Finite Group Databasebeta

← #14769300

Subgroups — #14769300

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic
2C2×#10622746C211yesmaximal, characteristic, complemented
3C2×#10622726C211yesmaximal, 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#13068632C211yesmaximal, characteristic, complemented
12#13068557C211yesmaximal, characteristic, complemented
13#13068557C211yesmaximal, characteristic, complemented
14#13068447C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66993—21no—
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26#10623084—24no—
27#10623084C418yescomplemented
28C2×#66946—21no—
29C2×#66937—21no—
30C2×#66937—21no—
31C2×#66927C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#435—24no—
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×#97C2211yescharacteristic
38#10622833—21no—
39#10622825C2211yescharacteristic
40#10622825C2211yescharacteristic
41#10622746—24no—
42#10622726—24no—
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×#66885C2211yescharacteristic
48C2×#66885C2211yescharacteristic
49C2×#66885C2211yescharacteristic
50C2×#66885C2211yescharacteristic
51C2×#66880C2211yescharacteristic
52C2×#66880C2211yescharacteristic
53C2×#66880C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55#10622594—21no—
56#10622564—21no—
57C22⋊C4×Dic11—21no—
58#10622549C2211yescharacteristic
59C4×C4⋊Dic11C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622189C2211yescharacteristic
63#10622189C2211yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C23×Dic11—21no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—22no—
76C2×#4339—22no—
77C2×#4339—22no—
78C2×#4339—41no—
79C2×#4339—41no—
80C2×#4339—41no—
81C2×#4339—41no—
82C2×#4339C2×C414yes—
83C2×#4339C2×C414yescomplemented
84C22×D44—21no—
85C22×D44—21no—
86C22×D44C2311yescharacteristic
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×Dic22C2311yescharacteristic
91C2×C11×M16—22no—
92C2×C11×M16—22no—
93C2×C11×M16—41no—
94C22×C8×C11—22no—
95C22×C8×C11—22no—
96C22×C8×C11—41no—
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C4×D4×C11C2×C414yes—
102C4×D4×C11D414yes—
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110#66993—28no—
111#66983—22no—
112#66983—22no—
113#66983C2×C414yes—
114#66983C2×C414yescomplemented
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117#66979—22no—
118#66979—41no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—41no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×Dic11⋊C4—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131#66946—28no—
132#66937—28no—
133#66937—28no—
134#66927—22no—
135#66927C2×C414yescomplemented
136C4×Dic22—22no—
137C4×Dic22C2×C414yescomplemented
138C11×C4⋊C8—22no—
139C11×C22⋊C8—22no—
140C11×C22⋊C8—22no—
141C11×#97—22no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147#66885—22no—
148#66885—22no—
149#66885—22no—
150#66885—22no—
151#66885—41no—
152#66885—41no—
153#66885—41no—
154#66885—41no—
155#66880—22no—
156#66880—22no—
157#66880—22no—
158#66880D414yescomplemented
159#22422—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11—21no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11C22⋊C414yes—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C22×C412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2411yescharacteristic
184C2×C22⋊D11—24no—
185C2×C22⋊D11—24no—
186C2×C22⋊D11—24no—
187C2×C22⋊D11—24no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—42no—
192C2×C22⋊D11—81no—
