Finite Group Databasebeta

← #15799597

Subgroups — #15799597

Order 3328.

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×#11718654C212yesmaximal, complemented
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718649C211yesmaximal, characteristic
5#13113084C212yesmaximal, complemented
6#13113084C212yesmaximal, complemented
7#13113078C212yesmaximal, complemented
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C13×#389—24no—
27C2×C13×#95C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36#11718654—28no—
37#11718649—24no—
38#11718649—24no—
39#11718600—24no—
40C24×D13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C22×D52—22no—
52C22×D52—22no—
53C22×D52—22no—
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52D414yes—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—24no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—24no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—42no—
66C2×C13×C4⋊C4D414yes—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13—22no—
70C2×#6103—24no—
71C2×#6103—24no—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—24no—
77C2×#6103—24no—
78C2×#6103—24no—
79C2×#6103—24no—
80C2×#6103—24no—
81C2×#6103—24no—
82C2×#6103—42no—
83C2×#6103—42no—
84C2×#6103—42no—
85C2×#6103—42no—
86C2×#6103—42no—
87C2×#6103—42no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—22no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13—22no—
94C2×C4×Dic13—22no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C13×#95—24no—
98#88071—22no—
99#88071—24no—
100#88071—24no—
101#88071—22no—
102#88071—22no—
103#88071—42no—
104#88071—42no—
105#88071D414yescomplemented
106#15138—131nomaximal, Sylow
107C24×C13C2411yescharacteristic
108C23×D13—22no—
109C23×D13—22no—
110C23×D13—22no—
111C23×D13—22no—
112C23×D13—22no—
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—22no—
116C23×D13—22no—
117C23×D13—22no—
118C23×D13—22no—
119C23×D13—22no—
120C23×D13—22no—
121C23×D13—22no—
122C23×D13C2×D414yes—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D414yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×C4×C13#4112yes—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13C2×D412yes—
190C22×Dic13C2×D412yes—
191C22×Dic13#4112yes—
192C22×Dic13#4112yes—
193C2×D52—28no—
194C2×D52—28no—
195C2×D52—28no—
196C2×D52—44no—
197C2×D52—44no—
198C2×D52—44no—
199C2×D52—44no—
200C13×C4⋊C4—28no—
201C13×C4⋊C4—48no—
202C13×C4⋊C4—44no—
203C42×C13—44no—
204#6103—48no—
205#6103—48no—
206#6103—48no—
207#6103—48no—
208#6103—48no—
209#6103—48no—
210C4⋊Dic13—44no—
211C4×Dic13—44no—
212C4×Dic13—44no—
213C2×#397—132no—
214C2×#390—131no—
215C2×#390—131no—
216C2×#390—131no—
217C2×#389D1311yescharacteristic, complemented
218#1440—132no—
219#1440—132no—
220#1439—132no—
221C4⋊#95—131no—
222C4⋊#95—131no—
223C4×#95—131no—
224C23×C13C22×D411yescharacteristic
225C23×C13C22×D411yescharacteristic
226C23×C13C22×D411yescharacteristic
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13C2×#4111yescharacteristic
230C23×C13C2×#4111yescharacteristic
231C23×C13C2×#4111yescharacteristic
232C23×C13C2×#4111yescharacteristic
233C23×C13C2×#4111yescharacteristic
234C23×C13C2×#4111yescharacteristic
235C23×C13H(5,𝔽2)11yescharacteristic
236C23×C13H(5,𝔽2)11yescharacteristic
237C23×C13H(5,𝔽2)11yescharacteristic
238C23×C132−1+411yescharacteristic
239C22×D13—24no—
240C22×D13—24no—
241C22×D13—24no—
242C22×D13—24no—
243C22×D13—24no—
244C22×D13—24no—
