Finite Group Databasebeta

← #15626876

Subgroups — #15626876

Order 2816.

1812 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082502C211yesmaximal, characteristic, complemented
2#13080062C214yesmaximal, complemented
3#13080042C214yesmaximal, complemented
4#13080003C212yesmaximal, complemented
5#13079989C212yesmaximal, complemented
6#13079953C212yesmaximal, complemented
7#13079932C212yesmaximal, complemented
8#13078452C212yesmaximal, complemented
9#13078413C211yesmaximal, characteristic, complemented
10#13078404C211yesmaximal, characteristic, complemented
11#13078309C212yesmaximal, complemented
12#13078252C212yesmaximal, complemented
13#13078133C212yesmaximal, complemented
14#13078103C211yesmaximal, characteristic, complemented
15C2×#10622632C211yesmaximal, characteristic, complemented
16#13077184C211yesmaximal, characteristic, complemented
17C11×#3460C211yesmaximal, characteristic
18C11×#544C2211yescharacteristic
19C11×#542—21no—
20C11×#542C2212yes—
21C11×#540—21no—
22C11×#540C2212yes—
23C11×#538—22no—
24C11×#537C2211yescharacteristic
25C11×#535C2211yescharacteristic
26C11×#535C2211yescharacteristic
27C11×#532—21no—
28C11×#532C2212yes—
29C11×#529—21no—
30C11×#529C2212yes—
31C11×#525—22no—
32C4×C11×#41C2211yescharacteristic
33C4×C11×#41C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35#10623356C2212yes—
36C2×#67004C2212yes—
37C2×#67001C2212yes—
38C22×#4324C2212yes—
39#10623098—21no—
40#10623098—21no—
41#10623073—21no—
42#10623073—21no—
43#10623072—22no—
44#10623072—22no—
45#10623049C2214yescomplemented
46#10623047C2212yes—
47#10623001C2211yescharacteristic
48#10623001C2212yescomplemented
49#10623001C2212yescomplemented
50C2×#66922C2211yescharacteristic
51#10622846C2212yes—
52#10622828C2212yes—
53#10622707C2214yescomplemented
54#10622704C2214yescomplemented
55#10622688C2214yes—
56#10622688C2214yes—
57#10622676C2214yescomplemented
58#10622676C2214yescomplemented
59#10622667C2214yes—
60#10622667C2214yes—
61#10622665C2214yescomplemented
62#10622664C2214yescomplemented
63#10622655C2214yes—
64#10622655C2214yes—
65#10622655C2214yescomplemented
66#10622654C2214yes—
67#10622654C2214yes—
68#10622654C2214yescomplemented
69#10622644C2212yescomplemented
70#10622644C2212yescomplemented
71#10622635C2212yescomplemented
72#10622634C2211yescharacteristic, complemented
73#10622633C2211yescharacteristic, complemented
74#10622632C2212yes—
75#10622632C2212yes—
76#10622632C2214yes—
77#10622632C2212yescomplemented
78#10622632C2212yescomplemented
79#10622622C2214yes—
80#10622622C2212yescomplemented
81#10622621C2212yes—
82#10622621C2211yescharacteristic, complemented
83#10622620C2212yes—
84#10622620C2211yescharacteristic, complemented
85#10622617C2212yes—
86#10622612C2212yes—
87#10622612C2214yescomplemented
88#10622611C2212yes—
89C2×#66874C2212yes—
90#10622577C2212yes—
91#10622537C2211yescharacteristic
92#10622537C2212yescomplemented
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yescomplemented
95C2×C11×#41—22no—
96C2×C11×#41C2311yescharacteristic
97C2×C11×#41C2311yescharacteristic
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100C22×Dic22C2312yes—
101C11×C4⋊Q8—21no—
102C11×C4⋊Q8C2312yes—
