Finite Group Databasebeta

← #15645997

Subgroups — #15645997

Order 2816.

1868 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082527C211yesmaximal, characteristic, complemented
2#13081608C212yesmaximal, complemented
3#13081301C212yesmaximal, complemented
4#13080527C212yesmaximal, complemented
5#13080512C214yesmaximal, complemented
6#13080353C214yesmaximal, complemented
7#13080346C212yesmaximal, complemented
8#13079953C212yesmaximal, complemented
9#13079923C211yesmaximal, characteristic, complemented
10#13079588C212yesmaximal, complemented
11#13079538C211yesmaximal, characteristic, complemented
12#13078687C212yesmaximal, complemented
13#13078647C211yesmaximal, characteristic, complemented
14#13078071C212yesmaximal, complemented
15C2×#10622644C211yesmaximal, characteristic, complemented
16#13077727C211yesmaximal, characteristic, complemented
17C11×#3480C211yesmaximal, characteristic, complemented
18C11×#559—21no—
19C11×#559C2211yescharacteristic
20C11×#557C2211yescharacteristic
21C11×#556—21no—
22C11×#556C2211yescharacteristic
23C11×#553—22no—
24C11×#553C2212yes—
25C11×#550C2211yescharacteristic
26C11×#548C2212yes—
27C11×#532—21no—
28C11×#532C2211yescharacteristic
29C11×#529—22no—
30C11×#529C2212yes—
31C4×C11×#41—21no—
32C4×C11×#41C2212yes—
33C4×C11×#41C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35#10623364—21no—
36C2×#67003C2214yes—
37C22×#4326C2212yes—
38#10623115C2212yes—
39#10623110—21no—
40#10623096—22no—
41#10623094—21no—
42#10623083C2214yes—
43#10623082C2212yes—
44#10623065—22no—
45#10623054—21no—
46#10623008C2212yes—
47#10623008C2211yescharacteristic
48#10623001C2212yes—
49C2×#66922C2211yescharacteristic
50#10622852C2214yes—
51#10622840C2212yes—
52#10622706C2212yes—
53#10622700C2212yes—
54#10622689C2212yes—
55#10622685C2212yes—
56#10622681C2214yes—
57#10622676C2214yes—
58#10622672C2214yes—
59#10622667C2214yes—
60#10622664C2214yes—
61#10622660C2214yes—
62#10622654C2214yes—
63#10622653C2214yes—
64#10622651C2214yes—
65#10622650C2214yes—
66#10622644C2212yes—
67#10622644C2212yes—
68#10622644C2212yes—
69#10622644C2212yes—
70C4×#4326C2214yes—
71#10622641C2214yes—
72#10622640C2211yescharacteristic
73#10622640C2211yescharacteristic
74C4×#4325C2212yes—
75C4×#4325C2212yes—
76Q8×C11⋊C8C2212yes—
77#10622633C2211yescharacteristic
78#10622633C2211yescharacteristic
79#10622632C2212yes—
80#10622632C2212yes—
81C4×#4324C2214yes—
82#10622629C2214yes—
83#10622628C2212yes—
84D4×C11⋊C8C2212yes—
85D4×C11⋊C8C2214yes—
86#10622620C2212yes—
87#10622615C2214yes—
88#10622609C2214yes—
89C2×#66874C2212yes—
90#10622581C2212yes—
91#10622538C2212yes—
92#10622538C2211yescharacteristic
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yes—
95C2×C11×#41—21no—
96C2×C11×#41D411yescharacteristic
97C2×C11×#41C2312yes—
98C22×Q8×C11C2311yescharacteristic
99C2×#4339—21no—
100C2×#4339C2314yes—
101C22×Dic22C2312yes—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8C2311yescharacteristic
104C11×#127—21no—
