Finite Group Databasebeta

← #15626767

Subgroups — #15626767

Order 2816.

2168 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2#13079999C212yesmaximal, complemented
3#13079994C212yesmaximal, complemented
4#13079978C214yesmaximal, complemented
5#13079942C214yesmaximal, complemented
6#13079928C212yesmaximal, complemented
7#13079923C212yesmaximal, complemented
8#13078431C212yesmaximal, complemented
9#13078409C212yesmaximal, complemented
10#13078237C214yesmaximal, complemented
11#13078096C212yesmaximal, complemented
12#13078076C212yesmaximal, complemented
13C2×#10622537C211yesmaximal, characteristic, complemented
14C11×#3444C211yesmaximal, characteristic, complemented
15C22×#4339—21no—
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic, complemented
18C11×#533C2211yescharacteristic, complemented
19C11×#532C2211yescharacteristic
20C11×#532C2211yescharacteristic, complemented
21C11×#532C2211yescharacteristic, complemented
22C11×#529—21no—
23C11×#529—21no—
24C11×#529—21no—
25C11×#529—21no—
26C11×#529C2212yescomplemented
27C11×#529C2212yescomplemented
28C11×#525—21no—
29C11×#525—21no—
30C11×#525C2212yes—
31C4×C11×#41—21no—
32C4×C11×#41—21no—
33C4×C11×#41C2212yes—
34C22×C42×C11C2211yescharacteristic
35C2×#67002C2214yes—
36C2×#66983—21no—
37C2×#66983C2212yes—
38C22×#4318C2212yes—
39#10623008—21no—
40#10623008—21no—
41#10623008—21no—
42#10623008—21no—
43#10623008C2212yes—
44#10623008C2212yes—
45#10623008C2212yes—
46#10623008C2212yes—
47C2×#66928—21no—
48C2×#66927C2211yescharacteristic
49C2×C4×D44—21no—
50C2×C4×D44C2212yes—
51C2×#66922C2211yescharacteristic
52#10622845C2214yes—
53#10622700C2214yescomplemented
54#10622697C2214yescomplemented
55#10622696C2214yescomplemented
56#10622685C2214yescomplemented
57#10622679C2218yescomplemented
58#10622670C2218yescomplemented
59#10622662C2218yescomplemented
60#10622661C2218yescomplemented
61#10622652C2218yescomplemented
62#10622651C2218yescomplemented
63#10622640C2214yescomplemented
64#10622640C2214yescomplemented
65#10622634C2214yescomplemented
66#10622633C2214yescomplemented
67#10622628C2214yescomplemented
68#10622628C2214yescomplemented
69#10622621C2214yescomplemented
70#10622620C2214yescomplemented
71#10622614C2214yes—
72#10622608C2214yes—
73#10622537C2212yes—
74#10622537C2212yes—
75#10622537C2212yescomplemented
76#10622537C2212yescomplemented
77C2×C4⋊(C11⋊C8)C2212yescomplemented
78C2×C4⋊(C11⋊C8)C2212yescomplemented
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41C2312yes—
82C23×C4×C11D411yescharacteristic
83C23×C4×C11D411yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—22no—
86C2×#4339—22no—
87C2×#4339—22no—
88C2×#4339—22no—
89C2×#4339—22no—
90C2×#4339—48no—
91C22×D44—21no—
92C22×D44—21no—
93C22×D44C2312yes—
94C22×C4×D11—22no—
95C22×Dic22—21no—
96C11×C4⋊Q8C2311yescharacteristic
97C11×C4⋊Q8C2311yescharacteristic
98C11×C4⋊Q8C2311yescharacteristic
99C11×#127C2311yescharacteristic
100C11×#126—22no—
101C11×#126—22no—
102C11×#125—21no—
103C11×#125—21no—
104C11×#125C2312yes—
105C11×#124—21no—
106C11×#124—21no—
107C11×#124C2312yes—
108C11×#123—22no—
109C11×#123—22no—
110C11×#123—22no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8C2312yes—
116C11×C22⋊Q8C2312yes—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121—21no—
120C11×#121—21no—
121C11×#121C2312yes—
122C11×#121C2312yes—
123C11×#120—22no—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11—21no—
127C4×Q8×C11—21no—
128C4×Q8×C11C2312yes—
129C4×Q8×C11C2312yes—
130C4×D4×C11—22no—
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11—22no—
134C4×D4×C11—22no—
135C4×D4×C11—22no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11C2312yes—
