Finite Group Databasebeta

← #14690451

Subgroups — #14690451

Order 2816.

1762 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622606C212yesmaximal, complemented
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622601C211yesmaximal, characteristic
5#13066864C212yesmaximal, complemented
6#13066864C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066845C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#389C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C11×#389—24no—
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36#10622606—28no—
37#10622601—24no—
38#10622601—24no—
39#10622552—24no—
40C24×D11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44D414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—42no—
66C2×C11×C4⋊C4D414yes—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C11×#95—24no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95D414yescomplemented
106#15138—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11C2×D414yes—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×C4×C11#4112yes—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11C2×D412yes—
190C22×Dic11C2×D412yes—
191C22×Dic11#4112yes—
192C22×Dic11#4112yes—
193C2×D44—28no—
194C2×D44—28no—
195C2×D44—28no—
196C2×D44—44no—
197C2×D44—44no—
198C2×D44—44no—
199C2×D44—44no—
200C11×C4⋊C4—28no—
201C11×C4⋊C4—48no—
202C11×C4⋊C4—44no—
203C42×C11—44no—
204(C2×D11)⋊C4—48no—
205(C2×D11)⋊C4—48no—
206(C2×D11)⋊C4—48no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4—48no—
209(C2×D11)⋊C4—48no—
210C4⋊Dic11—44no—
211C4×Dic11—44no—
212C4×Dic11—44no—
213C2×#397—112no—
214C2×#390—111no—
215C2×#390—111no—
216C2×#390—111no—
217C2×#389D1111yescharacteristic, complemented
218#1440—112no—
219#1440—112no—
220#1439—112no—
221C4⋊#95—111no—
222C4⋊#95—111no—
223C4×#95—111no—
224C23×C11C22×D411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C23×C11C22×D411yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11C2×#4111yescharacteristic
232C23×C11C2×#4111yescharacteristic
233C23×C11C2×#4111yescharacteristic
234C23×C11C2×#4111yescharacteristic
235C23×C11H(5,𝔽2)11yescharacteristic
236C23×C11H(5,𝔽2)11yescharacteristic
237C23×C11H(5,𝔽2)11yescharacteristic
238C23×C112−1+411yescharacteristic
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—42no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—42no—
262C22×D11—42no—
263C22×D11—42no—
264C22×D11—42no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—24no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—24no—
282C2×C4×C11—22no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—42no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11#12114yes—
303C2×C4×C11#12314yes—
304C2×C4×C11#12314yes—
305C2×C4×C11#12314yes—
306C2×C4×C11#12414yes—
307C2×C4×C11#12614yes—
308C2×C4×C11#12614yes—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344D44—416no—
345C23×D4—111no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C4⋊C4C2×D1112yes—
349C22×C4⋊C4C2×D1111yescharacteristic
350C22×C22⋊C4—112no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—112no—
356C22×C42—111no—
357C22×C42—111no—
358C22×C42C2×D1111yescharacteristic
359#397—228no—
360#390—224no—
361#390—224no—
362#390—224no—
363#389—24no—
364C2×#95—111no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—111no—
368C2×#95—111no—
369C2×#95—111no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95C2×D1112yes—
373C22×C11C2×#12111yescharacteristic
374C22×C11C2×#12311yescharacteristic
375C22×C11C2×#12311yescharacteristic
376C22×C11C2×#12311yescharacteristic
377C22×C11C2×#12411yescharacteristic
378C22×C11C2×#12611yescharacteristic
379C22×C11C2×#12611yescharacteristic
380C22×C11#52911yescharacteristic
381C22×C11#52911yescharacteristic
