Finite Group Databasebeta

← #14769314

Subgroups — #14769314

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×#10622740C211yesmaximal, characteristic, complemented
3C2×D11×#102C211yesmaximal, characteristic, complemented
4#13071546C211yesmaximal, characteristic, complemented
5#13069541C211yesmaximal, characteristic, complemented
6#13069438C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic, complemented
9#13068938C211yesmaximal, characteristic, complemented
10#13068930C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic, complemented
12#13068547C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068443C211yesmaximal, characteristic, complemented
15C2×C11×#418C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11—21no—
18C22×D4×D11C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic, complemented
20C2×C11×#117C2211yescharacteristic, complemented
21C2×#67006—21no—
22C2×#66993C2211yescharacteristic
23C2×#66992—21no—
24D4×C22⋊D11—24no—
25D4×C22⋊D11C418yescomplemented
26C2×#66991C2211yescharacteristic
27C2×#66990—21no—
28C2×D4×Dic11C2211yescharacteristic
29C2×#66983C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C22×C8×D11C2211yescharacteristic, complemented
32C2×C4⋊C4×D11C2211yescharacteristic, complemented
33C11×#418—24no—
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic, complemented
37C2×C11×#102C2211yescharacteristic, complemented
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic, complemented
41C2×#66896C2211yescharacteristic, complemented
42#10622825C2211yescharacteristic, complemented
43C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
44#10622740—24no—
45C2×#66885C2211yescharacteristic, complemented
46C2×#66885C2211yescharacteristic, complemented
47C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
48C2×#66879C2211yescharacteristic, complemented
49C2×Dic11⋊C8C2211yescharacteristic, complemented
50#10622600C2211yescharacteristic, complemented
51#10622590C2211yescharacteristic, complemented
52C4⋊C4×Dic11C2211yescharacteristic, complemented
53C2×#66873C2211yescharacteristic, complemented
54C2×#66873C2211yescharacteristic, complemented
55#10622569—21no—
56#10622558—21no—
57C4×(C2×D11)⋊C4—21no—
58#10622546—21no—
59D11×#102—24no—
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×C414yescomplemented
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—
86C2×D4×D11—22no—
87C2×D4×D11—22no—
88C2×D4×D11—22no—
89C2×D4×D11—41no—
90C2×D4×D11—41no—
91C2×D4×D11C2×C414yes—
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×C4×D11C2311yescharacteristic
95C2×C11×M16—22no—
96C2×C11×M16—22no—
97C2×C11×M16—41no—
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×#117—22no—
101C11×#117—41no—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C42×C11—21no—
106#67006—28no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11D411yescharacteristic
111#66993—22no—
112#66993C2×C414yescomplemented
113#66992—28no—
114#66991—22no—
115#66991C2×C414yes—
116#66990—28no—
117D4×Dic11—22no—
118D4×Dic11C2×C414yescomplemented
119#66983—22no—
120#66983C2×C414yescomplemented
121C4×C22⋊D11C2×C414yes—
122C4×C22⋊D11D414yes—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4D411yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4D411yescharacteristic
131C2×C4×Dic11—21no—
132C2×C4×Dic11C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×C8×D11—22no—
136C2×C8×D11—22no—
137C2×C8×D11—41no—
138C4⋊C4×D11—22no—
139C4⋊C4×D11—41no—
140C11×#102—22no—
141C11×#102—22no—
142C11×#102—22no—
143C11×#102D414yescomplemented
144#66896—22no—
145#66896—22no—
146#66896—41no—
147#66896—41no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153C22⋊(C11⋊C8)—22no—
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—24no—
215C2×C22⋊D11—22no—
216C2×C22⋊D11—22no—
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×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238D4×D11—28no—
239D4×D11—44no—
240D4×D11—44no—
241D4×D11—44no—
242C2×D44—21no—
243C2×D44—21no—
244C2×D44—21no—
245C2×D44—21no—
246C2×D44—21no—
247C2×D44C22×C412yes—
248C2×C4×D11—21no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—42no—
253C2×C4×D11—42no—
254C2×C4×D11—81no—
255C2×C4×D11C22×C412yes—
256C2×C4×D11C2×D412yes—
257C11×M16—44no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11C2×D412yescomplemented
