Finite Group Databasebeta

← #15626866

Subgroups — #15626866

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#13082032C211yesmaximal, characteristic
2#13080057C214yesmaximal, complemented
3#13080036C214yesmaximal, complemented
4#13079999C212yesmaximal, complemented
5#13079983C212yesmaximal, complemented
6#13079947C212yesmaximal, complemented
7#13079928C212yesmaximal, complemented
8#13078458C212yesmaximal, complemented
9#13078409C211yesmaximal, characteristic, complemented
10#13078398C211yesmaximal, characteristic, complemented
11#13078303C212yesmaximal, complemented
12#13078257C212yesmaximal, complemented
13#13078137C212yesmaximal, complemented
14#13078099C211yesmaximal, characteristic, complemented
15C2×#10622696C211yesmaximal, characteristic, complemented
16#13077184C211yesmaximal, characteristic, complemented
17C11×#3509C211yesmaximal, characteristic, complemented
18C11×#557—21no—
19C11×#557—21no—
20C11×#556—21no—
21C11×#556—21no—
22C11×#552—22no—
23C11×#552—22no—
24C11×#541C2214yescomplemented
25C11×#536C2212yes—
26C11×#533C2211yescharacteristic
27C11×#533C2212yescomplemented
28C11×#533C2212yescomplemented
29C2×C11×C4⋊Q8C2211yescharacteristic
30C11×#519C2212yes—
31C4×C11×#41C2211yescharacteristic
32#10623364C2211yescharacteristic
33#10623361C2211yescharacteristic
34C2×#67001C2212yes—
35C2×#66995C2212yes—
36C22×#4325C2212yes—
37#10623113—21no—
38#10623111—21no—
39#10623093—21no—
40#10623091—22no—
41#10623079—21no—
42#10623078—22no—
43#10623066C2212yes—
44#10623065C2212yes—
45#10623056C2211yescharacteristic
46#10623050C2211yescharacteristic
47#10623010C2212yes—
48#10623008C2212yes—
49C4×#4339C2211yescharacteristic
50C2×C4×D44C2211yescharacteristic
51#10622838C2212yes—
52C2×#66899C2212yes—
53#10622707C2211yescharacteristic, complemented
54#10622704C2211yescharacteristic, complemented
55#10622703C2212yescomplemented
56#10622703C2212yescomplemented
57#10622700C2212yes—
58#10622700C2211yescharacteristic, complemented
59#10622697C2212yes—
60#10622697C2211yescharacteristic, complemented
61#10622696C2212yes—
62#10622696C2212yes—
63#10622696C2214yes—
64#10622696C2212yescomplemented
65#10622696C2212yescomplemented
66#10622679C2214yes—
67#10622679C2212yescomplemented
68#10622676C2212yescomplemented
69#10622665C2214yescomplemented
70#10622664C2214yescomplemented
71#10622662C2214yes—
72#10622662C2214yes—
73#10622662C2214yescomplemented
74#10622661C2214yes—
75#10622661C2214yes—
76#10622661C2214yescomplemented
77#10622641C2214yes—
78#10622641C2214yes—
79#10622640C2214yes—
80#10622640C2214yes—
81#10622635C2214yescomplemented
82#10622635C2214yescomplemented
83#10622634C2214yescomplemented
84#10622633C2214yescomplemented
85#10622615C2212yes—
86#10622614C2212yes—
87#10622612C2212yes—
88#10622612C2214yescomplemented
89#10622611C2212yes—
90#10622608C2212yes—
91#10622537C2211yescharacteristic
92#10622537C2212yescomplemented
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11C2312yes—
97C2×#4339—22no—
98C2×#4339C2311yescharacteristic
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8C2312yes—
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2311yescharacteristic
107C11×C4⋊Q8C2311yescharacteristic
108C11×#126—24no—
109C11×#126—24no—
110C11×#125—24no—
111C11×#125—24no—
112C11×#125—22no—
113C11×#125—22no—
114C11×#125C2312yes—
115C11×#124—22no—
116C11×#123—24no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8—22no—
121C11×C22⋊Q8C2314yes—
122C11×C22⋊Q8C2314yes—
123C4×Q8×C11—22no—
124C4×Q8×C11—22no—
125C4×Q8×C11—21no—
126C4×Q8×C11—21no—
127C4×Q8×C11—22no—
128C4×Q8×C11—22no—
129C4×Q8×C11D411yescharacteristic
130C4×Q8×C11D411yescharacteristic
131C4×Q8×C11C2314yes—
132C4×Q8×C11C2314yes—
133C4×D4×C11D412yes—
134C4×D4×C11D411yescharacteristic
135C4×D4×C11D412yes—
136C4×D4×C11D411yescharacteristic
137C11×#117—22no—
138C11×#117—22no—
139C11×#117—24no—
140C11×#117C2312yes—
141C11×#117C2311yescharacteristic
