Finite Group Databasebeta

← #14785942

Subgroups — #14785942

Order 2816.

1338 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×#10622650C211yesmaximal, characteristic, complemented
2C2×#10622615C211yesmaximal, characteristic, complemented
3#13071961C211yesmaximal, characteristic, complemented
4#13069764C211yesmaximal, characteristic, complemented
5#13069759C211yesmaximal, characteristic, complemented
6#13069619C211yesmaximal, characteristic, complemented
7#13069612C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic, complemented
9#13068964C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068933C211yesmaximal, characteristic, complemented
12#13068923C211yesmaximal, characteristic, complemented
13#13068909C211yesmaximal, characteristic, complemented
14#13068711C211yesmaximal, characteristic, complemented
15C2×C11×#553C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C11×#553—24no—
18C11×#553—24no—
19C2×C11×#126—21no—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#121—21no—
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C23×C11⋊C8C2211yescharacteristic
35#10622836—21no—
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622650—24no—
43#10622615—24no—
44#10622602—21no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51#10622572—21no—
52#10622569—21no—
53#10622552C2211yescharacteristic
54#10622542C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—21no—
72C22×C22⋊D11—21no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—22no—
76C2×#4339—22no—
77C2×#4339—41no—
78C2×#4339—41no—
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C22×Dic22C2311yescharacteristic
82C11×#126—28no—
83C11×#125—22no—
84C11×#125—22no—
85C11×#123—28no—
86C11×#121—28no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121D414yescomplemented
91C4×D4×C11—28no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C11×#117—22no—
97C11×#117D414yescomplemented
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4D411yescharacteristic
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⋊C4—21no—
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×#4324—22no—
118C2×#4324—22no—
119C2×#4324—41no—
120C2×#4323—22no—
121C2×#4323—22no—
122C2×#4323—41no—
123#66983—22no—
124#66983—41no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130#66977—22no—
131#66977—41no—
132C2×Dic11⋊C4—21no—
133C22×C11⋊C8—22no—
134C22×C11⋊C8—41no—
135C22×C11⋊C8—41no—
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140#66896—41no—
141#66896—41no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C22⋊(C11⋊C8)—22no—
146C22⋊(C11⋊C8)—41no—
147C22⋊(C11⋊C8)—41no—
148#66874—22no—
149#66874—22no—
150#66874—22no—
151#66873—22no—
152#66873—22no—
153#66873—22no—
154#23962—111nomaximal, Sylow
155C24×C11—21no—
156C24×C11C2×D411yescharacteristic
157C24×C11C2×D411yescharacteristic
158C23×D11—21no—
159C2×D4×C11—24no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—24no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—41no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—81no—
172C2×D4×C11—81no—
173C2×D4×C11C2×D412yes—
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—24no—
182C22×C4×C11—24no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—81no—
190C22×C4×C11—81no—
191C22×C4×C11—81no—
192C22×C4×C11—81no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—42no—
201C2×C22⋊D11—42no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11—42no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—81no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209#4339—28no—
210#4339—44no—
211#4339—44no—
212#4339—44no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44#4112yes—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22#4112yes—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4C2×D412yes—
236C11×C4⋊C4C2×D412yes—
237C11×C4⋊C4C2×D412yes—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—22no—
244C42×C11—24no—
245C42×C11—21no—
246C42×C11—21no—
247C22⋊Dic11—42no—
248C22⋊Dic11—81no—
249#4324—44no—
250#4323—44no—
251(C2×D11)⋊C4—42no—
252(C2×D11)⋊C4—42no—
253(C2×D11)⋊C4—81no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258Dic11⋊C4—42no—
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⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—44no—
272C2×#553D1111yescharacteristic, complemented
273C2×#449—111no—
274C2×#416—111no—
275#2407—111no—
276#2026—111no—
277#2025—111no—
