Finite Group Databasebeta

← #14769307

Subgroups — #14769307

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×D44C211yesmaximal, characteristic
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×#10622614C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5#13069543C211yesmaximal, characteristic, complemented
6#13069439C211yesmaximal, characteristic, complemented
7#13069052C211yesmaximal, characteristic, complemented
8#13069042C211yesmaximal, characteristic, complemented
9#13068938C211yesmaximal, characteristic, complemented
10#13068933C211yesmaximal, characteristic, complemented
11#13068623C211yesmaximal, characteristic, complemented
12#13068546C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068444C211yesmaximal, characteristic, complemented
15C11×#2352C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic, complemented
21C22×C11×C4⋊C4C2211yescharacteristic, complemented
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C22×#4318C2211yescharacteristic, complemented
25C23×C11⋊C8C2211yescharacteristic, complemented
26D4×D44—24no—
27D4×D44C418yescomplemented
28C2×#66948—21no—
29C2×#66935—21no—
30C2×#66935—21no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C11×#388—21no—
34C11×#387—21no—
35C11×#386—21no—
36C11×#382C2211yescharacteristic, complemented
37C11×#380C2211yescharacteristic, complemented
38C11×#380C2211yescharacteristic, complemented
39C4×C11×C4⋊C4C2211yescharacteristic, complemented
40C4×C11×C22⋊C4—21no—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
42C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
43#10622624—24no—
44#10622614—24no—
45C2×#66873—24no—
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic, complemented
51C2×#66873C2211yescharacteristic, complemented
52C2×#66873C2211yescharacteristic, complemented
53C2×#66873C2211yescharacteristic, complemented
54C2×#66873C2211yescharacteristic, complemented
55C2×#66873C2211yescharacteristic, complemented
56C2×#66873C2211yescharacteristic, complemented
57C2×#66873C2211yescharacteristic, complemented
58C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C2×#66867C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C24×D11—21no—
66C22×D4×C11D411yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—21no—
71C22×C22⋊D11—21no—
72C2×D4×D11—28no—
73C2×D4×D11—44no—
74C2×D4×D11—44no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—21no—
80C22×D44—21no—
81C22×D44—21no—
82C22×D44—22no—
83C22×D44—22no—
84C22×D44—21no—
85C22×D44—41no—
86C22×D44—41no—
87C22×D44—41no—
88C22×D44—41no—
89C22×D44C2×C414yes—
90C22×D44C2×C414yescomplemented
91C22×D44C2311yescharacteristic
92C22×D44C2311yescharacteristic
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C4×D4×C11C2×C414yes—
96C4×D4×C11D414yes—
97C11×#117—22no—
98C11×#117—41no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—41no—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C42×C11—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115#66983—22no—
116#66983—22no—
117#66983C2×C414yes—
118#66983C2×C414yescomplemented
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×#4318—22no—
124C2×#4318—22no—
125C2×#4318—41no—
126C22×C11⋊C8—22no—
127C22×C11⋊C8—22no—
128C22×C11⋊C8—41no—
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133#66948—28no—
134#66935—28no—
135#66935—28no—
136#66927—22no—
137#66927C2×C414yescomplemented
138C4×D44—22no—
139C4×D44C2×C414yescomplemented