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4C2×D412yescomplemented
268C11×C22⋊C4—42no—
269C42×C11—42no—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272C22⋊Dic11—81no—
273C22⋊Dic11C22⋊C414yes—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—42no—
276(C2×D11)⋊C4C22⋊C414yes—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11C22×C412yes—
283Dic11⋊C4—42no—
284Dic11⋊C4C22⋊C414yes—
285C4×Dic11—81no—
286C4×Dic11C22×C412yes—
287C4×Dic11C2×D412yes—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8—21no—
293C2×C11⋊C8—21no—
294C8×D11—44no—
295C2×D42—111no—
296C2×#435—111no—
297C2×#418D1111yescharacteristic, complemented
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#1786—111no—
309#1762—111no—
310C23×C11—22no—
311C23×C11—21no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—22no—
320C23×C11—48no—
321C23×C11—48no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—84no—
333C23×C11—84no—
334C23×C11—84no—
335C23×C11—84no—
336C23×C11—84no—
337C23×C11C2×C22⋊C412yes—
338C23×C11C22×D411yescharacteristic
339C22×D11—21no—
340C22×D11—21no—
341C22×D11—21no—
342C22×D11—21no—
343C22×D11—22no—
344C22×D11—48no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—48no—
352C22×D11—84no—
353C22×D11—84no—
354C22×D11—84no—
355C22×D11—84no—
356C22×D11—84no—
357C22×D11C2×C22⋊C412yes—
358C22×D11AGL(1,ℤ/8)12yes—
359C22×D11AGL(1,ℤ/8)12yes—
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—22no—
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—48no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11C2×C22⋊C412yes—
411C2×Dic11C2×C22⋊C412yes—
412C2×Dic11C2×C22⋊C412yes—
413D44—22no—
414D44—22no—
415D44—41no—
416D44—41no—
417C4×D11—22no—
418C4×D11—22no—
419C4×D11—22no—
420C4×D11—22no—
421C4×D11—84no—
422C8×C11—22no—
423C8×C11—41no—
424C11⋊C8—41no—
425C11⋊C8—41no—
426C23×D4—111no—
427C23×D4—221no—
428C23×D4C2×D1111yescharacteristic
429C22×M16C2×D1111yescharacteristic, complemented
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×#117C2×D1111yescharacteristic, complemented
442C22×C4⋊C4—111no—
443#435—224no—
444C2×C4⋊C8—111no—
445#418—24no—
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⋊C8—111no—
461C2×#97—111no—
462#388—221no—
463#387—221no—
464#386—221no—
465#382—111no—
466#380—111no—
467#380—111no—
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—24no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—41no—
482C22×C11—42no—
483C22×C11—41no—
484C22×C11—42no—
485C22×C11—41no—
486C22×C11—42no—
487C22×C11—41no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—816no—
492C22×C11—81no—
493C22×C11—81no—
494C22×C11—81no—
495C22×C11—81no—
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—22no—
507C2×D11—22no—
508C2×D11—22no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—816no—
513C2×D11—81no—
514C2×D11—81no—
515C2×D11—81no—
516C2×D11—81no—
517C2×D11#41814yescomplemented
518C4×C11—22no—
519C4×C11—42no—
520C4×C11—81no—
521C4×C11C2×C4×D411yescharacteristic
522C4×C11#51811yescharacteristic
523C4×C11D4211yescharacteristic
524C4×C11#54611yescharacteristic
525Dic11—22no—
526Dic11—22no—
527Dic11—22no—
528Dic11—42no—
529Dic11—81no—
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×D1114yescomplemented
556C22×D4C22×D1111yescharacteristic
557C22×D4C22×D1111yescharacteristic
558C23×C4—111no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4C22×D1111yescharacteristic
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—41no—
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—22no—
586#117—41no—
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—21no—
605C2×C42—111no—
606C2×C42—221no—
607C4⋊C8—222no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—222no—
612#102—222no—
613#102—222no—
614#102—222no—
615#102—441no—
616#102—441no—
617#102—441no—
618#102—441no—
619#102C22⋊D1114yescomplemented
620C22⋊C8—222no—
621C22⋊C8—222no—
622#97—222no—
623#95—221no—
624#95—221no—
625#95—221no—
626#95—221no—
627#95—221no—
628C2×C11—44no—
629C2×C11—42no—
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—24no—
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×D4#433912yes—
706C2×D4C2×C22⋊D1112yes—
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—44no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—221no—
742C2×C8—221no—
743C2×C8—221no—
744C2×C8—221no—
745C2×C8—221no—
746C2×C8—221no—
747C2×C8—444no—
