Finite Group Databasebeta

← #15624660

Subgroups — #15624660

Order 2816.

2208 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081945C211yesmaximal, characteristic, complemented
2#13079522C212yesmaximal, complemented
3#13079513C212yesmaximal, complemented
4#13079468C212yesmaximal, complemented
5#13079468C212yesmaximal, complemented
6#13079453C212yesmaximal, complemented
7#13079430C212yesmaximal, complemented
8#13079404C212yesmaximal, complemented
9#13079381C212yesmaximal, complemented
10#13078585C211yesmaximal, characteristic, complemented
11#13078574C211yesmaximal, characteristic, complemented
12#13078552C211yesmaximal, characteristic, complemented
13#13078525C211yesmaximal, characteristic, complemented
14#13078309C211yesmaximal, characteristic, complemented
15#13078298C211yesmaximal, characteristic, complemented
16#13078261C211yesmaximal, characteristic, complemented
17#13078252C211yesmaximal, characteristic, complemented
18#13077893C211yesmaximal, characteristic, complemented
19#13077884C211yesmaximal, characteristic, complemented
20#13077856C211yesmaximal, characteristic, complemented
21C2×#10622650C211yesmaximal, characteristic, complemented
22#13077065C211yesmaximal, characteristic, complemented
23C11×#3488C211yesmaximal, characteristic, complemented
24C2×C11×H(5,𝔽2)C2211yescharacteristic
25C22×C11×#41C2211yescharacteristic
26C22×#4339C2211yescharacteristic, complemented
27C11×#550—21no—
28C11×#548—21no—
29C11×#546—22no—
30C11×#546—21no—
31D42×C11—21no—
32D42×C11—22no—
33C11×#537C2211yescharacteristic
34C11×#537C2212yescomplemented
35C11×#535C2211yescharacteristic
36C11×#535C2212yescomplemented
37C11×#525C2211yescharacteristic
38C11×#525C2212yescomplemented
39C2×C11×#121C2211yescharacteristic
40C2×C11×#121C2212yescomplemented
41C11×#520C2211yescharacteristic
42#10623364C2212yescomplemented
43#10623364C2212yescomplemented
44#10623363—21no—
45#10623363—21no—
46#10623361C2211yescharacteristic
47#10623361C2211yescharacteristic, complemented
48#10623359—22no—
49#10623356C2211yescharacteristic
50#10623356C2211yescharacteristic, complemented
51C2×#67004C2211yescharacteristic, complemented
52C2×#67002C2211yescharacteristic, complemented
53C2×#67001C2211yescharacteristic, complemented
54C2×#67001C2211yescharacteristic, complemented
55#10623347—21no—
56#10623336—21no—
57#10623335—22no—
58C22×#4324C2211yescharacteristic, complemented
59C22×#4323C2211yescharacteristic, complemented
60#10623322C2212yescomplemented
61#10623322C2212yescomplemented
62C2×#66979C2211yescharacteristic, complemented
63#10622852C2212yescomplemented
64#10622852C2212yescomplemented
65#10622851C2212yescomplemented
66#10622851C2212yescomplemented
67#10622847C2211yescharacteristic
68#10622847C2211yescharacteristic
69#10622847C2212yescomplemented
70#10622847C2212yescomplemented
71#10622846C2211yescharacteristic, complemented
72#10622846C2211yescharacteristic, complemented
73#10622831C2212yescomplemented
74#10622831C2212yescomplemented
75#10622830C2212yescomplemented
76#10622830C2212yescomplemented
77#10622828C2211yescharacteristic, complemented
78#10622828C2211yescharacteristic, complemented
79#10622820C2211yescharacteristic, complemented
80#10622820C2212yescomplemented
81C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
82C2×C22⋊(C11⋊C8)C2212yescomplemented
83#10622665C2212yescomplemented
84#10622664C2212yescomplemented
85#10622662C2212yescomplemented
86#10622661C2212yescomplemented
87#10622660C2212yescomplemented
88#10622660C2212yescomplemented
89#10622658C2211yescharacteristic, complemented
90#10622658C2211yescharacteristic, complemented
91#10622657C2211yescharacteristic, complemented
92#10622656C2211yescharacteristic, complemented
93#10622655C2212yescomplemented
94#10622655C2212yescomplemented
95#10622655C2212yescomplemented
96#10622654C2212yescomplemented
97#10622654C2212yescomplemented
98#10622654C2212yescomplemented
99#10622652C2212yescomplemented
