Finite Group Databasebeta

← #14770231

Subgroups — #14770231

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×#10623147C211yesmaximal, characteristic
2C2×#10622342C211yesmaximal, characteristic, complemented
3C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13069575C211yesmaximal, characteristic, complemented
5#13069562C211yesmaximal, characteristic, complemented
6#13069055C211yesmaximal, characteristic, complemented
7#13069051C211yesmaximal, characteristic, complemented
8#13068930C211yesmaximal, characteristic, complemented
9#13068712C211yesmaximal, characteristic, complemented
10#13068709C211yesmaximal, characteristic, complemented
11#13068614C211yesmaximal, characteristic, complemented
12#102×Dic11C211yesmaximal, characteristic, complemented
13#13068335C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1874C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66992—21no—
19C2×#66991C2211yescharacteristic
20C2×#66989—21no—
21C2×D4×Dic11C2211yescharacteristic
22C2×C4×C22⋊D11—21no—
23C2×C4×C22⋊D11C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C22×#4313C2211yescharacteristic
27#10623147—24no—
28#10623147C418yescomplemented
29C2×#66945C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×#66941C2211yescharacteristic
32C2×#66938—21no—
33C2×#66930—21no—
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic
40#10622823—21no—
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622602—21no—
45#10622600C2211yescharacteristic
46#10622589C2211yescharacteristic
47C4⋊C4×Dic11C2211yescharacteristic
48#10622585—21no—
49#10622342—24no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11D411yescharacteristic
68C23×Dic11—21no—
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#121—22no—
75C11×#121C2×C414yescomplemented
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11D411yescharacteristic
88#66992—28no—
89#66991—22no—
90#66991C2×C414yescomplemented
91#66989—28no—
92D4×Dic11—22no—
93D4×Dic11C2×C414yescomplemented
94C4×C22⋊D11—44no—
95C4×C22⋊D11C2×C414yes—
96C4×C22⋊D11D414yes—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4D411yescharacteristic
100#66979—22no—
101#66979C2×C414yescomplemented
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4D411yescharacteristic
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11C2311yescharacteristic
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318—41no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C2×#4313—22no—
121C2×#4313—22no—
122C2×#4313—41no—
123#66945—22no—
124#66945C2×C414yescomplemented
125C4⋊C4×D11—22no—
126C4⋊C4×D11—41no—
127#66941—22no—
128#66941C2×C414yescomplemented
129#66938—28no—
130#66930—28no—
131C11×#102—22no—
132C11×#102—41no—
133C11×C22⋊C8—22no—
134#66896—22no—
135#66896—41no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139(C2×D11)⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142#22503—111nomaximal, Sylow
143C24×C11—21no—
144C24×C11C2×D411yescharacteristic
145C23×D11C2×D411yescharacteristic
146C2×D4×C11—24no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—81no—
153C2×D4×C11—81no—
154C2×D4×C11C22×C412yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—81no—
165C22×C4×C11C22×C412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—24no—
172C2×C22⋊D11—81no—
173C2×C22⋊D11—81no—
174C2×C22⋊D11C22⋊C414yes—
175C22×Dic11—24no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184C22×Dic11C2×D411yescharacteristic
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
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—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4C22×C412yes—
209C11×C4⋊C4#4112yes—
210C11×C22⋊C4—24no—
211C22⋊Dic11—24no—
212C22⋊Dic11—24no—
213C22⋊Dic11—24no—
214C22⋊Dic11—42no—
215C22⋊Dic11C22⋊C414yes—
216(C2×D11)⋊C4—24no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4C22⋊C414yes—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11C22×C412yes—