382C22×C11#52911yescharacteristic
383C22×C11#53211yescharacteristic
384C22×C11#53211yescharacteristic
385C22×C11#53211yescharacteristic
386C22×C11#54011yescharacteristic
387C22×C11#54011yescharacteristic
388C22×C11#54011yescharacteristic
389C22×C11#54211yescharacteristic
390C22×C11#54211yescharacteristic
391C22×C11#54211yescharacteristic
392C22×C11D4211yescharacteristic
393C22×C11D4211yescharacteristic
394C22×C11#54611yescharacteristic
395C22×C11#54611yescharacteristic
396C22×C11#54611yescharacteristic
397C22×C11#54711yescharacteristic
398C22×C11#54711yescharacteristic
399C22×C11#54811yescharacteristic
400C22×C11#55011yescharacteristic
401C22×C11#55011yescharacteristic
402C22×C11#55311yescharacteristic
403C22×C11#55311yescharacteristic
404C22×C11#55511yescharacteristic
405C22×C11#55611yescharacteristic
406C22×C11#55911yescharacteristic
407C22×C11#55911yescharacteristic
408C2×D11—44no—
409C2×D11—44no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—82no—
416C2×D11—82no—
417C2×D11—82no—
418C2×D11—82no—
419C2×D11—82no—
420C2×D11—82no—
421C2×D11—82no—
422C2×D11—82no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—44no—
426C4×C11—82no—
427C4×C11#39718yescomplemented
428Dic11—42no—
429Dic11—42no—
430Dic11—42no—
431Dic11—42no—
432Dic11—82no—
433C25—112no—
434C22×D4—114no—
435C22×D4—222no—
436C22×D4—222no—
437C22×D4—222no—
438C22×D4—222no—
439C22×D4—222no—
440C22×D4—222no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—112no—
446C23×C4C22×D1112yes—
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1112yes—
450C23×C4C22×D1111yescharacteristic
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4C22⋊D1114yes—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—224no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—442no—
476C2×C22⋊C4—442no—
477C2×C22⋊C4—442no—
478C2×C22⋊C4—442no—
479C2×C22⋊C4—442no—
480C2×C22⋊C4—442no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—222no—
485C2×C42—222no—
486C2×C42—222no—
487C2×C42—222no—
488C2×C42—222no—
489C2×C42—222no—
490#95—24no—
491#95—114no—
492#95—222no—
493#95—222no—
494#95—224no—
495#95—224no—
496#95—222no—
497#95—442no—
498#95—442no—
499C2×C11C2×#39711yescharacteristic
500C2×C11#242011yescharacteristic
501C2×C11#242211yescharacteristic
502C2×C11#242711yescharacteristic
503C2×C11#242811yescharacteristic
504C2×C11#244511yescharacteristic
505C2×C11#244511yescharacteristic
506C2×C11#244711yescharacteristic
507C2×C11#244811yescharacteristic
508C2×C11#249011yescharacteristic
509C2×C11#249111yescharacteristic
510C2×C11#251211yescharacteristic
511C2×C11#251311yescharacteristic
512C2×C11#264411yescharacteristic
513C2×C11#286011yescharacteristic
514D11—84no—
515C24—114no—
516C24—222no—
517C24—222no—
518C24—222no—
519C24—222no—
520C24—222no—
521C24—222no—
522C24—222no—
523C24—222no—
524C24—222no—
525C24—222no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24—222no—
530C24C23×D1111yescharacteristic
531C2×D4—228no—
532C2×D4—228no—
533C2×D4—228no—
534C2×D4—444no—
535C2×D4—444no—
536C2×D4—444no—
537C2×D4—444no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—112no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4#433912yes—
599C22×C4#433912yes—
600C22×C4D4×D1112yes—
601C22×C4D4×D1112yes—
602C22×C4#434112yes—
603C22×C4#434312yes—
604C22×C4#434312yes—
605C22×C4#434312yes—
606C22×C4C2×C22⋊D1114yes—
607C22×C4C2×C22⋊D1112yes—
608C4⋊C4—28no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—444no—
612C22⋊C4—448no—
613C22⋊C4—448no—
614C22⋊C4—448no—
615C22⋊C4—448no—
616C22⋊C4—448no—
617C22⋊C4—448no—
618C42—44no—
619C42—444no—
620C42—444no—
621C11#1513811yescharacteristic, complemented, Sylow
622C23—224no—
623C23—224no—
624C23—224no—
625C23—224no—
626C23—224no—
627C23—224no—
628C23—224no—
