Finite Group Databasebeta

← #15624728

Subgroups — #15624728

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082296C211yesmaximal, characteristic, complemented
2#13079522C214yesmaximal, complemented
3#13079492C214yesmaximal, complemented
4#13079437C212yesmaximal, complemented
5#13079430C212yesmaximal, complemented
6#13079397C212yesmaximal, complemented
7#13079373C212yesmaximal, complemented
8#13078601C212yesmaximal, complemented
9#13078539C211yesmaximal, characteristic, complemented
10C2×#10622584C211yesmaximal, characteristic, complemented
11#13078309C212yesmaximal, complemented
12#13078275C212yesmaximal, complemented
13#13077928C212yesmaximal, complemented
14#13077876C211yesmaximal, characteristic, complemented
15#13077834C211yesmaximal, characteristic, complemented
16#13077065C211yesmaximal, characteristic, complemented
17C2×C11×#537C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C22×C11×#41C2211yescharacteristic
20C2×#67043C2211yescharacteristic, complemented
21C11×#537—22no—
22C11×#537—21no—
23C11×#537—21no—
24C11×#537C2212yes—
25C11×#537C2212yes—
26C11×#537C2214yes—
27C2×C11×C22⋊Q8—21no—
28C2×C11×C22⋊Q8C2212yes—
29C2×C11×#121—21no—
30C2×C11×#121—22no—
31C2×C11×#121C2212yes—
32C22×C11×C4⋊C4C2211yescharacteristic
33#10623364C2211yescharacteristic, complemented
34#10623364C2212yescomplemented
35#10623362—21no—
36#10623358C2211yescharacteristic, complemented
37#10623356C2211yescharacteristic, complemented
38#10623356C2212yescomplemented
39#10623355—22no—
40#10623355—21no—
41C2×#67004C2212yescomplemented
42C2×#67003C2212yescomplemented
43C2×#67001C2212yescomplemented
44Q8×C22⋊D11—21no—
45#10623337—21no—
46#10623337—22no—
47#10623322C2211yescharacteristic
48#10623322C2212yes—
49C2×#66977C2212yes—
50C2×#66977C2211yescharacteristic
51#10622852C2212yescomplemented
52#10622852C2214yescomplemented
53#10622851C2212yescomplemented
54#10622847C2212yescomplemented
55#10622847C2214yescomplemented
56#10622846C2212yescomplemented
57#10622845C2212yescomplemented
58#10622841C2211yescharacteristic
59#10622841C2212yes—
60#10622840C2211yescharacteristic
61#10622831C2211yescharacteristic
62#10622831C2212yes—
63#10622830C2211yescharacteristic
64#10622820C2211yescharacteristic
65#10622820C2212yes—
66C2×C22⋊(C11⋊C8)C2211yescharacteristic
67C2×C22⋊(C11⋊C8)C2212yes—
68#10622665C2214yescomplemented
69#10622665C2214yescomplemented
70#10622664C2214yescomplemented
71#10622663C2214yescomplemented
72#10622661C2214yescomplemented
73#10622660C2214yescomplemented
74#10622658C2214yescomplemented
75#10622656C2214yescomplemented
76#10622655C2214yescomplemented
77#10622654C2214yescomplemented
78#10622654C2214yescomplemented
79#10622653C2214yescomplemented
80#10622652C2214yescomplemented
81#10622650C2214yescomplemented
