Finite Group Databasebeta

← D11×#1486 #14720164

Subgroups — D11×#1486 #14720164

Order 2816.

1714 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2D11×#431C211yesmaximal, characteristic, complemented
3D11×#423C211yesmaximal, characteristic, complemented
4#13067042C211yesmaximal, characteristic, complemented
5#13067041C211yesmaximal, characteristic, complemented
6#13067040C211yesmaximal, characteristic, complemented
7#13067039C214yesmaximal, complemented
8D11×D4⋊C8C214yesmaximal, complemented
9C11×#1486C211yesmaximal, characteristic, complemented
10C22×D4×D11C411yescharacteristic
11C23×C4×D11—21no—
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11C411yescharacteristic
14C2×C4×C22⋊D11—21no—
15C2×M16×D11—21no—
16C4×D4×D11—21no—
17C4×D4×D11—21no—
18C4×D4×D11—21no—
19C4×D4×D11—21no—
20C4×D4×D11C412yes—
21C4×D4×D11C412yes—
22C4×D4×D11C2212yes—
23C4×D4×D11C2212yes—
24C2×#66946C411yescharacteristic
25C2×C4⋊C4×D11C411yescharacteristic
26C2×(C22⋊D11)⋊C4—21no—
27C2×C22⋊C4×D11—21no—
28C2×C4×D44C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C11×#431C2211yescharacteristic, complemented
31C11×#423C2211yescharacteristic, complemented
32#10622731—21no—
33#10622538C2211yescharacteristic, complemented
34#10622537C2211yescharacteristic, complemented
35#10622450—21no—
36#10622450C2212yescomplemented
37#10622446—21no—
38D11×C4⋊C8—21no—
39D11×C4⋊C8—21no—
40D11×C4⋊C8C2212yescomplemented
41D11×C22⋊C8—21no—
42#10622331—21no—
43#10622298C2212yescomplemented
44C4×C8×D11C2212yescomplemented
45C11×D4⋊C8C2214yescomplemented
46D4⋊(C11⋊C8)C2214yescomplemented
47#10622121C2214yescomplemented
48#10622097C2214yescomplemented
49C24×D11—21no—
50C22×D4×C11C2×C411yescharacteristic
51C23×C4×C11—21no—
52C22×C22⋊D11—21no—
53C23×Dic11—21no—
54C2×D4×D11—28no—
55C2×D4×D11—21no—
56C2×D4×D11—21no—
57C2×D4×D11C2×C412yes—
58C2×D4×D11C2×C412yes—
59C22×D44C2×C411yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11—44no—
68C22×C4×D11—44no—
69C22×C4×D11C2×C411yescharacteristic
70C22×C4×D11D411yescharacteristic
71C22×C4×D11D411yescharacteristic
72C2×C11×M16—21no—
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11C2×C412yes—
76C4×D4×C11C2312yes—
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81D4×Dic11—21no—
82D4×Dic11—21no—
83D4×Dic11C2×C412yes—
84D4×Dic11C2×C412yes—
85C4×C22⋊D11—22no—
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88C4×C22⋊D11—22no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×C4⋊Dic11C2×C411yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11C2×C411yescharacteristic
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×#4318—21no—
97M16×D11—44no—
98C2×#4313—22no—
99C2×C8×D11—22no—
100C2×C8×D11—22no—
101#66946—21no—
102#66946—21no—
103#66946C2×C412yes—
104#66946C2×C412yes—
105C4⋊C4×D11—21no—
106C4⋊C4×D11—21no—
107C4⋊C4×D11C2×C412yes—
108C4⋊C4×D11C2×C412yes—
109(C22⋊D11)⋊C4—22no—
110(C22⋊D11)⋊C4—22no—
111(C22⋊D11)⋊C4—22no—
112(C22⋊D11)⋊C4—22no—
113C22⋊C4×D11—22no—
114C22⋊C4×D11—22no—
115C22⋊C4×D11—22no—
116C22⋊C4×D11—22no—
117C4×D44—21no—
118C4×D44—21no—
119C4×D44C2×C412yes—
120C4×D44C2312yes—
121C42×D11C2×C411yescharacteristic
122C42×D11C2×C411yescharacteristic
123C42×D11D411yescharacteristic
124C42×D11D411yescharacteristic
125C42×D11D411yescharacteristic
126C42×D11D411yescharacteristic
127C42×D11C2311yescharacteristic
128C42×D11C2311yescharacteristic
