979C2311yescharacteristic
234#66979C2312yes—
235C2×C4⋊Dic11—21no—
236C2×C4⋊Dic11C2311yescharacteristic
237C2×C4⋊Dic11C2312yes—
238C2×C4×Dic11—21no—
239C2×C4×Dic11—21no—
240C2×C4×Dic11C2311yescharacteristic
241C2×#4318C2311yescharacteristic
242C2×#4318C2312yes—
243C22×C11⋊C8C2311yescharacteristic
244C22×C11⋊C8C2312yes—
245#66954—42no—
246C2×#4313C2312yes—
247C2×C8×D11C2312yes—
248#66951—22no—
249#66951—22no—
250#66950—22no—
251#66945—22no—
252#66945C2312yes—
253C4⋊C4×D11C2312yes—
254#66943—22no—
255#66943C2311yescharacteristic
256#66943C2311yescharacteristic
257#66942—22no—
258#66942—22no—
259#66941C2311yescharacteristic
260#66941C2311yescharacteristic
261#66940—22no—
262#66939—22no—
263#66938—22no—
264#66936—22no—
265(C22⋊D11)⋊C4—22no—
266(C22⋊D11)⋊C4—22no—
267#66932—22no—
268#66932—22no—
269#66931—21no—
270#66931—21no—
271#66931—22no—
272#66930—22no—
273C4×D44—21no—
274C4×Dic22—21no—
275C4×Dic22—21no—
276C4×Dic22—21no—
277C11×#103C2311yescharacteristic
278C11×#103C2311yescharacteristic
279C11×#102C2311yescharacteristic
280C11×#102C2312yes—
281C11×#102C2312yes—
282C11×#102C2311yescharacteristic
283C11×C22⋊C8C2312yes—
284C11×C22⋊C8C2312yes—
285#66899C2312yes—
286#66899C2312yes—
287#66899C2312yes—
288#66899C2311yescharacteristic
289#66899C2311yescharacteristic
290#66896C2312yes—
291#66896C2312yes—
292#66896C2312yes—
293#66896C2311yescharacteristic
294#66896C2311yescharacteristic
295#66896C2312yes—
296#66896C2312yes—
297#66885C2312yes—
298#66885C2312yes—
299#66885C2312yes—
300#66885C2312yes—
301(C2×D11)⋊C8C2312yes—
302(C2×D11)⋊C8C2312yes—
303#66882C2312yes—
304#66882C2311yescharacteristic
305#66882C2311yescharacteristic
306#66881C2312yes—
307#66881C2311yescharacteristic
308#66881C2311yescharacteristic
309#66879C2312yes—
310Dic11⋊C8C2311yescharacteristic
311Dic11⋊C8C2311yescharacteristic
312Dic11⋊C8C2311yescharacteristic
313Dic11⋊C8C2311yescharacteristic
314C8×Dic11C2312yes—
315#66873C2312yes—
316#66873C2312yes—
317#66872C2311yescharacteristic
318#66872C2311yescharacteristic
319#66871C2311yescharacteristic
320#66871C2311yescharacteristic
321#61206—111nomaximal, Sylow
322C24×C11—22no—
323C24×C11—21no—
324C23×D11—21no—
325C23×D11—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—24no—
330C11×#41—42no—
331C11×#41—44no—
332C11×#41#4114yes—
333C2×Q8×C11—21no—
334C2×Q8×C11—22no—
335C2×Q8×C11—22no—
336C2×Q8×C11C2×D411yescharacteristic
337C2×Q8×C11C2412yes—
338C2×Q8×C11C2411yescharacteristic
339C2×D4×C11—21no—
340C2×D4×C11—24no—
341C2×D4×C11—22no—
342C2×D4×C11—21no—
343C2×D4×C11—22no—
344C2×D4×C11—22no—
345C2×D4×C11—22no—
346C2×D4×C11—42no—
347C2×D4×C11—44no—
348C2×D4×C11—48no—
349C2×D4×C11C2×D411yescharacteristic
350C2×D4×C11C2×D412yes—
351C2×D4×C11C2412yes—
352C2×D4×C11C2411yescharacteristic
353C22×C4×C11—21no—
354C22×C4×C11—21no—
355C22×C4×C11—22no—
356C22×C4×C11C2412yes—
