Finite Group Databasebeta

← D4×#66869 #14769448

Subgroups — D4×#66869 #14769448

Order 2816.

1608 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4339C211yesmaximal, characteristic
2D4×#4318C211yesmaximal, characteristic, complemented
3C22×#66869C212yesmaximal, complemented
4#13069534C211yesmaximal, characteristic, complemented
5#13069444C211yesmaximal, characteristic, complemented
6#13069059C212yesmaximal, complemented
7#13068916C212yesmaximal, complemented
8#13068637C211yesmaximal, characteristic, complemented
9#13068561C212yesmaximal, complemented
10C4×#66869C211yesmaximal, characteristic, complemented
11C42×D4×C11C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C22×C42×C11C2212yescomplemented
16D4×C22⋊D11—21no—
17#10623322C2212yes—
18C22×#4318C2212yescomplemented
19#10623084C411yescharacteristic, complemented
20#10623083C412yescomplemented
21#10623082C411yescharacteristic, complemented
22#10623081C412yescomplemented
23D4×D44C411yescharacteristic, complemented
24#10623079—21no—
25#10623078—22no—
26C4×D4×D11—21no—
27D4×Dic22C411yescharacteristic, complemented
28#10623038—21no—
29#10623021—22no—
30#10623008C2211yescharacteristic
31C4×#4339C2211yescharacteristic
32C4×C11×C4⋊C4—21no—
33C4×C11×C4⋊C4C2211yescharacteristic, complemented
34C4×C11×C22⋊C4—22no—
35C4×C11×C22⋊C4C2212yescomplemented
36C43×C11C2211yescharacteristic, complemented
37#10622820C2212yescomplemented
38#10622625—21no—
39#10622624—22no—
40D4×C11⋊C8—21no—
41C2×#66869—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×C11—22no—
56C23×C4×C11C2312yes—
57C22×C22⋊D11—22no—
58C2×D4×D11—21no—
59C2×#4339—22no—
60C2×#4339—22no—
61C2×#4339—24no—
62C2×#4339—24no—
63C2×#4339—42no—
64C2×#4339—42no—
65C2×#4339C2×C412yescomplemented
66C2×#4339C2×C412yescomplemented
67C2×#4339C2312yes—
68C2×#4339C2311yescharacteristic
69C22×D44C2×C412yescomplemented
70C22×C4×D11—22no—
71C22×Dic22C2×C412yescomplemented
72C4×D4×C11—28no—
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2×C412yes—
75C4×D4×C11C2×C411yescharacteristic
76C4×D4×C11D411yescharacteristic
77C4×D4×C11D412yes—
78C4×D4×C11D411yescharacteristic
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4D412yes—
83C2×C42×C11—21no—
84C2×C42×C11—24no—
85C2×C42×C11—22no—
86C2×C42×C11—21no—
87C2×C42×C11—42no—
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92#67006—22no—
93#66993—21no—
94#66992—22no—
95#66991—21no—
96#66990—22no—
97D4×Dic11—21no—
98#66983—21no—
99#66983—21no—
100#66983C2×C412yescomplemented
101#66983C2×C412yescomplemented
102#66982—22no—
103C4×C22⋊D11—21no—
104C4×C22⋊D11—21no—
105C4×C22⋊D11—22no—
106C4×C22⋊D11—22no—
107#66979C2311yescharacteristic
108#66977C2×C412yescomplemented
109#66977C2×C412yescomplemented
110C2×#4318—22no—
111C2×#4318—24no—
112C2×#4318—42no—
113C2×#4318C2311yescharacteristic
114C2×#4318C2312yes—
115C2×#4318C2311yescharacteristic
116C22×C11⋊C8—22no—
117#66949—22no—
118#66948—21no—
119#66947—22no—
120#66946—21no—
121C4⋊C4×D11—21no—
122#66941—21no—