278#2000—111no—
279#1999—111no—
280#1893—111no—
281#1879—111no—
282#1877—111no—
283#1874—111no—
284#1872—111no—
285#1869—111no—
286#1825—111no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—22no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11#12012yes—
307C23×C11#13512yes—
308C23×C11C22×D411yescharacteristic
309C22×D11—22no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—44no—
319D4×C11—48no—
320D4×C11—41no—
321D4×C11—41no—
322D4×C11—84no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—21no—
330C2×C4×C11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—22no—
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—21no—
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—84no—
352C2×C4×C11—84no—
353C2×C4×C11#12012yes—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C22⋊D11—48no—
361C22⋊D11—84no—
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—
371D44—22no—
372D44—22no—
373D44—41no—
374D44—41no—
375C4×D11—48no—
376Dic22—22no—
377Dic22—22no—
378Dic22—41no—
379Dic22—41no—
380C11⋊C8—41no—
381C11⋊C8—41no—
382C11⋊C8—41no—
383C11⋊C8—41no—
384C22×#41—111no—
385C22×SD16—111no—
386C22×D8—111no—
387C23×C8—111no—
388#553—24no—
389#553—24no—
390C2×#126—21no—
391C2×#125C2×D1111yescharacteristic
392C2×#123—21no—
393C2×C22⋊Q8—111no—
394C2×#121—21no—
395C2×#121—111no—
396C2×#121C2×D1111yescharacteristic
397C2×#121C2×D1111yescharacteristic
398C2×C4×D4—21no—
399C2×C4×D4C2×D1111yescharacteristic
400C2×C4×D4C2×D1111yescharacteristic
401C2×#117C2×D1111yescharacteristic
402C22×C4⋊C4C2×D1111yescharacteristic
403#449—224no—
404#416—224no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×#102—111no—
411C2×#102—111no—
412C2×#102—111no—
413C2×C22⋊C8—111no—
414C2×C22⋊C8—111no—
415C2×C22⋊C8—111no—
416#394—221no—
417#392—221no—
418#391—111no—
419#390—111no—
420#386—221no—
421#385—221no—
422#380—111no—
423#340—111no—
424#340—111no—
425#340—111no—
426#340—111no—
427#340—111no—
428#340—111no—
429#336—111no—
430#336—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—41no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11—81no—
452C22×C11C2×#12011yescharacteristic
453C22×C11#54611yescharacteristic
454C22×C11#54611yescharacteristic
455C22×C11C2×#13511yescharacteristic
456C22×C11#57511yescharacteristic
457C22×C11#57611yescharacteristic
458C22×C11#57711yescharacteristic
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C2×D11—81no—
466C4×C11—22no—
467C4×C11—41no—
468C4×C11—41no—
469C4×C11—42no—
470C4×C11—41no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11#52511yescharacteristic
474C4×C11#53511yescharacteristic
475C4×C11#54611yescharacteristic
476C4×C11#54611yescharacteristic
477Dic11—42no—
478Dic11—81no—
479Dic11—81no—
480C2×#41—222no—
481C2×#41—222no—
482C2×#41—222no—
483C2×#41—222no—
484C2×#41—441no—
485C2×#41—441no—
486C22×Q8—111no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—111no—
490C22×D4—221no—
491C22×D4—221no—
492C22×D4C22⋊D1111yescharacteristic
493C22×D4C22×D1111yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1111yescharacteristic
499C2×SD16—222no—
500C2×SD16—222no—
501C2×SD16—441no—
502C2×D8—222no—
503C2×D8—222no—
504C2×D8—441no—
505C22×C8—111no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—222no—
510C22×C8—441no—
511C22×C8—441no—
512#126—28no—
513#125—22no—
514#125—22no—
515#123—28no—
516C22⋊Q8—222no—
517C22⋊Q8—441no—
518#121—28no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—222no—
523#121—441no—
524#121C22⋊D1114yescomplemented
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530#117—22no—
531#117C22⋊D1114yescomplemented
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—111no—
538C2×C4⋊C4—111no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4C22⋊D1111yescharacteristic
541C2×C4⋊C4C22×D1111yescharacteristic
542C2×C4⋊C4C22×D1111yescharacteristic
543C2×C4⋊C4C22×D1111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4C22⋊D1111yescharacteristic
554C2×C22⋊C4C22⋊D1111yescharacteristic
555C2×C42—21no—
556C2×C42C22×D1111yescharacteristic
557#103—222no—
558#103—222no—
559#103—222no—
560#102—222no—
561#102—222no—
562#102—222no—
563#102—441no—
564#102—441no—
565C22⋊C8—222no—
566C22⋊C8—441no—
567C22⋊C8—441no—
568#95—221no—
569#95—221no—
570#95—221no—
571C2×C11—42no—
572C2×C11—42no—
573C2×C11—82no—
574C2×C11#240411yescharacteristic
575C2×C11#300211yescharacteristic
576C2×C11#301211yescharacteristic
