Finite Group Databasebeta

← #104×D44 #14769449

Subgroups — #104×D44 #14769449

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
1#41×D44C211yesmaximal, characteristic
2M16×D44C211yesmaximal, characteristic, complemented
3C2×D11×#104C212yesmaximal, complemented
4C42×D44C211yesmaximal, characteristic, complemented
5#13069535C211yesmaximal, characteristic, complemented
6#13069444C211yesmaximal, characteristic, complemented
7#13069058C212yesmaximal, complemented
8#13068917C212yesmaximal, complemented
9#13068636C211yesmaximal, characteristic, complemented
10#13068558C212yesmaximal, complemented
11C4×C11×#104C211yesmaximal, characteristic, complemented
12C2×#41×D11C2212yes—
13C4×C11×#41C2211yescharacteristic
14C2×M16×D11C2212yescomplemented
15#10623108C411yescharacteristic, complemented
16#10623107C412yescomplemented
17Q8×D44C411yescharacteristic, complemented
18#10623086—21no—
19#10623086C411yescharacteristic, complemented
20#10623085—22no—
21#10623085C412yescomplemented
22D4×D44—21no—
23D4×D44C411yescharacteristic, complemented
24#10623055—22no—
25#10623055C2212yes—
26#10623008—21no—
27#10623008C2211yescharacteristic
28C2×C4×D44—21no—
29C2×C4×D44—21no—
30C2×C4×D44C2211yescharacteristic
31C2×C42×D11C2212yescomplemented
32C2×C11×#104C2211yescharacteristic
33C2×C11×#104C2211yescharacteristic
34C4×C11×M16C2211yescharacteristic, complemented
35C43×C11C2211yescharacteristic, complemented
36C2×#66901C2212yes—
37C2×#66889C2212yescomplemented
38C2×#66889C2212yescomplemented
39#10622739C2212yescomplemented
40C4×(C2×D11)⋊C4—22no—
41C4×(C2×D11)⋊C4C2212yescomplemented
42C4×C4⋊Dic11—21no—
43C4×C4⋊Dic11C2211yescharacteristic, complemented
44C2×#66869C2212yescomplemented
45C2×#66869C2212yescomplemented
46#10622537C2211yescharacteristic, complemented
47D11×#104—28no—
48#10622319—22no—
49#10622301—21no—
50C8×D44—21no—
51C11×#339C2211yescharacteristic, complemented
52C11×#339C2211yescharacteristic, complemented
53#10622170C2212yescomplemented
54C2×C11×#41C2311yescharacteristic
55#41×D11—24no—
56#41×D11—24no—
57#41×D11—42no—
58#41×D11—42no—
59C2×#4343C2×C412yescomplemented
60C2×Q8×D11C2×C412yescomplemented
61C2×#4341—22no—
62C2×#4341C2×C412yescomplemented
63C2×D4×D11—22no—
64C2×D4×D11C2×C412yescomplemented
65C2×#4339—22no—
66C2×#4339C2312yes—
67C22×D44—21no—
68C22×D44D411yescharacteristic
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11C2312yes—
72C2×C11×M16C2311yescharacteristic
73C2×C11×M16C2311yescharacteristic
74C4×Q8×C11C2×C411yescharacteristic, complemented
75C4×Q8×C11C2×C411yescharacteristic, complemented
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11C2×C411yescharacteristic, complemented
79C4×D4×C11C2×C411yescharacteristic, complemented
80C11×#117—21no—
81C11×#117C2311yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88#66983—21no—
89#66983—21no—
90#66983—21no—
91#66983—22no—
92#66983—21no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4D412yes—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11D411yescharacteristic
99C2×C4×Dic11—22no—