82#10622648C2214yescomplemented
83#10622647C2214yescomplemented
84#10622584C2212yes—
85#10622584C2212yes—
86#10622584C2212yes—
87#10622584C2214yescomplemented
88#10622583C2212yescomplemented
89C2×#66874C2212yescomplemented
90#10622581C2212yescomplemented
91#10622580C2212yes—
92#10622579C2212yescomplemented
93#10622577C2212yescomplemented
94C2×#66872C2212yescomplemented
95C2×C11×#41—21no—
96C2×C11×#41—21no—
97C2×C11×#41—44no—
98C2×C11×#41—44no—
99C2×C11×#41D412yes—
100C2×C11×#41D411yescharacteristic
101C2×C11×#41D411yescharacteristic
102C2×C11×#41C2312yes—
103C2×C11×#41C2312yes—
104C2×C11×#41C2311yescharacteristic
105C2×C11×#41C2311yescharacteristic
106C2×C11×#41C2312yes—
107C22×Q8×C11D411yescharacteristic
108C22×Q8×C11C2311yescharacteristic
109C22×D4×C11—21no—
110C22×D4×C11—22no—
111C22×D4×C11D411yescharacteristic
112C22×D4×C11D412yes—
113C22×D4×C11C2311yescharacteristic
114C23×C4×C11—21no—
115C23×C4×C11—21no—
116C23×C4×C11C2311yescharacteristic
117C23×C4×C11C2312yes—
118#67043—44no—
119C2×Q8×D11—21no—
120C2×#4341—22no—
121C2×#4341—21no—
122C2×#4339C2311yescharacteristic
123C2×#4339C2312yes—
124C22×Dic22C2311yescharacteristic
125C22×Dic22C2312yes—
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8—24no—
129C11×C22⋊Q8—22no—
130C11×C22⋊Q8—22no—
131C11×C22⋊Q8C2314yes—
132C11×C22⋊Q8C2314yes—
133C11×#121—22no—
134C11×#121—22no—
135C11×#121—24no—
136C11×#121—24no—
137C11×#121—24no—
138C11×#121—24no—
139C11×#121—24no—
140C11×#121—22no—
141C11×#121—22no—
142C11×#121C2314yes—
143C11×#121C2314yes—
144C2×C11×C4⋊C4—21no—
145C2×C11×C4⋊C4—21no—
146C2×C11×C4⋊C4—21no—
147C2×C11×C4⋊C4—22no—
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C4⋊C4C2312yes—
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C22⋊C4—22no—
152C2×C11×C22⋊C4—22no—
153#67006—21no—
154#67006—22no—
155C2×C22⋊Dic11—21no—
156C2×C22⋊Dic11—22no—
157#67004—44no—
158#67003—44no—
159#67001—44no—
160#66999—21no—
161#66999—22no—
162Q8×Dic11—21no—
163#66997—21no—
164#66997—22no—
165C2×#4326C2312yes—
166C2×#4326C2314yes—
167C2×#4325C2312yes—
168#66992—22no—
169#66992—22no—
170#66992—22no—
171#66991—21no—
172#66991—22no—
173#66989—21no—
174#66989—22no—
175#66988—22no—
176#66988—22no—
177#66988—22no—
178D4×Dic11—22no—
179D4×Dic11—21no—
180C2×#4324C2312yes—
181C2×#4324C2314yes—
182C2×#4323C2312yes—
183#66983C2311yescharacteristic
184#66983C2311yescharacteristic
185#66983C2312yes—
186#66982—21no—
187#66982—22no—
188C4×C22⋊D11—21no—
189C4×C22⋊D11—22no—
190C4×C22⋊D11—21no—
191C4×C22⋊D11—22no—
192#66979C2311yescharacteristic
193#66979C2312yes—
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2312yes—
196#66977—21no—
197#66977—22no—
198#66977—21no—
199#66977—22no—
200#66977C2311yescharacteristic
201#66977C2312yes—
