Finite Group Databasebeta

← #14759515

Subgroups — #14759515

Order 2816.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic, complemented
2C2×#10622851C211yesmaximal, characteristic
3C2×#10622430C211yesmaximal, characteristic, complemented
4C2×#10622369C211yesmaximal, characteristic, complemented
5#13071305C211yesmaximal, characteristic, complemented
6#13068969C211yesmaximal, characteristic, complemented
7#13068962C211yesmaximal, characteristic, complemented
8#13068931C211yesmaximal, characteristic, complemented
9#13068868C211yesmaximal, characteristic, complemented
10#13068861C211yesmaximal, characteristic, complemented
11#13068803C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#103×Dic11C211yesmaximal, characteristic, complemented
14#13068384C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17#10623358—24no—
18#10623358—24no—
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C2×D4×Dic11—21no—
23C2×D4×Dic11—21no—
24C2×D4×Dic11C2211yescharacteristic
25C2×D4×Dic11C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28C2×#66979—21no—
29C2×#66979C2211yescharacteristic
30C22×C4⋊Dic11—21no—
31C22×C4⋊Dic11C2211yescharacteristic
32C2×#66946C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C11×#380C2211yescharacteristic
39#10622851C418yescomplemented
40C2×#66899C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66879C2211yescharacteristic
46C2×C8×Dic11C2211yescharacteristic
47#10622601C2211yescharacteristic
48C4⋊C4×Dic11C2211yescharacteristic
49#10622586C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52#10622570—21no—
53#10622569—21no—
54#10622430—24no—
55#10622369—24no—
56#10622283—21no—
57#10622281—21no—
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41C2×C414yescomplemented
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C23×Dic11—21no—
77C23×Dic11—21no—
78C23×Dic11—21no—
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90Q8×Dic11—22no—
91Q8×Dic11—22no—
92Q8×Dic11—22no—
93Q8×Dic11D414yescomplemented
94C2×#4325—22no—
95C2×#4325—22no—
96C2×#4325C2×C414yescomplemented
97D4×Dic11—28no—
98D4×Dic11—28no—
99D4×Dic11—22no—
100D4×Dic11—22no—
101D4×Dic11—22no—
102D4×Dic11D414yescomplemented
103C2×#4323—22no—
104C2×#4323—22no—
105C2×#4323C2×C414yescomplemented
106#66983—22no—
107#66983C2×C414yescomplemented
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112#66979—28no—
113#66979—22no—
114#66979—22no—
115C2×C4⋊Dic11—28no—
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11D411yescharacteristic
122C2×C4⋊Dic11D411yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4—21no—
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134#66946—22no—
135#66946—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#102—22no—
139C11×#102—22no—
140C11×C22⋊C8—22no—
141C11×#95—21no—
142#66899C2×C414yescomplemented
143#66896C2×C414yescomplemented
144C11⋊#95—21no—
145C11⋊#95—21no—
146C22⋊(C11⋊C8)C2×C414yescomplemented
147#66885—22no—
148#66885—22no—
149#66879—22no—
150C8×Dic11—22no—
151#66871—22no—
152#66871—22no—
153#21460—111nomaximal, Sylow
154C24×C11—21no—
155C24×C11C2×D411yescharacteristic
156C23×D11—21no—
157C11×#41—28no—
158C11×#41—28no—
159C11×#41—28no—
160C11×#41—28no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11C22×C412yes—
165C2×Q8×C11C2×D412yes—
166C2×Q8×C11#4112yes—
167C2×D4×C11—24no—
168C2×D4×C11—24no—
169C2×D4×C11—24no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11C22×C412yes—
174C2×D4×C11C2×D412yes—
175C2×D4×C11#4112yes—
