Finite Group Databasebeta

← #14774079

Subgroups — #14774079

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622777C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic, complemented
3#13071658C211yesmaximal, characteristic, complemented
4#13071457C211yesmaximal, characteristic, complemented
5#13069493C211yesmaximal, characteristic, complemented
6#13069315C211yesmaximal, characteristic, complemented
7#13069238C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic, complemented
9#13068973C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic, complemented
11#13068886C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#13068395C211yesmaximal, characteristic, complemented
15C2×C11×#449C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C11×#449C418yescomplemented
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29#10622846—24no—
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622834—21no—
33#10622834—21no—
34#10622834—21no—
35#10622834C2211yescharacteristic
36#10622834C2211yescharacteristic
37#10622834C2211yescharacteristic
38#10622833—21no—
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825—21no—
44#10622825C2211yescharacteristic
45C4×C22⋊Dic11—21no—
46C4×C22⋊Dic11C2211yescharacteristic
47#10622777—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—
76C2×C11×SD16—22no—
77C2×C11×SD16—22no—
78C2×C11×SD16C2×C414yes—
79C2×C11×D8—41no—
80C2×C11×D8—41no—
81C2×C11×D8C2×C414yes—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×#121—22no—
85C11×#121C2×C414yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—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
99Q8×Dic11—22no—
100Q8×Dic11—22no—
101Q8×Dic11—41no—
102Q8×Dic11—41no—
103D4×Dic11—22no—
104D4×Dic11—41no—
105#66979—22no—
106#66979—41no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4×Dic11—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C2×C4×Dic11C2311yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C22×C11⋊C8—22no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—41no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C11×#103C2×C414yescomplemented
126C11×#102C2×C414yescomplemented
127C11×C22⋊C8C2×C414yescomplemented
128#66899—22no—
129#66899D414yescomplemented
130#66896—22no—
131#66896—22no—
132#66896—22no—
133#66896—41no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95D411yescharacteristic
138C11⋊#95D411yescharacteristic
139#66882—22no—
140#66881—41no—
141#66879—22no—
142#66879—41no—
143#22857—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×C11C22×C412yes—
155C2×Q8×C11C2×D412yes—
156C2×Q8×C11#4112yes—
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—21no—
168C2×D4×C11—21no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—81no—
172C2×D4×C11—81no—
173C2×D4×C11C22×C412yes—
174C2×D4×C11C22×C412yes—
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—81no—
195C22×Dic11C2×D411yescharacteristic
196C22×Dic11C2×D411yescharacteristic
197C22×Dic11C2×D411yescharacteristic
198C22×Dic11C2×D411yescharacteristic
199C11×SD16—28no—
200C11×D8—44no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11C22×C412yes—
206C2×C8×C11C22×C412yes—
207C11×C4⋊C4—21no—
208C11×C4⋊C4C22×C412yes—
209C11×C22⋊C4—24no—
210C22⋊Dic11—41no—
211C22⋊Dic11—41no—
212C22⋊Dic11—42no—
213C22⋊Dic11—42no—
214C22⋊Dic11—42no—
215C22⋊Dic11—42no—
216C22⋊Dic11—42no—
217C22⋊Dic11—81no—
218C22⋊Dic11—81no—
219C22⋊Dic11—81no—
220C22⋊Dic11—81no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—42no—
229C4⋊Dic11—42no—
230C4⋊Dic11—81no—
231C4⋊Dic11C2×D412yes—
232C4×Dic11—21no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—42no—
237C4×Dic11—42no—
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×#440—111no—
249C2×#416—111no—
250#2363—111no—
251#2341—111no—
252#1972—111no—
253#1936—111no—
254#1925—111no—
255#1893—111no—
256#1880—111no—
257#1879—111no—
258#1865—111no—
259#1854—111no—
