Finite Group Databasebeta

← #14801503

Subgroups — #14801503

Order 2816.

1310 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622670C211yesmaximal, characteristic, complemented
2C2×#10622659C211yesmaximal, characteristic, complemented
3C2×#10622649C211yesmaximal, characteristic
4C2×#10622627C211yesmaximal, characteristic, complemented
5C22⋊C4×D44C211yesmaximal, characteristic, complemented
6#13069987C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic, complemented
8#13069795C211yesmaximal, characteristic, complemented
9#13069693C211yesmaximal, characteristic, complemented
10#13069500C211yesmaximal, characteristic, complemented
11#13069231C211yesmaximal, characteristic, complemented
12#13068964C211yesmaximal, characteristic, complemented
13#13068953C211yesmaximal, characteristic, complemented
14#13068862C211yesmaximal, characteristic, complemented
15C11×#2427C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic, complemented
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic, complemented
21C22×#4325C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C2×C22⋊C4×D11—21no—
26C2×C4×D44C2211yescharacteristic
27C2×C4×D44C2211yescharacteristic
28C11×#397—21no—
29C11×#394—21no—
30C11×#391C2211yescharacteristic, complemented
31C11×#389C2211yescharacteristic, complemented
32C11×#386—21no—
33C11×#380—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35C2×#66899C2211yescharacteristic, complemented
36C2×#66899C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic, complemented
38C2×#66896C2211yescharacteristic, complemented
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622670—24no—
43#10622659—24no—
44#10622649—24no—
45#10622627—24no—
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66872C2211yescharacteristic, complemented
51C2×#66871C2211yescharacteristic, complemented
52#10622568—21no—
53#10622552C2211yescharacteristic
54#10622552C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×#66867C2211yescharacteristic, complemented
57#10622278—21no—
58#10622278—21no—
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63C24×D11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C22×D44—21no—
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—41no—
75C22×D44—41no—
76C22×D44C2311yescharacteristic
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C22×C4×D11—21no—
80C11×#124—22no—
81C11×#124—41no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—41no—
84C11×#121—22no—
85C11×#121—41no—
86C4×D4×C11—22no—
87C4×D4×C11—41no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×#4325—22no—
103C2×#4325—22no—
104C2×#4325—22no—
105C2×#4325—22no—
106C2×#4325—22no—
107C2×#4325—41no—
108C2×#4323—22no—
109C2×#4323—22no—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323—41no—
113C2×#4323D414yes—
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
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22⋊C4×D11—44no—
127C4×D44—22no—
128C4×D44—22no—
129C4×D44—41no—
130C4×D44—41no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95D411yescharacteristic
135C11×#95D411yescharacteristic
136#66899—22no—
137#66899—41no—
138#66896—22no—
139#66896—22no—
140C11⋊#95—21no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—22no—
143#66873—22no—
144#66873—22no—
145#66873—22no—
146#66873D414yescomplemented
147#66872—22no—
148#66871—41no—
149C4⋊(C11⋊C8)—22no—
150#66867—22no—
151#25172—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11C2×D411yescharacteristic
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—24no—
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—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11—81no—
177C2×D4×C11C2×D412yes—
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—21no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—81no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C22×Dic11—21no—
197C22×Dic11—21no—
198C2×D44—24no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—42no—
208C2×D44—42no—
209C2×D44—44no—
210C2×D44—44no—
211C2×D44—44no—
212C2×D44—44no—
213C2×D44C2×D412yes—
214C2×D44C2×D412yes—
215C2×D44#4112yes—
216C2×D44#4112yes—
217C2×C4×D11—42no—
218C2×C4×D11—42no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—81no—
222C2×C4×D11—81no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—81no—
228C11×C4⋊C4C2×D412yes—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—41no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C22⋊Dic11—42no—
241#4325—44no—
242#4325—44no—
243#4323—28no—
244#4323—44no—
245(C2×D11)⋊C4—42no—
246(C2×D11)⋊C4—42no—
247(C2×D11)⋊C4—42no—
248(C2×D11)⋊C4—42no—
249(C2×D11)⋊C4—81no—
250(C2×D11)⋊C4—81no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
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—21no—
265C2×C11⋊C8C2×D412yes—
266C2×C11⋊C8C2×D412yes—
267C2×#463—111no—
268C2×#450—111no—
269C2×#447—111no—
270C2×#442—111no—
271#2427D1111yescharacteristic, complemented
272D4×C22⋊C4—111no—
273#2065—111no—
274#2035—111no—
275#2033—111no—
276#2012—111no—
277#1973—111no—
278#1924—111no—
279#1879—111no—
280#1877—111no—
281#1862—111no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—22no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11AGL(1,ℤ/8)12yes—
296C23×C11C22×D411yescharacteristic
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—48no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—48no—
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—
318Q8×C11—41no—
319Q8×C11—41no—
320Q8×C11—41no—
321Q8×C11—41no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—41no—
325D4×C11—41no—
326D4×C11—84no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—22no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
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×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C2×#4111yescharacteristic
359C2×C4×C11C2×#4111yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368D44—22no—
369D44—22no—
370D44—22no—
371D44—22no—
372D44—22no—
373D44—48no—
374D44—41no—
375D44—41no—
376D44#12114yes—
377C4×D11—84no—
378C4×D11—84no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C11⋊C8—41no—
382C11⋊C8—41no—
383C23×D4—111no—
384C22×SD16—111no—
385C22×SD16—111no—
386C22×D8—111no—
387C22×D8—111no—
388C2×#124C2×D1111yescharacteristic, complemented
389C2×C22⋊Q8C2×D1111yescharacteristic
390C2×#121C2×D1111yescharacteristic
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×C4×D4C2×D1111yescharacteristic, complemented
394C22×C22⋊C4—221no—
395#463—224no—
396#450—224no—
397#447—224no—
398#442—224no—
399C2×#107—111no—
400C2×#106—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×C22⋊C8—111no—
411C2×C22⋊C8—111no—
412C2×#97—111no—
413#397—21no—
414#394—21no—
415#391C2×D1111yescharacteristic, complemented
416#390—111no—
417#390—111no—
