Finite Group Databasebeta

← #14787780

Subgroups — #14787780

Order 2816.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic
2C2×#10622635C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic, complemented
4#13069805C211yesmaximal, characteristic, complemented
5#13069798C211yesmaximal, characteristic, complemented
6#13069617C211yesmaximal, characteristic, complemented
7#13069617C211yesmaximal, characteristic, complemented
8#13069580C211yesmaximal, characteristic, complemented
9#13069411C211yesmaximal, characteristic, complemented
10#13068929C211yesmaximal, characteristic, complemented
11#13068924C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13#13068808C211yesmaximal, characteristic, complemented
14#13068623C211yesmaximal, characteristic, complemented
15C11×#2536C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66992—21no—
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26#10623096—24no—
27#10623096—24no—
28C2×#66951—21no—
29C2×#66936—21no—
30C2×(C22⋊D11)⋊C4—21no—
31C2×C4×D44C2211yescharacteristic
32C2×#66923C2211yescharacteristic
33C11×#398—21no—
34C11×#394—21no—
35C11×#388—21no—
36C11×#388—21no—
37C11×#382C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C11×#380C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47C4×#4325—24no—
48#10622635—24no—
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66872C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—41no—
75C11×C22⋊Q8—41no—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11—21no—
96C2×#4325—22no—
97C2×#4325—22no—
98C2×#4325—22no—
99#66992—28no—
100#66983—22no—
101#66983—22no—
102#66983—22no—
103#66983—22no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107#66979—22no—
108#66979—22no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×C4×Dic11—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122#66951—28no—
123#66936—28no—
124(C22⋊D11)⋊C4—28no—
125C4×D44—22no—
126C4×D44D414yes—
127#66923—22no—
128#66923D414yes—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133#66899—22no—
134#66899—22no—
135#66899—22no—
136C22⋊(C11⋊C8)—22no—
137C22⋊(C11⋊C8)—22no—
138C22⋊(C11⋊C8)—41no—
139C22⋊(C11⋊C8)—41no—
140#66873—22no—
141#66873—41no—
142#66873—41no—
143#66872—22no—
144#66872—22no—
145#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4×C11⋊C8—22no—
148#24126—111nomaximal, Sylow
149C24×C11C2×D411yescharacteristic
150C24×C11C2×D411yescharacteristic
151C23×D11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11#4112yes—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—41no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C2×C22⋊D11—24no—
183C2×C22⋊D11—24no—
184C2×C22⋊D11—42no—
185C2×C22⋊D11—42no—
186C2×C22⋊D11—81no—
187C2×C22⋊D11—81no—
188C22×Dic11—24no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—81no—
193C22×Dic11—81no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44C2×D412yes—
200C2×C4×D11—24no—
201C2×C4×D11—81no—
202C2×C4×D11—81no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—42no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C42×C11—42no—
220C42×C11C2×D412yes—
221C42×C11C2×D412yes—
222C22⋊Dic11—24no—
223#4325—28no—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—24no—
226(C2×D11)⋊C4—24no—
227C4⋊Dic11—24no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11C2×D412yes—
232C4⋊Dic11C2×D412yes—
233C4⋊Dic11C2×D412yes—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236C4×Dic11—24no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8#4112yes—
249C2×#553—111no—
250C2×#479—111no—
251C2×C4×SD16—111no—
252#2536D1111yescharacteristic, complemented
253#2034—111no—
254#2033—111no—
255#2000—111no—
256#2000—111no—
257#1991—111no—
258#1954—111no—
259#1873—111no—
260#1872—111no—