245C22×D13—24no—
246C22×D13—42no—
247C22×D13—42no—
248C22×D13—42no—
249C22×D13—42no—
250C22×D13—42no—
251C22×D13—42no—
252C22×D13—42no—
253C22×D13—42no—
254C22×D13—42no—
255C22×D13—42no—
256C22×D13—42no—
257C22×D13—42no—
258C22×D13—42no—
259C22×D13—42no—
260C22×D13—42no—
261C22×D13—42no—
262C22×D13—42no—
263C22×D13—42no—
264C22×D13—42no—
265C22×D13—42no—
266C22×D13—42no—
267C22×D13—42no—
268C22×D13—42no—
269C22×D13—42no—
270C22×D13—42no—
271C22×D13—42no—
272C22×D13—42no—
273C22×D13—42no—
274C2×C4×C13—24no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—24no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—24no—
282C2×C4×C13—22no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—42no—
286C2×C4×C13—41no—
287C2×C4×C13—42no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13#12114yes—
303C2×C4×C13#12314yes—
304C2×C4×C13#12314yes—
305C2×C4×C13#12314yes—
306C2×C4×C13#12414yes—
307C2×C4×C13#12614yes—
308C2×C4×C13#12614yes—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344D52—416no—
345C23×D4—131no—
346C22×C4⋊C4—131no—
347C22×C4⋊C4C2×D1311yescharacteristic
348C22×C4⋊C4C2×D1312yes—
349C22×C4⋊C4C2×D1311yescharacteristic
350C22×C22⋊C4—132no—
351C22×C22⋊C4—132no—
352C22×C22⋊C4—132no—
353C22×C22⋊C4—132no—
354C22×C22⋊C4—132no—
355C22×C22⋊C4—132no—
356C22×C42—131no—
357C22×C42—131no—
358C22×C42C2×D1311yescharacteristic
359#397—268no—
360#390—264no—
361#390—264no—
362#390—264no—
363#389—24no—
364C2×#95—131no—
365C2×#95—132no—
366C2×#95—132no—
367C2×#95—131no—
368C2×#95—131no—
369C2×#95—131no—
370C2×#95—132no—
371C2×#95—132no—
372C2×#95C2×D1312yes—
373C22×C13C2×#12111yescharacteristic
374C22×C13C2×#12311yescharacteristic
375C22×C13C2×#12311yescharacteristic
376C22×C13C2×#12311yescharacteristic
377C22×C13C2×#12411yescharacteristic
378C22×C13C2×#12611yescharacteristic
379C22×C13C2×#12611yescharacteristic
380C22×C13#52911yescharacteristic
381C22×C13#52911yescharacteristic
382C22×C13#52911yescharacteristic
383C22×C13#53211yescharacteristic
384C22×C13#53211yescharacteristic
385C22×C13#53211yescharacteristic
386C22×C13#54011yescharacteristic
387C22×C13#54011yescharacteristic
388C22×C13#54011yescharacteristic
389C22×C13#54211yescharacteristic
390C22×C13#54211yescharacteristic
391C22×C13#54211yescharacteristic
392C22×C13D4211yescharacteristic
393C22×C13D4211yescharacteristic
394C22×C13#54611yescharacteristic
395C22×C13#54611yescharacteristic
396C22×C13#54611yescharacteristic
397C22×C13#54711yescharacteristic
398C22×C13#54711yescharacteristic
399C22×C13#54811yescharacteristic
400C22×C13#55011yescharacteristic
401C22×C13#55011yescharacteristic
402C22×C13#55311yescharacteristic
403C22×C13#55311yescharacteristic
404C22×C13#55511yescharacteristic
405C22×C13#55611yescharacteristic
406C22×C13#55911yescharacteristic
407C22×C13#55911yescharacteristic
408C2×D13—44no—
409C2×D13—44no—
410C2×D13—44no—
411C2×D13—44no—
412C2×D13—44no—
413C2×D13—44no—
414C2×D13—44no—
415C2×D13—82no—
416C2×D13—82no—
417C2×D13—82no—
418C2×D13—82no—
419C2×D13—82no—
420C2×D13—82no—
421C2×D13—82no—
422C2×D13—82no—
423C4×C13—42no—
424C4×C13—42no—
425C4×C13—44no—
426C4×C13—82no—
427C4×C13#39718yescomplemented
428Dic13—42no—
429Dic13—42no—
430Dic13—42no—
431Dic13—42no—
432Dic13—82no—
433C25—132no—
434C22×D4—134no—
435C22×D4—262no—
436C22×D4—262no—
437C22×D4—262no—
438C22×D4—262no—
439C22×D4—262no—
440C22×D4—262no—
441C23×C4—131no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4—131no—