100C2×C4×Dic11C2312yes—
101C2×#4318C2312yes—
102M16×D11—24no—
103M16×D11—42no—
104C2×#4313—22no—
105C2×C8×D11—22no—
106#66950—22no—
107#66950—22no—
108#66950C2×C412yescomplemented
109#66950C2×C412yescomplemented
110#66948—22no—
111#66948—22no—
112#66948C2×C412yescomplemented
113#66948C2×C412yescomplemented
114#66939—22no—
115#66939—22no—
116#66939—22no—
117#66935—22no—
118#66935—22no—
119#66935—22no—
120#66928—22no—
121#66928C2×C412yescomplemented
122#66927—21no—
123#66927C2×C411yescharacteristic, complemented
124C4×D44—28no—
125C4×D44—21no—
126C4×D44—22no—
127C4×D44—22no—
128C4×D44—21no—
129C4×D44—21no—
130C4×D44—22no—
131C4×D44—21no—
132C4×D44C2×C411yescharacteristic
133C4×D44C2×C412yes—
134C4×D44C2×C411yescharacteristic
135C4×D44D411yescharacteristic
136C4×D44D411yescharacteristic
137C4×D44D412yes—
138C42×D11—24no—
139C42×D11—42no—
140#66922—21no—
141#66922C2×C411yescharacteristic, complemented
142C11×#104—22no—
143C11×#104D414yescomplemented
144C11×#97—21no—
145C4×C8×C11—21no—
146#66901—24no—
147C11⋊#95—21no—
148C11⋊#95—22no—
149#66889—24no—
150#66889—42no—
151(C2×D11)⋊C8—22no—
152(C2×D11)⋊C8—22no—
153#66869—24no—
154#66869—42no—
155C4⋊(C11⋊C8)—21no—
156C4⋊(C11⋊C8)—21no—
157D4×#104—111nomaximal, Sylow
158C23×D11—22no—
159C23×D11C2×D412yes—
160C11×#41—21no—
161C11×#41—21no—
162C11×#41C2×D412yes—
163C11×#41#4112yes—
164C2×Q8×C11C22×C411yescharacteristic
165C2×D4×C11—21no—
166C2×D4×C11C22×C411yescharacteristic
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C2×C22⋊D11—22no—
176C2×C22⋊D11—22no—
177C2×C22⋊D11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11C2×D412yes—
181#4343—24no—
182#4343—42no—
183Q8×D11—24no—
184Q8×D11—42no—
185#4341—24no—
186#4341—42no—
187#4341—44no—
188#4341—44no—
189D4×D11—24no—
190D4×D11—44no—
191D4×D11—44no—
192D4×D11—42no—
193#4339—22no—
194#4339—22no—
195#4339—22no—
196#4339—22no—
197#4339—44no—
198#4339—44no—
199C2×D44—24no—
200C2×D44—22no—
201C2×D44—22no—
202C2×D44—22no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—44no—
206C2×D44C22⋊C411yescharacteristic
207C2×D44C22⋊C412yes—
208C2×D44C22⋊C411yescharacteristic
209C2×D44C22×C412yes—
210C2×C4×D11—28no—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—22no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—44no—
219C2×C4×D11—44no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11C22×C412yes—
223C2×C4×D11C22×C412yes—
224C2×C4×D11C2×D412yes—
225C2×C4×D11C2×D412yes—
226C2×Dic22—22no—
227C2×Dic22C22×C412yes—
228C11×M16—21no—
229C11×M16—21no—
230C11×M16—21no—
231C11×M16C2×D412yescomplemented
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C22×C411yescharacteristic
237C11×C4⋊C4C22×C411yescharacteristic
238C11×C22⋊C4—21no—
239C11×C22⋊C4—21no—
240C11×C22⋊C4—21no—
241C42×C11—24no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—21no—
245C42×C11—21no—
246C42×C11—21no—
247C42×C11—21no—
248C42×C11—42no—
249C42×C11C22×C411yescharacteristic
250C42×C11C22×C411yescharacteristic
251C42×C11C2×D411yescharacteristic
252C42×C11C2×D411yescharacteristic
253C42×C11C2×D412yescomplemented