100#10622652C2212yescomplemented
101#10622652C2212yescomplemented
102#10622651C2212yescomplemented
103#10622651C2212yescomplemented
104#10622651C2212yescomplemented
105#10622650C2212yescomplemented
106#10622650C2212yescomplemented
107#10622650C2212yescomplemented
108#10622650C2212yescomplemented
109#10622650C2212yescomplemented
110#10622650C2212yescomplemented
111#10622648C2212yescomplemented
112#10622648C2212yescomplemented
113#10622648C2211yescharacteristic, complemented
114#10622648C2211yescharacteristic, complemented
115#10622647C2212yescomplemented
116#10622647C2211yescharacteristic, complemented
117#10622646C2212yescomplemented
118#10622646C2211yescharacteristic, complemented
119#10622617C2211yescharacteristic, complemented
120#10622616C2212yescomplemented
121#10622616C2212yescomplemented
122#10622614C2211yescharacteristic, complemented
123#10622611C2211yescharacteristic, complemented
124#10622611C2211yescharacteristic, complemented
125#10622609C2212yescomplemented
126#10622609C2212yescomplemented
127#10622584C2212yescomplemented
128#10622583C2212yescomplemented
129C2×#66874C2211yescharacteristic, complemented
130#10622581C2212yescomplemented
131#10622580C2212yescomplemented
132C2×#66873C2211yescharacteristic, complemented
133#10622577C2211yescharacteristic, complemented
134#10622577C2211yescharacteristic, complemented
135C11×H(5,𝔽2)—42no—
136C11×H(5,𝔽2)—42no—
137C2×C11×#41—21no—
138C2×C11×#41—42no—
139C2×C11×#41—42no—
140C2×C11×#41D412yes—
141C2×C11×#41D411yescharacteristic
142C2×C11×#41D411yescharacteristic
143C2×C11×#41C2311yescharacteristic
144C2×C11×#41C2312yes—
145C2×C11×#41C2311yescharacteristic
146C2×C11×#41C2311yescharacteristic
147C2×C11×#41C2312yes—
148C22×Q8×C11D411yescharacteristic
149C22×D4×C11—21no—
150C22×D4×C11—22no—
151C22×D4×C11—22no—
152C22×D4×C11—21no—
153C22×D4×C11D412yes—
154C22×D4×C11D411yescharacteristic
155C22×D4×C11C2311yescharacteristic
156C22×D4×C11C2312yes—
157C23×C4×C11C2311yescharacteristic
158C23×C4×C11C2312yes—
159C22×C22⋊D11—21no—
160C2×#4339—21no—
161C2×#4339—21no—
162C2×#4339—42no—
163C2×#4339—42no—
164C2×#4339C2312yes—
165C2×#4339C2312yes—
166C22×D44C2311yescharacteristic
167C22×C4×D11—21no—
168C22×Dic22C2311yescharacteristic
169C11×#127—21no—
170C11×#127—22no—
171C11×#124—21no—
172C11×#124—22no—
173C11×#123—21no—
174C11×#123—22no—
175C11×C22⋊Q8—21no—
176C11×C22⋊Q8—22no—
177C11×C22⋊Q8C2311yescharacteristic
178C11×C22⋊Q8C2311yescharacteristic
179C11×C22⋊Q8C2312yes—
180C11×#121—22no—
181C11×#121—21no—
182C11×#121—22no—
183C11×#121—22no—
184C11×#121—22no—
185C11×#121—21no—
186C11×#121—21no—
187C11×#121—22no—
188C11×#121—22no—
189C11×#121C2312yes—
190C11×#121C2312yes—
191C11×#121C2311yescharacteristic
192C11×#121C2312yes—
193C11×#121C2312yes—
194C11×#121C2311yescharacteristic
195C11×#121C2312yes—
196C11×#120—21no—
197C11×#120—22no—
198C11×#120—22no—
199C11×#120—22no—
200C11×#120—22no—
201C4×Q8×C11—21no—
202C4×D4×C11—22no—
203C4×D4×C11—21no—
204C4×D4×C11—21no—
205C4×D4×C11—21no—
206C4×D4×C11—22no—
207C4×D4×C11—22no—
208C11×#117C2312yes—
209C11×#117C2311yescharacteristic
210C2×C11×C4⋊C4C2311yescharacteristic
211C2×C11×C4⋊C4C2312yes—
212C2×C11×C22⋊C4—21no—
213C2×C11×C22⋊C4—22no—
214#67006—22no—
215#67006—22no—
216C2×C22⋊Dic11—21no—
217#67004—42no—
218#67002—42no—
219#67001—42no—
220#67001—42no—
221#67000—21no—
222#67000—21no—
223#66999—22no—
224#66999—22no—
225#66997—21no—
226#66997—21no—
227C2×#4326C2312yes—
228C2×#4325C2312yes—
229#66993—21no—
230#66993—21no—
231#66992—22no—
232#66992—22no—
233#66992—22no—
234#66992—22no—
235#66991—22no—
236#66991—22no—
237#66990—22no—
238#66990—22no—
239#66989—21no—
240#66989—21no—
241#66988—22no—
242#66988—22no—
243C2×#4324—42no—
244C2×#4324C2312yes—
245C2×#4324C2312yes—
246C2×#4324C2312yes—
247C2×#4323—42no—
248C2×#4323C2312yes—
249C2×#4323C2312yes—
250C2×#4323C2312yes—
251#66983C2312yes—
252#66983C2312yes—
253#66983C2312yes—
254#66983C2312yes—
255#66982—22no—
256#66982—22no—
