Finite Group Databasebeta

← #14774124

Subgroups — #14774124

Order 2816.

1174 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×#10622765C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic, complemented
3#13071658C211yesmaximal, characteristic, complemented
4#13071446C211yesmaximal, characteristic, complemented
5#13069499C211yesmaximal, characteristic, complemented
6#13069308C211yesmaximal, characteristic, complemented
7#13069252C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic, complemented
9#13068966C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068865C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic, complemented
14#13068395C211yesmaximal, characteristic, complemented
15C2×C11×#449C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C11×#449C418yescomplemented
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29#10622846—24no—
30#10622843C2211yescharacteristic
31#10622843C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622834—21no—
35#10622834C2211yescharacteristic
36#10622833—21no—
37#10622833—21no—
38#10622833—21no—
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44#10622824—21no—
45C4×C22⋊Dic11C2211yescharacteristic
46C2×C11⋊#95—21no—
47#10622765—24no—
48C2×#66882C2211yescharacteristic
49C2×#66881C2211yescharacteristic
50C2×#66879C2211yescharacteristic
51C2×#66879C2211yescharacteristic
52#10622598C2211yescharacteristic
53C4⋊C4×Dic11C2211yescharacteristic
54#10622564—21no—
55C22⋊C4×Dic11—21no—
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C2×C11×#41C2×C414yescomplemented
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11—21no—
70C22×D4×C11—21no—
71C22×D4×C11C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C23×Dic11—21no—
76C23×Dic11—21no—
77C23×Dic11—21no—
78C2×C11×SD16—41no—
79C2×C11×SD16—41no—
80C2×C11×SD16C2×C414yescomplemented
81C2×C11×D8—22no—
82C2×C11×D8—22no—
83C2×C11×D8C2×C414yes—
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C11×#121—22no—
87C11×#121C2×C414yescomplemented
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11D411yescharacteristic
98C2×C22⋊Dic11D411yescharacteristic
99D4×Dic11—22no—
100D4×Dic11—22no—
101D4×Dic11—22no—
102D4×Dic11—41no—
103D4×Dic11—41no—
104D4×Dic11—41no—
105#66979—22no—
106#66979—41no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C22×C11⋊C8—22no—
117C22×C11⋊C8—22no—
118C22×C11⋊C8—41no—
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C11×#103C2×C414yescomplemented
122C11×#102C2×C414yescomplemented
123C11×C22⋊C8C2×C414yescomplemented
124#66899—22no—
125#66899—22no—
126#66896—22no—
127#66896—22no—
128#66896—41no—
129#66896D414yescomplemented
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95D411yescharacteristic
138C11⋊#95D411yescharacteristic
139#66882—41no—
140#66881—22no—
141#66879—22no—
142#66879—41no—
143#22860—111nomaximal, Sylow
144C24×C11—21no—
145C24×C11—21no—
146C24×C11C2×D411yescharacteristic
147C11×#41—28no—
148C11×#41—44no—
149C11×#41—44no—
150C11×#41—44no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11C22×C412yes—
157C2×D4×C11—24no—
158C2×D4×C11—24no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—81no—
170C2×D4×C11—81no—
171C2×D4×C11C22×C412yes—
172C2×D4×C11C22×C412yes—
173C2×D4×C11C2×D412yes—
174C2×D4×C11#4112yes—
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—42no—
183C22×C4×C11—42no—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11#4112yes—
187C22×C4×C11C2411yescharacteristic
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—42no—
193C22×Dic11—42no—
194C22×Dic11—42no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11—81no—
199C22×Dic11—81no—
200C22×Dic11—81no—
201C22×Dic11C2×D411yescharacteristic
202C22×Dic11C2×D411yescharacteristic
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C11×SD16—44no—
206C11×D8—28no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11C22×C412yes—
212C2×C8×C11C22×C412yes—
213C11×C4⋊C4—21no—
214C11×C4⋊C4C22×C412yes—
215C11×C22⋊C4—24no—
216C22⋊Dic11—41no—
217C22⋊Dic11—41no—
218C22⋊Dic11—42no—
219C22⋊Dic11—42no—
220C22⋊Dic11—42no—
221C22⋊Dic11—42no—
222C22⋊Dic11—42no—
223C22⋊Dic11—81no—
224C22⋊Dic11—81no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—81no—
233C4⋊Dic11C2×D412yes—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—21no—
238C4×Dic11—42no—
239C4×Dic11—81no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—44no—