123#66938—22no—
124#66937—22no—
125#66937—22no—
126#66936—22no—
127#66935—22no—
128(C22⋊D11)⋊C4—22no—
129C22⋊C4×D11—22no—
130#66931—22no—
131#66928C2×C412yescomplemented
132#66927C2×C411yescharacteristic, complemented
133C4×D44—21no—
134C4×D44—21no—
135C4×D44C2×C411yescharacteristic, complemented
136C4×D44C2×C411yescharacteristic, complemented
137#66925—21no—
138C42×D11—21no—
139#66922C2×C411yescharacteristic, complemented
140C4×Dic22C2×C411yescharacteristic, complemented
141C4×Dic22C2×C411yescharacteristic, complemented
142C11×#95—21no—
143C11×#95—22no—
144C22⋊(C11⋊C8)—22no—
145C22⋊(C11⋊C8)—22no—
146#66869—24no—
147#66869—22no—
148#66869—24no—
149#66869—24no—
150#66869—42no—
151#66869—42no—
152#66869D414yesdirect product factor
153C4⋊(C11⋊C8)—21no—
154C4⋊(C11⋊C8)—21no—
155#66867—21no—
156C4×C11⋊C8—21no—
157D4×#104—111nomaximal, Sylow
158C24×C11C2×D412yes—
159C23×D11—22no—
160C2×D4×C11—24no—
161C2×D4×C11C22⋊C412yes—
162C2×D4×C11C22⋊C411yescharacteristic
163C2×D4×C11C22⋊C411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—28no—
170C22×C4×C11—21no—
171C22×C4×C11—22no—
172C22×C4×C11—44no—
173C22×C4×C11—44no—
174C22×C4×C11C22×C412yes—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C2×C22⋊D11—22no—
183C2×C22⋊D11—22no—
184C2×C22⋊D11—22no—
185C2×C22⋊D11—22no—
186C2×C22⋊D11—21no—
187C2×C22⋊D11—22no—
188C2×C22⋊D11—44no—
189C2×C22⋊D11—44no—
190C22×Dic11—22no—
191D4×D11—44no—
192#4339—24no—
193#4339—24no—
194#4339—22no—
195#4339—22no—
196#4339—21no—
197#4339—21no—
198#4339—22no—
199#4339—22no—
200#4339—42no—
201#4339—42no—
202#4339—44no—
203#4339—44no—
204#4339—44no—
205#4339—44no—
206#4339C2×D412yes—
207#4339#4112yes—
208C2×D44—24no—
209C2×D44—21no—
210C2×D44—22no—
211C2×D44—21no—
212C2×D44—42no—
213C2×D44C22×C412yes—
214C2×D44C22×C411yescharacteristic
215C2×C4×D11—21no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—21no—
219C2×C4×D11—21no—
220C2×C4×D11—22no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C2×Dic22—24no—
224C2×Dic22—22no—
225C2×Dic22—42no—
226C2×Dic22C22×C412yes—
227C2×Dic22C22×C411yescharacteristic
228C11×C4⋊C4—24no—
229C11×C4⋊C4C22⋊C411yescharacteristic
230C11×C4⋊C4C22⋊C411yescharacteristic
231C11×C4⋊C4C22⋊C412yes—
232C11×C22⋊C4—28no—
233C11×C22⋊C4C22⋊C412yes—
234C11×C22⋊C4C22⋊C412yes—
235C11×C22⋊C4C22⋊C412yes—
236C11×C22⋊C4C22⋊C412yes—
237C42×C11—24no—
238C42×C11—21no—
239C42×C11—22no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—22no—
243C42×C11—44no—
244C42×C11—42no—
245C42×C11C22×C411yescharacteristic
246C42×C11C22×C411yescharacteristic
247C42×C11C2×D411yescharacteristic
248C42×C11C2×D411yescharacteristic
249C42×C11C2×D412yescomplemented
250C22⋊Dic11—22no—
251C22⋊Dic11—22no—
252C22⋊Dic11—21no—
253(C2×D11)⋊C4—21no—
254(C2×D11)⋊C4—21no—
255(C2×D11)⋊C4—22no—
256(C2×D11)⋊C4—22no—
257(C2×D11)⋊C4—22no—
258(C2×D11)⋊C4—22no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11C22×C411yescharacteristic
262C4⋊Dic11C22×C411yescharacteristic
263Dic11⋊C4—21no—
