Finite Group Databasebeta

← #14762886

Subgroups — #14762886

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2C2×#10622340C211yesmaximal, characteristic, complemented
3#13071205C211yesmaximal, characteristic, complemented
4#13069051C211yesmaximal, characteristic, complemented
5#13069046C211yesmaximal, characteristic, complemented
6#13069041C211yesmaximal, characteristic, complemented
7#13069036C211yesmaximal, characteristic, complemented
8#13068935C211yesmaximal, characteristic, complemented
9#13068930C211yesmaximal, characteristic, complemented
10#13068925C211yesmaximal, characteristic, complemented
11#13068920C211yesmaximal, characteristic, complemented
12#13068704C211yesmaximal, characteristic, complemented
13#13068703C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18#10623364—24no—
19#10623364C418yescomplemented
20C2×#66999C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66992—21no—
23C2×#66992—21no—
24C2×#66991C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C2×#66983—21no—
27C22×C4⋊Dic11C2211yescharacteristic
28C2×#66977—21no—
29C22×#4313C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31C2×#66945C2211yescharacteristic
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47#10622600C2211yescharacteristic
48#10622600C2211yescharacteristic
49#10622570—21no—
50#10622569—21no—
51#10622340—24no—
52#10622278—21no—
53#10622259—21no—
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C2×C11×#41—22no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C2×C11×#41C2×C414yescomplemented
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—21no—
74C22×C22⋊D11—21no—
75C22×C22⋊D11D411yescharacteristic
76C22×C22⋊D11D411yescharacteristic
77C23×Dic11—21no—
78C2×#4339—41no—
79C2×#4339—41no—
80C2×#4339—41no—
81C2×#4339—41no—
82C2×#4339C2×C414yes—
83C2×#4339D414yes—
84C22×D44D411yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22D411yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97#66999—22no—
98#66999—22no—
99#66999C2×C414yes—
100#66999C2×C414yescomplemented
101#66992—28no—
102#66992—28no—
103#66991—22no—
104#66991—22no—
105#66991C2×C414yes—
106#66991C2×C414yescomplemented
107#66983—28no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11C2×C414yescomplemented
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120#66977—28no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C2×#4313—22no—
128C2×#4313—41no—
129C2×#4313—41no—
130C2×C8×D11—22no—
131C2×C8×D11—41no—
132C2×C8×D11—41no—
133#66945—41no—
134#66945—41no—
135C4⋊C4×D11—41no—
136C4⋊C4×D11—41no—
137C11×#103—41no—
138C11×#103—41no—
139C11×#102—41no—
140C11×#102—41no—
141C11×C22⋊C8—22no—
142C11×#95—21no—
143#66899—41no—
144#66899—41no—
145#66896—41no—
146#66896—41no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C22⋊(C11⋊C8)—22no—
151(C2×D11)⋊C8—22no—
152(C2×D11)⋊C8—22no—
153#21772—111nomaximal, Sylow
154C24×C11—21no—
155C24×C11C2×D411yescharacteristic
156C23×D11C2×D411yescharacteristic
157C23×D11C2×D411yescharacteristic
158C11×#41—44no—
159C11×#41—44no—
160C11×#41—44no—
161C11×#41—44no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11C22×C412yes—
168C2×D4×C11—24no—
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×C11C22×C412yes—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—24no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2411yescharacteristic
191C2×C22⋊D11—24no—
192C2×C22⋊D11—24no—
193C2×C22⋊D11—41no—
194C2×C22⋊D11—41no—
195C2×C22⋊D11—41no—
196C2×C22⋊D11—41no—
197C2×C22⋊D11—81no—
198C2×C22⋊D11—81no—
199C2×C22⋊D11—81no—
200C2×C22⋊D11—81no—
201C2×C22⋊D11C22⋊C414yes—
202C2×C22⋊D11C22⋊C414yes—
