Finite Group Databasebeta

← #15799536

Subgroups — #15799536

Order 3328.

1626 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718335C212yesmaximal
2C2×#11718646C211yesmaximal, characteristic, complemented
3C2×#11718648C211yesmaximal, characteristic
4C2×#11718648C211yesmaximal, characteristic
5C2×C4×#6103C211yesmaximal, characteristic
6#13113096C212yesmaximal, complemented
7#13113093C212yesmaximal, complemented
8#13113084C212yesmaximal
9#13113066C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35#11718648—24no—
36#11718648—24no—
37#11718646—24no—
38C4×#6103—24no—
39#11718335—28no—
40C24×D13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C22×C4×D13—22no—
52C22×C4×D13—22no—
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13D414yes—
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—22no—
68C2×#6103—22no—
69C2×#6103—22no—
70C2×#6103—22no—
71C2×#6103—22no—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—24no—
77C2×#6103—42no—
78C2×#6103D414yes—
79C2×C4⋊Dic13—24no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—24no—
87C2×C4⋊Dic13—42no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—22no—
91C13×#95—24no—
92C13×#95—24no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—22no—
98#88071—22no—
99#88071—24no—
100#88071—24no—
101#88071—42no—
102#15132—131nomaximal, Sylow
103C24×C13C2411yescharacteristic
104C23×D13—21no—
105C23×D13—21no—
106C23×D13—21no—
107C23×D13—21no—
108C23×D13—21no—
109C23×D13—21no—
110C23×D13—21no—
111C23×D13—21no—
112C23×D13—21no—
113C23×D13—21no—
114C23×D13—21no—
115C23×D13—21no—
116C23×D13C2×D412yes—
117C23×D13C2×D412yes—
118C23×D13#4112yes—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13C2×D414yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13#4112yes—
149C22×C4×C13#4112yes—
150C22×C4×C13#4112yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
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—22no—
173C22×Dic13—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13C2×D412yes—
187C22×Dic13C2×D412yes—
188C22×Dic13#4112yes—
189C2×C4×D13—28no—
190C2×C4×D13—28no—
191C2×C4×D13—28no—
192C2×C4×D13—44no—
193C2×C4×D13—44no—
194C2×C4×D13—44no—
195C2×C4×D13—44no—
196C13×C4⋊C4—28no—
197C13×C4⋊C4—44no—
198C42×C13—44no—
199#6103—28no—
200#6103—28no—
201#6103—48no—
202#6103—48no—
203C4⋊Dic13—48no—
204C4⋊Dic13—44no—
205C4⋊Dic13—44no—
206C4×Dic13—44no—
207C2×#397—132no—
208C2×#389—131no—
209C2×#380—131no—
210C2×#380—131no—
211C2×C4×C22⋊C4—131no—
212#1443—132no—
213#1442—132no—
214#1440—132no—
215C4⋊#95—131no—
216C4⋊#95—131no—
217C4⋊#95D1311yescharacteristic, complemented
218C23×C13C22×D411yescharacteristic
219C23×C13C22×D411yescharacteristic
220C23×C13C22×D411yescharacteristic
221C23×C13C2×#4111yescharacteristic
222C23×C13C2×#4111yescharacteristic
223C23×C13C2×#4111yescharacteristic
224C23×C13C2×#4111yescharacteristic
225C23×C13C2×#4111yescharacteristic
226C23×C13C2×#4111yescharacteristic
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13H(5,𝔽2)11yescharacteristic
230C23×C132−1+411yescharacteristic
231C23×C132−1+411yescharacteristic
232C23×C132−1+411yescharacteristic
233C22×D13—22no—
234C22×D13—22no—
235C22×D13—22no—
236C22×D13—22no—
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—22no—
240C22×D13—22no—
241C22×D13—22no—
242C22×D13—22no—
243C22×D13—22no—
244C22×D13—22no—
245C22×D13—22no—
246C22×D13—22no—