260#1763—111no—
261#1752—111no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—41no—
271C23×C11—41no—
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—22no—
287Q8×C11C4×D414yes—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—22no—
292D4×C11—48no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11—41no—
296D4×C11—41no—
297D4×C11—84no—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—21no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—48no—
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—
343C8×C11—22no—
344C8×C11—22no—
345C11⋊C8—22no—
346C11⋊C8—41no—
347C22×#41C2×D1111yescharacteristic
348C22×SD16C2×D1111yescharacteristic
349C22×D8C2×D1111yescharacteristic
350C23×C8—111no—
351C2×#121C2×D1111yescharacteristic
352C2×C4×Q8—111no—
353C2×C4×Q8—111no—
354C2×C4×D4—111no—
355C2×#117—111no—
356#449Dic1118yescomplemented
357#440—224no—
358C2×#107—111no—
359C2×#106—111no—
360#416—224no—
361C2×#103—111no—
362C2×#103—111no—
363C2×#103C2×D1111yescharacteristic
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102C2×D1111yescharacteristic
369C2×C22⋊C8C2×D1111yescharacteristic
370C2×#97—111no—
371C2×#97—111no—
372#390—111no—
373#390—111no—
374#390—111no—
375#390—221no—
376#390—221no—
377#390—221no—
378#389—111no—
379#388—221no—
380#386—221no—
381#380—111no—
382#380—221no—
383C4×C4⋊C4—111no—
384C4×C22⋊C4—111no—
385C4×C22⋊C4—221no—
386C4×C22⋊C4—221no—
387#340—111no—
388#340—111no—
389#340—111no—
390#340—111no—
391#336—111no—
392#336—111no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11C2×C4×D411yescharacteristic
415C22×C11D4211yescharacteristic
416C22×C11#54611yescharacteristic
417C22×C11#57511yescharacteristic
418C22×C11#57511yescharacteristic
419C22×C11#57611yescharacteristic
420C22×C11#57711yescharacteristic
421C4×C11—22no—
422C4×C11—24no—
423C4×C11—42no—
424C4×C11C2×C4×D411yescharacteristic
425C4×C11#51811yescharacteristic
426C4×C11#54611yescharacteristic
427C4×C11#55111yescharacteristic
428Dic11—41no—
429Dic11—42no—
430Dic11—41no—
431Dic11—41no—
432Dic11—41no—
433Dic11—81no—
434Dic11—81no—
435Dic11—81no—
436C2×#41—22no—
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—41no—
440C2×#41—41no—
441C2×#41C2×Dic1114yescomplemented
442C22×Q8C22×D1111yescharacteristic
443C22×D4—21no—
444C22×D4—21no—
445C22×D4C22×D1111yescharacteristic
446C22×D4C22×D1111yescharacteristic
447C23×C4—21no—
448C23×C4—221no—
449C23×C4C22×D1111yescharacteristic
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16C2×Dic1114yes—
453C2×D8—41no—
454C2×D8—41no—
455C2×D8C2×Dic1114yes—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—222no—
459C22×C8—222no—
460C22×C8—441no—
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463#121—22no—
464#121C2×Dic1114yes—
465C4×Q8—222no—
466C4×Q8—222no—
467C4×Q8—441no—
468C4×Q8—441no—
469C4×D4—222no—
470C4×D4—441no—
471#117—222no—
472#117—441no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
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—
497C2×C42—221no—
498C2×C42—221no—
499#107—222no—
500#106—441no—
501#103—114no—
502#103—222no—
503#103C2×Dic1114yescomplemented
504#102—222no—
505#102—222no—
506#102—222no—
507#102—441no—
508#102C2×Dic1114yescomplemented
509C22⋊C8C2×Dic1114yescomplemented
510#97—222no—
511#97—441no—
512#95—111no—
513#95—111no—
514#95—221no—
515#95—221no—
516#95—221no—
517C2×C11—42no—
518C2×C11—82no—
519C2×C11—82no—
520C2×C11#235811yescharacteristic
521C2×C11#294311yescharacteristic
522C2×C11#294611yescharacteristic
523C2×C11#326811yescharacteristic
524C2×C11#327111yescharacteristic
525C2×C11#330911yescharacteristic
526C2×C11#332111yescharacteristic
527C24—21no—
528C24—21no—
529C24D4×D1111yescharacteristic
530#41—28no—
531#41—44no—
532#41—44no—
533#41—44no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8D4×D1112yes—
538C2×Q8#434112yes—
539C2×Q8C22×Dic1112yes—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
