Finite Group Databasebeta

← #15622671

Subgroups — #15622671

Order 2816.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082353C211yesmaximal, characteristic, complemented
2#13081819C211yesmaximal, characteristic, complemented
3#13078901C212yesmaximal, complemented
4#13078853C212yesmaximal, complemented
5#13078846C212yesmaximal, complemented
6#13078801C212yesmaximal, complemented
7#13078760C212yesmaximal, complemented
8#13078726C212yesmaximal, complemented
9#13078669C212yesmaximal, complemented
10#13078635C212yesmaximal, complemented
11#13078545C211yesmaximal, characteristic, complemented
12C2×#10622350C211yesmaximal, characteristic, complemented
13#13078476C211yesmaximal, characteristic, complemented
14#13078465C211yesmaximal, characteristic, complemented
15#13078153C211yesmaximal, characteristic, complemented
16#13078153C211yesmaximal, characteristic, complemented
17#13077868C211yesmaximal, characteristic, complemented
18#13077500C211yesmaximal, characteristic, complemented
19#13077492C211yesmaximal, characteristic, complemented
20#13077451C211yesmaximal, characteristic, complemented
21#13077451C211yesmaximal, characteristic, complemented
22#13077270C211yesmaximal, characteristic, complemented
23C11×#3002C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C2×C11×#135C2211yescharacteristic
26C2×C11×#135C2211yescharacteristic
27C11×#525C2211yescharacteristic
28#10623361C2211yescharacteristic, complemented
29#10623358—21no—
30#10623358—21no—
31#10623358C2211yescharacteristic
32#10623358C2211yescharacteristic
33#10623358C2211yescharacteristic
34#10623358C2211yescharacteristic
35#10623358C2211yescharacteristic, complemented
36#41×Dic11—22no—
37#41×Dic11C2212yescomplemented
38#41×Dic11C2212yescomplemented
39C2×#67002C2211yescharacteristic
40C2×#67002C2211yescharacteristic
41#10623343C2212yescomplemented
42#10623329—22no—
43#10623329C2212yescomplemented
44C2×#66983C2211yescharacteristic
45C2×#66979—21no—
46C2×#66979—21no—
47C2×#66979C2211yescharacteristic
48C2×#66979C2211yescharacteristic
49#10623189—22no—
50#10623174C2212yes—
51#10623155C2212yescomplemented
52#10623150C2212yes—
53#10623127C2212yescomplemented
54#10623122—22no—
55#10623096—21no—
56#10623096—21no—
57#10623094—21no—
58#10623086—21no—
59#10623052C2211yescharacteristic, complemented
60#10623050C2211yescharacteristic, complemented
61C11×#452C2211yescharacteristic, complemented
62C11×#452C2211yescharacteristic, complemented
63C11×#451C2211yescharacteristic, complemented
64C11×#450C2211yescharacteristic, complemented
65C11×#449C2211yescharacteristic, complemented
66C11×#449C2211yescharacteristic, complemented
67C11×#448C2211yescharacteristic, complemented
68C11×#447C2211yescharacteristic, complemented
69C11×#416C2211yescharacteristic
70C11×#416C2211yescharacteristic
71C2×C11×C22⋊C8C2211yescharacteristic
72#10622851C2212yes—
73#10622851C2212yes—
74#10622845C2211yescharacteristic
75#10622845C2211yescharacteristic
76#10622845C2211yescharacteristic, complemented
77#10622845C2211yescharacteristic, complemented
78#10622840C2212yes—
79#10622830C2212yes—
80#10622820C2211yescharacteristic
81#10622798C2212yescomplemented
82#10622798C2212yescomplemented
83#10622797C2212yescomplemented
84Q16×Dic11C2212yescomplemented
85#10622778C2212yescomplemented
86#10622778C2212yescomplemented
87#10622777C2212yescomplemented
88#10622777C2212yescomplemented
89#10622776C2212yescomplemented
90#10622776C2212yescomplemented
91SD16×Dic11C2212yescomplemented
92SD16×Dic11C2212yescomplemented
93#10622765C2212yescomplemented
94#10622763C2212yescomplemented
95#10622763C2212yescomplemented
96D8×Dic11C2212yescomplemented
97C2×#66885C2211yescharacteristic, complemented
98C2×#66885C2211yescharacteristic, complemented