247C22×D13—22no—
248C22×D13—22no—
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—41no—
252C22×D13—41no—
253C22×D13—41no—
254C22×D13—41no—
255C22×D13—41no—
256C22×D13—41no—
257C22×D13—41no—
258C22×D13—41no—
259C22×D13—41no—
260C22×D13—41no—
261C22×D13—41no—
262C22×D13—41no—
263C22×D13—41no—
264C22×D13—41no—
265C22×D13—41no—
266C22×D13—41no—
267C22×D13#12114yes—
268C2×C4×C13—22no—
269C2×C4×C13—24no—
270C2×C4×C13—22no—
271C2×C4×C13—24no—
272C2×C4×C13—24no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—42no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—42no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13#12114yes—
297C2×C4×C13#12314yes—
298C2×C4×C13#12314yes—
299C2×C4×C13#12314yes—
300C2×C4×C13#12414yes—
301C2×C4×C13#12614yes—
302C2×C4×C13#12614yes—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—42no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C4×D13—416no—
339C24×C4—131no—
340C22×C4⋊C4—131no—
341C22×C4⋊C4—131no—
342C22×C4⋊C4—132no—
343C22×C4⋊C4C2×D1311yescharacteristic
344C22×C4⋊C4C2×D1311yescharacteristic
345C22×C22⋊C4—131no—
346C22×C22⋊C4—132no—
347C22×C22⋊C4—131no—
348C22×C22⋊C4—132no—
349C22×C42—131no—
350C22×C42C2×D1311yescharacteristic
351#397—268no—
352#389—264no—
353#380—264no—
354#380—264no—
355C4×C22⋊C4—264no—
356C2×#95—132no—
357C2×#95—132no—
358C2×#95—132no—
359C2×#95—132no—
360C2×#95—131no—
361C2×#95—132no—
362C2×#95—132no—
363C2×#95—131no—
364C2×#95—132no—
365C2×#95C2×D1312yes—
366C2×#95C2×D1312yes—
367C22×C13C2×#12111yescharacteristic
368C22×C13C2×#12111yescharacteristic
369C22×C13C2×#12311yescharacteristic
370C22×C13C2×#12311yescharacteristic
371C22×C13C2×#12311yescharacteristic
372C22×C13#52511yescharacteristic
373C22×C13C2×#12411yescharacteristic
374C22×C13C2×#12611yescharacteristic
375C22×C13C2×#12611yescharacteristic
376C22×C13#52911yescharacteristic
377C22×C13#52911yescharacteristic
378C22×C13#53211yescharacteristic
379C22×C13#53211yescharacteristic
380C22×C13#53611yescharacteristic
381C22×C13#53711yescharacteristic
382C22×C13#54111yescharacteristic
383C22×C13#54111yescharacteristic
384C22×C13#54211yescharacteristic
385C22×C13#54211yescharacteristic
386C22×C13D4211yescharacteristic
387C22×C13#54711yescharacteristic
388C22×C13#54711yescharacteristic
389C22×C13#54711yescharacteristic
390C22×C13#54711yescharacteristic
391C22×C13#54811yescharacteristic
392C22×C13#54811yescharacteristic
393C22×C13#55211yescharacteristic
394C22×C13#55211yescharacteristic
395C22×C13#55211yescharacteristic
396C22×C13#55211yescharacteristic
397C22×C13#55311yescharacteristic
398C22×C13#55311yescharacteristic
399C22×C13#55511yescharacteristic
400C22×C13#55611yescharacteristic
401C22×C13#55611yescharacteristic
402C2×D13—24no—
403C2×D13—24no—
404C2×D13—24no—
405C2×D13—42no—
406C2×D13—42no—
407C2×D13—42no—
408C2×D13—42no—
409C2×D13—42no—
410C2×D13—42no—
411C2×D13—42no—
412C2×D13—42no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—42no—
417C4×C13—44no—
418C4×C13—42no—
419C4×C13—42no—
420C4×C13—82no—
421C4×C13#39718yescomplemented
422Dic13—42no—
423Dic13—42no—
424Dic13—42no—
425Dic13—82no—
426Dic13—82no—
427C25—131no—
428C23×C4—131no—
429C23×C4—131no—
430C23×C4—131no—
431C23×C4—134no—
432C23×C4—132no—
433C23×C4—132no—
434C23×C4—262no—
435C23×C4—262no—
436C23×C4—262no—
437C23×C4—262no—
438C23×C4—262no—
439C23×C4—262no—
440C23×C4C22×D1312yes—