445C23×C4—132no—
446C23×C4C22×D1312yes—
447C23×C4C22×D1311yescharacteristic
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1312yes—
450C23×C4C22×D1311yescharacteristic
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—262no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4C22⋊D1314yes—
463C2×C22⋊C4—264no—
464C2×C22⋊C4—264no—
465C2×C22⋊C4—264no—
466C2×C22⋊C4—264no—
467C2×C22⋊C4—264no—
468C2×C22⋊C4—264no—
469C2×C22⋊C4—264no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—264no—
472C2×C22⋊C4—264no—
473C2×C22⋊C4—264no—
474C2×C22⋊C4—264no—
475C2×C22⋊C4—522no—
476C2×C22⋊C4—522no—
477C2×C22⋊C4—522no—
478C2×C22⋊C4—522no—
479C2×C22⋊C4—522no—
480C2×C22⋊C4—522no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—262no—
485C2×C42—262no—
486C2×C42—262no—
487C2×C42—262no—
488C2×C42—262no—
489C2×C42—262no—
490#95—24no—
491#95—134no—
492#95—262no—
493#95—262no—
494#95—264no—
495#95—264no—
496#95—262no—
497#95—522no—
498#95—522no—
499C2×C13C2×#39711yescharacteristic
500C2×C13#242011yescharacteristic
501C2×C13#242211yescharacteristic
502C2×C13#242711yescharacteristic
503C2×C13#242811yescharacteristic
504C2×C13#244511yescharacteristic
505C2×C13#244511yescharacteristic
506C2×C13#244711yescharacteristic
507C2×C13#244811yescharacteristic
508C2×C13#249011yescharacteristic
509C2×C13#249111yescharacteristic
510C2×C13#251211yescharacteristic
511C2×C13#251311yescharacteristic
512C2×C13#264411yescharacteristic
513C2×C13#286011yescharacteristic
514D13—84no—
515C24—134no—
516C24—262no—
517C24—262no—
518C24—262no—
519C24—262no—
520C24—262no—
521C24—262no—
522C24—262no—
523C24—262no—
524C24—262no—
525C24—262no—
526C24—262no—
527C24—262no—
528C24—262no—
529C24—262no—
530C24C23×D1311yescharacteristic
531C2×D4—268no—
532C2×D4—268no—
533C2×D4—268no—
534C2×D4—524no—
535C2×D4—524no—
536C2×D4—524no—
537C2×D4—524no—
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—132no—
564C22×C4—132no—
565C22×C4—132no—
566C22×C4—132no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4#612712yes—
599C22×C4#612712yes—
600C22×C4D4×D1312yes—
601C22×C4D4×D1312yes—
602C22×C4#612912yes—
603C22×C4#613112yes—
604C22×C4#613112yes—
605C22×C4#613112yes—
606C22×C4C2×C22⋊D1314yes—
607C22×C4C2×C22⋊D1312yes—
608C4⋊C4—28no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—524no—
612C22⋊C4—528no—
613C22⋊C4—528no—
614C22⋊C4—528no—
615C22⋊C4—528no—
616C22⋊C4—528no—
617C22⋊C4—528no—
618C42—44no—
619C42—524no—
620C42—524no—
621C13#1513811yescharacteristic, complemented, Sylow
622C23—264no—
623C23—264no—
624C23—264no—
625C23—264no—
626C23—264no—
627C23—264no—
628C23—264no—
629C23—522no—
630C23—522no—
631C23—522no—
632C23—522no—
633C23—522no—
634C23—522no—
635C23—522no—
636C23—522no—
637C23—522no—
638C23—522no—
639C23—522no—
640C23—522no—
641C23—522no—
642C23—522no—
643C23—522no—
644C23—522no—
645C23—522no—
646C23—522no—
647C23—522no—
648C23—522no—
649C23—522no—
650C23—522no—
651C23—522no—
652C23—522no—
653C23—522no—
654C23—522no—
655C23—522no—
656C23—522no—
657C23C2×#612711yescharacteristic
658C23C2×#612711yescharacteristic
659C23C2×D4×D1311yescharacteristic
660C23C2×D4×D1311yescharacteristic
661C23C2×#612911yescharacteristic
662C23#8825111yescharacteristic
663C23C2×#613111yescharacteristic
664C23C2×#613111yescharacteristic
665C23C2×#613111yescharacteristic
666C23#8825411yescharacteristic
667C23#41×D1311yescharacteristic
668C23#41×D1311yescharacteristic
