Finite Group Databasebeta

← #14800852

Subgroups — #14800852

Order 2816.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622662C211yesmaximal, characteristic, complemented
2C2×#10622659C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5#13071972C211yesmaximal, characteristic
6#13070001C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069798C211yesmaximal, characteristic, complemented
9#13069617C211yesmaximal, characteristic, complemented
10#13069500C211yesmaximal, characteristic, complemented
11#13069312C211yesmaximal, characteristic, complemented
12#13069052C211yesmaximal, characteristic, complemented
13#13069040C211yesmaximal, characteristic, complemented
14#13068804C211yesmaximal, characteristic, complemented
15C11×#2417C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66990—21no—
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C22×#4318C2211yescharacteristic, complemented
27C23×C11⋊C8C2211yescharacteristic
28C11×#398—21no—
29C11×#396—21no—
30C11×#391C2211yescharacteristic, complemented
31C11×#389C2211yescharacteristic, complemented
32C11×#386—21no—
33C11×#380—21no—
34C11×#380C2211yescharacteristic, complemented
35C2×#66899C2211yescharacteristic, complemented
36C2×#66899C2211yescharacteristic, complemented
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
40#10622662—24no—
41#10622659—24no—
42#10622624—24no—
43#10622604—21no—
44C2×#66873—24no—
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66871C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53#10622573—21no—
54#10622568—21no—
55#10622552C2211yescharacteristic
56#10622552C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×#66867C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C24×D11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11D411yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—21no—
76C22×D44—41no—
77C22×D44—41no—
78C22×D44C2311yescharacteristic
79C22×D44C2311yescharacteristic
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—41no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4D411yescharacteristic
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103C2×#4325—22no—
104C2×#4325—22no—
105C2×#4325—22no—
106C2×#4325—22no—
107C2×#4325—41no—
108C2×#4325—41no—
109#66990—44no—
110#66983—22no—
111#66983—22no—
112#66983—41no—
113#66983—41no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×#4318—22no—
123C2×#4318—22no—
124C2×#4318—41no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—22no—
127C22×C11⋊C8—41no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136#66899—22no—
137#66899—41no—
138C11⋊#95—21no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)D414yescomplemented
141#66873—22no—
142#66873—22no—
143#66873—22no—
144#66873—22no—
145#66873—22no—
146#66873D414yescomplemented
147#66871—22no—
148#66871—41no—
149C4⋊(C11⋊C8)—22no—
150#66867—22no—
151#25128—111nomaximal, Sylow
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—42no—
157C23×D11—42no—
158C23×D11—42no—
159C23×D11—42no—
160C23×D11—42no—
161C23×D11—81no—
162C23×D11—81no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—81no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D412yes—
194C22×C4×C11#4112yes—
195C22×C4×C11C2411yescharacteristic
196C2×C22⋊D11—42no—
197C2×C22⋊D11—42no—
198C2×C22⋊D11—42no—
199C2×C22⋊D11—42no—
200C2×C22⋊D11—81no—
201C2×C22⋊D11—81no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C2×D44—28no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—42no—
216C2×D44—42no—
217C2×D44—44no—
218C2×D44—44no—
219C2×D44—44no—
220C2×D44—42no—
221C2×D44C2×D412yes—
222C2×D44#4112yes—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—42no—
230C11×C4⋊C4—42no—
231C11×C4⋊C4—42no—
232C11×C4⋊C4—81no—
233C11×C4⋊C4C2×D412yes—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—81no—
239C42×C11—21no—
240C42×C11—21no—
241C22⋊Dic11—42no—
242#4325—44no—
243#4325—44no—
244(C2×D11)⋊C4—42no—
245(C2×D11)⋊C4—42no—
246(C2×D11)⋊C4—42no—
247(C2×D11)⋊C4—42no—
248(C2×D11)⋊C4—81no—
249(C2×D11)⋊C4—81no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254#4318—44no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—44no—
265C2×C11⋊C8C2×D412yes—
266C2×C11⋊C8C2×D412yes—
267C2×C11⋊C8C2×D412yes—
268C2×#468—111no—
269C2×#450—111no—
270C2×#435—111no—
271C22×#102—111no—
272#2417D1111yescharacteristic, complemented
273#2408—111no—
274#2067—111no—
275#2055—111no—
276#2033—111no—
277#2000—111no—
278#1973—111no—
279#1936—111no—
280#1895—111no—
281#1892—111no—
282#1852—111no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11#12112yes—
295C23×C11AGL(1,ℤ/8)12yes—
296C23×C11#13712yes—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—48no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—84no—