254(C2×D11)⋊C4—28no—
255(C2×D11)⋊C4—22no—
256(C2×D11)⋊C4—22no—
257(C2×D11)⋊C4—22no—
258(C2×D11)⋊C4—22no—
259(C2×D11)⋊C4—22no—
260(C2×D11)⋊C4—22no—
261(C2×D11)⋊C4C22⋊C412yes—
262(C2×D11)⋊C4C22⋊C412yes—
263(C2×D11)⋊C4C22⋊C412yes—
264(C2×D11)⋊C4C22⋊C412yes—
265C4⋊Dic11—24no—
266C4⋊Dic11—22no—
267C4⋊Dic11—22no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11C22⋊C411yescharacteristic
271C4⋊Dic11C22⋊C411yescharacteristic
272C4⋊Dic11C22⋊C412yes—
273C4×Dic11—22no—
274C4×Dic11—22no—
275C4×Dic11—44no—
276#4318—22no—
277#4318—22no—
278C2×C11⋊C8—22no—
279#4313—44no—
280C8×D11—44no—
281D4×#41—111no—
282D4×M16—111no—
283C22×#104—112no—
284C42×D4—111no—
285#1980—111no—
286#1962—111no—
287#1896—112no—
288#1871—112no—
289#1806—111no—
290#1789—112no—
291C4×#104D1111yescharacteristic, complemented
292C23×C11—21no—
293C23×C11C22×D411yescharacteristic
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—24no—
297C22×D11—22no—
298C22×D11—42no—
299C22×D11—44no—
300C22×D11—44no—
301C22×D11—82no—
302C22×D11C2×C22⋊C412yes—
303C22×D11C2×C22⋊C412yes—
304Q8×C11—21no—
305Q8×C11C4×D412yescomplemented
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—21no—
309D4×C11C4×D412yescomplemented
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—21no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—42no—
324C2×C4×C11—81no—
325C2×C4×C11C2×C22⋊C411yescharacteristic
326C2×C4×C11C2×C22⋊C411yescharacteristic
327C2×C4×C11C2×C22⋊C411yescharacteristic
328C2×C4×C11C2×C22⋊C411yescharacteristic
329C2×C4×C11C23×C411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11H(5,𝔽2)11yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C22⋊D11—44no—
336C22⋊D11—44no—
337C22⋊D11—42no—
338C22⋊D11—42no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—24no—
342C2×Dic11—22no—
343C2×Dic11—44no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11C2×C22⋊C412yes—
347C2×Dic11C2×C22⋊C412yes—
348D44—24no—
349D44—22no—
350D44—22no—
351D44—22no—
352D44—44no—
353D44—44no—
354D44—42no—
355D44—81no—
356D44—82no—
357D44#10414yesdirect product factor
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—22no—
365C4×D11—22no—
366C4×D11—44no—
367C4×D11—44no—
368C4×D11—416no—
369C4×D11—42no—
370C4×D11—42no—
371Dic22—22no—
372Dic22—22no—
373Dic22—44no—
374C8×C11—22no—
375C8×C11—41no—
376C11⋊C8—42no—
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×#41C2×D1111yescharacteristic
393C2×C4×D4—111no—
394C2×C4×D4—221no—
395C2×C4×D4—221no—
396C22×C42—112no—
397#436—221no—
398#435—222no—
399C8×D4—221no—
400#423—111no—
401C2×#104—112no—
402C2×#104—112no—
403C2×#104—112no—
404C2×#104—112no—
405C2×#104—112no—
406C2×#104—228no—
407C2×#104C2×D1111yescharacteristic
408C2×#104C2×D1111yescharacteristic
409#407—112no—
410C4×M16C2×D1111yescharacteristic, complemented
411C4×C4⋊C4—111no—
412C4×C4⋊C4—221no—
413C4×C22⋊C4—112no—
414C4×C22⋊C4—222no—
415C43C2×D1111yescharacteristic, complemented
416#339—112no—
417#339C2×D1111yescharacteristic, complemented
418#339C2×D1111yescharacteristic, complemented
419C22×C11—21no—
