Finite Group Databasebeta

← #14769474

Subgroups — #14769474

Order 2816.

1472 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4339C211yesmaximal, characteristic
2D4×#4318C211yesmaximal, characteristic, complemented
3C2×#10622618C212yesmaximal, complemented
4#13069534C211yesmaximal, characteristic, complemented
5#13069444C211yesmaximal, characteristic, complemented
6#13069064C212yesmaximal, complemented
7#13068916C212yesmaximal, complemented
8#13068637C211yesmaximal, characteristic, complemented
9#13068561C212yesmaximal, complemented
10C4×#66869C211yesmaximal, characteristic, complemented
11C11×#2293C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×C11×#117C2212yescomplemented
15D4×C22⋊D11—21no—
16#10623322C2212yes—
17C22×#4318C2212yescomplemented
18#10623084C411yescharacteristic, complemented
19#10623083C412yescomplemented
20#10623082C411yescharacteristic, complemented
21#10623081C412yescomplemented
22D4×D44C411yescharacteristic, complemented
23#10623079—21no—
24#10623078—22no—
25C4×D4×D11—21no—
26D4×Dic22C411yescharacteristic, complemented
27#10623038—21no—
28#10623021—22no—
29#10623008C2211yescharacteristic
30C4×#4339C2211yescharacteristic
31C11×#390—21no—
32C11×#389—21no—
33C11×#388—22no—
34C4×C11×C4⋊C4C2211yescharacteristic, complemented
35C4×C11×C22⋊C4C2212yescomplemented
36C43×C11C2211yescharacteristic, complemented
37#10622820C2212yescomplemented
38#10622625—21no—
39#10622624—22no—
40D4×C11⋊C8—21no—
41#10622618—28no—
42C2×#66869C2211yescharacteristic
43C2×#66869C2212yes—
44C2×#66869C2211yescharacteristic
45C2×#66869C2212yescomplemented
46C2×#66869C2212yescomplemented
47C2×#66869C2212yescomplemented
48C2×#66869C2212yescomplemented
49#10622537C2211yescharacteristic, complemented
50C4×#4318C2211yescharacteristic, complemented
51#10622161C2211yescharacteristic, complemented
52#10622161C2212yescomplemented
53#10622161C2211yescharacteristic, complemented
54C22×D4×C11D411yescharacteristic
55C23×C4×C11C2312yes—
56C22×C22⋊D11—22no—
57C2×D4×D11—21no—
58C2×#4339—22no—
59C2×#4339—22no—
60C2×#4339—24no—
61C2×#4339—24no—
62C2×#4339—42no—
63C2×#4339—42no—
64C2×#4339C2×C412yes—
65C2×#4339C2×C412yes—
66C2×#4339C2312yes—
67C2×#4339C2311yescharacteristic
68C22×D44C2×C412yes—
69C22×C4×D11—22no—
70C22×Dic22C2×C412yes—
71C4×D4×C11C2×C411yescharacteristic
72C4×D4×C11C2×C412yes—
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11D411yescharacteristic
75C4×D4×C11D412yes—
76C4×D4×C11D411yescharacteristic
77C11×#117—24no—
78C11×#117—42no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91#67006—22no—
92#66993—21no—
93#66992—22no—
94#66991—21no—
95#66990—22no—
96D4×Dic11—21no—
97#66983—21no—
98#66983—21no—
99#66983C2×C412yes—
100#66983C2×C412yes—
101#66982—22no—
102C4×C22⋊D11—21no—
103C4×C22⋊D11—21no—
104C4×C22⋊D11—22no—
105C4×C22⋊D11—22no—
106#66979C2311yescharacteristic