418#389C2×D1111yescharacteristic, complemented
419#386—21no—
420#386—221no—
421#386—221no—
422#380—21no—
423#380—111no—
424#379—221no—
425C4×C22⋊C4C2×D1111yescharacteristic
426#340—111no—
427#340—111no—
428#336—111no—
429#336—111no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—81no—
441C22×C11—81no—
442C22×C11—81no—
443C22×C11—81no—
444C22×C11#52511yescharacteristic
445C22×C11D4211yescharacteristic
446C22×C11D4211yescharacteristic
447C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
448C22×C11#57511yescharacteristic
449C22×C11#57611yescharacteristic
450C22×C11#57711yescharacteristic
451C2×D11—24no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—816no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C2×D11—81no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11—41no—
471C4×C11—42no—
472C4×C11—81no—
473C4×C11—81no—
474C4×C11C2×#12111yescharacteristic
475C4×C11#53811yescharacteristic
476C4×C11#54611yescharacteristic
477C4×C11#54611yescharacteristic
478Dic11—81no—
479Dic11—81no—
480C25—221no—
481C22×Q8C22×D1111yescharacteristic
482C22×D4—21no—
483C22×D4—111no—
484C22×D4—111no—
485C22×D4—222no—
486C22×D4—222no—
487C22×D4—222no—
488C22×D4—222no—
489C22×D4—221no—
490C22×D4—441no—
491C22×D4—441no—
492C22×D4C22×D1111yescharacteristic
493C23×C4—21no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C2×SD16—222no—
498C2×SD16—222no—
499C2×SD16—222no—
500C2×SD16—222no—
501C2×SD16—222no—
502C2×SD16—441no—
503C2×D8—114no—
504C2×D8—222no—
505C2×D8—222no—
506C2×D8—222no—
507C2×D8—222no—
508C2×D8—441no—
509C22×C8—111no—
510C22×C8—111no—
511C22×C8—111no—
512C22×C8—111no—
513#124—22no—
514#124—41no—
515C22⋊Q8—22no—
516C22⋊Q8—41no—
517#121—22no—
518#121—41no—
519C4×D4—22no—
520C4×D4—41no—
521C4×D4—222no—
522C4×D4—222no—
523C4×D4—441no—
524C4×D4—441no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4C22×D1111yescharacteristic
530C2×C4⋊C4C22×D1111yescharacteristic
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—221no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—444no—
544C2×C22⋊C4C22⋊D1111yescharacteristic
545C2×C22⋊C4C22⋊D1111yescharacteristic
546C2×C42C22×D1111yescharacteristic
547C2×C42C22×D1111yescharacteristic
548#107—441no—
549#106—222no—
550C4⋊C8—222no—
551#103—222no—
552#103—441no—
553#102—114no—
554#102—222no—
555#102—222no—
556#102—222no—
557#102—222no—
558#102—222no—
559C22⋊C8—222no—
560C22⋊C8—222no—
561#97—222no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—221no—
566#95C22⋊D1111yescharacteristic
567#95C22⋊D1111yescharacteristic
568C2×C11—42no—
569C2×C11—82no—
570C2×C11#242411yescharacteristic
571C2×C11#311411yescharacteristic
572C2×C11#311811yescharacteristic
573C2×C11#326411yescharacteristic
574C2×C11#326511yescharacteristic
575C2×C11#326711yescharacteristic
576C2×C11#327311yescharacteristic
577D11—44no—
578D11—82no—
579C24—21no—
580C24—224no—
581C24—221no—
582C24—221no—
583C24—442no—
584C24—442no—
585C24—442no—
586C24—442no—
587C24—881no—
588C24—881no—
589C24C2×C22⋊D1111yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—81no—
604C2×D4—112no—
605C2×D4—112no—
606C2×D4—112no—
607C2×D4—112no—
608C2×D4—224no—
609C2×D4—221no—
610C2×D4—221no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—221no—
614C2×D4—221no—
615C2×D4—221no—
616C2×D4—221no—
617C2×D4—442no—
618C2×D4—442no—
619C2×D4—444no—
620C2×D4—444no—
621C2×D4—444no—
622C2×D4—444no—
623C2×D4D4×D1112yes—
624C22×C4—21no—
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—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—442no—
639C22×C4—442no—
640C22×C4—442no—
641C22×C4—442no—
642C22×C4—881no—
643C22×C4—881no—
644C22×C4C2×C22⋊D1111yescharacteristic
645C22×C4C2×C22⋊D1111yescharacteristic
646C22×C4C2×C22⋊D1111yescharacteristic
647C22×C4C2×C22⋊D1111yescharacteristic
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C23×D1111yescharacteristic
650SD16—444no—
651SD16—444no—
652D8—228no—
653D8—444no—
654C2×C8—112no—
655C2×C8—112no—
656C2×C8—221no—
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—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—81no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4D4×D1112yes—
676C22⋊C4—22no—
677C22⋊C4—41no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—442no—
684C22⋊C4—442no—
685C22⋊C4—442no—
686C22⋊C4—442no—
687C22⋊C4—442no—
688C22⋊C4—881no—
689C22⋊C4—881no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C11#2517211yescharacteristic, complemented, Sylow
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—22no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—222no—
712C23—448no—
713C23—448no—
714C23—441no—
715C23—441no—
716C23—441no—
717C23—441no—
718C23—441no—
719C23—441no—
720C23—441no—
721C23—441no—
722C23—441no—
723C23—441no—
724C23—884no—
725C23—884no—
726C23—884no—
727C23—884no—
728C23—884no—
729C23#6700212yes—
730C23C22×C22⋊D1111yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—22no—
736D4—22no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—114no—
741D4—222no—
742D4—222no—
743D4—222no—
744D4—222no—
745D4—222no—
746D4—448no—
747D4—441no—
748D4—441no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
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—84no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—884no—
785C2×C4—884no—
786C2×C4C2×D4×D1111yescharacteristic
787C2×C4C2×D4×D1111yescharacteristic
788C2×C4#6703711yescharacteristic
789C2×C4#6703711yescharacteristic
790C2×C4#41×D1111yescharacteristic
791C2×C4#41×D1111yescharacteristic
792C8—222no—
793C8—222no—
794C8—441no—
795C8—441no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—224no—
811C22—442no—
812C22—442no—
813C22—442no—
814C22—442no—
815C22—442no—
816C22—442no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—8816no—
821C22—881no—
822C22—881no—
823C22—881no—
824C22—881no—
825C22D4×C22⋊D1111yescharacteristic
826C22D4×C22⋊D1111yescharacteristic
827C22C2×#6700211yescharacteristic
828C22#1062335311yescharacteristic
829C22#1062335911yescharacteristic
830C22#1062336611yescharacteristic
831C22#1062336811yescharacteristic
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—42no—
838C4—81no—
839C4—81no—
840C4—881no—
841C4—881no—
842C4D11×#12111yescharacteristic
843C4#1062314111yescharacteristic
844C4#1062314311yescharacteristic
845C4#1062314411yescharacteristic
846C2—42no—
847C2—82no—
848C2—444no—
849C2—882no—
850C2#1307214911yescharacteristic
851C2#1307875011yescharacteristic
852C2#1307879411yescharacteristic
853C2#1308009711yescharacteristic
854C2#1308011211yescharacteristic
855C2#1308014211yescharacteristic
856C2#1308022311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2427C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
hypercenter#2427D11
hypocenterC11#25172
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2427