420C22×C11—21no—
421C22×C11—22no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11C22×C22⋊C411yescharacteristic
425C22×C11D4211yescharacteristic
426C22×C11#54611yescharacteristic
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—44no—
433C2×D11—44no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—88no—
438C2×D11C2×#10414yescomplemented
439C4×C11—24no—
440C4×C11—22no—
441C4×C11—21no—
442C4×C11—21no—
443C4×C11—21no—
444C4×C11—42no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11C2×#10412yescomplemented
448C4×C11C2×C4×D411yescharacteristic
449C4×C11#51811yescharacteristic
450C4×C11D4211yescharacteristic
451C4×C11#54611yescharacteristic
452Dic11—22no—
453Dic11—22no—
454Dic11—44no—
455Dic11—42no—
456C2×#41—112no—
457C2×#41—112no—
458C2×#41—112no—
459C2×#41—222no—
460C2×#41—222no—
461C2×#41—224no—
462C2×#41—224no—
463C2×#41—442no—
464C2×#41—442no—
465C2×#41C22×D1111yescharacteristic
466C22×Q8—112no—
467C22×D4—112no—
468C22×D4—111no—
469C22×D4—221no—
470C22×D4—222no—
471C23×C4—112no—
472C23×C4—222no—
473C23×C4—222no—
474C2×M16—112no—
475C2×M16—222no—
476C2×M16—224no—
477C2×M16—442no—
478C2×M16C22×D1111yescharacteristic
479C2×M16C22×D1111yescharacteristic
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—222no—
498#121—222no—
499#121—221no—
500#121—221no—
501#121—221no—
502#121—221no—
503#120—222no—
504#120—222no—
505#120—222no—
506C4×Q8C4×D1111yescharacteristic, complemented
507C4×Q8C4×D1111yescharacteristic, complemented
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—111no—
511C4×D4—112no—
512C4×D4—111no—
513C4×D4—111no—
514C4×D4—112no—
515C4×D4—111no—
516C4×D4—222no—
517C4×D4—221no—
518C4×D4—222no—
519C4×D4—222no—
520C4×D4—221no—
521C4×D4—228no—
522C4×D4—221no—
523C4×D4—221no—
524C4×D4C4×D1111yescharacteristic, complemented
525C4×D4C4×D1111yescharacteristic, complemented
526#117—21no—
527#117C22×D1111yescharacteristic
528C2×C4⋊C4—111no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C22⋊C4—112no—
532C2×C22⋊C4—222no—
533C2×C22⋊C4—222no—
534C2×C42—21no—
535C2×C42—21no—
536C2×C42—21no—
537C2×C42—112no—
538C2×C42—224no—
539C2×C42—222no—
540C2×C42—442no—
541C2×C42C22×D1111yescharacteristic
542C2×C42C22×D1111yescharacteristic
543C2×C42C22×D1111yescharacteristic
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—22no—
547#104—224no—
548#104—224no—
549#104—224no—
550#104—442no—
551#104—442no—
552#104D4414yesdirect product factor
553C22⋊C8—222no—
554C22⋊C8—222no—
555#97—21no—
556C4×C8—21no—
557#95—222no—
558#95—221no—
559C2×C11—21no—
560C2×C11—21no—
561C2×C11—42no—
562C2×C11D4×C22⋊C411yescharacteristic
563C2×C11C22×#10411yescharacteristic
564C2×C11#290111yescharacteristic
565D11—24no—
566D11—42no—
567D11—82no—
568C24—112no—
569C24—222no—
570#41—21no—
571#41—21no—
572#41—224no—
573#41—224no—
574#41—222no—
575#41—222no—
576#41—222no—
577#41—222no—
578#41—444no—
579#41—444no—
580#41—442no—
581#41—444no—
582#41—444no—
583#41—442no—
584#41C2×D4412yes—
585#41#433912yes—
586C2×Q8—112no—
587C2×Q8—222no—
588C2×Q8—224no—
589C2×Q8—442no—