142C11×#117C2312yes—
143C2×C11×C4⋊C4—21no—
144C2×C11×C4⋊C4—21no—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2312yes—
147#67001—44no—
148#67000—21no—
149#66999—21no—
150C2×#4326C2314yes—
151#66995—44no—
152C2×#4325—44no—
153C2×#4325C2314yes—
154C2×#4325C2314yes—
155C2×#4325C2314yes—
156#66993—21no—
157#66992—22no—
158#66991—21no—
159#66990—22no—
160#66983—22no—
161#66983C2312yes—
162#66983C2312yes—
163#66983C2312yes—
164#66982—22no—
165C4×C22⋊D11—21no—
166C4×C22⋊D11—21no—
167C4×C22⋊D11—22no—
168C2×(C2×D11)⋊C4—21no—
169#66979C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171#66977C2312yes—
172C2×#4318C2312yes—
173C2×#4318C2314yes—
174C22×C11⋊C8C2312yes—
175C22×C11⋊C8C2314yes—
176#66951—22no—
177#66949—22no—
178#66948—21no—
179#66948—21no—
180#66947—22no—
181#66947—22no—
182#66943—21no—
183#66941—21no—
184#66938—22no—
185#66937—22no—
186#66937—22no—
187#66936—22no—
188#66935—22no—
189#66931—22no—
190#66929—22no—
191#66928—22no—
192#66928C2312yes—
193#66927C2312yes—
194C4×D44—21no—
195C4×D44—21no—
196C4×D44—22no—
197C4×D44C2312yes—
198C4×D44C2312yes—
199C4×D44C2311yescharacteristic
200C4×D44C2311yescharacteristic
201#66925—21no—
202#66925—22no—
203C42×D11—21no—
204#66923C2312yes—
205#66922C2312yes—
206C4×Dic22C2311yescharacteristic
207C4×Dic22C2311yescharacteristic
208#66899C2314yes—
209#66899C2314yes—
210#66899C2314yes—
211#66899C2314yes—
212#66874C2312yes—
213#66874C2312yes—
214#66873C2314yes—
215#66873C2314yes—
216#66873C2312yes—
217#66873C2312yes—
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
232C23×D11—21no—
233C11×#41—22no—
234C11×#41—22no—
235C2×Q8×C11—21no—
236C2×Q8×C11—21no—
237C2×Q8×C11—22no—
238C2×Q8×C11—24no—
239C2×Q8×C11—24no—
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2414yes—
242C2×D4×C11C2×D412yes—
243C2×D4×C11C2×D411yescharacteristic
244C22×C4×C11—22no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—21no—
252C2×C22⋊D11—22no—
253C2×C22⋊D11—22no—
254C2×C22⋊D11—22no—
255C22×Dic11—21no—
256#4339—22no—
257#4339—22no—
258#4339—84no—
259C2×D44—21no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44—22no—
264C2×D44C2411yescharacteristic
265C2×D44C2412yes—
266C2×C4×D11—21no—
267C2×C4×D11—21no—
268C2×C4×D11—22no—
269C2×C4×D11—21no—
270C2×C4×D11—22no—
271C2×C4×D11—82no—
272C2×Dic22—22no—
273C2×Dic22C2411yescharacteristic
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—24no—
281C11×C4⋊C4—24no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—24no—
285C11×C4⋊C4—24no—
286C11×C4⋊C4C2×D411yescharacteristic
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D412yes—
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2412yes—
291C11×C4⋊C4C2412yes—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—24no—
295C11×C22⋊C4C2×D412yes—
296C11×C22⋊C4C2×D412yes—
297C11×C22⋊C4C2×D412yes—
298C42×C11—24no—
299C42×C11—24no—
300C42×C11—22no—
301C42×C11C2×D411yescharacteristic
302C42×C11C2×D412yes—
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D412yes—
305C42×C11C2411yescharacteristic
306C42×C11C2411yescharacteristic
307C42×C11C2412yes—
308C22⋊Dic11—21no—
309C22⋊Dic11—22no—
310#4326—44no—
311#4325—44no—
312#4325—44no—
313#4325—44no—
314(C2×D11)⋊C4—21no—
315(C2×D11)⋊C4—21no—
316(C2×D11)⋊C4—22no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323C4⋊Dic11—22no—
324C4⋊Dic11—21no—
325C4⋊Dic11C2411yescharacteristic
326C4⋊Dic11C2411yescharacteristic
327C4⋊Dic11C2412yes—
328Dic11⋊C4—21no—
329Dic11⋊C4—21no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333C4×Dic11—21no—
334C4×Dic11—21no—
335C4×Dic11—21no—
336#4318—24no—
337#4318—44no—
338C2×C11⋊C8—24no—
339C2×C11⋊C8—44no—
340C2×C11⋊C8C2412yes—
341C2×C11⋊C8C2414yes—
342C2×C11⋊C8C2412yes—
343#3509D1111yescharacteristic, complemented
344#3460—111no—
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×C11C22×D412yes—
361C23×C11C22×D411yescharacteristic
362C22×D11—22no—
363C22×D11—21no—
364C22×D11—42no—
365C22×D11—81no—