441C23×C4C22×D1312yes—
442C23×C4C22×D1311yescharacteristic
443C23×C4C22×D1311yescharacteristic
444C23×C4C22×D1311yescharacteristic
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—264no—
451C2×C4⋊C4—262no—
452C2×C4⋊C4—264no—
453C2×C4⋊C4—262no—
454C2×C4⋊C4—262no—
455C2×C4⋊C4—262no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—262no—
458C2×C4⋊C4—522no—
459C2×C4⋊C4D5214yes—
460C2×C22⋊C4—134no—
461C2×C22⋊C4—262no—
462C2×C22⋊C4—262no—
463C2×C22⋊C4—262no—
464C2×C22⋊C4—262no—
465C2×C22⋊C4—262no—
466C2×C22⋊C4—264no—
467C2×C22⋊C4—264no—
468C2×C22⋊C4—264no—
469C2×C22⋊C4—264no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—522no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—262no—
476C2×C42—262no—
477C2×C42—262no—
478#95—24no—
479#95—24no—
480#95—264no—
481#95—262no—
482#95—262no—
483#95—264no—
484#95—264no—
485#95—264no—
486#95—264no—
487#95—264no—
488#95—522no—
489C2×C13C2×#39711yescharacteristic
490C2×C13#241511yescharacteristic
491C2×C13#241611yescharacteristic
492C2×C13#242111yescharacteristic
493C2×C13#242211yescharacteristic
494C2×C13#248511yescharacteristic
495C2×C13#248611yescharacteristic
496C2×C13#248911yescharacteristic
497C2×C13#249111yescharacteristic
498C2×C13#249411yescharacteristic
499C2×C13#249511yescharacteristic
500C2×C13#249611yescharacteristic
501C2×C13#249611yescharacteristic
502C2×C13#262511yescharacteristic
503C2×C13#285411yescharacteristic
504D13—44no—
505C24—132no—
506C24—132no—
507C24—132no—
508C24—261no—
509C24—261no—
510C24—261no—
511C24—261no—
512C24—261no—
513C24—261no—
514C24—261no—
515C24—261no—
516C24—261no—
517C24—261no—
518C24—261no—
519C24—261no—
520C24C23×D1311yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—132no—
547C22×C4—132no—
548C22×C4—132no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—268no—
568C22×C4—268no—
569C22×C4—268no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—524no—
585C22×C4—524no—
586C22×C4—524no—
587C22×C4—524no—
588C22×C4C2×D5214yes—
589C22×C4C2×D5212yes—
590C22×C4#612712yes—
591C22×C4#612712yes—
592C22×C4D4×D1312yes—
593C22×C4D4×D1312yes—
594C22×C4#612912yes—
595C22×C4#612912yes—
596C22×C4#612912yes—
597C22×C4#613112yes—
598C4⋊C4—28no—
599C4⋊C4—44no—
600C4⋊C4—528no—
601C4⋊C4—524no—
602C4⋊C4—524no—
603C22⋊C4—268no—
604C22⋊C4—268no—
605C22⋊C4—528no—
606C22⋊C4—528no—
607C42—44no—
608C42—524no—
609C13#1513211yescharacteristic, complemented, Sylow
610C23—134no—
611C23—262no—
612C23—262no—
613C23—262no—
614C23—262no—
615C23—262no—
616C23—262no—
617C23—262no—
618C23—262no—
619C23—262no—
620C23—262no—
621C23—262no—
622C23—262no—
623C23—262no—
624C23—262no—
625C23—262no—
626C23—262no—
627C23—262no—
628C23—262no—
629C23—521no—
630C23—521no—
631C23—521no—
632C23—521no—
633C23—521no—
634C23—521no—
635C23—521no—
636C23—521no—
637C23—521no—
638C23—521no—
639C23—521no—
640C23—521no—
641C23—521no—
642C23—521no—
643C23—521no—
644C23—521no—
645C23C22×D5211yescharacteristic
646C23C2×#612711yescharacteristic
647C23C2×#612711yescharacteristic
648C23C2×D4×D1311yescharacteristic
649C23C2×D4×D1311yescharacteristic
650C23C2×#612911yescharacteristic
651C23C2×#612911yescharacteristic
652C23C2×#612911yescharacteristic
653C23C2×#613111yescharacteristic
654C23#8825411yescharacteristic
655C23#8825411yescharacteristic
656C23#41×D1311yescharacteristic
657C23#41×D1311yescharacteristic
658C23#8825611yescharacteristic