203C22×Dic11—24no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—81no—
209C22×Dic11—81no—
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212#4339—44no—
213#4339—44no—
214#4339—44no—
215#4339—44no—
216C2×D44—41no—
217C2×D44—41no—
218C2×D44C22⋊C414yes—
219C2×C4×D11—21no—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—21no—
226C2×C4×D11—21no—
227C2×C4×D11—42no—
228C2×C4×D11—81no—
229C2×C4×D11—81no—
230C2×C4×D11C22×C412yes—
231C2×C4×D11C22×C412yes—
232C2×C4×D11C2×D412yes—
233C2×C4×D11C2×D412yes—
234C2×Dic22—41no—
235C2×Dic22—41no—
236C2×Dic22C22⋊C414yes—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C22⋊C4—81no—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11—81no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—42no—
254(C2×D11)⋊C4—81no—
255(C2×D11)⋊C4—81no—
256C4⋊Dic11—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11C22×C412yes—
264C4⋊Dic11C22×C412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—42no—
268C4×Dic11—42no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275#4313—44no—
276C8×D11—44no—
277C2×#537—111no—
278C2×#408—111no—
279#2311—111no—
280#1895—111no—
281#1894—111no—
282#1893—111no—
283#1892—111no—
284#1875—111no—
285#1874—111no—
286#1873—111no—
287#1872—111no—
288#1824—111no—
289#1823—111no—
290#1788—111no—
291#1788D1111yescharacteristic, complemented
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—22no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11C2×C22⋊C412yes—
306C23×C11C22×D411yescharacteristic
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11C2×C22⋊C412yes—
320C22×D11C2×C22⋊C412yes—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—41no—
324Q8×C11—41no—
325D4×C11—22no—
326D4×C11—22no—
327D4×C11—48no—
328D4×C11—41no—
329D4×C11—41no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—48no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
347C2×C4×C11C23×C411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11H(5,𝔽2)11yescharacteristic
350C2×C4×C11H(5,𝔽2)11yescharacteristic
351C2×C4×C11H(5,𝔽2)11yescharacteristic
352C2×C4×C11H(5,𝔽2)11yescharacteristic
353C22⋊D11—44no—
354C22⋊D11—44no—
355C22⋊D11—84no—
356C22⋊D11—84no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—21no—
360C2×Dic11—21no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—84no—
374C2×Dic11C2×C22⋊C412yes—
375C2×Dic11C2×C22⋊C412yes—
376D44—44no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—22no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—84no—
386Dic22—44no—
387C8×C11—41no—
388C8×C11—41no—
389C11⋊C8—41no—
390C11⋊C8—41no—
391C22×#41—111no—
392C22×#41C2×D1111yescharacteristic
393C22×M16—111no—
394C23×C8—111no—
395#537—118no—
396#537—224no—
397C2×C22⋊Q8—111no—
398C2×C22⋊Q8—111no—
399C2×C22⋊Q8—221no—
400C2×#121—111no—
401C2×#121—111no—
402C2×#121—221no—
403C2×#121—221no—
404C2×#121—221no—
405C2×#117—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103C2×D1111yescharacteristic
411C2×#103C2×D1111yescharacteristic
412C2×#102—111no—
413C2×#102—111no—
414C2×#102C2×D1111yescharacteristic
415C2×#102C2×D1111yescharacteristic
416#408—224no—
417C2×C22⋊C8—111no—
418C2×C22⋊C8—111no—
419C2×C22⋊C8—111no—
420C2×C22⋊C8C2×D1111yescharacteristic
421#391—221no—
422#390—221no—
423#386—221no—
424#386—221no—
425#380—111no—
426#380—111no—
427#380—111no—
428#380C2×D1111yescharacteristic
429#340—111no—
430#340—111no—
431#340—111no—
432#340—111no—
433#340—111no—
434#340—111no—
435#340—111no—
436#340—111no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—81no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11C22×C22⋊C411yescharacteristic
452C22×C11#53411yescharacteristic