257C4×C22⋊D11—22no—
258C4×C22⋊D11—22no—
259C4×C22⋊D11—22no—
260C4×C22⋊D11—22no—
261#66979—21no—
262#66979—21no—
263#66979C2311yescharacteristic
264#66979C2311yescharacteristic
265#66979C2311yescharacteristic
266#66979C2311yescharacteristic
267C2×C4⋊Dic11C2311yescharacteristic
268C2×C4⋊Dic11C2311yescharacteristic
269#66977C2312yes—
270#66977C2312yes—
271#66977C2312yes—
272#66977C2312yes—
273C2×C4×Dic11—21no—
274C2×#4318C2311yescharacteristic
275C2×#4318C2311yescharacteristic
276C2×#4318C2312yes—
277C2×#4318C2312yes—
278C22×C11⋊C8C2311yescharacteristic
279C22×C11⋊C8C2311yescharacteristic
280C22×C11⋊C8C2312yes—
281C22×C11⋊C8C2312yes—
282#66899C2311yescharacteristic
283#66899C2311yescharacteristic
284#66899C2311yescharacteristic
285#66899C2311yescharacteristic
286#66896C2312yes—
287#66896C2312yes—
288#66896C2312yes—
289#66896C2312yes—
290#66896C2311yescharacteristic
291#66896C2311yescharacteristic
292#66896C2311yescharacteristic
293#66896C2311yescharacteristic
294C22⋊(C11⋊C8)C2311yescharacteristic
295C22⋊(C11⋊C8)C2312yes—
296C22⋊(C11⋊C8)C2311yescharacteristic
297C22⋊(C11⋊C8)C2312yes—
298C22⋊(C11⋊C8)C2312yes—
299C22⋊(C11⋊C8)C2311yescharacteristic
300C22⋊(C11⋊C8)C2311yescharacteristic
301C22⋊(C11⋊C8)C2312yes—
302C22⋊(C11⋊C8)C2312yes—
303C22⋊(C11⋊C8)C2312yes—
304#66874C2312yes—
305#66874C2312yes—
306#66874C2312yes—
307#66874C2312yes—
308#66873C2312yes—
309#66873C2312yes—
310#66873C2312yes—
311#66873C2312yes—
312#66872C2312yes—
313#66872C2312yes—
314#66872C2311yescharacteristic
315#66872C2311yescharacteristic
316#66872C2311yescharacteristic
317#66872C2311yescharacteristic
318#66871C2312yes—
319#66871C2312yes—
320#66871C2311yescharacteristic
321#66871C2311yescharacteristic
322#66871C2311yescharacteristic
323#66871C2311yescharacteristic
324#60760—111nomaximal, Sylow
325C24×C11—22no—
326C24×C11—21no—
327C24×C11C2×D411yescharacteristic
328C24×C11C2×D412yes—
329C23×D11—21no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—22no—
333C11×#41—22no—
334C11×#41—22no—
335C11×#41—22no—
336C11×#41—42no—
337C11×#41—42no—
338C11×#41—44no—
339C11×#41—42no—
340C11×#41—42no—
341C11×#41—42no—
342C11×#41—42no—
343C11×#41—44no—
344C2×Q8×C11—42no—
345C2×Q8×C11C2×D411yescharacteristic
346C2×Q8×C11C2×D411yescharacteristic
347C2×Q8×C11C2×D412yes—
348C2×Q8×C11C2411yescharacteristic
349C2×D4×C11—21no—
350C2×D4×C11—22no—
351C2×D4×C11—22no—
352C2×D4×C11—21no—
353C2×D4×C11—22no—
354C2×D4×C11—21no—
355C2×D4×C11—22no—
356C2×D4×C11—22no—
357C2×D4×C11—22no—
358C2×D4×C11—22no—
359C2×D4×C11—21no—
360C2×D4×C11—22no—
361C2×D4×C11—22no—
362C2×D4×C11—42no—
363C2×D4×C11—42no—
364C2×D4×C11—42no—
365C2×D4×C11—44no—
366C2×D4×C11—48no—
367C2×D4×C11—44no—
368C2×D4×C11—82no—
369C2×D4×C11—84no—
370C2×D4×C11C2×D412yes—
371C2×D4×C11C2×D412yes—
372C2×D4×C11C2×D411yescharacteristic
373C2×D4×C11C2×D411yescharacteristic
374C2×D4×C11C2×D412yes—
375C2×D4×C11C2×D412yes—
376C2×D4×C11C2×D412yes—
377C2×D4×C11C2412yes—
378C2×D4×C11C2411yescharacteristic
379C22×C4×C11—22no—
380C22×C4×C11—22no—
381C22×C4×C11—22no—
382C22×C4×C11—21no—
383C22×C4×C11—22no—
384C22×C4×C11—21no—
385C22×C4×C11—42no—
386C22×C4×C11—42no—
387C22×C4×C11C2×D411yescharacteristic
388C22×C4×C11C2×D411yescharacteristic
389C22×C4×C11C2×D411yescharacteristic
390C22×C4×C11C2×D412yes—
391C22×C4×C11C2×D412yes—
392C22×C4×C11C2×D412yes—
393C22×C4×C11C2412yes—
394C22×C4×C11C2411yescharacteristic
395C22×C4×C11C2411yescharacteristic
396C22×C4×C11C2412yes—
397C22×C4×C11C2411yescharacteristic
398C2×C22⋊D11—22no—
399C2×C22⋊D11—22no—
400C2×C22⋊D11—22no—
401C2×C22⋊D11—22no—
402C2×C22⋊D11—22no—
403C2×C22⋊D11—22no—
404C2×C22⋊D11—44no—
405C22×Dic11—21no—
406C22×Dic11—21no—
407C22×Dic11—21no—
408#4339—42no—
409#4339—42no—
410#4339—42no—
411#4339—42no—
412#4339—44no—
413#4339—44no—
414C2×D44—21no—
415C2×D44—22no—
416C2×D44—22no—
417C2×D44C2412yes—
418C2×C4×D11—22no—
419C2×C4×D11—22no—
420C2×C4×D11—44no—
421C2×Dic22—21no—
422C2×Dic22—22no—
423C2×Dic22—22no—
424C2×Dic22C2412yes—