99C2×#66882C2211yescharacteristic, complemented
100C2×#66881C2211yescharacteristic, complemented
101#10622715C2211yescharacteristic, complemented
102#10622715C2211yescharacteristic, complemented
103#10622714C2211yescharacteristic, complemented
104#10622714C2211yescharacteristic, complemented
105#10622658C2212yescomplemented
106#10622658C2212yescomplemented
107#10622648C2212yescomplemented
108#10622648C2212yescomplemented
109#10622608C2211yescharacteristic, complemented
110#10622608C2211yescharacteristic, complemented
111#10622430C2212yescomplemented
112#10622430C2212yescomplemented
113#10622412C2212yescomplemented
114#10622409C2212yescomplemented
115#10622407C2212yescomplemented
116#10622404C2212yescomplemented
117#10622401C2212yescomplemented
118#10622401C2212yescomplemented
119#10622398C2212yescomplemented
120#10622398C2212yescomplemented
121#10622379C2212yescomplemented
122#10622376C2212yescomplemented
123#10622374C2212yescomplemented
124#10622372C2212yescomplemented
125#10622369C2212yescomplemented
126#10622369C2212yescomplemented
127#10622350C2212yes—
128#10622350C2212yes—
129#10622350C2212yescomplemented
130#10622350C2212yescomplemented
131#10622333C2212yescomplemented
132#10622333C2212yescomplemented
133#10622332C2212yescomplemented
134#10622331C2212yescomplemented
135C2×C11×#41—24no—
136C2×C11×#41—24no—
137C2×C11×#41—21no—
138C2×C11×#41—21no—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2311yescharacteristic
141C2×C11×#41C2311yescharacteristic
142C2×C11×#41C2311yescharacteristic
143C2×C11×#41C2311yescharacteristic
144C22×Q8×C11C2311yescharacteristic
145C22×D4×C11—21no—
146C22×D4×C11C2311yescharacteristic
147C23×C4×C11—21no—
148C23×C4×C11C2311yescharacteristic
149C22×C22⋊D11—21no—
150C2×#4341—22no—
151C22×D44C2311yescharacteristic
152C11×#135—24no—
153C11×#135—24no—
154C2×C11×Q16C2311yescharacteristic
155C2×C11×Q16C2311yescharacteristic
156C2×C11×SD16C2311yescharacteristic
157C2×C11×SD16C2311yescharacteristic
158C2×C11×SD16C2311yescharacteristic
159C2×C11×SD16C2311yescharacteristic
160C2×C11×D8C2311yescharacteristic
161C2×C11×D8C2311yescharacteristic
162C22×C8×C11C2311yescharacteristic
163C22×C8×C11C2311yescharacteristic
164C11×#123—21no—
165C11×C22⋊Q8C2311yescharacteristic
166C11×C22⋊Q8C2311yescharacteristic
167C11×#121C2311yescharacteristic
168C11×#121C2311yescharacteristic
169C11×#120—21no—
170C4×D4×C11—21no—
171C4×D4×C11—21no—
172C11×#117C2311yescharacteristic
173C2×C22⋊Dic11—21no—
174C2×C22⋊Dic11—22no—
175C2×C22⋊Dic11—22no—
176C2×C22⋊Dic11D412yes—
177#67002—24no—
178#67002—24no—
179#67000C2312yes—
180Q8×Dic11—22no—
181Q8×Dic11—22no—
182Q8×Dic11C2312yes—
183Q8×Dic11C2312yes—
184Q8×Dic11C2312yes—
185Q8×Dic11C2312yes—
186Q8×Dic11C2312yes—
187C2×#4325C2312yes—
188C2×#4325C2312yes—
189#66993C2312yes—
190#66992—22no—
191#66992—22no—
192#66991—22no—
193#66990—22no—
194D4×Dic11—22no—
195D4×Dic11—22no—
196D4×Dic11—22no—
197D4×Dic11—22no—
198D4×Dic11—22no—
199D4×Dic11—22no—
200D4×Dic11—22no—
201D4×Dic11—22no—
202D4×Dic11—22no—
203D4×Dic11—22no—
204D4×Dic11—22no—
205D4×Dic11C2312yes—
206D4×Dic11C2312yes—
207D4×Dic11C2312yes—
208D4×Dic11C2312yes—
209D4×Dic11C2312yes—
210C2×#4323C2312yes—
211C2×#4323C2312yes—
212#66983—21no—
213#66983—21no—
214#66983—21no—
215#66983—21no—
216#66983C2312yes—
217#66983C2312yes—
218C2×(C2×D11)⋊C4—21no—
219#66979—21no—
220#66979—21no—
221#66979—22no—
222#66979—22no—
223#66979—21no—
224#66979—21no—
225#66979—21no—
226#66979—21no—
227#66979—21no—
228#66979—22no—
229#66979—22no—
230#66979D411yescharacteristic
231#66979D411yescharacteristic
232#66979D412yes—
233#66979C2312yes—
234#66979C2312yes—
235#66979C2311yescharacteristic
236#66979C2311yescharacteristic
237#66979C2312yes—