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144C11×#95—21no—
145C22⋊(C11⋊C8)—22no—
146C22⋊(C11⋊C8)—22no—
147#66873—22no—
148#66873—22no—
149#66873—22no—
150#66873—22no—
151#66873—22no—
152#66873—22no—
153#66873—22no—
154#66873—41no—
155#66873—41no—
156#66873—41no—
157#66873—41no—
158#66873D414yescomplemented
159C4⋊(C11⋊C8)—22no—
160#66867—22no—
161#22423—111nomaximal, Sylow
162C24×C11C2×D411yescharacteristic
163C24×C11C2×D411yescharacteristic
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—24no—
168C23×D11—24no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11—42no—
175C23×D11—42no—
176C23×D11—42no—
177C23×D11—81no—
178C23×D11—81no—
179C23×D11—81no—
180C23×D11—81no—
181C2×D4×C11—22no—
182C2×D4×C11—22no—
183C2×D4×C11C22⋊C414yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11—81no—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—42no—
211C2×C22⋊D11—42no—
212C2×C22⋊D11—42no—
213C2×C22⋊D11—42no—
214C22×Dic11—21no—
215D4×D11—432no—
216C2×D44—28no—
217C2×D44—28no—
218C2×D44—24no—
219C2×D44—24no—
220C2×D44—24no—
221C2×D44—24no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—21no—
226C2×D44—21no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—42no—
236C2×D44—42no—
237C2×D44—42no—
238C2×D44—42no—
239C2×D44—44no—
240C2×D44—44no—
241C2×D44—44no—
242C2×D44—44no—
243C2×D44—44no—
244C2×D44—44no—
245C2×D44—42no—
246C2×D44—42no—
247C2×D44—81no—
248C2×D44—81no—
249C2×D44C22×C412yes—
250C2×D44C22×C412yes—
251C2×D44C22×C412yes—
252C2×D44C2×D412yes—
253C2×D44#4112yes—
254C2×C4×D11—24no—
255C2×C4×D11—42no—
256C2×C4×D11—42no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—42no—
265C11×C4⋊C4C22⋊C414yes—
266C11×C4⋊C4C2×D412yescomplemented
267C11×C22⋊C4—42no—
268C11×C22⋊C4—42no—
269C11×C22⋊C4—81no—
270C11×C22⋊C4C22⋊C414yes—
271C11×C22⋊C4C22⋊C414yes—
272C42×C11—42no—
273C42×C11—81no—
274C42×C11C22×C412yes—
275C42×C11C2×D412yes—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279C4⋊Dic11—21no—
280C4⋊Dic11C22×C412yes—
281#4318—44no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286C2×C11⋊C8—21no—
287C2×C11⋊C8—21no—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8—21no—
293C2×C11⋊C8—44no—
294C2×C11⋊C8C2×D412yescomplemented
295C2×D42—111no—
296C2×#435—111no—
297C2×#418—111no—
298C22×#102—111no—
299#2352D1111yescharacteristic, complemented
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—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11C2×C22⋊C412yes—
321C23×C11C2×C22⋊C412yes—
322C23×C11AGL(1,ℤ/8)12yes—
323C23×C11AGL(1,ℤ/8)12yes—
324C23×C11C22×D411yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—48no—
331C22×D11—48no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—48no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—48no—
350C22×D11—84no—
351C22×D11—84no—
352C22×D11—84no—
353C22×D11—84no—
354C22×D11—84no—
355C22×D11—84no—
356C22×D11—84no—
357C22×D11—84no—
358C22×D11—84no—
359C22×D11—84no—
360D4×C11—28no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—84no—
390C2×C4×C11C2×C22⋊C412yes—
391C2×C4×C11C2×C22⋊C412yes—
392C2×C4×C11C2×C22⋊C412yes—
393C2×C4×C11C2×C22⋊C412yes—
394C2×C4×C11C23×C411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C2×#4111yescharacteristic
398C2×C4×C11H(5,𝔽2)11yescharacteristic
399C2×C4×C11H(5,𝔽2)11yescharacteristic
400C22⋊D11—48no—
401C22⋊D11—48no—
402C2×Dic11—22no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405D44—22no—
406D44—22no—
407D44—22no—
408D44—22no—
409D44—22no—
