Finite Group Databasebeta

← #15784964

Subgroups — #15784964

Order 3328.

2330 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C212yesmaximal, complemented
2C2×#11718872C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
4#13113081C212yesmaximal, complemented
5#13113077C212yesmaximal
6#13113068C212yesmaximal, complemented
7#13113066C211yesmaximal, characteristic, complemented
8#13113063C211yesmaximal, characteristic, complemented
9#13113059C211yesmaximal, characteristic, complemented
10#13113059C211yesmaximal, characteristic, complemented
11C22×C4×D4×C13C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C2×C4×D4×C13—28no—
16C2×C4×D4×C13C418yescomplemented
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C22⋊Dic13C2212yes—
22C22×C22⋊Dic13C2212yes—
23C22×C22⋊Dic13C2212yes—
24C22×C22⋊Dic13C2212yes—
25C22×C4⋊Dic13C2212yes—
26C22×C4×Dic13C2212yes—
27#11718872—24no—
28C4×C22⋊Dic13—24no—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2211yescharacteristic
39#11718612—28no—
40C25×C13C2311yescharacteristic
41C25×C13C2311yescharacteristic
42C22×D4×C13—24no—
43C22×D4×C13—24no—
44C22×D4×C13—22no—
45C22×D4×C13—22no—
46C22×D4×C13C2×C414yes—
47C23×C4×C13—24no—
48C23×C4×C13—24no—
49C23×C4×C13—22no—
50C23×C4×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13—22no—
53C23×C4×C13—42no—
54C23×C4×C13—42no—
55C23×C4×C13C2×C414yes—
56C23×C4×C13C2×C414yes—
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13C2312yes—
63C23×Dic13C2312yes—
64C23×Dic13C2312yes—
65C23×Dic13C2312yes—
66C4×D4×C13—232no—
67C2×C13×C4⋊C4—24no—
68C2×C13×C4⋊C4C2×C414yes—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4C2×C414yes—
71C2×C13×C22⋊C4C2×C414yes—
72C2×C13×C22⋊C4D418yes—
73C2×C42×C13—24no—
74C2×C42×C13C2×C414yes—
75C2×C22⋊Dic13—24no—
76C2×C22⋊Dic13—24no—
77C2×C22⋊Dic13—24no—
78C2×C22⋊Dic13—24no—
79C2×C22⋊Dic13—24no—
80C2×C22⋊Dic13—24no—
81C2×C22⋊Dic13—24no—
82C2×C22⋊Dic13—24no—
83C2×C22⋊Dic13—42no—
84C2×C22⋊Dic13—42no—
85C2×C22⋊Dic13—42no—
86C2×C22⋊Dic13—42no—
87C2×C4⋊Dic13—24no—
88C2×C4⋊Dic13—24no—
89C2×C4⋊Dic13—42no—
90C2×C4×Dic13—24no—
91C2×C4×Dic13—24no—
92C2×C4×Dic13—42no—
93#88071—24no—
94#88071—24no—
95#88071—22no—
96#88071—22no—
97#88071—24no—
98#88071—24no—
99#88071—22no—
100#88071—24no—
101#88071—42no—
102#88071D414yescomplemented
103#13886—131nomaximal, Sylow
104C24×C13—21no—
105C24×C13—21no—
106C24×C13—22no—
107C24×C13—22no—
108C24×C13—22no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—22no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—21no—
117C24×C13—21no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—21no—
121C24×C13—21no—
122C24×C13C22×C412yes—
123C24×C13C22×C412yes—
124C24×C13C2×D414yes—
125C24×C13#4114yes—
126C24×C13C2411yescharacteristic
127C2×D4×C13—216no—
128C2×D4×C13—216no—
129C2×D4×C13—28no—
130C2×D4×C13—28no—
131C2×D4×C13—28no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—28no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—28no—
148C22×C4×C13—28no—
149C22×C4×C13—28no—
150C22×C4×C13—44no—
151C22×C4×C13—44no—
152C22×C4×C13—48no—
153C22×C4×C13—48no—
154C22×C4×C13—48no—
155C22×C4×C13—48no—
156C22×C4×C13C22×C412yes—
157C22×C4×C13C22×C412yes—
158C22×C4×C13C22×C412yes—