176C22×C4×C11—24no—
177C22×C4×C11—24no—
178C22×C4×C11—21no—
179C22×C4×C11—24no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11#4112yes—
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—24no—
191C2×C22⋊D11—81no—
192C2×C22⋊D11—81no—
193C22×Dic11—24no—
194C22×Dic11—24no—
195C22×Dic11—24no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—81no—
200C22×Dic11—81no—
201C22×Dic11—81no—
202C22×Dic11—81no—
203C22×Dic11—81no—
204C22×Dic11—81no—
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44C22×C412yes—
215C2×C4×D11—42no—
216C2×C4×D11—81no—
217C2×C4×D11—81no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C22⋊C4—81no—
229C22⋊Dic11—24no—
230C22⋊Dic11—22no—
231C22⋊Dic11—22no—
232C22⋊Dic11—24no—
233#4325—28no—
234#4323—28no—
235(C2×D11)⋊C4—24no—
236(C2×D11)⋊C4—42no—
237(C2×D11)⋊C4—81no—
238(C2×D11)⋊C4—81no—
239C4⋊Dic11—24no—
240C4⋊Dic11—24no—
241C4⋊Dic11—22no—
242C4⋊Dic11—24no—
243C4⋊Dic11—22no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11C22×C412yes—
248C4⋊Dic11C2×D412yes—
249C4⋊Dic11C2×D412yes—
250Dic11⋊C4—81no—
251C4×Dic11—24no—
252C4×Dic11—24no—
253C4×Dic11—21no—
254C4×Dic11—21no—
255C4×Dic11—81no—
256C4×Dic11C2×D412yes—
257C4×Dic11C2×D412yes—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8C22×C412yes—
263C2×C11⋊C8C22×C412yes—
264C2×#520—111no—
265C2×#449—111no—
266C2×#440—111no—
267C2×C4×D8—111no—
268#2324—111no—
269#1880—111no—
270#1879—111no—
271#1874—111no—
272#1863—111no—
273#1862—111no—
274#1852—111no—
275#1788D1111yescharacteristic, complemented
276#1762—111no—
277C4×#103—111no—
278#1750—111no—
279C23×C11—22no—
280C23×C11—21no—
281C23×C11—22no—
282C23×C11—21no—
283C23×C11—22no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11C4×D412yes—
293C23×C11C22×D411yescharacteristic
294C22×D11—22no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11C4×D414yes—
305D4×C11—216no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11C4×D414yes—
310C2×C4×C11—216no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11C4×D412yes—
327C2×C4×C11C23×C411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C22⋊D11—84no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—22no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—84no—
354C2×Dic11—84no—
355C2×Dic11—84no—
356C2×Dic11#12012yes—
357C2×Dic11#12012yes—
358D44—22no—
359D44—22no—
360D44—41no—
361D44—41no—
362C4×D11—84no—
363C8×C11—41no—
364C8×C11—41no—
365C11⋊C8—22no—
366C11⋊C8—22no—
367C22×#41C2×D1111yescharacteristic
368C22×SD16—111no—
369C22×D8—111no—
370C2×#121—111no—
371#520—224no—
372#520—224no—
373C2×C4×Q8—111no—
374C2×C4×Q8—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4—111no—
378C2×C4×D4—221no—
379C2×C4×D4—221no—
380C2×#117—111no—
381C2×#117—221no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4—221no—
384#449—118no—
385#440—224no—
386C4×D8—224no—
387C2×#107—111no—
388C2×#107—111no—
389C2×#103—111no—
390C2×#103C2×D1111yescharacteristic
391C2×#103C2×D1111yescharacteristic
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102C2×D1111yescharacteristic
396C2×#102C2×D1111yescharacteristic
397C2×C22⋊C8—111no—
398C2×C22⋊C8C2×D1111yescharacteristic
399C2×#97—111no—
400C2×C4×C8—111no—
401#390—111no—
402#390—221no—
403#389—111no—
404#388—221no—
405#386—221no—
406#385—221no—
407#380C2×D1111yescharacteristic
408C4×C4⋊C4—111no—
409#340—111no—
410#340—111no—
411#340—111no—
412#340—111no—
413#336—111no—
414#336—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—24no—
419C22×C11—41no—