410D44—22no—
411D44—22no—
412D44—48no—
413D44—48no—
414D44—48no—
415D44—41no—
416D44—41no—
417D44—41no—
418D44—41no—
419D44—84no—
420D44C4×D414yes—
421C4×D11—48no—
422C11⋊C8—22no—
423C11⋊C8—41no—
424C11⋊C8—41no—
425C11⋊C8—41no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4—221no—
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×D4C2×D1111yescharacteristic
441C2×#117C2×D1111yescharacteristic, complemented
442C22×C4⋊C4C2×D1111yescharacteristic, complemented
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—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—224no—
459C2×C22⋊C8—111no—
460C2×C22⋊C8—111no—
461C2×#97—111no—
462#388—21no—
463#387—21no—
464#386—21no—
465#382C2×D1111yescharacteristic, complemented
466#380C2×D1111yescharacteristic, complemented
467#380C2×D1111yescharacteristic, complemented
468C4×C4⋊C4C2×D1111yescharacteristic, complemented
469C4×C22⋊C4—21no—
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—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11#41814yescomplemented
488C22×C11C22×C22⋊C411yescharacteristic
489C22×C11D4211yescharacteristic
490C22×C11#54611yescharacteristic
491C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
492C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
493C22×C11#57611yescharacteristic
494C22×C11#57711yescharacteristic
495C2×D11—24no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—816no—
509C2×D11—816no—
510C2×D11—81no—
511C2×D11—81no—
512C2×D11—81no—
513C2×D11—81no—
514C2×D11—81no—
515C2×D11—81no—
516C2×D11—81no—
517C2×D11—81no—
518C4×C11—22no—
519C4×C11—22no—
520C4×C11—22no—
521C4×C11—22no—
522C4×C11—42no—
523C4×C11—81no—
524C4×C11—81no—
525C4×C11—81no—
526C4×C11C2×C4×D411yescharacteristic
527C4×C11#51811yescharacteristic
528C4×C11D4211yescharacteristic
529C4×C11#54611yescharacteristic
530Dic11—42no—
531C25—221no—
532C25—221no—
533C22×D4—114no—
534C22×D4—114no—
535C22×D4—111no—
536C22×D4—111no—
537C22×D4—111no—
538C22×D4—222no—
539C22×D4—222no—
540C22×D4—222no—
541C22×D4—222no—
542C22×D4—221no—
543C22×D4—221no—
544C22×D4—228no—
545C22×D4—222no—
546C22×D4—222no—
547C22×D4—221no—
548C22×D4—221no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—441no—
552C22×D4—441no—
553C22×D4—441no—
554C22×D4—441no—
555C22×D4—444no—
556C22×D4—444no—
557C22×D4C22⋊D1111yescharacteristic
558C23×C4—21no—
559C23×C4—221no—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C2×M16—222no—
563C2×M16—222no—
564C2×M16—441no—
565C22×C8—111no—
566C22×C8—111no—
567C22×C8—111no—
568C22×C8—111no—
569C22×C8—222no—
570C22×C8—222no—
571C22×C8—441no—
572#127—114no—
573#127—222no—
574#121—114no—
575#121—114no—
576#121—222no—
577#121—222no—
578#121—228no—
579#120—228no—
580#120—228no—
581C4×D4—114no—
582C4×D4—222no—
583C4×D4C4×D1114yes—
584C4×D4D4414yes—
585#117—22no—
586#117—41no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4C22⋊D1111yescharacteristic
592C2×C4⋊C4C22×D1111yescharacteristic
593C2×C4⋊C4C22×D1111yescharacteristic
594C2×C4⋊C4C22×D1111yescharacteristic
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4C22⋊D1111yescharacteristic
603C2×C22⋊C4C22⋊D1111yescharacteristic
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C22×D1111yescharacteristic
607C4⋊C8—222no—
608#102—114no—
609#102—222no—
610#102—222no—
611#102—222no—
612#102—222no—
613#102—222no—
614#102—222no—
615#102—222no—
616#102—441no—
617#102—441no—
618#102—441no—
619#102—441no—
620C22⋊C8—222no—
