Finite Group Databasebeta

← #14769317

Subgroups — #14769317

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622343C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic, complemented
5#13071547C211yesmaximal, characteristic, complemented
6#13069541C211yesmaximal, characteristic, complemented
7#13069438C211yesmaximal, characteristic, complemented
8#13069051C211yesmaximal, characteristic, complemented
9#13069042C211yesmaximal, characteristic, complemented
10#13068935C211yesmaximal, characteristic, complemented
11#13068931C211yesmaximal, characteristic, complemented
12#13068624C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068443C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11—21no—
18C22×D4×D11C2211yescharacteristic
19C2×#67006—21no—
20C2×#66993C2211yescharacteristic
21C2×#66992—21no—
22D4×C22⋊D11—24no—
23D4×C22⋊D11C418yescomplemented
24C2×#66991C2211yescharacteristic
25C2×#66990—21no—
26C2×D4×Dic11C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28C2×C4×C22⋊D11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic, complemented
30C23×C11⋊C8C2211yescharacteristic, complemented
31C22×#4313C2211yescharacteristic, complemented
32C2×#66945C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic, complemented
36C2×C11×#102C2211yescharacteristic, complemented
37C2×C11×C22⋊C8C2211yescharacteristic, complemented
38C11×#380C2211yescharacteristic, complemented
39C2×#66896—24no—
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic, complemented
43C2×#66896C2211yescharacteristic, complemented
44C2×#66885C2211yescharacteristic, complemented
45C2×#66885C2211yescharacteristic, complemented
46C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
47C2×#66879C2211yescharacteristic, complemented
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49#10622600C2211yescharacteristic, complemented
50#10622590C2211yescharacteristic, complemented
51C4⋊C4×Dic11C2211yescharacteristic, complemented
52C2×#66873C2211yescharacteristic, complemented
53C2×#66873C2211yescharacteristic, complemented
54#10622571—21no—
55C22⋊C4×Dic11—21no—
56#10622383—24no—
57#10622343—24no—
58#10622283—21no—
59#10622268—21no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C25×C11—21no—
65C24×D11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—21no—
69C22×D4×C11—22no—
70C22×D4×C11—41no—
71C22×D4×C11—41no—
72C22×D4×C11C2×C414yes—
73C22×D4×C11C2311yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×C22⋊D11—28no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—44no—
83C22×C22⋊D11—44no—
84C22×C22⋊D11D411yescharacteristic
85C23×Dic11—21no—
86C23×Dic11—21no—
87C2×D4×D11—22no—
88C2×D4×D11—22no—
89C2×D4×D11—22no—
90C2×D4×D11—41no—
91C2×D4×D11—41no—
92C2×D4×D11C2×C414yescomplemented
93C22×D44C2311yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100#67006—28no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11D411yescharacteristic
104#66993—22no—
105#66993C2×C414yescomplemented
106#66992—28no—
107#66991—22no—
108#66991C2×C414yescomplemented
109#66990—28no—
110D4×Dic11—22no—
111D4×Dic11C2×C414yescomplemented
112#66983—22no—
113#66983C2×C414yes—
114C4×C22⋊D11C2×C414yes—
115C4×C22⋊D11D414yes—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—41no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4D411yescharacteristic
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C22×C11⋊C8—22no—
131C22×C11⋊C8—22no—
132C22×C11⋊C8—41no—
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×#4313—22no—
136C2×#4313—22no—
137C2×#4313—41no—
138#66945—22no—
139#66945—41no—
140C11×#102—22no—
141C11×#102—22no—
142C11×#102—41no—
143C11×#102—41no—