107#66977C2×C412yes—
108#66977C2×C412yes—
109C2×#4318—22no—
110C2×#4318—24no—
111C2×#4318—42no—
112C2×#4318C2311yescharacteristic
113C2×#4318C2312yes—
114C2×#4318C2311yescharacteristic
115C22×C11⋊C8—22no—
116#66949—22no—
117#66948—21no—
118#66947—22no—
119#66946—21no—
120C4⋊C4×D11—21no—
121#66941—21no—
122#66938—22no—
123#66937—22no—
124#66937—22no—
125#66936—22no—
126#66935—22no—
127(C22⋊D11)⋊C4—22no—
128C22⋊C4×D11—22no—
129#66931—22no—
130#66928C2×C412yes—
131#66927C2×C411yescharacteristic
132C4×D44—21no—
133C4×D44—21no—
134C4×D44C2×C411yescharacteristic
135C4×D44C2×C411yescharacteristic
136#66925—21no—
137C42×D11—21no—
138#66922C2×C411yescharacteristic
139C4×Dic22C2×C411yescharacteristic
140C4×Dic22C2×C411yescharacteristic
141C11×#95—22no—
142C11×#95—21no—
143C22⋊(C11⋊C8)—22no—
144C22⋊(C11⋊C8)—22no—
145#66869—24no—
146#66869—22no—
147#66869—24no—
148#66869—24no—
149#66869—42no—
150#66869—42no—
151#66869D414yescomplemented
152C4⋊(C11⋊C8)—21no—
153C4⋊(C11⋊C8)—21no—
154#66867—21no—
155C4×C11⋊C8—21no—
156#22435—111nomaximal, Sylow
157C24×C11C2×D412yes—
158C23×D11—22no—
159C2×D4×C11—42no—
160C2×D4×C11C22⋊C411yescharacteristic
161C2×D4×C11C22⋊C411yescharacteristic
162C2×D4×C11C22⋊C412yes—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—22no—
170C22×C4×C11C22×C412yes—
171C22×C4×C11C22×C412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—22no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11—22no—
181C2×C22⋊D11—22no—
182C2×C22⋊D11—21no—
183C2×C22⋊D11—22no—
184C2×C22⋊D11—44no—
185C2×C22⋊D11—44no—
186C22×Dic11—22no—
187D4×D11—44no—
188#4339—24no—
189#4339—24no—
190#4339—22no—
191#4339—22no—
192#4339—21no—
193#4339—21no—
194#4339—22no—
195#4339—22no—
196#4339—42no—
197#4339—42no—
198#4339—44no—
199#4339—44no—
200#4339—44no—
201#4339—44no—
202#4339C2×D412yes—
203#4339#4112yes—
204C2×D44—24no—
205C2×D44—21no—
206C2×D44—22no—
207C2×D44—21no—
208C2×D44—42no—
209C2×D44C22×C412yes—
210C2×D44C22×C411yescharacteristic
211C2×C4×D11—21no—
212C2×C4×D11—22no—
213C2×C4×D11—22no—
214C2×C4×D11—21no—
215C2×C4×D11—21no—
216C2×C4×D11—22no—
217C2×C4×D11—44no—
218C2×C4×D11—44no—
219C2×Dic22—24no—
220C2×Dic22—22no—
221C2×Dic22—42no—
222C2×Dic22C22×C412yes—
223C2×Dic22C22×C411yescharacteristic
224C11×C4⋊C4—44no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4C22⋊C411yescharacteristic
227C11×C4⋊C4C22⋊C411yescharacteristic
228C11×C4⋊C4C22⋊C412yes—
229C11×C22⋊C4—44no—
230C11×C22⋊C4—44no—
231C11×C22⋊C4C22⋊C412yes—
232C11×C22⋊C4C22⋊C412yes—
233C11×C22⋊C4C22⋊C412yes—
234C11×C22⋊C4C22⋊C412yes—
235C42×C11—21no—
236C42×C11—22no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—22no—
240C42×C11—42no—
241C42×C11—42no—
242C42×C11C22×C411yescharacteristic
243C42×C11C22×C411yescharacteristic
244C42×C11C2×D411yescharacteristic
245C42×C11C2×D411yescharacteristic
246C42×C11C2×D412yescomplemented
247C22⋊Dic11—22no—