366C22×D11—81no—
367Q8×C11—22no—
368Q8×C11—24no—
369Q8×C11—24no—
370Q8×C11—42no—
371Q8×C11—44no—
372Q8×C11—42no—
373D4×C11—24no—
374D4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—24no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—24no—
382C2×C4×C11—41no—
383C2×C4×C11—42no—
384C2×C4×C11—44no—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11H(5,𝔽2)12yes—
394C2×C4×C112−1+412yes—
395C2×C4×C11C2511yescharacteristic
396C22⋊D11—42no—
397C22⋊D11—82no—
398C22⋊D11—82no—
399C22⋊D11—82no—
400C2×Dic11—21no—
401C2×Dic11—21no—
402C2×Dic11—21no—
403C2×Dic11—22no—
404C2×Dic11—81no—
405D44—22no—
406D44—21no—
407D44—22no—
408D44—21no—
409D44—42no—
410D44—82no—
411D44—82no—
412C4×D11—42no—
413C4×D11—44no—
414C4×D11—42no—
415C4×D11—81no—
416C4×D11—82no—
417Dic22—21no—
418Dic22—21no—
419Dic22—82no—
420C11⋊C8—22no—
421C11⋊C8—22no—
422C11⋊C8—24no—
423C2×#137—112no—
424C22×SD16—112no—
425C2×#131—112no—
426#557—21no—
427#557—21no—
428#556—21no—
429#556—21no—
430#552—22no—
431#552—22no—
432#544—111no—
433#542—112no—
434#542—221no—
435#541C2×D1114yescomplemented
436#540—112no—
437#540—221no—
438#538—222no—
439#537—111no—
440#536C2×D1112yes—
441#535—111no—
442#535—111no—
443#533C2×D1111yescharacteristic
444#533C2×D1112yescomplemented
445#533C2×D1112yescomplemented
446#532—112no—
447#532—221no—
448C2×C4⋊Q8C2×D1111yescharacteristic
449#529—112no—
450#529—221no—
451#525—222no—
452#519C2×D1112yes—
453C4×#41—111no—
454C4×#41C2×D1111yescharacteristic
455C2×C4×D4—111no—
456#479—112no—
457#479—114no—
458#479—114no—
459#478—112no—
460#478—114no—
461#477—111no—
462#477—114no—
463#476—111no—
464#476—112no—
465#475—111no—
466#475—114no—
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—112no—
484#461—114no—
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#53712yes—
506C22×C11C23×D411yescharacteristic
507C2×D11—42no—
508C2×D11—41no—
509C2×D11—42no—
510C2×D11—41no—
511C2×D11—42no—
512C2×D11—41no—
513C2×D11—84no—
514C4×C11—21no—
515C4×C11—21no—
516C4×C11—22no—
517C4×C11—22no—
518C4×C11—22no—
519C4×C11—21no—
520C4×C11—42no—
521C4×C11—44no—
522C4×C11—42no—
523C4×C11#53712yes—
524C4×C11#57712yes—
525C4×C11C2×H(5,𝔽2)11yescharacteristic
526C4×C11C2×2−1+411yescharacteristic
527Dic11—41no—
528Dic11—41no—
529Dic11—41no—
530Dic11—42no—
531C2×#41—111no—
532C2×#41—222no—
533C2×#41C22×D1111yescharacteristic
534C22×Q8C22×D1112yes—
535C22×D4—111no—
536C23×C4—221no—
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—22no—
549C4⋊Q8—21no—
550C4⋊Q8—21no—
551C4⋊Q8—112no—
552C4⋊Q8—221no—
553C4⋊Q8C22×D1112yes—
554C4⋊Q8C22×D1112yes—
555C4⋊Q8C22×D1111yescharacteristic
556C4⋊Q8C22×D1111yescharacteristic
557#127—112no—
558#127—221no—
559#126—24no—
560#126—24no—
561#126—222no—
562#126—222no—
563#125—24no—
564#125—24no—
565#125—22no—
566#125—22no—
567#125—112no—
568#125—221no—
569#125C22×D1112yes—
570#124—22no—
571#124—112no—
572#124—221no—
573#124—222no—
574#124—222no—
575#123—24no—
576#123—222no—
577#123—222no—
578#123—222no—
579#123—222no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—112no—
585C22⋊Q8—221no—
586C22⋊Q8—222no—
587C22⋊Q8—222no—
588C22⋊Q8C22×D1114yes—
589C22⋊Q8C22×D1114yes—
590#121—112no—
591#121—112no—
592#121—112no—
593#121—222no—
594#121—221no—
595#121—222no—
596#121—221no—
597#121—221no—
598#121—222no—
599#121—222no—
600#120—222no—
601#120—222no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—21no—
605C4×Q8—21no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—111no—
609C4×Q8—111no—
610C4×Q8C22⋊D1111yescharacteristic
611C4×Q8C22⋊D1111yescharacteristic
612C4×Q8C22×D1114yes—
613C4×Q8C22×D1114yes—
614C4×D4—112no—
615C4×D4—112no—
616C4×D4—111no—
617C4×D4—111no—
618C4×D4—221no—
619C4×D4—221no—
620C4×D4—222no—
621C4×D4—221no—
622C4×D4—221no—
623C4×D4—222no—
624C4×D4C22⋊D1112yes—
625C4×D4C22⋊D1111yescharacteristic
626C4×D4C22⋊D1112yes—
627C4×D4C22⋊D1111yescharacteristic
628#117—22no—
629#117—22no—
630#117—24no—