357C22×C4×C11C2411yescharacteristic
358C2×C22⋊D11—22no—
359C2×C22⋊D11—22no—
360C2×C22⋊D11—22no—
361C2×C22⋊D11—22no—
362C2×C22⋊D11—22no—
363C2×C22⋊D11—22no—
364C2×C22⋊D11—22no—
365C2×C22⋊D11—22no—
366C2×C22⋊D11—22no—
367C2×C22⋊D11—82no—
368C2×C22⋊D11—84no—
369C2×C22⋊D11—84no—
370C2×C22⋊D11—82no—
371C2×C22⋊D11C2×D412yes—
372C2×C22⋊D11C2×D412yes—
373C2×C22⋊D11C2×D412yes—
374C22×Dic11—21no—
375C22×Dic11—21no—
376C22×Dic11—22no—
377C22×Dic11—21no—
378C22×Dic11C2×D411yescharacteristic
379C22×Dic11C2×D411yescharacteristic
380#4343—24no—
381#4343—42no—
382D4×D11—24no—
383D4×D11—42no—
384D4×D11—48no—
385#4339—22no—
386#4339—22no—
387#4339—44no—
388C2×D44—22no—
389C2×D44—21no—
390C2×D44—22no—
391C2×D44—22no—
392C2×D44—44no—
393C2×D44C2×D411yescharacteristic
394C2×D44C2412yes—
395C2×C4×D11—22no—
396C2×C4×D11—22no—
397C2×C4×D11C2412yes—
398C2×Dic22—21no—
399C2×Dic22—21no—
400C2×Dic22C2×D411yescharacteristic
401C11×Q16—24no—
402C11×SD16—24no—
403C11×SD16—42no—
404C11×SD16—42no—
405C11×M16—22no—
406C2×C8×C11—22no—
407C2×C8×C11C2412yes—
408C2×C8×C11C2411yescharacteristic
409C2×C8×C11C2411yescharacteristic
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4C2411yescharacteristic
413C11×C4⋊C4C2411yescharacteristic
414C11×C22⋊C4—22no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—22no—
417C42×C11—21no—
418C22⋊Dic11—21no—
419C22⋊Dic11—21no—
420C22⋊Dic11—22no—
421C22⋊Dic11—22no—
422C22⋊Dic11—21no—
423C22⋊Dic11—22no—
424C22⋊Dic11—21no—
425C22⋊Dic11C2×D412yes—
426C22⋊Dic11C2×D412yes—
427#4325—42no—
428#4325—42no—
429(C2×D11)⋊C4—22no—
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—22no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4C2×D412yes—
435(C2×D11)⋊C4C2×D412yes—
436C4⋊Dic11—21no—
437C4⋊Dic11—21no—
438C4⋊Dic11—22no—
439C4⋊Dic11—22no—
440C4⋊Dic11—21no—
441C4⋊Dic11—21no—
442C4⋊Dic11—21no—
443C4⋊Dic11—22no—
444C4⋊Dic11C2411yescharacteristic
445C4⋊Dic11C2411yescharacteristic
446C4⋊Dic11C2411yescharacteristic
447C4⋊Dic11C2411yescharacteristic
448C4⋊Dic11C2412yes—
449Dic11⋊C4—21no—
450Dic11⋊C4—21no—
451Dic11⋊C4—22no—
452Dic11⋊C4—21no—
453Dic11⋊C4—21no—
454Dic11⋊C4—22no—
455Dic11⋊C4—22no—
456Dic11⋊C4C2×D412yes—
457Dic11⋊C4C2×D412yes—
458C4×Dic11—22no—
459C4×Dic11—22no—
460C4×Dic11—22no—
461C4×Dic11—21no—
462C4×Dic11—21no—
463C4×Dic11—21no—
464C4×Dic11—22no—
465C4×Dic11—21no—
466C4×Dic11C2×D411yescharacteristic
467C4×Dic11C2×D411yescharacteristic
468C4×Dic11C2411yescharacteristic
469C4×Dic11C2411yescharacteristic
470#4318—22no—
471#4318—42no—
472C2×C11⋊C8—22no—
473C2×C11⋊C8—42no—
474C2×C11⋊C8C2411yescharacteristic
475C2×C11⋊C8C2411yescharacteristic
476C2×C11⋊C8C2412yes—
477#4313—42no—
478C8×D11—42no—
479#3507—111no—
480#3498—111no—
481#3333—112no—
482#3324—112no—
483#3317—112no—
484#3317—112no—
485#3310—112no—
486#3310—112no—
487#3304—112no—
488#3295—112no—
489#3138—111no—
490#3096—111no—