103C11×#127—21no—
104C11×#127C2312yes—
105C11×#126—22no—
106C11×#126—22no—
107C11×#125—21no—
108C11×#125C2312yes—
109C11×#124—21no—
110C11×#124—22no—
111C11×#124—22no—
112C11×#124C2312yes—
113C11×#123—22no—
114C11×#123—22no—
115C11×#123—22no—
116C11×#123—22no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8C2312yes—
121C11×#121—22no—
122C11×#121—21no—
123C11×#121—22no—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121—22no—
127C11×#121—22no—
128C11×#121C2312yes—
129C11×#121C2312yes—
130C11×#121C2312yes—
131C11×#120—22no—
132C11×#120—22no—
133C4×Q8×C11D411yescharacteristic
134C4×Q8×C11D411yescharacteristic
135C4×Q8×C11C2311yescharacteristic
136C4×Q8×C11C2311yescharacteristic
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11—22no—
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11—22no—
143C4×D4×C11D412yes—
144C4×D4×C11D412yes—
145C4×D4×C11D411yescharacteristic
146C4×D4×C11D411yescharacteristic
147C4×D4×C11C2312yes—
148C4×D4×C11C2312yes—
149C4×D4×C11C2311yescharacteristic
150C4×D4×C11C2311yescharacteristic
151C11×#117—21no—
152C11×#117—22no—
153C11×#117C2311yescharacteristic
154C11×#117C2311yescharacteristic
155C11×#117C2312yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—21no—
158C2×C42×C11—21no—
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2312yes—
161#67004—44no—
162#67001—44no—
163#66997—22no—
164C2×#4326C2314yes—
165#66989—22no—
166#66988—24no—
167C2×#4324—44no—
168C2×#4324C2314yes—
169C2×#4324C2314yes—
170C2×#4324C2314yes—
171#66979—22no—
172#66979—22no—
173#66979C2312yes—
174C2×C4⋊Dic11—21no—
175C2×C4⋊Dic11—21no—
176#66977—21no—
177#66977—21no—
178#66977—22no—
179#66977—22no—
180#66977C2314yes—
181#66977C2314yes—
182C2×#4318C2312yes—
183C2×#4318C2314yes—
184C22×C11⋊C8C2312yes—
185C22×C11⋊C8C2314yes—
186#66942—24no—
187#66942—24no—
188#66940—22no—
189#66940—22no—
190#66932—24no—
191#66932—24no—
192#66930—24no—
193#66923—22no—
194#66923—22no—
195#66923C2312yes—
196#66922—21no—
197#66922—21no—
198#66922C2312yes—
199#66922C2312yes—
200#66922C2311yescharacteristic
201#66922C2311yescharacteristic
202C4×Dic22—21no—
203C4×Dic22—21no—
204C4×Dic22—22no—
205C4×Dic22—22no—
206C4×Dic22C2314yes—
207C4×Dic22C2314yes—
208#66899C2312yes—
209#66899C2312yes—
210#66896C2314yes—
211#66896C2314yes—
212#66896C2312yes—
213#66896C2312yes—
214#66874C2314yes—
215#66874C2314yes—
216#66874C2314yes—
217#66874C2314yes—
218#66872C2314yes—
219#66872C2312yes—
220#66872C2312yes—
221#66871C2314yes—
222#66871C2312yes—
223#66871C2312yes—
224C4⋊(C11⋊C8)C2311yescharacteristic
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4⋊(C11⋊C8)C2312yes—
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2314yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2314yes—
231#60923—111nomaximal, Sylow
232C24×C11—21no—
233C11×#41—22no—
234C11×#41—22no—
235C11×#41—22no—
236C11×#41—22no—
237C11×#41—84no—
238C2×Q8×C11—22no—
239C2×Q8×C11C2×D411yescharacteristic
240C2×Q8×C11C2411yescharacteristic
241C2×D4×C11—21no—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—21no—
246C2×D4×C11—22no—
247C2×D4×C11—22no—
248C2×D4×C11—22no—
249C2×D4×C11—22no—
250C2×D4×C11C2×D412yes—
251C2×D4×C11C2×D411yescharacteristic