105C11×#127C2311yescharacteristic
106C11×#126—22no—
107C11×#126—22no—
108C11×#126—22no—
109C11×#125—22no—
110C11×#125C2312yes—
111C11×#124—21no—
112C11×#124—21no—
113C11×#124—22no—
114C11×#124—21no—
115C11×#124C2312yes—
116C11×#123—22no—
117C11×#123—22no—
118C11×#123—22no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8C2312yes—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121—21no—
124C11×#121—22no—
125C11×#121C2312yes—
126C11×#121C2312yes—
127C4×Q8×C11—21no—
128C4×Q8×C11—21no—
129C4×Q8×C11—21no—
130C4×Q8×C11—21no—
131C4×Q8×C11D411yescharacteristic
132C4×Q8×C11C2311yescharacteristic
133C4×Q8×C11C2311yescharacteristic
134C4×Q8×C11C2311yescharacteristic
135C4×Q8×C11C2311yescharacteristic
136C4×Q8×C11C2312yes—
137C4×Q8×C11C2311yescharacteristic
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—22no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11—21no—
146C4×D4×C11D411yescharacteristic
147C4×D4×C11D412yes—
148C4×D4×C11C2312yes—
149C4×D4×C11C2312yes—
150C4×D4×C11C2311yescharacteristic
151C4×D4×C11C2312yes—
152C11×#117—22no—
153C11×#117—22no—
154C11×#117D411yescharacteristic
155C11×#117D412yes—
156C11×#117C2312yes—
157C2×C11×C4⋊C4—21no—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C42×C11—21no—
160C2×C42×C11—22no—
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2312yes—
163#67003—48no—
164#66999—22no—
165C2×#4326—44no—
166C2×#4326C2314yes—
167C2×#4326C2314yes—
168C2×#4325C2312yes—
169C2×#4325C2312yes—
170#66992—24no—
171#66991—22no—
172C2×#4324C2314yes—
173C2×#4324C2314yes—
174C2×#4323C2314yes—
175#66983—22no—
176#66983—22no—
177#66983—21no—
178#66983C2312yes—
179#66979—22no—
180C2×C4⋊Dic11—21no—
181C2×C4⋊Dic11—21no—
182#66977—22no—
183#66977C2314yes—
184C22×C11⋊C8C2312yes—
185C22×C11⋊C8C2314yes—
186#66951—24no—
187#66949—24no—
188#66945—22no—
189C4⋊C4×D11—22no—
190#66938—24no—
191#66936—24no—
192(C22⋊D11)⋊C4—24no—
193#66928—21no—
194#66928C2314yes—
195#66927C2311yescharacteristic
196C4×D44—22no—
197C4×D44—21no—
198C4×D44—22no—
199C4×D44C2312yes—
200#66923—22no—
201#66922—21no—
202#66922—21no—
203#66922C2312yes—
204#66922C2312yes—
205#66922C2311yescharacteristic
206C4×Dic22—22no—
207C4×Dic22C2314yes—
208#66899C2312yes—
209#66899C2312yes—
210#66896C2314yes—
211C22⋊(C11⋊C8)C2312yes—
212C22⋊(C11⋊C8)C2314yes—
213#66874C2314yes—
214#66874C2314yes—
215#66874C2314yes—
216#66874C2314yes—
217#66873C2312yes—
218#66873C2312yes—
219#66873C2314yes—
220#66872C2312yes—
221#66872C2312yes—
222#66871C2314yes—
223C4⋊(C11⋊C8)C2312yes—
224C4⋊(C11⋊C8)C2311yescharacteristic
225C4⋊(C11⋊C8)C2314yes—
226C4⋊(C11⋊C8)C2312yes—
227C4⋊(C11⋊C8)C2311yescharacteristic
228C4×C11⋊C8C2314yes—
229C4×C11⋊C8C2312yes—
230#61954—111nomaximal, Sylow
231C11×#41—24no—
232C11×#41—24no—
233C11×#41—42no—
234C11×#41—44no—
235C2×Q8×C11—21no—
236C2×Q8×C11—21no—
237C2×Q8×C11—22no—
238C2×Q8×C11—41no—
239C2×Q8×C11C2×D411yescharacteristic
240C2×Q8×C11C2411yescharacteristic
241C2×Q8×C11C2411yescharacteristic
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—21no—