238C2×C4⋊Dic11—21no—
239C2×C4⋊Dic11—21no—
240C2×C4⋊Dic11—21no—
241C2×C4⋊Dic11—21no—
242C2×C4⋊Dic11—21no—
243C2×C4⋊Dic11D411yescharacteristic
244C2×C4⋊Dic11D411yescharacteristic
245C2×C4⋊Dic11C2311yescharacteristic
246C2×C4⋊Dic11C2311yescharacteristic
247C2×C4⋊Dic11C2311yescharacteristic
248C2×C4×Dic11—21no—
249C2×C4×Dic11—22no—
250C2×C4×Dic11—22no—
251C2×C4×Dic11C2312yes—
252C2×#4318C2311yescharacteristic
253C2×#4318C2311yescharacteristic
254#66951—22no—
255#66951—22no—
256#66950—22no—
257#66946C2312yes—
258#66946C2312yes—
259#66945—22no—
260#66943C2312yes—
261#66941C2312yes—
262#66939—22no—
263#66939—22no—
264#66938—22no—
265#66938—22no—
266#66936—22no—
267#66936—22no—
268(C22⋊D11)⋊C4—22no—
269(C22⋊D11)⋊C4—22no—
270C22⋊C4×D11—22no—
271#66931—22no—
272C4×D44—21no—
273C4×D44—21no—
274#66923—21no—
275#66922—21no—
276C11×#103C2311yescharacteristic
277C11×#103C2311yescharacteristic
278C11×#103C2311yescharacteristic
279C11×#103C2311yescharacteristic
280C11×#102C2311yescharacteristic
281C11×#102C2311yescharacteristic
282C11×#102C2311yescharacteristic
283C11×#102C2311yescharacteristic
284C11×C22⋊C8C2311yescharacteristic
285C11×C22⋊C8C2311yescharacteristic
286C11×C22⋊C8C2311yescharacteristic
287C11×C22⋊C8C2311yescharacteristic
288#66899C2312yes—
289#66899C2312yes—
290#66899C2312yes—
291#66899C2312yes—
292#66896C2312yes—
293#66896C2312yes—
294#66896C2312yes—
295#66896C2312yes—
296C22⋊(C11⋊C8)C2312yes—
297C22⋊(C11⋊C8)C2312yes—
298#66885C2312yes—
299#66885C2312yes—
300#66885C2312yes—
301#66885C2312yes—
302#66882C2312yes—
303#66882C2312yes—
304#66881C2312yes—
305#66881C2312yes—
306#66879C2312yes—
307#66879C2312yes—
308Dic11⋊C8C2312yes—
309Dic11⋊C8C2312yes—
310Dic11⋊C8C2312yes—
311Dic11⋊C8C2312yes—
312C8×Dic11C2312yes—
313C8×Dic11C2312yes—
314#66872C2312yes—
315#66872C2312yes—
316#66871C2312yes—
317#66871C2312yes—
318#60587—111nomaximal, Sylow
319C24×C11—21no—
320C24×C11C2×D411yescharacteristic
321C23×D11—21no—
322C11×#41—28no—
323C11×#41—28no—
324C11×#41—22no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41#4114yescomplemented
333C11×#41#4114yescomplemented
334C2×Q8×C11—22no—
335C2×Q8×C11—22no—
336C2×Q8×C11—21no—
337C2×Q8×C11C2411yescharacteristic
338C2×Q8×C11C2411yescharacteristic
339C2×Q8×C11C2411yescharacteristic
340C2×D4×C11—28no—
341C2×D4×C11—21no—
342C2×D4×C11—21no—
343C2×D4×C11—21no—
344C2×D4×C11—21no—
345C2×D4×C11—22no—
346C2×D4×C11—22no—
347C2×D4×C11—21no—
348C2×D4×C11—21no—
349C2×D4×C11—21no—
350C2×D4×C11—21no—
351C2×D4×C11C2411yescharacteristic
352C2×D4×C11C2411yescharacteristic
353C2×D4×C11C2411yescharacteristic
354C22×C4×C11—28no—
355C22×C4×C11—21no—
356C22×C4×C11—21no—
357C22×C4×C11—21no—
358C22×C4×C11—21no—
359C22×C4×C11—21no—
360C22×C4×C11—22no—
361C22×C4×C11—22no—
362C22×C4×C11—21no—
363C22×C4×C11C2×D411yescharacteristic
364C22×C4×C11C2×D411yescharacteristic
365C22×C4×C11C2×D411yescharacteristic
366C22×C4×C11C2411yescharacteristic
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2411yescharacteristic
369C2×C22⋊D11—22no—
370C2×C22⋊D11—22no—
371C2×C22⋊D11—22no—
372C2×C22⋊D11—22no—
373C2×C22⋊D11—82no—
374C22×Dic11—22no—
375C22×Dic11—22no—
376C22×Dic11—22no—
377C22×Dic11—22no—
378C22×Dic11—22no—
379C22×Dic11—21no—
380C22×Dic11—21no—
381C22×Dic11—21no—
382C22×Dic11C2×D412yes—
383C22×Dic11C2×D412yes—
384#4341—84no—
385C2×D44—21no—
386C2×D44—22no—
387C2×D44—22no—
388C2×D44C2412yes—
389C2×C4×D11—22no—
390C2×C4×D11—22no—
391C2×Dic22—22no—
392C11×Q16—22no—
393C11×Q16—22no—
394C11×SD16—22no—
395C11×SD16—22no—
396C11×SD16—22no—
397C11×SD16—22no—
398C11×D8—22no—
399C11×D8—22no—
400C2×C8×C11—22no—
401C2×C8×C11—22no—
402C2×C8×C11C2411yescharacteristic
403C2×C8×C11C2411yescharacteristic
404C2×C8×C11C2411yescharacteristic