248C22⋊Dic11—22no—
249C22⋊Dic11—21no—
250(C2×D11)⋊C4—21no—
251(C2×D11)⋊C4—21no—
252(C2×D11)⋊C4—22no—
253(C2×D11)⋊C4—22no—
254(C2×D11)⋊C4—22no—
255(C2×D11)⋊C4—22no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11C22×C411yescharacteristic
259C4⋊Dic11C22×C411yescharacteristic
260Dic11⋊C4—21no—
261Dic11⋊C4—21no—
262Dic11⋊C4—22no—
263Dic11⋊C4—22no—
264C4×Dic11—21no—
265C4×Dic11—21no—
266C4×Dic11—21no—
267#4318—22no—
268#4318—21no—
269#4318—21no—
270#4318—21no—
271#4318—22no—
272#4318—44no—
273#4318C2×D412yescomplemented
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—44no—
278D4×#41—111no—
279D4×M16—111no—
280C2×#421—112no—
281#2293D1111yescharacteristic, complemented
282#1980—111no—
283#1962—111no—
284#1897—112no—
285#1871—112no—
286#1806—111no—
287#1789—112no—
288C4×#104—111no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—42no—
292C23×C11—42no—
293C23×C11C2×C22⋊C412yes—
294C23×C11C2×C22⋊C412yes—
295C23×C11C22×D411yescharacteristic
296C22×D11—21no—
297C22×D11—22no—
298C22×D11—44no—
299C22×D11—44no—
300C22×D11—82no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—42no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11C2×C22⋊C411yescharacteristic
326C2×C4×C11C2×C22⋊C411yescharacteristic
327C2×C4×C11C2×C22⋊C411yescharacteristic
328C2×C4×C11C2×C22⋊C412yes—
329C2×C4×C11C2×C22⋊C412yes—
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C23×C411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C22⋊D11—22no—
338C22⋊D11—22no—
339C22⋊D11—44no—
340C22⋊D11—44no—
341C22⋊D11—44no—
342C22⋊D11—42no—
343C22⋊D11—42no—
344C22⋊D11—82no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—22no—
349C2×Dic11—44no—
350D44—22no—
351D44—21no—
352D44—22no—
353D44—44no—
354D44—42no—
355D44—81no—
356D44C4×D412yes—
357C4×D11—22no—
358C4×D11—22no—
359C4×D11—44no—
360C4×D11—44no—
361C4×D11—42no—
362C4×D11—42no—
363C4×D11—42no—
364C4×D11—81no—
365Dic22—21no—
366Dic22—22no—
367Dic22—22no—
368Dic22—44no—
369Dic22C4×D412yes—
370C11⋊C8—22no—
371C11⋊C8—42no—
372C11⋊C8—41no—
373C22×#41—112no—
374C22×M16—112no—
375#550—111no—
376D4×Q8—111no—
377#548—112no—
378#547—111no—
379#547—221no—
380#546—112no—
381#546—222no—
382D42—111no—
383D42—221no—
384#532—111no—
385#532—221no—
386#525—112no—
387#525—222no—
388C4×#41—111no—
389C2×C4×D4—221no—
390C2×C4×D4C2×D1111yescharacteristic
391C2×#117C2×D1112yescomplemented
392#436—221no—
393#435—222no—
394C8×D4—221no—
395#423—111no—
396#421—228no—
397C2×#104—111no—
398C2×#104—112no—
399C2×#104—111no—
400C2×#104—112no—
401C2×#104—112no—
402C2×#104—112no—
403C2×#104—112no—
404#407—112no—
405C4×M16—111no—
406#390—21no—
407#389—21no—
408#388—22no—
409C4×C4⋊C4C2×D1111yescharacteristic, complemented
410C4×C22⋊C4C2×D1112yescomplemented
411C43C2×D1111yescharacteristic, complemented
412#339—112no—
413#339—111no—
414#339—111no—
415C22×C11—21no—