252C2×D4×C11C2412yes—
253C2×D4×C11C2411yescharacteristic
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—22no—
258C22×C4×C11—21no—
259C22×C4×C11—22no—
260C22×C4×C11—82no—
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D412yes—
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2412yes—
266C22×C4×C11C2411yescharacteristic
267C22×Dic11—22no—
268C2×Dic22—21no—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—24no—
272C2×Dic22—24no—
273C2×Dic22C2414yes—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4C2×D411yescharacteristic
282C11×C4⋊C4C2×D411yescharacteristic
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D412yes—
285C11×C4⋊C4C2412yes—
286C11×C4⋊C4C2411yescharacteristic
287C11×C4⋊C4C2411yescharacteristic
288C11×C22⋊C4—21no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C11×C22⋊C4C2×D412yes—
302C42×C11—21no—
303C42×C11—21no—
304C42×C11—21no—
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D411yescharacteristic
307C42×C11C2×D412yes—
308C42×C11C2×D412yes—
309C42×C11C2412yes—
310C42×C11C2411yescharacteristic
311C42×C11C2411yescharacteristic
312C22⋊Dic11—22no—
313C22⋊Dic11—24no—
314C22⋊Dic11—24no—
315#4326—44no—
316#4324—44no—
317#4324—44no—
318#4324—44no—
319C4⋊Dic11—22no—
320C4⋊Dic11—22no—
321C4⋊Dic11—21no—
322C4⋊Dic11—21no—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11C2412yes—
326C4⋊Dic11C2412yes—
327Dic11⋊C4—24no—
328Dic11⋊C4—24no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—24no—
332Dic11⋊C4—24no—
333C4×Dic11—22no—
334C4×Dic11—24no—
335C4×Dic11—24no—
336#4318—24no—
337#4318—44no—
338C2×C11⋊C8—24no—
339C2×C11⋊C8—44no—
340C2×C11⋊C8C2412yes—
341C2×C11⋊C8C2414yes—
342C2×C11⋊C8C2412yes—
343#3509—111no—
344#3460D1111yescharacteristic
345#3260—114no—
346#3258—114no—
347#3254—112no—
348#3252—112no—
349#3248—112no—
350#3246—112no—
351#3082—112no—
352#3077—111no—
353#3076—111no—
354#3063—112no—
355#3057—112no—
356#3043—112no—
357#3039—111no—
358C2×#461—111no—
359#2906—111no—
360C23×C11—22no—
361C23×C11—21no—
362C23×C11—42no—
363C23×C11—81no—
364C23×C11—81no—
365C23×C11C22×D412yes—
366C23×C11C22×D411yescharacteristic
367Q8×C11—22no—
368Q8×C11—21no—
369Q8×C11—21no—
370Q8×C11—82no—
371D4×C11—24no—
372D4×C11—22no—
373D4×C11—22no—
374D4×C11—21no—
375D4×C11—22no—
376D4×C11—21no—
377D4×C11—42no—
378D4×C11—42no—
379D4×C11—82no—
380D4×C11—82no—
381D4×C11—82no—
382D4×C11—82no—
383D4×C11—82no—
384C2×C4×C11—22no—
385C2×C4×C11—24no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—22no—
392C2×C4×C11—41no—
393C2×C4×C11—42no—
394C2×C4×C11—42no—
395C2×C4×C11—44no—
396C2×C4×C11—42no—
397C2×C4×C11—81no—
398C2×C4×C11—82no—
399C2×C4×C11—81no—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11H(5,𝔽2)12yes—
409C2×C4×C112−1+412yes—
410C2×C4×C11C2511yescharacteristic
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—24no—
414C2×Dic11—44no—
415Dic22—24no—
416Dic22—24no—
417Dic22—42no—
418Dic22—44no—
419Dic22—42no—
420C11⋊C8—22no—
421C11⋊C8—22no—
422C11⋊C8—24no—
423C2×#137—112no—
424C22×SD16—112no—
425C2×#131—112no—
426#557—221no—
427#557—221no—
428#556—221no—
429#556—221no—
430#552—222no—
431#552—222no—
432#544C2×D1111yescharacteristic
433#542—21no—