129C11×C4⋊C8—21no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8C2312yescomplemented
132C11×C22⋊C8—21no—
133C4×C8×C11C2312yescomplemented
134C22⋊(C11⋊C8)—21no—
135(C2×D11)⋊C8—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138Dic11⋊C8—22no—
139C8×Dic11—22no—
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)C2312yescomplemented
143C4×C11⋊C8C2312yescomplemented
144C2×#1486—111nomaximal, Sylow
145C24×C11—21no—
146C23×D11—28no—
147C23×D11—21no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—44no—
151C23×D11—44no—
152C23×D11C22⋊C411yescharacteristic
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11C22×C412yes—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C2×C22⋊D11—28no—
165C2×C22⋊D11—22no—
166C2×C22⋊D11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—44no—
171C22×Dic11C22⋊C411yescharacteristic
172C22×Dic11C22⋊C411yescharacteristic
173C22×Dic11C22⋊C411yescharacteristic
174D4×D11—28no—
175D4×D11—28no—
176D4×D11—24no—
177D4×D11—24no—
178D4×D11—24no—
179D4×D11M1618yescomplemented
180C2×D44—24no—
181C2×D44—21no—
182C2×D44C22×C412yes—
183C2×C4×D11—24no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—22no—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11—42no—
191C2×C4×D11—44no—
192C2×C4×D11—48no—
193C2×C4×D11—48no—
194C2×C4×D11—44no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11—44no—
198C2×C4×D11—44no—
199C2×C4×D11—42no—
200C2×C4×D11—42no—
201C2×C4×D11C22⋊C411yescharacteristic
202C2×C4×D11C22⋊C411yescharacteristic
203C2×C4×D11C22⋊C411yescharacteristic
204C2×C4×D11C22⋊C411yescharacteristic
205C2×C4×D11C22⋊C411yescharacteristic
206C2×C4×D11C22⋊C411yescharacteristic
207C2×C4×D11D814yes—
208C2×C4×D11SD1614yes—
209C2×C4×D11C22×C411yescharacteristic
210C2×C4×D11C22×C411yescharacteristic
211C2×C4×D11C2×D411yescharacteristic
212C2×C4×D11C2×D411yescharacteristic
213C2×C4×D11C2×D411yescharacteristic
214C2×C4×D11C2×D411yescharacteristic
215C11×M16—42no—
216C2×C8×C11—22no—
217C2×C8×C11—22no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4C22×C412yes—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C42×C11C22×C411yescharacteristic
223C42×C11C2×D411yescharacteristic
224C42×C11C2×D411yescharacteristic
225C42×C11C2411yescharacteristic
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—22no—
231(C2×D11)⋊C4—22no—
232C4⋊Dic11—21no—
233C4⋊Dic11C22×C412yes—
234Dic11⋊C4—22no—
235Dic11⋊C4—22no—
236C4×Dic11C22⋊C411yescharacteristic
237C4×Dic11C22⋊C411yescharacteristic
238C4×Dic11C22⋊C411yescharacteristic
239C4×Dic11C22⋊C411yescharacteristic
240C4×Dic11C22⋊C411yescharacteristic
241C4×Dic11C22⋊C411yescharacteristic
242C4×Dic11C22×C411yescharacteristic
243C4×Dic11C22×C411yescharacteristic
244C4×Dic11C2×D411yescharacteristic
245C4×Dic11C2×D411yescharacteristic
246C4×Dic11C2×D411yescharacteristic
247C4×Dic11C2×D411yescharacteristic
248#4318—42no—
249C2×C11⋊C8—22no—
250C2×C11⋊C8—22no—
251#4313—44no—
252C8×D11—44no—
253C8×D11—44no—
254C22×C4×D4—111no—
255C2×#431—111no—
256C2×#423—111no—
257#1486—111no—
258#1486—111no—
259#1486—114no—
260#1486—111no—
261#1486D1111yescharacteristic, direct product factor
262C2×D4⋊C8—114no—
263C23×C11—24no—
264C23×C11—22no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11C2×C22⋊C411yescharacteristic
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—24no—
271C22×D11—28no—
272C22×D11—22no—
273C22×D11—28no—