226C4⋊Dic11C22×C412yes—
227Dic11⋊C4—24no—
228Dic11⋊C4—42no—
229Dic11⋊C4—42no—
230Dic11⋊C4—81no—
231Dic11⋊C4C22⋊C414yes—
232C4×Dic11—24no—
233C4×Dic11—24no—
234C4×Dic11—42no—
235C4×Dic11C22×C412yes—
236C4×Dic11C2×D412yes—
237#4318—44no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8#4112yes—
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#1874D1111yescharacteristic, complemented
254#1825—111no—
255#1825—111no—
256#1802—111no—
257C4×#102—111no—
258#1736—111no—
259#1736—111no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—22no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11C2×C22⋊C412yes—
274C23×C11C22×D411yescharacteristic
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11C2×C22⋊C412yes—
282D4×C11—22no—
283D4×C11—22no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—84no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—84no—
303C2×C4×C11C2×C22⋊C412yes—
304C2×C4×C11C23×C411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C112−1+411yescharacteristic
310C22⋊D11—28no—
311C22⋊D11—84no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—48no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11C2×C22⋊C412yes—
330C2×Dic11C2×C22⋊C412yes—
331C2×Dic11C2×C22⋊C412yes—
332C2×Dic11AGL(1,ℤ/8)12yes—
333C2×Dic11#13712yes—
334C4×D11—22no—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—22no—
338C4×D11—84no—
339Dic22—84no—
340C8×C11—41no—
341C8×C11—41no—
342C11⋊C8—22no—
343C11⋊C8—41no—
344C22×M16—111no—
345C22×M16—111no—
346#555—118no—
347#555—224no—
348C2×C4⋊Q8—111no—
349C2×#124—221no—
350C2×#124—221no—
351C2×#121—111no—
352C2×#121—221no—
353C2×#121C2×D1111yescharacteristic
354C2×C4×D4—111no—
355C2×C4×D4—111no—
356C2×C4×D4—221no—
357C2×#117—111no—
358C2×#117—111no—
359C2×#117—221no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4C2×D1111yescharacteristic
362#436—224no—
363C2×C4⋊C8—111no—
364C2×#102—111no—
365C2×#102—111no—
366C2×#102C2×D1111yescharacteristic
367C2×#102C2×D1111yescharacteristic
368C2×C22⋊C8—111no—
369C2×C22⋊C8C2×D1111yescharacteristic
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#340—111no—
387#340—111no—
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×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11C22×C22⋊C411yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11#54711yescharacteristic
407C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C11C2×#13711yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57711yescharacteristic
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11—41no—
417C2×D11—41no—
418C4×C11—22no—
419C4×C11—42no—
420C4×C11—42no—
421C4×C11—81no—
422C4×C11C4×#4111yescharacteristic
423C4×C11#52011yescharacteristic
424C4×C11#54611yescharacteristic
425C4×C11#54711yescharacteristic
426Dic11—22no—
427Dic11—22no—
428Dic11—42no—
429Dic11—42no—
430Dic11—81no—
431Dic11—81no—
432Dic11#41714yes—
433C22×Q8—221no—
434C22×D4—21no—
435C22×D4—111no—
436C22×D4—221no—
437C22×D4C22×D1111yescharacteristic
438C23×C4—21no—
439C23×C4—111no—
440C23×C4—221no—
441C23×C4—221no—
442C23×C4C22×D1111yescharacteristic
443C2×M16—222no—
444C2×M16—222no—
445C2×M16—222no—
446C2×M16—222no—
447C2×M16—441no—
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—22no—
458#121—114no—
459#121—222no—
460#121—228no—
461#121C4×D1114yescomplemented
462C4×D4—114no—
463C4×D4—114no—
464C4×D4—114no—
465C4×D4—222no—
466C4×D4—444no—
467#117—114no—
468#117—114no—
469#117—228no—
470#117—222no—
471#117—222no—
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—111no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—222no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—441no—
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—111no—
499C2×C42—221no—
500C2×C42—221no—
501C2×C42—221no—
502C4⋊C8—222no—
503#102—22no—
504#102—41no—
505#102—222no—
506#102—441no—
507C22⋊C8—22no—
508C22⋊C8—222no—
509C4×C8—222no—
510#95—221no—
