Finite Group Databasebeta

← #15624672

Subgroups — #15624672

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#13082285C211yesmaximal, characteristic, complemented
2#13079522C212yesmaximal, complemented
3#13079513C212yesmaximal, complemented
4#13079462C212yesmaximal, complemented
5#13079462C212yesmaximal, complemented
6#13079453C212yesmaximal, complemented
7#13079426C212yesmaximal, complemented
8#13079404C212yesmaximal, complemented
9#13079377C212yesmaximal, complemented
10#13078579C211yesmaximal, characteristic, complemented
11#13078568C211yesmaximal, characteristic, complemented
12#13078556C211yesmaximal, characteristic, complemented
13#13078529C211yesmaximal, characteristic, complemented
14#13078303C211yesmaximal, characteristic, complemented
15#13078292C211yesmaximal, characteristic, complemented
16#13078261C211yesmaximal, characteristic, complemented
17#13078257C211yesmaximal, characteristic, complemented
18#13077891C211yesmaximal, characteristic, complemented
19#13077882C211yesmaximal, characteristic, complemented
20#13077858C211yesmaximal, characteristic, complemented
21C2×#10622851C211yesmaximal, characteristic, complemented
22#13077065C211yesmaximal, characteristic, complemented
23C11×#3449C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C22×C11×#41C2211yescharacteristic, complemented
26C2×#67042C2211yescharacteristic
27C11×#537C2212yescomplemented
28C11×#537C2212yescomplemented
29C11×#536—21no—
30C11×#536C2211yescharacteristic
31C11×#536C2211yescharacteristic, complemented
32C11×#535—21no—
33C11×#535C2211yescharacteristic
34C11×#535C2211yescharacteristic, complemented
35C11×#534—22no—
36C11×#532—21no—
37C11×#532—21no—
38C11×#525—22no—
39C11×#525C2212yescomplemented
40C11×#525C2212yescomplemented
41C2×C11×#117C2211yescharacteristic, complemented
42#10623365—21no—
43#10623364C2211yescharacteristic
44#10623364C2212yescomplemented
45#10623361C2211yescharacteristic
46#10623361C2212yescomplemented
47#10623360—22no—
48#10623360—21no—
49#10623358C2211yescharacteristic
50C2×#67001C2211yescharacteristic, complemented
51C2×#67001C2211yescharacteristic, complemented
52#10623348—21no—
53C2×#66995C2211yescharacteristic, complemented
54C22×#4325C2211yescharacteristic, complemented
55D4×C22⋊D11—21no—
56D4×C22⋊D11—22no—
57C2×#66985C2211yescharacteristic, complemented
58C22×#4323C2211yescharacteristic, complemented
59#10623322C2211yescharacteristic
60#10623322C2212yescomplemented
61C2×#66983C2211yescharacteristic
62C2×#66983C2212yescomplemented
63#10622852C2212yescomplemented
64#10622852C2212yescomplemented
65#10622851C2212yescomplemented
66#10622851C2212yescomplemented
67#10622851C2212yescomplemented
68#10622851C2212yescomplemented
69#10622851C2212yescomplemented
70#10622851C2212yescomplemented
71#10622847C2211yescharacteristic
72#10622847C2211yescharacteristic
73#10622847C2212yescomplemented
74#10622847C2212yescomplemented
75#10622838C2211yescharacteristic, complemented
76C2×#66899C2211yescharacteristic, complemented
77#10622828C2211yescharacteristic, complemented
78C2×#66896C2211yescharacteristic, complemented
79#10622820C2211yescharacteristic, complemented
80#10622820C2212yescomplemented
81C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
82C2×C22⋊(C11⋊C8)C2212yescomplemented
83#10622665C2212yescomplemented
84#10622664C2212yescomplemented
85#10622662C2212yescomplemented
86#10622662C2212yescomplemented
87#10622662C2212yescomplemented
88#10622661C2212yescomplemented
89#10622661C2212yescomplemented
90#10622661C2212yescomplemented