491#3096—111no—
492#3076—111no—
493#3057—111no—
494#3057—111no—
495C2×#460—111no—
496#3009—111no—
497#3009D1111yescharacteristic, complemented
498C4×#137—111no—
499#2935—111no—
500#2897—111no—
501#2897—111no—
502C23×C11—21no—
503C23×C11—22no—
504C23×C11—44no—
505C23×C11—42no—
506C23×C11—81no—
507C23×C11—81no—
508C23×C11—82no—
509C23×C11—82no—
510C23×C11C22×D412yes—
511C23×C11C22×D411yescharacteristic
512C22×D11—22no—
513C22×D11—44no—
514C22×D11—42no—
515C22×D11—82no—
516C22×D11—82no—
517C22×D11—81no—
518C22×D11—81no—
519C22×D11C22×D412yes—
520Q8×C11—22no—
521Q8×C11—21no—
522Q8×C11—22no—
523Q8×C11—22no—
524Q8×C11—42no—
525Q8×C11C2×#4112yes—
526D4×C11—24no—
527D4×C11—24no—
528D4×C11—22no—
529D4×C11—22no—
530D4×C11—21no—
531D4×C11—22no—
532D4×C11—44no—
533D4×C11—44no—
534D4×C11—42no—
535D4×C11C2×#4112yes—
536C2×C4×C11—21no—
537C2×C4×C11—24no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—21no—
542C2×C4×C11—21no—
543C2×C4×C11—44no—
544C2×C4×C11—42no—
545C2×C4×C11C22×D412yes—
546C2×C4×C11C22×D411yescharacteristic
547C2×C4×C11C2×#4112yes—
548C2×C4×C11H(5,𝔽2)12yes—
549C2×C4×C11C2511yescharacteristic
550C22⋊D11—24no—
551C22⋊D11—24no—
552C22⋊D11—42no—
553C22⋊D11—44no—
554C22⋊D11—44no—
555C22⋊D11—44no—
556C22⋊D11—82no—
557C22⋊D11—82no—
558C22⋊D11—82no—
559C22⋊D11—82no—
560C22⋊D11—82no—
561C22⋊D11—82no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—21no—
565C2×Dic11—21no—
566C2×Dic11—21no—
567C2×Dic11—21no—
568C2×Dic11—41no—
569C2×Dic11—42no—
570C2×Dic11—42no—
571C2×Dic11—82no—
572C2×Dic11—81no—
573C2×Dic11C22×D411yescharacteristic
574C2×Dic11C22×D411yescharacteristic
575C2×Dic11C22×D412yes—
576C2×Dic11C22×D411yescharacteristic
577C2×Dic11C22×D411yescharacteristic
578D44—22no—
579D44—22no—
580D44—22no—
581D44—44no—
582D44—42no—
583C4×D11—22no—
584C4×D11—22no—
585C4×D11—44no—
586C4×D11—82no—
587Dic22—22no—
588Dic22—42no—
589Dic22—81no—
590C8×C11—22no—
591C8×C11—21no—
592C8×C11—21no—
593C11⋊C8—22no—
594C11⋊C8—21no—
595C11⋊C8—21no—
596C2×H(5,𝔽2)—111no—
597C2×H(5,𝔽2)C2×D1111yescharacteristic
598C2×#137C2×D1111yescharacteristic
599C22×SD16—111no—
600C22×SD16C2×D1111yescharacteristic, complemented
601C2×#131—111no—
602C2×#131—111no—
603#559—221no—
604#557—221no—
605#556—112no—
606#556—221no—
607#556—221no—
608#554—112no—
609#552—112no—
610#552—112no—
611#550—112no—
612#550—112no—
613D42—112no—
614D42—112no—
615D42—222no—
616D42—222no—
617#539—222no—
618#536—111no—
619#536C2×D1111yescharacteristic, complemented
620#535—111no—
621#535—111no—
622#535—221no—
623#535—221no—
624#533—111no—
625#532—111no—
626#532—221no—
627C2×#127—111no—
628C2×#127—221no—
629#529—222no—
630#520—111no—
631#520—111no—
632C4×#41—111no—
633C2×C4×Q8—111no—
634#490—112no—
635#490—112no—
636#486—112no—
637#486—112no—
638#482—112no—
639#482—112no—
640#482—112no—
641#482—112no—
642#481—112no—
643#481—112no—
644#480—112no—