274C22×D11—44no—
275C22×D11—432no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—44no—
279C22×D11—44no—
280C22×D11—44no—
281C22×D11#10214yes—
282C22×D11C2×C22⋊C411yescharacteristic
283C22×D11C2×C22⋊C411yescharacteristic
284D4×C11—24no—
285D4×C11—22no—
286D4×C11C2×M1614yescomplemented
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—44no—
294C2×C4×C11C2×C22⋊C411yescharacteristic
295C2×C4×C11C2×C22⋊C411yescharacteristic
296C2×C4×C11C2×C22⋊C411yescharacteristic
297C2×C4×C11C2×D812yes—
298C2×C4×C11C2×SD1612yes—
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C22⋊D11—28no—
303C22⋊D11—28no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—41no—
307C2×Dic11—42no—
308C2×Dic11—44no—
309C2×Dic11—44no—
310C2×Dic11#10214yes—
311C2×Dic11C2×C22⋊C411yescharacteristic
312C2×Dic11C2×C22⋊C411yescharacteristic
313C2×Dic11C2×C22⋊C411yescharacteristic
314C2×Dic11C2×C22⋊C411yescharacteristic
315C2×Dic11C2×C22⋊C411yescharacteristic
316C2×Dic11C2×C22⋊C411yescharacteristic
317D44—24no—
318D44—22no—
319D44C2×M1614yescomplemented
320C4×D11—22no—
321C4×D11—22no—
322C4×D11—22no—
323C4×D11—22no—
324C4×D11—22no—
325C4×D11—41no—
326C4×D11—41no—
327C4×D11—44no—
328C4×D11—44no—
329C4×D11—42no—
330C4×D11—42no—
331C4×D11—44no—
332C4×D11—44no—
333C4×D11—44no—
334C4×D11#10214yes—
335C4×D11#10214yes—
336C4×D11C2×M1614yes—
337C4×D11C2×D812yes—
338C4×D11C2×D812yes—
339C4×D11C2×SD1612yes—
340C4×D11C2×SD1612yes—
341C8×C11—42no—
342C8×C11—42no—
343C11⋊C8—42no—
344C11⋊C8—42no—
345C23×D4—111no—
346C24×C4—221no—
347C22×M16—221no—
348C2×C4×D4—111no—
349C2×C4×D4—112no—
350C2×C4×D4—112no—
351C2×C4×D4—112no—
352C2×C4×D4—112no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4—221no—
356C2×C4×D4—221no—
357C2×C4×D4—221no—
358C2×C4×D4—221no—
359C2×C4×D4—221no—
360C2×C4×D4—221no—
361C2×C4×D4C2×D1111yescharacteristic
362C22×C4⋊C4—111no—
363C22×C22⋊C4—221no—
364C22×C42—111no—
365#431—111no—
366#431—112no—
367#431—221no—
368#431—221no—
369#431C2×D1111yescharacteristic, complemented
370#423—111no—
371#423—112no—
372#423—221no—
373#423—221no—
374#423C2×D1111yescharacteristic, complemented
375C2×C4⋊C8—112no—
376C2×C4⋊C8—221no—
377C2×C4⋊C8—221no—
378C2×C22⋊C8—221no—
379C2×C4×C8—112no—
380D4⋊C8—114no—
381D4⋊C8—114no—
382D4⋊C8—114no—
383D4⋊C8C2×D1114yescomplemented
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—24no—
387C22×C11—48no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11C2×#10212yes—
391C22×C11C22×C22⋊C411yescharacteristic
392C2×D11—21no—
393C2×D11—21no—
394C2×D11—28no—
395C2×D11—24no—
396C2×D11—416no—
397C2×D11—48no—
398C2×D11—42no—
399C2×D11—42no—
400C2×D11—416no—
401C2×D11#40712yes—
402C2×D11C2×#10212yes—
403C2×D11C2×#10212yes—
404C2×D11#42112yes—
405C4×C11—21no—
406C4×C11—21no—
407C4×C11—21no—
408C4×C11—42no—
409C4×C11C2×#10212yes—
410C4×C11C22×M1612yes—
411C4×C11C22×D811yescharacteristic
412C4×C11C22×SD1611yescharacteristic
413Dic11—21no—
414Dic11—21no—
415Dic11—21no—
416Dic11—42no—
417Dic11#40712yes—
418Dic11C2×#10212yes—
419Dic11C2×#10212yes—
420C25—221no—
421C22×D4—112no—
422C22×D4—112no—
423C22×D4—111no—
424C22×D4—221no—
425C22×D4—221no—
426C22×D4—221no—
427C22×D4—228no—
428C22×D4C4×D1111yescharacteristic
429C23×C4—21no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—111no—
433C23×C4—221no—
434C23×C4—222no—
435C23×C4—222no—
436C23×C4—222no—
437C23×C4—222no—
438C23×C4—221no—
