Finite Group Databasebeta

← #15624683

Subgroups — #15624683

Order 2816.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1290 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#13079498C212yesmaximal, complemented
5#13079498C212yesmaximal, complemented
6#13079453C212yesmaximal, complemented
7#13079446C212yesmaximal, complemented
8#13079404C212yesmaximal, complemented
9#13079397C212yesmaximal, complemented
10#13078585C211yesmaximal, characteristic, complemented
11#13078574C211yesmaximal, characteristic, complemented
12#13078560C211yesmaximal, characteristic, complemented
13#13078525C211yesmaximal, characteristic, complemented
14#13078309C211yesmaximal, characteristic, complemented
15#13078298C211yesmaximal, characteristic, complemented
16#13078268C211yesmaximal, characteristic, complemented
17#13078257C211yesmaximal, characteristic, complemented
18#13077911C211yesmaximal, characteristic, complemented
19#13077902C211yesmaximal, characteristic, complemented
20#13077856C211yesmaximal, characteristic, complemented
21C2×#10622660C211yesmaximal, characteristic, complemented
22#13077065C211yesmaximal, characteristic, complemented
23C11×#3489C211yesmaximal, characteristic, complemented
24C2×C11×2−1+4C2211yescharacteristic
25C22×C11×#41C2211yescharacteristic
26C22×#4339C2211yescharacteristic
27D4×Q8×C11—21no—
28C11×#548—21no—
29C11×#547—22no—
30C11×#547—21no—
31C11×#546—22no—
32C11×#546—21no—
33C11×#537C2211yescharacteristic
34C11×#537C2212yescomplemented
35C11×#536C2211yescharacteristic
36C11×#536C2212yescomplemented
37C11×#525C2211yescharacteristic
38C11×#525C2212yescomplemented
39C2×C11×C22⋊Q8C2211yescharacteristic
40C2×C11×C22⋊Q8C2212yescomplemented
41C11×#520C2211yescharacteristic
42#10623364C2212yes—
43#10623364C2212yes—
44#10623363—21no—
45#10623363—21no—
46#10623361C2211yescharacteristic
47#10623361C2211yescharacteristic
48#10623359—22no—
49#10623356C2211yescharacteristic
50#10623356C2211yescharacteristic
51C2×#67004C2211yescharacteristic, complemented
52C2×#67002C2211yescharacteristic, complemented
53C2×#67001C2211yescharacteristic
54C2×#67001C2211yescharacteristic
55#10623347—21no—
56C22×#4326C2211yescharacteristic, complemented
57C22×#4325C2211yescharacteristic, complemented
58#10623336—21no—
59#10623335—22no—
60#10623322C2212yes—
61#10623322C2212yes—
62C2×#66979C2211yescharacteristic
63#10622852C2212yescomplemented
64#10622852C2212yescomplemented
65#10622851C2212yescomplemented
66#10622851C2212yescomplemented
67#10622847C2211yescharacteristic
68#10622847C2211yescharacteristic
69#10622847C2212yescomplemented
70#10622847C2212yescomplemented
71#10622846C2211yescharacteristic, complemented
72#10622846C2211yescharacteristic, complemented
73#10622841C2212yescomplemented
74#10622841C2212yescomplemented
75#10622840C2212yescomplemented
76#10622840C2212yescomplemented
77#10622838C2211yescharacteristic, complemented
78#10622838C2211yescharacteristic, complemented
79#10622820C2211yescharacteristic
80#10622820C2212yescomplemented
81C2×C22⋊(C11⋊C8)C2211yescharacteristic
82C2×C22⋊(C11⋊C8)C2212yescomplemented
83#10622665C2212yescomplemented
84#10622665C2212yescomplemented
85#10622665C2212yescomplemented
86#10622664C2212yescomplemented
87#10622664C2212yescomplemented
88#10622664C2212yescomplemented
89#10622662C2212yescomplemented
90#10622662C2212yescomplemented
91#10622662C2212yescomplemented
92#10622661C2212yescomplemented
93#10622661C2212yescomplemented