144C11×C22⋊C8—22no—
145C11×#95—21no—
146#66896—22no—
147#66896—22no—
148#66896—22no—
149#66896D414yescomplemented
150C11⋊#95—21no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153C11⋊#95—21no—
154#66885—22no—
155#66885—41no—
156(C2×D11)⋊C8—22no—
157#66879—22no—
158Dic11⋊C8—22no—
159#66873—22no—
160#66873—41no—
161#22423—111nomaximal, Sylow
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—24no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—81no—
170C24×C11—81no—
171C24×C11C2×D411yescharacteristic
172C23×D11—21no—
173C23×D11—24no—
174C23×D11—42no—
175C23×D11—42no—
176C23×D11—42no—
177C23×D11—42no—
178C23×D11—81no—
179C23×D11—81no—
180C23×D11C2×D411yescharacteristic
181C2×D4×C11—28no—
182C2×D4×C11—24no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—42no—
195C2×D4×C11—42no—
196C2×D4×C11C22×C412yes—
197C2×D4×C11C22×C412yes—
198C2×D4×C11C2×D412yes—
199C2×D4×C11#4112yes—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11C22×C412yes—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—22no—
215C2×C22⋊D11—22no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—42no—
218C2×C22⋊D11—42no—
219C2×C22⋊D11—42no—
220C2×C22⋊D11—42no—
221C2×C22⋊D11—42no—
222C2×C22⋊D11—42no—
223C2×C22⋊D11—432no—
224C2×C22⋊D11—42no—
225C2×C22⋊D11—42no—
226C2×C22⋊D11—81no—
227C2×C22⋊D11—81no—
228C2×C22⋊D11C22⋊C414yes—
229C22×Dic11—24no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—42no—
234C22×Dic11—42no—
235C22×Dic11—42no—
236C22×Dic11—42no—
237C22×Dic11—81no—
238C22×Dic11C2×D411yescharacteristic
239C22×Dic11C2×D411yescharacteristic
240C22×Dic11C2×D411yescharacteristic
241D4×D11—28no—
242D4×D11—44no—
243D4×D11—44no—
244D4×D11—44no—
245C2×D44—21no—
246C2×D44—21no—
247C2×D44—21no—
248C2×D44—21no—
249C2×D44—21no—
250C2×D44C22×C412yes—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11C22×C412yes—
256C2×C4×D11C2×D412yes—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C22⋊C4—42no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11C22⋊C414yes—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—42no—
273(C2×D11)⋊C4—81no—
274(C2×D11)⋊C4C22⋊C414yes—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11—42no—
280C4⋊Dic11C22×C412yes—
281C4⋊Dic11C2×D412yescomplemented
282Dic11⋊C4C22⋊C414yes—
283C4×Dic11—42no—
284C4×Dic11—81no—
285C4×Dic11C22×C412yes—
286C4×Dic11C2×D412yes—
287C2×C11⋊C8—21no—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8—44no—
293C2×C11⋊C8C2×D412yescomplemented
294#4313—44no—
295C2×D42—111no—
296C2×#435—111no—
297C2×#418—111no—
298C22×#102—111no—
299#2352—111no—
300#1982—111no—
301#1961—111no—
302#1895—111no—
303#1893—111no—
304#1875—111no—
305#1874—111no—
306#1804—111no—
307#1786—111no—
308#1786D1111yescharacteristic, complemented
309#1762—111no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—48no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—48no—
330C23×C11—84no—
331C23×C11—84no—
332C23×C11—84no—
333C23×C11—84no—
334C23×C11—84no—
335C23×C11C2×C22⋊C412yes—
336C23×C11AGL(1,ℤ/8)12yes—
337C23×C11AGL(1,ℤ/8)12yes—
338C23×C11C22×D411yescharacteristic
339C22×D11—21no—
340C22×D11—21no—
341C22×D11—21no—
342C22×D11—21no—
343C22×D11—21no—
344C22×D11—21no—
345C22×D11—22no—
346C22×D11—48no—
347C22×D11—48no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—84no—
355C22×D11—84no—
356C22×D11—84no—
357C22×D11—84no—
358C22×D11—84no—
359C22×D11C2×C22⋊C412yes—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—48no—
366D4×C11—41no—
367D4×C11—41no—
368D4×C11C4×D414yes—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11C2×C22⋊C412yes—
382C2×C4×C11C23×C411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C2×#4111yescharacteristic