748C2×C8C2×C22⋊D1112yescomplemented
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—114no—
753C4⋊C4—112no—
754C4⋊C4—221no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—442no—
760C4⋊C4C2×C22⋊D1112yescomplemented
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—42no—
770C42—112no—
771C42—112no—
772C42—881no—
773C11#2242311yescharacteristic, complemented, Sylow
774C23—22no—
775C23—21no—
776C23—22no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—48no—
785C23—48no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—112no—
802C23—112no—
803C23—112no—
804C23—221no—
805C23—221no—
806C23—221no—
807C23—221no—
808C23—222no—
809C23—448no—
810C23—448no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—441no—
817C23—884no—
818C23—884no—
819C23—884no—
820C23—884no—
821C23—884no—
822C23C22⋊C4×D1112yes—
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—
842D4C4×C22⋊D1114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
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—448no—
870C2×C4—441no—
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×#433911yescharacteristic
882C2×C4C2×D4×D1111yescharacteristic
883C2×C4#6703711yescharacteristic
884C2×C4#6703711yescharacteristic
885C2×C4C22×C22⋊D1111yescharacteristic
886C8—22no—
887C8—41no—
888C8—441no—
889C8—441no—
890C22—22no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—114no—
913C22—222no—
914C22—222no—
915C22—222no—
916C22—222no—
917C22—222no—
918C22—222no—
919C22—442no—
920C22—442no—
921C22—442no—
922C22—8816no—
923C22—881no—
924C22—881no—
925C22—881no—
926C22—881no—
927C22C2×C22⋊C4×D1111yescharacteristic
928C22#1062302111yescharacteristic
929C22D11×AGL(1,ℤ/8)11yescharacteristic
930C22D11×AGL(1,ℤ/8)11yescharacteristic
931C22#1062330511yescharacteristic
932C22#1062330611yescharacteristic
933C22D4×C22⋊D1111yescharacteristic
934C4—22no—
935C4—42no—
936C4—81no—
937C4—222no—
938C4—222no—
939C4—222no—
940C4—442no—
941C4—881no—
942C4—881no—
943C4#1062301711yescharacteristic
944C4#1062302111yescharacteristic
945C4C2×C4×C22⋊D1111yescharacteristic
946C4D4×C22⋊D1111yescharacteristic
947C2—42no—
948C2—44no—
949C2—82no—
950C2—224no—
951C2—882no—
952C2C22⋊C4×C22⋊D1111yescharacteristic
953C2D11×#41811yescharacteristic
954C2#1307714111yescharacteristic
955C2#1308009011yescharacteristic
956C2#1308010511yescharacteristic
957C2#1308063811yescharacteristic
958C2#1308075811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC23×C11C22×D4
prime radicalC2×D4×C22⋊D11C2
cosocleC22×C4×C11C24
hypercenterC2×#418D11
hypocenterC11#22423
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#10622740C2semidirect
3. C2×D11×#102C2semidirect
4. #13071546C2semidirect
5. #13069541C2semidirect
6. #13069438C2semidirect
7. #13069054C2semidirect
8. #13069041C2semidirect
9. #13068938C2semidirect
10. #13068930C2semidirect
11. #13068624C2semidirect
12. #13068547C2semidirect
13. #13068545C2semidirect
14. #13068443C2semidirect
15. C2×C11×#418C2semidirect
19. C22×C11×M16C22semidirect
20. C2×C11×#117C22semidirect
25. D4×C22⋊D11C4semidirect
31. C22×C8×D11C22semidirect
32. C2×C4⋊C4×D11C22semidirect
36. C2×C11×#102C22semidirect
37. C2×C11×#102C22semidirect
40. C2×#66896C22semidirect
41. C2×#66896C22semidirect
42. #10622825C22semidirect
43. C2×C22⋊(C11⋊C8)C22semidirect
45. C2×#66885C22semidirect
46. C2×#66885C22semidirect
47. C2×(C2×D11)⋊C8C22semidirect
48. C2×#66879C22semidirect
49. C2×Dic11⋊C8C22semidirect
50. #10622600C22semidirect
51. #10622590C22semidirect
52. C4⋊C4×Dic11C22semidirect
53. C2×#66873C22semidirect
54. C2×#66873C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
72. C22×D4×C11C2×C4semidirect
112. #66993C2×C4semidirect
118. D4×Dic11C2×C4semidirect
120. #66983C2×C4semidirect
143. C11×#102D4semidirect
263. C2×C8×C11C2×D4semidirect
267. C11×C4⋊C4C2×D4semidirect
297. C2×#418D11semidirect
429. C22×M16C2×D11semidirect
441. C2×#117C2×D11semidirect
457. C2×#102C2×D11semidirect
458. C2×#102C2×D11semidirect
517. C2×D11#418semidirect
555. C22×D4C4×D11semidirect
619. #102C22⋊D11semidirect
748. C2×C8C2×C22⋊D11semidirect
760. C4⋊C4C2×C22⋊D11semidirect
773. C11#22423semidirect

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×#106227402
C2×D11×#1022
#130715462
#130695412
#130694382
#130690542
#130690412
#130689382
#130689302
#130686242
#130685472
#130685452
#130684432
C2×C11×#4182
#2242311