420C22×C11—42no—
421C22×C11—41no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—41no—
426C22×C11—42no—
427C22×C11—41no—
428C22×C11—42no—
429C22×C11C2×C4×D411yescharacteristic
430C22×C11C2×#12011yescharacteristic
431C22×C11#52511yescharacteristic
432C22×C11#57611yescharacteristic
433C22×C11#57611yescharacteristic
434C22×C11#57711yescharacteristic
435C22×C11#57811yescharacteristic
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—81no—
440C2×D11—81no—
441C2×D11—81no—
442C2×D11—81no—
443C4×C11—22no—
444C4×C11—24no—
445C4×C11—81no—
446C4×C11—81no—
447C4×C11C2×C4×D411yescharacteristic
448C4×C11C2×C4×D411yescharacteristic
449C4×C11#52511yescharacteristic
450C4×C11#52511yescharacteristic
451Dic11—22no—
452Dic11—22no—
453Dic11—42no—
454Dic11—41no—
455Dic11—42no—
456Dic11—42no—
457Dic11—41no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C2×#41C4×D1114yescomplemented
464C22×Q8C22×D1111yescharacteristic
465C22×D4—21no—
466C22×D4—111no—
467C22×D4—221no—
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—221no—
471C23×C4—221no—
472C23×C4—221no—
473C23×C4—221no—
474C23×C4C22×D1111yescharacteristic
475C2×SD16—114no—
476C2×SD16—222no—
477C2×SD16—222no—
478C2×D8—114no—
479C2×D8—222no—
480C2×D8—222no—
481C22×C8—111no—
482C22×C8—111no—
483C22×C8C22×D1111yescharacteristic
484C22×C8C22×D1111yescharacteristic
485#121—114no—
486#121—222no—
487C4×Q8—114no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8—222no—
491C4×D4—114no—
492C4×D4—222no—
493C4×D4—222no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—228no—
497C4×D4—228no—
498C4×D4—222no—
499#117—222no—
500#117—222no—
501#117—228no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—228no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C42—111no—
526C2×C42—111no—
527C2×C42—221no—
528C2×C42—221no—
529C2×C42—221no—
530#107—222no—
531#107—222no—
532#103—22no—
533#103—22no—
534#103—114no—
535#102—22no—
536#102—22no—
537#102—114no—
538#102—222no—
539#102—222no—
540C22⋊C8—22no—
541C22⋊C8—114no—
542#97—222no—
543C4×C8—222no—
544#95—21no—
545#95—221no—
546#95—221no—
547C2×C11—42no—
548C2×C11—44no—
549C2×C11C4×#12011yescharacteristic
550C2×C11#294611yescharacteristic
551C2×C11#295111yescharacteristic
552C2×C11#300811yescharacteristic
553C2×C11#301311yescharacteristic
554C2×C11#311911yescharacteristic
555C2×C11#312411yescharacteristic
556D11—82no—
557C24—21no—
558C24—221no—
559C24D4×D1111yescharacteristic
560#41—28no—
561#41—28no—
562#41—28no—
563#41—28no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C2×C4×D1112yes—
568C2×Q8D4×D1112yes—
569C2×Q8#434112yes—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—112no—
577C2×D4—224no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4—221no—
582C2×D4—221no—
583C2×D4—881no—
584C2×D4—881no—
585C2×D4C2×C4×D1112yes—
586C2×D4D4×D1112yes—
587C2×D4#434112yes—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—224no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—442no—
609C22×C4—881no—
610C22×C4—881no—
611C22×C4—881no—
612C22×C4—881no—
613C22×C4—881no—
614C22×C4—881no—
615C22×C4—881no—
616C22×C4—881no—
617C22×C4C2×C4×D1112yes—
618C22×C4D4×D1111yescharacteristic
619C22×C4#434112yes—
620C22×C4C23×D1111yescharacteristic
621SD16—228no—
622D8—228no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—112no—
630C2×C8—112no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8—221no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—112no—
640C4⋊C4—112no—
641C4⋊C4—112no—