405C2×C8×C11C2411yescharacteristic
406C11×C4⋊C4—21no—
407C11×C4⋊C4—21no—
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2411yescharacteristic
410C11×C22⋊C4—21no—
411C11×C22⋊C4—21no—
412C11×C22⋊C4—21no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—21no—
415C42×C11—21no—
416C22⋊Dic11—22no—
417C22⋊Dic11—22no—
418C22⋊Dic11—22no—
419C22⋊Dic11—22no—
420C22⋊Dic11—22no—
421C22⋊Dic11—22no—
422C22⋊Dic11—22no—
423C22⋊Dic11C2×D412yes—
424C22⋊Dic11C2×D412yes—
425C22⋊Dic11C2×D412yes—
426C22⋊Dic11C2×D412yes—
427#4325—24no—
428#4325—24no—
429#4323—24no—
430#4323—24no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—22no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437C4⋊Dic11—22no—
438C4⋊Dic11—22no—
439C4⋊Dic11—22no—
440C4⋊Dic11—22no—
441C4⋊Dic11—22no—
442C4⋊Dic11—22no—
443C4⋊Dic11—21no—
444C4⋊Dic11—21no—
445C4⋊Dic11—21no—
446C4⋊Dic11C2×D411yescharacteristic
447C4⋊Dic11C2×D411yescharacteristic
448C4⋊Dic11C2×D411yescharacteristic
449C4⋊Dic11C2×D411yescharacteristic
450C4⋊Dic11C2×D412yes—
451C4⋊Dic11C2×D412yes—
452C4⋊Dic11C2412yes—
453C4⋊Dic11C2412yes—
454C4⋊Dic11C2412yes—
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457C4×Dic11—22no—
458C4×Dic11—22no—
459C4×Dic11—22no—
460C4×Dic11—22no—
461C4×Dic11—22no—
462C4×Dic11—22no—
463C4×Dic11—22no—
464C4×Dic11C2×D412yes—
465C4×Dic11C2×D412yes—
466C4×Dic11C2412yes—
467C4×Dic11C2412yes—
468#4318—22no—
469#4318—22no—
470C2×C11⋊C8C2412yes—
471C2×C11⋊C8C2412yes—
472#3494—111no—
473#3428—111no—
474#3126—112no—
475#3122—112no—
476#3121—112no—
477#3118—112no—
478#3115—112no—
479#3111—112no—
480#3106—112no—
481#3102—112no—
482#3093—111no—
483C2×#482—111no—
484#3084—111no—
485#3083—111no—
486#3045—111no—
487#3045—111no—
488#3006—111no—
489#3002D1111yescharacteristic, complemented
490#2952—111no—
491#2951—111no—
492#2946—111no—
493#2946—111no—
494#2924—111no—
495C23×C11—24no—
496C23×C11—21no—
497C23×C11—21no—
498C23×C11—22no—
499C23×C11—21no—
500C23×C11—41no—
501C23×C11—41no—
502C23×C11—81no—
503C23×C11—81no—
504C23×C11C22×D411yescharacteristic
505C23×C11C22×D411yescharacteristic
506C23×C11C22×D411yescharacteristic
507C22×D11—22no—
508C22×D11—42no—
509C22×D11—81no—
510C22×D11—81no—
511Q8×C11—24no—
512Q8×C11—21no—
513Q8×C11—21no—
514Q8×C11—21no—
515Q8×C11—21no—
516Q8×C11C2×#4112yes—
517Q8×C11C2×#4112yes—
518D4×C11—24no—
519D4×C11—24no—
520D4×C11—24no—
521D4×C11—24no—
522D4×C11—24no—
523D4×C11—21no—
524D4×C11—21no—
525D4×C11—21no—
526D4×C11—21no—
527D4×C11—42no—
528D4×C11—42no—
529D4×C11—81no—
530D4×C11C2×#4112yes—
531D4×C11C2×#4112yes—
532C2×C4×C11—24no—
533C2×C4×C11—24no—
534C2×C4×C11—24no—
535C2×C4×C11—22no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—22no—
539C2×C4×C11—24no—
540C2×C4×C11—24no—
541C2×C4×C11—22no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—42no—
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C2×#4112yes—
554C2×C4×C11C2×#4112yes—
555C2×C4×C11C2511yescharacteristic
556C22⋊D11—44no—
557C22⋊D11—82no—
558C22⋊D11—82no—
559C22⋊D11—82no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—42no—
564C2×Dic11—42no—
565C2×Dic11—82no—
566C2×Dic11—82no—
567C2×Dic11—82no—
568C2×Dic11—82no—
569C2×Dic11—82no—
570C2×Dic11—81no—
571C2×Dic11—81no—
572C2×Dic11—81no—
573C2×Dic11C22×D412yes—
574C2×Dic11C22×D412yes—
575C2×Dic11C22×D412yes—
576C2×Dic11C22×D412yes—
577D44—22no—
578D44—22no—
579D44—42no—
580C4×D11—82no—
581C4×D11—82no—
582Dic22—82no—
583C8×C11—21no—
584C8×C11—21no—
585C8×C11—21no—
586C8×C11—21no—
587C11⋊C8—22no—
588C11⋊C8—22no—
589C22×#41C2×D1111yescharacteristic
590C2×AGL(1,ℤ/8)—111no—
591C2×AGL(1,ℤ/8)—111no—
592C2×#135C2×D1111yescharacteristic
593C2×#135C2×D1111yescharacteristic
594#555—221no—
595#553—221no—
596#553—221no—
597#551—222no—
598#547—221no—
599#546—222no—
