Finite Group Databasebeta

← #14753590

Subgroups — #14753590

Order 2816.

1374 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623054C211yesmaximal, characteristic
2C2×#10622340C211yesmaximal, characteristic
3#13071205C211yesmaximal, characteristic
4#13068711C211yesmaximal, characteristic, complemented
5#13068710C211yesmaximal, characteristic, complemented
6#13068709C211yesmaximal, characteristic, complemented
7#13068705C211yesmaximal, characteristic, complemented
8#13068704C211yesmaximal, characteristic, complemented
9#13068703C211yesmaximal, characteristic, complemented
10#13068701C211yesmaximal, characteristic, complemented
11#13068334C211yesmaximal, characteristic, complemented
12#13068334C211yesmaximal, characteristic, complemented
13#13068331C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21#10623054—24no—
22#10623054C418yescomplemented
23C2×#66945C2211yescharacteristic
24C2×#66945C2211yescharacteristic
25C2×#66945C2211yescharacteristic
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×(C22⋊D11)⋊C4—21no—
30C2×(C22⋊D11)⋊C4—21no—
31C2×C4×D44—21no—
32C2×C4×Dic22—21no—
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#380C2211yescharacteristic
35#10622825C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622600C2211yescharacteristic
41#10622570—21no—
42#10622569—21no—
43#10622340—24no—
44#10622278—21no—
45#10622259—21no—
46C11×#340C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11D411yescharacteristic
64C22×C22⋊D11D411yescharacteristic
65C23×Dic11—21no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339C2×C414yes—
71C2×#4339D414yes—
72C22×D44D411yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×Dic22D411yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#117—22no—
82C11×#117C2×C414yescomplemented
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11—21no—
90C2×C22⋊Dic11—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11C2×C414yescomplemented
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C2×#4313—22no—
112C2×#4313—22no—
113C2×#4313—22no—
114C2×C8×D11—22no—
115C2×C8×D11—22no—
116C2×C8×D11—22no—
117#66945—22no—
118#66945—22no—
119#66945—22no—
120#66945—22no—
121#66945C2×C414yes—
122#66945C2×C414yescomplemented
123C4⋊C4×D11—22no—
124C4⋊C4×D11—22no—
125C4⋊C4×D11—22no—
126C4⋊C4×D11—22no—
127C4⋊C4×D11C2×C414yes—
128C4⋊C4×D11C2×C414yescomplemented
129(C22⋊D11)⋊C4—28no—
130(C22⋊D11)⋊C4—28no—
131C4×D44—28no—
132C4×Dic22—28no—
133C11×C22⋊C8—22no—
134C11×#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C22⋊(C11⋊C8)—22no—
139(C2×D11)⋊C8—22no—
140(C2×D11)⋊C8—22no—
141#20703—111nomaximal, Sylow
142C24×C11C2×D411yescharacteristic
143C23×D11C2×D411yescharacteristic
144C23×D11C2×D411yescharacteristic
145C22×C4×C11—21no—
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×C11C22×C412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—22no—
158C2×C22⋊D11—22no—
159C2×C22⋊D11—22no—
160C2×C22⋊D11—22no—
161C2×C22⋊D11C22⋊C414yes—
162C2×C22⋊D11C22⋊C414yes—
163C22×Dic11—24no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—81no—
169C22×Dic11—81no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172#4339—28no—
173#4339—28no—
174#4339—28no—
175#4339—28no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44C22⋊C414yes—
179C2×C4×D11—24no—
180C2×C4×D11—24no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—42no—
186C2×C4×D11—81no—
187C2×C4×D11—81no—
188C2×C4×D11—81no—
189C2×C4×D11—81no—
190C2×C4×D11—81no—
191C2×C4×D11—81no—
192C2×C4×D11C22×C412yes—
193C2×C4×D11C22×C412yes—
194C2×C4×D11C2×D412yes—
195C2×C4×D11C2×D412yes—
196C2×C4×D11#4112yes—
197C2×C4×D11#4112yes—
198C2×C4×D11#4112yes—
199C2×C4×D11#4112yes—
200C2×Dic22—22no—
201C2×Dic22—22no—
202C2×Dic22C22⋊C414yes—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4C22×C412yes—
216C11×C4⋊C4C22×C412yes—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—81no—
219C42×C11—24no—
220C22⋊Dic11—81no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—81no—
225(C2×D11)⋊C4—81no—
226C4⋊Dic11—24no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11C22×C412yes—
234C4⋊Dic11C22×C412yes—
235Dic11⋊C4—24no—
236Dic11⋊C4—24no—
237Dic11⋊C4—42no—
238C4×Dic11—24no—
239C4×Dic11—24no—
240C4×Dic11—42no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247#4313—44no—
248C8×D11—44no—