425C11×C4⋊C4—22no—
426C11×C4⋊C4—21no—
427C11×C4⋊C4—21no—
428C11×C4⋊C4—22no—
429C11×C4⋊C4—21no—
430C11×C4⋊C4C2412yes—
431C11×C4⋊C4C2411yescharacteristic
432C11×C4⋊C4C2411yescharacteristic
433C11×C22⋊C4—22no—
434C11×C22⋊C4—21no—
435C11×C22⋊C4—21no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—21no—
440C11×C22⋊C4—22no—
441C11×C22⋊C4—22no—
442C11×C22⋊C4—22no—
443C11×C22⋊C4—22no—
444C11×C22⋊C4—21no—
445C42×C11—22no—
446C42×C11—21no—
447C22⋊Dic11—22no—
448C22⋊Dic11—22no—
449C22⋊Dic11—22no—
450C22⋊Dic11—22no—
451C22⋊Dic11—21no—
452C22⋊Dic11—21no—
453C22⋊Dic11—21no—
454C22⋊Dic11—21no—
455#4326—42no—
456#4325—42no—
457#4324—42no—
458#4324—42no—
459#4324—42no—
460#4323—42no—
461#4323—42no—
462#4323—42no—
463(C2×D11)⋊C4—22no—
464(C2×D11)⋊C4—22no—
465(C2×D11)⋊C4—22no—
466(C2×D11)⋊C4—22no—
467C4⋊Dic11—21no—
468C4⋊Dic11—21no—
469C4⋊Dic11C2411yescharacteristic
470C4⋊Dic11C2411yescharacteristic
471C4⋊Dic11C2411yescharacteristic
472C4⋊Dic11C2411yescharacteristic
473Dic11⋊C4—22no—
474Dic11⋊C4—22no—
475Dic11⋊C4—22no—
476Dic11⋊C4—22no—
477C4×Dic11—21no—
478C4×Dic11—21no—
479C4×Dic11—21no—
480C4×Dic11—21no—
481#4318—22no—
482#4318—22no—
483#4318—42no—
484#4318—42no—
485C2×C11⋊C8—22no—
486C2×C11⋊C8—22no—
487C2×C11⋊C8—42no—
488C2×C11⋊C8—42no—
489C2×C11⋊C8C2411yescharacteristic
490C2×C11⋊C8C2411yescharacteristic
491C2×C11⋊C8C2412yes—
492C2×C11⋊C8C2412yes—
493C2×C11⋊C8C2411yescharacteristic
494C2×C11⋊C8C2411yescharacteristic
495#3488D1111yescharacteristic, complemented
496#3449—111no—
497#3204—112no—
498#3203—112no—
499#3198—112no—
500#3198—112no—
501#3197—112no—
502#3194—112no—
503#3191—112no—
504#3188—112no—
505#3097—111no—
506#3096—111no—
507#3094—111no—
508#3091—111no—
509#3063—111no—
510#3062—111no—
511#3058—111no—
512#3057—111no—
513#3009—111no—
514#3008—111no—
515#3005—111no—
516C2×#449—111no—
517#2880—111no—
518C23×C11—22no—
519C23×C11—22no—
520C23×C11—21no—
521C23×C11—42no—
522C23×C11—41no—
523C23×C11—42no—
524C23×C11—41no—
525C23×C11—42no—
526C23×C11—44no—
527C23×C11—42no—
528C23×C11—81no—
529C23×C11—82no—
530C23×C11—81no—
531C23×C11—82no—
532C23×C11C22×D412yes—
533C23×C11C22×D411yescharacteristic
534C23×C11C22×D412yes—
535C23×C11C22×D411yescharacteristic
536C23×C11C22×D411yescharacteristic
537C22×D11—22no—
538C22×D11—42no—
539C22×D11—81no—
540C22×D11—81no—
541Q8×C11—22no—
542Q8×C11—22no—
543Q8×C11—21no—
544Q8×C11—21no—
545Q8×C11—42no—
546D4×C11—24no—
547D4×C11—24no—
548D4×C11—22no—
549D4×C11—22no—
550D4×C11—22no—
551D4×C11—21no—
552D4×C11—22no—
553D4×C11—21no—
554D4×C11—42no—
555D4×C11—42no—
556D4×C11—42no—
557D4×C11—44no—
558D4×C11—44no—
559D4×C11—42no—
560D4×C11—44no—
561D4×C11—42no—
562D4×C11—42no—
563D4×C11—81no—
564D4×C11—82no—
565D4×C11—82no—
566D4×C11—82no—
567D4×C11—82no—
568C2×C4×C11—22no—
569C2×C4×C11—22no—
570C2×C4×C11—22no—
571C2×C4×C11—22no—
572C2×C4×C11—22no—
573C2×C4×C11—21no—
574C2×C4×C11—21no—
575C2×C4×C11—21no—
576C2×C4×C11—21no—
577C2×C4×C11—22no—
578C2×C4×C11—22no—
579C2×C4×C11—21no—
580C2×C4×C11—22no—
581C2×C4×C11—21no—
582C2×C4×C11—21no—
583C2×C4×C11—42no—
584C2×C4×C11—42no—
585C2×C4×C11—42no—
586C2×C4×C11—44no—
587C2×C4×C11—42no—
588C2×C4×C11—81no—
589C2×C4×C11—82no—
590C2×C4×C11C22×D411yescharacteristic
591C2×C4×C11C22×D412yes—
592C2×C4×C11C22×D412yes—
593C2×C4×C11C22×D411yescharacteristic
594C2×C4×C11C22×D411yescharacteristic
595C2×C4×C11H(5,𝔽2)12yes—
596C2×C4×C11H(5,𝔽2)12yes—
597C2×C4×C11C2511yescharacteristic
598C22⋊D11—44no—
599C22⋊D11—44no—
600C22⋊D11—82no—
601C22⋊D11—82no—
602C22⋊D11—82no—
603C22⋊D11—82no—
604C2×Dic11—21no—
605C2×Dic11—21no—
606C2×Dic11—21no—
607C2×Dic11—21no—
608C2×Dic11—22no—
609C2×Dic11—42no—
610C2×Dic11—81no—
611C2×Dic11—81no—
612D44—22no—
613D44—22no—
614D44—42no—
615C4×D11—44no—
616C4×D11—44no—
617Dic22—22no—
618Dic22—22no—
619Dic22—42no—
620C11⋊C8—21no—
621C11⋊C8—21no—
622C11⋊C8—21no—
623C11⋊C8—21no—
624C11⋊C8—22no—
625C11⋊C8—22no—
626C2×H(5,𝔽2)C2×D1111yescharacteristic
627C22×#41—111no—
