Finite Group Databasebeta

← #14769315

Subgroups — #14769315

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×#10622744C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4#13071545C211yesmaximal, characteristic, complemented
5#13069542C211yesmaximal, characteristic, complemented
6#13069440C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069044C211yesmaximal, characteristic, complemented
9#13068936C211yesmaximal, characteristic, complemented
10#13068931C211yesmaximal, characteristic, complemented
11#13068627C211yesmaximal, characteristic, complemented
12#13068548C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14#13068442C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic, complemented
20C23×C8×C11C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66979C2211yescharacteristic, complemented
25C22×C4⋊Dic11C2211yescharacteristic, complemented
26D4×D44—24no—
27D4×D44C418yescomplemented
28C2×#66948—21no—
29C2×#66935—21no—
30C2×#66935—21no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C11×#435—24no—
34C2×C11×C4⋊C8C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic, complemented
36C2×C11×C22⋊C8C2211yescharacteristic, complemented
37C2×C11×#97C2211yescharacteristic, complemented
38#10622833—21no—
39#10622825C2211yescharacteristic, complemented
40#10622825C2211yescharacteristic, complemented
41#10622744—24no—
42C2×#66885—24no—
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×#66885C2211yescharacteristic, complemented
48C2×#66885C2211yescharacteristic, complemented
49C2×#66885C2211yescharacteristic, complemented
50C2×#66885C2211yescharacteristic, complemented
51C2×#66885C2211yescharacteristic, complemented
52C2×#66885C2211yescharacteristic, complemented
53C2×#66885C2211yescharacteristic, complemented
54C2×#66885C2211yescharacteristic, complemented
55#10622594—21no—
56#10622564—21no—
57C22⋊C4×Dic11—21no—
58#10622549C2211yescharacteristic, complemented
59C4×C4⋊Dic11C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63#10622189C2211yescharacteristic, complemented
64C24×D11—21no—
65C24×D11—21no—
66C22×D4×C11D411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C23×Dic11—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—
95C2×C11×M16—22no—
96C2×C11×M16—22no—
97C2×C11×M16—41no—
98C22×C8×C11—22no—
99C22×C8×C11—22no—
100C22×C8×C11—41no—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C4×D4×C11C2×C414yes—
106C4×D4×C11D414yes—
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114#66983—22no—
115#66983—22no—
116#66983C2×C414yes—
117#66983C2×C414yescomplemented
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121#66979—22no—
122#66979—41no—
123C2×C4⋊Dic11—22no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—41no—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133#66948—28no—
134#66935—28no—
135#66935—28no—
136#66927—22no—
137#66927C2×C414yescomplemented
138C4×D44—22no—
139C4×D44C2×C414yescomplemented
140C11×C4⋊C8—22no—
141C11×C22⋊C8—22no—
142C11×C22⋊C8—22no—
143C11×#97—22no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149#66885—22no—
150#66885—22no—
151#66885—22no—
152#66885—22no—
153#66885—22no—
154#66885—22no—
155#66885—22no—
156#66885—41no—
157#66885—41no—
158#66885—41no—
159#66885—41no—
160#66885D414yescomplemented
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×C11C22×C412yes—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—42no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—42no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—42no—
213C22×Dic11—42no—
214C22×Dic11—81no—
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×M16—44no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—44no—
270C2×C8×C11C2×D412yescomplemented
271C11×C4⋊C4C22⋊C414yes—
272C11×C22⋊C4C22⋊C414yes—
273C11×C22⋊C4C22⋊C414yes—
274C42×C11C22×C412yes—
275C42×C11C2×D412yes—
276C22⋊Dic11—42no—
277C22⋊Dic11—42no—
