Finite Group Databasebeta

← #14770229

Subgroups — #14770229

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623063C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13069575C211yesmaximal, characteristic, complemented
5#13069562C211yesmaximal, characteristic, complemented
6#13069054C211yesmaximal, characteristic, complemented
7#13069053C211yesmaximal, characteristic, complemented
8#13068933C211yesmaximal, characteristic, complemented
9#13068932C211yesmaximal, characteristic, complemented
10#13068711C211yesmaximal, characteristic, complemented
11#13068710C211yesmaximal, characteristic, complemented
12#13068615C211yesmaximal, characteristic, complemented
13#13068430C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23#10623063—24no—
24#10623063C418yescomplemented
25C2×#66948C2211yescharacteristic
26C2×#66946C2211yescharacteristic
27C2×#66945C2211yescharacteristic
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×#66941C2211yescharacteristic
30C2×#66938—21no—
31C2×#66937—21no—
32C2×#66928—21no—
33C2×#66925—21no—
34#10622825C2211yescharacteristic
35#10622823—21no—
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622741—24no—
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622602—21no—
44#10622600C2211yescharacteristic
45#10622589C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47#10622585—21no—
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11D411yescharacteristic
66C22×D44—21no—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—41no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#117—22no—
78C11×#117C2×C414yescomplemented
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11D411yescharacteristic
90#66983—22no—
91#66983C2×C414yescomplemented
92C4×C22⋊D11—44no—
93C4×C22⋊D11C2×C414yes—
94C4×C22⋊D11D414yes—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4D411yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4D411yescharacteristic
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C2×#4313—22no—
115C2×#4313—22no—
116C2×#4313—41no—
117#66948—22no—
118#66948C2×C414yescomplemented
119#66946—22no—
120#66946C2×C414yescomplemented
121#66945—22no—
122#66945C2×C414yescomplemented
123C4⋊C4×D11—22no—
124C4⋊C4×D11—41no—
125#66941—22no—
126#66941C2×C414yescomplemented
127#66938—28no—
128#66937—28no—
129#66928—28no—
130#66925—28no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C22⋊(C11⋊C8)—22no—
135#66885—22no—
136#66885—41no—
137(C2×D11)⋊C8—22no—
138Dic11⋊C8—22no—
139C8×Dic11—22no—
140#66873—22no—
141#66873—41no—
142#22503—111nomaximal, Sylow
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C23×D11C2×D411yescharacteristic
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—81no—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—22no—
162C2×C22⋊D11—22no—
163C2×C22⋊D11—24no—
164C2×C22⋊D11—81no—
165C2×C22⋊D11—81no—
166C2×C22⋊D11C22⋊C414yes—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C2×D44—24no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—81no—
180C2×D44—81no—
181C2×D44C22×C412yes—
182C2×C4×D11—24no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—42no—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—81no—
192C2×C4×D11C22×C412yes—
193C2×C4×D11C2×D412yes—
194C2×Dic22—24no—
195C2×Dic22—81no—
196C2×Dic22—81no—
197C11×M16—44no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11#4112yes—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4C22×C412yes—
211C11×C4⋊C4C22×C412yes—
212C11×C4⋊C4#4112yes—
213C11×C22⋊C4—24no—
214C42×C11—24no—
215C22⋊Dic11—42no—
216C22⋊Dic11C22⋊C414yes—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—24no—
219(C2×D11)⋊C4—24no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4C22⋊C414yes—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11C22×C412yes—
229Dic11⋊C4—24no—
230Dic11⋊C4—42no—
231Dic11⋊C4—42no—
232Dic11⋊C4—81no—
233Dic11⋊C4C22⋊C414yes—
234C4×Dic11—24no—
235C4×Dic11—42no—
236C4×Dic11C22×C412yes—
237C4×Dic11C2×D412yes—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244#4313—44no—
245C2×#555—111no—
246C2×#436—111no—
247D4×C4⋊C4—111no—
248#1990—111no—
249#1987—111no—
250#1895—111no—
251#1895—111no—
252#1874—111no—
253#1874—111no—
254#1825—111no—