246C2×D4×C11—21no—
247C2×D4×C11C2×D411yescharacteristic
248C2×D4×C11C2×D412yes—
249C2×D4×C11C2412yes—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C2×C22⋊D11—22no—
262C2×C22⋊D11—24no—
263C22×Dic11—22no—
264#4339—44no—
265#4339—44no—
266#4339—44no—
267C2×D44—21no—
268C2×D44—21no—
269C2×D44C2412yes—
270C2×C4×D11—22no—
271C2×C4×D11—24no—
272C2×Dic22—21no—
273C2×Dic22—22no—
274C2×Dic22—42no—
275C2×Dic22—42no—
276C2×Dic22C2414yes—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2×D412yes—
291C11×C4⋊C4C2412yes—
292C11×C4⋊C4C2411yescharacteristic
293C11×C4⋊C4C2411yescharacteristic
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C11×C22⋊C4C2×D412yes—
305C42×C11—21no—
306C42×C11—21no—
307C42×C11—22no—
308C42×C11—22no—
309C42×C11—21no—
310C42×C11—21no—
311C42×C11C2×D412yes—
312C42×C11C2×D411yescharacteristic
313C42×C11C2×D411yescharacteristic
314C42×C11C2×D412yes—
315C42×C11C2412yes—
316C42×C11C2411yescharacteristic
317C42×C11C2411yescharacteristic
318C22⋊Dic11—24no—
319#4326—28no—
320#4326—44no—
321#4325—24no—
322#4325—42no—
323#4324—44no—
324#4324—44no—
325#4323—44no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—22no—
330C4⋊Dic11—22no—
331C4⋊Dic11—22no—
332C4⋊Dic11—22no—
333C4⋊Dic11—22no—
334C4⋊Dic11—21no—
335C4⋊Dic11C2412yes—
336Dic11⋊C4—24no—
337Dic11⋊C4—24no—
338C4×Dic11—24no—
339C2×C11⋊C8—42no—
340C2×C11⋊C8—44no—
341C2×C11⋊C8C2412yes—
342C2×C11⋊C8C2414yes—
343C2×C11⋊C8C2412yes—
344#3511—111no—
345#3480D1111yescharacteristic, complemented
346#3394—112no—
347#3364—112no—
348#3302—112no—
349#3301—114no—
350#3285—114no—
351#3284—112no—
352#3248—112no—
353#3245—111no—
354#3212—112no—
355#3206—111no—
356#3107—112no—
357#3103—111no—
358#3035—112no—
359C2×#462—111no—
360#2988—111no—
361C23×C11—22no—
362C23×C11C22×D412yes—
363C23×C11C22×D411yescharacteristic
364C22×D11—22no—
365Q8×C11—22no—
366Q8×C11—21no—
367Q8×C11—21no—
368Q8×C11—21no—
369Q8×C11—42no—
370Q8×C11—42no—
371Q8×C11H(5,𝔽2)12yes—
372D4×C11—24no—
373D4×C11—22no—
374D4×C11—22no—
375D4×C11—22no—
376D4×C11—44no—
377D4×C11—44no—
378D4×C11—42no—
379D4×C11—81no—
380D4×C11—82no—
381C2×C4×C11—21no—
382C2×C4×C11—24no—
383C2×C4×C11—21no—
384C2×C4×C11—22no—
385C2×C4×C11—21no—
386C2×C4×C11—22no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—22no—
390C2×C4×C11—21no—
391C2×C4×C11—42no—
392C2×C4×C11—41no—
393C2×C4×C11—44no—
394C2×C4×C11—42no—
395C2×C4×C11—44no—
396C2×C4×C11—82no—
397C2×C4×C11—81no—
398C2×C4×C11#13514yescomplemented
399C2×C4×C11C22×D412yes—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C2511yescharacteristic
408C22⋊D11—44no—
409C22⋊D11—84no—
410C2×Dic11—22no—
411C2×Dic11—24no—
412C2×Dic11—82no—
413D44—22no—
414D44—22no—
415D44—42no—
416D44—42no—
417C4×D11—44no—
418C4×D11—84no—
419Dic22—24no—
420Dic22—24no—
421Dic22—42no—
422Dic22—82no—
423C11⋊C8—24no—
424C11⋊C8—22no—
425C11⋊C8—22no—
426C2×#135—114no—
427C22×Q16—112no—
428#559—21no—
429#559C2×D1111yescharacteristic
430#557C2×D1111yescharacteristic