261#1854—111no—
262#1853—111no—
263#1804—111no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11#13512yes—
278C23×C11C22×D411yescharacteristic
279C22×D11—22no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286Q8×C11—22no—
287Q8×C11—22no—
288Q8×C11—41no—
289Q8×C11—41no—
290D4×C11—44no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11#12012yes—
322C2×C4×C11#12012yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×C4×C112−1+411yescharacteristic
329C22⋊D11—48no—
330C22⋊D11—84no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—84no—
341D44—22no—
342D44—22no—
343D44—41no—
344D44—41no—
345C4×D11—84no—
346C11⋊C8—22no—
347C11⋊C8—41no—
348C11⋊C8—41no—
349C11⋊C8—41no—
350C22×SD16—111no—
351#553—224no—
352#553—224no—
353C2×#126—221no—
354C2×#125—111no—
355C2×#123—221no—
356C2×C22⋊Q8C2×D1111yescharacteristic
357C2×C22⋊Q8C2×D1111yescharacteristic
358C2×#121—111no—
359C2×#121—111no—
360C2×#121—221no—
361C2×C4×Q8C2×D1111yescharacteristic
362C2×C4×D4—111no—
363C2×C4×D4—221no—
364C2×C4×D4C2×D1111yescharacteristic
365C2×#117—111no—
366C22×C4⋊C4—111no—
367#479—224no—
368C4×SD16—224no—
369C2×#107—111no—
370C2×#106—111no—
371C2×#106—111no—
372C2×C4⋊C8—111no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#103—111no—
376C2×#102—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×C22⋊C8—111no—
380C2×C22⋊C8—111no—
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×C4×C8—111no—
384#398—21no—
385#394—21no—
386#388—21no—
387#388—21no—
388#382C2×D1111yescharacteristic
389#380C2×D1111yescharacteristic
390#380C2×D1111yescharacteristic
391#340—111no—
392#340—111no—
393#340—111no—
394#340—111no—
395#340—111no—
396#340—111no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11C2×#12011yescharacteristic
412C22×C11#54611yescharacteristic
413C22×C11#54711yescharacteristic
414C22×C11C2×#13511yescharacteristic
415C22×C11#57511yescharacteristic
416C22×C11#57711yescharacteristic
417C22×C11#57711yescharacteristic
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—81no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—81no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—42no—
430C4×C11—81no—
431C4×C11—81no—
432C4×C11—81no—
433C4×C11#52511yescharacteristic
434C4×C11#53711yescharacteristic
435C4×C11#54811yescharacteristic
436C4×C11#55011yescharacteristic
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440C22×Q8C22×D1111yescharacteristic
441C22×D4—111no—
442C22×D4—221no—
443C22×D4—221no—
444C22×D4C22⋊D1111yescharacteristic
445C23×C4—221no—
446C23×C4—221no—
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C2×SD16—222no—
450C2×SD16—222no—
451C2×SD16—222no—
452C22×C8—111no—
453C22×C8—111no—
454C22×C8—111no—
455C22×C8—111no—
456#126—228no—
457#125—114no—
458#125—222no—
459#123—228no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463C22⋊Q8—41no—
464#121—222no—
465#121—222no—
466#121—222no—
467#121—222no—
468#121—228no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—114no—
474C4×D4—228no—
475C4×D4—222no—
476#117—222no—
477#117—222no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—222no—
485C2×C4⋊C4—222no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4C22⋊D1111yescharacteristic
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C4⋊C4C22×D1111yescharacteristic
492C2×C4⋊C4C22×D1111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4C22⋊D1111yescharacteristic
502C2×C22⋊C4C22⋊D1111yescharacteristic
503C2×C42—21no—
504C2×C42—221no—
505C2×C42C22×D1111yescharacteristic
506#107—222no—
507#106—222no—
508#106—222no—
509C4⋊C8—222no—
510#103—222no—
511#103—222no—
512#103—222no—
513#102—222no—
514#102—441no—
515#102—441no—
516C22⋊C8—222no—
517C22⋊C8—222no—
518C22⋊C8—441no—
519C22⋊C8—441no—
