Finite Group Databasebeta

← #14769384

Subgroups — #14769384

Order 2816.

1910 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic, complemented
4#13071566C211yesmaximal, characteristic, complemented
5#13069541C211yesmaximal, characteristic, complemented
6#13069420C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069051C211yesmaximal, characteristic, complemented
9#13068938C211yesmaximal, characteristic, complemented
10#13068935C211yesmaximal, characteristic, complemented
11#13068614C211yesmaximal, characteristic, complemented
12#13068547C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, 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×#4313C2211yescharacteristic, complemented
32C2×#66945C2211yescharacteristic, 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#10622741—24no—
45C2×#66885C2211yescharacteristic, complemented
46C2×#66885C2211yescharacteristic, complemented
47C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49C2×C8×Dic11C2211yescharacteristic, complemented
50#10622600C2211yescharacteristic, complemented
51#10622589C2211yescharacteristic, complemented
52C4⋊C4×Dic11C2211yescharacteristic, complemented
53C2×#66873C2211yescharacteristic, complemented
54C2×#66873C2211yescharacteristic, complemented
55#10622570—21no—
56#10622557—21no—
57#10622553—21no—
58C4×Dic11⋊C4—21no—
59#10622383—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×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—
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×D11C2311yescharacteristic
94C2×C11×M16—22no—
95C2×C11×M16—22no—
96C2×C11×M16—41no—
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C11×#117—22no—
100C11×#117—41no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C42×C11—21no—
105#67006—28no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11D411yescharacteristic
110#66993—22no—
111#66993C2×C414yes—
112#66992—28no—
113#66991—22no—
114#66991C2×C414yes—
115#66990—28no—
116D4×Dic11—22no—
117D4×Dic11C2×C414yes—
118#66983—22no—
119#66983C2×C414yes—
120C4×C22⋊D11C2×C414yes—
121C4×C22⋊D11D414yes—
122C2×(C2×D11)⋊C4—21no—
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⋊C4—21no—
131C2×Dic11⋊C4D411yescharacteristic
132C2×C4×Dic11—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C2×#4313—22no—
138C2×#4313—22no—
139C2×#4313—41no—
140#66945—22no—
141#66945—41no—
142C11×#102—22no—
143C11×#102—22no—
144C11×#102—22no—
145C11×#102D414yescomplemented
146#66896—22no—
147#66896—22no—
148#66896—41no—
149#66896—41no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153C22⋊(C11⋊C8)—22no—
154#66885—22no—
155#66885—41no—
156(C2×D11)⋊C8—22no—
157Dic11⋊C8—22no—
158C8×Dic11—22no—
159#66873—22no—
160#66873—41no—
161#22428—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—22no—
214C2×C22⋊D11—22no—
215C2×C22⋊D11—24no—
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×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×D11C22×C412yes—
253C2×C4×D11C2×D412yes—
254C11×M16—44no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11C2×D412yescomplemented
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4C2×D412yescomplemented
265C11×C22⋊C4—42no—
266C42×C11—42no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—81no—
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—21no—
280C4⋊Dic11C22×C412yes—
281Dic11⋊C4—42no—
282Dic11⋊C4—81no—
283Dic11⋊C4C22⋊C414yes—
284C4×Dic11—42no—
285C4×Dic11—42no—
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—
294#4313—44no—
295C2×D42—111no—
296C2×#436—111no—
297C2×#418—111no—
298C2×#418D1111yescharacteristic, complemented