434#542C2×D1112yes—
435#541—114no—
436#540—21no—
437#540C2×D1112yes—
438#538—22no—
439#537C2×D1111yescharacteristic
440#536—112no—
441#535C2×D1111yescharacteristic
442#535C2×D1111yescharacteristic
443#533—111no—
444#533—112no—
445#533—112no—
446#532—21no—
447#532C2×D1112yes—
448C2×C4⋊Q8—111no—
449#529—21no—
450#529C2×D1112yes—
451#525—22no—
452#519—112no—
453C4×#41C2×D1111yescharacteristic
454C4×#41C2×D1111yescharacteristic
455C2×C4×D4C2×D1111yescharacteristic
456#479—114no—
457#479—114no—
458#479—112no—
459#478—112no—
460#478—114no—
461#477—114no—
462#477—111no—
463#476—111no—
464#476—112no—
465#475—114no—
466#475—111no—
467#474—111no—
468#474—112no—
469#470—114no—
470#468—114no—
471#468—114no—
472#468—114no—
473#467—114no—
474#465—114no—
475#465—114no—
476#465—114no—
477#464—114no—
478#464—114no—
479#462—112no—
480#462—112no—
481#461—112no—
482#461—112no—
483#461—114no—
484#461—112no—
485#461—112no—
486#460—114no—
487#460—114no—
488#428—112no—
489#427—112no—
490#424—112no—
491#424—114no—
492#423—111no—
493#423—112no—
494C2×C4⋊C8—111no—
495C2×C4⋊C8—112no—
496#419—112no—
497#418—112no—
498#416—112no—
499C2×#103—112no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—41no—
506C22×C11—42no—
507C22×C11—41no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—41no—
511C22×C11—84no—
512C22×C11#53712yes—
513C22×C11C23×D411yescharacteristic
514C4×C11—21no—
515C4×C11—21no—
516C4×C11—22no—
517C4×C11—22no—
518C4×C11—21no—
519C4×C11—22no—
520C4×C11—41no—
521C4×C11—41no—
522C4×C11—42no—
523C4×C11—41no—
524C4×C11#53712yes—
525C4×C11#57712yes—
526C4×C11C2×H(5,𝔽2)11yescharacteristic
527C4×C11C2×2−1+411yescharacteristic
528Dic11—42no—
529Dic11—44no—
530Dic11—42no—
531C2×#41—22no—
532C2×#41C22×D1111yescharacteristic
533C2×#41C22×D1111yescharacteristic
534C22×Q8—112no—
535C22×D4C22×D1111yescharacteristic
536C23×C4—21no—
537#137—444no—
538C2×Q16—114no—
539C2×SD16—114no—
540C2×SD16—114no—
541C2×SD16—114no—
542C2×SD16—444no—
543#131—444no—
544C2×M16—112no—
545C2×M16—114no—
546C22×C8—112no—
547C22×C8—114no—
548C4⋊Q8—21no—
549C4⋊Q8—111no—
550C4⋊Q8—111no—
551C4⋊Q8—112no—
552C4⋊Q8—112no—
553C4⋊Q8—222no—
554C4⋊Q8—221no—
555C4⋊Q8—221no—
556C4⋊Q8C22×D1112yes—
557#127—21no—
558#127C22×D1112yes—
559#126—22no—
560#126—22no—
561#126—224no—
562#126—224no—
563#125—21no—
564#125—112no—
565#125—224no—
566#125—224no—
567#125—222no—
568#125—222no—
569#125C22×D1112yes—
570#124—21no—
571#124—22no—
572#124—22no—
573#124—222no—
574#124C22×D1112yes—
575#123—22no—
576#123—22no—
577#123—22no—
578#123—22no—
579#123—224no—
580C22⋊Q8—21no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—114no—
584C22⋊Q8—114no—
585C22⋊Q8—221no—
586C22⋊Q8—221no—
587C22⋊Q8—222no—
588C22⋊Q8—222no—
589C22⋊Q8C22×D1112yes—
590#121—22no—
591#121—21no—
592#121—22no—
593#121—21no—
594#121—21no—
595#121—22no—
596#121—22no—
597#121C22×D1112yes—
598#121C22×D1112yes—
599#121C22×D1112yes—
600#120—22no—
601#120—22no—
602C4×Q8—114no—
603C4×Q8—114no—
604C4×Q8—222no—
605C4×Q8—222no—
606C4×Q8—222no—
607C4×Q8—222no—
608C4×Q8—221no—
609C4×Q8—221no—
610C4×Q8C22⋊D1111yescharacteristic
611C4×Q8C22⋊D1111yescharacteristic
612C4×Q8C22×D1111yescharacteristic