631#117—111no—
632#117—221no—
633#117—222no—
634#117C22×D1112yes—
635#117C22×D1111yescharacteristic
636#117C22×D1112yes—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—111no—
640C2×C22⋊C4—221no—
641C2×C42—221no—
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—114no—
658#103—114no—
659#103—114no—
660#103—114no—
661#103—112no—
662#103—112no—
663#102—112no—
664#102—112no—
665#102—114no—
666#102—114no—
667C2×C11—22no—
668C2×C11—42no—
669C2×C11C2×#53711yescharacteristic
670C2×C11C2×#57711yescharacteristic
671C2×C11#358611yescharacteristic
672D11—81no—
673D11—82no—
674C24—221no—
675#41—22no—
676#41—22no—
677#41—222no—
678#41—222no—
679#41—884no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—22no—
683C2×Q8—24no—
684C2×Q8—24no—
685C2×Q8—111no—
686C2×Q8—222no—
687C2×Q8C2×C22⋊D1111yescharacteristic
688C2×Q8C23×D1114yes—
689C2×D4—112no—
690C2×D4—111no—
691C2×D4—221no—
692C2×D4—222no—
693C2×D4—222no—
694C2×D4—222no—
695C2×D4—222no—
696C2×D4—222no—
697C2×D4—221no—
698C2×D4—222no—
699C2×D4—222no—
700C2×D4C2×C22⋊D1112yes—
701C2×D4C2×C22⋊D1111yescharacteristic
702C22×C4—22no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—222no—
707C22×C4—221no—
708C22×C4—222no—
709C22×C4—882no—
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—22no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—112no—
740C4⋊C4—111no—
741C4⋊C4—111no—
742C4⋊C4—221no—
743C4⋊C4—221no—
744C4⋊C4—221no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—222no—
748C4⋊C4—222no—
749C4⋊C4C2×C22⋊D1111yescharacteristic
750C4⋊C4C2×C22⋊D1111yescharacteristic
751C4⋊C4C2×C22⋊D1112yes—
752C4⋊C4C2×C22⋊D1112yes—
753C4⋊C4C23×D1112yes—
754C4⋊C4C23×D1112yes—
755C22⋊C4—22no—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—221no—
759C22⋊C4—222no—
760C22⋊C4—222no—
761C22⋊C4—222no—
762C22⋊C4—221no—
763C22⋊C4—221no—
764C22⋊C4—222no—
765C22⋊C4—222no—
766C22⋊C4—222no—
767C22⋊C4—222no—
768C22⋊C4—222no—
769C22⋊C4C2×C22⋊D1112yes—
770C22⋊C4C2×C22⋊D1112yes—
771C22⋊C4C2×C22⋊D1112yes—
772C42—24no—
773C42—24no—
774C42—22no—
775C42—221no—
776C42—221no—
777C42—221no—
778C42C2×C22⋊D1111yescharacteristic
779C42C2×C22⋊D1112yes—
780C42C2×C22⋊D1111yescharacteristic
781C42C2×C22⋊D1112yes—
782C42C23×D1111yescharacteristic
783C42C23×D1111yescharacteristic
784C42C23×D1112yes—
785C11#6092311yescharacteristic, complemented, Sylow
786C23—222no—
787C23—221no—
788C23—442no—
789C23—881no—
790C23—881no—
791C23C22×C22⋊D1112yes—
792C23C22×C22⋊D1111yescharacteristic
793Q8—22no—
794Q8—24no—
795Q8—24no—
796Q8—42no—
797Q8—44no—
798Q8—42no—
799Q8—221no—
800Q8—221no—
801Q8—882no—
802D4—24no—
803D4—22no—
804D4—222no—
805D4—221no—
806D4—222no—
807D4—221no—
808D4—442no—
809D4—442no—
810D4—882no—
811D4—882no—
812D4—882no—
813D4—882no—
814D4—882no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—44no—
825C2×C4—221no—
826C2×C4—221no—
827C2×C4—221no—
828C2×C4—222no—
829C2×C4—442no—
830C2×C4—444no—
831C2×C4—442no—
832C2×C4—882no—
833C2×C4—881no—
834C2×C4—881no—
835C2×C4#6704212yes—
836C2×C4#6704312yes—
837C2×C4C22×C22⋊D1112yes—
838C2×C4C22×C22⋊D1112yes—
839C2×C4C22×C22⋊D1111yescharacteristic
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—441no—
855C22—442no—
856C22—441no—
857C22—442no—
858C22—442no—
859C22—441no—
860C22—884no—
861C22#1062336412yes—
862C22C23×C22⋊D1111yescharacteristic
863C4—21no—
864C4—21no—
865C4—22no—
866C4—22no—
867C4—21no—
868C4—22no—
869C4—42no—
870C4—44no—
871C4—42no—
872C4—441no—
873C4—441no—
874C4—442no—
875C4—441no—
876C4#1062336412yes—
877C4#1062336812yes—
878C4C2×#6704211yescharacteristic
879C4C2×#6704311yescharacteristic
880C2—22no—
881C2—42no—
882C2—882no—
883C2—881no—
884C2C2×#1062336411yescharacteristic
885C2C2×#1062336811yescharacteristic
886C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3509C2
socleC22×C11C23×D4
prime radical#13082032C2
hypercenter#3509D11
hypocenterC11#60923
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3509