453C22×C11#53411yescharacteristic
454C22×C11#57611yescharacteristic
455C22×C11#57711yescharacteristic
456C22×C11#57711yescharacteristic
457C22×C11#57811yescharacteristic
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—41no—
465C2×D11—41no—
466C2×D11—41no—
467C2×D11—41no—
468C2×D11—41no—
469C2×D11—41no—
470C2×D11—41no—
471C2×D11—41no—
472C4×C11—22no—
473C4×C11—42no—
474C4×C11—81no—
475C4×C11—81no—
476C4×C11#51811yescharacteristic
477C4×C11#51811yescharacteristic
478C4×C11#53411yescharacteristic
479C4×C11#53411yescharacteristic
480Dic11—22no—
481Dic11—22no—
482Dic11—42no—
483Dic11—42no—
484Dic11—81no—
485Dic11—81no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41—114no—
492C2×#41—114no—
493C2×#41—441no—
494C2×#41—441no—
495C2×#41—441no—
496C2×#41—441no—
497C2×#41C4×D1114yescomplemented
498C22×Q8—111no—
499C22×Q8C22×D1111yescharacteristic
500C22×D4—21no—
501C22×D4—111no—
502C22×D4—111no—
503C22×D4—111no—
504C22×D4—221no—
505C22×D4—221no—
506C22×D4C22×D1111yescharacteristic
507C23×C4—21no—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—221no—
511C23×C4—221no—
512C23×C4C22×D1111yescharacteristic
513C2×M16—222no—
514C2×M16—441no—
515C2×M16—441no—
516C22×C8—111no—
517C22×C8—111no—
518C22×C8—222no—
519C22×C8—441no—
520C22×C8—441no—
521C22×C8C22×D1111yescharacteristic
522C22×C8C22×D1111yescharacteristic
523C22⋊Q8—114no—
524C22⋊Q8—114no—
525C22⋊Q8—228no—
526C22⋊Q8—222no—
527C22⋊Q8—222no—
528#121—114no—
529#121—114no—
530#121—228no—
531#121—222no—
532#121—222no—
533#121—228no—
534#121—228no—
535#117—441no—
536#117—441no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—111no—
539C2×C4⋊C4—111no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—222no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—441no—
548C2×C4⋊C4—441no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C42—221no—
561#103—41no—
562#103—41no—
563#103—441no—
564#103—441no—
565#102—41no—
566#102—41no—
567#102—441no—
568#102—441no—
569C22⋊C8—22no—
570C22⋊C8—222no—
571C22⋊C8—222no—
572C22⋊C8—222no—
573#95—21no—
574#95—221no—
575#95—221no—
576#95—221no—
577C2×C11—42no—
578C2×C11—82no—
579C2×C11#230811yescharacteristic
580C2×C11#289711yescharacteristic
581C2×C11#289811yescharacteristic
582C2×C11#319811yescharacteristic
583C2×C11#320111yescharacteristic
584C2×C11#320311yescharacteristic
585C2×C11#320411yescharacteristic
586D11—42no—
587D11—42no—
588C24—21no—
589C24—111no—
590C24—111no—
591C24D4×D1111yescharacteristic
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—444no—
597#41—444no—
598#41—444no—
599#41—444no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—114no—
606C2×Q8—441no—
607C2×Q8—441no—
608C2×Q8C2×C4×D1112yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—114no—
618C2×D4—114no—
619C2×D4—114no—
620C2×D4—224no—
621C2×D4—224no—
622C2×D4—441no—
623C2×D4—441no—
624C2×D4—441no—
625C2×D4—441no—
626C2×D4—441no—
627C2×D4—441no—
628C2×D4—881no—
629C2×D4—881no—
630C2×D4—881no—
631C2×D4—881no—
632C2×D4C2×C4×D1112yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—111no—
644C22×C4—111no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—112no—
648C22×C4—112no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—221no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—224no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—442no—
663C22×C4—881no—
664C22×C4—881no—
665C22×C4—881no—
666C22×C4—881no—
667C22×C4C2×C4×D1112yes—
668C22×C4D4×D1111yescharacteristic
669C22×C4D4×D1112yes—
670C22×C4C23×D1111yescharacteristic
671M16—444no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—221no—
679C2×C8—221no—