264Dic11⋊C4—21no—
265Dic11⋊C4—22no—
266Dic11⋊C4—22no—
267C4×Dic11—21no—
268C4×Dic11—21no—
269C4×Dic11—21no—
270#4318—22no—
271#4318—21no—
272#4318—21no—
273#4318—21no—
274#4318—22no—
275#4318—44no—
276#4318C2×D412yescomplemented
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8—44no—
281D4×#41—111no—
282D4×M16—111no—
283C22×#104—112no—
284C42×D4D1111yescharacteristic, complemented
285#1980—111no—
286#1962—111no—
287#1896—112no—
288#1871—112no—
289#1806—111no—
290#1789—112no—
291C4×#104—111no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—24no—
295C23×C11—42no—
296C23×C11C2×C22⋊C412yes—
297C23×C11C2×C22⋊C412yes—
298C23×C11C22×D411yescharacteristic
299C22×D11—21no—
300C22×D11—22no—
301C22×D11—44no—
302C22×D11—44no—
303C22×D11—82no—
304D4×C11—24no—
305D4×C11—22no—
306D4×C11#10414yescomplemented
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—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—41no—
324C2×C4×C11—416no—
325C2×C4×C11—41no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—41no—
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C2×C22⋊C411yescharacteristic
332C2×C4×C11C2×C22⋊C412yes—
333C2×C4×C11C2×C22⋊C412yes—
334C2×C4×C11C2×C22⋊C411yescharacteristic
335C2×C4×C11C23×C411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C22⋊D11—22no—
342C22⋊D11—22no—
343C22⋊D11—44no—
344C22⋊D11—44no—
345C22⋊D11—42no—
346C22⋊D11—42no—
347C22⋊D11—44no—
348C22⋊D11—82no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—22no—
353C2×Dic11—44no—
354D44—22no—
355D44—21no—
356D44—22no—
357D44—44no—
358D44—42no—
359D44—81no—
360D44C4×D412yescomplemented
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—44no—
364C4×D11—44no—
365C4×D11—42no—
366C4×D11—42no—
367C4×D11—42no—
368C4×D11—81no—
369Dic22—21no—
370Dic22—22no—
371Dic22—22no—
372Dic22—44no—
373Dic22C4×D412yescomplemented
374C11⋊C8—22no—
375C11⋊C8—42no—
376C11⋊C8—41no—
377C22×#41—112no—
378C22×M16—112no—
379#550—111no—
380D4×Q8—111no—
381#548—112no—
382#547—111no—
383#547—221no—
384#546—112no—
385#546—222no—
386D42—111no—
387D42—221no—
388#532—111no—
389#532—221no—
390#525—112no—
391#525—222no—
392C4×#41—111no—
393C2×C4×D4—21no—
394C2×C4×D4—221no—
395C2×C4×D4C2×D1111yescharacteristic
396C22×C42C2×D1112yescomplemented
397#436—221no—
398#435—222no—
399C8×D4—221no—
400#423—111no—
401C2×#104—111no—
402C2×#104—112no—
403C2×#104—111no—
404C2×#104—112no—
405C2×#104—112no—
406C2×#104—112no—
407C2×#104—112no—
408C2×#104—228no—
409#407—112no—
410C4×M16—111no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4C2×D1111yescharacteristic, complemented
413C4×C22⋊C4—22no—
414C4×C22⋊C4C2×D1112yescomplemented
415C43C2×D1111yescharacteristic, complemented
416#339—112no—
417#339—111no—
418#339—111no—
419C22×C11—22no—
420C22×C11—21no—
421C22×C11—21no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—44no—
427C22×C11—44no—
428C22×C11C2×#10414yescomplemented
429C22×C11C22×C22⋊C411yescharacteristic
430C22×C11D4211yescharacteristic
431C22×C11#54611yescharacteristic