669C23#8825611yescharacteristic
670C23#8825611yescharacteristic
671C23C22×C22⋊D1311yescharacteristic
672D4—5216no—
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—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—521no—
714C2×C4—521no—
715C2×C4—521no—
716C2×C4—521no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—521no—
720C2×C4—521no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—521no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4#8814814yes—
737C2×C4#8814814yes—
738C2×C4#8815214yes—
739C2×C4#8815214yes—
740C2×C4#8818314yes—
741C2×C4#8819214yes—
742C2×C4#8820114yes—
743C22—524no—
744C22—524no—
745C22—524no—
746C22—524no—
747C22—524no—
748C22—524no—
749C22—524no—
750C22—1042no—
751C22—1042no—
752C22—1042no—
753C22—1042no—
754C22—1042no—
755C22—1042no—
756C22—1042no—
757C22—1042no—
758C22C2×#8814811yescharacteristic
759C22C2×#8814811yescharacteristic
760C22C2×#8815211yescharacteristic
761C22C2×#8815211yescharacteristic
762C22#1171925311yescharacteristic
763C22#1171925811yescharacteristic
764C22#1171926411yescharacteristic
765C22#1171926711yescharacteristic
766C22#1171927311yescharacteristic
767C22#1171928511yescharacteristic
768C22#1171928711yescharacteristic
769C22#1171929011yescharacteristic
770C22#1171930111yescharacteristic
771C22#1171931411yescharacteristic
772C22#1171931711yescharacteristic
773C22#1171932411yescharacteristic
774C22#1171932911yescharacteristic
775C22#1171933511yescharacteristic
776C22#1171933611yescharacteristic
777C22#1171934811yescharacteristic
778C22#1171939611yescharacteristic
779C22#1171940011yescharacteristic
780C22#1171940011yescharacteristic
781C22#1171940311yescharacteristic
782C22#1171943011yescharacteristic
783C22#1171943111yescharacteristic
784C22#1171943811yescharacteristic
785C22#1171943911yescharacteristic
786C22C2×#8818311yescharacteristic
787C22C2×#8819211yescharacteristic
788C22D4×C22⋊D1311yescharacteristic
789C22C2×#8820111yescharacteristic
790C22#1171952211yescharacteristic
791C22#1171953411yescharacteristic
792C22#1171953911yescharacteristic
793C4—44no—
794C4—42no—
795C4—42no—
796C4—82no—
797C4—522no—
798C4—522no—
799C4—522no—
800C4—522no—
801C4—1042no—
802C4#1171865418yescomplemented
803C2—1044no—
804C2C2×#1171865411yescharacteristic
805C2#1311832911yescharacteristic
806C2#1311835111yescharacteristic
807C2#1311840911yescharacteristic
808C2#1311842011yescharacteristic
809C2#1311859511yescharacteristic
810C2#1311860311yescharacteristic
811C2#1311862511yescharacteristic
812C2#1311862811yescharacteristic
813C2#1311919111yescharacteristic
814C2#1311920211yescharacteristic
815C2#1311942511yescharacteristic
816C2#1311943611yescharacteristic
817C2#1312079911yescharacteristic
818C2#1312320411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#389C2
prime radicalC23×D52C22
hypercenterC2×#389D13
hypocenterC13#15138
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#11718654C2semidirect
5. #13113084C2semidirect
6. #13113084C2semidirect
7. #13113078C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. C4×#88071C2semidirect
11. C2×C13×#389C2semidirect
105. #88071D4semidirect
217. C2×#389D13semidirect
427. C4×C13#397semidirect
621. C13#15138semidirect
802. C4#11718654semidirect

Maximal subgroups

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

subgroupindex
C2×#117186542
C2×#117186002
C2×#117186492
#131130842
#131130782
#131130652
C4×#880712
C2×C13×#3892
#1513813