246C2×C11⋊C8C2×D412yes—
247C2×#449D1111yescharacteristic
248C2×#442—111no—
249C2×#416—111no—
250#2363—111no—
251#2339—111no—
252#1973—111no—
253#1935—111no—
254#1927—111no—
255#1893—111no—
256#1879—111no—
257#1877—111no—
258#1862—111no—
259#1854—111no—
260#1762—111no—
261#1752—111no—
262C23×C11—22no—
263C23×C11—21no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—22no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11C4×D412yes—
283C23×C11C22×D411yescharacteristic
284Q8×C11—22no—
285Q8×C11—22no—
286Q8×C11—41no—
287Q8×C11—41no—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—22no—
292D4×C11—22no—
293D4×C11—48no—
294D4×C11—41no—
295D4×C11—41no—
296D4×C11—84no—
297D4×C11C4×D414yes—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—48no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11C4×D412yes—
312C2×C4×C11C23×C411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—22no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—84no—
343C2×Dic11—84no—
344C2×Dic11—84no—
345C8×C11—22no—
346C8×C11—22no—
347C11⋊C8—22no—
348C11⋊C8—41no—
349C22×#41C2×D1111yescharacteristic
350C22×SD16C2×D1111yescharacteristic
351C22×D8C2×D1111yescharacteristic
352C23×C8—111no—
353C2×#121C2×D1111yescharacteristic
354C2×C4×D4—111no—
355C2×C4×D4—111no—
356C2×C4×D4—111no—
357C2×#117—111no—
358#449Dic1118yescomplemented
359#442—224no—
360C2×#107—111no—
361C2×#106—111no—
362#416—224no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#103C2×D1111yescharacteristic
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102C2×D1111yescharacteristic
371C2×C22⋊C8C2×D1111yescharacteristic
372C2×#97—111no—
373C2×#97—111no—
374#391—111no—
375#391—111no—
376#390—111no—
377#390—221no—
378#389—111no—
379#388—221no—
380#386—221no—
381#386—221no—
382#386—221no—
383#381—221no—
384#380—111no—
385C4×C4⋊C4—111no—
386C4×C22⋊C4—111no—
387C4×C22⋊C4—221no—
388C2×#95—221no—
389#340—111no—
390#340—111no—
391#340—111no—
392#340—111no—
393#336—111no—
394#336—111no—
395C22×C11—22no—
396C22×C11—24no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—41no—
402C22×C11—42no—
403C22×C11—41no—
404C22×C11—42no—
405C22×C11—41no—
406C22×C11—42no—
407C22×C11—41no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11C2×C4×D411yescharacteristic
417C22×C11D4211yescharacteristic
418C22×C11#54611yescharacteristic
419C22×C11#57511yescharacteristic
420C22×C11#57511yescharacteristic
421C22×C11#57611yescharacteristic
422C22×C11#57711yescharacteristic
423C4×C11—22no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11C2×C4×D411yescharacteristic
427C4×C11#51811yescharacteristic
428C4×C11#54611yescharacteristic
429C4×C11#55111yescharacteristic
430Dic11—41no—
431Dic11—42no—
432Dic11—41no—
433Dic11—41no—
434Dic11—41no—
435Dic11—81no—
436Dic11—81no—
437Dic11—81no—
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41C2×Dic1114yescomplemented
444C22×Q8C22×D1111yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C22×D1111yescharacteristic
448C22×D4C22×D1111yescharacteristic
449C23×C4—21no—
450C23×C4—221no—
451C23×C4—221no—
452C23×C4—221no—
453C23×C4C22×D1111yescharacteristic
454C2×SD16—41no—
455C2×SD16—41no—
456C2×SD16C2×Dic1114yescomplemented
457C2×D8—22no—
458C2×D8—22no—
459C2×D8C2×Dic1114yes—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—222no—
463C22×C8—222no—
464C22×C8—441no—
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1111yescharacteristic
467#121—22no—
468#121C2×Dic1114yescomplemented
469C4×D4—222no—
470C4×D4—222no—
471C4×D4—222no—
472C4×D4—441no—
473C4×D4—441no—
474C4×D4—441no—
475#117—222no—
476#117—441no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—111no—
485C2×C22⋊C4—111no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C42—111no—
494C2×C42—111no—
495C2×C42—221no—
496C2×C42—221no—
497#107—441no—
498#106—222no—
499#103—222no—
500#103—222no—
501#103C2×Dic1114yescomplemented
502#102—114no—
503#102—222no—
504#102—222no—
505#102—441no—
506#102C2×Dic1114yescomplemented
507C22⋊C8C2×Dic1114yescomplemented
508#97—222no—
509#97—441no—
510#95—111no—
511#95—111no—
512#95—221no—
513#95—221no—
514#95—221no—
515#95—221no—
516#95—221no—
517#95—221no—
518#95—221no—
519C2×C11—42no—
520C2×C11—44no—
521C2×C11—82no—
522C2×C11#235811yescharacteristic
523C2×C11#294311yescharacteristic
524C2×C11#294611yescharacteristic
525C2×C11#326711yescharacteristic
526C2×C11#326811yescharacteristic