600#544—111no—
601#542—112no—
602#540—112no—
603#535—111no—
604#532—112no—
605#529—112no—
606#525C2×D1111yescharacteristic
607C2×#121—111no—
608#520—111no—
609#520—111no—
610#520—111no—
611#520—111no—
612#520—111no—
613#520—221no—
614#520—221no—
615#519—112no—
616#518—112no—
617#518—111no—
618#518—222no—
619C4×#41—112no—
620C4×#41—112no—
621C4×#41—222no—
622C2×#117—111no—
623C2×#117—111no—
624C2×#117—221no—
625C2×#117—221no—
626#485—112no—
627#485—112no—
628#482—112no—
629#482—112no—
630#482—112no—
631#482—112no—
632#482—112no—
633#482—112no—
634#479—112no—
635#479—112no—
636#478—112no—
637#478—112no—
638#477—112no—
639#476—112no—
640#475—112no—
641#474—112no—
642#464—112no—
643#464—112no—
644#463—112no—
645#463—112no—
646#460—112no—
647#460—112no—
648#459—112no—
649#459—112no—
650#452C2×D1111yescharacteristic, complemented
651#452C2×D1111yescharacteristic, complemented
652#451C2×D1111yescharacteristic, complemented
653#450C2×D1111yescharacteristic, complemented
654#449—112no—
655#449—112no—
656#449C2×D1111yescharacteristic, complemented
657#449C2×D1111yescharacteristic, complemented
658#448—112no—
659#448C2×D1111yescharacteristic, complemented
660#447—112no—
661#447C2×D1111yescharacteristic, complemented
662#442—112no—
663#442—112no—
664#442—112no—
665#441—112no—
666#440—112no—
667#440—112no—
668#440—112no—
669#440—112no—
670C4×Q16—112no—
671C4×SD16—112no—
672C4×SD16—112no—
673C4×SD16—112no—
674C4×SD16—112no—
675C4×D8—112no—
676C4×D8—112no—
677C4×D8—112no—
678#433—112no—
679#433—112no—
680#432—112no—
681#431—112no—
682#428—111no—
683#428—111no—
684C2×#107—111no—
685C2×#106—111no—
686#424—111no—
687#424—111no—
688#417—111no—
689#417—111no—
690#417—111no—
691#417—111no—
692#416C2×D1111yescharacteristic
693#416C2×D1111yescharacteristic
694C2×#102—111no—
695C2×#102—111no—
696#407—111no—
697C2×C22⋊C8C2×D1111yescharacteristic
698#405—111no—
699#405—111no—
700C22×C11—21no—
701C22×C11—21no—
702C22×C11—21no—
703C22×C11—21no—
704C22×C11—21no—
705C22×C11—21no—
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—22no—
709C22×C11—22no—
710C22×C11—41no—
711C22×C11—41no—
712C22×C11—41no—
713C22×C11—41no—
714C22×C11—41no—
715C22×C11—41no—
716C22×C11—41no—
717C22×C11—82no—
718C22×C11—84no—
719C22×C11#52512yes—
720C22×C11C23×D411yescharacteristic
721C2×D11—42no—
722C2×D11—42no—
723C2×D11—42no—
724C2×D11—162no—
725C4×C11—21no—
726C4×C11—22no—
727C4×C11—22no—
728C4×C11—21no—
729C4×C11—41no—
730C4×C11—41no—
731C4×C11—41no—
732C4×C11#52512yes—
733C4×C11C22×#4111yescharacteristic
734C4×C11C22×#4111yescharacteristic
735Dic11—22no—
736Dic11—22no—
737Dic11—22no—
738Dic11—22no—
739Dic11—42no—
740Dic11—42no—
741Dic11—42no—
742C2×#41—24no—
743C2×#41—24no—
744C2×#41—21no—
745C2×#41—21no—
746C2×#41—222no—
747C2×#41C22×D1111yescharacteristic
748C2×#41C22×D1111yescharacteristic
749C2×#41C22×D1111yescharacteristic
750C2×#41C22×D1111yescharacteristic
751C2×#41C22×D1111yescharacteristic
752C22×Q8C22×D1111yescharacteristic
753C22×D4—21no—
754C22×D4—111no—
755C22×D4—221no—
756C22×D4C22×D1111yescharacteristic
757C23×C4—21no—
758C23×C4C22×D1111yescharacteristic
759AGL(1,ℤ/8)—224no—
760AGL(1,ℤ/8)—224no—
761#135—24no—
762#135—24no—
763C2×Q16C22×D1111yescharacteristic
764C2×Q16C22×D1111yescharacteristic
765C2×SD16—112no—
766C2×SD16—112no—
767C2×SD16C22×D1111yescharacteristic
768C2×SD16C22×D1111yescharacteristic
769C2×SD16C22×D1111yescharacteristic
770C2×SD16C22×D1111yescharacteristic
771C2×D8—112no—
772C2×D8—112no—
773C2×D8C22×D1111yescharacteristic
774C2×D8C22×D1111yescharacteristic
775C2×M16—111no—
776C2×M16—111no—
777C22×C8C22×D1111yescharacteristic
778C22×C8C22×D1111yescharacteristic
779C4⋊Q8—112no—
780C4⋊Q8—221no—
781#127—112no—
782#126—222no—
783#126—222no—