613C4×Q8C22×D1111yescharacteristic
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—22no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—22no—
620C4×D4C22⋊D1112yes—
621C4×D4C22⋊D1111yescharacteristic
622C4×D4C22⋊D1112yes—
623C4×D4C22⋊D1111yescharacteristic
624C4×D4C22×D1112yes—
625C4×D4C22×D1112yes—
626C4×D4C22×D1111yescharacteristic
627C4×D4C22×D1111yescharacteristic
628#117—21no—
629#117—22no—
630#117—112no—
631#117—222no—
632#117—222no—
633#117—224no—
634#117C22×D1111yescharacteristic
635#117C22×D1111yescharacteristic
636#117C22×D1112yes—
637C2×C4⋊C4—221no—
638C2×C4⋊C4—221no—
639C2×C4⋊C4C22×D1111yescharacteristic
640C2×C22⋊C4—21no—
641C2×C42—21no—
642C2×C42C22×D1111yescharacteristic
643C2×C42C22×D1112yes—
644#107—112no—
645#107—112no—
646#107—114no—
647#106—112no—
648#106—112no—
649#106—114no—
650C4⋊C8—111no—
651C4⋊C8—111no—
652C4⋊C8—112no—
653C4⋊C8—114no—
654C4⋊C8—112no—
655C4⋊C8—114no—
656C4⋊C8—112no—
657#103—112no—
658#103—112no—
659#103—114no—
660#103—114no—
661#103—114no—
662#103—114no—
663#102—112no—
664#102—112no—
665#102—114no—
666#102—114no—
667C2×C11—22no—
668C2×C11—42no—
669C2×C11—81no—
670C2×C11—82no—
671C2×C11C2×#53711yescharacteristic
672C2×C11C2×#57711yescharacteristic
673C2×C11#358611yescharacteristic
674C24—21no—
675#41—22no—
676#41—22no—
677#41—22no—
678#41—22no—
679#41—84no—
680C2×Q8—22no—
681C2×Q8—114no—
682C2×Q8—221no—
683C2×Q8—221no—
684C2×Q8—222no—
685C2×Q8—224no—
686C2×Q8—224no—
687C2×Q8C2×C22⋊D1111yescharacteristic
688C2×Q8C23×D1111yescharacteristic
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4C2×C22⋊D1112yes—
699C2×D4C2×C22⋊D1111yescharacteristic
700C2×D4C23×D1112yes—
701C2×D4C23×D1111yescharacteristic
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—22no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—82no—
709C22×C4—222no—
710C22×C4C2×C22⋊D1111yescharacteristic
711C22×C4C2×C22⋊D1112yes—
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1112yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1111yescharacteristic
716Q16—444no—
717SD16—444no—
718SD16—444no—
719SD16—444no—
720M16—224no—
721M16—444no—
722C2×C8—114no—
723C2×C8—112no—
724C2×C8—112no—
725C2×C8—224no—
726C2×C8—444no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—112no—
735C4⋊C4—112no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4—221no—
741C4⋊C4—221no—
742C4⋊C4—224no—
743C4⋊C4—224no—
744C4⋊C4—224no—
745C4⋊C4—224no—
746C4⋊C4—222no—
747C4⋊C4—222no—
748C4⋊C4C2×C22⋊D1111yescharacteristic
749C4⋊C4C2×C22⋊D1111yescharacteristic
750C4⋊C4C2×C22⋊D1112yes—
751C4⋊C4C2×C22⋊D1112yes—
752C4⋊C4C23×D1112yes—
753C4⋊C4C23×D1111yescharacteristic
754C4⋊C4C23×D1111yescharacteristic
755C22⋊C4—21no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—222no—
767C22⋊C4—224no—
768C22⋊C4—224no—
769C22⋊C4C2×C22⋊D1112yes—
770C22⋊C4C2×C22⋊D1112yes—
771C22⋊C4C2×C22⋊D1112yes—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—222no—
776C42—224no—
777C42—224no—
778C42C2×C22⋊D1111yescharacteristic
779C42C2×C22⋊D1112yes—
780C42C2×C22⋊D1111yescharacteristic
781C42C2×C22⋊D1112yes—
782C42C23×D1111yescharacteristic
783C42C23×D1111yescharacteristic
784C42C23×D1112yes—
785C11#6092311yescharacteristic, complemented, Sylow