91#10622660C2212yescomplemented
92#10622660C2212yescomplemented
93#10622659C2212yescomplemented
94#10622659C2212yescomplemented
95#10622658C2212yescomplemented
96#10622658C2212yescomplemented
97#10622657C2212yescomplemented
98#10622656C2212yescomplemented
99#10622655C2212yescomplemented
100#10622654C2212yescomplemented
101#10622652C2212yescomplemented
102#10622652C2212yescomplemented
103#10622652C2212yescomplemented
104#10622651C2212yescomplemented
105#10622651C2212yescomplemented
106#10622651C2212yescomplemented
107#10622650C2212yescomplemented
108#10622650C2212yescomplemented
109#10622649C2212yescomplemented
110#10622649C2212yescomplemented
111#10622648C2212yescomplemented
112#10622648C2212yescomplemented
113#10622647C2212yescomplemented
114#10622646C2212yescomplemented
115#10622616C2211yescharacteristic, complemented
116#10622616C2211yescharacteristic, complemented
117#10622616C2212yescomplemented
118#10622616C2212yescomplemented
119#10622615C2211yescharacteristic, complemented
120#10622615C2211yescharacteristic, complemented
121#10622614C2211yescharacteristic, complemented
122#10622614C2211yescharacteristic, complemented
123#10622611C2211yescharacteristic, complemented
124#10622611C2211yescharacteristic, complemented
125#10622609C2211yescharacteristic, complemented
126#10622609C2211yescharacteristic, complemented
127#10622608C2211yescharacteristic, complemented
128#10622608C2211yescharacteristic, complemented
129#10622584C2211yescharacteristic, complemented
130#10622583C2211yescharacteristic, complemented
131#10622581C2211yescharacteristic, complemented
132#10622581C2212yescomplemented
133#10622580C2211yescharacteristic, complemented
134#10622580C2212yescomplemented
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41—42no—
138C2×C11×#41—42no—
139C2×C11×#41—42no—
140C2×C11×#41—42no—
141C2×C11×#41D412yes—
142C2×C11×#41D411yescharacteristic
143C2×C11×#41D411yescharacteristic
144C2×C11×#41C2312yes—
145C2×C11×#41C2312yes—
146C2×C11×#41C2311yescharacteristic
147C2×C11×#41C2311yescharacteristic
148C2×C11×#41C2312yes—
149C22×Q8×C11D411yescharacteristic
150C22×Q8×C11C2311yescharacteristic
151C22×D4×C11—21no—
152C22×D4×C11D412yes—
153C22×D4×C11D411yescharacteristic
154C22×D4×C11C2311yescharacteristic
155C23×C4×C11—21no—
156C23×C4×C11C2311yescharacteristic
157C23×C4×C11C2312yes—
158C22×C22⋊D11—21no—
159C22×C22⋊D11—22no—
160#67042—42no—
161#67042—42no—
162C2×#4343—21no—
163C2×D4×D11—22no—
164C2×D4×D11—21no—
165C2×#4339C2311yescharacteristic
166C2×#4339C2312yes—
167C22×D44C2311yescharacteristic
168C22×D44C2312yes—
169C11×C4⋊Q8—21no—
170C11×C4⋊Q8—21no—
171C11×#127—21no—
172C11×#127—21no—
173C11×#124—21no—
174C11×#124—21no—
175C11×#124—21no—
176C11×#124—21no—
177C11×#123—22no—
178C11×#123—22no—
179C11×#123—22no—
180C11×#123—22no—
181C11×C22⋊Q8—22no—
182C11×C22⋊Q8—22no—
183C11×C22⋊Q8C2312yes—
184C11×C22⋊Q8C2312yes—
185C11×C22⋊Q8C2312yes—
186C11×C22⋊Q8C2312yes—
187C11×#121—22no—
188C11×#121—22no—
189C11×#121—22no—
190C11×#121—22no—
191C11×#121—22no—
192C11×#121—22no—
193C11×#121C2312yes—
194C11×#121C2312yes—
195C11×#121C2312yes—
196C11×#121C2312yes—
197C11×#120—22no—
198C11×#120—22no—
199C11×#120—22no—
200C11×#120—22no—
201C4×D4×C11—22no—
202C4×D4×C11—22no—
203C4×D4×C11—22no—
204C4×D4×C11—22no—
205C11×#117—21no—
206C11×#117—21no—
207C11×#117C2311yescharacteristic
208C11×#117C2311yescharacteristic
209C11×#117C2311yescharacteristic
210C11×#117C2311yescharacteristic
211C2×C11×C4⋊C4C2311yescharacteristic
212C2×C11×C4⋊C4C2311yescharacteristic
213C2×C11×C22⋊C4—21no—