432C2×D11—22no—
433C2×D11—41no—
434C2×D11—41no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—88no—
439C4×C11—24no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—21no—
443C4×C11—21no—
444C4×C11—21no—
445C4×C11—42no—
446C4×C11—44no—
447C4×C11C2×#10412yescomplemented
448C4×C11C2×C4×D411yescharacteristic
449C4×C11#51811yescharacteristic
450C4×C11D4211yescharacteristic
451C4×C11#54611yescharacteristic
452Dic11—22no—
453Dic11—42no—
454Dic11—41no—
455Dic11—41no—
456C2×#41—112no—
457C2×#41—112no—
458C2×#41—111no—
459C2×#41—112no—
460C2×#41—224no—
461C2×#41—224no—
462C2×#41—222no—
463C2×#41—222no—
464C2×#41—442no—
465C2×#41—442no—
466C22×Q8—112no—
467C22×D4—112no—
468C22×D4—222no—
469C22×D4—221no—
470C22×D4C22⋊D1111yescharacteristic
471C23×C4—22no—
472C23×C4—222no—
473C23×C4C22×D1112yes—
474C2×M16—111no—
475C2×M16—112no—
476C2×M16—111no—
477C2×M16—222no—
478C2×M16—224no—
479C2×M16—442no—
480C22×C8—222no—
481C4⋊Q8—111no—
482C4⋊Q8—221no—
483#127—111no—
484#127—221no—
485#124—112no—
486#124—222no—
487#123—222no—
488#123—222no—
489#123—222no—
490C22⋊Q8—112no—
491C22⋊Q8—112no—
492C22⋊Q8—222no—
493C22⋊Q8—222no—
494#121—112no—
495#121—112no—
496#121—222no—
497#121—221no—
498#121—221no—
499#121—221no—
500#121—221no—
501#121—222no—
502#121—222no—
503#120—222no—
504#120—222no—
505#120—222no—
506C4×Q8—111no—
507C4×Q8—111no—
508C4×D4—28no—
509C4×D4—111no—
510C4×D4—111no—
511C4×D4—221no—
512C4×D4—222no—
513C4×D4—222no—
514C4×D4—221no—
515C4×D4—221no—
516C4×D4—221no—
517C4×D4—222no—
518C4×D4—221no—
519C4×D4—221no—
520C4×D4C4×D1111yescharacteristic
521C4×D4C4×D1112yes—
522C4×D4C4×D1111yescharacteristic
523C4×D4D4411yescharacteristic
524C4×D4D4412yes—
525C4×D4D4411yescharacteristic
526#117—111no—
527#117—221no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4C22⋊D1111yescharacteristic
531C2×C22⋊C4—22no—
532C2×C22⋊C4—222no—
533C2×C22⋊C4C22⋊D1112yes—
534C2×C42—21no—
535C2×C42—24no—
536C2×C42—21no—
537C2×C42—22no—
538C2×C42—42no—
539C2×C42—221no—
540C2×C42C22×D1111yescharacteristic
541C2×C42C22×D1112yes—
542C2×C42C22×D1111yescharacteristic
543C2×C42C22×D1111yescharacteristic
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—114no—
547#104—224no—
548#104—222no—
549#104—224no—
550#104—224no—
551#104—442no—
552#104—442no—
553C22⋊C8—222no—
554C22⋊C8—222no—
555#97—221no—
556C4×C8—221no—
557#95—21no—
558#95—22no—
559C2×C11—21no—
560C2×C11—21no—
561C2×C11—24no—
562C2×C11—42no—
563C2×C11D4×C22⋊C411yescharacteristic
564C2×C11C22×#10411yescharacteristic
565C2×C11#290111yescharacteristic
566D11—42no—
567D11—82no—
568C24—222no—
569C24C2×C22⋊D1112yes—
570#41—112no—
571#41—112no—
572#41—224no—
573#41—224no—
574#41—221no—
575#41—221no—
576#41—222no—
577#41—222no—
578#41—222no—
579#41—222no—
580#41—444no—
581#41—444no—
582#41—442no—
583#41—442no—
584#41—444no—
585#41—444no—
586C2×Q8—111no—
587C2×Q8—112no—
588C2×Q8—224no—
589C2×Q8—222no—
590C2×Q8—442no—
591C2×D4—24no—
592C2×D4—111no—
593C2×D4—112no—