439C23×C4—221no—
440C23×C4—221no—
441C23×C4—444no—
442C23×C4—444no—
443C2×M16—21no—
444C2×M16—222no—
445C2×M16—221no—
446C2×M16—444no—
447C22×C8—222no—
448C22×C8—222no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—112no—
452C4×D4—112no—
453C4×D4—112no—
454C4×D4—112no—
455C4×D4—112no—
456C4×D4—112no—
457C4×D4—222no—
458C4×D4—222no—
459C4×D4—222no—
460C4×D4—222no—
461C4×D4—221no—
462C4×D4—221no—
463C4×D4—222no—
464C4×D4—222no—
465C4×D4—222no—
466C4×D4—222no—
467C4×D4—221no—
468C4×D4—221no—
469C4×D4—221no—
470C4×D4—221no—
471C4×D4C4×D1112yes—
472C4×D4C22×D1112yes—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—112no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4C4×D1111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—222no—
482C2×C22⋊C4—222no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C42—111no—
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—111no—
492C2×C42—111no—
493C2×C42—111no—
494C2×C42—111no—
495C2×C42—111no—
496C2×C42—111no—
497C2×C42—111no—
498C2×C42—111no—
499C2×C42C22×D1111yescharacteristic
500C4⋊C8—21no—
501C4⋊C8—21no—
502C4⋊C8—112no—
503C4⋊C8—222no—
504C4⋊C8—222no—
505C4⋊C8—222no—
506C4⋊C8—221no—
507C4⋊C8—221no—
508C4⋊C8C22×D1112yescomplemented
509C22⋊C8—21no—
510C22⋊C8—222no—
511C22⋊C8—221no—
512C4×C8—112no—
513C4×C8—222no—
514C4×C8C22×D1112yescomplemented
515C2×C11—22no—
516C2×C11—44no—
517C2×C11C2×#40711yescharacteristic
518C2×C11C22×#10211yescharacteristic
519C2×C11C2×#42111yescharacteristic
520D11—22no—
521D11—44no—
522D11#148614yesdirect product factor
523C24—21no—
524C24—111no—
525C24—222no—
526C24—222no—
527C24—228no—
528C24—221no—
529C24—444no—
530C24—444no—
531C2×D4—24no—
532C2×D4—21no—
533C2×D4—118no—
534C2×D4—112no—
535C2×D4—224no—
536C2×D4—224no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—224no—
540C2×D4—228no—
541C2×D4—228no—
542C2×D4—228no—
543C2×D4—224no—
544C2×D4—221no—
545C2×D4C2×C4×D1112yes—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—111no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—114no—
555C22×C4—114no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—111no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—111no—
565C22×C4—111no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—224no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—444no—
579C22×C4—444no—
580C22×C4—444no—
581C22×C4—444no—
582C22×C4—444no—
583C22×C4—448no—
584C22×C4—448no—
585C22×C4—442no—
586C22×C4—444no—
587C22×C4—444no—
588C22×C4—442no—
589C22×C4—442no—
590C22×C4C2×C4×D1111yescharacteristic
591C22×C4D4×D1111yescharacteristic
592C22×C4D4×D1111yescharacteristic
593M16—42no—
594M16—444no—
595M16—442no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—222no—
599C2×C8—222no—
600C2×C8—444no—
601C2×C8—444no—
602C4⋊C4—21no—
603C4⋊C4—112no—
604C4⋊C4—222no—
605C4⋊C4—222no—
606C4⋊C4—221no—
607C4⋊C4C2×C4×D1112yes—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—222no—
611C22⋊C4—222no—
612C22⋊C4—222no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—222no—
616C42—111no—
617C42—111no—
618C42—111no—
619C42—111no—
620C42—111no—
621C42—111no—
622C42—111no—
623C42—111no—
624C42—111no—
625C42—111no—
626C42—111no—
627C42—111no—
628C42C2×C4×D1111yescharacteristic
629C42D4×D1111yescharacteristic
630C42D4×D1111yescharacteristic
631C42C23×D1111yescharacteristic
632C11C2×#148611yescharacteristic, complemented, Sylow