202#66977C2312yes—
203#66977C2312yes—
204#66977C2312yes—
205#66977C2311yescharacteristic
206#66977C2312yes—
207C2×Dic11⋊C4—21no—
208C2×Dic11⋊C4—22no—
209C2×#4318C2312yes—
210C2×#4318C2314yes—
211C22×C11⋊C8C2312yes—
212C22×C11⋊C8C2314yes—
213#66899C2312yes—
214#66899C2314yes—
215#66899C2312yes—
216#66896C2312yes—
217#66896C2314yes—
218#66896C2312yes—
219C22⋊(C11⋊C8)C2311yescharacteristic
220C22⋊(C11⋊C8)C2311yescharacteristic
221C22⋊(C11⋊C8)C2312yes—
222C22⋊(C11⋊C8)C2312yes—
223C22⋊(C11⋊C8)C2314yes—
224C22⋊(C11⋊C8)C2312yes—
225C22⋊(C11⋊C8)C2314yes—
226#66874C2314yes—
227#66874C2314yes—
228#66874C2314yes—
229#66873C2314yes—
230#66872C2314yes—
231#66872C2314yes—
232#66872C2314yes—
233#66871C2314yes—
234#60763—111nomaximal, Sylow
235C24×C11—21no—
236C24×C11C2×D411yescharacteristic
237C24×C11C2×D412yes—
238C11×#41—24no—
239C11×#41—24no—
240C11×#41—24no—
241C11×#41—24no—
242C11×#41—44no—
243C11×#41—44no—
244C11×#41—42no—
245C11×#41—42no—
246C11×#41—42no—
247C11×#41—42no—
248C11×#41—44no—
249C11×#41—44no—
250C2×Q8×C11—21no—
251C2×Q8×C11—42no—
252C2×Q8×C11—42no—
253C2×Q8×C11C2×D411yescharacteristic
254C2×Q8×C11C2×D411yescharacteristic
255C2×Q8×C11C2×D412yes—
256C2×Q8×C11C2412yes—
257C2×D4×C11—22no—
258C2×D4×C11—22no—
259C2×D4×C11—24no—
260C2×D4×C11—24no—
261C2×D4×C11—21no—
262C2×D4×C11—42no—
263C2×D4×C11—42no—
264C2×D4×C11—44no—
265C2×D4×C11—44no—
266C2×D4×C11—84no—
267C2×D4×C11C2×D412yes—
268C2×D4×C11C2×D411yescharacteristic
269C2×D4×C11C2×D412yes—
270C2×D4×C11C2×D411yescharacteristic
271C2×D4×C11C2×D412yes—
272C2×D4×C11C2×D412yes—
273C2×D4×C11C2×D412yes—
274C2×D4×C11C2412yes—
275C22×C4×C11—24no—
276C22×C4×C11—22no—
277C22×C4×C11—21no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—44no—
283C22×C4×C11—44no—
284C22×C4×C11—82no—
285C22×C4×C11C2×D411yescharacteristic
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2×D412yes—
289C22×C4×C11C2×D412yes—
290C22×C4×C11C2×D412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2412yes—
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C2×C22⋊D11—21no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—21no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—21no—
301C22×Dic11—22no—
302C22×Dic11—21no—
303C22×Dic11—22no—
304C22×Dic11—21no—
305Q8×D11—44no—
306#4341—48no—
307#4341—44no—
308#4339—24no—
309#4339—44no—
310C2×D44C2411yescharacteristic
311C2×C4×D11—22no—
312C2×C4×D11—21no—
313C2×Dic22—22no—
314C2×Dic22—21no—
315C2×Dic22—24no—
316C2×Dic22—44no—
317C2×Dic22C2412yes—
318C2×Dic22C2411yescharacteristic
319C11×C4⋊C4—22no—
320C11×C4⋊C4—22no—
321C11×C4⋊C4—22no—
322C11×C4⋊C4—24no—
323C11×C4⋊C4—24no—
324C11×C4⋊C4C2414yes—
325C11×C22⋊C4—24no—
326C11×C22⋊C4—24no—
327C11×C22⋊C4—24no—
328C11×C22⋊C4—24no—
329C22⋊Dic11—22no—
330C22⋊Dic11—21no—