159C22×C4×C13C22×C412yes—
160C22×C4×C13C22×C412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D414yes—
163C22×C4×C13C2×D414yes—
164C22×C4×C13#4112yes—
165C22×C4×C13#4112yes—
166C22×C4×C13#4112yes—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
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×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13C2×D414yes—
194C22×Dic13#4114yes—
195C13×C4⋊C4—28no—
196C13×C22⋊C4—28no—
197C13×C22⋊C4C22⋊C4116yescomplemented
198C42×C13—28no—
199C22⋊Dic13—216no—
200C22⋊Dic13—48no—
201C22⋊Dic13—48no—
202C22⋊Dic13—48no—
203C4⋊Dic13—48no—
204C4×Dic13—48no—
205C22×C4×D4D1311yescharacteristic
206C2×#388—132no—
207C2×#381—131no—
208C2×C4×C22⋊C4—131no—
209#1439—132no—
210#1438—132no—
211#1436—132no—
212C4⋊#95—131no—
213#1434—131no—
214C22⋊#95—131no—
215C22⋊#95—131no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—24no—
229C23×C13—24no—
230C23×C13—24no—
231C23×C13—24no—
232C23×C13—24no—
233C23×C13—24no—
234C23×C13—24no—
235C23×C13—24no—
236C23×C13—24no—
237C23×C13—24no—
238C23×C13—24no—
239C23×C13—24no—
240C23×C13—42no—
241C23×C13—42no—
242C23×C13—42no—
243C23×C13—42no—
244C23×C13—42no—
245C23×C13—42no—
246C23×C13—42no—
247C23×C13—42no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—42no—
253C23×C13—42no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13—41no—
258C23×C13—42no—
259C23×C13—42no—
260C23×C13C2×C22⋊C414yes—
261C23×C13#11714yes—
262C23×C13C23×C411yescharacteristic
263C23×C13C22×D412yes—
264C23×C13C22×D411yescharacteristic
265C23×C13C2×#4112yes—
266C23×C13C2×#4111yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13C2×#4111yescharacteristic
269C23×C13C2×#4112yes—
270C23×C13H(5,𝔽2)12yes—
271C23×C13H(5,𝔽2)11yescharacteristic
272C23×C132−1+411yescharacteristic
273D4×C13—232no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—24no—
283C2×C4×C13—24no—
284C2×C4×C13—24no—
285C2×C4×C13—24no—
286C2×C4×C13—24no—
287C2×C4×C13—24no—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—416no—
294C2×C4×C13—416no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13C2×C22⋊C414yes—
298C2×C4×C13C2×C22⋊C414yes—
299C2×C4×C13#11714yes—
300C2×C4×C13C4×D414yes—
301C2×Dic13—24no—
302C2×Dic13—24no—
303C2×Dic13—24no—
304C2×Dic13—24no—
305C2×Dic13—24no—
306C2×Dic13—24no—
307C2×Dic13—42no—
308C2×Dic13—42no—
309C2×Dic13—42no—
310C2×Dic13—42no—
311C2×Dic13—42no—
312C2×Dic13—42no—
313C2×Dic13—42no—
314C2×Dic13—42no—
315C2×Dic13—42no—
316C2×Dic13—42no—
317C2×Dic13—42no—
318C2×Dic13—42no—
319C2×Dic13—42no—
320C2×Dic13—42no—
321C2×Dic13—42no—
322C2×Dic13—42no—
323C2×Dic13—42no—
324C2×Dic13—42no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C23×D4C2×D1311yescharacteristic
330C24×C4C2×D1311yescharacteristic
331C24×C4C2×D1311yescharacteristic
332C2×C4×D4—28no—
333C2×C4×D4Dic1318yescomplemented
334C22×C4⋊C4—132no—
335C22×C4⋊C4C2×D1311yescharacteristic
336C22×C22⋊C4—132no—
337C22×C22⋊C4—132no—
338C22×C22⋊C4—132no—
339C22×C22⋊C4—132no—
340C22×C22⋊C4C2×D1311yescharacteristic
341C22×C22⋊C4C2×D1311yescharacteristic
342C22×C42—132no—
343C22×C42C2×D1311yescharacteristic
344#388—268no—
345#381—264no—
346C4×C22⋊C4—264no—
347C2×#95—131no—
348C2×#95—131no—