Complements

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

NH ≅ G/Ntype
1. C2×#10622670C2semidirect
2. C2×#10622659C2semidirect
4. C2×#10622627C2semidirect
5. C22⋊C4×D44C2semidirect
6. #13069987C2semidirect
7. #13069809C2semidirect
8. #13069795C2semidirect
9. #13069693C2semidirect
10. #13069500C2semidirect
11. #13069231C2semidirect
12. #13068964C2semidirect
13. #13068953C2semidirect
14. #13068862C2semidirect
15. C11×#2427C2semidirect
17. C2×C11×#124C22semidirect
20. C2×C4×D4×C11C22semidirect
30. C11×#391C22semidirect
31. C11×#389C22semidirect
35. C2×#66899C22semidirect
36. C2×#66899C22semidirect
37. C2×#66896C22semidirect
38. C2×#66896C22semidirect
50. C2×#66872C22semidirect
51. C2×#66871C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×#66867C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
62. #10622162C22semidirect
146. #66873D4semidirect
271. #2427D11semidirect
388. C2×#124C2×D11semidirect
393. C2×C4×D4C2×D11semidirect
415. #391C2×D11semidirect
418. #389C2×D11semidirect
694. C11#25172semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×#106226592
C2×#106226492
C2×#106226272
C22⋊C4×D442
#130699872
#130698092
#130697952
#130696932
#130695002
#130692312
#130689642
#130689532
#130688622
C11×#24272
#2517211