214C2×C42×C11—21no—
215#67006—21no—
216#67006—22no—
217#67001—42no—
218#67001—42no—
219#67000—21no—
220#67000—22no—
221#66999—21no—
222#66999—22no—
223Q8×Dic11—21no—
224C2×#4326C2312yes—
225#66995—42no—
226C2×#4325—42no—
227C2×#4325C2312yes—
228C2×#4325C2312yes—
229C2×#4325C2312yes—
230#66993—21no—
231#66993—22no—
232#66992—22no—
233#66992—22no—
234#66992—22no—
235#66991—21no—
236#66991—22no—
237#66990—22no—
238#66990—22no—
239#66990—22no—
240D4×Dic11—22no—
241D4×Dic11—21no—
242C2×#4324C2312yes—
243#66985—42no—
244C2×#4323—42no—
245C2×#4323C2312yes—
246C2×#4323C2312yes—
247C2×#4323C2312yes—
248#66983—21no—
249#66983—21no—
250#66983—22no—
251#66983—22no—
252#66983C2312yes—
253#66983C2312yes—
254#66983C2311yescharacteristic
255#66983C2312yes—
256#66983C2312yes—
257#66983C2311yescharacteristic
258#66983C2312yes—
259#66982—21no—
260#66982—22no—
261C4×C22⋊D11—21no—
262C4×C22⋊D11—21no—
263C4×C22⋊D11—22no—
264C4×C22⋊D11—22no—
265C2×(C2×D11)⋊C4—21no—
266C2×(C2×D11)⋊C4—22no—
267#66979C2311yescharacteristic
268#66979C2312yes—
269C2×C4⋊Dic11C2311yescharacteristic
270C2×C4⋊Dic11C2312yes—
271#66977C2311yescharacteristic
272#66977C2311yescharacteristic
273#66977C2312yes—
274C2×#4318C2311yescharacteristic
275C2×#4318C2311yescharacteristic
276C2×#4318C2312yes—
277C2×#4318C2312yes—
278C22×C11⋊C8C2311yescharacteristic
279C22×C11⋊C8C2311yescharacteristic
280C22×C11⋊C8C2312yes—
281C22×C11⋊C8C2312yes—
282#66899C2312yes—
283#66899C2312yes—
284#66899C2312yes—
285#66899C2312yes—
286#66896C2312yes—
287#66896C2312yes—
288#66896C2312yes—
289#66896C2312yes—
290C22⋊(C11⋊C8)C2311yescharacteristic
291C22⋊(C11⋊C8)C2311yescharacteristic
292C22⋊(C11⋊C8)C2312yes—
293C22⋊(C11⋊C8)C2311yescharacteristic
294C22⋊(C11⋊C8)C2311yescharacteristic
295C22⋊(C11⋊C8)C2312yes—
296C22⋊(C11⋊C8)C2312yes—
297C22⋊(C11⋊C8)C2312yes—
298C22⋊(C11⋊C8)C2312yes—
299C22⋊(C11⋊C8)C2312yes—
300#66874C2311yescharacteristic
301#66874C2311yescharacteristic
302#66874C2311yescharacteristic
303#66874C2311yescharacteristic
304#66873C2312yes—
305#66873C2312yes—
306#66873C2311yescharacteristic
307#66873C2311yescharacteristic
308#66873C2312yes—
309#66873C2312yes—
310#66873C2311yescharacteristic
311#66873C2311yescharacteristic
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—21no—
326C24×C11C2×D411yescharacteristic
327C24×C11C2×D412yes—
328C23×D11—22no—
329C23×D11—21no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—22no—
333C11×#41—22no—
334C11×#41—42no—
335C11×#41—42no—
336C11×#41—44no—
337C11×#41—42no—
338C11×#41—42no—
339C11×#41—42no—
340C11×#41—42no—
341C11×#41—42no—
342C11×#41—42no—
343C11×#41—44no—
344C11×#41—44no—
345C2×Q8×C11—21no—
346C2×Q8×C11—22no—
347C2×Q8×C11—22no—
348C2×Q8×C11—42no—
349C2×Q8×C11C2×D411yescharacteristic
350C2×Q8×C11C2×D411yescharacteristic
351C2×Q8×C11C2×D412yes—
352C2×Q8×C11C2412yes—
353C2×D4×C11—22no—
354C2×D4×C11—22no—
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—44no—
364C2×D4×C11—44no—
365C2×D4×C11C2×D412yes—
366C2×D4×C11C2×D411yescharacteristic
367C2×D4×C11C2×D412yes—
368C2×D4×C11C2×D411yescharacteristic
369C2×D4×C11C2×D412yes—
370C2×D4×C11C2×D412yes—
371C2×D4×C11C2×D412yes—
372C2×D4×C11C2412yes—
373C22×C4×C11—22no—
374C22×C4×C11—22no—
375C22×C4×C11—21no—
376C22×C4×C11—21no—
377C22×C4×C11—21no—
378C22×C4×C11—22no—
379C22×C4×C11—22no—
380C22×C4×C11—42no—
381C22×C4×C11—42no—
382C22×C4×C11—44no—
383C22×C4×C11C2×D411yescharacteristic
384C22×C4×C11C2×D411yescharacteristic
385C22×C4×C11C2×D411yescharacteristic
386C22×C4×C11C2×D412yes—
387C22×C4×C11C2×D412yes—
388C22×C4×C11C2×D412yes—