659C23#8825711yescharacteristic
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—521no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4—521no—
701C2×C4—521no—
702C2×C4—521no—
703C2×C4—521no—
704C2×C4—521no—
705C2×C4—521no—
706C2×C4—521no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—5216no—
710C2×C4—522no—
711C2×C4—522no—
712C2×C4—522no—
713C2×C4—522no—
714C2×C4—522no—
715C2×C4—522no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—522no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4#8812914yes—
725C2×C4#8813714yes—
726C2×C4#8813714yes—
727C2×C4#8814014yes—
728C2×C4#8814914yes—
729C2×C4#8815214yes—
730C2×C4#8815214yes—
731C22—264no—
732C22—264no—
733C22—264no—
734C22—522no—
735C22—522no—
736C22—522no—
737C22—522no—
738C22—522no—
739C22—522no—
740C22—522no—
741C22—522no—
742C22—522no—
743C22—522no—
744C22—522no—
745C22—522no—
746C22C2×#8812911yescharacteristic
747C22C2×#8813711yescharacteristic
748C22C2×#8813711yescharacteristic
749C22C2×#8814011yescharacteristic
750C22C2×#8814911yescharacteristic
751C22#1171921211yescharacteristic
752C22C2×#8815211yescharacteristic
753C22C2×#8815211yescharacteristic
754C22#1171921811yescharacteristic
755C22#1171923411yescharacteristic
756C22#1171923711yescharacteristic
757C22#1171925311yescharacteristic
758C22D4×D5211yescharacteristic
759C22#1171926011yescharacteristic
760C22#1171926211yescharacteristic
761C22#1171928111yescharacteristic
762C22#1171928111yescharacteristic
763C22#1171928711yescharacteristic
764C22#1171928811yescharacteristic
765C22D13×#12111yescharacteristic
766C22#1171931111yescharacteristic
767C22#1171931611yescharacteristic
768C22#1171932311yescharacteristic
769C22#1171933311yescharacteristic
770C22#1171933411yescharacteristic
771C22#1171934411yescharacteristic
772C22#1171934611yescharacteristic
773C22#1171938511yescharacteristic
774C22#1171938711yescharacteristic
775C22#1171939911yescharacteristic
776C22#1171940011yescharacteristic
777C22#1171942111yescharacteristic
778C22#1171943111yescharacteristic
779C22#1171943611yescharacteristic
780C22#1171943711yescharacteristic
781C4—44no—
782C4—42no—
783C4—42no—
784C4—82no—
785C4—522no—
786C4—522no—
787C4—522no—
788C4—1042no—
789C4—1042no—
790C4#1171833518yescomplemented
791C2—524no—
792C2C2×#1171833511yescharacteristic
793C2#1311826311yescharacteristic
794C2#1311827411yescharacteristic
795C2#1311833711yescharacteristic
796C2#1311834811yescharacteristic
797C2#1311912911yescharacteristic
798C2#1311914011yescharacteristic
799C2#1311917111yescharacteristic
800C2#1311919311yescharacteristic
801C2#1311923711yescharacteristic
802C2#1311925011yescharacteristic
803C2#1311925911yescharacteristic
804C2#1311926111yescharacteristic
805C2#1312063611yescharacteristic
806C2#1312316611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC13×C4⋊#95C2
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#15132
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718646C2semidirect
6. #13113096C2semidirect
7. #13113093C2semidirect
9. #13113066C2semidirect
10. #13113065C2semidirect
11. C13×C4⋊#95C2semidirect
217. C4⋊#95D13semidirect
421. C4×C13#397semidirect
609. C13#15132semidirect
790. 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×#117186462
C2×#117186482
C2×C4×#61032
#131130962
#131130932
#131130842
#131130662
#131130652
C13×C4⋊#952
#1513213