386C2×C4×C11H(5,𝔽2)11yescharacteristic
387C2×C4×C11H(5,𝔽2)11yescharacteristic
388C22⋊D11—28no—
389C22⋊D11—48no—
390C22⋊D11—48no—
391C22⋊D11—48no—
392C22⋊D11—48no—
393C22⋊D11—84no—
394C2×Dic11—21no—
395C2×Dic11—21no—
396C2×Dic11—21no—
397C2×Dic11—21no—
398C2×Dic11—21no—
399C2×Dic11—21no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—48no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—84no—
411C2×Dic11C2×C22⋊C412yes—
412C2×Dic11C2×C22⋊C412yes—
413C2×Dic11C2×C22⋊C412yes—
414D44—22no—
415D44—22no—
416D44—41no—
417D44—41no—
418C4×D11—22no—
419C4×D11—22no—
420C4×D11—22no—
421C4×D11—22no—
422C8×C11—41no—
423C8×C11—41no—
424C11⋊C8—22no—
425C11⋊C8—41no—
426C23×D4—111no—
427C23×D4—221no—
428C23×D4C2×D1111yescharacteristic
429C22×M16—111no—
430C23×C8—111no—
431D42—118no—
432D42—224no—
433C2×#127—111no—
434C2×#121—111no—
435C2×#121—111no—
436C2×#121—221no—
437C2×#120—221no—
438C2×#120—221no—
439C2×C4×D4—111no—
440C2×C4×D4—111no—
441C2×#117—111no—
442C22×C4⋊C4—111no—
443#435—224no—
444C2×C4⋊C8—111no—
445#418—224no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—224no—
455C2×#102C2×D1111yescharacteristic
456C2×#102C2×D1111yescharacteristic
457C2×#102C2×D1111yescharacteristic, complemented
458C2×#102C2×D1111yescharacteristic, complemented
459C2×C22⋊C8—111no—
460C2×C22⋊C8C2×D1111yescharacteristic, complemented
461C2×#97—111no—
462#388—221no—
463#387—221no—
464#386—221no—
465#382—111no—
466#380—111no—
467#380C2×D1111yescharacteristic, complemented
468C4×C4⋊C4—111no—
469C4×C22⋊C4—221no—
470#340—111no—
471#340—111no—
472#340—111no—
473#340—111no—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—24no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—816no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11—81no—
494C22×C11—81no—
495C22×C11#41814yescomplemented
496C22×C11C22×C22⋊C411yescharacteristic
497C22×C11D4211yescharacteristic
498C22×C11#54611yescharacteristic
499C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
500C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
501C22×C11#57611yescharacteristic
502C22×C11#57711yescharacteristic
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—22no—
506C2×D11—41no—
507C2×D11—41no—
508C2×D11—41no—
509C2×D11—41no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—816no—
514C2×D11—81no—
515C2×D11—81no—
516C2×D11—81no—
517C2×D11—81no—
518C4×C11—22no—
519C4×C11—81no—
520C4×C11—81no—
521C4×C11C2×C4×D411yescharacteristic
522C4×C11#51811yescharacteristic
523C4×C11D4211yescharacteristic
524C4×C11#54611yescharacteristic
525Dic11—22no—
526Dic11—22no—
527Dic11—22no—
528Dic11—42no—
529Dic11—42no—
530Dic11—81no—
531C25—21no—
532C25—221no—
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4—111no—
540C22×D4—114no—
541C22×D4—111no—
542C22×D4—222no—
543C22×D4—221no—
544C22×D4—221no—
545C22×D4—221no—
546C22×D4—228no—
547C22×D4—222no—
548C22×D4—222no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—441no—
552C22×D4—441no—
553C22×D4—444no—
554C22×D4—444no—
555C22×D4C4×D1114yes—
556C22×D4C22×D1111yescharacteristic
557C22×D4C22×D1111yescharacteristic
558C23×C4—111no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4C22×D1111yescharacteristic
562C2×M16—222no—
563C2×M16—222no—
564C2×M16—441no—
565C22×C8—111no—
566C22×C8—111no—
567C22×C8—222no—
568C22×C8—222no—
569C22×C8—441no—
570C22×C8C22×D1111yescharacteristic
571C22×C8C22×D1111yescharacteristic
572#127—114no—
573#127—222no—
574#121—114no—
575#121—114no—
576#121—228no—
577#121—222no—
578#121—222no—
579#120—228no—
580#120—228no—
581C4×D4—114no—
582C4×D4—114no—
583C4×D4—114no—
584C4×D4—222no—