431#556—21no—
432#556—112no—
433#556C2×D1111yescharacteristic
434#555—221no—
435#554—221no—
436#553—22no—
437#553—222no—
438#553C2×D1112yes—
439#550C2×D1111yescharacteristic
440#548—114no—
441#548C2×D1112yes—
442#547—112no—
443#542—222no—
444#537—221no—
445#533—112no—
446#532—21no—
447#532—111no—
448#532—112no—
449#532C2×D1111yescharacteristic
450C2×C4⋊Q8—111no—
451#529—22no—
452#529C2×D1112yes—
453#520—221no—
454C4×#41—21no—
455C4×#41C2×D1112yes—
456C4×#41C2×D1111yescharacteristic
457C2×C4×Q8C2×D1111yescharacteristic
458#495—114no—
459#492—112no—
460#488—114no—
461#487—112no—
462#485—114no—
463#481—112no—
464#479—114no—
465#475—111no—
466#475—111no—
467#474—112no—
468#474—112no—
469#467—114no—
470#466—114no—
471#465—114no—
472#464—114no—
473#464—114no—
474#463—114no—
475#462—112no—
476#462—112no—
477#462—112no—
478#462—112no—
479#461—112no—
480#461—112no—
481#460—111no—
482#460—111no—
483#459—112no—
484#459—112no—
485#452—114no—
486#452—114no—
487#449—114no—
488#448—112no—
489#448—114no—
490C8×Q8—112no—
491C4×Q16—114no—
492C4×SD16—112no—
493C4×SD16—112no—
494C4×SD16—114no—
495C8×D4—112no—
496C8×D4—114no—
497#431—111no—
498#431—112no—
499C2×C4⋊C8—111no—
500C2×C4⋊C8—112no—
501#416—114no—
502C2×#103—112no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11C2×#13512yes—
512C22×C11C23×D411yescharacteristic
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C4×C11—21no—
517C4×C11—22no—
518C4×C11—21no—
519C4×C11—22no—
520C4×C11—21no—
521C4×C11—22no—
522C4×C11—22no—
523C4×C11—41no—
524C4×C11—41no—
525C4×C11—41no—
526C4×C11—42no—
527C4×C11C2×#13512yes—
528C4×C11C2×#13512yes—
529C4×C11C2×H(5,𝔽2)11yescharacteristic
530C4×C11#58511yescharacteristic
531Dic11—44no—
532Dic11—42no—
533C2×#41—21no—
534C2×#41—114no—
535C2×#41—221no—
536C2×#41C22⋊D1111yescharacteristic
537C2×#41C22×D1112yes—
538C22×Q8—112no—
539C22×Q8C22×D1111yescharacteristic
540#135—448no—
541C2×Q16—114no—
542C2×Q16—114no—
543C2×Q16—444no—
544C2×SD16—112no—
545C2×SD16—112no—
546C2×SD16—114no—
547C2×SD16—114no—
548C2×D8—114no—
549C22×C8—112no—
550C22×C8—114no—
551C4⋊Q8—21no—
552C4⋊Q8—111no—
553C4⋊Q8—112no—
554C4⋊Q8—112no—
555C4⋊Q8—221no—
556C4⋊Q8—221no—
557C4⋊Q8C22×D1111yescharacteristic
558#127—21no—
559#127—111no—
560#127C22×D1111yescharacteristic
561#126—22no—
562#126—22no—
563#126—22no—
564#126—224no—
565#125—22no—
566#125—222no—
567#125C22×D1112yes—
568#124—21no—
569#124—21no—
570#124—22no—
571#124—21no—
572#124—114no—
573#124—224no—
574#124—221no—
575#124C22×D1112yes—
576#123—22no—
577#123—22no—
578#123—22no—
579#123—224no—
580C22⋊Q8—22no—
581C22⋊Q8—114no—
582C22⋊Q8—222no—
583C22⋊Q8—222no—
584C22⋊Q8—224no—
585C22⋊Q8C22×D1112yes—
586#121—22no—
587#121—22no—
588#121—21no—
589#121—22no—
590#121—112no—
591#121—222no—
592#121—224no—
593#121—222no—
594#121—221no—
595#121—222no—
596#121C22×D1112yes—
597#121C22×D1112yes—
598C4×Q8—21no—
599C4×Q8—21no—
600C4×Q8—21no—
601C4×Q8—21no—
602C4×Q8—114no—
603C4×Q8—222no—
604C4×Q8C22⋊D1111yescharacteristic