331C22⋊Dic11—22no—
332C22⋊Dic11—22no—
333C22⋊Dic11—22no—
334C22⋊Dic11—22no—
335C22⋊Dic11—21no—
336C22⋊Dic11—22no—
337C22⋊Dic11—21no—
338#4326—42no—
339#4326—44no—
340#4325—42no—
341#4324—42no—
342#4324—44no—
343#4323—42no—
344(C2×D11)⋊C4—21no—
345(C2×D11)⋊C4—22no—
346(C2×D11)⋊C4—21no—
347C4⋊Dic11—22no—
348C4⋊Dic11—21no—
349C4⋊Dic11C2411yescharacteristic
350C4⋊Dic11C2412yes—
351C4⋊Dic11C2411yescharacteristic
352Dic11⋊C4—22no—
353Dic11⋊C4—21no—
354Dic11⋊C4—22no—
355Dic11⋊C4—22no—
356Dic11⋊C4—22no—
357Dic11⋊C4—22no—
358Dic11⋊C4—21no—
359C4×Dic11—22no—
360C4×Dic11—21no—
361#4318—24no—
362#4318—44no—
363C2×C11⋊C8—24no—
364C2×C11⋊C8—44no—
365C2×C11⋊C8C2414yes—
366C2×C11⋊C8C2412yes—
367C2×C11⋊C8C2412yes—
368#3489—111no—
369C2×#537D1111yescharacteristic, complemented
370#3204—114no—
371#3201—114no—
372#3195—112no—
373#3194—112no—
374#3190—112no—
375#3187—112no—
376#3099—112no—
377#3092—111no—
378C2×#483—111no—
379#3063—112no—
380#3060—112no—
381#3013—112no—
382#3007—111no—
383#3002—111no—
384#2880—111no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—24no—
388C23×C11—22no—
389C23×C11—41no—
390C23×C11—42no—
391C23×C11—42no—
392C23×C11—42no—
393C23×C11—42no—
394C23×C11—42no—
395C23×C11C22×D412yes—
396C23×C11C22×D411yescharacteristic
397C23×C11C22×D412yes—
398C23×C11C22×D411yescharacteristic
399C23×C11C22×D411yescharacteristic
400C22×D11—21no—
401Q8×C11—22no—
402Q8×C11—22no—
403Q8×C11—22no—
404Q8×C11—22no—
405Q8×C11—42no—
406Q8×C11—42no—
407D4×C11—24no—
408D4×C11—24no—
409D4×C11—22no—
410D4×C11—22no—
411D4×C11—22no—
412D4×C11—22no—
413D4×C11—42no—
414D4×C11—42no—
415D4×C11—42no—
416D4×C11—42no—
417D4×C11—44no—
418D4×C11—44no—
419D4×C11—84no—
420D4×C11—84no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—24no—
425C2×C4×C11—24no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—24no—
429C2×C4×C11—22no—
430C2×C4×C11—42no—
431C2×C4×C11—42no—
432C2×C4×C11—42no—
433C2×C4×C11—44no—
434C2×C4×C11—42no—
435C2×C4×C11—44no—
436C2×C4×C11—44no—
437C2×C4×C11—82no—
438C2×C4×C11—82no—
439C2×C4×C11C22×D412yes—
440C2×C4×C11C22×D412yes—
441C2×C4×C11C22×D411yescharacteristic
442C2×C4×C11C22×D411yescharacteristic
443C2×C4×C11C22×D411yescharacteristic
444C2×C4×C11H(5,𝔽2)14yes—
445C2×C4×C11C2511yescharacteristic
446C22⋊D11—44no—
447C22⋊D11—42no—
448C22⋊D11—42no—
449C22⋊D11—81no—
450C22⋊D11—82no—
451C2×Dic11—21no—
452C2×Dic11—22no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—21no—
456C2×Dic11—44no—
457C2×Dic11—42no—
458C2×Dic11—81no—
459C2×Dic11—82no—
460D44—22no—
461C4×D11—44no—
462C4×D11—42no—
463Dic22—24no—
464Dic22—22no—
465Dic22—44no—
466Dic22—42no—
467C11⋊C8—22no—
468C11⋊C8—22no—
469C11⋊C8—24no—
470C2×2−1+4—111no—
471C22×#41C2×D1111yescharacteristic
472C22×#41C2×D1111yescharacteristic