645#480—112no—
646#479—111no—
647#479—111no—
648#478—111no—
649#478—111no—
650#477—111no—
651#476—111no—
652#475—111no—
653#474—111no—
654#468—112no—
655#468—112no—
656#468—112no—
657#468—112no—
658#465—112no—
659#465—112no—
660#465—112no—
661#465—112no—
662#460—112no—
663#460—112no—
664#460—112no—
665#460—112no—
666#452—112no—
667#452—112no—
668#452C2×D1112yescomplemented
669#452C2×D1112yescomplemented
670#450—112no—
671#450—112no—
672#450C2×D1112yescomplemented
673#450C2×D1112yescomplemented
674#441—112no—
675#440—112no—
676C4×Q16—112no—
677C4×SD16—112no—
678#436—112no—
679#435—112no—
680#435—112no—
681C8×D4—112no—
682#428—111no—
683#427—111no—
684#427—111no—
685C2×C4⋊C8—111no—
686#419—111no—
687#418—111no—
688#418—112no—
689#418—111no—
690#418—111no—
691#418—112no—
692#418C2×D1111yescharacteristic, complemented
693#417—112no—
694#417—111no—
695#417—112no—
696#416—111no—
697#416—112no—
698#416—112no—
699#416C2×D1111yescharacteristic
700C2×#102—111no—
701C2×#102—112no—
702C2×#102—111no—
703C2×#102—112no—
704#408—111no—
705#408C2×D1111yescharacteristic, complemented
706C4×M16—111no—
707C22×C11—21no—
708C22×C11—21no—
709C22×C11—22no—
710C22×C11—22no—
711C22×C11—22no—
712C22×C11—22no—
713C22×C11—41no—
714C22×C11—41no—
715C22×C11—42no—
716C22×C11—42no—
717C22×C11—42no—
718C22×C11—162no—
719C22×C11—164no—
720C22×C11#54612yes—
721C22×C11C23×D411yescharacteristic
722C2×D11—22no—
723C2×D11—22no—
724C2×D11—22no—
725C2×D11—42no—
726C2×D11—42no—
727C2×D11—42no—
728C2×D11—164no—
729C2×D11—162no—
730C4×C11—22no—
731C4×C11—22no—
732C4×C11—41no—
733C4×C11—42no—
734C4×C11—41no—
735C4×C11#54612yes—
736C4×C11C22×#4111yescharacteristic
737C4×C11C2×H(5,𝔽2)11yescharacteristic
738Dic11—21no—
739Dic11—21no—
740Dic11—22no—
741Dic11—21no—
742Dic11—41no—
743Dic11—42no—
744Dic11—41no—
745Dic11—41no—
746Dic11—41no—
747Dic11#57712yes—
748H(5,𝔽2)—24no—
749H(5,𝔽2)—42no—
750H(5,𝔽2)—224no—
751H(5,𝔽2)—442no—
752C2×#41—21no—
753C2×#41—111no—
754C2×#41—112no—
755C2×#41—221no—
756C2×#41C22×D1112yes—
757C2×#41C22×D1111yescharacteristic
758C2×#41C22×D1111yescharacteristic
759C22×Q8C22×D1111yescharacteristic
760C22×D4—21no—
761C22×D4—22no—
762C22×D4—112no—
763C22×D4—111no—
764C22×D4—221no—
765C22×D4—221no—
766C22×D4—221no—
767C22×D4—222no—
768C22×D4—222no—
769C22×D4—222no—
770C22×D4C22×D1111yescharacteristic
771C22×D4C22×D1112yes—
772#137—24no—
773C2×Q16C22×D1112yes—
774C2×SD16—42no—
775C2×SD16—112no—
776C2×SD16—112no—
777C2×SD16—442no—
778C2×SD16C22×D1112yes—
779C2×SD16C22×D1112yes—
780C2×SD16C22×D1112yes—
781#131—442no—
782#131—442no—
783C2×M16—111no—
784C2×M16—112no—
785C2×M16—112no—
786C2×M16C22×D1111yescharacteristic
787C22×C8—111no—
788C22×C8—112no—
789C22×C8—112no—
790C22×C8C22×D1111yescharacteristic
791C4⋊Q8—21no—
792C4⋊Q8—111no—
793C4⋊Q8—111no—
794C4⋊Q8—111no—
795C4⋊Q8—221no—
796#127—111no—
797#127—112no—