590C2×Q8C2×C4×D1111yescharacteristic
591C2×D4—21no—
592C2×D4—111no—
593C2×D4—112no—
594C2×D4—111no—
595C2×D4—112no—
596C2×D4—224no—
597C2×D4—222no—
598C2×D4—222no—
599C2×D4—222no—
600C2×D4—222no—
601C2×D4—224no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—221no—
605C2×D4—221no—
606C2×D4—444no—
607C2×D4—442no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4C2×C4×D1111yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—112no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—228no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—444no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4—444no—
635C22×C4D4×D1111yescharacteristic
636C22×C4D4×D1111yescharacteristic
637C22×C4C23×D1111yescharacteristic
638M16—21no—
639M16—21no—
640M16—21no—
641M16—222no—
642M16—222no—
643M16—444no—
644M16C2×D4412yescomplemented
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—222no—
648C2×C8—444no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—111no—
652C4⋊C4—111no—
653C4⋊C4—112no—
654C4⋊C4—222no—
655C4⋊C4—222no—
656C4⋊C4—224no—
657C4⋊C4—221no—
658C4⋊C4—221no—
659C4⋊C4C2×C4×D1111yescharacteristic
660C4⋊C4C2×C4×D1111yescharacteristic
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—112no—
665C22⋊C4—112no—
666C22⋊C4—112no—
667C22⋊C4—112no—
668C22⋊C4—222no—
669C22⋊C4—222no—
670C22⋊C4—222no—
671C22⋊C4—222no—
672C22⋊C4—228no—
673C22⋊C4—222no—
674C22⋊C4—222no—
675C42—24no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—42no—
683C42—222no—
684C42—222no—
685C42—444no—
686C42C2×C4×D1111yescharacteristic
687C42C2×C4×D1111yescharacteristic
688C42C2×D4412yescomplemented
689C42D4×D1111yescharacteristic
690C42D4×D1111yescharacteristic
691C11D4×#10411yescharacteristic, complemented, Sylow
692C23—21no—
693C23—112no—
694C23—112no—
695C23—224no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—442no—
700C23—444no—
701C23—444no—
702C23—882no—
703C23C2×D4×D1111yescharacteristic
704Q8—21no—
705Q8—222no—
706Q8—222no—
707Q8—444no—
708Q8C4×D4412yescomplemented
709D4—22no—
710D4—22no—
711D4—21no—
712D4—114no—
713D4—224no—
714D4—222no—
715D4—222no—
716D4—222no—
717D4—444no—
718D4—444no—
719D4—444no—
720D4—444no—
721D4—442no—
722D4—442no—
723D4—442no—
724D4—881no—
725D4—882no—
726D4C4×D4412yescomplemented
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—81no—
742C2×C4—112no—
743C2×C4—112no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—224no—
755C2×C4—222no—
756C2×C4—444no—
757C2×C4—444no—
758C2×C4—4416no—
759C2×C4—444no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4C22⋊C4×D1111yescharacteristic
765C2×C4C22⋊C4×D1111yescharacteristic
766C2×C4C22⋊C4×D1111yescharacteristic
767C2×C4C22⋊C4×D1111yescharacteristic
768C2×C4C22×C4×D1111yescharacteristic
769C2×C4C22×D4411yescharacteristic
770C2×C4C2×#433911yescharacteristic
771C2×C4C2×D4×D1111yescharacteristic
772C2×C4#6704211yescharacteristic
773C2×C4#6704211yescharacteristic
774C8—22no—
775C8—41no—
776C8—442no—
777C22—21no—
778C22—21no—
779C22—22no—
780C22—41no—
781C22—41no—
782C22—114no—
783C22—222no—
784C22—222no—