628C22×#41C2×D1111yescharacteristic
629C2×#137—111no—
630C2×AGL(1,ℤ/8)—111no—
631C22×SD16—111no—
632C22×D8—111no—
633C2×#131—111no—
634C2×#131—111no—
635#550—21no—
636#548—21no—
637#546—22no—
638#546—21no—
639D42—21no—
640D42—22no—
641#537—112no—
642#537—112no—
643#537C2×D1111yescharacteristic
644#537C2×D1112yescomplemented
645#536—111no—
646#536—111no—
647#536—221no—
648#535—111no—
649#535—111no—
650#535—221no—
651#535C2×D1111yescharacteristic
652#535C2×D1112yescomplemented
653#534—222no—
654#532—221no—
655#532—221no—
656#525—112no—
657#525—112no—
658#525—222no—
659#525C2×D1111yescharacteristic
660#525C2×D1112yescomplemented
661C2×#121C2×D1111yescharacteristic
662C2×#121C2×D1112yescomplemented
663#520C2×D1111yescharacteristic
664C2×#117—111no—
665#485—111no—
666#485—111no—
667#485—112no—
668#485—112no—
669#484—111no—
670#484—112no—
671#483—111no—
672#483—112no—
673#482—111no—
674#482—111no—
675#482—112no—
676#482—112no—
677#482—112no—
678#482—112no—
679#481—111no—
680#481—112no—
681#481—112no—
682#480—111no—
683#480—112no—
684#480—112no—
685#470—112no—
686#469—112no—
687#469—112no—
688#469—112no—
689#468—112no—
690#468—112no—
691#468—112no—
692#468—112no—
693#467—112no—
694#466—112no—
695#466—112no—
696#466—112no—
697#465—112no—
698#465—112no—
699#465—112no—
700#465—112no—
701#452—112no—
702#452—112no—
703#452—112no—
704#452—112no—
705#450—112no—
706#450—112no—
707#449—112no—
708#449—112no—
709#449—112no—
710#449—112no—
711#449—112no—
712#449—112no—
713#449—112no—
714#449—112no—
715#447—112no—
716#447—112no—
717#428—111no—
718#428—111no—
719#427—111no—
720#427—111no—
721#419—111no—
722#418—111no—
723#418—111no—
724#418—111no—
725#416—111no—
726#416—111no—
727C2×#103—111no—
728C2×#102—111no—
729#408—111no—
730#408—111no—
731#408—112no—
732#408—112no—
733#407—111no—
734#407—112no—
735C2×C22⋊C8—111no—
736C2×C22⋊C8—112no—
737C22×C11—21no—
738C22×C11—21no—
739C22×C11—21no—
740C22×C11—22no—
741C22×C11—21no—
742C22×C11—22no—
743C22×C11—22no—
744C22×C11—21no—
745C22×C11—21no—
746C22×C11—22no—
747C22×C11—21no—
748C22×C11—21no—
749C22×C11—22no—
750C22×C11—22no—
751C22×C11—42no—
752C22×C11—41no—
753C22×C11—42no—
754C22×C11—41no—
755C22×C11—42no—
756C22×C11—41no—
757C22×C11—82no—
758C22×C11—84no—
759C22×C11—162no—
760C22×C11—164no—
761C22×C11#53412yes—
762C22×C11C23×D411yescharacteristic
763C2×D11—42no—
764C2×D11—42no—
765C2×D11—42no—
766C2×D11—84no—
767C4×C11—21no—
768C4×C11—21no—
769C4×C11—22no—
770C4×C11—22no—
771C4×C11—41no—
772C4×C11—42no—
773C4×C11—41no—
774C4×C11—41no—
775C4×C11#53412yes—
776C4×C11C2×H(5,𝔽2)11yescharacteristic
777C4×C11C2×H(5,𝔽2)11yescharacteristic
778Dic11—41no—
779Dic11—41no—
780Dic11—41no—
781Dic11—41no—
782Dic11—42no—
783H(5,𝔽2)—42no—
784H(5,𝔽2)—42no—
785C2×#41—21no—
786C2×#41—42no—
787C2×#41—42no—
788C2×#41—112no—
789C2×#41—112no—
790C2×#41—221no—
791C2×#41—221no—
792C2×#41—442no—
793C2×#41—442no—
794C2×#41C22⋊D1112yes—
795C2×#41C22⋊D1111yescharacteristic
796C2×#41C22⋊D1111yescharacteristic
797C2×#41C22×D1111yescharacteristic
798C2×#41C22×D1112yes—
799C2×#41C22×D1111yescharacteristic
800C2×#41C22×D1111yescharacteristic
801C2×#41C22×D1112yes—
802C22×Q8—111no—
803C22×Q8C22⋊D1111yescharacteristic
804C22×D4—21no—
805C22×D4—22no—
806C22×D4—22no—
807C22×D4—21no—
808C22×D4—111no—
809C22×D4—221no—
810C22×D4C22⋊D1112yes—
811C22×D4C22⋊D1111yescharacteristic
812C22×D4C22×D1111yescharacteristic
813C22×D4C22×D1112yes—
814C23×C4—221no—
815C23×C4C22×D1111yescharacteristic
816C23×C4C22×D1112yes—
817#137—442no—
818AGL(1,ℤ/8)—442no—
819C2×Q16—112no—
820C2×SD16—112no—
821C2×SD16—112no—
822C2×SD16—112no—
823C2×SD16—112no—
824C2×SD16—442no—
825C2×D8—112no—
826C2×D8—112no—
827C2×D8—112no—
828C2×D8—442no—
829#131—442no—
830#131—442no—
831C2×M16—111no—
832C2×M16—111no—
833C2×M16—112no—
834C2×M16—112no—
835C22×C8—111no—
836C22×C8—111no—
837C22×C8—112no—
838C22×C8—112no—
839C4⋊Q8—221no—
840C4⋊Q8—221no—
841#127—21no—
842#127—22no—
843#127—221no—