94#10622661C2212yescomplemented
95#10622660C2212yes—
96#10622660C2212yes—
97#10622660C2212yes—
98#10622660C2212yescomplemented
99#10622660C2212yescomplemented
100#10622660C2212yescomplemented
101#10622658C2212yescomplemented
102#10622658C2212yescomplemented
103#10622658C2211yescharacteristic, complemented
104#10622658C2211yescharacteristic, complemented
105#10622657C2212yescomplemented
106#10622657C2211yescharacteristic, complemented
107#10622656C2212yescomplemented
108#10622656C2211yescharacteristic, complemented
109#10622655C2212yescomplemented
110#10622654C2212yescomplemented
111#10622652C2212yescomplemented
112#10622651C2212yescomplemented
113#10622650C2212yes—
114#10622650C2212yescomplemented
115#10622648C2211yescharacteristic, complemented
116#10622648C2211yescharacteristic, complemented
117#10622647C2211yescharacteristic, complemented
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
135C11×2−1+4—42no—
136C11×2−1+4—42no—
137C2×C11×#41—22no—
138C2×C11×#41—21no—
139C2×C11×#41—42no—
140C2×C11×#41—42no—
141C2×C11×#41D412yes—
142C2×C11×#41D411yescharacteristic
143C2×C11×#41D411yescharacteristic
144C2×C11×#41C2311yescharacteristic
145C2×C11×#41C2312yes—
146C2×C11×#41C2311yescharacteristic
147C2×C11×#41C2311yescharacteristic
148C2×C11×#41C2312yes—
149C22×Q8×C11—21no—
150C22×Q8×C11D411yescharacteristic
151C22×Q8×C11C2311yescharacteristic
152C22×Q8×C11C2312yes—
153C22×D4×C11D412yes—
154C22×D4×C11D411yescharacteristic
155C23×C4×C11C2311yescharacteristic
156C23×C4×C11C2312yes—
157C22×C22⋊D11—21no—
158C2×#4339—21no—
159C2×#4339—21no—
160C2×#4339—42no—
161C2×#4339—42no—
162C2×#4339C2312yes—
163C2×#4339C2312yes—
164C22×D44C2311yescharacteristic
165C22×C4×D11—21no—
166C22×Dic22C2311yescharacteristic
167C11×C4⋊Q8—21no—
168C11×C4⋊Q8—22no—
169C11×#124—21no—
170C11×#124—22no—
171C11×#123—22no—
172C11×#123—22no—
173C11×#123—22no—
174C11×#123—21no—
175C11×#123—22no—
176C11×C22⋊Q8—21no—
177C11×C22⋊Q8—22no—
178C11×C22⋊Q8—21no—
179C11×C22⋊Q8—21no—
180C11×C22⋊Q8—22no—
181C11×C22⋊Q8—22no—
182C11×C22⋊Q8C2312yes—
183C11×C22⋊Q8C2312yes—
184C11×C22⋊Q8C2311yescharacteristic
185C11×C22⋊Q8C2312yes—
186C11×C22⋊Q8C2312yes—
187C11×C22⋊Q8C2311yescharacteristic
188C11×C22⋊Q8C2312yes—
189C11×#121—22no—
190C11×#121—21no—
191C11×#121—22no—
192C11×#121—22no—
193C11×#121—22no—
194C11×#121C2311yescharacteristic
195C11×#121C2311yescharacteristic
196C11×#121C2312yes—
197C11×#120—21no—
198C11×#120—22no—
199C4×Q8×C11—21no—
200C4×D4×C11—22no—
201C4×D4×C11—21no—
202C4×D4×C11—21no—
203C4×D4×C11—21no—
204C4×D4×C11—22no—
205C4×D4×C11—22no—
206C11×#117C2312yes—
207C11×#117C2311yescharacteristic
208C2×C11×C4⋊C4—21no—
209C2×C11×C4⋊C4—22no—
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×#4326—42no—
228C2×#4326C2312yes—
229C2×#4326C2312yes—
230C2×#4326C2312yes—
231C2×#4325—42no—
232C2×#4325C2312yes—
233C2×#4325C2312yes—
234C2×#4325C2312yes—
235#66993—21no—
236#66993—21no—
237#66992—22no—
238#66992—22no—
239#66992—22no—
240#66992—22no—
241#66991—22no—
242#66991—22no—
243#66990—22no—
244#66990—22no—
245#66989—21no—
246#66989—21no—
247#66988—22no—
248#66988—22no—
249C2×#4324C2312yes—
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#66899C2312yes—
283#66899C2312yes—
284#66899C2312yes—
285#66899C2312yes—
286#66899C2311yescharacteristic
287#66899C2311yescharacteristic
288#66899C2311yescharacteristic
289#66899C2311yescharacteristic
290#66896C2311yescharacteristic
291#66896C2311yescharacteristic
292#66896C2311yescharacteristic