193C2×C22⋊D11—81no—
194C2×C22⋊D11—81no—
195C2×C22⋊D11—81no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—42no—
203C22×Dic11—42no—
204C22×Dic11—81no—
205#4339—28no—
206#4339—28no—
207#4339—44no—
208#4339—44no—
209#4339—44no—
210#4339—44no—
211#4339—44no—
212#4339—44no—
213C2×D44—24no—
214C2×D44—24no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—42no—
226C2×D44—42no—
227C2×D44—81no—
228C2×D44—81no—
229C2×D44C22×C412yes—
230C2×D44C22×C412yes—
231C2×C4×D11—24no—
232C2×C4×D11—24no—
233C2×C4×D11—42no—
234C2×C4×D11—42no—
235C2×C4×D11—42no—
236C2×C4×D11—42no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22C22×C412yes—
241C2×Dic22C2×D412yes—
242C2×Dic22#4112yes—
243C11×M16—44no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—44no—
256C2×C8×C11C2×D412yes—
257C11×C4⋊C4C22⋊C414yes—
258C11×C22⋊C4C22⋊C414yes—
259C11×C22⋊C4C22⋊C414yes—
260C42×C11C22×C412yes—
261C42×C11C2×D412yes—
262C22⋊Dic11—42no—
263C22⋊Dic11—42no—
264C22⋊Dic11—81no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—42no—
276C4⋊Dic11C22×C412yes—
277C4⋊Dic11C2×D412yes—
278Dic11⋊C4—24no—
279C4×Dic11—24no—
280C4×Dic11—42no—
281C4×Dic11—81no—
282C2×#550—111no—
283C2×#435D1111yescharacteristic, complemented
284C2×#417—111no—
285C2×#416—111no—
286#2352—111no—
287#1982—111no—
288#1961—111no—
289#1895—111no—
290#1893—111no—
291#1875—111no—
292#1874—111no—
293#1805—111no—
294#1788—111no—
295#1788—111no—
296#1763—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11C2×C22⋊C412yes—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326D4×C11—44no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11C2×C22⋊C412yes—
344C2×C4×C11C2×C22⋊C412yes—
345C2×C4×C11C2×C22⋊C412yes—
346C2×C4×C11C2×C22⋊C412yes—
347C2×C4×C11C23×C411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C2×#4111yescharacteristic
351C2×C4×C11H(5,𝔽2)11yescharacteristic
352C2×C4×C11H(5,𝔽2)11yescharacteristic
353C22⋊D11—48no—
354C22⋊D11—48no—
355C22⋊D11—84no—
356C22⋊D11—84no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—41no—
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—41no—
374C2×Dic11—41no—
375C2×Dic11—84no—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—22no—
380D44—48no—
381D44—41no—
382D44—41no—
383D44—41no—
384D44—41no—
385D44—84no—
386C4×D11—48no—
387C4×D11—48no—
388Dic22—22no—
389Dic22—22no—
390Dic22—22no—
391Dic22C4×D414yes—
392C8×C11—22no—
393C8×C11—41no—
394C8×C11—41no—
395C8×C11—41no—
396C22×#41—111no—
397C22×#41—111no—
398C22×M16C2×D1111yescharacteristic
399C23×C8C2×D1111yescharacteristic
400#550—118no—
401#550—224no—
402C2×#127—111no—
403C2×#127—221no—
404C2×#121—111no—
405C2×#121—111no—
406C2×#121—221no—
407C2×#121—221no—
408C2×C4×Q8—111no—
409C2×C4×D4—221no—
410C2×C4×D4C2×D1111yescharacteristic
411C2×#117—111no—
412C22×C4⋊C4—111no—
413#435—24no—
414C2×C4⋊C8C2×D1111yescharacteristic
415#417—224no—
416#416—224no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#103—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×C22⋊C8C2×D1111yescharacteristic
430C2×C22⋊C8C2×D1111yescharacteristic
431C2×#97C2×D1111yescharacteristic
432#388—221no—
433#387—221no—
434#386—221no—
435#382—111no—
436#380—111no—
437#380—111no—
438C4×C4⋊C4—111no—
439C4×C22⋊C4—221no—
440#340—111no—
441#340—111no—
442#340—111no—
443#340—111no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11C22×C22⋊C411yescharacteristic
459C22×C11D4211yescharacteristic
460C22×C11#54611yescharacteristic
461C22×C11#57511yescharacteristic