633C23—24no—
634C23—22no—
635C23—42no—
636C23—42no—
637C23—111no—
638C23—111no—
639C23—114no—
640C23—222no—
641C23—222no—
642C23—228no—
643C23—224no—
644C23—228no—
645C23—222no—
646C23—442no—
647C23—444no—
648C23—444no—
649C23—444no—
650C23—4432no—
651C23—444no—
652C23—442no—
653C23C22⋊C4×D1111yescharacteristic
654D4—24no—
655D4—22no—
656D4—114no—
657D4—224no—
658D4—228no—
659D4—228no—
660D4—222no—
661D4M16×D1114yescomplemented
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—44no—
669C2×C4—111no—
670C2×C4—111no—
671C2×C4—111no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—112no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—114no—
679C2×C4—114no—
680C2×C4—111no—
681C2×C4—111no—
682C2×C4—111no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—444no—
693C2×C4—444no—
694C2×C4—444no—
695C2×C4—444no—
696C2×C4—444no—
697C2×C4—444no—
698C2×C4—441no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4—442no—
702C2×C4—444no—
703C2×C4C22⋊C4×D1111yescharacteristic
704C2×C4C22⋊C4×D1111yescharacteristic
705C2×C4C22⋊C4×D1111yescharacteristic
706C2×C4D8×D1112yes—
707C2×C4SD16×D1112yes—
708C2×C4C22×C4×D1111yescharacteristic
709C2×C4C2×D4×D1111yescharacteristic
710C2×C4C2×D4×D1111yescharacteristic
711C8—42no—
712C8—42no—
713C8—442no—
714C8—442no—
715C22—21no—
716C22—21no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—112no—
722C22—112no—
723C22—112no—
724C22—112no—
725C22—228no—
726C22—221no—
727C22—221no—
728C22—224no—
729C22—448no—
730C22—4416no—
731C22—4416no—
732C22—442no—
733C22—442no—
734C22D11×#10212yes—
735C22C2×C22⋊C4×D1111yescharacteristic
736C4—21no—
737C4—21no—
738C4—21no—
739C4—42no—
740C4—112no—
741C4—112no—
742C4—112no—
743C4—221no—
744C4—221no—
745C4—221no—
746C4—442no—
747C4D11×#10212yes—
748C4C2×M16×D1112yes—
749C4C2×D8×D1111yescharacteristic
750C4C2×SD16×D1111yescharacteristic
751C2—22no—
752C2—44no—
753C2—114no—
754C2—222no—
755C2—444no—
756C2D11×#40711yescharacteristic
757C2C2×D11×#10211yescharacteristic
758C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1486C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×D11C4
cosocleC42×C11C24
hypercenter#1486D11
hypocenterC11C2×#1486
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. D11×#431C2semidirect
3. D11×#423C2semidirect
4. #13067042C2semidirect
5. #13067041C2semidirect
6. #13067040C2semidirect
7. #13067039C2semidirect
8. D11×D4⋊C8C2semidirect
9. C11×#1486C2semidirect
30. C11×#431C22semidirect
31. C11×#423C22semidirect
33. #10622538C22semidirect
34. #10622537C22semidirect
36. #10622450C22semidirect
40. D11×C4⋊C8C22semidirect
43. #10622298C22semidirect
44. C4×C8×D11C22semidirect
45. C11×D4⋊C8C22semidirect
46. D4⋊(C11⋊C8)C22semidirect
47. #10622121C22semidirect
48. #10622097C22semidirect
131. C11×C4⋊C8C23semidirect
133. C4×C8×C11C23semidirect
142. C4⋊(C11⋊C8)C23semidirect
143. C4×C11⋊C8C23semidirect
179. D4×D11M16semidirect
261. #1486D11direct (N × H)
286. D4×C11C2×M16semidirect
319. D44C2×M16semidirect
369. #431C2×D11semidirect
374. #423C2×D11semidirect
383. D4⋊C8C2×D11semidirect
508. C4⋊C8C22×D11semidirect
514. C4×C8C22×D11semidirect
522. D11#1486direct (N × H)
632. C11C2×#1486semidirect
661. D4M16×D11semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
D11×#4312
D11×#4232
#130670422
#130670412
#130670402
#130670392
D11×D4⋊C82
C11×#14862
C2×#148611