473C2×#137—112no—
474C2×#135—112no—
475C2×#131—112no—
476D4×Q8—221no—
477#548—221no—
478#547—222no—
479#547—221no—
480#546—222no—
481#546—221no—
482#537—22no—
483#537—21no—
484#537—21no—
485#537—112no—
486#537—111no—
487#537C2×D1112yes—
488#537C2×D1114yes—
489#537C2×D1112yes—
490#536—112no—
491#536—111no—
492#525—111no—
493#525—112no—
494C2×C22⋊Q8—21no—
495C2×C22⋊Q8—111no—
496C2×C22⋊Q8—112no—
497C2×C22⋊Q8C2×D1112yes—
498C2×#121—21no—
499C2×#121—22no—
500C2×#121C2×D1112yes—
501#520—111no—
502C22×C4⋊C4C2×D1111yescharacteristic
503#485—114no—
504#484—112no—
505#483—114no—
506#483—112no—
507#483—112no—
508#483—114no—
509#483—112no—
510#482—114no—
511#481—114no—
512#481—112no—
513#480—112no—
514#470—114no—
515#470—114no—
516#469—114no—
517#468—114no—
518#467—114no—
519#465—114no—
520#465—114no—
521#465—114no—
522#452—112no—
523#452—114no—
524#452—114no—
525#451—112no—
526#451—111no—
527#451—114no—
528#450—111no—
529#450—112no—
530#449—112no—
531#449—114no—
532#448—111no—
533#448—114no—
534#447—111no—
535#428—112no—
536C2×#106—112no—
537#417—112no—
538#417—112no—
539#416—112no—
540C2×#103—112no—
541#408—112no—
542#408—114no—
543#407—111no—
544#407—112no—
545C2×C22⋊C8—111no—
546C2×C22⋊C8—112no—
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—21no—
550C22×C11—21no—
551C22×C11—22no—
552C22×C11—21no—
553C22×C11—22no—
554C22×C11—21no—
555C22×C11—22no—
556C22×C11—22no—
557C22×C11—21no—
558C22×C11—22no—
559C22×C11—22no—
560C22×C11—44no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—84no—
565C22×C11—84no—
566C22×C11#53412yes—
567C22×C11#57712yes—
568C22×C11C23×D411yescharacteristic
569C2×D11—41no—
570C2×D11—41no—
571C2×D11—41no—
572C4×C11—21no—
573C4×C11—21no—
574C4×C11—22no—
575C4×C11—22no—
576C4×C11—42no—
577C4×C11—44no—
578C4×C11#53412yes—
579C4×C11C2×H(5,𝔽2)12yes—
580Dic11—42no—
581Dic11—41no—
582Dic11—42no—
583Dic11—41no—
584Dic11—41no—
5852−1+4—444no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—44no—
589C2×#41—44no—
590C2×#41—111no—
591C2×#41—112no—
592C2×#41—221no—
593C2×#41—222no—
594C2×#41C22⋊D1112yes—
595C2×#41C22⋊D1111yescharacteristic
596C2×#41C22⋊D1111yescharacteristic
597C2×#41C22×D1112yes—
598C2×#41C22×D1112yes—
599C2×#41C22×D1111yescharacteristic
600C2×#41C22×D1111yescharacteristic
601C2×#41C22×D1112yes—
602C22×Q8—111no—
603C22×Q8—112no—
604C22×Q8—221no—
605C22×Q8C22⋊D1111yescharacteristic
606C22×Q8C22×D1111yescharacteristic
607C22×D4—21no—
608C22×D4—22no—
609C22×D4C22⋊D1111yescharacteristic
610C22×D4C22⋊D1112yes—
611C22×D4C22×D1111yescharacteristic
612C23×C4—21no—
613C23×C4—21no—
614C23×C4C22×D1111yescharacteristic
615C23×C4C22×D1112yes—
616#137—444no—
617#135—444no—
618C2×Q16—112no—
619C2×Q16—114no—
620C2×SD16—112no—
621C2×SD16—112no—
622C2×SD16—114no—
623C2×D8—112no—