798#127—112no—
799#127—221no—
800#127—221no—
801#127—221no—
802#127—222no—
803#127—222no—
804#127—221no—
805#126—222no—
806#126—222no—
807#126—222no—
808#126—222no—
809#125—111no—
810#125—111no—
811#125—222no—
812#125—222no—
813#125—222no—
814#124—21no—
815#124—111no—
816#124—111no—
817#124—222no—
818#124—221no—
819#124—221no—
820#124—221no—
821#123—22no—
822#123—222no—
823#123—222no—
824#123—222no—
825C22⋊Q8—112no—
826C22⋊Q8—112no—
827C22⋊Q8—222no—
828C22⋊Q8—221no—
829C22⋊Q8—221no—
830C22⋊Q8—222no—
831C22⋊Q8C22×D1112yes—
832C22⋊Q8C22×D1112yes—
833#121—112no—
834#121—112no—
835#121—112no—
836#121—112no—
837#121—112no—
838#121—112no—
839#121—222no—
840#121—222no—
841#121—222no—
842#121—222no—
843#121—222no—
844#121—222no—
845#120—222no—
846#120—222no—
847#120—222no—
848#120—222no—
849#120—222no—
850#120—222no—
851C4×Q8—112no—
852C4×Q8—112no—
853C4×Q8—111no—
854C4×Q8—111no—
855C4×Q8—221no—
856C4×Q8—221no—
857C4×Q8—221no—
858C4×Q8—221no—
859C4×Q8—221no—
860C4×Q8—222no—
861C4×Q8—221no—
862C4×D4—112no—
863C4×D4—112no—
864C4×D4—111no—
865C4×D4—111no—
866C4×D4—221no—
867C4×D4—222no—
868C4×D4—222no—
869C4×D4—222no—
870C4×D4—222no—
871C4×D4—221no—
872C4×D4—221no—
873C4×D4—222no—
874C4×D4—221no—
875#117—111no—
876#117—111no—
877#117—112no—
878#117—112no—
879#117—221no—
880#117—222no—
881#117—222no—
882#117C22×D1111yescharacteristic
883C2×C4⋊C4—111no—
884C2×C4⋊C4—112no—
885C2×C4⋊C4—112no—
886C2×C4⋊C4—221no—
887C2×C42—111no—
888C2×C42—221no—
889C2×C42—221no—
890#107—111no—
891#107—111no—
892#107—112no—
893#107—111no—
894#107—111no—
895#106—111no—
896#106—111no—
897#106—112no—
898#106—111no—
899#106—111no—
900C4⋊C8—111no—
901C4⋊C8—111no—
902C4⋊C8—111no—
903C4⋊C8—111no—
904#103—111no—
905#103—112no—
906#103—111no—
907#103—112no—
908#103—112no—
909#103C22×D1111yescharacteristic
910#103C22×D1111yescharacteristic
911#102—111no—
912#102—112no—
913#102—112no—
914#102—112no—
915#102—112no—
916#102—111no—
917#102—112no—
918#102—112no—
919#102—112no—
920#102—112no—
921#102—112no—
922#102—112no—
923#102—112no—
924#102C22×D1111yescharacteristic
925#102C22×D1111yescharacteristic
926#102C22×D1112yes—
927#102C22×D1112yes—
928C22⋊C8—112no—
929C22⋊C8—112no—
930C22⋊C8C22×D1112yes—
931C22⋊C8C22×D1112yes—
932#97—112no—
933C4×C8—112no—
934C2×C11—22no—
935C2×C11—42no—
936C2×C11—42no—
937C2×C11—82no—
938C2×C11C2×#54611yescharacteristic
939C2×C11C2×#57711yescharacteristic
940C2×C11#358511yescharacteristic
941D11—42no—
942D11—82no—
943C24—22no—
944C24—21no—
945C24—222no—
946C24—221no—
947#41—22no—
948#41—22no—
949#41—22no—
950#41—24no—
951#41—42no—
952#41—44no—
953#41—222no—
954#41—222no—
955#41—224no—
956#41—444no—
957#41—442no—
958#41#434114yes—
959C2×Q8—21no—
960C2×Q8—22no—
961C2×Q8—22no—
962C2×Q8—111no—
963C2×Q8—221no—
964C2×Q8—221no—
965C2×Q8D4×D1111yescharacteristic
966C2×Q8C23×D1112yes—
967C2×Q8C23×D1111yescharacteristic