785C22—222no—
786C22—222no—
787C22—222no—
788C22—444no—
789C22—444no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—888no—
794C22C2×C22⋊C4×D1111yescharacteristic
795C22D4×D4411yescharacteristic
796C22#1062308111yescharacteristic
797C4—24no—
798C4—22no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—41no—
804C4—41no—
805C4—222no—
806C4—222no—
807C4—444no—
808C4—442no—
809C4D11×#10412yescomplemented
810C4C2×C4×D4411yescharacteristic
811C4#1062305211yescharacteristic
812C4D4×D4411yescharacteristic
813C4#1062308111yescharacteristic
814C2—21no—
815C2—21no—
816C2—42no—
817C2—224no—
818C2—442no—
819C2—882no—
820C2C22⋊C4×D4411yescharacteristic
821C2C2×D11×#10411yescharacteristic
822C2#1307716011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#104C2
socleC22×C11C22×C22⋊C4
prime radical#41×D44C2
cosocleC22×C4×C11C24
hypercenterC4×#104D11
hypocenterC11D4×#104
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. M16×D44C2semidirect
3. C2×D11×#104C2semidirect
4. C42×D44C2semidirect
5. #13069535C2semidirect
6. #13069444C2semidirect
7. #13069058C2semidirect
8. #13068917C2semidirect
9. #13068636C2semidirect
10. #13068558C2semidirect
11. C4×C11×#104C2semidirect
14. C2×M16×D11C22semidirect
15. #10623108C4semidirect
16. #10623107C4semidirect
17. Q8×D44C4semidirect
19. #10623086C4semidirect
21. #10623085C4semidirect
23. D4×D44C4semidirect
31. C2×C42×D11C22semidirect
34. C4×C11×M16C22semidirect
35. C43×C11C22semidirect
37. C2×#66889C22semidirect
38. C2×#66889C22semidirect
39. #10622739C22semidirect
41. C4×(C2×D11)⋊C4C22semidirect
43. C4×C4⋊Dic11C22semidirect
44. C2×#66869C22semidirect
45. C2×#66869C22semidirect
46. #10622537C22semidirect
51. C11×#339C22semidirect
52. C11×#339C22semidirect
53. #10622170C22semidirect
59. C2×#4343C2×C4semidirect
60. C2×Q8×D11C2×C4semidirect
62. C2×#4341C2×C4semidirect
64. C2×D4×D11C2×C4semidirect
74. C4×Q8×C11C2×C4semidirect
75. C4×Q8×C11C2×C4semidirect
78. C4×D4×C11C2×C4semidirect
79. C4×D4×C11C2×C4semidirect
108. #66950C2×C4semidirect
109. #66950C2×C4semidirect
112. #66948C2×C4semidirect
113. #66948C2×C4semidirect
121. #66928C2×C4semidirect
123. #66927C2×C4semidirect
141. #66922C2×C4semidirect
143. C11×#104D4semidirect
231. C11×M16C2×D4semidirect
253. C42×C11C2×D4semidirect
291. C4×#104D11semidirect
305. Q8×C11C4×D4semidirect
309. D4×C11C4×D4semidirect
357. D44#104direct (N × H)
410. C4×M16C2×D11semidirect
415. C43C2×D11semidirect
417. #339C2×D11semidirect
418. #339C2×D11semidirect
438. C2×D11C2×#104semidirect
447. C4×C11C2×#104semidirect
506. C4×Q8C4×D11semidirect
507. C4×Q8C4×D11semidirect
524. C4×D4C4×D11semidirect
525. C4×D4C4×D11semidirect
552. #104D44direct (N × H)
644. M16C2×D44semidirect
688. C42C2×D44semidirect
691. C11D4×#104semidirect
708. Q8C4×D44semidirect
726. D4C4×D44semidirect
809. C4D11×#104semidirect

Maximal subgroups

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

subgroupindex
#41×D442
M16×D442
C2×D11×#1042
C42×D442
#130695352
#130694442
#130690582
#130689172
#130686362
#130685582
C4×C11×#1042
D4×#10411