293#66896C2311yescharacteristic
294C22⋊(C11⋊C8)C2311yescharacteristic
295C22⋊(C11⋊C8)C2311yescharacteristic
296C22⋊(C11⋊C8)C2311yescharacteristic
297C22⋊(C11⋊C8)C2311yescharacteristic
298C22⋊(C11⋊C8)C2312yes—
299C22⋊(C11⋊C8)C2312yes—
300C22⋊(C11⋊C8)C2312yes—
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#60761—111nomaximal, Sylow
325C24×C11C2×D411yescharacteristic
326C24×C11C2×D412yes—
327C23×D11—21no—
328C11×#41—22no—
329C11×#41—22no—
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—48no—
342C11×#41—44no—
343C2×Q8×C11—22no—
344C2×Q8×C11—21no—
345C2×Q8×C11—22no—
346C2×Q8×C11—22no—
347C2×Q8×C11—42no—
348C2×Q8×C11—42no—
349C2×Q8×C11—42no—
350C2×Q8×C11—44no—
351C2×Q8×C11C2×D411yescharacteristic
352C2×Q8×C11C2×D411yescharacteristic
353C2×Q8×C11C2×D412yes—
354C2×Q8×C11C2412yes—
355C2×Q8×C11C2411yescharacteristic
356C2×D4×C11—21no—
357C2×D4×C11—22no—
358C2×D4×C11—21no—
359C2×D4×C11—22no—
360C2×D4×C11—21no—
361C2×D4×C11—42no—
362C2×D4×C11—44no—
363C2×D4×C11C2×D412yes—
364C2×D4×C11C2×D412yes—
365C2×D4×C11C2×D411yescharacteristic
366C2×D4×C11C2×D411yescharacteristic
367C2×D4×C11C2×D412yes—
368C2×D4×C11C2×D412yes—
369C2×D4×C11C2×D412yes—
370C2×D4×C11C2411yescharacteristic
371C22×C4×C11—22no—
372C22×C4×C11—22no—
373C22×C4×C11—22no—
374C22×C4×C11—21no—
375C22×C4×C11—22no—
376C22×C4×C11—21no—
377C22×C4×C11—22no—
378C22×C4×C11—21no—
379C22×C4×C11—42no—
380C22×C4×C11—42no—
381C22×C4×C11C2×D411yescharacteristic
382C22×C4×C11C2×D411yescharacteristic
383C22×C4×C11C2×D411yescharacteristic
384C22×C4×C11C2×D412yes—
385C22×C4×C11C2×D412yes—
386C22×C4×C11C2×D412yes—
387C22×C4×C11C2412yes—
388C22×C4×C11C2411yescharacteristic
389C22×C4×C11C2411yescharacteristic
390C22×C4×C11C2412yes—
391C22×C4×C11C2411yescharacteristic
392C2×C22⋊D11—22no—
393C2×C22⋊D11—22no—
394C2×C22⋊D11—22no—
395C2×C22⋊D11—22no—
396C2×C22⋊D11—22no—
397C2×C22⋊D11—22no—
398C2×C22⋊D11—44no—
399C22×Dic11—21no—
400C22×Dic11—21no—
401C22×Dic11—21no—
402#4339—42no—
403#4339—42no—
404#4339—42no—
405#4339—42no—
406#4339—44no—
407#4339—44no—
408C2×D44—21no—
409C2×D44—22no—
410C2×D44—22no—
411C2×D44C2412yes—
412C2×C4×D11—22no—
413C2×C4×D11—22no—
414C2×C4×D11—44no—
415C2×Dic22—21no—
416C2×Dic22—22no—
417C2×Dic22—22no—
418C2×Dic22C2412yes—
419C11×C4⋊C4—22no—
420C11×C4⋊C4—21no—
421C11×C4⋊C4—22no—
422C11×C4⋊C4—22no—
423C11×C4⋊C4—22no—
424C11×C4⋊C4—22no—
425C11×C4⋊C4—21no—
426C11×C4⋊C4—22no—
427C11×C4⋊C4—21no—
428C11×C4⋊C4C2412yes—
429C11×C4⋊C4C2411yescharacteristic
430C11×C4⋊C4C2411yescharacteristic
431C11×C22⋊C4—22no—
432C11×C22⋊C4—21no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—21no—
440C11×C22⋊C4—21no—
441C11×C22⋊C4—22no—
442C11×C22⋊C4—21no—
443C42×C11—22no—
444C42×C11—21no—
445C22⋊Dic11—22no—
446C22⋊Dic11—22no—
447C22⋊Dic11—22no—
448C22⋊Dic11—22no—
449C22⋊Dic11—21no—
450C22⋊Dic11—21no—
451C22⋊Dic11—21no—
452C22⋊Dic11—21no—
453#4326—42no—
454#4326—42no—
455#4326—42no—
456#4325—42no—
457#4325—42no—
458#4325—42no—
459#4324—42no—
460#4323—42no—
461(C2×D11)⋊C4—22no—
462(C2×D11)⋊C4—22no—
463(C2×D11)⋊C4—22no—
464(C2×D11)⋊C4—22no—
465C4⋊Dic11—21no—
466C4⋊Dic11—21no—
467C4⋊Dic11C2411yescharacteristic
468C4⋊Dic11C2411yescharacteristic
469C4⋊Dic11C2411yescharacteristic
470C4⋊Dic11C2411yescharacteristic
471Dic11⋊C4—22no—
472Dic11⋊C4—22no—
473Dic11⋊C4—22no—
474Dic11⋊C4—22no—
475C4×Dic11—21no—
476C4×Dic11—21no—
477C4×Dic11—21no—
478C4×Dic11—21no—
479#4318—22no—
480#4318—22no—
481#4318—42no—
482#4318—42no—
483C2×C11⋊C8—22no—