577C2×C11#329711yescharacteristic
578C2×C11#330111yescharacteristic
579C2×C11#330711yescharacteristic
580C2×C11#330911yescharacteristic
581D11—82no—
582C24—21no—
583C24—221no—
584C24C2×C22⋊D1111yescharacteristic
585C24C2×C22⋊D1111yescharacteristic
586#41—228no—
587#41—444no—
588#41—444no—
589#41—444no—
590C2×Q8—112no—
591C2×Q8—221no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—221no—
596C2×D4—24no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—41no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—112no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—221no—
614C2×D4—221no—
615C2×D4—221no—
616C2×D4—442no—
617C2×D4—442no—
618C2×D4—442no—
619C2×D4—442no—
620C2×D4—442no—
621C2×D4—881no—
622C2×D4C2×C22⋊D1112yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4—81no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—442no—
646C22×C4—442no—
647C22×C4—442no—
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C2×C22⋊D1112yes—
653C22×C4C2×C22⋊D1112yes—
654C22×C4C23×D1111yescharacteristic
655SD16—444no—
656D8—444no—
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—221no—
667C2×C8—221no—
668C2×C8—221no—
669C2×C8—444no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4—442no—
682C4⋊C4C2×C22⋊D1112yes—
683C4⋊C4C2×C22⋊D1112yes—
684C4⋊C4C2×C22⋊D1112yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—22no—
689C22⋊C4—24no—
690C22⋊C4—22no—
691C22⋊C4—442no—
692C22⋊C4—442no—
693C22⋊C4—442no—
694C22⋊C4—881no—
695C22⋊C4—881no—
696C42—24no—
697C42—21no—
698C42—21no—
699C11#2396211yescharacteristic, complemented, Sylow
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—222no—
720C23—441no—
721C23—441no—
722C23—441no—
723C23—441no—
724C23—441no—
725C23—441no—
726C23#6700312yes—
727C23#6700612yes—
728C23C22×C22⋊D1111yescharacteristic
729Q8—222no—
730Q8—222no—
731Q8—441no—
732Q8—441no—
733D4—22no—
734D4—22no—
735D4—44no—
736D4—48no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—222no—
741D4—222no—
742D4—448no—
743D4—441no—
744D4—441no—
745D4—884no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—22no—
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—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—222no—
777C2×C4—448no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4#6700612yes—
787C2×C4#41×D1111yescharacteristic
788C2×C4#41×D1111yescharacteristic
789C2×C4#6704211yescharacteristic
790C2×C4#6704211yescharacteristic
791C2×C4C22×C22⋊D1111yescharacteristic
792C2×C4C22×C22⋊D1111yescharacteristic
793C8—441no—
794C8—441no—
795C8—441no—
796C8—441no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—442no—
819C22—442no—
820C22—442no—
821C22—881no—
822C22—881no—
823C22—881no—
824C22—881no—
825C22C2×#6700311yescharacteristic
826C22#1062335311yescharacteristic
827C22#1062336011yescharacteristic
828C22#1062336011yescharacteristic
829C22#1062336611yescharacteristic
830C22#1062336711yescharacteristic
831C22C2×#6700611yescharacteristic
832C4—22no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—42no—
838C4—42no—
839C4—442no—
840C4—881no—
841C4—881no—
842C4#1062335911yescharacteristic
843C4#1062336011yescharacteristic
844C4#1062336011yescharacteristic
845C4#1062336111yescharacteristic
846C2—42no—
847C2—42no—
848C2—82no—
849C2—882no—
850C2#1307193111yescharacteristic
851C2#1307783411yescharacteristic
852C2#1307792011yescharacteristic
853C2#1308046011yescharacteristic
854C2#1308051211yescharacteristic
855C2#1308058611yescharacteristic
856C2#1308061611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#553C2
socleC23×C11C22×D4
hypercenterC2×#553D11
hypocenterC11#23962
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#10622650C2semidirect
2. C2×#10622615C2semidirect
3. #13071961C2semidirect
4. #13069764C2semidirect
5. #13069759C2semidirect
6. #13069619C2semidirect
7. #13069612C2semidirect
8. #13069045C2semidirect
9. #13068964C2semidirect
10. #13068950C2semidirect
11. #13068933C2semidirect
12. #13068923C2semidirect
13. #13068909C2semidirect
14. #13068711C2semidirect
15. C2×C11×#553C2semidirect
90. C11×#121D4semidirect
97. C11×#117D4semidirect
272. C2×#553D11semidirect
524. #121C22⋊D11semidirect
531. #117C22⋊D11semidirect
699. C11#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#106226502
C2×#106226152
#130719612
#130697642
#130697592
#130696192
#130696122
#130690452
#130689642
#130689502
#130689332
#130689232
#130689092
#130687112
C2×C11×#5532
#2396211