527C2×C11#330711yescharacteristic
528C2×C11#331911yescharacteristic
529C24—21no—
530C24—21no—
531C24D4×D1111yescharacteristic
532#41—28no—
533#41—44no—
534#41—44no—
535#41—44no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C22×Dic1112yes—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4D4×D1112yes—
557C2×D4#434112yes—
558C2×D4C22×Dic1112yes—
559C2×D4C22×Dic1112yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—111no—
570C22×C4—111no—
571C22×C4—111no—
572C22×C4—111no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—442no—
578C22×C4—442no—
579C22×C4—442no—
580C22×C4—442no—
581C22×C4—442no—
582C22×C4—442no—
583C22×C4—881no—
584C22×C4—881no—
585C22×C4—881no—
586C22×C4D4×D1111yescharacteristic
587C22×C4#434112yes—
588C22×C4C22×Dic1112yes—
589C22×C4C23×D1111yescharacteristic
590SD16—44no—
591D8—28no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—112no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—444no—
603C2×C8C22×Dic1112yes—
604C2×C8C22×Dic1112yes—
605C4⋊C4—21no—
606C4⋊C4—112no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—221no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—881no—
615C4⋊C4C22×Dic1112yes—
616C22⋊C4—24no—
617C22⋊C4—441no—
618C22⋊C4—441no—
619C22⋊C4—442no—
620C22⋊C4—442no—
621C22⋊C4—442no—
622C22⋊C4—442no—
623C22⋊C4—442no—
624C22⋊C4—881no—
625C22⋊C4—881no—
626C42—221no—
627C42—221no—
628C42—221no—
629C42—221no—
630C42—442no—
631C42—881no—
632C11#2286011yescharacteristic, complemented, Sylow
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23D4×Dic1112yes—
654C23C2×D4×D1111yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—48no—
665D4—41no—
666D4—41no—
667D4—84no—
668D4D4×Dic1114yes—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—222no—
693C2×C4—221no—
694C2×C4—221no—
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—441no—
706C2×C4—884no—
707C2×C4—884no—
708C2×C4—884no—
709C2×C4D4×Dic1112yes—
710C2×C4C2×D4×D1111yescharacteristic
711C2×C4C2×#434111yescharacteristic
712C2×C4C2×#434111yescharacteristic
713C2×C4#6703711yescharacteristic
714C2×C4#6703711yescharacteristic
715C2×C4C23×Dic1111yescharacteristic
716C8—22no—
717C8—22no—
718C8—222no—
719C8—441no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—41no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22#1062312111yescharacteristic
742C22#1062312211yescharacteristic
743C22#1062329911yescharacteristic
744C22#1062329911yescharacteristic
745C22#1062330511yescharacteristic
746C22#1062330611yescharacteristic
747C22C2×D4×Dic1111yescharacteristic
748C4—22no—
749C4—42no—
750C4—42no—
751C4—441no—
752C4—441no—
753C4—442no—
754C4—441no—
755C4—441no—
756C4—881no—
757C4—881no—
758C4—881no—
759C4#1062311811yescharacteristic
760C4#1062312211yescharacteristic
761C4C2×D4×Dic1111yescharacteristic
762C4#1062332911yescharacteristic
763C2—42no—
764C2—44no—
765C2—82no—
766C2#1307160011yescharacteristic
767C2#1307741711yescharacteristic
768C2#1307744911yescharacteristic
769C2#1308013411yescharacteristic
770C2#1308016011yescharacteristic
771C2#1308059611yescharacteristic
772C2#1308077611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#449C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#449D11
hypocenterC11#22860
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#10622765C2semidirect
2. C2×#10622846C2semidirect
3. #13071658C2semidirect
4. #13071446C2semidirect
5. #13069499C2semidirect
6. #13069308C2semidirect
7. #13069252C2semidirect
8. #13069045C2semidirect
9. #13068966C2semidirect
10. #13068952C2semidirect
11. #13068865C2semidirect
12. #13068817C2semidirect
13. #13068443C2semidirect
14. #13068395C2semidirect
25. C11×#449C4semidirect
67. C2×C11×#41C2×C4semidirect
80. C2×C11×SD16C2×C4semidirect
87. C11×#121C2×C4semidirect
121. C11×#103C2×C4semidirect
122. C11×#102C2×C4semidirect
123. C11×C22⋊C8C2×C4semidirect
129. #66896D4semidirect
358. #449Dic11semidirect
443. C2×#41C2×Dic11semidirect
456. C2×SD16C2×Dic11semidirect
468. #121C2×Dic11semidirect
501. #103C2×Dic11semidirect
506. #102C2×Dic11semidirect
507. C22⋊C8C2×Dic11semidirect
632. C11#22860semidirect

Maximal subgroups

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

subgroupindex
C2×#106227652
C2×#106228462
#130716582
#130714462
#130694992
#130693082
#130692522
#130690452
#130689662
#130689522
#130688652
#130688172
#130684432
#130683952
C2×C11×#4492
#2286011