629C23—442no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—442no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23—442no—
639C23—442no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23C2×#433911yescharacteristic
658C23C2×#433911yescharacteristic
659C23C2×D4×D1111yescharacteristic
660C23C2×D4×D1111yescharacteristic
661C23C2×#434111yescharacteristic
662C23#6703711yescharacteristic
663C23C2×#434311yescharacteristic
664C23C2×#434311yescharacteristic
665C23C2×#434311yescharacteristic
666C23#6704011yescharacteristic
667C23#41×D1111yescharacteristic
668C23#41×D1111yescharacteristic
669C23#6704211yescharacteristic
670C23#6704211yescharacteristic
671C23C22×C22⋊D1111yescharacteristic
672D4—4416no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4#6694714yes—
737C2×C4#6694714yes—
738C2×C4#6695114yes—
739C2×C4#6695114yes—
740C2×C4#6698214yes—
741C2×C4#6699114yes—
742C2×C4#6700014yes—
743C22—444no—
744C22—444no—
745C22—444no—
746C22—444no—
747C22—444no—
748C22—444no—
749C22—444no—
750C22—882no—
751C22—882no—
752C22—882no—
753C22—882no—
754C22—882no—
755C22—882no—
756C22—882no—
757C22—882no—
758C22C2×#6694711yescharacteristic
759C22C2×#6694711yescharacteristic
760C22C2×#6695111yescharacteristic
761C22C2×#6695111yescharacteristic
762C22#1062307911yescharacteristic
763C22#1062308411yescharacteristic
764C22#1062309011yescharacteristic
765C22#1062309311yescharacteristic
766C22#1062309911yescharacteristic
767C22#1062311111yescharacteristic
768C22#1062311311yescharacteristic
769C22#1062311611yescharacteristic
770C22#1062312711yescharacteristic
771C22#1062314011yescharacteristic
772C22#1062314311yescharacteristic
773C22#1062315011yescharacteristic
774C22#1062315511yescharacteristic
775C22#1062316111yescharacteristic
776C22#1062316211yescharacteristic
777C22#1062317411yescharacteristic
778C22#1062322211yescharacteristic
779C22#1062322611yescharacteristic
780C22#1062322611yescharacteristic
781C22#1062322911yescharacteristic
782C22#1062325611yescharacteristic
783C22#1062325711yescharacteristic
784C22#1062326411yescharacteristic
785C22#1062326511yescharacteristic
786C22C2×#6698211yescharacteristic
787C22C2×#6699111yescharacteristic
788C22D4×C22⋊D1111yescharacteristic
789C22C2×#6700011yescharacteristic
790C22#1062334811yescharacteristic
791C22#1062336011yescharacteristic
792C22#1062336511yescharacteristic
793C4—42no—
794C4—42no—
795C4—44no—
796C4—82no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4—442no—
801C4—882no—
802C4#1062260618yescomplemented
803C2—884no—
804C2C2×#1062260611yescharacteristic
805C2#1307210911yescharacteristic
806C2#1307213111yescharacteristic
807C2#1307218911yescharacteristic
808C2#1307220011yescharacteristic
809C2#1307237511yescharacteristic
810C2#1307238311yescharacteristic
811C2#1307240511yescharacteristic
812C2#1307240811yescharacteristic
813C2#1307297111yescharacteristic
814C2#1307298211yescharacteristic
815C2#1307320511yescharacteristic
816C2#1307321611yescharacteristic
817C2#1307457911yescharacteristic
818C2#1307698411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#389C2
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11#15138
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#10622606C2semidirect
5. #13066864C2semidirect
6. #13066864C2semidirect
7. #13066858C2semidirect
8. #13066845C2semidirect
9. #13066845C2semidirect
10. C4×C11⋊#95C2semidirect
11. C2×C11×#389C2semidirect
105. C11⋊#95D4semidirect
217. C2×#389D11semidirect
427. C4×C11#397semidirect
621. C11#15138semidirect
802. C4#10622606semidirect

Maximal subgroups

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

subgroupindex
C2×#106226062
C2×#106225522
C2×#106226012
#130668642
#130668582
#130668452
C4×C11⋊#952
C2×C11×#3892
#1513811