484C2×C11⋊C8—22no—
485C2×C11⋊C8—42no—
486C2×C11⋊C8—42no—
487C2×C11⋊C8C2411yescharacteristic
488C2×C11⋊C8C2411yescharacteristic
489C2×C11⋊C8C2412yes—
490C2×C11⋊C8C2412yes—
491C2×C11⋊C8C2411yescharacteristic
492C2×C11⋊C8C2411yescharacteristic
493#3489D1111yescharacteristic, complemented
494#3449—111no—
495#3204—112no—
496#3203—112no—
497#3201—112no—
498#3201—112no—
499#3197—112no—
500#3196—112no—
501#3191—112no—
502#3190—112no—
503#3097—111no—
504#3096—111no—
505#3095—111no—
506#3091—111no—
507#3063—111no—
508#3062—111no—
509#3059—111no—
510#3057—111no—
511#3011—111no—
512#3010—111no—
513#3005—111no—
514C2×#452—111no—
515#2880—111no—
516C23×C11—22no—
517C23×C11—21no—
518C23×C11—42no—
519C23×C11—41no—
520C23×C11—41no—
521C23×C11—42no—
522C23×C11—42no—
523C23×C11C22×D411yescharacteristic
524C23×C11C22×D412yes—
525C23×C11C22×D412yes—
526C23×C11C22×D411yescharacteristic
527C23×C11C22×D411yescharacteristic
528C22×D11—22no—
529C22×D11—42no—
530C22×D11—81no—
531C22×D11—81no—
532Q8×C11—22no—
533Q8×C11—22no—
534Q8×C11—22no—
535Q8×C11—21no—
536Q8×C11—22no—
537Q8×C11—21no—
538Q8×C11—42no—
539Q8×C11—44no—
540Q8×C11—42no—
541D4×C11—24no—
542D4×C11—24no—
543D4×C11—22no—
544D4×C11—22no—
545D4×C11—21no—
546D4×C11—21no—
547D4×C11—42no—
548D4×C11—42no—
549D4×C11—42no—
550D4×C11—42no—
551D4×C11—44no—
552D4×C11—42no—
553D4×C11—81no—
554D4×C11—82no—
555C2×C4×C11—22no—
556C2×C4×C11—22no—
557C2×C4×C11—22no—
558C2×C4×C11—22no—
559C2×C4×C11—22no—
560C2×C4×C11—21no—
561C2×C4×C11—21no—
562C2×C4×C11—21no—
563C2×C4×C11—21no—
564C2×C4×C11—22no—
565C2×C4×C11—22no—
566C2×C4×C11—21no—
567C2×C4×C11—22no—
568C2×C4×C11—21no—
569C2×C4×C11—22no—
570C2×C4×C11—21no—
571C2×C4×C11—42no—
572C2×C4×C11—42no—
573C2×C4×C11—42no—
574C2×C4×C11—44no—
575C2×C4×C11—44no—
576C2×C4×C11—42no—
577C2×C4×C11—42no—
578C2×C4×C11—81no—
579C2×C4×C11—82no—
580C2×C4×C11C22×D411yescharacteristic
581C2×C4×C11C22×D412yes—
582C2×C4×C11C22×D412yes—
583C2×C4×C11C22×D411yescharacteristic
584C2×C4×C11C22×D411yescharacteristic
585C2×C4×C11H(5,𝔽2)12yes—
586C2×C4×C11H(5,𝔽2)12yes—
587C2×C4×C11C2511yescharacteristic
588C22⋊D11—44no—
589C22⋊D11—44no—
590C22⋊D11—82no—
591C22⋊D11—82no—
592C22⋊D11—82no—
593C22⋊D11—82no—
594C2×Dic11—21no—
595C2×Dic11—21no—
596C2×Dic11—21no—
597C2×Dic11—21no—
598C2×Dic11—22no—
599C2×Dic11—42no—
600C2×Dic11—81no—
601C2×Dic11—81no—
602D44—22no—
603D44—22no—
604D44—42no—
605C4×D11—44no—
606C4×D11—44no—
607Dic22—22no—
608Dic22—22no—
609Dic22—42no—
610C11⋊C8—21no—
611C11⋊C8—21no—
612C11⋊C8—21no—
613C11⋊C8—21no—
614C11⋊C8—22no—
615C11⋊C8—22no—
616C2×2−1+4C2×D1111yescharacteristic
617C22×#41—111no—
618C22×#41C2×D1111yescharacteristic
619C2×#137—111no—
620C2×AGL(1,ℤ/8)—111no—
621C22×Q16—111no—
622C22×SD16—111no—
623C2×#131—111no—
624C2×#131—111no—
625D4×Q8—21no—
626#548—21no—
627#547—22no—
628#547—21no—
629#546—22no—
630#546—21no—
631#537—112no—
632#537—112no—
633#537C2×D1111yescharacteristic
634#537C2×D1112yescomplemented
635#536—111no—
636#536—111no—
637#536—221no—
638#536C2×D1111yescharacteristic
639#536C2×D1112yescomplemented
640#535—111no—
641#535—111no—
642#535—221no—
643#534—222no—
644#532—221no—
645#532—221no—
646#525—112no—
647#525—112no—
648#525—222no—
649#525C2×D1111yescharacteristic
650#525C2×D1112yescomplemented
651C2×C22⋊Q8C2×D1111yescharacteristic
652C2×C22⋊Q8C2×D1112yescomplemented
653#520C2×D1111yescharacteristic
654C2×#117—111no—
655#485—111no—
656#485—111no—
657#485—112no—
658#485—112no—
659#485—112no—