621C22⋊C8—222no—
622#97—222no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627#95—21no—
628C2×C11—24no—
629C2×C11—42no—
630C2×C11D4×C22⋊C411yescharacteristic
631C2×C11C2×#41811yescharacteristic
632C2×C11#289711yescharacteristic
633C2×C11#326411yescharacteristic
634C2×C11#326511yescharacteristic
635C2×C11#331011yescharacteristic
636C2×C11#331811yescharacteristic
637D11—44no—
638D11—82no—
639D11—82no—
640C24—221no—
641C24—221no—
642C24—221no—
643C24—224no—
644C24—224no—
645C24—442no—
646C24—442no—
647C24—442no—
648C24—442no—
649C24—442no—
650C24—442no—
651C24—442no—
652C24—442no—
653C24—881no—
654C24—881no—
655C24—881no—
656C24—881no—
657C24C2×C22⋊D1111yescharacteristic
658C24C2×C22⋊D1111yescharacteristic
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—112no—
662C2×D4—112no—
663C2×D4—112no—
664C2×D4—112no—
665C2×D4—112no—
666C2×D4—228no—
667C2×D4—228no—
668C2×D4—224no—
669C2×D4—224no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—224no—
673C2×D4—224no—
674C2×D4—221no—
675C2×D4—221no—
676C2×D4—221no—
677C2×D4—221no—
678C2×D4—221no—
679C2×D4—221no—
680C2×D4—221no—
681C2×D4—221no—
682C2×D4—221no—
683C2×D4—221no—
684C2×D4—221no—
685C2×D4—221no—
686C2×D4—221no—
687C2×D4—444no—
688C2×D4—444no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—442no—
694C2×D4—442no—
695C2×D4—442no—
696C2×D4—442no—
697C2×D4—442no—
698C2×D4—442no—
699C2×D4—4432no—
700C2×D4—442no—
701C2×D4—442no—
702C2×D4—442no—
703C2×D4—442no—
704C2×D4—881no—
705C2×D4—881no—
706C2×D4(C2×D11)⋊C414yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—81no—
722C22×C4—221no—
723C22×C4—224no—
724C22×C4—442no—
725C22×C4—442no—
726C22×C4C2×C4×D1112yes—
727C22×C4C2×C4×D1112yes—
728C22×C4C2×D4412yes—
729C22×C4C2×D4412yes—
730C22×C4C2×C22⋊D1111yescharacteristic
731C22×C4C2×C22⋊D1111yescharacteristic
732C22×C4C2×C22⋊D1111yescharacteristic
733C22×C4C2×C22⋊D1111yescharacteristic
734C22×C4C23×D1111yescharacteristic
735M16—444no—
736C2×C8—112no—
737C2×C8—221no—
738C2×C8—221no—
739C2×C8—221no—
740C2×C8—221no—
741C2×C8—221no—
742C2×C8—221no—
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—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—42no—
757C4⋊C4—112no—
758C4⋊C4—221no—
759C4⋊C4(C2×D11)⋊C414yes—
760C4⋊C4D4×D1112yescomplemented
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—81no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—224no—
767C22⋊C4(C2×D11)⋊C414yes—
768C22⋊C4(C2×D11)⋊C414yes—
769C42—42no—
770C42—81no—
771C42C2×C4×D1112yes—
772C42C2×D4412yes—
773C11#2242311yescharacteristic, complemented, Sylow
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—448no—
790C23—448no—
791C23—448no—
792C23—441no—
793C23—441no—
794C23—441no—
795C23—441no—
796C23—441no—
797C23—441no—
798C23—441no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—448no—
809C23—884no—
810C23—884no—
811C23—884no—
812C23—884no—
813C23—884no—
814C23—884no—
815C23—884no—
816C23—884no—
817C23—884no—
818C23—884no—
819C23C2×(C2×D11)⋊C412yes—
820C23C2×(C2×D11)⋊C412yes—
821C23#6700212yes—
822C23#6700212yes—
823C23C22×C22⋊D1111yescharacteristic
824D4—28no—
825D4—114no—
826D4—222no—
827D4—222no—
828D4—222no—
829D4—222no—
830D4—222no—
831D4—222no—
832D4—222no—
833D4—448no—
834D4—448no—
835D4—448no—
836D4—448no—
837D4—448no—
838D4—441no—
839D4—441no—
840D4—441no—
841D4—441no—
842D4—884no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—84no—
872C2×C4—222no—