642C4⋊C4—222no—
643C4⋊C4—222no—
644C4⋊C4—224no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—221no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—881no—
651C22⋊C4—81no—
652C22⋊C4—222no—
653C22⋊C4—222no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—442no—
658C22⋊C4—881no—
659C22⋊C4—881no—
660C42—112no—
661C42—112no—
662C42—224no—
663C42—224no—
664C42—221no—
665C42—221no—
666C42—881no—
667C11#2146011yescharacteristic, complemented, Sylow
668C23—22no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—222no—
682C23—441no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23(C22⋊D11)⋊C412yes—
689C23C2×D4×D1111yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8(C22⋊D11)⋊C414yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—222no—
699D4—222no—
700D4—441no—
701D4—441no—
702D4—884no—
703D4(C22⋊D11)⋊C414yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—112no—
721C2×C4—112no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—222no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—221no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—884no—
742C2×C4—884no—
743C2×C4—884no—
744C2×C4—884no—
745C2×C4(C22⋊D11)⋊C412yes—
746C2×C4C22×C4×D1111yescharacteristic
747C2×C4C2×D4×D1111yescharacteristic
748C2×C4C2×D4×D1111yescharacteristic
749C2×C4C2×#434111yescharacteristic
750C2×C4C2×#434111yescharacteristic
751C2×C4C2×#434111yescharacteristic
752C8—41no—
753C8—41no—
754C8—222no—
755C8—222no—
756C22—22no—
757C22—24no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—442no—
771C22—442no—
772C22—442no—
773C22—881no—
774C22—881no—
775C22—881no—
776C22—881no—
777C22C2×(C22⋊D11)⋊C411yescharacteristic
778C22#1062311711yescharacteristic
779C22D11×#12011yescharacteristic
780C22#1062330011yescharacteristic
781C22#1062330111yescharacteristic
782C22#1062330511yescharacteristic
783C22#1062331011yescharacteristic
784C4—22no—
785C4—24no—
786C4—81no—
787C4—81no—
788C4—222no—
789C4—222no—
790C4—441no—
791C4—442no—
792C4—442no—
793C4—441no—
794C4—442no—
795C4C2×(C22⋊D11)⋊C411yescharacteristic
796C4C2×(C22⋊D11)⋊C411yescharacteristic
797C4#1062311711yescharacteristic
798C4#1062311711yescharacteristic
799C2—42no—
800C2—44no—
801C2—882no—
802C2#1307111511yescharacteristic
803C2#1307745111yescharacteristic
804C2#1307748711yescharacteristic
805C2#1307788111yescharacteristic
806C2#1307793511yescharacteristic
807C2#1307881611yescharacteristic
808C2#1307887911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#21460
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
1. C2×#10623358C2semidirect
3. C2×#10622430C2semidirect
4. C2×#10622369C2semidirect
5. #13071305C2semidirect
6. #13068969C2semidirect
7. #13068962C2semidirect
8. #13068931C2semidirect
9. #13068868C2semidirect
10. #13068861C2semidirect
11. #13068803C2semidirect
12. #13068443C2semidirect
13. #103×Dic11C2semidirect
14. #13068384C2semidirect
15. C11×#1788C2semidirect
39. #10622851C4semidirect
69. C2×C11×#41C2×C4semidirect
93. Q8×Dic11D4semidirect
96. C2×#4325C2×C4semidirect
102. D4×Dic11D4semidirect
105. C2×#4323C2×C4semidirect
107. #66983C2×C4semidirect
142. #66899C2×C4semidirect
143. #66896C2×C4semidirect
146. C22⋊(C11⋊C8)C2×C4semidirect
275. #1788D11semidirect
463. C2×#41C4×D11semidirect
667. C11#21460semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#106228512
C2×#106224302
C2×#106223692
#130713052
#130689692
#130689622
#130689312
#130688682
#130688612
#130688032
#130684432
#103×Dic112
#130683842
C11×#17882
#2146011