349C2×#95—131no—
350C2×#95—131no—
351C2×#95—132no—
352C2×#95—132no—
353C2×#95—132no—
354C2×#95—132no—
355C2×#95—132no—
356C2×#95—132no—
357C22×C13—24no—
358C22×C13—24no—
359C22×C13—24no—
360C22×C13—24no—
361C22×C13—24no—
362C22×C13—24no—
363C22×C13—42no—
364C22×C13—42no—
365C22×C13—42no—
366C22×C13—42no—
367C22×C13—42no—
368C22×C13—42no—
369C22×C13—42no—
370C22×C13—44no—
371C22×C13—44no—
372C22×C13—44no—
373C22×C13—44no—
374C22×C13—44no—
375C22×C13—44no—
376C22×C13—44no—
377C22×C13—44no—
378C22×C13—42no—
379C22×C13C22×C22⋊C411yescharacteristic
380C22×C13C2×#11711yescharacteristic
381C22×C13C2×#11711yescharacteristic
382C22×C13C2×C4×D411yescharacteristic
383C22×C13C4×#4111yescharacteristic
384C22×C13#51811yescharacteristic
385C22×C13#52011yescharacteristic
386C22×C13#52512yes—
387C22×C13#52512yes—
388C22×C13#52512yes—
389C22×C13#52912yes—
390C22×C13#53812yes—
391C22×C13#53912yes—
392C22×C13D4212yes—
393C22×C13#54612yes—
394C22×C13#54612yes—
395C22×C13#54711yescharacteristic
396C22×C13#54712yes—
397C22×C13#55011yescharacteristic
398C22×C13#55312yes—
399C22×C13#55511yescharacteristic
400C22×C13#55611yescharacteristic
401C22×C13#55912yes—
402C4×C13—24no—
403C4×C13—24no—
404C4×C13—24no—
405C4×C13—24no—
406C4×C13—42no—
407Dic13—44no—
408Dic13—44no—
409Dic13—82no—
410Dic13—82no—
411C25C22×D1311yescharacteristic
412C25C22×D1311yescharacteristic
413C22×D4—24no—
414C22×D4—24no—
415C22×D4—22no—
416C22×D4—22no—
417C22×D4C2×Dic1314yes—
418C23×C4—24no—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—24no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—132no—
427C23×C4—132no—
428C23×C4—132no—
429C23×C4—132no—
430C23×C4C2×Dic1314yes—
431C23×C4C2×Dic1314yes—
432C23×C4C22×D1311yescharacteristic
433C23×C4C22×D1311yescharacteristic
434C23×C4C22×D1311yescharacteristic
435C23×C4C22×D1311yescharacteristic
436C23×C4C22×D1311yescharacteristic
437C4×D4—232no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—264no—
440C2×C4⋊C4—264no—
441C2×C4⋊C4—522no—
442C2×C4⋊C4C2×Dic1314yes—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—264no—
445C2×C22⋊C4—264no—
446C2×C22⋊C4—264no—
447C2×C22⋊C4—264no—
448C2×C22⋊C4—264no—
449C2×C22⋊C4—264no—
450C2×C22⋊C4—264no—
451C2×C22⋊C4—264no—
452C2×C22⋊C4—522no—
453C2×C22⋊C4—522no—
454C2×C22⋊C4—522no—
455C2×C22⋊C4—522no—
456C2×C22⋊C4C2×Dic1314yes—
457C2×C22⋊C4C2×Dic1314yes—
458C2×C22⋊C4C22⋊D1318yes—
459C2×C42—24no—
460C2×C42—264no—
461C2×C42—264no—
462C2×C42—522no—
463C2×C42C2×Dic1314yes—
464#95—134no—
465#95—264no—
466#95—264no—
467#95—264no—
468#95—262no—
469#95—262no—
470#95—262no—
471#95—264no—
472#95—264no—
473#95—522no—
474C2×C13—44no—
475C2×C13—44no—
476C2×C13#228011yescharacteristic
477C2×C13#229011yescharacteristic
478C2×C13#231811yescharacteristic
479C2×C13D4×C22⋊C411yescharacteristic
480C2×C13#233911yescharacteristic
481C2×C13#235411yescharacteristic
482C2×C13#235711yescharacteristic
483C2×C13#245512yes—
484C2×C13#245612yes—
485C2×C13#245912yes—
486C2×C13#246612yes—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—22no—
505C24#612714yes—
506C24C22×Dic1312yes—
507C24C22×Dic1312yes—
508C24C2×C22⋊D1314yes—
509C24C23×D1311yescharacteristic
510C2×D4—216no—