416C22×C11—21no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—82no—
424C22×C11—82no—
425C22×C11C22×C22⋊C411yescharacteristic
426C22×C11D4211yescharacteristic
427C22×C11#54611yescharacteristic
428C2×D11—22no—
429C2×D11—41no—
430C2×D11—41no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—88no—
435C4×C11—22no—
436C4×C11—22no—
437C4×C11—21no—
438C4×C11—21no—
439C4×C11—21no—
440C4×C11—42no—
441C4×C11—42no—
442C4×C11—82no—
443C4×C11#42112yescomplemented
444C4×C11C2×C4×D411yescharacteristic
445C4×C11#51811yescharacteristic
446C4×C11D4211yescharacteristic
447C4×C11#54611yescharacteristic
448Dic11—22no—
449Dic11—42no—
450Dic11—41no—
451Dic11—41no—
452C2×#41—112no—
453C2×#41—112no—
454C2×#41—111no—
455C2×#41—112no—
456C2×#41—224no—
457C2×#41—224no—
458C2×#41—222no—
459C2×#41—222no—
460C2×#41—442no—
461C2×#41—442no—
462C22×Q8—112no—
463C22×D4—112no—
464C22×D4—222no—
465C22×D4—221no—
466C22×D4C22⋊D1111yescharacteristic
467C23×C4—222no—
468C23×C4C22×D1112yes—
469C2×M16—111no—
470C2×M16—112no—
471C2×M16—111no—
472C2×M16—222no—
473C2×M16—224no—
474C2×M16—442no—
475C22×C8—222no—
476C4⋊Q8—111no—
477C4⋊Q8—221no—
478#127—111no—
479#127—221no—
480#124—112no—
481#124—222no—
482#123—222no—
483#123—222no—
484#123—222no—
485C22⋊Q8—112no—
486C22⋊Q8—112no—
487C22⋊Q8—222no—
488C22⋊Q8—222no—
489#121—112no—
490#121—112no—
491#121—222no—
492#121—221no—
493#121—221no—
494#121—221no—
495#121—221no—
496#121—222no—
497#121—222no—
498#120—222no—
499#120—222no—
500#120—222no—
501C4×Q8—111no—
502C4×Q8—111no—
503C4×D4—111no—
504C4×D4—111no—
505C4×D4—221no—
506C4×D4—222no—
507C4×D4—222no—
508C4×D4—221no—
509C4×D4—221no—
510C4×D4—221no—
511C4×D4—222no—
512C4×D4—221no—
513C4×D4—221no—
514C4×D4C4×D1111yescharacteristic
515C4×D4C4×D1112yes—
516C4×D4C4×D1111yescharacteristic
517C4×D4D4411yescharacteristic
518C4×D4D4412yes—
519C4×D4D4411yescharacteristic
520#117—24no—
521#117—42no—
522#117—111no—
523#117—221no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—221no—
527C2×C4⋊C4C22⋊D1111yescharacteristic
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—222no—
531C2×C22⋊C4C22⋊D1112yes—
532C2×C42—21no—
533C2×C42—21no—
534C2×C42—221no—
535C2×C42C22×D1112yes—
536C2×C42C22×D1111yescharacteristic
537C2×C42C22×D1111yescharacteristic
538C2×C42C22×D1111yescharacteristic
539C4⋊C8—221no—
540C4⋊C8—221no—
541#104—114no—
542#104—224no—
543#104—222no—
544#104—224no—
545#104—224no—
546#104—442no—
547#104—442no—
548C22⋊C8—222no—
549C22⋊C8—222no—
550#97—221no—
551C4×C8—221no—
552#95—22no—
553#95—21no—
554C2×C11—21no—
555C2×C11—21no—
556C2×C11—42no—
557C2×C11—42no—
558C2×C11D4×C22⋊C411yescharacteristic
559C2×C11C2×#42111yescharacteristic
560C2×C11#290111yescharacteristic
561D11—42no—
562D11—82no—
563C24—222no—
564C24C2×C22⋊D1112yes—
565#41—112no—
566#41—112no—
567#41—224no—
568#41—224no—
569#41—221no—
570#41—221no—
571#41—222no—
572#41—222no—
573#41—222no—