389C22×C4×C11C2411yescharacteristic
390C22×C4×C11C2411yescharacteristic
391C22×C4×C11C2412yes—
392C22×C4×C11C2412yes—
393C22×C4×C11C2411yescharacteristic
394C2×C22⋊D11—21no—
395C2×C22⋊D11—22no—
396C2×C22⋊D11—22no—
397C2×C22⋊D11—21no—
398C2×C22⋊D11—22no—
399C2×C22⋊D11—21no—
400C2×C22⋊D11—22no—
401C2×C22⋊D11—22no—
402C2×C22⋊D11—22no—
403C2×C22⋊D11—82no—
404C2×C22⋊D11—84no—
405C22×Dic11—22no—
406C22×Dic11—21no—
407#4343—44no—
408D4×D11—48no—
409D4×D11—44no—
410#4339—22no—
411#4339—22no—
412#4339—42no—
413#4339—42no—
414C2×D44—22no—
415C2×D44—21no—
416C2×D44—22no—
417C2×D44—22no—
418C2×D44—42no—
419C2×D44—42no—
420C2×D44C2412yes—
421C2×D44C2411yescharacteristic
422C2×C4×D11—22no—
423C2×C4×D11—21no—
424C2×Dic22C2411yescharacteristic
425C11×C4⋊C4—21no—
426C11×C4⋊C4—21no—
427C11×C4⋊C4—22no—
428C11×C4⋊C4—22no—
429C11×C4⋊C4—22no—
430C11×C4⋊C4—22no—
431C11×C4⋊C4C2411yescharacteristic
432C11×C4⋊C4C2411yescharacteristic
433C11×C4⋊C4C2411yescharacteristic
434C11×C4⋊C4C2411yescharacteristic
435C11×C22⋊C4—21no—
436C11×C22⋊C4—21no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—21no—
439C11×C22⋊C4—22no—
440C11×C22⋊C4—22no—
441C11×C22⋊C4—22no—
442C11×C22⋊C4—22no—
443C11×C22⋊C4—22no—
444C11×C22⋊C4—22no—
445C11×C22⋊C4—22no—
446C11×C22⋊C4—22no—
447C42×C11—21no—
448C42×C11—21no—
449C42×C11—21no—
450C42×C11—21no—
451C22⋊Dic11—21no—
452C22⋊Dic11—22no—
453C22⋊Dic11—21no—
454C22⋊Dic11—22no—
455C22⋊Dic11—21no—
456#4326—42no—
457#4325—42no—
458#4325—42no—
459#4325—42no—
460#4324—42no—
461#4323—42no—
462#4323—42no—
463#4323—42no—
464(C2×D11)⋊C4—22no—
465(C2×D11)⋊C4—21no—
466(C2×D11)⋊C4—22no—
467(C2×D11)⋊C4—22no—
468(C2×D11)⋊C4—22no—
469(C2×D11)⋊C4—22no—
470(C2×D11)⋊C4—21no—
471C4⋊Dic11—22no—
472C4⋊Dic11—21no—
473C4⋊Dic11C2412yes—
474C4⋊Dic11C2411yescharacteristic
475C4⋊Dic11C2411yescharacteristic
476Dic11⋊C4—21no—
477Dic11⋊C4—22no—
478Dic11⋊C4—21no—
479C4×Dic11—22no—
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#3488—111no—
496#3449D1111yescharacteristic, complemented
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—41no—
521C23×C11—42no—
522C23×C11—42no—
523C23×C11—41no—
524C23×C11—42no—
525C23×C11—42no—
526C23×C11—81no—
527C23×C11—81no—
528C23×C11C22×D412yes—
529C23×C11C22×D411yescharacteristic
530C23×C11C22×D412yes—
531C23×C11C22×D411yescharacteristic
532C23×C11C22×D411yescharacteristic
533C22×D11—21no—
534C22×D11—22no—
535C22×D11—44no—
536C22×D11—42no—
537C22×D11—81no—
538C22×D11—82no—
539C22×D11—81no—
540C22×D11—82no—
541Q8×C11—22no—
542Q8×C11—22no—
543Q8×C11—22no—
544Q8×C11—22no—
545Q8×C11—42no—
546Q8×C11—42no—
547D4×C11—24no—
548D4×C11—24no—
549D4×C11—22no—
550D4×C11—22no—
551D4×C11—22no—
552D4×C11—22no—
553D4×C11—42no—
554D4×C11—42no—
555D4×C11—42no—
556D4×C11—44no—
557D4×C11—44no—
558D4×C11—42no—
559D4×C11—82no—
560D4×C11—82no—
561D4×C11—82no—
562D4×C11—82no—
563C2×C4×C11—22no—
564C2×C4×C11—22no—
565C2×C4×C11—22no—
566C2×C4×C11—22no—
567C2×C4×C11—22no—
568C2×C4×C11—22no—
569C2×C4×C11—22no—
570C2×C4×C11—21no—
571C2×C4×C11—21no—
572C2×C4×C11—21no—
573C2×C4×C11—21no—
574C2×C4×C11—21no—
575C2×C4×C11—21no—
576C2×C4×C11—21no—
577C2×C4×C11—21no—
578C2×C4×C11—22no—
579C2×C4×C11—42no—
580C2×C4×C11—42no—
581C2×C4×C11—42no—
582C2×C4×C11—44no—
583C2×C4×C11—44no—
584C2×C4×C11—42no—
585C2×C4×C11—81no—
586C2×C4×C11—81no—
587C2×C4×C11C22×D412yes—
588C2×C4×C11C22×D411yescharacteristic
589C2×C4×C11C22×D412yes—
590C2×C4×C11C22×D411yescharacteristic
591C2×C4×C11C22×D411yescharacteristic
592C2×C4×C11H(5,𝔽2)12yes—
593C2×C4×C11H(5,𝔽2)12yes—
594C2×C4×C11C2511yescharacteristic