141C4×D4×C11C2312yes—
142C11×#117—21no—
143C11×#117—21no—
144C11×#117—22no—
145C11×#117—22no—
146C11×#117—22no—
147C11×#117C2312yes—
148C2×C42×C11—22no—
149C2×C42×C11D411yescharacteristic
150C2×C42×C11D411yescharacteristic
151C2×C42×C11D411yescharacteristic
152C2×C42×C11D411yescharacteristic
153C2×C42×C11D411yescharacteristic
154C2×C42×C11D411yescharacteristic
155C2×C42×C11C2311yescharacteristic
156C2×C42×C11C2311yescharacteristic
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2311yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161#67002—48no—
162C2×#4325C2318yes—
163C2×#4323C2318yes—
164#66983—22no—
165#66983—22no—
166#66983—22no—
167#66983—22no—
168#66983—22no—
169#66983—22no—
170#66983C2314yes—
171#66983C2314yes—
172C2×(C2×D11)⋊C4—22no—
173C2×(C2×D11)⋊C4—22no—
174C2×C4⋊Dic11—21no—
175C2×C4⋊Dic11C2312yes—
176C2×#4318—44no—
177C2×#4318C2314yes—
178C2×#4318C2314yes—
179C22×C11⋊C8C2314yes—
180#66928—22no—
181#66928—22no—
182#66928—22no—
183#66928—22no—
184#66927—21no—
185#66927—21no—
186#66927C2312yes—
187#66927C2312yes—
188C4×D44—22no—
189C4×D44—22no—
190C4×D44—22no—
191C4×D44—22no—
192C4×D44—22no—
193C4×D44—22no—
194C4×D44C2314yes—
195C4×D44C2314yes—
196#66922—21no—
197#66922—21no—
198#66922C2312yes—
199#66922C2312yes—
200#66899C2318yes—
201#66896C2318yes—
202#66873C2318yes—
203#66873C2318yes—
204#66872C2318yes—
205#66871C2318yes—
206C4⋊(C11⋊C8)C2314yes—
207C4⋊(C11⋊C8)C2314yes—
208C4⋊(C11⋊C8)C2314yes—
209C4⋊(C11⋊C8)C2314yes—
210#60916—111nomaximal, Sylow
211C24×C11C2×D411yescharacteristic
212C23×D11—22no—
213C11×#41—24no—
214C11×#41—24no—
215C11×#41—44no—
216C11×#41—44no—
217C2×Q8×C11—21no—
218C2×Q8×C11—21no—
219C2×Q8×C11C2412yes—
220C2×D4×C11—22no—
221C2×D4×C11—22no—
222C2×D4×C11—22no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11C2412yes—
226C22×C4×C11—24no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—42no—
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—24no—
252C2×C22⋊D11—24no—
253C2×C22⋊D11—48no—
254C22×Dic11—22no—
255#4339—48no—
256#4339—48no—
257#4339—48no—
258#4339—48no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—24no—
265C2×D44—24no—
266C2×D44—44no—
267C2×D44—44no—
268C2×D44C2414yes—
269C2×C4×D11—24no—
270C2×C4×D11—24no—
271C2×C4×D11—48no—
272C2×Dic22—22no—
273C2×Dic22—22no—
274C2×Dic22—44no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4C2412yes—
286C11×C4⋊C4C2412yes—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C42×C11—22no—
297C42×C11—22no—
298C42×C11—22no—
299C42×C11C2×D411yescharacteristic
300C42×C11C2×D411yescharacteristic
301C42×C11C2×D411yescharacteristic
302C42×C11C2×D411yescharacteristic
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D411yescharacteristic
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D411yescharacteristic
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2411yescharacteristic
312C42×C11C2411yescharacteristic
313C42×C11C2411yescharacteristic
314C42×C11C2411yescharacteristic
315#4325—48no—
316#4323—48no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321C4⋊Dic11—22no—
322C4⋊Dic11—22no—
323C4⋊Dic11—22no—
324C4⋊Dic11C2414yes—
325#4318—28no—
326#4318—44no—
327C2×C11⋊C8—44no—
328C2×C11⋊C8C2418yes—
329#3444D1111yescharacteristic, complemented
330C2×#532—111no—
331#3254—112no—
332#3253—112no—
333#3251—114no—
334#3247—114no—
335#3246—112no—
336#3245—112no—
337#3079—112no—
338#3077—112no—
339#3055—114no—
340#3038—112no—
341#3036—112no—
342C2×#423—111no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—41no—
347C23×C11C22×D411yescharacteristic
348C23×C11C22×D411yescharacteristic
349C23×C11C22×D411yescharacteristic
350C22×D11—24no—
351C22×D11—44no—