299#2354—111no—
300#1982—111no—
301#1957—111no—
302#1895—111no—
303#1895—111no—
304#1875—111no—
305#1875—111no—
306#1802—111no—
307#1786—111no—
308#1786—111no—
309C4×#102—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—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—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—22no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—48no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11C2×C22⋊C412yes—
409C2×Dic11C2×C22⋊C412yes—
410C2×Dic11C2×C22⋊C412yes—
411C2×Dic11AGL(1,ℤ/8)12yes—
412C2×Dic11AGL(1,ℤ/8)12yes—
413D44—22no—
414D44—22no—
415D44—41no—
416D44—41no—
417C4×D11—22no—
418C4×D11—22no—
419C4×D11—22no—
420C4×D11—22no—
421C8×C11—22no—
422C8×C11—41no—
423C11⋊C8—41no—
424C11⋊C8—41no—
425C23×D4—111no—
426C23×D4—221no—
427C23×D4C2×D1111yescharacteristic
428C22×M16—111no—
429C22×M16C2×D1111yescharacteristic, complemented
430D42—118no—
431D42—224no—
432C2×#127—111no—
433C2×#121—111no—
434C2×#121—111no—
435C2×#121—221no—
436C2×#120—221no—
437C2×#120—221no—
438C2×C4×D4—111no—
439C2×C4×D4—111no—
440C2×#117—111no—
441C2×#117C2×D1111yescharacteristic, complemented
442#436—224no—
443C2×C4⋊C8—111no—
444#418—24no—
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×#102C2×D1111yescharacteristic
455C2×#102C2×D1111yescharacteristic
456C2×#102C2×D1111yescharacteristic, complemented
457C2×#102C2×D1111yescharacteristic, complemented
458C2×C22⋊C8—111no—
459C2×C22⋊C8—111no—
460C2×C4×C8—111no—
461#390—221no—
462#388—221no—
463#388—221no—
464#384—111no—
465#380—111no—
466#380—111no—
467C4×C4⋊C4—111no—
468C4×C4⋊C4—221no—
469#340—111no—
470#340—111no—
471#340—111no—
472#340—111no—
473C22×C11—22no—
474C22×C11—24no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—41no—
481C22×C11—42no—
482C22×C11—41no—
483C22×C11—42no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11—41no—
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×C11C22×C22⋊C411yescharacteristic
496C22×C11D4211yescharacteristic
497C22×C11#54611yescharacteristic
498C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
499C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
500C22×C11#57611yescharacteristic
501C22×C11#57711yescharacteristic
502C2×D11—22no—
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—41no—
506C2×D11—41no—
507C2×D11—41no—
508C2×D11—41no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—816no—
513C2×D11—81no—
514C2×D11—81no—
515C2×D11—81no—
516C2×D11—81no—
517C4×C11—22no—
518C4×C11—42no—
519C4×C11—81no—
520C4×C11C2×C4×D411yescharacteristic
521C4×C11#51811yescharacteristic
522C4×C11D4211yescharacteristic
523C4×C11#54611yescharacteristic
524Dic11—22no—
525Dic11—22no—
526Dic11—42no—
527Dic11—81no—
528Dic11—81no—
529Dic11#41814yescomplemented
530C25—21no—
531C25—221no—
532C22×D4—22no—
533C22×D4—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4—111no—
539C22×D4—114no—
540C22×D4—111no—
541C22×D4—222no—
542C22×D4—221no—
543C22×D4—221no—
544C22×D4—221no—
545C22×D4—228no—
546C22×D4—222no—
547C22×D4—222no—
548C22×D4—221no—
549C22×D4—221no—
550C22×D4—441no—
551C22×D4—441no—
552C22×D4—444no—
553C22×D4—444no—
554C22×D4C4×D1114yes—
555C22×D4C22×D1111yescharacteristic
556C22×D4C22×D1111yescharacteristic
557C23×C4—111no—
558C23×C4—221no—
559C23×C4C22×D1111yescharacteristic
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C2×M16—222no—
564C2×M16—222no—
565C2×M16—441no—
566C22×C8—111no—
567C22×C8—111no—
568C22×C8C22×D1111yescharacteristic
569C22×C8C22×D1111yescharacteristic
570#127—114no—
571#127—222no—
572#121—114no—
573#121—114no—
574#121—228no—
575#121—222no—