680C2×C8—221no—
681C2×C8—221no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—444no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—112no—
690C4⋊C4—112no—
691C4⋊C4—224no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—442no—
701C22⋊C4—81no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—442no—
707C22⋊C4—881no—
708C22⋊C4—881no—
709C22⋊C4—881no—
710C42—442no—
711C11#2177211yescharacteristic, complemented, Sylow
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—112no—
726C23—112no—
727C23—221no—
728C23—221no—
729C23—221no—
730C23—221no—
731C23—221no—
732C23—221no—
733C23—221no—
734C23—221no—
735C23—221no—
736C23—221no—
737C23—221no—
738C23—221no—
739C23C22⋊C4×D1112yes—
740C23C2×D4×D1111yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—41no—
744Q8—41no—
745Q8—444no—
746D4—22no—
747D4—22no—
748D4—48no—
749D4—41no—
750D4—41no—
751D4—444no—
752D4—444no—
753D4—444no—
754D4—884no—
755D4—884no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—48no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—112no—
773C2×C4—112no—
774C2×C4—221no—
775C2×C4—221no—
776C2×C4—221no—
777C2×C4—221no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—441no—
789C2×C4—441no—
790C2×C4—441no—
791C2×C4—441no—
792C2×C4—441no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—884no—
799C2×C4—884no—
800C2×C4C22⋊C4×D1112yes—
801C2×C4C22×C4×D1111yescharacteristic
802C2×C4C2×D4×D1111yescharacteristic
803C2×C4#6703711yescharacteristic
804C2×C4#6703711yescharacteristic
805C2×C4#6703711yescharacteristic
806C2×C4#6703711yescharacteristic
807C8—41no—
808C8—41no—
809C8—441no—
810C8—441no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—222no—
826C22—222no—
827C22—222no—
828C22—222no—
829C22—222no—
830C22—222no—
831C22—441no—
832C22—441no—
833C22—441no—
834C22—441no—
835C22—441no—
836C22—441no—
837C22—441no—
838C22—441no—
839C22C2×C22⋊C4×D1111yescharacteristic
840C22#1062312011yescharacteristic
841C22#1062312011yescharacteristic
842C22#1062330011yescharacteristic
843C22#1062330111yescharacteristic
844C22#1062330611yescharacteristic
845C22#1062331011yescharacteristic
846C4—22no—
847C4—42no—
848C4—81no—
849C4—81no—
850C4—222no—
851C4—222no—
852C4—442no—
853C4—442no—
854C4—881no—
855C4—881no—
856C4#1062301711yescharacteristic
857C4#1062301711yescharacteristic
858C4#1062312011yescharacteristic
859C4#1062312011yescharacteristic
860C2—42no—
861C2—82no—
862C2—442no—
863C2—442no—
864C2#1307119211yescharacteristic
865C2#1307713811yescharacteristic
866C2#1307714711yescharacteristic
867C2#1307946511yescharacteristic
868C2#1307949511yescharacteristic
869C2#1307951711yescharacteristic
870C2#1307952511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#21772
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622340C2semidirect
3. #13071205C2semidirect
4. #13069051C2semidirect
5. #13069046C2semidirect
6. #13069041C2semidirect
7. #13069036C2semidirect
8. #13068935C2semidirect
9. #13068930C2semidirect
10. #13068925C2semidirect
11. #13068920C2semidirect
12. #13068704C2semidirect
13. #13068703C2semidirect
14. #13068556C2semidirect
15. C11×#1788C2semidirect
19. #10623364C4semidirect
67. C2×C11×#41C2×C4semidirect
100. #66999C2×C4semidirect
106. #66991C2×C4semidirect
115. C2×C4⋊Dic11C2×C4semidirect
291. #1788D11semidirect
497. C2×#41C4×D11semidirect
711. C11#21772semidirect

Maximal subgroups

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

subgroupindex
C2×#106233642
C2×#106223402
#130712052
#130690512
#130690462
#130690412
#130690362
#130689352
#130689302
#130689252
#130689202
#130687042
#130687032
#130685562
C11×#17882
#2177211