844#127—221no—
845#124—21no—
846#124—22no—
847#124—221no—
848#124—221no—
849#124—221no—
850#124—221no—
851#123—21no—
852#123—22no—
853#123—222no—
854#123—222no—
855#123—222no—
856#123—222no—
857C22⋊Q8—21no—
858C22⋊Q8—22no—
859C22⋊Q8—112no—
860C22⋊Q8—112no—
861C22⋊Q8—112no—
862C22⋊Q8—112no—
863C22⋊Q8—222no—
864C22⋊Q8—222no—
865C22⋊Q8C22×D1111yescharacteristic
866C22⋊Q8C22×D1111yescharacteristic
867C22⋊Q8C22×D1112yes—
868#121—22no—
869#121—21no—
870#121—22no—
871#121—22no—
872#121—22no—
873#121—21no—
874#121—21no—
875#121—22no—
876#121—22no—
877#121—112no—
878#121—112no—
879#121—112no—
880#121—112no—
881#121—222no—
882#121—222no—
883#121—222no—
884#121—222no—
885#121—222no—
886#121—222no—
887#121C22×D1112yes—
888#121C22×D1112yes—
889#121C22×D1111yescharacteristic
890#121C22×D1112yes—
891#121C22×D1112yes—
892#121C22×D1111yescharacteristic
893#121C22×D1112yes—
894#120—21no—
895#120—22no—
896#120—22no—
897#120—22no—
898#120—22no—
899#120—222no—
900#120—222no—
901#120—222no—
902#120—222no—
903C4×Q8—21no—
904C4×D4—22no—
905C4×D4—21no—
906C4×D4—21no—
907C4×D4—21no—
908C4×D4—22no—
909C4×D4—22no—
910C4×D4—222no—
911C4×D4—222no—
912C4×D4—222no—
913C4×D4—222no—
914#117—111no—
915#117—111no—
916#117—111no—
917#117—111no—
918#117—221no—
919#117—221no—
920#117C22×D1111yescharacteristic
921#117C22×D1112yes—
922C2×C4⋊C4—111no—
923C2×C4⋊C4—111no—
924C2×C4⋊C4C22×D1111yescharacteristic
925C2×C4⋊C4C22×D1112yes—
926C2×C22⋊C4—21no—
927C2×C22⋊C4—22no—
928C2×C22⋊C4—221no—
929C2×C42—221no—
930#107—111no—
931#107—111no—
932#107—111no—
933#107—111no—
934#107—112no—
935#107—112no—
936#106—111no—
937#106—111no—
938#106—111no—
939#106—111no—
940#106—112no—
941#106—112no—
942#103—111no—
943#103—111no—
944#103—111no—
945#103—111no—
946#103—112no—
947#103—112no—
948#103—112no—
949#103—112no—
950#102—111no—
951#102—111no—
952#102—111no—
953#102—111no—
954#102—112no—
955#102—112no—
956#102—112no—
957#102—112no—
958#102—112no—
959#102—112no—
960#102—112no—
961#102—112no—
962C22⋊C8—111no—
963C22⋊C8—111no—
964C22⋊C8—112no—
965C22⋊C8—112no—
966C22⋊C8—111no—
967C22⋊C8—111no—
968C22⋊C8—112no—
969C22⋊C8—112no—
970C22⋊C8—112no—
971C22⋊C8—112no—
972C2×C11—22no—
973C2×C11—41no—
974C2×C11—42no—
975C2×C11—41no—
976C2×C11—42no—
977C2×C11—82no—
978C2×C11—81no—
979C2×C11C2×#53411yescharacteristic
980C2×C11#358411yescharacteristic
981C2×C11#358511yescharacteristic
982D11—82no—
983C24—22no—
984C24—21no—
985C24—221no—
986C24C2×C22⋊D1111yescharacteristic
987C24C2×C22⋊D1112yes—
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—44no—
997#41—42no—
998#41—42no—
999#41—42no—
1000#41—42no—
1001#41—44no—
1002#41—442no—
1003#41—442no—
1004#41—442no—
1005#41—442no—
1006#41—444no—
1007#41—444no—
1008C2×Q8—42no—
1009C2×Q8—112no—
1010C2×Q8—221no—
1011C2×Q8—222no—
1012C2×Q8—222no—
1013C2×Q8C2×C22⋊D1111yescharacteristic
1014C2×Q8C2×C22⋊D1111yescharacteristic
1015C2×Q8C2×C22⋊D1112yes—
1016C2×Q8C23×D1111yescharacteristic
1017C2×D4—21no—
1018C2×D4—22no—
1019C2×D4—22no—
1020C2×D4—21no—
1021C2×D4—22no—
1022C2×D4—21no—
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—22no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C2×D4—22no—
1029C2×D4—21no—
1030C2×D4—42no—
1031C2×D4—42no—
1032C2×D4—42no—
1033C2×D4—44no—
1034C2×D4—48no—
1035C2×D4—44no—
1036C2×D4—82no—
1037C2×D4—84no—
1038C2×D4—112no—
1039C2×D4—222no—
1040C2×D4—222no—
1041C2×D4—222no—
1042C2×D4—222no—
1043C2×D4—222no—
1044C2×D4—222no—
1045C2×D4—222no—
1046C2×D4—222no—
1047C2×D4—221no—
1048C2×D4—444no—
1049C2×D4C2×C22⋊D1112yes—
1050C2×D4C2×C22⋊D1111yescharacteristic
1051C2×D4C2×C22⋊D1112yes—
1052C2×D4C2×C22⋊D1111yescharacteristic
1053C2×D4C2×C22⋊D1112yes—
1054C2×D4C2×C22⋊D1112yes—
1055C2×D4C2×C22⋊D1112yes—
1056C2×D4C23×D1112yes—
1057C2×D4C23×D1111yescharacteristic
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—22no—
1061C22×C4—21no—
1062C22×C4—22no—
1063C22×C4—21no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—221no—
1067C22×C4—221no—