576#121—222no—
577#120—228no—
578#120—228no—
579C4×D4—114no—
580C4×D4—114no—
581C4×D4—114no—
582C4×D4—222no—
583#117—22no—
584#117—41no—
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—221no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4C22×D1111yescharacteristic
594C2×C4⋊C4C22×D1111yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—111no—
597C2×C22⋊C4—111no—
598C2×C22⋊C4—221no—
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—
607C2×C42—221no—
608C4⋊C8—222no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—222no—
613#102—222no—
614#102—222no—
615#102—222no—
616#102—441no—
617#102—441no—
618#102—441no—
619#102—441no—
620#102C22⋊D1114yescomplemented
621C22⋊C8—222no—
622C22⋊C8—222no—
623C4×C8—222no—
624#95—221no—
625#95—221no—
626#95—221no—
627C2×C11—44no—
628C2×C11—42no—
629C2×C11—82no—
630C2×C11D4×C22⋊C411yescharacteristic
631C2×C11C2×#41811yescharacteristic
632C2×C11#289711yescharacteristic
633C2×C11#327211yescharacteristic
634C2×C11#327411yescharacteristic
635C2×C11#332411yescharacteristic
636C2×C11#332511yescharacteristic
637D11—42no—
638D11—82no—
639C24—21no—
640C24—21no—
641C24—24no—
642C24—42no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—81no—
647C24—81no—
648C24—111no—
649C24—224no—
650C24—221no—
651C24—442no—
652C24—442no—
653C24—442no—
654C24—442no—
655C24—881no—
656C24—881no—
657C24D4×D1111yescharacteristic
658C2×D4—28no—
659C2×D4—24no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—114no—
674C2×D4—112no—
675C2×D4—222no—
676C2×D4—222no—
677C2×D4—224no—
678C2×D4—224no—
679C2×D4—224no—
680C2×D4—228no—
681C2×D4—224no—
682C2×D4—224no—
683C2×D4—221no—
684C2×D4—221no—
685C2×D4—221no—
686C2×D4—221no—
687C2×D4—221no—
688C2×D4—442no—
689C2×D4—442no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—442no—
694C2×D4—442no—
695C2×D4—4432no—
696C2×D4—442no—
697C2×D4—442no—
698C2×D4—442no—
699C2×D4—442no—
700C2×D4—881no—
701C2×D4—881no—
702C2×D4C2×C4×D1112yes—
703C2×D4C2×C4×D1112yes—
704C2×D4#433912yes—
705C2×D4C2×C22⋊D1112yes—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—111no—
713C22×C4—111no—
714C22×C4—111no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—224no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—442no—
726C22×C4—442no—
727C22×C4C2×C4×D1112yes—
728C22×C4D4×D1111yescharacteristic
729C22×C4D4×D1112yes—
730C22×C4C23×D1111yescharacteristic
731M16—44no—
732M16—444no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—221no—
739C2×C8—221no—
740C2×C8—221no—
741C2×C8—221no—
742C2×C8—221no—
743C2×C8—221no—
744C2×C8C2×C22⋊D1112yescomplemented
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—114no—
749C4⋊C4—112no—
750C4⋊C4—221no—
751C4⋊C4—221no—
752C4⋊C4—221no—
753C4⋊C4—221no—
754C4⋊C4—221no—
755C4⋊C4—442no—
756C4⋊C4—881no—
757C4⋊C4C2×C22⋊D1112yescomplemented
758C22⋊C4—42no—
759C22⋊C4—114no—
760C22⋊C4—114no—
761C22⋊C4—224no—
762C22⋊C4—224no—
763C22⋊C4—224no—
764C22⋊C4—442no—
765C22⋊C4—881no—
766C22⋊C4—881no—
767C42—42no—
768C42—112no—
769C42—112no—
770C42—442no—
771C42—442no—
772C11#2242811yescharacteristic, complemented, Sylow
773C23—22no—
774C23—21no—
775C23—22no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—48no—
784C23—48no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—112no—
801C23—221no—
802C23—221no—
803C23—221no—
804C23—221no—
805C23—221no—
806C23—221no—
807C23—222no—
808C23—448no—
809C23—448no—
810C23—441no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—884no—
817C23—884no—
818C23—884no—
819C23—884no—
820C23—884no—
821C23C22⋊C4×D1112yes—
822C23C2×D4×D1111yescharacteristic