314C22×D11—84no—
315C22×D11—84no—
316C22×D11—84no—
317C22×D11—84no—
318C22×D11—84no—
319Q8×C11—41no—
320Q8×C11—41no—
321Q8×C11—41no—
322Q8×C11—41no—
323D4×C11—44no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—22no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—84no—
356C2×C4×C11#12112yes—
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C2×#4111yescharacteristic
360C2×C4×C11C2×#4111yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C22⋊D11—84no—
364C22⋊D11—84no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371D44—22no—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—48no—
376D44—41no—
377D44—41no—
378D44—41no—
379D44—41no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C11⋊C8—22no—
383C11⋊C8—41no—
384C23×D4—111no—
385C22×SD16—111no—
386C22×SD16—111no—
387C22×M16—111no—
388C23×C8—111no—
389C2×C22⋊Q8C2×D1111yescharacteristic
390C2×C22⋊Q8C2×D1111yescharacteristic, complemented
391C2×#121—111no—
392C2×#121—111no—
393C2×#120—221no—
394C2×C4×D4C2×D1111yescharacteristic
395C22×C4⋊C4C2×D1111yescharacteristic
396#468—224no—
397#450—224no—
398#435—224no—
399C2×#107—111no—
400C2×#107—111no—
401C2×C4⋊C8—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×#102—224no—
411C2×C22⋊C8—111no—
412C2×C22⋊C8—111no—
413C2×#97—111no—
414#398—21no—
415#396—21no—
416#394—221no—
417#392—221no—
418#391C2×D1111yescharacteristic, complemented
419#390—111no—
420#390—111no—
421#389C2×D1111yescharacteristic, complemented
422#386—21no—
423#380—21no—
424#380—111no—
425#380C2×D1111yescharacteristic, complemented
426#379—221no—
427#340—111no—
428#340—111no—
429#340—111no—
430#340—111no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11#46814yescomplemented
445C22×C11C2×#12111yescharacteristic
446C22×C11D4211yescharacteristic
447C22×C11#54611yescharacteristic
448C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
449C22×C11C2×#13711yescharacteristic
450C22×C11#57611yescharacteristic
451C22×C11#57711yescharacteristic
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—816no—
459C2×D11—81no—
460C2×D11—81no—
461C2×D11—81no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C2×D11—81no—
466C2×D11—81no—
467C4×C11—22no—
468C4×C11—41no—
469C4×C11—42no—
470C4×C11—41no—
471C4×C11—41no—
472C4×C11—81no—
473C4×C11—81no—
474C4×C11—81no—
475C4×C11#52511yescharacteristic
476C4×C11#53811yescharacteristic
477C4×C11D4211yescharacteristic
478C4×C11#54611yescharacteristic
479Dic11—81no—
480Dic11—81no—
481C25—221no—
482C22×Q8C22×D1111yescharacteristic
483C22×D4—111no—
484C22×D4—111no—
485C22×D4—222no—
486C22×D4—222no—
487C22×D4—221no—
488C22×D4—221no—
489C22×D4—222no—
490C22×D4—222no—
491C22×D4—221no—
492C22×D4—441no—
493C22×D4—441no—
494C22×D4C22⋊D1111yescharacteristic
495C23×C4—21no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×SD16—222no—
499C2×SD16—222no—
500C2×SD16—222no—
501C2×SD16—222no—
502C2×SD16—441no—
503C2×SD16—441no—
504C2×M16—222no—
505C2×M16—222no—
506C2×M16—441no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—111no—
511C22×C8—222no—
512C22×C8—222no—
513C22×C8—441no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—41no—
518#121—222no—
519#121—222no—
520#121—441no—
521#121—441no—
522#120—444no—
523C4×D4—22no—
524C4×D4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—41no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4C22⋊D1111yescharacteristic
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4C22⋊D1111yescharacteristic
548C2×C22⋊C4C22⋊D1111yescharacteristic
549C2×C42C22×D1111yescharacteristic
550#107—222no—
551#107—441no—
552C4⋊C8—222no—
553#103—222no—
554#103—441no—
555#102—114no—
556#102—222no—
557#102—222no—
558#102—222no—
559#102—222no—
560#102—222no—
561C22⋊C8—114no—
562C22⋊C8—222no—
563#97—222no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—221no—
569C2×C11—24no—
570C2×C11—81no—
571C2×C11#242411yescharacteristic
572C2×C11C2×#46811yescharacteristic
573C2×C11#306211yescharacteristic
574C2×C11#326411yescharacteristic
575C2×C11#326611yescharacteristic
576C2×C11#331011yescharacteristic
577C2×C11#331411yescharacteristic
578D11—82no—
579D11—82no—
580C24—221no—
581C24—221no—
582C24—442no—
583C24—442no—
584C24—442no—
585C24—442no—
586C24—442no—
587C24—881no—
588C24—881no—
589C24C2×C22⋊D1111yescharacteristic
590C24C2×C22⋊D1111yescharacteristic
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—112no—
601C2×D4—112no—
602C2×D4—228no—
603C2×D4—221no—
604C2×D4—221no—
605C2×D4—221no—
606C2×D4—221no—
607C2×D4—221no—
608C2×D4—221no—
609C2×D4—221no—
610C2×D4—221no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—444no—
614C2×D4—444no—