462C22×C11#57511yescharacteristic
463C22×C11#57611yescharacteristic
464C22×C11#57711yescharacteristic
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—81no—
472C2×D11—81no—
473C2×D11—81no—
474C2×D11—81no—
475C2×D11—81no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C4×C11—22no—
480C4×C11—22no—
481C4×C11—22no—
482C4×C11—22no—
483C4×C11C2×C4×D411yescharacteristic
484C4×C11#51811yescharacteristic
485C4×C11D4211yescharacteristic
486C4×C11#54611yescharacteristic
487Dic11—24no—
488Dic11—42no—
489Dic11—42no—
490Dic11—81no—
491Dic11—81no—
492Dic11—81no—
493C2×#41—114no—
494C2×#41—114no—
495C2×#41—222no—
496C2×#41—222no—
497C2×#41—222no—
498C2×#41—222no—
499C2×#41—222no—
500C2×#41—222no—
501C2×#41—441no—
502C2×#41—441no—
503C2×#41—441no—
504C2×#41—441no—
505C22×Q8—111no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4D4411yescharacteristic
515C23×C4—221no—
516C23×C4—221no—
517C23×C4—221no—
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520C2×M16—22no—
521C2×M16—22no—
522C2×M16—41no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—41no—
526C22×C8C22×D1111yescharacteristic
527C22×C8C22×D1111yescharacteristic
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530#127—114no—
531#127—228no—
532#127—222no—
533#121—114no—
534#121—114no—
535#121—222no—
536#121—222no—
537#121—228no—
538#121—228no—
539C4×Q8—114no—
540C4×Q8—222no—
541C4×D4—228no—
542C4×D4C4×D1114yes—
543C4×D4C22⋊D1114yes—
544#117—222no—
545#117—441no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—441no—
555C2×C4⋊C4D4411yescharacteristic
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4D4411yescharacteristic
562C2×C22⋊C4D4411yescharacteristic
563C2×C42—221no—
564C2×C42—221no—
565C2×C42—221no—
566C2×C42C22×D1111yescharacteristic
567C4⋊C8—22no—
568#103—114no—
569#103—222no—
570#103—222no—
571#103—222no—
572#102—222no—
573#102—222no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578#102—441no—
579#102—441no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582#97—22no—
583#95—221no—
584#95—221no—
585#95—221no—
586#95—221no—
587#95—221no—
588C2×C11—42no—
589C2×C11—42no—
590C2×C11D4×C22⋊C411yescharacteristic
591C2×C11#289611yescharacteristic
592C2×C11#289711yescharacteristic
593C2×C11#326811yescharacteristic
594C2×C11#327111yescharacteristic
595C2×C11#330911yescharacteristic
596C2×C11#331711yescharacteristic
597D11—82no—
598D11—82no—
599C24—221no—
600C24—221no—
601C24C2×D4411yescharacteristic
602C24C2×D4411yescharacteristic
603#41—228no—
604#41—228no—
605#41—444no—
606#41—444no—
607#41—444no—
608#41—444no—
609#41—444no—
610#41—444no—
611C2×Q8—112no—
612C2×Q8—112no—
613C2×Q8—112no—
614C2×Q8—221no—
615C2×Q8—221no—
616C2×Q8—221no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—112no—
620C2×D4—112no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—221no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—442no—
638C2×D4—442no—
639C2×D4—442no—
640C2×D4—442no—
641C2×D4—442no—
642C2×D4—442no—
643C2×D4—881no—
644C2×D4—881no—
645C2×D4—881no—
646C2×D4—881no—
647C2×D4—881no—
648C2×D4—881no—
649C2×D4(C2×D11)⋊C414yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—224no—
662C22×C4—224no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—881no—
673C22×C4C2×C4×D1112yes—
674C22×C4C2×C4×D1112yes—
675C22×C4C2×D4411yescharacteristic
676C22×C4C2×D4411yescharacteristic
677C22×C4C2×D4411yescharacteristic
678C22×C4C2×D4411yescharacteristic
679C22×C4C2×C22⋊D1112yes—