595C22⋊D11—44no—
596C22⋊D11—42no—
597C22⋊D11—44no—
598C22⋊D11—42no—
599C22⋊D11—81no—
600C22⋊D11—82no—
601C22⋊D11—82no—
602C22⋊D11—82no—
603C22⋊D11—82no—
604C2×Dic11—21no—
605C2×Dic11—22no—
606C2×Dic11—21no—
607C2×Dic11—21no—
608C2×Dic11—81no—
609C2×Dic11—82no—
610D44—22no—
611D44—21no—
612D44—22no—
613D44—21no—
614D44—44no—
615D44—42no—
616C4×D11—44no—
617C4×D11—42no—
618Dic22—21no—
619Dic22—21no—
620C11⋊C8—21no—
621C11⋊C8—21no—
622C11⋊C8—21no—
623C11⋊C8—21no—
624C11⋊C8—22no—
625C11⋊C8—22no—
626C2×H(5,𝔽2)—111no—
627C22×#41C2×D1111yescharacteristic
628C22×#41C2×D1111yescharacteristic, complemented
629C2×#137—111no—
630C2×AGL(1,ℤ/8)—111no—
631C22×SD16—111no—
632C22×D8—111no—
633C2×#131—111no—
634C2×#131—111no—
635#550—221no—
636#548—221no—
637#546—222no—
638#546—221no—
639D42—222no—
640D42—221no—
641#537—112no—
642#537—111no—
643#537C2×D1112yescomplemented
644#537C2×D1112yescomplemented
645#536—21no—
646#536C2×D1111yescharacteristic
647#536C2×D1111yescharacteristic, complemented
648#535—21no—
649#535—112no—
650#535—111no—
651#535C2×D1111yescharacteristic
652#535C2×D1111yescharacteristic, complemented
653#534—22no—
654#532—21no—
655#532—21no—
656#525—22no—
657#525—111no—
658#525—112no—
659#525C2×D1112yescomplemented
660#525C2×D1112yescomplemented
661C2×#121—111no—
662C2×#121—112no—
663#520—111no—
664C2×#117C2×D1111yescharacteristic, complemented
665#485—112no—
666#485—112no—
667#485—111no—
668#485—111no—
669#484—112no—
670#484—111no—
671#483—112no—
672#483—111no—
673#482—112no—
674#482—112no—
675#482—111no—
676#482—111no—
677#482—112no—
678#482—112no—
679#481—112no—
680#481—111no—
681#481—112no—
682#480—112no—
683#480—111no—
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—22no—
742C22×C11—21no—
743C22×C11—21no—
744C22×C11—22no—
745C22×C11—22no—
746C22×C11—21no—
747C22×C11—21no—
748C22×C11—21no—
749C22×C11—22no—
750C22×C11—22no—
751C22×C11—42no—
752C22×C11—42no—
753C22×C11—42no—
754C22×C11—82no—
755C22×C11—84no—
756C22×C11—84no—
757C22×C11#53412yes—
758C22×C11C23×D411yescharacteristic
759C2×D11—42no—
760C2×D11—41no—
761C2×D11—42no—
762C2×D11—41no—
763C2×D11—41no—
764C2×D11—42no—
765C2×D11—162no—
766C2×D11—164no—
767C4×C11—21no—
768C4×C11—21no—
769C4×C11—22no—
770C4×C11—22no—
771C4×C11—41no—
772C4×C11—41no—
773C4×C11—41no—
774C4×C11—41no—
775C4×C11—42no—
776C4×C11#53412yes—
777C4×C11C2×H(5,𝔽2)11yescharacteristic
778C4×C11C2×H(5,𝔽2)11yescharacteristic
779Dic11—41no—
780Dic11—42no—
781Dic11—41no—
782Dic11—41no—
783H(5,𝔽2)—442no—
784H(5,𝔽2)—442no—
785C2×#41—21no—
786C2×#41—21no—
787C2×#41—42no—
788C2×#41—42no—
789C2×#41—42no—
790C2×#41—42no—
791C2×#41—111no—
792C2×#41—112no—
793C2×#41—221no—
794C2×#41C22⋊D1112yes—
795C2×#41C22⋊D1111yescharacteristic
796C2×#41C22⋊D1111yescharacteristic
797C2×#41C22×D1112yes—
798C2×#41C22×D1112yes—
799C2×#41C22×D1111yescharacteristic
800C2×#41C22×D1111yescharacteristic
801C2×#41C22×D1112yes—
802C22×Q8C22⋊D1111yescharacteristic
803C22×Q8C22×D1111yescharacteristic
804C22×D4—21no—
805C22×D4—111no—
806C22×D4—112no—
807C22×D4—221no—
808C22×D4—222no—
809C22×D4—222no—
810C22×D4—221no—
811C22×D4C22⋊D1112yes—
812C22×D4C22⋊D1111yescharacteristic
813C22×D4C22×D1111yescharacteristic
814C23×C4—21no—
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—21no—
840C4⋊Q8—21no—
841#127—21no—
842#127—21no—
843#127—221no—
844#127—222no—
845#124—21no—
846#124—21no—
847#124—21no—
848#124—21no—
849#124—221no—
850#124—222no—
851#123—22no—
852#123—22no—
853#123—22no—
854#123—22no—
855#123—221no—
856#123—222no—
857C22⋊Q8—22no—
858C22⋊Q8—22no—