615C2×D4—442no—
616C2×D4—442no—
617C2×D4—444no—
618C2×D4—442no—
619C2×D4—442no—
620C2×D4—442no—
621C2×D4—442no—
622C2×D4—442no—
623C2×D4—881no—
624C2×D4—881no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—81no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4D4×D1112yes—
645C22×C4#434112yes—
646C22×C4C2×C22⋊D1111yescharacteristic
647C22×C4C2×C22⋊D1111yescharacteristic
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C23×D1111yescharacteristic
651SD16—444no—
652SD16—444no—
653M16—444no—
654C2×C8—112no—
655C2×C8—112no—
656C2×C8—112no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C2×C8—221no—
665C2×C8—221no—
666C2×C8—444no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—81no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4D4×D1112yes—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—442no—
688C22⋊C4—442no—
689C22⋊C4—442no—
690C22⋊C4—442no—
691C22⋊C4—442no—
692C22⋊C4—881no—
693C22⋊C4—881no—
694C42—21no—
695C42—21no—
696C11#2512811yescharacteristic, complemented, Sylow
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—222no—
709C23—222no—
710C23—448no—
711C23—441no—
712C23—441no—
713C23—441no—
714C23—441no—
715C23—441no—
716C23—441no—
717C23—441no—
718C23—441no—
719C23—441no—
720C23—441no—
721C23—441no—
722C23—441no—
723C23—884no—
724C23—884no—
725C23—884no—
726C23—884no—
727C23—884no—
728C23—884no—
729C23#6699212yes—
730C23#6699512yes—
731C23#6700212yes—
732C23C22×C22⋊D1111yescharacteristic
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—44no—
738D4—222no—
739D4—222no—
740D4—222no—
741D4—222no—
742D4—448no—
743D4—441no—
744D4—441no—
745D4—441no—
746D4—441no—
747D4—884no—
748D4—884no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—84no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4—441no—
787C2×C4#6699212yes—
788C2×C4C2×D4×D1111yescharacteristic
789C2×C4C2×D4×D1111yescharacteristic
790C2×C4C2×#434111yescharacteristic
791C2×C4#6703711yescharacteristic
792C2×C4#41×D1111yescharacteristic
793C2×C4#6704211yescharacteristic
794C8—222no—
795C8—222no—
796C8—222no—
797C8—441no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—442no—
812C22—442no—
813C22—442no—
814C22—442no—
815C22—442no—
816C22—442no—
817C22—8816no—
818C22—881no—
819C22—881no—
820C22—881no—
821C22—881no—
822C22—881no—
823C22—881no—
824C22—881no—
825C22—881no—
826C22#1062266214yescomplemented
827C22D4×C22⋊D1111yescharacteristic
828C22C2×#6699211yescharacteristic
829C22C2×#6699511yescharacteristic
830C22C2×#6700211yescharacteristic
831C22#1062336011yescharacteristic
832C22#1062336611yescharacteristic
833C22#1062336811yescharacteristic
834C4—22no—
835C4—41no—
836C4—41no—
837C4—42no—
838C4—41no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—881no—
843C4—881no—
844C4#1062313711yescharacteristic
845C4#1062314011yescharacteristic
846C4#1062314111yescharacteristic
847C4#1062314811yescharacteristic
848C2—24no—
849C2—81no—
850C2—882no—
851C2—882no—
852C2#1307215811yescharacteristic
853C2C2×#1062266211yescharacteristic
854C2#1307829811yescharacteristic
855C2#1308009711yescharacteristic
856C2#1308012711yescharacteristic
857C2#1308063111yescharacteristic
858C2#1308069111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2417C2
socleC23×C11C22×D4
prime radical#13071972C2
hypercenter#2417D11
hypocenterC11#25128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
1. C2×#10622662C2semidirect
2. C2×#10622659C2semidirect
3. C2×#10622624C2semidirect
4. C22×#66873C2semidirect
6. #13070001C2semidirect
7. #13069931C2semidirect
8. #13069798C2semidirect
9. #13069617C2semidirect
10. #13069500C2semidirect
11. #13069312C2semidirect
12. #13069052C2semidirect
13. #13069040C2semidirect
14. #13068804C2semidirect
15. C11×#2417C2semidirect
18. C2×C11×C22⋊Q8C22semidirect
26. C22×#4318C22semidirect
30. C11×#391C22semidirect
31. C11×#389C22semidirect
34. C11×#380C22semidirect
35. C2×#66899C22semidirect
36. C2×#66899C22semidirect
39. C2×C22⋊(C11⋊C8)C22semidirect
51. C2×#66871C22semidirect
52. C2×#66871C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×#66867C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
140. C22⋊(C11⋊C8)D4semidirect
146. #66873D4semidirect
272. #2417D11semidirect
390. C2×C22⋊Q8C2×D11semidirect
418. #391C2×D11semidirect
421. #389C2×D11semidirect
425. #380C2×D11semidirect
444. C22×C11#468semidirect
696. C11#25128semidirect
826. C22#10622662semidirect

Maximal subgroups

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

subgroupindex
C2×#106226622
C2×#106226592
C2×#106226242
C22×#668732
#130719722
#130700012
#130699312
#130697982
#130696172
#130695002
#130693122
#130690522
#130690402
#130688042
C11×#24172
#2512811