574#41—222no—
575#41—444no—
576#41—444no—
577#41—442no—
578#41—442no—
579#41—444no—
580#41—444no—
581C2×Q8—111no—
582C2×Q8—112no—
583C2×Q8—224no—
584C2×Q8—222no—
585C2×Q8—442no—
586C2×D4—42no—
587C2×D4—111no—
588C2×D4—112no—
589C2×D4—224no—
590C2×D4—221no—
591C2×D4—222no—
592C2×D4—222no—
593C2×D4—222no—
594C2×D4—222no—
595C2×D4—222no—
596C2×D4—221no—
597C2×D4—222no—
598C2×D4—221no—
599C2×D4—442no—
600C2×D4—444no—
601C2×D4—444no—
602C2×D4—444no—
603C2×D4(C2×D11)⋊C411yescharacteristic
604C2×D4(C2×D11)⋊C411yescharacteristic
605C2×D4(C2×D11)⋊C412yes—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—221no—
614C22×C4—222no—
615C22×C4—221no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—221no—
620C22×C4—444no—
621C22×C4—444no—
622C22×C4C2×C4×D1112yes—
623C22×C4C2×C4×D1112yes—
624C22×C4C2×D4412yes—
625C22×C4C2×D4412yes—
626C22×C4C2×C22⋊D1112yes—
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C2×C22⋊D1111yescharacteristic
629C22×C4C23×D1111yescharacteristic
630M16—112no—
631M16—221no—
632M16—222no—
633M16—221no—
634M16—221no—
635M16—222no—
636M16—444no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—222no—
640C2×C8—444no—
641C4⋊C4—44no—
642C4⋊C4—42no—
643C4⋊C4—111no—
644C4⋊C4—111no—
645C4⋊C4—221no—
646C4⋊C4—222no—
647C4⋊C4—221no—
648C4⋊C4—221no—
649C4⋊C4—222no—
650C4⋊C4—221no—
651C4⋊C4(C2×D11)⋊C411yescharacteristic
652C4⋊C4(C2×D11)⋊C411yescharacteristic
653C4⋊C4(C2×D11)⋊C412yes—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—222no—
657C22⋊C4—222no—
658C22⋊C4—221no—
659C22⋊C4—222no—
660C22⋊C4—222no—
661C22⋊C4—221no—
662C22⋊C4—221no—
663C22⋊C4—222no—
664C22⋊C4—222no—
665C22⋊C4(C2×D11)⋊C412yes—
666C22⋊C4(C2×D11)⋊C412yes—
667C22⋊C4(C2×D11)⋊C412yes—
668C22⋊C4(C2×D11)⋊C412yes—
669C42—21no—
670C42—22no—
671C42—22no—
672C42—21no—
673C42—21no—
674C42—42no—
675C42—42no—
676C42—221no—
677C42—221no—
678C42—221no—
679C42C2×C4×D1111yescharacteristic
680C42C2×C4×D1111yescharacteristic
681C42C2×D4411yescharacteristic
682C42C2×D4411yescharacteristic
683C42D4×D1112yescomplemented
684C11#2243511yescharacteristic, complemented, Sylow
685C23—22no—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—221no—
690C23—222no—
691C23—444no—
692C23—444no—
693C23—882no—
694C23C2×(C2×D11)⋊C412yes—
695C23C2×(C2×D11)⋊C412yes—
696C23C22×C22⋊D1111yescharacteristic
697Q8—112no—
698Q8—221no—
699Q8—222no—
700Q8—222no—
701Q8—444no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—112no—
706D4—222no—
707D4—222no—
708D4—222no—
709D4—221no—
710D4—222no—
711D4—444no—
712D4—444no—
713D4—444no—
714D4—444no—
715D4—442no—
716D4—442no—
717D4—442no—
718D4—881no—
719D4—882no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—221no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—222no—
747C2×C4—444no—
748C2×C4—444no—
749C2×C4—444no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—881no—