859C22⋊Q8—111no—
860C22⋊Q8—111no—
861C22⋊Q8—112no—
862C22⋊Q8—221no—
863C22⋊Q8—222no—
864C22⋊Q8C22×D1112yes—
865C22⋊Q8C22×D1112yes—
866C22⋊Q8C22×D1112yes—
867C22⋊Q8C22×D1112yes—
868#121—22no—
869#121—22no—
870#121—22no—
871#121—22no—
872#121—22no—
873#121—22no—
874#121—112no—
875#121—111no—
876#121—112no—
877#121—112no—
878#121—112no—
879#121—111no—
880#121—112no—
881#121—222no—
882#121—222no—
883#121—222no—
884#121—221no—
885#121—222no—
886#121—221no—
887#121—222no—
888#121—221no—
889#121—222no—
890#121C22×D1112yes—
891#121C22×D1112yes—
892#121C22×D1112yes—
893#121C22×D1112yes—
894#120—22no—
895#120—22no—
896#120—22no—
897#120—22no—
898#120—221no—
899#120—222no—
900#120—222no—
901#120—222no—
902#120—222no—
903C4×Q8—221no—
904C4×D4—22no—
905C4×D4—22no—
906C4×D4—22no—
907C4×D4—22no—
908C4×D4—222no—
909C4×D4—221no—
910C4×D4—221no—
911C4×D4—222no—
912C4×D4—221no—
913C4×D4—222no—
914#117—21no—
915#117—21no—
916#117—111no—
917#117—112no—
918#117C22×D1111yescharacteristic
919#117C22×D1111yescharacteristic
920#117C22×D1111yescharacteristic
921#117C22×D1111yescharacteristic
922C2×C4⋊C4—111no—
923C2×C4⋊C4—112no—
924C2×C4⋊C4C22×D1111yescharacteristic
925C2×C4⋊C4C22×D1111yescharacteristic
926C2×C22⋊C4—21no—
927C2×C22⋊C4—221no—
928C2×C22⋊C4—222no—
929C2×C42—21no—
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—112no—
943#103—112no—
944#103—112no—
945#103—112no—
946#103—111no—
947#103—111no—
948#103—111no—
949#103—111no—
950#102—112no—
951#102—112no—
952#102—112no—
953#102—112no—
954#102—111no—
955#102—111no—
956#102—111no—
957#102—111no—
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—42no—
974C2×C11—41no—
975C2×C11—42no—
976C2×C11—41no—
977C2×C11—82no—
978C2×C11C2×#53411yescharacteristic
979C2×C11#358411yescharacteristic
980C2×C11#358511yescharacteristic
981D11—82no—
982D11—81no—
983C24—21no—
984C24—222no—
985C24—221no—
986C24C2×C22⋊D1111yescharacteristic
987C24C2×C22⋊D1112yes—
988#41—22no—
989#41—22no—
990#41—22no—
991#41—22no—
992#41—42no—
993#41—42no—
994#41—44no—
995#41—42no—
996#41—42no—
997#41—42no—
998#41—42no—
999#41—42no—
1000#41—42no—
1001#41—44no—
1002#41—44no—
1003#41—222no—
1004#41—222no—
1005#41—442no—
1006#41—442no—
1007#41—444no—
1008C2×Q8—21no—
1009C2×Q8—22no—
1010C2×Q8—22no—
1011C2×Q8—42no—
1012C2×Q8—111no—
1013C2×Q8C2×C22⋊D1111yescharacteristic
1014C2×Q8C2×C22⋊D1111yescharacteristic
1015C2×Q8C2×C22⋊D1112yes—
1016C2×Q8C23×D1112yes—
1017C2×D4—22no—
1018C2×D4—22no—
1019C2×D4—22no—
1020C2×D4—22no—
1021C2×D4—22no—
1022C2×D4—22no—
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—21no—
1026C2×D4—42no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—112no—
1030C2×D4—111no—
1031C2×D4—221no—
1032C2×D4—222no—
1033C2×D4—222no—
1034C2×D4—221no—
1035C2×D4—222no—
1036C2×D4—221no—
1037C2×D4—222no—
1038C2×D4—222no—
1039C2×D4—222no—
1040C2×D4—222no—
1041C2×D4—222no—
1042C2×D4—222no—
1043C2×D4—221no—
1044C2×D4—442no—
1045C2×D4—442no—
1046C2×D4—448no—
1047C2×D4—444no—
1048C2×D4—882no—
1049C2×D4—884no—
1050C2×D4C2×C22⋊D1112yes—
1051C2×D4C2×C22⋊D1111yescharacteristic
1052C2×D4C2×C22⋊D1112yes—
1053C2×D4C2×C22⋊D1111yescharacteristic
1054C2×D4C2×C22⋊D1112yes—
1055C2×D4C2×C22⋊D1112yes—
1056C2×D4C2×C22⋊D1112yes—
1057C2×D4C23×D1112yes—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—21no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—222no—
1069C22×C4—221no—
1070C22×C4—222no—
1071C22×C4—221no—
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×D1112yes—
1079C22×C4C23×D1111yescharacteristic
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—21no—