968C2×D4—21no—
969C2×D4—24no—
970C2×D4—22no—
971C2×D4—22no—
972C2×D4—21no—
973C2×D4—22no—
974C2×D4—22no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—48no—
978C2×D4—112no—
979C2×D4—112no—
980C2×D4—112no—
981C2×D4—111no—
982C2×D4—112no—
983C2×D4—222no—
984C2×D4—222no—
985C2×D4—222no—
986C2×D4—222no—
987C2×D4—222no—
988C2×D4—222no—
989C2×D4—224no—
990C2×D4—222no—
991C2×D4—222no—
992C2×D4—222no—
993C2×D4—222no—
994C2×D4—221no—
995C2×D4—222no—
996C2×D4—222no—
997C2×D4—444no—
998C2×D4—442no—
999C2×D4—448no—
1000C2×D4—882no—
1001C2×D4—884no—
1002C2×D4—882no—
1003C2×D4—884no—
1004C2×D4D4×D1112yes—
1005C2×D4D4×D1111yescharacteristic
1006C2×D4C23×D1112yes—
1007C2×D4C23×D1111yescharacteristic
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—22no—
1011C22×C4—111no—
1012C22×C4—111no—
1013C22×C4—112no—
1014C22×C4—222no—
1015C22×C4—222no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—221no—
1019C22×C4—222no—
1020C22×C4C23×D1112yes—
1021C22×C4C23×D1111yescharacteristic
1022Q16—24no—
1023SD16—24no—
1024SD16—42no—
1025SD16—42no—
1026SD16—442no—
1027SD16—442no—
1028M16—22no—
1029M16—222no—
1030M16—442no—
1031M16—442no—
1032C2×C8—22no—
1033C2×C8—112no—
1034C2×C8—111no—
1035C2×C8—111no—
1036C2×C8—222no—
1037C2×C8—442no—
1038C2×C8—442no—
1039C2×C8C23×D1112yes—
1040C2×C8C23×D1111yescharacteristic
1041C2×C8C23×D1111yescharacteristic
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—112no—
1045C4⋊C4—112no—
1046C4⋊C4—112no—
1047C4⋊C4—111no—
1048C4⋊C4—111no—
1049C4⋊C4—111no—
1050C4⋊C4—111no—
1051C4⋊C4—222no—
1052C4⋊C4—222no—
1053C4⋊C4—222no—
1054C4⋊C4—221no—
1055C4⋊C4—221no—
1056C4⋊C4—221no—
1057C4⋊C4—221no—
1058C4⋊C4—222no—
1059C4⋊C4—221no—
1060C4⋊C4—222no—
1061C4⋊C4—221no—
1062C4⋊C4—221no—
1063C4⋊C4—221no—
1064C4⋊C4—221no—
1065C4⋊C4—222no—
1066C4⋊C4C23×D1111yescharacteristic
1067C4⋊C4C23×D1111yescharacteristic
1068C22⋊C4—22no—
1069C22⋊C4—21no—
1070C22⋊C4—22no—
1071C22⋊C4—112no—
1072C22⋊C4—112no—
1073C22⋊C4—112no—
1074C22⋊C4—112no—
1075C22⋊C4—222no—
1076C22⋊C4—222no—
1077C22⋊C4—222no—
1078C22⋊C4—221no—
1079C22⋊C4—221no—
1080C22⋊C4—222no—
1081C22⋊C4—222no—
1082C22⋊C4—221no—
1083C22⋊C4—221no—
1084C22⋊C4—222no—
1085C22⋊C4—222no—
1086C22⋊C4—222no—
1087C42—21no—
1088C42—111no—
1089C42—111no—
1090C42—111no—
1091C42—111no—
1092C42—222no—
1093C42—221no—
1094C42—221no—
1095C42—222no—
1096C42—222no—
1097C42—221no—
1098C42—222no—
1099C42—221no—
1100C11#6120611yescharacteristic, complemented, Sylow
1101C23—21no—
1102C23—22no—
1103C23—44no—
1104C23—42no—
1105C23—81no—
1106C23—81no—
1107C23—82no—
1108C23—82no—
1109C23—112no—
1110C23—222no—
1111C23—444no—
1112C23—442no—
1113C23—881no—
1114C23—881no—
1115C23—882no—
1116C23—882no—
1117C23C2×D4×D1112yes—
1118C23C2×D4×D1111yescharacteristic
1119Q8—22no—
1120Q8—21no—
1121Q8—22no—
1122Q8—22no—
1123Q8—42no—
1124Q8—222no—
1125Q8—442no—