352C22×D11—44no—
353C22×D11—44no—
354Q8×C11—22no—
355Q8×C11—22no—
356Q8×C11—42no—
357Q8×C11—42no—
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—42no—
361D4×C11—44no—
362D4×C11—44no—
363D4×C11—44no—
364D4×C11—42no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—44no—
387C2×C4×C11—44no—
388C2×C4×C11—44no—
389C2×C4×C11AGL(1,ℤ/8)14yescomplemented
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11H(5,𝔽2)12yes—
402C2×C4×C112−1+412yes—
403C2×C4×C11C2511yescharacteristic
404C22⋊D11—48no—
405C22⋊D11—48no—
406C2×Dic11—24no—
407C2×Dic11—44no—
408D44—24no—
409D44—24no—
410D44—44no—
411D44—44no—
412D44—44no—
413D44—44no—
414D44—44no—
415C4×D11—48no—
416C4×D11—48no—
417Dic22—44no—
418Dic22—44no—
419C11⋊C8—28no—
420C22×#41—221no—
421C2×AGL(1,ℤ/8)—114no—
422C22×M16—112no—
423#533C2×D1111yescharacteristic
424#533C2×D1111yescharacteristic, complemented
425#533C2×D1111yescharacteristic, complemented
426#532—112no—
427#532—112no—
428#532—112no—
429#532—112no—
430#532—221no—
431#532—221no—
432#532—221no—
433#532—221no—
434#532C2×D1111yescharacteristic
435#532C2×D1111yescharacteristic, complemented
436#532C2×D1111yescharacteristic, complemented
437C2×C4⋊Q8—111no—
438C2×#127—111no—
439#529—21no—
440#529—21no—
441#529—21no—
442#529—21no—
443#529C2×D1112yescomplemented
444#529C2×D1112yescomplemented
445C2×#124—221no—
446#525—21no—
447#525—21no—
448#525C2×D1112yes—
449C2×#121—112no—
450C2×#121—221no—
451C4×#41—21no—
452C4×#41—21no—
453C4×#41C2×D1112yes—
454C2×C4×D4—112no—
455C2×C4×D4—221no—
456C22×C42C2×D1111yescharacteristic
457#478—118no—
458#477—114no—
459#476—114no—
460#476—114no—
461#475—114no—
462#474—114no—
463#474—114no—
464#469—118no—
465#468—118no—
466#466—118no—
467#465—118no—
468#463—118no—
469#461—114no—
470#460—114no—
471#460—114no—
472#459—114no—
473#459—114no—
474#459—114no—
475#428—114no—
476#423—112no—
477#423—112no—
478#423—112no—
479#423—112no—
480C2×C4⋊C8—112no—
481C2×C4⋊C8—112no—
482#418—114no—
483#417—114no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—44no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11#53712yes—
496C22×C11C2×AGL(1,ℤ/8)12yes—
497C22×C11C23×D411yescharacteristic
498C2×D11—44no—
499C2×D11—44no—
500C2×D11—44no—
501C2×D11—88no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11#53712yes—
513C4×C11C2×AGL(1,ℤ/8)12yes—
514C4×C11C2×AGL(1,ℤ/8)12yes—
515C4×C11#57512yes—
516C4×C11C2×H(5,𝔽2)11yescharacteristic
517C4×C11C2×2−1+411yescharacteristic
518Dic11—44no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—222no—
522C2×#41—222no—
523C2×#41—222no—
524C2×#41—222no—
525C2×#41—448no—
526C2×#41C22×D1112yes—
527C22×Q8—221no—
528C22×D4—112no—
529C22×D4—222no—
530C22×D4—221no—
531C22×D4—221no—
532C23×C4—222no—
533C23×C4C22⋊D1111yescharacteristic
534C23×C4C22⋊D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536AGL(1,ℤ/8)—448no—
537C2×SD16—118no—
538C2×D8—118no—
539C2×M16—114no—
540C2×M16—114no—
541C2×M16—444no—
542C22×C8—114no—
543C4⋊Q8—112no—
544C4⋊Q8—112no—
545C4⋊Q8—221no—
546C4⋊Q8—221no—
547C4⋊Q8C22×D1111yescharacteristic
548C4⋊Q8C22×D1111yescharacteristic
549C4⋊Q8C22×D1111yescharacteristic
550#127—112no—
551#127—112no—
552#127—221no—
553#127—221no—
554#127C22×D1111yescharacteristic
555#126—22no—
556#126—22no—
557#125—21no—
558#125—21no—
559#125C22×D1112yes—
560#124—21no—
561#124—21no—
562#124—222no—
563#124—222no—
564#124—222no—
565#124—222no—
566#124C22×D1112yes—
567#123—22no—
568#123—22no—
569#123—22no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8C22×D1112yes—
575C22⋊Q8C22×D1112yes—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—114no—
581#121—114no—
582#121—222no—
583#121—222no—
584#121—222no—