1106C4⋊C4—21no—
1107C4⋊C4—22no—
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—22no—
1111C4⋊C4—112no—
1112C4⋊C4—111no—
1113C4⋊C4—111no—
1114C4⋊C4—222no—
1115C4⋊C4—221no—
1116C4⋊C4—221no—
1117C4⋊C4—222no—
1118C4⋊C4—221no—
1119C4⋊C4C23×D1111yescharacteristic
1120C4⋊C4C23×D1111yescharacteristic
1121C4⋊C4C23×D1111yescharacteristic
1122C4⋊C4C23×D1111yescharacteristic
1123C22⋊C4—21no—
1124C22⋊C4—21no—
1125C22⋊C4—21no—
1126C22⋊C4—21no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—22no—
1130C22⋊C4—22no—
1131C22⋊C4—22no—
1132C22⋊C4—22no—
1133C22⋊C4—22no—
1134C22⋊C4—22no—
1135C22⋊C4—222no—
1136C22⋊C4—221no—
1137C22⋊C4—221no—
1138C22⋊C4—222no—
1139C22⋊C4—221no—
1140C22⋊C4—222no—
1141C22⋊C4—221no—
1142C22⋊C4—222no—
1143C22⋊C4—222no—
1144C22⋊C4—222no—
1145C22⋊C4—222no—
1146C22⋊C4—221no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—222no—
1152C42—221no—
1153C11#6076011yescharacteristic, complemented, Sylow
1154C23—22no—
1155C23—22no—
1156C23—42no—
1157C23—41no—
1158C23—42no—
1159C23—41no—
1160C23—42no—
1161C23—42no—
1162C23—81no—
1163C23—81no—
1164C23—222no—
1165C23—221no—
1166C23—444no—
1167C23—442no—
1168C23—881no—
1169C23—882no—
1170C23—881no—
1171C23—882no—
1172C23C22×C22⋊D1112yes—
1173C23C22×C22⋊D1111yescharacteristic
1174C23C22×C22⋊D1112yes—
1175C23C22×C22⋊D1111yescharacteristic
1176C23C22×C22⋊D1111yescharacteristic
1177Q8—22no—
1178Q8—22no—
1179Q8—22no—
1180Q8—22no—
1181Q8—42no—
1182Q8—42no—
1183Q8—221no—
1184Q8—221no—
1185D4—24no—
1186D4—24no—
1187D4—22no—
1188D4—22no—
1189D4—22no—
1190D4—22no—
1191D4—42no—
1192D4—42no—
1193D4—42no—
1194D4—44no—
1195D4—44no—
1196D4—42no—
1197D4—82no—
1198D4—82no—
1199D4—82no—
1200D4—82no—
1201D4—222no—
1202D4—221no—
1203D4—222no—
1204D4—221no—
1205D4—444no—
1206D4—444no—
1207D4—444no—
1208D4—442no—
1209D4—442no—
1210D4—442no—
1211D4—882no—
1212D4—882no—
1213D4—882no—
1214D4—881no—
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—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—44no—
1236C2×C4—44no—
1237C2×C4—42no—
1238C2×C4—81no—
1239C2×C4—81no—
1240C2×C4—221no—
1241C2×C4—222no—
1242C2×C4—221no—
1243C2×C4—221no—
1244C2×C4—444no—
1245C2×C4—442no—
1246C2×C4—881no—
1247C2×C4—882no—
1248C2×C4#6703712yes—
1249C2×C4#6703712yes—
1250C2×C4C22×C22⋊D1111yescharacteristic
1251C2×C4C22×C22⋊D1112yes—
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—21no—
1265C22—22no—
1266C22—22no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—22no—
1271C22—22no—
1272C22—21no—
1273C22—22no—
1274C22—22no—
1275C22—21no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—82no—
1280C22—84no—
1281C22—84no—
1282C22—442no—
1283C22—441no—
1284C22—442no—
1285C22—441no—
1286C22—442no—
1287C22—441no—
1288C22—1762no—
1289C22—1764no—
1290C22#1062333512yes—
1291C22C23×C22⋊D1111yescharacteristic
1292C4—21no—
1293C4—21no—
1294C4—22no—
1295C4—22no—
1296C4—41no—
1297C4—41no—
1298C4—42no—
1299C4—41no—
1300C4—41no—
1301C4—442no—
1302C4—441no—
1303C4—441no—
1304C4—441no—
1305C4#1062333512yes—
1306C4C2×#6703711yescharacteristic
1307C4C2×#6703711yescharacteristic
1308C2—22no—
1309C2—41no—
1310C2—42no—
1311C2—41no—
1312C2—42no—
1313C2—82no—
1314C2—882no—
1315C2—881no—
1316C2C2×#1062333511yescharacteristic
1317C2#1308338711yescharacteristic
1318C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3449C2
socleC22×C11C23×D4
hypercenter#3449D11
hypocenterC11#60760
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #13082285C2semidirect
2. #13079522C2semidirect
3. #13079513C2semidirect
4. #13079462C2semidirect