605C4×Q8C22×D1111yescharacteristic
606C4×Q8C22×D1111yescharacteristic
607C4×Q8C22×D1111yescharacteristic
608C4×Q8C22×D1111yescharacteristic
609C4×Q8C22×D1112yes—
610C4×Q8C22×D1111yescharacteristic
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—21no—
619C4×D4—112no—
620C4×D4—224no—
621C4×D4—222no—
622C4×D4—222no—
623C4×D4—221no—
624C4×D4C22⋊D1112yes—
625C4×D4C22⋊D1111yescharacteristic
626C4×D4C22×D1112yes—
627C4×D4C22×D1112yes—
628C4×D4C22×D1111yescharacteristic
629C4×D4C22×D1112yes—
630#117—22no—
631#117—22no—
632#117—222no—
633#117—222no—
634#117C22⋊D1111yescharacteristic
635#117C22⋊D1112yes—
636#117C22×D1112yes—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—221no—
639C2×C4⋊C4—221no—
640C2×C4⋊C4—222no—
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C42—21no—
643C2×C42—22no—
644C2×C42C22×D1111yescharacteristic
645C2×C42C22×D1112yes—
646#107—114no—
647#106—112no—
648#106—112no—
649C4⋊C8—112no—
650C4⋊C8—111no—
651C4⋊C8—112no—
652C4⋊C8—114no—
653C4⋊C8—111no—
654#103—112no—
655#103—112no—
656#103—114no—
657#103—114no—
658#103—114no—
659#103—114no—
660#102—114no—
661#102—112no—
662#102—114no—
663#102—112no—
664C22⋊C8—112no—
665C22⋊C8—114no—
666C4×C8—112no—
667C4×C8—114no—
668C2×C11—22no—
669C2×C11—42no—
670C2×C11—82no—
671C2×C11#348811yescharacteristic
672C2×C11C22×#13511yescharacteristic
673C2×C11#358611yescharacteristic
674D11—82no—
675#41—24no—
676#41—24no—
677#41—42no—
678#41—44no—
679#41—444no—
680#41—444no—
681#41—444no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—22no—
685C2×Q8—41no—
686C2×Q8—114no—
687C2×Q8—221no—
688C2×Q8—222no—
689C2×Q8—442no—
690C2×Q8—442no—
691C2×Q8C2×C22⋊D1111yescharacteristic
692C2×Q8C23×D1111yescharacteristic
693C2×Q8C23×D1111yescharacteristic
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—112no—
700C2×D4—222no—
701C2×D4—224no—
702C2×D4—221no—
703C2×D4—221no—
704C2×D4C2×C22⋊D1112yes—
705C2×D4C2×C22⋊D1111yescharacteristic
706C2×D4C23×D1112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—224no—
715C22×C4C2×C22⋊D1112yes—
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1112yes—
718C22×C4C2×C22⋊D1111yescharacteristic
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1112yes—
721Q16—228no—
722Q16—444no—
723SD16—224no—
724SD16—444no—
725SD16—444no—
726SD16—442no—
727D8—444no—
728C2×C8—112no—
729C2×C8—114no—
730C2×C8—112no—
731C2×C8—442no—
732C2×C8—444no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—21no—
742C4⋊C4—22no—
743C4⋊C4—112no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—224no—
748C4⋊C4—222no—
749C4⋊C4—221no—
750C4⋊C4—224no—
751C4⋊C4C2×C22⋊D1111yescharacteristic
752C4⋊C4C2×C22⋊D1111yescharacteristic
753C4⋊C4C2×C22⋊D1112yes—
754C4⋊C4C2×C22⋊D1112yes—
755C4⋊C4C23×D1111yescharacteristic
756C4⋊C4C23×D1111yescharacteristic
757C4⋊C4C23×D1112yes—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—22no—
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—224no—
767C22⋊C4—224no—
768C22⋊C4—222no—
769C22⋊C4—222no—
770C22⋊C4—224no—