255#1825—111no—
256#1802—111no—
257C4×#102—111no—
258#1736—111no—
259#1736D1111yescharacteristic, complemented
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11C2×C22⋊C412yes—
267C23×C11C22×D411yescharacteristic
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—22no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11C2×C22⋊C412yes—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—84no—
301C2×C4×C11C2×C22⋊C412yes—
302C2×C4×C11C23×C411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11H(5,𝔽2)11yescharacteristic
307C2×C4×C112−1+411yescharacteristic
308C22⋊D11—28no—
309C22⋊D11—84no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—22no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11C2×C22⋊C412yes—
324C2×Dic11C2×C22⋊C412yes—
325C2×Dic11C2×C22⋊C412yes—
326C2×Dic11AGL(1,ℤ/8)12yes—
327C2×Dic11#13712yes—
328D44—22no—
329D44—22no—
330D44—41no—
331D44—41no—
332D44—84no—
333C4×D11—22no—
334C4×D11—22no—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—48no—
338C4×D11—84no—
339Dic22—84no—
340C8×C11—22no—
341C8×C11—41no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C22×M16—111no—
345C22×M16C2×D1111yescharacteristic
346#555—118no—
347#555—224no—
348C2×C4⋊Q8—111no—
349C2×#124—221no—
350C2×#124—221no—
351C2×#121—111no—
352C2×#121—111no—
353C2×#121—221no—
354C2×C4×D4—111no—
355C2×C4×D4—111no—
356C2×C4×D4—221no—
357C2×#117—111no—
358C2×#117—221no—
359C2×#117C2×D1111yescharacteristic
360C22×C4⋊C4—111no—
361C22×C4⋊C4C2×D1111yescharacteristic
362#436—224no—
363C2×C4⋊C8—111no—
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C4×C8—111no—
371#389—221no—
372#385—221no—
373#385—221no—
374#384—111no—
375#380—111no—
376#380—111no—
377C4×C4⋊C4—111no—
378#340—111no—
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340C2×D1111yescharacteristic
387#340C2×D1111yescharacteristic
388#340C2×D1111yescharacteristic
389#340C2×D1111yescharacteristic
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11C22×C22⋊C411yescharacteristic
398C22×C11#54611yescharacteristic
399C22×C11#54711yescharacteristic
400C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C11C2×#13711yescharacteristic
402C22×C11#57611yescharacteristic
403C22×C11#57711yescharacteristic
404C2×D11—22no—
405C2×D11—22no—
406C2×D11—22no—
407C2×D11—41no—
408C2×D11—41no—
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C2×D11—81no—
418C4×C11—22no—
419C4×C11—42no—
420C4×C11—42no—
421C4×C11—42no—
422C4×C11—81no—
423C4×C11C4×#4111yescharacteristic
424C4×C11#52011yescharacteristic
425C4×C11#54611yescharacteristic
426C4×C11#54711yescharacteristic
427Dic11—22no—
428Dic11—22no—
429Dic11—42no—
430Dic11—81no—
431Dic11—81no—
432Dic11#41714yes—
433C22×Q8—221no—
434C22×D4—111no—
435C22×D4—111no—
436C22×D4—221no—
437C22×D4—221no—
438C23×C4—21no—
439C23×C4—111no—
440C23×C4—221no—
441C23×C4—221no—
442C23×C4C22×D1111yescharacteristic
443C2×M16—22no—
444C2×M16—22no—
445C2×M16—41no—
446C2×M16—222no—
447C2×M16—222no—
448C2×M16—441no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8C22×D1111yescharacteristic
452C22×C8C22×D1111yescharacteristic
453C4⋊Q8—114no—
454C4⋊Q8—222no—
455#124—228no—
456#124—228no—
457#121—114no—
458#121—114no—
459#121—228no—
460#121—222no—
461#121—222no—
462C4×D4—114no—
463C4×D4—114no—
464C4×D4—114no—
465C4×D4—222no—
466C4×D4—444no—
467#117—22no—
468#117—114no—
469#117—228no—
470#117—222no—
471#117C4×D1114yescomplemented
472C2×C4⋊C4—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—222no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—441no—
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—111no—
491C2×C22⋊C4—111no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C42—21no—
499C2×C42—111no—
500C2×C42—221no—
501C2×C42—221no—
502C4⋊C8—222no—
503#102—222no—
504#102—222no—
505#102—441no—
506#102—441no—
507C22⋊C8—222no—
508C22⋊C8—222no—
509C4×C8—222no—
510#95—221no—
511#95—221no—
512#95—221no—
513C2×C11—42no—
514C2×C11#233911yescharacteristic
515C2×C11C2×#41711yescharacteristic
516C2×C11#289711yescharacteristic
517C2×C11#332511yescharacteristic
518C2×C11#332911yescharacteristic
519C2×C11#335411yescharacteristic
520C2×C11#335711yescharacteristic
521D11—42no—
522D11—82no—
523C24—111no—