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×D4C22×Dic1112yes—
557C2×D4C22×Dic1112yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—111no—
568C22×C4—111no—
569C22×C4—111no—
570C22×C4—111no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—442no—
576C22×C4—442no—
577C22×C4—881no—
578C22×C4D4×D1111yescharacteristic
579C22×C4#434112yes—
580C22×C4C22×Dic1112yes—
581C22×C4C23×D1111yescharacteristic
582SD16—28no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—112no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—444no—
595C2×C8C22×Dic1112yes—
596C2×C8C22×Dic1112yes—
597C4⋊C4—21no—
598C4⋊C4—112no—
599C4⋊C4—221no—
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⋊C4C22×Dic1112yes—
610C22⋊C4—24no—
611C22⋊C4—441no—
612C22⋊C4—441no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—881no—
619C22⋊C4—881no—
620C22⋊C4—881no—
621C22⋊C4—881no—
622C42—221no—
623C42—221no—
624C42—221no—
625C42—221no—
626C42—442no—
627C42—442no—
628C42—442no—
629C42—881no—
630C11#2285711yescharacteristic, complemented, Sylow
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23D4×Dic1112yes—
652C23C2×D4×D1111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8D4×Dic1114yes—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—48no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—84no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
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—221no—
681C2×C4—221no—
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—222no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—441no—
694C2×C4—441no—
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—884no—
705C2×C4D4×Dic1112yes—
706C2×C4C2×D4×D1111yescharacteristic
707C2×C4C2×#434111yescharacteristic
708C2×C4C2×#434111yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4#6703711yescharacteristic
711C2×C4C23×Dic1111yescharacteristic
712C8—22no—
713C8—22no—
714C8—222no—
715C8—441no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22#1062312111yescharacteristic
738C22#1062312211yescharacteristic
739C22#1062329911yescharacteristic
740C22#1062329911yescharacteristic
741C22#1062330511yescharacteristic
742C22#1062330611yescharacteristic
743C22C2×D4×Dic1111yescharacteristic
744C4—22no—
745C4—24no—
746C4—42no—
747C4—441no—
748C4—441no—
749C4—442no—
750C4—441no—
751C4—441no—
752C4—881no—
753C4—881no—
754C4—881no—
755C4#1062311811yescharacteristic
756C4#1062312211yescharacteristic
757C4C2×D4×Dic1111yescharacteristic
758C4#1062332911yescharacteristic
759C2—42no—
760C2—82no—
761C2—82no—
762C2#1307160011yescharacteristic
763C2#1307741711yescharacteristic
764C2#1307744911yescharacteristic
765C2#1308014911yescharacteristic
766C2#1308019411yescharacteristic
767C2#1308062611yescharacteristic
768C2#1308080611yescharacteristic
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#22857
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×#10622777C2semidirect
2. C2×#10622846C2semidirect
3. #13071658C2semidirect
4. #13071457C2semidirect
5. #13069493C2semidirect
6. #13069315C2semidirect
7. #13069238C2semidirect
8. #13069045C2semidirect
9. #13068973C2semidirect
10. #13068966C2semidirect
11. #13068886C2semidirect
12. #13068817C2semidirect
13. #13068448C2semidirect
14. #13068395C2semidirect
25. C11×#449C4semidirect
67. C2×C11×#41C2×C4semidirect
125. C11×#103C2×C4semidirect
126. C11×#102C2×C4semidirect
127. C11×C22⋊C8C2×C4semidirect
129. #66899D4semidirect
356. #449Dic11semidirect
441. C2×#41C2×Dic11semidirect
503. #103C2×Dic11semidirect
508. #102C2×Dic11semidirect
509. C22⋊C8C2×Dic11semidirect
630. C11#22857semidirect

Maximal subgroups

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

subgroupindex
C2×#106227772
C2×#106228462
#130716582
#130714572
#130694932
#130693152
#130692382
#130690452
#130689732
#130689662
#130688862
#130688172
#130684482
#130683952
C2×C11×#4492
#2285711