520C4×C8—222no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525C2×C11—42no—
526C2×C11—81no—
527C2×C11#240711yescharacteristic
528C2×C11#300211yescharacteristic
529C2×C11#300911yescharacteristic
530C2×C11#330111yescharacteristic
531C2×C11#332611yescharacteristic
532C2×C11#333711yescharacteristic
533C2×C11#335111yescharacteristic
534D11—82no—
535C24—221no—
536C24C2×C22⋊D1111yescharacteristic
537C24C2×C22⋊D1111yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8#434112yes—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—41no—
547C2×D4—112no—
548C2×D4—224no—
549C2×D4—224no—
550C2×D4—221no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—442no—
556C2×D4—442no—
557C2×D4—881no—
558C2×D4—881no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—224no—
579C22×C4—224no—
580C22×C4—881no—
581C22×C4—881no—
582C22×C4—881no—
583C22×C4—881no—
584C22×C4C2×C22⋊D1111yescharacteristic
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C23×D1111yescharacteristic
589SD16—228no—
590C2×C8—112no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—112no—
613C4⋊C4—112no—
614C4⋊C4—112no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C42—42no—
632C42—224no—
633C42D4×D1112yes—
634C42D4×D1112yes—
635C11#2412611yescharacteristic, complemented, Sylow
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—222no—
650C23—441no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23#6700312yes—
657C23C22×C22⋊D1111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—44no—
663D4—222no—
664D4—222no—
665D4—448no—
666D4—441no—
667D4—441no—
668D4—884no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—884no—
709C2×C4—884no—
710C2×C4#6699012yes—
711C2×C4#6699012yes—
712C2×C4C2×D4×D1111yescharacteristic
713C2×C4C2×D4×D1111yescharacteristic
714C2×C4C2×#434111yescharacteristic
715C2×C4#6703711yescharacteristic
716C2×C4#41×D1111yescharacteristic
717C2×C4#6704311yescharacteristic
718C8—222no—
719C8—441no—
720C8—441no—
721C8—441no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—442no—
737C22—442no—
738C22—442no—
739C22—881no—
740C22—881no—
741C22—881no—
742C22—881no—
743C22C2×#6699011yescharacteristic
744C22#1062333711yescharacteristic
745C22C2×#6700311yescharacteristic
746C22#1062335311yescharacteristic
747C22#1062335511yescharacteristic
748C22#1062336811yescharacteristic
749C22#1062336811yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—42no—
755C4—81no—
756C4—81no—
757C4—81no—
758C4—442no—
759C4—442no—
760C4—442no—
761C4#1062312911yescharacteristic
762C4#1062313011yescharacteristic
763C4#1062313711yescharacteristic
764C4#1062313911yescharacteristic
765C2—42no—
766C2—81no—
767C2—882no—
768C2#1307195711yescharacteristic
769C2#1307783211yescharacteristic
770C2#1307789111yescharacteristic
771C2#1308051811yescharacteristic
772C2#1308086911yescharacteristic
773C2#1308099511yescharacteristic
774C2#1308117611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2536C2
socleC23×C11C22×D4
prime radicalC2×#10623096C2
hypercenter#2536D11
hypocenterC11#24126
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. C2×#10622635C2semidirect
3. C2×C4×#4325C2semidirect
4. #13069805C2semidirect
5. #13069798C2semidirect
6. #13069617C2semidirect
7. #13069617C2semidirect
8. #13069580C2semidirect
9. #13069411C2semidirect
10. #13068929C2semidirect
11. #13068924C2semidirect
12. #13068813C2semidirect
13. #13068808C2semidirect
14. #13068623C2semidirect
15. C11×#2536C2semidirect
252. #2536D11semidirect
635. C11#24126semidirect

Maximal subgroups

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

subgroupindex
C2×#106230962
C2×#106226352
C2×C4×#43252
#130698052
#130697982
#130696172
#130695802
#130694112
#130689292
#130689242
#130688132
#130688082
#130686232
C11×#25362
#2412611