1126Q8—881no—
1127Q8C2×#434112yes—
1128D4—24no—
1129D4—24no—
1130D4—22no—
1131D4—22no—
1132D4—21no—
1133D4—22no—
1134D4—44no—
1135D4—44no—
1136D4—42no—
1137D4—224no—
1138D4—224no—
1139D4—222no—
1140D4—222no—
1141D4—222no—
1142D4—444no—
1143D4—444no—
1144D4—442no—
1145D4—444no—
1146D4—444no—
1147D4—442no—
1148D4—882no—
1149D4—882no—
1150D4—882no—
1151D4—882no—
1152D4—882no—
1153D4—882no—
1154D4C2×#434112yes—
1155C2×C4—21no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—44no—
1163C2×C4—42no—
1164C2×C4—111no—
1165C2×C4—111no—
1166C2×C4—111no—
1167C2×C4—111no—
1168C2×C4—112no—
1169C2×C4—222no—
1170C2×C4—222no—
1171C2×C4—222no—
1172C2×C4—222no—
1173C2×C4—221no—
1174C2×C4—221no—
1175C2×C4—221no—
1176C2×C4—221no—
1177C2×C4—444no—
1178C2×C4—442no—
1179C2×C4—441no—
1180C2×C4—442no—
1181C2×C4—882no—
1182C2×C4—881no—
1183C2×C4—882no—
1184C2×C4C2×D4×D1112yes—
1185C2×C4C2×D4×D1111yescharacteristic
1186C2×C4C2×#434112yes—
1187C2×C4#6703712yes—
1188C2×C4C24×D1111yescharacteristic
1189C8—22no—
1190C8—21no—
1191C8—21no—
1192C8—221no—
1193C8—221no—
1194C8—222no—
1195C22—21no—
1196C22—21no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—41no—
1202C22—41no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—162no—
1207C22—164no—
1208C22—222no—
1209C22—222no—
1210C22—222no—
1211C22—442no—
1212C22—442no—
1213C22—442no—
1214C22—1762no—
1215C22—1764no—
1216C22#1062312212yes—
1217C22C22×D4×D1111yescharacteristic
1218C4—22no—
1219C4—22no—
1220C4—41no—
1221C4—42no—
1222C4—41no—
1223C4—112no—
1224C4—221no—
1225C4—221no—
1226C4—222no—
1227C4—221no—
1228C4—441no—
1229C4—442no—
1230C4—441no—
1231C4—441no—
1232C4—441no—
1233C4#1062312212yes—
1234C4C22×#434111yescharacteristic
1235C4C2×#6703711yescharacteristic
1236C2—22no—
1237C2—42no—
1238C2—42no—
1239C2—82no—
1240C2—442no—
1241C2—882no—
1242C2C2×#1062312211yescharacteristic
1243C2D11×#57711yescharacteristic
1244C2#1308339411yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3009C2
socleC22×C11C23×D4
prime radical#13082390C2
hypercenter#3009D11
hypocenterC11#61206
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3009

Complements

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

NH ≅ G/Ntype
1. #13082480C2semidirect
3. #13080947C2semidirect
4. #13080840C2semidirect
5. #13080746C2semidirect
6. #13080735C2semidirect
7. #13080641C2semidirect
8. #13080630C2semidirect
9. #13080548C2semidirect
10. #13080433C2semidirect
11. #13078988C2semidirect
12. #13078575C2semidirect
13. #13078572C2semidirect
14. #13078400C2semidirect
15. #13078257C2semidirect
16. #13078251C2semidirect
17. C2×#10622776C2semidirect
18. #13077892C2semidirect
19. #137×Dic11C2semidirect
20. #13077356C2semidirect
21. #13077142C2semidirect
22. #13077138C2semidirect
23. C11×#3009C2semidirect
27. C22×C11×SD16C22semidirect
28. C11×#536C22semidirect
35. #10623358C22semidirect