680C22×C4C2×C22⋊D1112yes—
681C22×C4C23×D1111yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8D4×D1112yes—
696C4⋊C4—112no—
697C4⋊C4—112no—
698C4⋊C4—224no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—442no—
708C4⋊C4(C2×D11)⋊C414yes—
709C22⋊C4—224no—
710C22⋊C4—224no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C22⋊C4—881no—
714C22⋊C4(C2×D11)⋊C414yes—
715C22⋊C4(C2×D11)⋊C414yes—
716C42—224no—
717C42—442no—
718C42—881no—
719C42C2×C4×D1112yes—
720C42C2×C22⋊D1112yes—
721C11#2242211yescharacteristic, complemented, Sylow
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—222no—
735C23—222no—
736C23—441no—
737C23—441no—
738C23—441no—
739C23—441no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23C2×(C2×D11)⋊C412yes—
749C23C2×(C2×D11)⋊C412yes—
750C23C22×D4411yescharacteristic
751Q8—114no—
752Q8—222no—
753Q8—222no—
754Q8—222no—
755D4—44no—
756D4—222no—
757D4—222no—
758D4—222no—
759D4—222no—
760D4—448no—
761D4—448no—
762D4—448no—
763D4—441no—
764D4—441no—
765D4—441no—
766D4—441no—
767D4—884no—
768D4—884no—
769D4—884no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—448no—
792C2×C4—448no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—884no—
807C2×C4C2×(C2×D11)⋊C412yes—
808C2×C4C2×(C2×D11)⋊C412yes—
809C2×C4C2×(C2×D11)⋊C412yes—
810C2×C4C2×(C2×D11)⋊C412yes—
811C2×C4C22×C4×D1111yescharacteristic
812C2×C4C2×D4×D1111yescharacteristic
813C2×C4#6703711yescharacteristic
814C2×C4#41×D1111yescharacteristic
815C2×C4#6704211yescharacteristic
816C2×C4C22×C22⋊D1111yescharacteristic
817C8—22no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—881no—
842C22—881no—
843C22—881no—
844C22—881no—
845C22—881no—
846C22—881no—
847C22—881no—
848C22—881no—
849C22D4×D4411yescharacteristic
850C22#1062308511yescharacteristic
851C22#1062327911yescharacteristic
852C22#1062327911yescharacteristic
853C22#1062328211yescharacteristic
854C22#1062328311yescharacteristic
855C22C22×(C2×D11)⋊C411yescharacteristic
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—224no—
861C4—442no—
862C4—442no—
863C4—881no—
864C4—881no—
865C4—881no—
866C4C4×D4×D1111yescharacteristic
867C4#1062307611yescharacteristic
868C4D4×C22⋊D1111yescharacteristic
869C4#1062336011yescharacteristic
870C2—42no—
871C2—42no—
872C2—882no—
873C2—882no—
874C2D4×(C2×D11)⋊C411yescharacteristic
875C2#1307713611yescharacteristic
876C2#1307714311yescharacteristic
877C2#1308016111yescharacteristic
878C2#1308020611yescharacteristic
879C2#1308062411yescharacteristic
880C2#1308074411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
cosocleC22×C4×C11C24
hypercenterC2×#435D11
hypocenterC11#22422
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×#10622746C2semidirect
3. C2×#10622726C2semidirect
4. #13071545C2semidirect
5. #13069542C2semidirect
6. #13069440C2semidirect
7. #13069054C2semidirect
8. #13069044C2semidirect
9. #13068936C2semidirect
10. #13068931C2semidirect
11. #13068632C2semidirect
12. #13068557C2semidirect
13. #13068557C2semidirect
14. #13068447C2semidirect
15. C2×C11×#435C2semidirect
27. #10623084C4semidirect
83. C2×#4339C2×C4semidirect
114. #66983C2×C4semidirect
135. #66927C2×C4semidirect
137. C4×Dic22C2×C4semidirect
158. #66880D4semidirect
283. C2×#435D11semidirect
721. C11#22422semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106227462
C2×#106227262
#130715452
#130695422
#130694402
#130690542
#130690442
#130689362
#130689312
#130686322
#130685572
#130684472
C2×C11×#4352
#2242211