660#485—112no—
661#484—111no—
662#484—112no—
663#484—112no—
664#483—111no—
665#483—112no—
666#483—112no—
667#482—111no—
668#482—111no—
669#482—112no—
670#482—112no—
671#481—111no—
672#481—112no—
673#480—111no—
674#480—112no—
675#470—112no—
676#470—112no—
677#470—112no—
678#469—112no—
679#468—112no—
680#468—112no—
681#468—112no—
682#468—112no—
683#467—112no—
684#467—112no—
685#467—112no—
686#466—112no—
687#465—112no—
688#465—112no—
689#465—112no—
690#465—112no—
691#452—112no—
692#452—112no—
693#452—112no—
694#452—112no—
695#452—112no—
696#452—112no—
697#452—112no—
698#452—112no—
699#451—112no—
700#451—112no—
701#449—112no—
702#449—112no—
703#449—112no—
704#449—112no—
705#448—112no—
706#448—112no—
707#428—111no—
708#428—111no—
709#427—111no—
710#427—111no—
711#419—111no—
712#419—111no—
713#419—111no—
714#418—111no—
715#416—111no—
716#416—111no—
717C2×#103—111no—
718C2×#102—111no—
719#408—111no—
720#408—111no—
721#408—112no—
722#408—112no—
723#407—111no—
724#407—112no—
725C2×C22⋊C8—111no—
726C2×C22⋊C8—112no—
727C22×C11—21no—
728C22×C11—21no—
729C22×C11—22no—
730C22×C11—21no—
731C22×C11—22no—
732C22×C11—21no—
733C22×C11—21no—
734C22×C11—21no—
735C22×C11—22no—
736C22×C11—22no—
737C22×C11—21no—
738C22×C11—21no—
739C22×C11—22no—
740C22×C11—22no—
741C22×C11—41no—
742C22×C11—41no—
743C22×C11—41no—
744C22×C11—82no—
745C22×C11—84no—
746C22×C11#53412yes—
747C22×C11C23×D411yescharacteristic
748C2×D11—42no—
749C2×D11—42no—
750C2×D11—42no—
751C2×D11—84no—
752C4×C11—21no—
753C4×C11—21no—
754C4×C11—22no—
755C4×C11—22no—
756C4×C11—42no—
757C4×C11—41no—
758C4×C11—41no—
759C4×C11—42no—
760C4×C11—41no—
761C4×C11#53412yes—
762C4×C11C2×H(5,𝔽2)11yescharacteristic
763C4×C11C2×H(5,𝔽2)11yescharacteristic
764Dic11—41no—
765Dic11—41no—
766Dic11—41no—
767Dic11—41no—
768Dic11—42no—
7692−1+4—42no—
7702−1+4—42no—
771C2×#41—22no—
772C2×#41—21no—
773C2×#41—42no—
774C2×#41—42no—
775C2×#41—112no—
776C2×#41—112no—
777C2×#41—221no—
778C2×#41—221no—
779C2×#41—442no—
780C2×#41—442no—
781C2×#41C22⋊D1112yes—
782C2×#41C22⋊D1111yescharacteristic
783C2×#41C22⋊D1111yescharacteristic
784C2×#41C22×D1111yescharacteristic
785C2×#41C22×D1112yes—
786C2×#41C22×D1111yescharacteristic
787C2×#41C22×D1111yescharacteristic
788C2×#41C22×D1112yes—
789C22×Q8—21no—
790C22×Q8—111no—
791C22×Q8C22⋊D1111yescharacteristic
792C22×Q8C22×D1111yescharacteristic
793C22×Q8C22×D1112yes—
794C22×D4—111no—
795C22×D4—221no—
796C22×D4C22⋊D1112yes—
797C22×D4C22⋊D1111yescharacteristic
798C23×C4—221no—
799C23×C4C22×D1111yescharacteristic
800C23×C4C22×D1112yes—
801#137—442no—
802AGL(1,ℤ/8)—442no—
803C2×Q16—112no—
804C2×Q16—112no—
805C2×Q16—112no—
806C2×Q16—442no—
807C2×SD16—112no—
808C2×SD16—112no—
809C2×SD16—112no—
810C2×SD16—112no—
811C2×SD16—442no—
812C2×D8—112no—
813#131—442no—
814#131—442no—
815C2×M16—111no—
816C2×M16—111no—
817C2×M16—112no—
818C2×M16—112no—
819C22×C8—111no—
820C22×C8—111no—
821C22×C8—112no—
822C22×C8—112no—
823C4⋊Q8—21no—
824C4⋊Q8—22no—
825C4⋊Q8—221no—
826C4⋊Q8—221no—
827#127—221no—
828#127—221no—
829#124—21no—
830#124—22no—
831#124—221no—
832#124—221no—
833#124—221no—
834#124—221no—
835#123—22no—
836#123—22no—
837#123—22no—
838#123—21no—
839#123—22no—
840#123—222no—
841#123—222no—
842#123—222no—
843#123—222no—
844C22⋊Q8—21no—
845C22⋊Q8—22no—
846C22⋊Q8—21no—
847C22⋊Q8—21no—
848C22⋊Q8—22no—
849C22⋊Q8—22no—
850C22⋊Q8—112no—
851C22⋊Q8—112no—
852C22⋊Q8—112no—
853C22⋊Q8—112no—
854C22⋊Q8—222no—
855C22⋊Q8—222no—
856C22⋊Q8C22×D1112yes—