5. #13079462C2semidirect
6. #13079453C2semidirect
7. #13079426C2semidirect
8. #13079404C2semidirect
9. #13079377C2semidirect
10. #13078579C2semidirect
11. #13078568C2semidirect
12. #13078556C2semidirect
13. #13078529C2semidirect
14. #13078303C2semidirect
15. #13078292C2semidirect
16. #13078261C2semidirect
17. #13078257C2semidirect
18. #13077891C2semidirect
19. #13077882C2semidirect
20. #13077858C2semidirect
21. C2×#10622851C2semidirect
22. #13077065C2semidirect
23. C11×#3449C2semidirect
25. C22×C11×#41C22semidirect
27. C11×#537C22semidirect
28. C11×#537C22semidirect
31. C11×#536C22semidirect
34. C11×#535C22semidirect
39. C11×#525C22semidirect
40. C11×#525C22semidirect
41. C2×C11×#117C22semidirect
44. #10623364C22semidirect
46. #10623361C22semidirect
50. C2×#67001C22semidirect
51. C2×#67001C22semidirect
53. C2×#66995C22semidirect
54. C22×#4325C22semidirect
57. C2×#66985C22semidirect
58. C22×#4323C22semidirect
60. #10623322C22semidirect
62. C2×#66983C22semidirect
63. #10622852C22semidirect
64. #10622852C22semidirect
65. #10622851C22semidirect
66. #10622851C22semidirect
67. #10622851C22semidirect
68. #10622851C22semidirect
69. #10622851C22semidirect
70. #10622851C22semidirect
73. #10622847C22semidirect
74. #10622847C22semidirect
75. #10622838C22semidirect
76. C2×#66899C22semidirect
77. #10622828C22semidirect
78. C2×#66896C22semidirect
79. #10622820C22semidirect
80. #10622820C22semidirect
81. C2×C22⋊(C11⋊C8)C22semidirect
82. C2×C22⋊(C11⋊C8)C22semidirect
83. #10622665C22semidirect
84. #10622664C22semidirect
85. #10622662C22semidirect
86. #10622662C22semidirect
87. #10622662C22semidirect
88. #10622661C22semidirect
89. #10622661C22semidirect
90. #10622661C22semidirect
91. #10622660C22semidirect
92. #10622660C22semidirect
93. #10622659C22semidirect
94. #10622659C22semidirect
95. #10622658C22semidirect
96. #10622658C22semidirect
97. #10622657C22semidirect
98. #10622656C22semidirect
99. #10622655C22semidirect
100. #10622654C22semidirect
101. #10622652C22semidirect
102. #10622652C22semidirect
103. #10622652C22semidirect
104. #10622651C22semidirect
105. #10622651C22semidirect
106. #10622651C22semidirect
107. #10622650C22semidirect
108. #10622650C22semidirect
109. #10622649C22semidirect
110. #10622649C22semidirect
111. #10622648C22semidirect
112. #10622648C22semidirect
113. #10622647C22semidirect
114. #10622646C22semidirect
115. #10622616C22semidirect
116. #10622616C22semidirect
117. #10622616C22semidirect
118. #10622616C22semidirect
119. #10622615C22semidirect
120. #10622615C22semidirect
121. #10622614C22semidirect
122. #10622614C22semidirect
123. #10622611C22semidirect
124. #10622611C22semidirect
125. #10622609C22semidirect
126. #10622609C22semidirect
127. #10622608C22semidirect
128. #10622608C22semidirect
129. #10622584C22semidirect
130. #10622583C22semidirect
131. #10622581C22semidirect
132. #10622581C22semidirect
133. #10622580C22semidirect
134. #10622580C22semidirect
496. #3449D11semidirect
628. C22×#41C2×D11semidirect
643. #537C2×D11semidirect
644. #537C2×D11semidirect
647. #536C2×D11semidirect
652. #535C2×D11semidirect
659. #525C2×D11semidirect
660. #525C2×D11semidirect
664. C2×#117C2×D11semidirect
1153. C11#60760semidirect

Maximal subgroups

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

subgroupindex
#130822852
#130795222
#130795132
#130794622
#130794532
#130794262
#130794042
#130793772
#130785792
#130785682
#130785562
#130785292
#130783032
#130782922
#130782612
#130782572
#130778912
#130778822
#130778582
C2×#106228512
#130770652
C11×#34492
#6076011