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—228no—
832D4—222no—
833D4—222no—
834D4—448no—
835D4—448no—
836D4—448no—
837D4—448no—
838D4—441no—
839D4—441no—
840D4—884no—
841D4C4×C22⋊D1114yes—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
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—112no—
855C2×C4—112no—
856C2×C4—112no—
857C2×C4—112no—
858C2×C4—112no—
859C2×C4—221no—
860C2×C4—221no—
861C2×C4—221no—
862C2×C4—221no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—448no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4C22⋊C4×D1112yes—
878C2×C4C22×C4×D1111yescharacteristic
879C2×C4C2×#433911yescharacteristic
880C2×C4C2×D4×D1111yescharacteristic
881C2×C4#6703711yescharacteristic
882C2×C4#6703711yescharacteristic
883C2×C4C22×C22⋊D1111yescharacteristic
884C8—22no—
885C8—41no—
886C8—441no—
887C8—441no—
888C22—22no—
889C22—24no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—42no—
894C22—41no—
895C22—42no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—816no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—222no—
911C22—222no—
912C22—222no—
913C22—441no—
914C22—441no—
915C22—441no—
916C22—441no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—8816no—
921C22—881no—
922C22—881no—
923C22—881no—
924C22—881no—
925C22C2×C22⋊C4×D1111yescharacteristic
926C22#1062302111yescharacteristic
927C22D11×AGL(1,ℤ/8)11yescharacteristic
928C22D11×AGL(1,ℤ/8)11yescharacteristic
929C22#1062330511yescharacteristic
930C22#1062330611yescharacteristic
931C22D4×C22⋊D1111yescharacteristic
932C4—22no—
933C4—42no—
934C4—81no—
935C4—114no—
936C4—222no—
937C4—222no—
938C4—442no—
939C4—881no—
940C4—881no—
941C4#1062301711yescharacteristic
942C4#1062302111yescharacteristic
943C4C2×C4×C22⋊D1111yescharacteristic
944C4D4×C22⋊D1111yescharacteristic
945C2—42no—
946C2—44no—
947C2—82no—
948C2—442no—
949C2—882no—
950C2C22⋊C4×C22⋊D1111yescharacteristic
951C2D11×#41811yescharacteristic
952C2#1307714111yescharacteristic
953C2#1308021011yescharacteristic
954C2#1308023011yescharacteristic
955C2#1308084311yescharacteristic
956C2#1308085411yescharacteristic
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#22428
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×#10622741C2semidirect
3. C2×#10622383C2semidirect
4. #13071566C2semidirect
5. #13069541C2semidirect
6. #13069420C2semidirect
7. #13069054C2semidirect
8. #13069051C2semidirect
9. #13068938C2semidirect
10. #13068935C2semidirect
11. #13068614C2semidirect
12. #13068547C2semidirect
13. #13068545C2semidirect
14. #102×Dic11C2semidirect
15. C2×C11×#418C2semidirect
19. C22×C11×M16C22semidirect
20. C2×C11×#117C22semidirect
25. D4×C22⋊D11C4semidirect
31. C22×#4313C22semidirect
32. C2×#66945C22semidirect
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×Dic11⋊C8C22semidirect
49. C2×C8×Dic11C22semidirect
50. #10622600C22semidirect
51. #10622589C22semidirect
52. C4⋊C4×Dic11C22semidirect
53. C2×#66873C22semidirect
54. C2×#66873C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
145. C11×#102D4semidirect
260. C2×C8×C11C2×D4semidirect
264. C11×C4⋊C4C2×D4semidirect
298. C2×#418D11semidirect
429. C22×M16C2×D11semidirect
441. C2×#117C2×D11semidirect
456. C2×#102C2×D11semidirect
457. C2×#102C2×D11semidirect
529. Dic11#418semidirect
620. #102C22⋊D11semidirect
744. C2×C8C2×C22⋊D11semidirect
757. C4⋊C4C2×C22⋊D11semidirect
772. C11#22428semidirect

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×#106227412
C2×#106223832
#130715662
#130695412
#130694202
#130690542
#130690512
#130689382
#130689352
#130686142
#130685472
#130685452
#102×Dic112
C2×C11×#4182
#2242811