524C24—221no—
525C24D4×D1111yescharacteristic
526C2×Q8—224no—
527C2×Q8—881no—
528C2×Q8—881no—
529C2×D4—114no—
530C2×D4—112no—
531C2×D4—224no—
532C2×D4—222no—
533C2×D4—222no—
534C2×D4—224no—
535C2×D4—221no—
536C2×D4—221no—
537C2×D4—221no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—881no—
541C2×D4—881no—
542C2×D4—881no—
543C2×D4—881no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—81no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—224no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—442no—
569C22×C4—442no—
570C22×C4—442no—
571C22×C4—442no—
572C22×C4—881no—
573C22×C4C2×C4×D1112yes—
574C22×C4D4×D1111yescharacteristic
575C22×C4D4×D1112yes—
576C22×C4C23×D1111yescharacteristic
577M16—44no—
578M16—444no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8#433912yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—114no—
598C4⋊C4—112no—
599C4⋊C4—224no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—442no—
606C4⋊C4—442no—
607C4⋊C4—881no—
608C4⋊C4C2×C4×D1112yes—
609C4⋊C4C2×C4×D1112yes—
610C4⋊C4#433912yes—
611C22⋊C4—24no—
612C22⋊C4—114no—
613C22⋊C4—114no—
614C22⋊C4—224no—
615C22⋊C4—224no—
616C22⋊C4—224no—
617C22⋊C4—224no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C42—24no—
621C42—112no—
622C42—112no—
623C42—224no—
624C42—442no—
625C11#2250311yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—112no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—222no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23C22⋊C4×D1112yes—
647C23C2×D4×D1111yescharacteristic
648Q8—884no—
649D4—228no—
650D4—222no—
651D4—222no—
652D4—441no—
653D4—441no—
654D4—884no—
655D4—884no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—84no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—448no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—884no—
699C2×C4C22⋊C4×D1112yes—
700C2×C4C22×C4×D1111yescharacteristic
701C2×C4C2×#433911yescharacteristic
702C2×C4C2×#433911yescharacteristic
703C2×C4C2×D4×D1111yescharacteristic
704C2×C4#6703711yescharacteristic
705C2×C4#6704011yescharacteristic
706C8—22no—
707C8—41no—
708C8—441no—
709C8—441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—222no—
718C22—222no—
719C22—222no—
720C22—441no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—442no—
725C22—442no—
726C22—442no—
727C22—881no—
728C22—881no—
729C22—881no—
730C22—881no—
731C22C2×C22⋊C4×D1111yescharacteristic
732C22#1062302111yescharacteristic
733C22#1062303811yescharacteristic
734C22D11×AGL(1,ℤ/8)11yescharacteristic
735C22#1062330511yescharacteristic
736C22D11×#13711yescharacteristic
737C22#1062330911yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—81no—
743C4—114no—
744C4—222no—
745C4—222no—
746C4—442no—
747C4—881no—
748C4—881no—
749C4C4×#433911yescharacteristic
750C4#1062302111yescharacteristic
751C4#1062303511yescharacteristic
752C4#1062303811yescharacteristic
753C2—42no—
754C2—442no—
755C2—882no—
756C2#1307144311yescharacteristic
757C2D11×#41711yescharacteristic
758C2#1307714011yescharacteristic
759C2#1308085411yescharacteristic
760C2#1308090611yescharacteristic
761C2#1308120711yescharacteristic
762C2#1308123811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC2×#10623063C2
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#22503
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C4⋊C4×C22⋊D11C2semidirect
4. #13069575C2semidirect
5. #13069562C2semidirect
6. #13069054C2semidirect
7. #13069053C2semidirect
8. #13068933C2semidirect
9. #13068932C2semidirect
10. #13068711C2semidirect
11. #13068710C2semidirect
12. #13068615C2semidirect
13. #13068430C2semidirect
14. #13068334C2semidirect
15. C11×#1736C2semidirect
24. #10623063C4semidirect
78. C11×#117C2×C4semidirect
91. #66983C2×C4semidirect
118. #66948C2×C4semidirect
120. #66946C2×C4semidirect
122. #66945C2×C4semidirect
126. #66941C2×C4semidirect
259. #1736D11semidirect
471. #117C4×D11semidirect
625. C11#22503semidirect

Maximal subgroups

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

subgroupindex
C2×#106230632
C2×#106227412
C4⋊C4×C22⋊D112
#130695752
#130695622
#130690542
#130690532
#130689332
#130689322
#130687112
#130687102
#130686152
#130684302
#130683342
C11×#17362
#2250311