786C23—22no—
787C23—21no—
788C23—42no—
789C23—81no—
790C23—81no—
791C23C22×C22⋊D1112yes—
792C23C22×C22⋊D1111yescharacteristic
793Q8—22no—
794Q8—21no—
795Q8—21no—
796Q8—82no—
797Q8—224no—
798Q8—224no—
799Q8—442no—
800Q8—444no—
801Q8—442no—
802D4—24no—
803D4—22no—
804D4—22no—
805D4—21no—
806D4—22no—
807D4—21no—
808D4—42no—
809D4—42no—
810D4—82no—
811D4—82no—
812D4—82no—
813D4—82no—
814D4—82no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—81no—
829C2×C4—82no—
830C2×C4—81no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—224no—
834C2×C4—444no—
835C2×C4#6704212yes—
836C2×C4#6704312yes—
837C2×C4C22×C22⋊D1111yescharacteristic
838C2×C4C22×C22⋊D1112yes—
839C2×C4C22×C22⋊D1112yes—
840C2×C4C22×C22⋊D1111yescharacteristic
841C2×C4C22×C22⋊D1112yes—
842C2×C4C22×C22⋊D1111yescharacteristic
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C22×C22⋊D1111yescharacteristic
845C2×C4C24×D1111yescharacteristic
846C8—222no—
847C8—222no—
848C8—224no—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—42no—
859C22—41no—
860C22—84no—
861C22#1062336412yes—
862C22C23×C22⋊D1111yescharacteristic
863C4—21no—
864C4—21no—
865C4—22no—
866C4—22no—
867C4—21no—
868C4—22no—
869C4—41no—
870C4—41no—
871C4—42no—
872C4—41no—
873C4—442no—
874C4—444no—
875C4—442no—
876C4#1062336412yes—
877C4#1062336712yes—
878C4C2×#6704211yescharacteristic
879C4C2×#6704311yescharacteristic
880C2—22no—
881C2—42no—
882C2—82no—
883C2—81no—
884C2C2×#1062336411yescharacteristic
885C2C2×#1062336711yescharacteristic
886C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3460C2
socleC22×C11C23×D4
hypercenter#3460D11
hypocenterC11#60923
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3460

Complements

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

NH ≅ G/Ntype
1. #13082502C2semidirect
2. #13080062C2semidirect
3. #13080042C2semidirect
4. #13080003C2semidirect
5. #13079989C2semidirect
6. #13079953C2semidirect
7. #13079932C2semidirect
8. #13078452C2semidirect
9. #13078413C2semidirect
10. #13078404C2semidirect
11. #13078309C2semidirect
12. #13078252C2semidirect
13. #13078133C2semidirect
14. #13078103C2semidirect
15. C2×#10622632C2semidirect
16. #13077184C2semidirect
45. #10623049C22semidirect
48. #10623001C22semidirect
49. #10623001C22semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
57. #10622676C22semidirect
58. #10622676C22semidirect
61. #10622665C22semidirect
62. #10622664C22semidirect
65. #10622655C22semidirect
68. #10622654C22semidirect
69. #10622644C22semidirect
70. #10622644C22semidirect
71. #10622635C22semidirect
72. #10622634C22semidirect
73. #10622633C22semidirect
77. #10622632C22semidirect
78. #10622632C22semidirect
80. #10622622C22semidirect
82. #10622621C22semidirect
84. #10622620C22semidirect
87. #10622612C22semidirect
92. #10622537C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
785. C11#60923semidirect

Maximal subgroups

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

subgroupindex
#130825022
#130800622
#130800422
#130800032
#130799892
#130799532
#130799322
#130784522
#130784132
#130784042
#130783092
#130782522
#130781332
#130781032
C2×#106226322
#130771842
C11×#34602
#6092311