857C22⋊Q8C22×D1112yes—
858C22⋊Q8C22×D1111yescharacteristic
859C22⋊Q8C22×D1112yes—
860C22⋊Q8C22×D1112yes—
861C22⋊Q8C22×D1111yescharacteristic
862C22⋊Q8C22×D1112yes—
863#121—22no—
864#121—21no—
865#121—22no—
866#121—22no—
867#121—22no—
868#121—112no—
869#121—112no—
870#121—112no—
871#121—112no—
872#121—222no—
873#121—222no—
874#121—222no—
875#121—222no—
876#121—222no—
877#121—222no—
878#121C22×D1111yescharacteristic
879#121C22×D1111yescharacteristic
880#121C22×D1112yes—
881#120—21no—
882#120—22no—
883#120—222no—
884#120—222no—
885#120—222no—
886#120—222no—
887C4×Q8—21no—
888C4×D4—22no—
889C4×D4—21no—
890C4×D4—21no—
891C4×D4—21no—
892C4×D4—22no—
893C4×D4—22no—
894C4×D4—222no—
895C4×D4—222no—
896C4×D4—222no—
897C4×D4—222no—
898#117—111no—
899#117—111no—
900#117—111no—
901#117—111no—
902#117—221no—
903#117—221no—
904#117C22×D1111yescharacteristic
905#117C22×D1112yes—
906C2×C4⋊C4—21no—
907C2×C4⋊C4—22no—
908C2×C4⋊C4—111no—
909C2×C4⋊C4—111no—
910C2×C4⋊C4C22×D1111yescharacteristic
911C2×C4⋊C4C22×D1112yes—
912C2×C22⋊C4—21no—
913C2×C22⋊C4—22no—
914C2×C22⋊C4—221no—
915C2×C42—221no—
916#107—111no—
917#107—111no—
918#107—111no—
919#107—111no—
920#107—112no—
921#107—112no—
922#106—111no—
923#106—111no—
924#106—111no—
925#106—111no—
926#106—112no—
927#106—112no—
928#103—111no—
929#103—111no—
930#103—111no—
931#103—111no—
932#103—112no—
933#103—112no—
934#103—112no—
935#103—112no—
936#103—112no—
937#103—112no—
938#103—112no—
939#103—112no—
940#102—111no—
941#102—111no—
942#102—111no—
943#102—111no—
944#102—112no—
945#102—112no—
946#102—112no—
947#102—112no—
948C22⋊C8—111no—
949C22⋊C8—112no—
950C22⋊C8—111no—
951C22⋊C8—112no—
952C22⋊C8—112no—
953C22⋊C8—111no—
954C22⋊C8—111no—
955C22⋊C8—112no—
956C22⋊C8—112no—
957C22⋊C8—112no—
958C2×C11—22no—
959C2×C11—42no—
960C2×C11—41no—
961C2×C11—42no—
962C2×C11—41no—
963C2×C11—81no—
964C2×C11C2×#53411yescharacteristic
965C2×C11#358411yescharacteristic
966C2×C11#358611yescharacteristic
967D11—82no—
968C24—221no—
969C24C2×C22⋊D1111yescharacteristic
970C24C2×C22⋊D1112yes—
971#41—22no—
972#41—22no—
973#41—22no—
974#41—22no—
975#41—22no—
976#41—22no—
977#41—42no—
978#41—42no—
979#41—44no—
980#41—42no—
981#41—42no—
982#41—42no—
983#41—42no—
984#41—48no—
985#41—44no—
986#41—442no—
987#41—442no—
988#41—442no—
989#41—442no—
990#41—444no—
991#41—444no—
992C2×Q8—22no—
993C2×Q8—21no—
994C2×Q8—22no—
995C2×Q8—22no—
996C2×Q8—42no—
997C2×Q8—42no—
998C2×Q8—42no—
999C2×Q8—44no—
1000C2×Q8—112no—
1001C2×Q8—221no—
1002C2×Q8—222no—
1003C2×Q8—222no—
1004C2×Q8C2×C22⋊D1111yescharacteristic
1005C2×Q8C2×C22⋊D1111yescharacteristic
1006C2×Q8C2×C22⋊D1112yes—
1007C2×Q8C23×D1112yes—
1008C2×Q8C23×D1111yescharacteristic
1009C2×D4—21no—
1010C2×D4—22no—
1011C2×D4—21no—
1012C2×D4—22no—
1013C2×D4—21no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—112no—
1017C2×D4—222no—
1018C2×D4—222no—
1019C2×D4—222no—
1020C2×D4—222no—
1021C2×D4—222no—
1022C2×D4—222no—
1023C2×D4—222no—
1024C2×D4—222no—
1025C2×D4—221no—
1026C2×D4—444no—
1027C2×D4C2×C22⋊D1112yes—
1028C2×D4C2×C22⋊D1111yescharacteristic
1029C2×D4C2×C22⋊D1112yes—
1030C2×D4C2×C22⋊D1111yescharacteristic
1031C2×D4C2×C22⋊D1112yes—
1032C2×D4C2×C22⋊D1112yes—
1033C2×D4C2×C22⋊D1112yes—
1034C2×D4C23×D1111yescharacteristic
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—21no—
1039C22×C4—22no—
1040C22×C4—21no—
1041C22×C4—22no—
1042C22×C4—21no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—221no—
1046C22×C4—221no—
1047C22×C4—221no—