754C2×C4C2×(C2×D11)⋊C411yescharacteristic
755C2×C4C2×(C2×D11)⋊C411yescharacteristic
756C2×C4C2×(C2×D11)⋊C411yescharacteristic
757C2×C4C2×(C2×D11)⋊C412yes—
758C2×C4C2×(C2×D11)⋊C412yes—
759C2×C4C2×(C2×D11)⋊C411yescharacteristic
760C2×C4C22×C4×D1111yescharacteristic
761C2×C4C22×D4411yescharacteristic
762C2×C4C2×D4×D1111yescharacteristic
763C2×C4#6703711yescharacteristic
764C2×C4#41×D1111yescharacteristic
765C2×C4#6704211yescharacteristic
766C8—222no—
767C8—442no—
768C8—441no—
769C22—21no—
770C22—21no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—82no—
778C22—82no—
779C22—222no—
780C22—441no—
781C22—441no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—888no—
786C22C22×(C2×D11)⋊C411yescharacteristic
787C22D4×C22⋊D1111yescharacteristic
788C22#1062336011yescharacteristic
789C4—22no—
790C4—22no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—42no—
795C4—42no—
796C4—82no—
797C4—222no—
798C4—442no—
799C4—441no—
800C4—441no—
801C4#1062261812yescomplemented
802C4C4×D4×D1111yescharacteristic
803C4#1062307611yescharacteristic
804C4D4×D4411yescharacteristic
805C4#1062308511yescharacteristic
806C2—21no—
807C2—21no—
808C2—42no—
809C2—42no—
810C2—442no—
811C2—882no—
812C2D4×(C2×D11)⋊C411yescharacteristic
813C2C2×#1062261811yescharacteristic
814C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2293C2
socleC22×C11C22×C22⋊C4
prime radicalD4×#4339C2
cosocleC22×C4×C11C24
hypercenter#2293D11
hypocenterC11#22435
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. D4×#4318C2semidirect
3. C2×#10622618C2semidirect
4. #13069534C2semidirect
5. #13069444C2semidirect
6. #13069064C2semidirect
7. #13068916C2semidirect
8. #13068637C2semidirect
9. #13068561C2semidirect
10. C4×#66869C2semidirect
11. C11×#2293C2semidirect
14. C2×C11×#117C22semidirect
17. C22×#4318C22semidirect
18. #10623084C4semidirect
19. #10623083C4semidirect
20. #10623082C4semidirect
21. #10623081C4semidirect
22. D4×D44C4semidirect
26. D4×Dic22C4semidirect
34. C4×C11×C4⋊C4C22semidirect
35. C4×C11×C22⋊C4C22semidirect
36. C43×C11C22semidirect
37. #10622820C22semidirect
45. C2×#66869C22semidirect
46. C2×#66869C22semidirect
47. C2×#66869C22semidirect
48. C2×#66869C22semidirect
49. #10622537C22semidirect
50. C4×#4318C22semidirect
51. #10622161C22semidirect
52. #10622161C22semidirect
53. #10622161C22semidirect
151. #66869D4semidirect
246. C42×C11C2×D4semidirect
273. #4318C2×D4semidirect
281. #2293D11semidirect
391. C2×#117C2×D11semidirect
409. C4×C4⋊C4C2×D11semidirect
410. C4×C22⋊C4C2×D11semidirect
411. C43C2×D11semidirect
443. C4×C11#421semidirect
683. C42D4×D11semidirect
684. C11#22435semidirect
801. C4#10622618semidirect

Maximal subgroups

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

subgroupindex
D4×#43392
D4×#43182
C2×#106226182
#130695342
#130694442
#130690642
#130689162
#130686372
#130685612
C4×#668692
C11×#22932
#2243511