585#121—222no—
586#121—222no—
587#121—222no—
588#121C22×D1112yes—
589#121C22×D1112yes—
590#120—22no—
591C4×Q8—21no—
592C4×Q8—21no—
593C4×Q8—21no—
594C4×Q8—21no—
595C4×Q8C22×D1112yes—
596C4×Q8C22×D1112yes—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—114no—
608C4×D4—114no—
609C4×D4—222no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—222no—
613C4×D4—222no—
614C4×D4—222no—
615C4×D4C22×D1112yes—
616C4×D4C22×D1112yes—
617#117—21no—
618#117—21no—
619#117—22no—
620#117—22no—
621#117—22no—
622#117C22×D1112yes—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—221no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C42—22no—
628C2×C42C22⋊D1111yescharacteristic
629C2×C42C22⋊D1111yescharacteristic
630C2×C42C22⋊D1111yescharacteristic
631C2×C42C22⋊D1111yescharacteristic
632C2×C42C22⋊D1111yescharacteristic
633C2×C42C22⋊D1111yescharacteristic
634C2×C42C22×D1111yescharacteristic
635C2×C42C22×D1111yescharacteristic
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1111yescharacteristic
640#107—118no—
641#106—118no—
642C4⋊C8—114no—
643C4⋊C8—114no—
644C4⋊C8—114no—
645C4⋊C8—114no—
646#103—118no—
647#102—118no—
648#102—118no—
649#102—118no—
650C2×C11—22no—
651C2×C11—22no—
652C2×C11—41no—
653C2×C11—82no—
654C2×C11C2×#53711yescharacteristic
655C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
656C2×C11C2×#57511yescharacteristic
657D11—84no—
658C24—222no—
659C24C2×C22⋊D1111yescharacteristic
660#41—24no—
661#41—24no—
662#41—44no—
663#41—44no—
664#41—448no—
665#41—448no—
666#41—448no—
667#41—448no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—222no—
671C2×Q8—222no—
672C2×Q8—444no—
673C2×Q8C23×D1112yes—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—114no—
680C2×D4—224no—
681C2×D4—224no—
682C2×D4—224no—
683C2×D4—224no—
684C2×D4—222no—
685C2×D4—222no—
686C2×D4—222no—
687C2×D4—222no—
688C2×D4—222no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—448no—
692C2×D4C23×D1112yes—
693C22×C4—24no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—42no—
700C22×C4—222no—
701C22×C4—224no—
702C22×C4—224no—
703C22×C4—448no—
704C22×C4C2×C22⋊D1111yescharacteristic
705C22×C4C2×C22⋊D1111yescharacteristic
706C22×C4C2×C22⋊D1111yescharacteristic
707C22×C4C2×C22⋊D1111yescharacteristic
708C22×C4C2×C22⋊D1111yescharacteristic
709C22×C4C2×C22⋊D1111yescharacteristic
710C22×C4C2×C22⋊D1111yescharacteristic
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1111yescharacteristic
714C22×C4C2×C22⋊D1111yescharacteristic
715C22×C4C2×C22⋊D1111yescharacteristic
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1111yescharacteristic
718C22×C4C2×C22⋊D1111yescharacteristic
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1111yescharacteristic
721C22×C4C23×D1111yescharacteristic
722SD16—448no—
723D8—448no—
724M16—228no—
725M16—444no—
726C2×C8—118no—
727C2×C8—444no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—114no—
739C4⋊C4—222no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C4⋊C4C23×D1112yes—
743C4⋊C4C23×D1112yes—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—224no—
754C22⋊C4—224no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C42—22no—
758C42—22no—
759C42—22no—
760C42C2×C22⋊D1111yescharacteristic
761C42C2×C22⋊D1111yescharacteristic
762C42C2×C22⋊D1111yescharacteristic
763C42C2×C22⋊D1111yescharacteristic
764C42C2×C22⋊D1111yescharacteristic
765C42C2×C22⋊D1111yescharacteristic
766C42C2×C22⋊D1111yescharacteristic
767C42C2×C22⋊D1111yescharacteristic
768C42C2×C22⋊D1111yescharacteristic
769C42C2×C22⋊D1111yescharacteristic
770C42C2×C22⋊D1111yescharacteristic
771C42C2×C22⋊D1111yescharacteristic
772C42C23×D1111yescharacteristic
773C42C23×D1111yescharacteristic