594C2×D4—224no—
595C2×D4—221no—
596C2×D4—222no—
597C2×D4—222no—
598C2×D4—222no—
599C2×D4—222no—
600C2×D4—222no—
601C2×D4—221no—
602C2×D4—222no—
603C2×D4—221no—
604C2×D4—442no—
605C2×D4—444no—
606C2×D4—444no—
607C2×D4—444no—
608C2×D4(C2×D11)⋊C412yes—
609C2×D4(C2×D11)⋊C411yescharacteristic
610C2×D4(C2×D11)⋊C411yescharacteristic
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—28no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—221no—
622C22×C4—222no—
623C22×C4—221no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—221no—
628C22×C4—444no—
629C22×C4—444no—
630C22×C4C2×C4×D1112yes—
631C22×C4C2×C4×D1112yes—
632C22×C4C2×D4412yes—
633C22×C4C2×D4412yes—
634C22×C4C2×C22⋊D1112yes—
635C22×C4C2×C22⋊D1111yescharacteristic
636C22×C4C2×C22⋊D1111yescharacteristic
637C22×C4C23×D1111yescharacteristic
638M16—112no—
639M16—221no—
640M16—222no—
641M16—221no—
642M16—221no—
643M16—222no—
644M16—444no—
645C2×C8—221no—
646C2×C8—221no—
647C2×C8—222no—
648C2×C8—444no—
649C4⋊C4—24no—
650C4⋊C4—111no—
651C4⋊C4—111no—
652C4⋊C4—221no—
653C4⋊C4—222no—
654C4⋊C4—221no—
655C4⋊C4—221no—
656C4⋊C4—222no—
657C4⋊C4—221no—
658C4⋊C4(C2×D11)⋊C411yescharacteristic
659C4⋊C4(C2×D11)⋊C411yescharacteristic
660C4⋊C4(C2×D11)⋊C412yes—
661C22⋊C4—28no—
662C22⋊C4—222no—
663C22⋊C4—222no—
664C22⋊C4—221no—
665C22⋊C4—222no—
666C22⋊C4—222no—
667C22⋊C4—221no—
668C22⋊C4—221no—
669C22⋊C4—222no—
670C22⋊C4—222no—
671C22⋊C4(C2×D11)⋊C412yes—
672C22⋊C4(C2×D11)⋊C412yes—
673C22⋊C4(C2×D11)⋊C412yes—
674C22⋊C4(C2×D11)⋊C412yes—
675C42—24no—
676C42—21no—
677C42—22no—
678C42—22no—
679C42—21no—
680C42—21no—
681C42—44no—
682C42—42no—
683C42—221no—
684C42—221no—
685C42—221no—
686C42C2×C4×D1111yescharacteristic
687C42C2×C4×D1111yescharacteristic
688C42C2×D4411yescharacteristic
689C42C2×D4411yescharacteristic
690C42D4×D1112yescomplemented
691C11D4×#10411yescharacteristic, complemented, Sylow
692C23—24no—
693C23—22no—
694C23—22no—
695C23—42no—
696C23—221no—
697C23—222no—
698C23—444no—
699C23—444no—
700C23—882no—
701C23C2×(C2×D11)⋊C412yes—
702C23C2×(C2×D11)⋊C412yes—
703C23C22×C22⋊D1111yescharacteristic
704Q8—112no—
705Q8—221no—
706Q8—222no—
707Q8—222no—
708Q8—444no—
709D4—24no—
710D4—22no—
711D4—112no—
712D4—222no—
713D4—222no—
714D4—222no—
715D4—221no—
716D4—222no—
717D4—444no—
718D4—444no—
719D4—444no—
720D4—444no—
721D4—442no—
722D4—442no—
723D4—442no—
724D4—881no—
725D4—882no—
726D4#6686914yesdirect product factor
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—41no—
744C2×C4—416no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—221no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—221no—
753C2×C4—221no—
754C2×C4—222no—
755C2×C4—444no—
756C2×C4—444no—
757C2×C4—444no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—881no—
762C2×C4C2×(C2×D11)⋊C411yescharacteristic
763C2×C4C2×(C2×D11)⋊C411yescharacteristic
764C2×C4C2×(C2×D11)⋊C411yescharacteristic
765C2×C4C2×(C2×D11)⋊C412yes—
766C2×C4C2×(C2×D11)⋊C412yes—
767C2×C4C2×(C2×D11)⋊C411yescharacteristic