1068C22×C4—221no—
1069C22×C4—222no—
1070C22×C4—222no—
1071C22×C4—444no—
1072C22×C4C2×C22⋊D1111yescharacteristic
1073C22×C4C2×C22⋊D1111yescharacteristic
1074C22×C4C2×C22⋊D1111yescharacteristic
1075C22×C4C2×C22⋊D1112yes—
1076C22×C4C2×C22⋊D1112yes—
1077C22×C4C2×C22⋊D1112yes—
1078C22×C4C23×D1111yescharacteristic
1079C22×C4C23×D1112yes—
1080C22×C4C23×D1111yescharacteristic
1081C22×C4C23×D1112yes—
1082C22×C4C23×D1111yescharacteristic
1083Q16—442no—
1084SD16—442no—
1085SD16—442no—
1086SD16—442no—
1087SD16—442no—
1088D8—442no—
1089D8—442no—
1090D8—442no—
1091M16—222no—
1092M16—222no—
1093M16—442no—
1094M16—442no—
1095C2×C8—112no—
1096C2×C8—111no—
1097C2×C8—111no—
1098C2×C8—112no—
1099C2×C8—111no—
1100C2×C8—111no—
1101C2×C8—222no—
1102C2×C8—222no—
1103C2×C8—442no—
1104C2×C8—442no—
1105C4⋊C4—22no—
1106C4⋊C4—21no—
1107C4⋊C4—21no—
1108C4⋊C4—22no—
1109C4⋊C4—21no—
1110C4⋊C4—111no—
1111C4⋊C4—111no—
1112C4⋊C4—111no—
1113C4⋊C4—111no—
1114C4⋊C4—221no—
1115C4⋊C4—221no—
1116C4⋊C4—222no—
1117C4⋊C4—222no—
1118C4⋊C4—222no—
1119C4⋊C4—222no—
1120C4⋊C4C23×D1112yes—
1121C4⋊C4C23×D1111yescharacteristic
1122C4⋊C4C23×D1111yescharacteristic
1123C22⋊C4—22no—
1124C22⋊C4—21no—
1125C22⋊C4—21no—
1126C22⋊C4—22no—
1127C22⋊C4—21no—
1128C22⋊C4—22no—
1129C22⋊C4—21no—
1130C22⋊C4—22no—
1131C22⋊C4—22no—
1132C22⋊C4—22no—
1133C22⋊C4—22no—
1134C22⋊C4—21no—
1135C22⋊C4—221no—
1136C22⋊C4—221no—
1137C22⋊C4—221no—
1138C22⋊C4—221no—
1139C22⋊C4—222no—
1140C22⋊C4—222no—
1141C22⋊C4—222no—
1142C22⋊C4—222no—
1143C22⋊C4—222no—
1144C22⋊C4—222no—
1145C22⋊C4—222no—
1146C22⋊C4—222no—
1147C42—22no—
1148C42—21no—
1149C42—221no—
1150C42—221no—
1151C42—221no—
1152C42—221no—
1153C11#6076011yescharacteristic, complemented, Sylow
1154C23—22no—
1155C23—22no—
1156C23—21no—
1157C23—42no—
1158C23—41no—
1159C23—42no—
1160C23—41no—
1161C23—42no—
1162C23—44no—
1163C23—42no—
1164C23—81no—
1165C23—82no—
1166C23—81no—
1167C23—82no—
1168C23—222no—
1169C23—442no—
1170C23—881no—
1171C23—881no—
1172C23C22×C22⋊D1112yes—
1173C23C22×C22⋊D1111yescharacteristic
1174C23C22×C22⋊D1112yes—
1175C23C22×C22⋊D1111yescharacteristic
1176C23C22×C22⋊D1111yescharacteristic
1177Q8—22no—
1178Q8—22no—
1179Q8—21no—
1180Q8—21no—
1181Q8—42no—
1182Q8—222no—
1183Q8—222no—
1184Q8—442no—
1185D4—24no—
1186D4—24no—
1187D4—22no—
1188D4—22no—
1189D4—22no—
1190D4—21no—
1191D4—22no—
1192D4—21no—
1193D4—42no—
1194D4—42no—
1195D4—42no—
1196D4—44no—
1197D4—44no—
1198D4—42no—
1199D4—44no—
1200D4—42no—
1201D4—42no—
1202D4—81no—
1203D4—82no—
1204D4—82no—
1205D4—82no—
1206D4—82no—
1207D4—222no—
1208D4—222no—
1209D4—444no—
1210D4—444no—
1211D4—442no—
1212D4—882no—
1213D4—882no—
1214D4—882no—
1215D4—882no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—44no—
1235C2×C4—42no—
1236C2×C4—81no—
1237C2×C4—82no—
1238C2×C4—221no—
1239C2×C4—221no—
1240C2×C4—221no—
1241C2×C4—221no—
1242C2×C4—222no—
1243C2×C4—444no—
1244C2×C4—444no—
1245C2×C4—442no—
1246C2×C4—881no—
1247C2×C4—881no—
1248C2×C4#6703712yes—
1249C2×C4#6703712yes—
1250C2×C4C22×C22⋊D1112yes—
1251C2×C4C22×C22⋊D1111yescharacteristic
1252C2×C4C22×C22⋊D1112yes—
1253C2×C4C22×C22⋊D1111yescharacteristic
1254C2×C4C22×C22⋊D1111yescharacteristic
1255C2×C4C24×D1111yescharacteristic
1256C8—221no—
1257C8—221no—
1258C8—221no—
1259C8—221no—
1260C8—222no—
1261C8—222no—
1262C22—21no—
1263C22—21no—
1264C22—22no—
1265C22—21no—
1266C22—21no—
1267C22—22no—
1268C22—21no—
1269C22—21no—
1270C22—22no—
1271C22—22no—
1272C22—21no—
1273C22—22no—
1274C22—22no—
1275C22—21no—
1276C22—42no—
1277C22—41no—
1278C22—42no—
1279C22—41no—
1280C22—42no—
1281C22—41no—
1282C22—82no—
1283C22—84no—
1284C22—162no—
1285C22—164no—
1286C22—442no—
1287C22—442no—
1288C22—442no—
1289C22—884no—
1290C22#1062333512yes—
1291C22C23×C22⋊D1111yescharacteristic
1292C4—21no—
1293C4—21no—
1294C4—22no—
1295C4—22no—
1296C4—42no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—441no—
1301C4—441no—
1302C4—442no—
1303C4—441no—
1304C4—441no—
1305C4#1062333512yes—
1306C4C2×#6703711yescharacteristic