774C42C23×D1111yescharacteristic
775C42C23×D1111yescharacteristic
776C11#6091611yescharacteristic, complemented, Sylow
777C23—22no—
778C23—22no—
779C23—22no—
780C23—41no—
781C23—224no—
782C23—444no—
783C23—444no—
784C23—444no—
785C23C22×C22⋊D1111yescharacteristic
786C23C22×C22⋊D1111yescharacteristic
787C23C22×C22⋊D1111yescharacteristic
788Q8—22no—
789Q8—22no—
790Q8—42no—
791Q8—42no—
792Q8—444no—
793Q8—444no—
794D4—22no—
795D4—22no—
796D4—42no—
797D4—44no—
798D4—44no—
799D4—44no—
800D4—42no—
801D4—224no—
802D4—224no—
803D4—444no—
804D4—444no—
805D4—448no—
806D4—448no—
807D4—444no—
808D4—444no—
809D4—444no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—224no—
835C2×C4—448no—
836C2×C4—444no—
837C2×C4—448no—
838C2×C4#6700214yescomplemented
839C2×C4#6704212yes—
840C2×C4#6704312yes—
841C2×C4C22×C22⋊D1111yescharacteristic
842C2×C4C22×C22⋊D1111yescharacteristic
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C22×C22⋊D1111yescharacteristic
845C2×C4C22×C22⋊D1111yescharacteristic
846C2×C4C22×C22⋊D1111yescharacteristic
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C22×C22⋊D1111yescharacteristic
849C2×C4C22×C22⋊D1111yescharacteristic
850C2×C4C22×C22⋊D1111yescharacteristic
851C2×C4C22×C22⋊D1111yescharacteristic
852C2×C4C24×D1111yescharacteristic
853C8—228no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—44no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—444no—
866C22—444no—
867C22—444no—
868C22—888no—
869C22C2×#6700212yes—
870C22#1062336412yes—
871C22C23×C22⋊D1111yescharacteristic
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—444no—
883C4C2×#6700212yes—
884C4C2×#6700212yes—
885C4#1062335312yes—
886C4#1062336412yes—
887C4C2×#6704211yescharacteristic
888C4C2×#6704311yescharacteristic
889C2—22no—
890C2—22no—
891C2—41no—
892C2—82no—
893C2—884no—
894C2C2×#1062336411yescharacteristic
895C2C22×#6700211yescharacteristic
896C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3444C2
socleC22×C11C23×D4
hypercenter#3444D11
hypocenterC11#60916
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. #13079999C2semidirect
3. #13079994C2semidirect
4. #13079978C2semidirect
5. #13079942C2semidirect
6. #13079928C2semidirect
7. #13079923C2semidirect
8. #13078431C2semidirect
9. #13078409C2semidirect
10. #13078237C2semidirect
11. #13078096C2semidirect
12. #13078076C2semidirect
13. C2×#10622537C2semidirect
14. C11×#3444C2semidirect
17. C11×#533C22semidirect
18. C11×#533C22semidirect
20. C11×#532C22semidirect
21. C11×#532C22semidirect
26. C11×#529C22semidirect
27. C11×#529C22semidirect
53. #10622700C22semidirect
54. #10622697C22semidirect
55. #10622696C22semidirect
56. #10622685C22semidirect
57. #10622679C22semidirect
58. #10622670C22semidirect
59. #10622662C22semidirect
60. #10622661C22semidirect
61. #10622652C22semidirect
62. #10622651C22semidirect
63. #10622640C22semidirect
64. #10622640C22semidirect
65. #10622634C22semidirect
66. #10622633C22semidirect
67. #10622628C22semidirect
68. #10622628C22semidirect
69. #10622621C22semidirect
70. #10622620C22semidirect
75. #10622537C22semidirect
76. #10622537C22semidirect
77. C2×C4⋊(C11⋊C8)C22semidirect
78. C2×C4⋊(C11⋊C8)C22semidirect
329. #3444D11semidirect
389. C2×C4×C11AGL(1,ℤ/8)semidirect
424. #533C2×D11semidirect
425. #533C2×D11semidirect
435. #532C2×D11semidirect
436. #532C2×D11semidirect
443. #529C2×D11semidirect
444. #529C2×D11semidirect
776. C11#60916semidirect
838. C2×C4#67002semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
#130799992
#130799942
#130799782
#130799422
#130799282
#130799232
#130784312
#130784092
#130782372
#130780962
#130780762
C2×#106225372
C11×#34442
#6091611