585#117—222no—
586#117—441no—
587C2×C4⋊C4—111no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4—441no—
594C2×C4⋊C4C22×D1111yescharacteristic
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—111no—
598C2×C22⋊C4—111no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C42—111no—
605C2×C42—221no—
606C2×C42—221no—
607C4⋊C8—222no—
608#102—22no—
609#102—22no—
610#102—41no—
611#102—41no—
612#102—114no—
613#102—222no—
614#102—222no—
615#102—222no—
616#102—222no—
617#102—222no—
618#102—441no—
619#102—441no—
620C22⋊C8—22no—
621C22⋊C8—222no—
622#97—222no—
623#95—21no—
624#95—221no—
625#95—221no—
626#95—221no—
627#95—221no—
628C2×C11—24no—
629C2×C11—44no—
630C2×C11—82no—
631C2×C11D4×C22⋊C411yescharacteristic
632C2×C11C2×#41811yescharacteristic
633C2×C11#289711yescharacteristic
634C2×C11#326411yescharacteristic
635C2×C11#326511yescharacteristic
636C2×C11#331011yescharacteristic
637C2×C11#331811yescharacteristic
638D11—42no—
639D11—82no—
640C24—21no—
641C24—21no—
642C24—24no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24—111no—
650C24—224no—
651C24—221no—
652C24—442no—
653C24—442no—
654C24—442no—
655C24—442no—
656C24—881no—
657C24—881no—
658C24D4×D1111yescharacteristic
659C2×D4—28no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—114no—
675C2×D4—112no—
676C2×D4—224no—
677C2×D4—224no—
678C2×D4—224no—
679C2×D4—222no—
680C2×D4—222no—
681C2×D4—228no—
682C2×D4—224no—
683C2×D4—224no—
684C2×D4—221no—
685C2×D4—221no—
686C2×D4—221no—
687C2×D4—221no—
688C2×D4—221no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—442no—
693C2×D4—442no—
694C2×D4—442no—
695C2×D4—442no—
696C2×D4—4432no—
697C2×D4—442no—
698C2×D4—442no—
699C2×D4—442no—
700C2×D4—442no—
701C2×D4—881no—
702C2×D4—881no—
703C2×D4C2×C4×D1112yes—
704C2×D4C2×C4×D1112yes—
705C2×D4D4×D1112yes—
706C2×D4#434112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—111no—
714C22×C4—111no—
715C22×C4—111no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—224no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—442no—
727C22×C4—442no—
728C22×C4—442no—
729C22×C4—442no—
730C22×C4—881no—
731C22×C4C2×C4×D1112yes—
732C22×C4D4×D1111yescharacteristic
733C22×C4D4×D1112yes—
734C22×C4C23×D1111yescharacteristic
735M16—444no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—112no—
743C2×C8—221no—
744C2×C8—221no—
745C2×C8—221no—
746C2×C8—221no—
747C2×C8—221no—
748C2×C8—444no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—114no—
754C4⋊C4—112no—
755C4⋊C4—112no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—221no—
760C4⋊C4—442no—
761C22⋊C4—42no—
762C22⋊C4—114no—
763C22⋊C4—114no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—224no—
767C22⋊C4—442no—
768C22⋊C4—881no—
769C42—112no—
770C42—112no—
771C42—442no—
772C42—881no—
773C11#2242311yescharacteristic, complemented, Sylow
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—48no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—48no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—112no—
800C23—221no—
801C23—221no—
802C23—221no—
803C23—221no—
804C23—221no—
805C23—221no—
806C23—222no—
807C23—448no—
808C23—448no—
809C23—441no—
810C23—441no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—884no—
816C23—884no—
817C23—884no—
818C23—884no—
819C23—884no—
820C23C22⋊C4×D1112yes—
821C23#6696412yes—
822C23#6696712yes—
823C23C2×D4×D1111yescharacteristic
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—41no—
831D4—41no—
832D4—228no—
833D4—222no—
834D4—222no—
835D4—448no—
836D4—448no—
837D4—448no—
838D4—448no—
839D4—441no—
840D4—441no—
841D4—884no—
842D4(C22⋊D11)⋊C414yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—112no—