771C22⋊C4C2×C22⋊D1112yes—
772C22⋊C4C2×C22⋊D1112yes—
773C22⋊C4C2×C22⋊D1112yes—
774C42—21no—
775C42—21no—
776C42—22no—
777C42—22no—
778C42—21no—
779C42—21no—
780C42—224no—
781C42C2×C22⋊D1112yes—
782C42C2×C22⋊D1112yes—
783C42C2×C22⋊D1111yescharacteristic
784C42C2×C22⋊D1111yescharacteristic
785C42C23×D1111yescharacteristic
786C42C23×D1112yes—
787C42C23×D1111yescharacteristic
788C11#6195411yescharacteristic, complemented, Sylow
789C23—22no—
790C23—222no—
791C23C22×C22⋊D1112yes—
792C23C22×C22⋊D1111yescharacteristic
793Q8—22no—
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—42no—
798Q8—42no—
799Q8—224no—
800Q8—224no—
801Q8—442no—
802Q8—882no—
803Q8#6704212yes—
804D4—24no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—44no—
809D4—44no—
810D4—42no—
811D4—81no—
812D4—82no—
813D4—222no—
814D4—222no—
815D4—442no—
816D4—444no—
817D4—442no—
818D4—884no—
819C2×C4—21no—
820C2×C4—24no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—82no—
835C2×C4—81no—
836C2×C4—222no—
837C2×C4—224no—
838C2×C4—444no—
839C2×C4—884no—
840C2×C4—882no—
841C2×C4#6700314yescomplemented
842C2×C4C22×C22⋊D1112yes—
843C2×C4C22×C22⋊D1112yes—
844C2×C4C22×C22⋊D1111yescharacteristic
845C2×C4C22×C22⋊D1111yescharacteristic
846C2×C4C22×C22⋊D1112yes—
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C22×C22⋊D1111yescharacteristic
849C2×C4C22×C22⋊D1111yescharacteristic
850C2×C4C24×D1111yescharacteristic
851C8—224no—
852C8—222no—
853C8—222no—
854C22—21no—
855C22—21no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22C2×#6700312yes—
866C22C23×C22⋊D1111yescharacteristic
867C4—21no—
868C4—22no—
869C4—21no—
870C4—22no—
871C4—21no—
872C4—22no—
873C4—22no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—42no—
878C4—444no—
879C4—442no—
880C4C2×#6700312yes—
881C4C2×#6700312yes—
882C4C2×#6704211yescharacteristic
883C4#1062345311yescharacteristic
884C2—22no—
885C2—42no—
886C2—82no—
887C2—882no—
888C2#1308228511yescharacteristic
889C2C22×#6700311yescharacteristic
890C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3480C2
socleC22×C11C23×D4
hypercenter#3480D11
hypocenterC11#61954
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #13082527C2semidirect
2. #13081608C2semidirect
3. #13081301C2semidirect
4. #13080527C2semidirect
5. #13080512C2semidirect
6. #13080353C2semidirect
7. #13080346C2semidirect
8. #13079953C2semidirect
9. #13079923C2semidirect
10. #13079588C2semidirect
11. #13079538C2semidirect
12. #13078687C2semidirect
13. #13078647C2semidirect
14. #13078071C2semidirect
15. C2×#10622644C2semidirect
16. #13077727C2semidirect
17. C11×#3480C2semidirect
345. #3480D11semidirect
398. C2×C4×C11#135semidirect
788. C11#61954semidirect
841. C2×C4#67003semidirect

Maximal subgroups

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

subgroupindex
#130825272
#130816082
#130813012
#130805272
#130805122
#130803532
#130803462
#130799532
#130799232
#130795882
#130795382
#130786872
#130786472
#130780712
C2×#106226442
#130777272
C11×#34802
#6195411