784#125—112no—
785#125—221no—
786#124—112no—
787#124—222no—
788#124—222no—
789#123—21no—
790#123—222no—
791#123—222no—
792#123—222no—
793#123—222no—
794C22⋊Q8—222no—
795C22⋊Q8—222no—
796C22⋊Q8C22×D1111yescharacteristic
797C22⋊Q8C22×D1111yescharacteristic
798#121—112no—
799#121—112no—
800#121—222no—
801#121—222no—
802#121—221no—
803#121—221no—
804#121—222no—
805#121—221no—
806#121—221no—
807#121C22×D1111yescharacteristic
808#121C22×D1111yescharacteristic
809#120—21no—
810#120—222no—
811C4×Q8—112no—
812C4×Q8—112no—
813C4×Q8—112no—
814C4×Q8—112no—
815C4×Q8—112no—
816C4×Q8—222no—
817C4×Q8—222no—
818C4×D4—21no—
819C4×D4—21no—
820C4×D4—112no—
821C4×D4—112no—
822C4×D4—112no—
823C4×D4—112no—
824C4×D4—112no—
825C4×D4—112no—
826C4×D4—112no—
827C4×D4—221no—
828C4×D4—221no—
829C4×D4—222no—
830C4×D4—222no—
831C4×D4—222no—
832C4×D4—222no—
833C4×D4—222no—
834C4×D4—222no—
835C4×D4—222no—
836C4×D4—222no—
837C4×D4—222no—
838C4×D4—222no—
839C4×D4—222no—
840C4×D4—222no—
841C4×D4—222no—
842#117—111no—
843#117—111no—
844#117—112no—
845#117—112no—
846#117—111no—
847#117—111no—
848#117—112no—
849#117—112no—
850#117—222no—
851#117—222no—
852#117—222no—
853#117—222no—
854#117—222no—
855#117—221no—
856#117—221no—
857#117—221no—
858#117—221no—
859#117—221no—
860#117—221no—
861#117—221no—
862#117C22×D1111yescharacteristic
863C2×C4⋊C4—111no—
864C2×C4⋊C4—111no—
865C2×C4⋊C4—111no—
866C2×C4⋊C4—111no—
867C2×C4⋊C4—111no—
868C2×C4⋊C4—221no—
869C2×C4⋊C4—221no—
870C2×C4⋊C4—221no—
871C2×C4⋊C4—221no—
872C2×C4⋊C4—221no—
873C2×C22⋊C4—112no—
874C2×C22⋊C4—222no—
875C2×C22⋊C4—222no—
876C2×C22⋊C4—222no—
877C2×C22⋊C4—221no—
878C2×C22⋊C4—221no—
879C2×C42—112no—
880C2×C42—222no—
881C2×C42—222no—
882C2×C42—221no—
883#107—112no—
884#107—112no—
885#107—112no—
886#107—112no—
887#106—112no—
888#106—112no—
889#106—112no—
890#106—112no—
891C4⋊C8—112no—
892C4⋊C8—112no—
893C4⋊C8—112no—
894C4⋊C8—112no—
895#103—112no—
896#103—112no—
897#103—112no—
898#103—112no—
899#103C22×D1111yescharacteristic
900#103C22×D1111yescharacteristic
901#103C22×D1111yescharacteristic
902#103C22×D1111yescharacteristic
903#102—112no—
904#102—112no—
905#102—112no—
906#102—112no—
907#102—112no—
908#102—112no—
909#102—112no—
910#102—112no—
911#102C22×D1111yescharacteristic
912#102C22×D1111yescharacteristic
913#102C22×D1111yescharacteristic
914#102C22×D1111yescharacteristic
915C22⋊C8—112no—
916C22⋊C8—112no—
917C22⋊C8C22×D1111yescharacteristic
918C22⋊C8C22×D1111yescharacteristic
919C22⋊C8C22×D1111yescharacteristic
920C22⋊C8C22×D1111yescharacteristic
921#97—112no—
922#97—112no—
923C4×C8—112no—
924C4×C8—112no—
925C2×C11—22no—
926C2×C11—41no—
927C2×C11—41no—
928C2×C11—42no—
929C2×C11—42no—
930C2×C11—81no—
931C2×C11C2×#52511yescharacteristic
932C2×C11#358411yescharacteristic
933C2×C11#358511yescharacteristic
934D11—82no—
935C24—21no—
936C24—221no—
937C24D4×D1111yescharacteristic
938#41—28no—
939#41—28no—
940#41—22no—
941#41—22no—
942#41—22no—
943#41—22no—
944#41—22no—
945#41—22no—
946#41—22no—
947#41—22no—
948#41—884no—
949#41#434114yescomplemented
950#41#434114yescomplemented
951C2×Q8—22no—
952C2×Q8—22no—
953C2×Q8—21no—
954C2×Q8—222no—
955C2×Q8C23×D1111yescharacteristic
956C2×Q8C23×D1111yescharacteristic
957C2×Q8C23×D1111yescharacteristic
958C2×D4—28no—
959C2×D4—21no—
960C2×D4—21no—
961C2×D4—21no—
962C2×D4—21no—
963C2×D4—22no—
964C2×D4—22no—
965C2×D4—21no—
966C2×D4—21no—
967C2×D4—21no—
968C2×D4—21no—
969C2×D4—112no—
970C2×D4—222no—
971C2×D4—222no—
972C2×D4—222no—
973C2×D4—222no—
974C2×D4—221no—
975C2×D4—222no—
976C2×D4—222no—
977C2×D4—882no—
978C2×D4C23×D1111yescharacteristic
979C2×D4C23×D1111yescharacteristic
980C2×D4C23×D1111yescharacteristic
981C22×C4—28no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—21no—