1048C22×C4—222no—
1049C22×C4—222no—
1050C22×C4—444no—
1051C22×C4C2×C22⋊D1111yescharacteristic
1052C22×C4C2×C22⋊D1111yescharacteristic
1053C22×C4C2×C22⋊D1111yescharacteristic
1054C22×C4C2×C22⋊D1112yes—
1055C22×C4C2×C22⋊D1112yes—
1056C22×C4C2×C22⋊D1112yes—
1057C22×C4C23×D1111yescharacteristic
1058C22×C4C23×D1112yes—
1059C22×C4C23×D1111yescharacteristic
1060C22×C4C23×D1112yes—
1061C22×C4C23×D1111yescharacteristic
1062Q16—442no—
1063Q16—442no—
1064Q16—442no—
1065SD16—442no—
1066SD16—442no—
1067SD16—442no—
1068SD16—442no—
1069D8—442no—
1070M16—222no—
1071M16—222no—
1072M16—442no—
1073M16—442no—
1074C2×C8—111no—
1075C2×C8—111no—
1076C2×C8—112no—
1077C2×C8—111no—
1078C2×C8—111no—
1079C2×C8—112no—
1080C2×C8—222no—
1081C2×C8—222no—
1082C2×C8—442no—
1083C2×C8—442no—
1084C4⋊C4—22no—
1085C4⋊C4—21no—
1086C4⋊C4—22no—
1087C4⋊C4—22no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—21no—
1091C4⋊C4—22no—
1092C4⋊C4—21no—
1093C4⋊C4—111no—
1094C4⋊C4—111no—
1095C4⋊C4—111no—
1096C4⋊C4—111no—
1097C4⋊C4—221no—
1098C4⋊C4—221no—
1099C4⋊C4—222no—
1100C4⋊C4—222no—
1101C4⋊C4—222no—
1102C4⋊C4—222no—
1103C4⋊C4C23×D1112yes—
1104C4⋊C4C23×D1111yescharacteristic
1105C4⋊C4C23×D1111yescharacteristic
1106C22⋊C4—22no—
1107C22⋊C4—21no—
1108C22⋊C4—22no—
1109C22⋊C4—22no—
1110C22⋊C4—22no—
1111C22⋊C4—22no—
1112C22⋊C4—21no—
1113C22⋊C4—22no—
1114C22⋊C4—21no—
1115C22⋊C4—21no—
1116C22⋊C4—22no—
1117C22⋊C4—21no—
1118C22⋊C4—221no—
1119C22⋊C4—221no—
1120C22⋊C4—221no—
1121C22⋊C4—221no—
1122C22⋊C4—222no—
1123C22⋊C4—222no—
1124C22⋊C4—222no—
1125C22⋊C4—222no—
1126C22⋊C4—222no—
1127C22⋊C4—222no—
1128C22⋊C4—222no—
1129C22⋊C4—222no—
1130C42—22no—
1131C42—21no—
1132C42—221no—
1133C42—221no—
1134C42—221no—
1135C42—221no—
1136C11#6076111yescharacteristic, complemented, Sylow
1137C23—22no—
1138C23—21no—
1139C23—42no—
1140C23—41no—
1141C23—41no—
1142C23—42no—
1143C23—42no—
1144C23—222no—
1145C23—442no—
1146C23—881no—
1147C23—881no—
1148C23C22×C22⋊D1111yescharacteristic
1149C23C22×C22⋊D1112yes—
1150C23C22×C22⋊D1111yescharacteristic
1151C23C22×C22⋊D1112yes—
1152C23C22×C22⋊D1111yescharacteristic
1153Q8—22no—
1154Q8—22no—
1155Q8—22no—
1156Q8—21no—
1157Q8—22no—
1158Q8—21no—
1159Q8—42no—
1160Q8—44no—
1161Q8—42no—
1162Q8—222no—
1163Q8—222no—
1164Q8—442no—
1165D4—24no—
1166D4—24no—
1167D4—22no—
1168D4—22no—
1169D4—21no—
1170D4—21no—
1171D4—42no—
1172D4—42no—
1173D4—42no—
1174D4—42no—
1175D4—44no—
1176D4—42no—
1177D4—81no—
1178D4—82no—
1179D4—222no—
1180D4—222no—
1181D4—444no—
1182D4—444no—
1183D4—442no—
1184D4—882no—
1185D4—882no—
1186D4—882no—
1187D4—882no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—44no—
1208C2×C4—44no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—81no—
1212C2×C4—82no—
1213C2×C4—221no—
1214C2×C4—221no—
1215C2×C4—221no—
1216C2×C4—221no—
1217C2×C4—222no—
1218C2×C4—444no—
1219C2×C4—444no—
1220C2×C4—442no—
1221C2×C4—881no—
1222C2×C4—881no—
1223C2×C4#6703712yes—
1224C2×C4#6703712yes—
1225C2×C4C22×C22⋊D1112yes—
1226C2×C4C22×C22⋊D1111yescharacteristic
1227C2×C4C22×C22⋊D1112yes—
1228C2×C4C22×C22⋊D1111yescharacteristic
1229C2×C4C22×C22⋊D1111yescharacteristic
1230C2×C4C24×D1111yescharacteristic
1231C8—221no—
1232C8—221no—
1233C8—221no—
1234C8—221no—
1235C8—222no—
1236C8—222no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—22no—
1242C22—22no—
1243C22—21no—
1244C22—21no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—21no—
1249C22—22no—
1250C22—21no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—82no—