37. C2×#67001C22semidirect
38. #10623347C22semidirect
39. C2×Q8×Dic11C22semidirect
40. C22×#4325C22semidirect
49. C2×#66954C22semidirect
56. #10623173C22semidirect
57. #10623172C22semidirect
58. #10623170C22semidirect
59. #10623166C22semidirect
60. #10623054C22semidirect
61. #10623048C22semidirect
62. C11×#452C22semidirect
63. C11×#452C22semidirect
64. C11×#450C22semidirect
65. C11×#450C22semidirect
66. C11×#418C22semidirect
68. C11×#408C22semidirect
70. #10622846C22semidirect
72. #10622845C22semidirect
73. #10622838C22semidirect
74. #10622828C22semidirect
75. #10622828C22semidirect
76. C2×#66896C22semidirect
77. C2×#66896C22semidirect
78. #10622800C22semidirect
79. #10622800C22semidirect
80. #10622797C22semidirect
81. Q16×Dic11C22semidirect
82. #10622787C22semidirect
83. #10622787C22semidirect
84. #10622784C22semidirect
85. #10622784C22semidirect
86. #10622782C22semidirect
87. #10622782C22semidirect
88. #10622777C22semidirect
89. #10622776C22semidirect
90. #10622776C22semidirect
91. #10622776C22semidirect
92. #10622776C22semidirect
93. SD16×Dic11C22semidirect
94. #10622744C22semidirect
95. #10622742C22semidirect
96. #10622734C22semidirect
97. M16×Dic11C22semidirect
98. C2×#66885C22semidirect
99. #10622719C22semidirect
100. C2×Dic11⋊C8C22semidirect
101. #10622662C22semidirect
102. #10622662C22semidirect
103. #10622661C22semidirect
104. #10622661C22semidirect
105. #10622614C22semidirect
106. #10622611C22semidirect
107. #10622417C22semidirect
108. #10622416C22semidirect
109. #10622412C22semidirect
110. #10622409C22semidirect
111. #10622407C22semidirect
112. #10622404C22semidirect
113. #10622397C22semidirect
114. #10622392C22semidirect
115. #10622390C22semidirect
116. #10622387C22semidirect
117. #10622383C22semidirect
118. D11×#102C22semidirect
119. #10622379C22semidirect
120. #10622377C22semidirect
121. #10622377C22semidirect
122. #10622376C22semidirect
123. #10622374C22semidirect
124. #10622373C22semidirect
125. #10622373C22semidirect
126. #10622372C22semidirect
127. #10622350C22semidirect
128. #10622350C22semidirect
129. #10622349C22semidirect
130. #10622348C22semidirect
131. #10622343C22semidirect
132. #10622342C22semidirect
133. #10622341C22semidirect
134. (C22⋊D11)⋊C8C22semidirect
497. #3009D11semidirect
600. C22×SD16C2×D11semidirect
619. #536C2×D11semidirect
668. #452C2×D11semidirect
669. #452C2×D11semidirect
672. #450C2×D11semidirect
673. #450C2×D11semidirect
692. #418C2×D11semidirect
705. #408C2×D11semidirect
1100. C11#61206semidirect

Maximal subgroups

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

subgroupindex
#130824802
#130823902
#130809472
#130808402
#130807462
#130807352
#130806412
#130806302
#130805482
#130804332
#130789882
#130785752
#130785722
#130784002
#130782572
#130782512
C2×#106227762
#130778922
#137×Dic112
#130773562
#130771422
#130771382
C11×#30092
#6120611