1307C4C2×#6703711yescharacteristic
1308C2—22no—
1309C2—41no—
1310C2—42no—
1311C2—41no—
1312C2—42no—
1313C2—82no—
1314C2—81no—
1315C2—882no—
1316C2C2×#1062333511yescharacteristic
1317C2#1308338711yescharacteristic
1318C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3488C2
socleC22×C11C23×D4
hypercenter#3488D11
hypocenterC11#60760
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #13081945C2semidirect
2. #13079522C2semidirect
3. #13079513C2semidirect
4. #13079468C2semidirect
5. #13079468C2semidirect
6. #13079453C2semidirect
7. #13079430C2semidirect
8. #13079404C2semidirect
9. #13079381C2semidirect
10. #13078585C2semidirect
11. #13078574C2semidirect
12. #13078552C2semidirect
13. #13078525C2semidirect
14. #13078309C2semidirect
15. #13078298C2semidirect
16. #13078261C2semidirect
17. #13078252C2semidirect
18. #13077893C2semidirect
19. #13077884C2semidirect
20. #13077856C2semidirect
21. C2×#10622650C2semidirect
22. #13077065C2semidirect
23. C11×#3488C2semidirect
26. C22×#4339C22semidirect
34. C11×#537C22semidirect
36. C11×#535C22semidirect
38. C11×#525C22semidirect
40. C2×C11×#121C22semidirect
42. #10623364C22semidirect
43. #10623364C22semidirect
47. #10623361C22semidirect
50. #10623356C22semidirect
51. C2×#67004C22semidirect
52. C2×#67002C22semidirect
53. C2×#67001C22semidirect
54. C2×#67001C22semidirect
58. C22×#4324C22semidirect
59. C22×#4323C22semidirect
60. #10623322C22semidirect
61. #10623322C22semidirect
62. C2×#66979C22semidirect
63. #10622852C22semidirect
64. #10622852C22semidirect
65. #10622851C22semidirect
66. #10622851C22semidirect
69. #10622847C22semidirect
70. #10622847C22semidirect
71. #10622846C22semidirect
72. #10622846C22semidirect
73. #10622831C22semidirect
74. #10622831C22semidirect
75. #10622830C22semidirect
76. #10622830C22semidirect
77. #10622828C22semidirect
78. #10622828C22semidirect
79. #10622820C22semidirect
80. #10622820C22semidirect
81. C2×C22⋊(C11⋊C8)C22semidirect
82. C2×C22⋊(C11⋊C8)C22semidirect
83. #10622665C22semidirect
84. #10622664C22semidirect
85. #10622662C22semidirect
86. #10622661C22semidirect
87. #10622660C22semidirect
88. #10622660C22semidirect
89. #10622658C22semidirect
90. #10622658C22semidirect
91. #10622657C22semidirect
92. #10622656C22semidirect
93. #10622655C22semidirect
94. #10622655C22semidirect
95. #10622655C22semidirect
96. #10622654C22semidirect
97. #10622654C22semidirect
98. #10622654C22semidirect
99. #10622652C22semidirect
100. #10622652C22semidirect
101. #10622652C22semidirect
102. #10622651C22semidirect
103. #10622651C22semidirect
104. #10622651C22semidirect
105. #10622650C22semidirect
106. #10622650C22semidirect
107. #10622650C22semidirect
108. #10622650C22semidirect
109. #10622650C22semidirect
110. #10622650C22semidirect
111. #10622648C22semidirect
112. #10622648C22semidirect
113. #10622648C22semidirect
114. #10622648C22semidirect
115. #10622647C22semidirect
116. #10622647C22semidirect
117. #10622646C22semidirect
118. #10622646C22semidirect
119. #10622617C22semidirect
120. #10622616C22semidirect
121. #10622616C22semidirect
122. #10622614C22semidirect
123. #10622611C22semidirect
124. #10622611C22semidirect
125. #10622609C22semidirect
126. #10622609C22semidirect
127. #10622584C22semidirect
128. #10622583C22semidirect
129. C2×#66874C22semidirect
130. #10622581C22semidirect
131. #10622580C22semidirect
132. C2×#66873C22semidirect
133. #10622577C22semidirect
134. #10622577C22semidirect
495. #3488D11semidirect
644. #537C2×D11semidirect
652. #535C2×D11semidirect
660. #525C2×D11semidirect
662. C2×#121C2×D11semidirect
1153. C11#60760semidirect

Maximal subgroups

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

subgroupindex
#130819452
#130795222
#130795132
#130794682
#130794532
#130794302
#130794042
#130793812
#130785852
#130785742
#130785522
#130785252
#130783092
#130782982
#130782612
#130782522
#130778932
#130778842
#130778562
C2×#106226502
#130770652
C11×#34882
#6076011