278C22⋊Dic11—81no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11—21no—
285C4⋊Dic11—21no—
286C4⋊Dic11—21no—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11—21no—
290C4⋊Dic11—42no—
291C4⋊Dic11C22×C412yes—
292C4⋊Dic11C2×D412yescomplemented
293C4×Dic11—42no—
294C4×Dic11—81no—
295C2×D42—111no—
296C2×#435D1111yescharacteristic, complemented
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#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×C11C2×C22⋊C412yes—
378C2×C4×C11C2×C22⋊C412yes—
379C2×C4×C11C2×C22⋊C412yes—
380C2×C4×C11C2×C22⋊C412yes—
381C2×C4×C11C23×C411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C2×#4111yescharacteristic
385C2×C4×C11H(5,𝔽2)11yescharacteristic
386C2×C4×C11H(5,𝔽2)11yescharacteristic
387C22⋊D11—48no—
388C22⋊D11—48no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—84no—
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—
422C8×C11—22no—
423C8×C11—41no—
424C8×C11—41no—
425C8×C11—41no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4—221no—
429C22×M16C2×D1111yescharacteristic, complemented
430C23×C8C2×D1111yescharacteristic, complemented
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×#117—111no—
442C22×C4⋊C4—111no—
443#435—24no—
444C2×C4⋊C8C2×D1111yescharacteristic, complemented
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⋊C8C2×D1111yescharacteristic, complemented
460C2×C22⋊C8C2×D1111yescharacteristic, complemented
461C2×#97C2×D1111yescharacteristic, complemented
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—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×C11C2×C4×D411yescharacteristic
523C4×C11#51811yescharacteristic
524C4×C11D4211yescharacteristic
525C4×C11#54611yescharacteristic
526Dic11—42no—
527Dic11—42no—
528Dic11—81no—
529Dic11—81no—
530Dic11—81no—
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—221no—
546C22×D4—221no—
547C22×D4—221no—
548C22×D4—221no—
549C22×D4—222no—
550C22×D4—222no—
551C22×D4—441no—
552C22×D4—441no—
553C22×D4—441no—
554C22×D4—441no—
555C22×D4—444no—
556C22×D4—444no—
557C22×D4D4411yescharacteristic
558C23×C4—221no—
559C23×C4—221no—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—41no—
565C22×C8—22no—
566C22×C8—22no—
567C22×C8—41no—
568C22×C8C22×D1111yescharacteristic
569C22×C8C22×D1111yescharacteristic
570C22×C8C22×D1111yescharacteristic
571C22×C8C22×D1111yescharacteristic
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×D4C22⋊D1114yes—
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—111no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—441no—
595C2×C4⋊C4D4411yescharacteristic
596C2×C22⋊C4—221no—
597C2×C22⋊C4—221no—
598C2×C22⋊C4—221no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4D4411yescharacteristic
603C2×C22⋊C4D4411yescharacteristic
604C2×C42—221no—
605C2×C42—221no—
606C2×C42C22×D1111yescharacteristic
607C4⋊C8—22no—
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—22no—
621C22⋊C8—22no—
622#97—22no—
623#95—221no—
624#95—221no—
625#95—221no—
626#95—221no—
627#95—221no—
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×D4411yescharacteristic
658C24C2×D4411yescharacteristic
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—221no—
716C22×C4—221no—
717C22×C4—224no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—442no—
722C22×C4—442no—
723C22×C4—442no—
724C22×C4—442no—
725C22×C4—881no—
726C22×C4C2×C4×D1112yes—
727C22×C4C2×C4×D1112yes—
728C22×C4C2×D4411yescharacteristic
729C22×C4C2×D4411yescharacteristic
730C22×C4C2×D4411yescharacteristic
731C22×C4C2×D4411yescharacteristic
732C22×C4C2×C22⋊D1112yes—
733C22×C4C2×C22⋊D1112yes—
734C22×C4C23×D1111yescharacteristic
735M16—44no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—44no—
748C2×C8D4×D1112yescomplemented
749C4⋊C4—112no—
750C4⋊C4—112no—
751C4⋊C4—221no—
752C4⋊C4—221no—
753C4⋊C4—221no—
754C4⋊C4—221no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—442no—
760C4⋊C4(C2×D11)⋊C414yes—
761C22⋊C4—224no—