624#131—444no—
625C2×M16—112no—
626C2×M16—114no—
627C22×C8—112no—
628C22×C8—114no—
629C4⋊Q8—221no—
630C4⋊Q8—222no—
631#124—221no—
632#124—222no—
633#123—222no—
634#123—222no—
635#123—222no—
636#123—221no—
637#123—222no—
638C22⋊Q8—22no—
639C22⋊Q8—22no—
640C22⋊Q8—24no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—112no—
644C22⋊Q8—111no—
645C22⋊Q8—112no—
646C22⋊Q8—112no—
647C22⋊Q8—112no—
648C22⋊Q8—111no—
649C22⋊Q8—112no—
650C22⋊Q8—221no—
651C22⋊Q8—222no—
652C22⋊Q8—221no—
653C22⋊Q8—222no—
654C22⋊Q8—221no—
655C22⋊Q8—222no—
656C22⋊Q8C22×D1114yes—
657C22⋊Q8C22×D1114yes—
658#121—22no—
659#121—22no—
660#121—24no—
661#121—24no—
662#121—24no—
663#121—24no—
664#121—24no—
665#121—22no—
666#121—22no—
667#121—111no—
668#121—111no—
669#121—112no—
670#121—222no—
671#121—222no—
672#121—222no—
673#121—221no—
674#121—222no—
675#121C22×D1114yes—
676#121C22×D1114yes—
677#120—221no—
678#120—222no—
679C4×Q8—221no—
680C4×D4—222no—
681C4×D4—221no—
682C4×D4—221no—
683C4×D4—222no—
684C4×D4—221no—
685C4×D4—222no—
686#117—111no—
687#117—112no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—111no—
693C2×C4⋊C4—112no—
694C2×C4⋊C4—221no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4C22×D1112yes—
697C2×C4⋊C4C22×D1112yes—
698C2×C4⋊C4C22×D1112yes—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—221no—
702C2×C22⋊C4—222no—
703#107—114no—
704#106—114no—
705#106—114no—
706#106—114no—
707#103—112no—
708#103—112no—
709#103—114no—
710#103—114no—
711#103—114no—
712#103—114no—
713#102—112no—
714#102—112no—
715#102—114no—
716#102—114no—
717C22⋊C8—111no—
718C22⋊C8—111no—
719C22⋊C8—112no—
720C22⋊C8—114no—
721C22⋊C8—112no—
722C22⋊C8—114no—
723C22⋊C8—112no—
724C2×C11—22no—
725C2×C11—22no—
726C2×C11—41no—
727C2×C11—42no—
728C2×C11—42no—
729C2×C11—82no—
730C2×C11C2×#53411yescharacteristic
731C2×C11C2×#57711yescharacteristic
732C2×C11#358611yescharacteristic
733D11—81no—
734C24—21no—
735C24C2×C22⋊D1111yescharacteristic
736C24C2×C22⋊D1112yes—
737#41—24no—
738#41—24no—
739#41—24no—
740#41—24no—
741#41—44no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—42no—
747#41—44no—
748#41—44no—
749#41—224no—
750#41—444no—
751#41—448no—
752#41—444no—
753C2×Q8—21no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—112no—
757C2×Q8—111no—
758C2×Q8—222no—
759C2×Q8—221no—
760C2×Q8—224no—
761C2×Q8—444no—
762C2×Q8—444no—
763C2×Q8C2×C22⋊D1111yescharacteristic
764C2×Q8C2×C22⋊D1111yescharacteristic
765C2×Q8C2×C22⋊D1112yes—
766C2×Q8C23×D1112yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—21no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—84no—
777C2×D4—111no—
778C2×D4—221no—
779C2×D4—222no—
780C2×D4—221no—
781C2×D4—222no—
782C2×D4—221no—
783C2×D4C2×C22⋊D1112yes—
784C2×D4C2×C22⋊D1111yescharacteristic