1255C22—84no—
1256C22—442no—
1257C22—442no—
1258C22—442no—
1259C22—884no—
1260C22#1062333512yes—
1261C22C23×C22⋊D1111yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—22no—
1265C4—22no—
1266C4—41no—
1267C4—42no—
1268C4—41no—
1269C4—42no—
1270C4—41no—
1271C4—441no—
1272C4—441no—
1273C4—442no—
1274C4—441no—
1275C4—441no—
1276C4#1062333512yes—
1277C4C2×#6703711yescharacteristic
1278C4C2×#6703711yescharacteristic
1279C2—22no—
1280C2—41no—
1281C2—41no—
1282C2—42no—
1283C2—42no—
1284C2—81no—
1285C2—882no—
1286C2C2×#1062333511yescharacteristic
1287C2#1308338711yescharacteristic
1288C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3489C2
socleC22×C11C23×D4
hypercenter#3489D11
hypocenterC11#60761
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #13081945C2semidirect
2. #13079522C2semidirect
3. #13079513C2semidirect
4. #13079498C2semidirect
5. #13079498C2semidirect
6. #13079453C2semidirect
7. #13079446C2semidirect
8. #13079404C2semidirect
9. #13079397C2semidirect
10. #13078585C2semidirect
11. #13078574C2semidirect
12. #13078560C2semidirect
13. #13078525C2semidirect
14. #13078309C2semidirect
15. #13078298C2semidirect
16. #13078268C2semidirect
17. #13078257C2semidirect
18. #13077911C2semidirect
19. #13077902C2semidirect
20. #13077856C2semidirect
21. C2×#10622660C2semidirect
22. #13077065C2semidirect
23. C11×#3489C2semidirect
34. C11×#537C22semidirect
36. C11×#536C22semidirect
38. C11×#525C22semidirect
40. C2×C11×C22⋊Q8C22semidirect
51. C2×#67004C22semidirect
52. C2×#67002C22semidirect
56. C22×#4326C22semidirect
57. C22×#4325C22semidirect
63. #10622852C22semidirect
64. #10622852C22semidirect
65. #10622851C22semidirect
66. #10622851C22semidirect
69. #10622847C22semidirect
70. #10622847C22semidirect
71. #10622846C22semidirect
72. #10622846C22semidirect
73. #10622841C22semidirect
74. #10622841C22semidirect
75. #10622840C22semidirect
76. #10622840C22semidirect
77. #10622838C22semidirect
78. #10622838C22semidirect
80. #10622820C22semidirect
82. C2×C22⋊(C11⋊C8)C22semidirect
83. #10622665C22semidirect
84. #10622665C22semidirect
85. #10622665C22semidirect
86. #10622664C22semidirect
87. #10622664C22semidirect
88. #10622664C22semidirect
89. #10622662C22semidirect
90. #10622662C22semidirect
91. #10622662C22semidirect
92. #10622661C22semidirect
93. #10622661C22semidirect
94. #10622661C22semidirect
98. #10622660C22semidirect
99. #10622660C22semidirect
100. #10622660C22semidirect
101. #10622658C22semidirect
102. #10622658C22semidirect
103. #10622658C22semidirect
104. #10622658C22semidirect
105. #10622657C22semidirect
106. #10622657C22semidirect
107. #10622656C22semidirect
108. #10622656C22semidirect
109. #10622655C22semidirect
110. #10622654C22semidirect
111. #10622652C22semidirect
112. #10622651C22semidirect
114. #10622650C22semidirect
115. #10622648C22semidirect
116. #10622648C22semidirect
117. #10622647C22semidirect
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
493. #3489D11semidirect
634. #537C2×D11semidirect
639. #536C2×D11semidirect
650. #525C2×D11semidirect
652. C2×C22⋊Q8C2×D11semidirect
1136. C11#60761semidirect

Maximal subgroups

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

subgroupindex
#130819452
#130795222
#130795132
#130794982
#130794532
#130794462
#130794042
#130793972
#130785852
#130785742
#130785602
#130785252
#130783092
#130782982
#130782682
#130782572
#130779112
#130779022
#130778562
C2×#106226602
#130770652
C11×#34892
#6076111