856C2×C4—112no—
857C2×C4—112no—
858C2×C4—221no—
859C2×C4—221no—
860C2×C4—221no—
861C2×C4—221no—
862C2×C4—221no—
863C2×C4—221no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—448no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—884no—
879C2×C4C22⋊C4×D1112yes—
880C2×C4C22×C4×D1111yescharacteristic
881C2×C4C2×D4×D1111yescharacteristic
882C2×C4C2×D4×D1111yescharacteristic
883C2×C4C2×#434111yescharacteristic
884C2×C4#6703711yescharacteristic
885C2×C4#6703711yescharacteristic
886C8—41no—
887C8—41no—
888C8—222no—
889C8—441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—24no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—816no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—222no—
912C22—222no—
913C22—222no—
914C22—441no—
915C22—441no—
916C22—441no—
917C22—441no—
918C22—442no—
919C22—442no—
920C22—442no—
921C22—8816no—
922C22—881no—
923C22—881no—
924C22—881no—
925C22—881no—
926C22#1062238314yescomplemented
927C22C2×C22⋊C4×D1111yescharacteristic
928C22#1062312111yescharacteristic
929C22#1062312211yescharacteristic
930C22C2×#6696411yescharacteristic
931C22C2×#6696711yescharacteristic
932C22#1062330511yescharacteristic
933C22#1062330611yescharacteristic
934C4—22no—
935C4—81no—
936C4—81no—
937C4—222no—
938C4—222no—
939C4—222no—
940C4—442no—
941C4—442no—
942C4—881no—
943C4C2×(C22⋊D11)⋊C411yescharacteristic
944C4#1062301711yescharacteristic
945C4#1062312111yescharacteristic
946C4#1062312211yescharacteristic
947C2—24no—
948C2—44no—
949C2—82no—
950C2—442no—
951C2—882no—
952C2#1307143211yescharacteristic
953C2C2×#1062238311yescharacteristic
954C2#1307714111yescharacteristic
955C2#1308010011yescharacteristic
956C2#1308011511yescharacteristic
957C2#1308064111yescharacteristic
958C2#1308076111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1786C2
socleC23×C11C22×D4
prime radicalC2×D4×C22⋊D11C2
cosocleC22×C4×C11C24
hypercenter#1786D11
hypocenterC11#22423
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#10622343C2semidirect
3. C2×#10622383C2semidirect
4. C22×#66896C2semidirect
5. #13071547C2semidirect
6. #13069541C2semidirect
7. #13069438C2semidirect
8. #13069051C2semidirect
9. #13069042C2semidirect
10. #13068935C2semidirect
11. #13068931C2semidirect
12. #13068624C2semidirect
13. #13068545C2semidirect
14. #13068443C2semidirect
15. C11×#1786C2semidirect
23. D4×C22⋊D11C4semidirect
29. C22×C4⋊Dic11C22semidirect
30. C23×C11⋊C8C22semidirect
31. C22×#4313C22semidirect
32. C2×#66945C22semidirect
35. C2×C11×#102C22semidirect
36. C2×C11×#102C22semidirect
37. C2×C11×C22⋊C8C22semidirect
38. C11×#380C22semidirect
42. C2×#66896C22semidirect
43. C2×#66896C22semidirect
44. C2×#66885C22semidirect
45. C2×#66885C22semidirect
46. C2×(C2×D11)⋊C8C22semidirect
47. C2×#66879C22semidirect
48. C2×Dic11⋊C8C22semidirect
49. #10622600C22semidirect
50. #10622590C22semidirect
51. C4⋊C4×Dic11C22semidirect
52. C2×#66873C22semidirect
53. C2×#66873C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
92. C2×D4×D11C2×C4semidirect
105. #66993C2×C4semidirect
108. #66991C2×C4semidirect
111. D4×Dic11C2×C4semidirect
149. #66896D4semidirect
281. C4⋊Dic11C2×D4semidirect
293. C2×C11⋊C8C2×D4semidirect
308. #1786D11semidirect
457. C2×#102C2×D11semidirect
458. C2×#102C2×D11semidirect
460. C2×C22⋊C8C2×D11semidirect
467. #380C2×D11semidirect
495. C22×C11#418semidirect
773. C11#22423semidirect
926. C22#10622383semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D112
C2×#106223432
C2×#106223832
C22×#668962
#130715472
#130695412
#130694382
#130690512
#130690422
#130689352
#130689312
#130686242
#130685452
#130684432
C11×#17862
#2242311