Complements

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

NH ≅ G/Ntype
2. #13080057C2semidirect
3. #13080036C2semidirect
4. #13079999C2semidirect
5. #13079983C2semidirect
6. #13079947C2semidirect
7. #13079928C2semidirect
8. #13078458C2semidirect
9. #13078409C2semidirect
10. #13078398C2semidirect
11. #13078303C2semidirect
12. #13078257C2semidirect
13. #13078137C2semidirect
14. #13078099C2semidirect
15. C2×#10622696C2semidirect
16. #13077184C2semidirect
17. C11×#3509C2semidirect
24. C11×#541C22semidirect
27. C11×#533C22semidirect
28. C11×#533C22semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
55. #10622703C22semidirect
56. #10622703C22semidirect
58. #10622700C22semidirect
60. #10622697C22semidirect
64. #10622696C22semidirect
65. #10622696C22semidirect
67. #10622679C22semidirect
68. #10622676C22semidirect
69. #10622665C22semidirect
70. #10622664C22semidirect
73. #10622662C22semidirect
76. #10622661C22semidirect
81. #10622635C22semidirect
82. #10622635C22semidirect
83. #10622634C22semidirect
84. #10622633C22semidirect
88. #10622612C22semidirect
92. #10622537C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
343. #3509D11semidirect
435. #541C2×D11semidirect
444. #533C2×D11semidirect
445. #533C2×D11semidirect
785. C11#60923semidirect

Maximal subgroups

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

subgroupindex
#130820322
#130800572
#130800362
#130799992
#130799832
#130799472
#130799282
#130784582
#130784092
#130783982
#130783032
#130782572
#130781372
#130780992
C2×#106226962
#130771842
C11×#35092
#6092311