249C2×#520—111no—
250C2×#408—111no—
251#2311—111no—
252#1825—111no—
253#1825—111no—
254#1825—111no—
255#1825D1111yescharacteristic, complemented
256#1824—111no—
257#1824—111no—
258#1823—111no—
259#1823—111no—
260#1736—111no—
261#1736—111no—
262#1735—111no—
263C2×#340—111no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11C2×C22⋊C412yes—
271C23×C11C22×D411yescharacteristic
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11C2×C22⋊C412yes—
283C22×D11C2×C22⋊C412yes—
284C22×D11#12312yes—
285C22×D11#12312yes—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
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—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11C2×C22⋊C412yes—
305C2×C4×C11C23×C411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C22⋊D11—28no—
312C22⋊D11—28no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—84no—
328C2×Dic11C2×C22⋊C412yes—
329C2×Dic11C2×C22⋊C412yes—
330C2×Dic11#12312yes—
331C2×Dic11#12312yes—
332D44—28no—
333C4×D11—22no—
334C4×D11—22no—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—84no—
338C4×D11—84no—
339C4×D11—84no—
340C4×D11#11714yes—
341C4×D11#11714yes—
342C4×D11#12314yes—
343C4×D11#12314yes—
344Dic22—28no—
345C8×C11—41no—
346C8×C11—41no—
347C11⋊C8—41no—
348C11⋊C8—41no—
349C22×#41—111no—
350C22×M16—111no—
351C23×C8—111no—
352#520—118no—
353#520—224no—
354C2×C4×Q8—221no—
355C2×C4×D4—221no—
356C2×C4×D4—221no—
357C2×C4×D4—221no—
358C2×#117—111no—
359C2×#117—111no—
360C2×#117—111no—
361C2×#117C2×D1111yescharacteristic
362C22×C4⋊C4—111no—
363C22×C4⋊C4—111no—
364C22×C4⋊C4—111no—
365C22×C4⋊C4—111no—
366#408—224no—
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8C2×D1111yescharacteristic
371#391—221no—
372#390—221no—
373#386—221no—
374#386—221no—
375#380—111no—
376#380—111no—
377#380—111no—
378#380C2×D1111yescharacteristic
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#340—111no—
389#340—111no—
390#340—111no—
391#340C2×D1111yescharacteristic
392#340C2×D1111yescharacteristic
393#340C2×D1111yescharacteristic
394#340C2×D1111yescharacteristic
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11C22×C22⋊C411yescharacteristic
403C22×C11C2×#12311yescharacteristic
404C22×C11C2×#12311yescharacteristic
405C22×C11#57611yescharacteristic
406C22×C11#57711yescharacteristic
407C22×C11#57711yescharacteristic
408C22×C11#57811yescharacteristic
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C2×D11#38114yes—
423C4×C11—22no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11C2×#11711yescharacteristic
429C4×C11C2×#11711yescharacteristic
430C4×C11C2×#12311yescharacteristic
431C4×C11C2×#12311yescharacteristic
432Dic11—22no—
433Dic11—42no—
434Dic11—42no—
435Dic11—81no—
436Dic11—81no—
437Dic11#38114yes—
438C2×#41—114no—
439C2×#41—114no—
440C2×#41—222no—
441C2×#41—222no—
442C2×#41—222no—
443C2×#41—222no—
444C22×Q8—111no—
445C22×D4—111no—
446C22×D4—111no—
447C22×D4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—221no—
451C23×C4—221no—
452C23×C4—221no—
453C23×C4—221no—
454C23×C4C22×D1111yescharacteristic
455C2×M16—222no—
456C2×M16—222no—
457C2×M16—222no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8—222no—
461C22×C8—222no—
462C22×C8—222no—
463C22×C8C22×D1111yescharacteristic
464C22×C8C22×D1111yescharacteristic
465C4×Q8—228no—
466C4×D4—228no—
467C4×D4—228no—
468C4×D4—228no—
469#117—22no—
470#117—114no—
471#117—114no—
472#117—222no—
473#117—222no—
474#117—222no—
475#117—222no—
476#117C4×D1114yescomplemented
477C2×C4⋊C4—114no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—114no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—222no—
485C2×C4⋊C4—222no—
486C2×C4⋊C4—222no—
487C2×C4⋊C4—222no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—222no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C4⋊C4C22×D1111yescharacteristic
495C2×C4⋊C4C22×D1111yescharacteristic
496C2×C4⋊C4C22×D1111yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C42—21no—
506C2×C42—221no—
507C2×C42—221no—
508C2×C42—221no—
509C22⋊C8—22no—
510C22⋊C8—222no—
511C22⋊C8—222no—
512C22⋊C8—222no—
513#95—21no—
514#95—221no—
515#95—221no—
516#95—221no—
517C2×C11—42no—
518C2×C11C2×#38111yescharacteristic
519C2×C11#289711yescharacteristic
520C2×C11#289811yescharacteristic
521C2×C11#309611yescharacteristic
522C2×C11#309711yescharacteristic