511#95—221no—
512#95—221no—
513C2×C11—42no—
514C2×C11—82no—
515C2×C11#233911yescharacteristic
516C2×C11C2×#41711yescharacteristic
517C2×C11#289711yescharacteristic
518C2×C11#332511yescharacteristic
519C2×C11#332911yescharacteristic
520C2×C11#335411yescharacteristic
521C2×C11#335711yescharacteristic
522D11—42no—
523C24—21no—
524C24—111no—
525C24D4×D1111yescharacteristic
526C2×Q8—224no—
527C2×Q8—881no—
528C2×Q8—881no—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—114no—
538C2×D4—222no—
539C2×D4—222no—
540C2×D4—224no—
541C2×D4—881no—
542C2×D4—881no—
543C2×D4C2×C4×D1112yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—224no—
560C22×C4—221no—
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—444no—
578M16—444no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—112no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—114no—
597C4⋊C4—112no—
598C4⋊C4—112no—
599C4⋊C4—224no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—442no—
607C4⋊C4—442no—
608C4⋊C4—881no—
609C4⋊C4C2×C4×D1112yes—
610C4⋊C4#434112yes—
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—112no—
621C42—112no—
622C42—224no—
623C42—224no—
624C42—442no—
625C11#2250311yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—112no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23C22⋊C4×D1112yes—
647C23C2×D4×D1111yescharacteristic
648Q8—884no—
649D4—22no—
650D4—22no—
651D4—41no—
652D4—41no—
653D4—84no—
654D4—228no—
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—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—84no—
672C2×C4—112no—
673C2×C4—112no—
674C2×C4—112no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—448no—
688C2×C4—441no—
689C2×C4—441no—
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×D4×D1111yescharacteristic
702C2×C4C2×#434111yescharacteristic
703C2×C4#6703711yescharacteristic
704C2×C4#41×D1111yescharacteristic
705C2×C4#6704311yescharacteristic
706C8—41no—
707C8—41no—
708C8—222no—
709C8—441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—222no—
725C22—222no—
726C22—222no—
727C22—441no—
728C22—441no—
729C22—441no—
730C22—441no—
731C22C2×C22⋊C4×D1111yescharacteristic
732C22#1062312211yescharacteristic
733C22#1062318611yescharacteristic
734C22#1062328811yescharacteristic
735C22#1062329311yescharacteristic
736C22D11×AGL(1,ℤ/8)11yescharacteristic
737C22D11×#13711yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—81no—
742C4—114no—
743C4—222no—
744C4—222no—
745C4—442no—
746C4—442no—
747C4—881no—
748C4—881no—
749C4C4×#434111yescharacteristic
750C4#1062307711yescharacteristic
751C4#1062314111yescharacteristic
752C4#1062314211yescharacteristic
753C2—42no—
754C2—82no—
755C2—442no—
756C2#1307144211yescharacteristic
757C2D11×#41711yescharacteristic
758C2#1307713711yescharacteristic
759C2#1308085111yescharacteristic
760C2#1308090311yescharacteristic
761C2#1308120411yescharacteristic
762C2#1308123511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×#10623147C2
cosocleC22×C4×C11C24
hypercenter#1874D11
hypocenterC11#22503
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#10622342C2semidirect
3. C4⋊C4×C22⋊D11C2semidirect
4. #13069575C2semidirect
5. #13069562C2semidirect
6. #13069055C2semidirect
7. #13069051C2semidirect
8. #13068930C2semidirect
9. #13068712C2semidirect
10. #13068709C2semidirect
11. #13068614C2semidirect
12. #102×Dic11C2semidirect
13. #13068335C2semidirect
14. #13068334C2semidirect
15. C11×#1874C2semidirect
28. #10623147C4semidirect
75. C11×#121C2×C4semidirect
90. #66991C2×C4semidirect
93. D4×Dic11C2×C4semidirect
101. #66979C2×C4semidirect
124. #66945C2×C4semidirect
128. #66941C2×C4semidirect
253. #1874D11semidirect
461. #121C4×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×#106231472
C2×#106223422
C4⋊C4×C22⋊D112
#130695752
#130695622
#130690552
#130690512
#130689302
#130687122
#130687092
#130686142
#102×Dic112
#130683352
#130683342
C11×#18742
#2250311