990C22×C4—112no—
991C22×C4—112no—
992C22×C4—222no—
993C22×C4—222no—
994C22×C4—222no—
995C22×C4—222no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4—222no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—221no—
1002C22×C4D4×D1111yescharacteristic
1003C22×C4D4×D1111yescharacteristic
1004C22×C4D4×D1111yescharacteristic
1005C22×C4C23×D1111yescharacteristic
1006C22×C4C23×D1111yescharacteristic
1007C22×C4C23×D1111yescharacteristic
1008Q16—22no—
1009Q16—22no—
1010SD16—22no—
1011SD16—22no—
1012SD16—22no—
1013SD16—22no—
1014SD16—224no—
1015SD16—224no—
1016D8—22no—
1017D8—22no—
1018D8—224no—
1019D8—224no—
1020M16—222no—
1021M16—222no—
1022C2×C8—22no—
1023C2×C8—22no—
1024C2×C8—112no—
1025C2×C8—112no—
1026C2×C8C23×D1111yescharacteristic
1027C2×C8C23×D1111yescharacteristic
1028C2×C8C23×D1111yescharacteristic
1029C2×C8C23×D1111yescharacteristic
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—111no—
1033C4⋊C4—111no—
1034C4⋊C4—111no—
1035C4⋊C4—111no—
1036C4⋊C4—112no—
1037C4⋊C4—112no—
1038C4⋊C4—112no—
1039C4⋊C4—112no—
1040C4⋊C4—112no—
1041C4⋊C4—222no—
1042C4⋊C4—222no—
1043C4⋊C4—222no—
1044C4⋊C4—222no—
1045C4⋊C4—222no—
1046C4⋊C4—222no—
1047C4⋊C4—222no—
1048C4⋊C4—222no—
1049C4⋊C4—221no—
1050C4⋊C4—221no—
1051C4⋊C4—221no—
1052C4⋊C4C23×D1111yescharacteristic
1053C4⋊C4C23×D1111yescharacteristic
1054C22⋊C4—21no—
1055C22⋊C4—21no—
1056C22⋊C4—21no—
1057C22⋊C4—21no—
1058C22⋊C4—21no—
1059C22⋊C4—112no—
1060C22⋊C4—112no—
1061C22⋊C4—112no—
1062C22⋊C4—112no—
1063C22⋊C4—222no—
1064C22⋊C4—222no—
1065C22⋊C4—222no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—222no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C22⋊C4—222no—
1076C42—21no—
1077C42—112no—
1078C42—112no—
1079C42—112no—
1080C42—112no—
1081C42—222no—
1082C42—222no—
1083C42—222no—
1084C42—222no—
1085C42—222no—
1086C42—222no—
1087C42—222no—
1088C11#6058711yescharacteristic, complemented, Sylow
1089C23—24no—
1090C23—21no—
1091C23—21no—
1092C23—22no—
1093C23—21no—
1094C23—41no—
1095C23—41no—
1096C23—81no—
1097C23—81no—
1098C23—222no—
1099C23—442no—
1100C23—881no—
1101C23—881no—
1102C23C2×D4×D1111yescharacteristic
1103C23C2×D4×D1111yescharacteristic
1104C23C2×D4×D1111yescharacteristic
1105Q8—24no—
1106Q8—21no—
1107Q8—21no—
1108Q8—21no—
1109Q8—21no—
1110Q8—882no—
1111Q8C2×#434112yes—
1112Q8C2×#434112yes—
1113D4—24no—
1114D4—24no—
1115D4—24no—
1116D4—24no—
1117D4—24no—
1118D4—21no—
1119D4—21no—
1120D4—21no—
1121D4—21no—
1122D4—42no—
1123D4—42no—
1124D4—81no—
1125D4—222no—
1126D4—222no—
1127D4—444no—
1128D4—442no—
1129D4—882no—
1130D4—882no—
1131D4—882no—
1132D4C2×#434112yes—
1133D4C2×#434112yes—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—42no—
1152C2×C4—112no—
1153C2×C4—112no—
1154C2×C4—112no—
1155C2×C4—112no—
1156C2×C4—222no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—442no—
1160C2×C4—442no—
1161C2×C4—882no—
1162C2×C4—882no—
1163C2×C4—882no—
1164C2×C4—882no—
1165C2×C4—882no—
1166C2×C4—882no—
1167C2×C4—882no—
1168C2×C4—881no—
1169C2×C4—881no—
1170C2×C4—881no—
1171C2×C4C2×D4×D1111yescharacteristic
1172C2×C4C2×D4×D1111yescharacteristic
1173C2×C4C2×D4×D1111yescharacteristic
1174C2×C4C2×#434112yes—
1175C2×C4C2×#434112yes—
1176C2×C4C24×D1111yescharacteristic
1177C8—21no—
1178C8—21no—
1179C8—21no—
1180C8—21no—
1181C8—222no—
1182C8—222no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—22no—
1192C22—22no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—82no—
1201C22—84no—
1202C22—442no—
1203C22—442no—
1204C22—442no—
1205C22—1762no—
1206C22#1062311712yes—
1207C22C22×D4×D1111yescharacteristic
1208C4—21no—
1209C4—22no—
1210C4—22no—
1211C4—21no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—222no—
1216C4—222no—
1217C4—222no—
1218C4—222no—
1219C4—442no—
1220C4—442no—