523C2×C11#309811yescharacteristic
524C2×C11#309911yescharacteristic
525D11—24no—
526D11—42no—
527C24—111no—
528C24—111no—
529C24D4×D1111yescharacteristic
530#41—228no—
531#41—228no—
532#41—228no—
533#41—228no—
534C2×Q8—114no—
535C2×Q8—222no—
536C2×Q8—222no—
537C2×D4—114no—
538C2×D4—114no—
539C2×D4—114no—
540C2×D4—222no—
541C2×D4—222no—
542C2×D4—222no—
543C2×D4—222no—
544C2×D4—222no—
545C2×D4—222no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—111no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—111no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—224no—
565C22×C4—224no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—224no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—442no—
576C22×C4—881no—
577C22×C4—881no—
578C22×C4—881no—
579C22×C4—881no—
580C22×C4—881no—
581C22×C4—881no—
582C22×C4—881no—
583C22×C4—881no—
584C22×C4C2×C4×D1112yes—
585C22×C4D4×D1111yescharacteristic
586C22×C4D4×D1112yes—
587C22×C4C23×D1111yescharacteristic
588M16—444no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—444no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—112no—
609C4⋊C4—112no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—442no—
620C4⋊C4C2×C4×D1112yes—
621C4⋊C4C2×C4×D1112yes—
622C22⋊C4—24no—
623C22⋊C4—81no—
624C22⋊C4—224no—
625C22⋊C4—224no—
626C22⋊C4—442no—
627C22⋊C4—881no—
628C22⋊C4—881no—
629C22⋊C4—881no—
630C42—24no—
631C42—224no—
632C42—224no—
633C42—442no—
634C11#2070311yescharacteristic, complemented, Sylow
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—112no—
642C23—112no—
643C23—112no—
644C23—112no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23—221no—
652C23—221no—
653C23—221no—
654C23—221no—
655C23C22⋊C4×D1112yes—
656C23C2×D4×D1111yescharacteristic
657Q8—228no—
658D4—228no—
659D4—228no—
660D4—228no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—112no—
682C2×C4—114no—
683C2×C4—114no—
684C2×C4—114no—
685C2×C4—114no—
686C2×C4—112no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—884no—
706C2×C4—884no—
707C2×C4—884no—
708C2×C4—884no—
709C2×C4C22⋊C4×D1112yes—
710C2×C4C22×C4×D1111yescharacteristic
711C2×C4C2×D4×D1111yescharacteristic
712C2×C4#41×D1111yescharacteristic
713C2×C4#41×D1111yescharacteristic
714C2×C4#41×D1111yescharacteristic
715C2×C4#41×D1111yescharacteristic
716C8—41no—
717C8—41no—
718C8—441no—
719C8—441no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—114no—
728C22—222no—
729C22—222no—
730C22—222no—
731C22—222no—
732C22—222no—
733C22—222no—
734C22—222no—
735C22—222no—
736C22—222no—
737C22—441no—
738C22—441no—
739C22—441no—
740C22—441no—
741C22C2×C22⋊C4×D1111yescharacteristic
742C22D11×#12311yescharacteristic
743C22D11×#12311yescharacteristic
744C22#1062330011yescharacteristic
745C22#1062330111yescharacteristic
746C22#1062330611yescharacteristic
747C22#1062331011yescharacteristic
748C4—22no—
749C4—42no—
750C4—42no—
751C4—81no—
752C4—81no—
753C4—114no—
754C4—222no—
755C4—442no—
756C4—442no—
757C4—881no—
758C4—881no—
759C4D11×#11711yescharacteristic
760C4D11×#11711yescharacteristic
761C4D11×#12311yescharacteristic
762C4D11×#12311yescharacteristic
763C2—42no—
764C2—224no—
765C2—442no—
766C2D11×#38111yescharacteristic
767C2#1307713811yescharacteristic
768C2#1307714711yescharacteristic
769C2#1307857111yescharacteristic
770C2#1307858211yescharacteristic
771C2#1307859711yescharacteristic
772C2#1307860811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1825D11
hypocenterC11#20703
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. #13068711C2semidirect
5. #13068710C2semidirect
6. #13068709C2semidirect
7. #13068705C2semidirect
8. #13068704C2semidirect
9. #13068703C2semidirect
10. #13068701C2semidirect
11. #13068334C2semidirect
12. #13068334C2semidirect
13. #13068331C2semidirect
14. D11×#340C2semidirect
15. C11×#1825C2semidirect
22. #10623054C4semidirect
82. C11×#117C2×C4semidirect
98. C2×C4⋊Dic11C2×C4semidirect
122. #66945C2×C4semidirect
128. C4⋊C4×D11C2×C4semidirect
255. #1825D11semidirect
476. #117C4×D11semidirect
634. C11#20703semidirect

Maximal subgroups

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

subgroupindex
C2×#106230542
C2×#106223402
#130712052
#130687112
#130687102
#130687092
#130687052
#130687042
#130687032
#130687012
#130683342
#130683312
D11×#3402
C11×#18252
#2070311