Finite Group Databasebeta

← #15799598

Subgroups — #15799598

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×#11718335C212yesmaximal, complemented
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718649C211yesmaximal, characteristic
5C2×#11718646C211yesmaximal, characteristic, complemented
6#13113084C212yesmaximal, complemented
7#13113084C212yesmaximal, complemented
8#13113082C212yesmaximal, complemented
9#13113065C211yesmaximal, characteristic, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35#11718649—24no—
36#11718649—24no—
37#11718646—24no—
38#11718600—24no—
39#11718335—28no—
40C24×D13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
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—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4D414yes—
64C2×C42×C13—22no—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×#6103—24no—
68C2×#6103—24no—
69C2×#6103—24no—
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—42no—
80C2×#6103—42no—
81C2×#6103—42no—
82C2×#6103—42no—
83C2×#6103—42no—
84C2×#6103—42no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—24no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—24no—
90C2×C4⋊Dic13—42no—
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—
98C13×#95—42no—
99#88071—24no—
100#88071—22no—
101#88071—24no—
102#88071—22no—
103#88071—22no—
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—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—21no—
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×D414yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D412yes—
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—44no—
202C42×C13—44no—
203#6103—48no—
204#6103—48no—
205#6103—48no—
206#6103—48no—
207#6103—48no—
208#6103—48no—
209C4⋊Dic13—48no—
210C4⋊Dic13—44no—
211C4×Dic13—44no—
212C4×Dic13—44no—
213C2×#397—132no—
214C2×#390—131no—
215C2×#390—131no—
216C2×#390—131no—
217C2×#389—131no—
218#1440—132no—
219#1440—132no—
220#1439—132no—
221C4⋊#95—131no—
222C4⋊#95D1311yescharacteristic, complemented
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—24no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—24no—
281C2×C4×C13—22no—
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—42no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
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⋊C4—132no—
348C22×C4⋊C4C2×D1311yescharacteristic
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—264no—
364C2×#95—131no—
365C2×#95—132no—
366C2×#95—131no—
367C2×#95—131no—
368C2×#95—131no—
369C2×#95—132no—
370C2×#95—132no—
371C2×#95C2×D1312yes—
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×D1312yes—
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C23×C4C22×D1311yescharacteristic
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—264no—
457C2×C4⋊C4—264no—
458C2×C4⋊C4—262no—
459C2×C4⋊C4—262no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—522no—
462C2×C4⋊C4D5214yes—
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—42no—
492#95—134no—
493#95—262no—
494#95—262no—
495#95—264no—
496#95—264no—
497#95—262no—
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—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
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×C4C2×D5214yes—
599C22×C4C2×D5212yes—
600C22×C4#612712yes—
601C22×C4#612712yes—
602C22×C4D4×D1312yes—
603C22×C4D4×D1312yes—
604C22×C4#612912yes—
605C22×C4#612912yes—
606C22×C4#613112yes—
607C22×C4#613112yes—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—528no—
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—
657C23C22×D5211yescharacteristic
658C23C2×#612711yescharacteristic
659C23C2×#612711yescharacteristic
660C23C2×D4×D1311yescharacteristic
661C23C2×D4×D1311yescharacteristic
662C23C2×#612911yescharacteristic
663C23C2×#612911yescharacteristic
664C23#8825111yescharacteristic
665C23C2×#613111yescharacteristic
666C23C2×#613111yescharacteristic
667C23#8825411yescharacteristic
668C23#41×D1311yescharacteristic
669C23#41×D1311yescharacteristic
670C23#8825611yescharacteristic
671C23#8825611yescharacteristic
672D4—5216no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
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#8812914yes—
737C2×C4#8813714yes—
738C2×C4#8813714yes—
739C2×C4#8814014yes—
740C2×C4#8814914yes—
741C2×C4#8815214yes—
742C2×C4#8815214yes—
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×#8812911yescharacteristic
759C22C2×#8813711yescharacteristic
760C22C2×#8813711yescharacteristic
761C22C2×#8814011yescharacteristic
762C22C2×#8814911yescharacteristic
763C22#1171921211yescharacteristic
764C22C2×#8815211yescharacteristic
765C22C2×#8815211yescharacteristic
766C22#1171921911yescharacteristic
767C22#1171923511yescharacteristic
768C22#1171923711yescharacteristic
769C22#1171925311yescharacteristic
770C22D4×D5211yescharacteristic
771C22#1171925911yescharacteristic
772C22#1171926711yescharacteristic
773C22#1171928111yescharacteristic
774C22#1171928211yescharacteristic
775C22#1171928511yescharacteristic
776C22#1171928711yescharacteristic
777C22#1171930111yescharacteristic
778C22#1171931411yescharacteristic
779C22#1171931711yescharacteristic
780C22#1171932411yescharacteristic
781C22#1171932911yescharacteristic
782C22#1171933511yescharacteristic
783C22#1171933611yescharacteristic
784C22#1171934811yescharacteristic
785C22#1171938611yescharacteristic
786C22#1171938611yescharacteristic
787C22#1171939611yescharacteristic
788C22#1171940311yescharacteristic
789C22#1171942311yescharacteristic
790C22#1171943011yescharacteristic
791C22#1171943711yescharacteristic
792C22#1171943811yescharacteristic
793C4—42no—
794C4—44no—
795C4—42no—
796C4—82no—
797C4—522no—
798C4—522no—
799C4—522no—
800C4—522no—
801C4—1042no—
802C4#1171833518yescomplemented
803C2—1044no—
804C2C2×#1171833511yescharacteristic
805C2#1311833011yescharacteristic
806C2#1311835211yescharacteristic
807C2#1311841111yescharacteristic
808C2#1311842211yescharacteristic
809C2#1311859911yescharacteristic
810C2#1311860211yescharacteristic
811C2#1311862411yescharacteristic
812C2#1311863211yescharacteristic
813C2#1311918211yescharacteristic
814C2#1311919311yescharacteristic
815C2#1311941811yescharacteristic
816C2#1311942911yescharacteristic
817C2#1312079911yescharacteristic
818C2#1312320411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC13×C4⋊#95C2
prime radicalC23×D52C22
hypercenterC4⋊#95D13
hypocenterC13#15138
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#11718335C2semidirect
5. C2×#11718646C2semidirect
6. #13113084C2semidirect
7. #13113084C2semidirect
8. #13113082C2semidirect
9. #13113065C2semidirect
10. C4×#88071C2semidirect
11. C13×C4⋊#95C2semidirect
105. #88071D4semidirect
222. C4⋊#95D13semidirect
427. C4×C13#397semidirect
621. C13#15138semidirect
802. C4#11718335semidirect

Maximal subgroups

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

subgroupindex
C2×#117183352
C2×#117186002
C2×#117186492
C2×#117186462
#131130842
#131130822
#131130652
C4×#880712
C13×C4⋊#952
#1513813