785C2×D4C2×C22⋊D1112yes—
786C2×D4C2×C22⋊D1111yescharacteristic
787C2×D4C2×C22⋊D1112yes—
788C2×D4C2×C22⋊D1112yes—
789C2×D4C2×C22⋊D1112yes—
790C2×D4C23×D1112yes—
791C22×C4—24no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—82no—
801C22×C4—222no—
802C22×C4—221no—
803C22×C4—222no—
804C22×C4—221no—
805C22×C4—222no—
806C22×C4—221no—
807C22×C4C2×C22⋊D1111yescharacteristic
808C22×C4C2×C22⋊D1111yescharacteristic
809C22×C4C2×C22⋊D1111yescharacteristic
810C22×C4C2×C22⋊D1112yes—
811C22×C4C2×C22⋊D1112yes—
812C22×C4C2×C22⋊D1112yes—
813C22×C4C23×D1112yes—
814C22×C4C23×D1111yescharacteristic
815C22×C4C23×D1111yescharacteristic
816C22×C4C23×D1112yes—
817C22×C4C23×D1111yescharacteristic
818Q16—442no—
819Q16—444no—
820SD16—442no—
821SD16—444no—
822SD16—442no—
823D8—442no—
824M16—224no—
825M16—444no—
826C2×C8—114no—
827C2×C8—112no—
828C2×C8—112no—
829C2×C8—224no—
830C2×C8—444no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—111no—
837C4⋊C4—112no—
838C4⋊C4—111no—
839C4⋊C4—222no—
840C4⋊C4—221no—
841C4⋊C4—222no—
842C4⋊C4—221no—
843C4⋊C4—222no—
844C4⋊C4—222no—
845C4⋊C4—222no—
846C4⋊C4—222no—
847C4⋊C4—221no—
848C4⋊C4C23×D1114yes—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—222no—
854C22⋊C4—221no—
855C22⋊C4—222no—
856C22⋊C4—222no—
857C22⋊C4—222no—
858C22⋊C4—222no—
859C22⋊C4—221no—
860C22⋊C4—222no—
861C22⋊C4—221no—
862C22⋊C4—221no—
863C22⋊C4—222no—
864C22⋊C4—221no—
865C42—222no—
866C42—221no—
867C11#6076311yescharacteristic, complemented, Sylow
868C23—22no—
869C23—22no—
870C23—24no—
871C23—22no—
872C23—41no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—221no—
879C23C22×C22⋊D1112yes—
880C23C22×C22⋊D1112yes—
881C23C22×C22⋊D1111yescharacteristic
882C23C22×C22⋊D1111yescharacteristic
883C23C22×C22⋊D1111yescharacteristic
884Q8—22no—
885Q8—22no—
886Q8—22no—
887Q8—22no—
888Q8—42no—
889Q8—42no—
890Q8—224no—
891Q8—222no—
892Q8—444no—
893Q8—442no—
894D4—24no—
895D4—24no—
896D4—22no—
897D4—22no—
898D4—22no—
899D4—22no—
900D4—42no—
901D4—42no—
902D4—42no—
903D4—42no—
904D4—44no—
905D4—44no—
906D4—84no—
907D4—84no—
908D4—222no—
909D4—444no—
910D4—442no—
911D4—442no—
912D4—881no—
913D4—882no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—22no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—44no—
927C2×C4—42no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—82no—
931C2×C4—82no—
932C2×C4—221no—
933C2×C4—222no—
934C2×C4—221no—
935C2×C4—222no—
936C2×C4—221no—
937C2×C4—444no—
938C2×C4—444no—
939C2×C4—442no—
940C2×C4—442no—
941C2×C4—881no—
942C2×C4—882no—
943C2×C4#6703714yes—
944C2×C4C22×C22⋊D1112yes—
945C2×C4C22×C22⋊D1112yes—
946C2×C4C22×C22⋊D1111yescharacteristic
947C2×C4C22×C22⋊D1111yescharacteristic
948C2×C4C22×C22⋊D1111yescharacteristic
949C2×C4C24×D1111yescharacteristic
950C8—222no—
951C8—222no—