768C2×C4C22×C4×D1111yescharacteristic
769C2×C4C22×D4411yescharacteristic
770C2×C4C2×D4×D1111yescharacteristic
771C2×C4#6703711yescharacteristic
772C2×C4#41×D1111yescharacteristic
773C2×C4#6704211yescharacteristic
774C8—222no—
775C8—442no—
776C8—441no—
777C22—22no—
778C22—21no—
779C22—21no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—44no—
785C22—44no—
786C22—222no—
787C22—441no—
788C22—441no—
789C22—442no—
790C22—442no—
791C22—442no—
792C22—888no—
793C22C2×#6686914yescomplemented
794C22C22×(C2×D11)⋊C411yescharacteristic
795C22D4×C22⋊D1111yescharacteristic
796C22#1062336011yescharacteristic
797C4—24no—
798C4—22no—
799C4—22no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—44no—
804C4—42no—
805C4—222no—
806C4—442no—
807C4—441no—
808C4—441no—
809C4C2×#6686912yescomplemented
810C4C4×D4×D1111yescharacteristic
811C4#1062307611yescharacteristic
812C4D4×D4411yescharacteristic
813C4#1062308511yescharacteristic
814C2—21no—
815C2—21no—
816C2—24no—
817C2—42no—
818C2—442no—
819C2—882no—
820C2D4×(C2×D11)⋊C411yescharacteristic
821C2C22×#6686911yescharacteristic
822C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC42×D4×C11C2
socleC22×C11C22×C22⋊C4
prime radicalD4×#4339C2
cosocleC22×C4×C11C24
hypercenterC42×D4D11
hypocenterC11D4×#104
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. D4×#4318C2semidirect
3. C22×#66869C2semidirect
4. #13069534C2semidirect
5. #13069444C2semidirect
6. #13069059C2semidirect
7. #13068916C2semidirect
8. #13068637C2semidirect
9. #13068561C2semidirect
10. C4×#66869C2semidirect
11. C42×D4×C11C2semidirect
15. C22×C42×C11C22semidirect
18. C22×#4318C22semidirect
19. #10623084C4semidirect
20. #10623083C4semidirect
21. #10623082C4semidirect
22. #10623081C4semidirect
23. D4×D44C4semidirect
27. D4×Dic22C4semidirect
33. 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
65. C2×#4339C2×C4semidirect
66. C2×#4339C2×C4semidirect
69. C22×D44C2×C4semidirect
71. C22×Dic22C2×C4semidirect
100. #66983C2×C4semidirect
101. #66983C2×C4semidirect
108. #66977C2×C4semidirect
109. #66977C2×C4semidirect
131. #66928C2×C4semidirect
132. #66927C2×C4semidirect
135. C4×D44C2×C4semidirect
136. C4×D44C2×C4semidirect
139. #66922C2×C4semidirect
140. C4×Dic22C2×C4semidirect
141. C4×Dic22C2×C4semidirect
152. #66869D4direct (N × H)
249. C42×C11C2×D4semidirect
276. #4318C2×D4semidirect
284. C42×D4D11semidirect
306. D4×C11#104semidirect
360. D44C4×D4semidirect
373. Dic22C4×D4semidirect
396. C22×C42C2×D11semidirect
412. C4×C4⋊C4C2×D11semidirect
414. C4×C22⋊C4C2×D11semidirect
415. C43C2×D11semidirect
428. C22×C11C2×#104semidirect
447. C4×C11C2×#104semidirect
690. C42D4×D11semidirect
691. C11D4×#104semidirect
726. D4#66869direct (N × H)
793. C22C2×#66869semidirect
809. C4C2×#66869semidirect

Maximal subgroups

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

subgroupindex
D4×#43392
D4×#43182
C22×#668692
#130695342
#130694442
#130690592
#130689162
#130686372
#130685612
C4×#668692
C42×D4×C112
D4×#10411