873C2×C4—448no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4C2×(C2×D11)⋊C412yes—
877C2×C4C2×(C2×D11)⋊C412yes—
878C2×C4C2×(C2×D11)⋊C412yes—
879C2×C4C2×(C2×D11)⋊C412yes—
880C2×C4C22×C4×D1111yescharacteristic
881C2×C4C22×D4411yescharacteristic
882C2×C4C2×D4×D1111yescharacteristic
883C2×C4#6703711yescharacteristic
884C2×C4#41×D1111yescharacteristic
885C2×C4#6704211yescharacteristic
886C8—222no—
887C8—441no—
888C8—441no—
889C8—441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—224no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—442no—
912C22—442no—
913C22—442no—
914C22—442no—
915C22—442no—
916C22—8816no—
917C22—8816no—
918C22—881no—
919C22—881no—
920C22—881no—
921C22—881no—
922C22—881no—
923C22—881no—
924C22—881no—
925C22—881no—
926C22#1062261414yescomplemented
927C22C22×(C2×D11)⋊C411yescharacteristic
928C22D4×C22⋊D1111yescharacteristic
929C22C2×#6700211yescharacteristic
930C22C2×#6700211yescharacteristic
931C22#1062336011yescharacteristic
932C22#1062336611yescharacteristic
933C22#1062336811yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4—81no—
942C4—442no—
943C4C4×D4×D1111yescharacteristic
944C4#1062307611yescharacteristic
945C4D4×D4411yescharacteristic
946C4#1062308511yescharacteristic
947C2—24no—
948C2—42no—
949C2—444no—
950C2—882no—
951C2—882no—
952C2D4×(C2×D11)⋊C411yescharacteristic
953C2C2×#1062261411yescharacteristic
954C2#1307713911yescharacteristic
955C2#1308009711yescharacteristic
956C2#1308011211yescharacteristic
957C2#1308063111yescharacteristic
958C2#1308075111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2352C2
socleC23×C11C22×D4
prime radicalC2×D4×D44C2
cosocleC22×C4×C11C24
hypercenter#2352D11
hypocenterC11#22423
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#10622624C2semidirect
3. C2×#10622614C2semidirect
4. C22×#66873C2semidirect
5. #13069543C2semidirect
6. #13069439C2semidirect
7. #13069052C2semidirect
8. #13069042C2semidirect
9. #13068938C2semidirect
10. #13068933C2semidirect
11. #13068623C2semidirect
12. #13068546C2semidirect
13. #13068546C2semidirect
14. #13068444C2semidirect
15. C11×#2352C2semidirect
20. C2×C11×#117C22semidirect
21. C22×C11×C4⋊C4C22semidirect
24. C22×#4318C22semidirect
25. C23×C11⋊C8C22semidirect
27. D4×D44C4semidirect
36. C11×#382C22semidirect
37. C11×#380C22semidirect
38. C11×#380C22semidirect
39. C4×C11×C4⋊C4C22semidirect
41. C2×C22⋊(C11⋊C8)C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
50. C2×#66873C22semidirect
51. C2×#66873C22semidirect
52. C2×#66873C22semidirect
53. C2×#66873C22semidirect
54. C2×#66873C22semidirect
55. C2×#66873C22semidirect
56. C2×#66873C22semidirect
57. C2×#66873C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
59. C2×#66867C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
90. C22×D44C2×C4semidirect
118. #66983C2×C4semidirect
137. #66927C2×C4semidirect
139. C4×D44C2×C4semidirect
158. #66873D4semidirect
266. C11×C4⋊C4C2×D4semidirect
294. C2×C11⋊C8C2×D4semidirect
299. #2352D11semidirect
441. C2×#117C2×D11semidirect
442. C22×C4⋊C4C2×D11semidirect
465. #382C2×D11semidirect
466. #380C2×D11semidirect
467. #380C2×D11semidirect
468. C4×C4⋊C4C2×D11semidirect
487. C22×C11#418semidirect
760. C4⋊C4D4×D11semidirect
773. C11#22423semidirect
926. C22#10622614semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D442
C2×#106226242
C2×#106226142
C22×#668732
#130695432
#130694392
#130690522
#130690422
#130689382
#130689332
#130686232
#130685462
#130684442
C11×#23522
#2242311