952C8—224no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—22no—
958C22—21no—
959C22—22no—
960C22—21no—
961C22—22no—
962C22—22no—
963C22—21no—
964C22—22no—
965C22—22no—
966C22—44no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—84no—
971C22—84no—
972C22—441no—
973C22—441no—
974C22—441no—
975C22#1062333512yes—
976C22#1062336712yes—
977C22C23×C22⋊D1111yescharacteristic
978C4—21no—
979C4—21no—
980C4—22no—
981C4—22no—
982C4—42no—
983C4—44no—
984C4—442no—
985C4—441no—
986C4—442no—
987C4—441no—
988C4—441no—
989C4#1062333512yes—
990C4C2×#6703712yes—
991C2—22no—
992C2—22no—
993C2—41no—
994C2—42no—
995C2—42no—
996C2—82no—
997C2—881no—
998C2C2×#1062333511yescharacteristic
999C2C2×#1062336711yescharacteristic
1000C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#537C2
socleC22×C11C23×D4
hypercenterC2×#537D11
hypocenterC11#60763
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13082296C2semidirect
2. #13079522C2semidirect
3. #13079492C2semidirect
4. #13079437C2semidirect
5. #13079430C2semidirect
6. #13079397C2semidirect
7. #13079373C2semidirect
8. #13078601C2semidirect
9. #13078539C2semidirect
10. C2×#10622584C2semidirect
11. #13078309C2semidirect
12. #13078275C2semidirect
13. #13077928C2semidirect
14. #13077876C2semidirect
15. #13077834C2semidirect
16. #13077065C2semidirect
17. C2×C11×#537C2semidirect
20. C2×#67043C22semidirect
33. #10623364C22semidirect
34. #10623364C22semidirect
36. #10623358C22semidirect
37. #10623356C22semidirect
38. #10623356C22semidirect
41. C2×#67004C22semidirect
42. C2×#67003C22semidirect
43. C2×#67001C22semidirect
51. #10622852C22semidirect
52. #10622852C22semidirect
53. #10622851C22semidirect
54. #10622847C22semidirect
55. #10622847C22semidirect
56. #10622846C22semidirect
57. #10622845C22semidirect
68. #10622665C22semidirect
69. #10622665C22semidirect
70. #10622664C22semidirect
71. #10622663C22semidirect
72. #10622661C22semidirect
73. #10622660C22semidirect
74. #10622658C22semidirect
75. #10622656C22semidirect
76. #10622655C22semidirect
77. #10622654C22semidirect
78. #10622654C22semidirect
79. #10622653C22semidirect
80. #10622652C22semidirect
81. #10622650C22semidirect
82. #10622648C22semidirect
83. #10622647C22semidirect
87. #10622584C22semidirect
88. #10622583C22semidirect
89. C2×#66874C22semidirect
90. #10622581C22semidirect
92. #10622579C22semidirect
93. #10622577C22semidirect
94. C2×#66872C22semidirect
369. C2×#537D11semidirect
867. C11#60763semidirect

Maximal subgroups

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

subgroupindex
#130822962
#130795222
#130794922
#130794372
#130794302
#130793972
#130793732
#130786012
#130785392
C2×#106225842
#130783092
#130782752
#130779282
#130778762
#130778342
#130770652
C2×C11×#5372
#6076311