1221C4—442no—
1222C4#1062311712yes—
1223C4C22×#434111yescharacteristic
1224C4C22×#434111yescharacteristic
1225C2—22no—
1226C2—41no—
1227C2—41no—
1228C2—42no—
1229C2—42no—
1230C2—81no—
1231C2—882no—
1232C2C2×#1062311711yescharacteristic
1233C2#1308338511yescharacteristic
1234C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3002C2
socleC22×C11C23×D4
hypercenter#3002D11
hypocenterC11#60587
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. #13082353C2semidirect
2. #13081819C2semidirect
3. #13078901C2semidirect
4. #13078853C2semidirect
5. #13078846C2semidirect
6. #13078801C2semidirect
7. #13078760C2semidirect
8. #13078726C2semidirect
9. #13078669C2semidirect
10. #13078635C2semidirect
11. #13078545C2semidirect
12. C2×#10622350C2semidirect
13. #13078476C2semidirect
14. #13078465C2semidirect
15. #13078153C2semidirect
16. #13078153C2semidirect
17. #13077868C2semidirect
18. #13077500C2semidirect
19. #13077492C2semidirect
20. #13077451C2semidirect
21. #13077451C2semidirect
22. #13077270C2semidirect
23. C11×#3002C2semidirect
28. #10623361C22semidirect
35. #10623358C22semidirect
37. #41×Dic11C22semidirect
38. #41×Dic11C22semidirect
41. #10623343C22semidirect
43. #10623329C22semidirect
51. #10623155C22semidirect
53. #10623127C22semidirect
59. #10623052C22semidirect
60. #10623050C22semidirect
61. C11×#452C22semidirect
62. C11×#452C22semidirect
63. C11×#451C22semidirect
64. C11×#450C22semidirect
65. C11×#449C22semidirect
66. C11×#449C22semidirect
67. C11×#448C22semidirect
68. C11×#447C22semidirect
76. #10622845C22semidirect
77. #10622845C22semidirect
81. #10622798C22semidirect
82. #10622798C22semidirect
83. #10622797C22semidirect
84. Q16×Dic11C22semidirect
85. #10622778C22semidirect
86. #10622778C22semidirect
87. #10622777C22semidirect
88. #10622777C22semidirect
89. #10622776C22semidirect
90. #10622776C22semidirect
91. SD16×Dic11C22semidirect
92. SD16×Dic11C22semidirect
93. #10622765C22semidirect
94. #10622763C22semidirect
95. #10622763C22semidirect
96. D8×Dic11C22semidirect
97. C2×#66885C22semidirect
98. C2×#66885C22semidirect
99. C2×#66882C22semidirect
100. C2×#66881C22semidirect
101. #10622715C22semidirect
102. #10622715C22semidirect
103. #10622714C22semidirect
104. #10622714C22semidirect
105. #10622658C22semidirect
106. #10622658C22semidirect
107. #10622648C22semidirect
108. #10622648C22semidirect
109. #10622608C22semidirect
110. #10622608C22semidirect
111. #10622430C22semidirect
112. #10622430C22semidirect
113. #10622412C22semidirect
114. #10622409C22semidirect
115. #10622407C22semidirect
116. #10622404C22semidirect
117. #10622401C22semidirect
118. #10622401C22semidirect
119. #10622398C22semidirect
120. #10622398C22semidirect
121. #10622379C22semidirect
122. #10622376C22semidirect
123. #10622374C22semidirect
124. #10622372C22semidirect
125. #10622369C22semidirect
126. #10622369C22semidirect
129. #10622350C22semidirect
130. #10622350C22semidirect
131. #10622333C22semidirect
132. #10622333C22semidirect
133. #10622332C22semidirect
134. #10622331C22semidirect
332. C11×#41#41semidirect
333. C11×#41#41semidirect
489. #3002D11semidirect
650. #452C2×D11semidirect
651. #452C2×D11semidirect
652. #451C2×D11semidirect
653. #450C2×D11semidirect
656. #449C2×D11semidirect
657. #449C2×D11semidirect
659. #448C2×D11semidirect
661. #447C2×D11semidirect
949. #41#4341semidirect
950. #41#4341semidirect
1088. C11#60587semidirect

Maximal subgroups

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

subgroupindex
#130823532
#130818192
#130789012
#130788532
#130788462
#130788012
#130787602
#130787262
#130786692
#130786352
#130785452
C2×#106223502
#130784762
#130784652
#130781532
#130778682
#130775002
#130774922
#130774512
#130772702
C11×#30022
#6058711