762C22⋊C4—224no—
763C22⋊C4—224no—
764C22⋊C4—442no—
765C22⋊C4—442no—
766C22⋊C4—881no—
767C22⋊C4(C2×D11)⋊C414yes—
768C22⋊C4(C2×D11)⋊C414yes—
769C42—442no—
770C42—881no—
771C42C2×C4×D1112yes—
772C42C2×C22⋊D1112yes—
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—448no—
797C23—441no—
798C23—441no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—884no—
810C23—884no—
811C23—884no—
812C23—884no—
813C23—884no—
814C23—884no—
815C23—884no—
816C23—884no—
817C23—884no—
818C23—884no—
819C23#6696112yes—
820C23#6696112yes—
821C23C2×(C2×D11)⋊C412yes—
822C23C2×(C2×D11)⋊C412yes—
823C23C22×D4411yescharacteristic
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—222no—
860C2×C4—222no—
861C2×C4—448no—
862C2×C4—441no—
863C2×C4—441no—
864C2×C4—441no—
865C2×C4—441no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—884no—
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×C4C2×D4×D1111yescharacteristic
882C2×C4#6703711yescharacteristic
883C2×C4#41×D1111yescharacteristic
884C2×C4#6704211yescharacteristic
885C2×C4C22×C22⋊D1111yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
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#1062274414yescomplemented
927C22D4×D4411yescharacteristic
928C22#1062308511yescharacteristic
929C22C2×#6696111yescharacteristic
930C22C2×#6696111yescharacteristic
931C22#1062328211yescharacteristic
932C22#1062328311yescharacteristic
933C22C22×(C2×D11)⋊C411yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—442no—
939C4—442no—
940C4—881no—
941C4—881no—
942C4—881no—
943C4C4×D4×D1111yescharacteristic
944C4#1062307611yescharacteristic
945C4D4×C22⋊D1111yescharacteristic
946C4#1062336011yescharacteristic
947C2—24no—
948C2—42no—
949C2—444no—
950C2—882no—
951C2—882no—
952C2D4×(C2×D11)⋊C411yescharacteristic
953C2C2×#1062274411yescharacteristic
954C2#1307714311yescharacteristic
955C2#1308010111yescharacteristic
956C2#1308011611yescharacteristic
957C2#1308063911yescharacteristic
958C2#1308075911yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×D4×D44C2
cosocleC22×C4×C11C24
hypercenterC2×#435D11
hypocenterC11#22423
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#10622744C2semidirect
3. C22×#66885C2semidirect
4. #13071545C2semidirect
5. #13069542C2semidirect
6. #13069440C2semidirect
7. #13069054C2semidirect
8. #13069044C2semidirect
9. #13068936C2semidirect
10. #13068931C2semidirect
11. #13068627C2semidirect
12. #13068548C2semidirect
13. #13068548C2semidirect
14. #13068442C2semidirect
15. C2×C11×#435C2semidirect
19. C22×C11×M16C22semidirect
20. C23×C8×C11C22semidirect
24. C2×#66979C22semidirect
25. C22×C4⋊Dic11C22semidirect
27. D4×D44C4semidirect
34. C2×C11×C4⋊C8C22semidirect
35. C2×C11×C22⋊C8C22semidirect
36. C2×C11×C22⋊C8C22semidirect
37. C2×C11×#97C22semidirect
39. #10622825C22semidirect
40. #10622825C22semidirect
47. C2×#66885C22semidirect
48. C2×#66885C22semidirect
49. C2×#66885C22semidirect
50. C2×#66885C22semidirect
51. C2×#66885C22semidirect
52. C2×#66885C22semidirect
53. C2×#66885C22semidirect
54. C2×#66885C22semidirect
58. #10622549C22semidirect
59. C4×C4⋊Dic11C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622189C22semidirect
63. #10622189C22semidirect
90. C22×D44C2×C4semidirect
117. #66983C2×C4semidirect
137. #66927C2×C4semidirect
139. C4×D44C2×C4semidirect
160. #66885D4semidirect
270. C2×C8×C11C2×D4semidirect
292. C4⋊Dic11C2×D4semidirect
296. C2×#435D11semidirect
429. C22×M16C2×D11semidirect
430. C23×C8C2×D11semidirect
444. C2×C4⋊C8C2×D11semidirect
459. C2×C22⋊C8C2×D11semidirect
460. C2×C22⋊C8C2×D11semidirect
461. C2×#97C2×D11semidirect
487. C22×C11#418semidirect
748. C2×C8D4×D11semidirect
773. C11#22423semidirect
926. C22#10622744semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D442
C2×#106227442
C22×#668852
#130715452
#130695422
#130694402
#130690542
#130690442
#130689362
#130689312
#130686272
#130685482
#130684422
C2×C11×#4352
#2242311