511C2×D4—216no—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—28no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—28no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—134no—
540C22×C4—134no—
541C22×C4—262no—
542C22×C4—262no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—262no—
546C22×C4—262no—
547C22×C4—262no—
548C22×C4—262no—
549C22×C4—262no—
550C22×C4—262no—
551C22×C4—262no—
552C22×C4—262no—
553C22×C4—262no—
554C22×C4—262no—
555C22×C4—262no—
556C22×C4—262no—
557C22×C4—262no—
558C22×C4—262no—
559C22×C4—262no—
560C22×C4—262no—
561C22×C4—262no—
562C22×C4—262no—
563C22×C4—262no—
564C22×C4—262no—
565C22×C4—262no—
566C22×C4—262no—
567C22×C4#612712yes—
568C22×C4#612712yes—
569C22×C4D4×D1312yes—
570C22×C4#612912yes—
571C22×C4C22×Dic1312yes—
572C22×C4C22×Dic1312yes—
573C22×C4C22×Dic1312yes—
574C22×C4C22×Dic1312yes—
575C22×C4C22×Dic1312yes—
576C22×C4C2×C22⋊D1314yes—
577C22×C4C2×C22⋊D1314yes—
578C4⋊C4—28no—
579C4⋊C4—528no—
580C22⋊C4—28no—
581C22⋊C4—2616no—
582C22⋊C4—528no—
583C22⋊C4—528no—
584C22⋊C4—528no—
585C22⋊C4C22⋊Dic13116yescomplemented
586C42—28no—
587C42—528no—
588C13#1388611yescharacteristic, complemented, Sylow
589C23—22no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—41no—
629C23—41no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23#8818014yes—
634C23C2×C22⋊Dic1314yes—
635C23C2×#612712yes—
636C23C2×#612711yescharacteristic
637C23C2×#612711yescharacteristic
638C23C2×D4×D1311yescharacteristic
639C23C2×#612911yescharacteristic
640C23#8825112yes—
641C23#41×D1312yes—
642C23#8825611yescharacteristic
643C23#8825711yescharacteristic
644C23C23×Dic1311yescharacteristic
645C23C22×C22⋊D1312yes—
646D4—232no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—416no—
667C2×C4—416no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—264no—
671C2×C4—264no—
672C2×C4—264no—
673C2×C4—264no—
674C2×C4—264no—
675C2×C4—264no—
676C2×C4—522no—
677C2×C4—522no—
678C2×C4—522no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4—522no—
682C2×C4—522no—
683C2×C4—522no—
684C2×C4—522no—
685C2×C4—522no—
686C2×C4—522no—
687C2×C4—522no—
688C2×C4—522no—
689C2×C4—522no—
690C2×C4—522no—
691C2×C4—522no—
692C2×C4—522no—
693C2×C4—522no—
694C2×C4—522no—
695C2×C4—522no—
696C2×C4—522no—
697C2×C4—522no—
698C2×C4#8818014yes—
699C2×C4D4×Dic1314yes—
700C2×C4C2×C22⋊Dic1314yes—
701C2×C4C2×C22⋊Dic1314yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—44no—
709C22—44no—
710C22—42no—
711C22—44no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—44no—
719C22—44no—
720C22—42no—
721C22—42no—
722C22—44no—
723C22—44no—
724C22#1171924312yes—
725C22#1171924711yescharacteristic
726C22#1171925212yes—
727C22#1171925611yescharacteristic
728C22#1171925811yescharacteristic
729C22#1171926312yes—
730C22#1171926412yes—
731C22#1171926512yes—
732C22#1171926811yescharacteristic
733C22#1171926912yes—
734C22C2×#8818011yescharacteristic
735C22C2×#8818011yescharacteristic
736C22#1171949612yes—
737C22#1171949612yes—
738C22C2×D4×Dic1311yescharacteristic
739C22#1171950311yescharacteristic
740C22D4×C22⋊D1312yes—
741C22#1171951112yes—
742C22#1171952912yes—
743C22#41×Dic1311yescharacteristic
744C22#1171953211yescharacteristic
745C22#1171953412yes—
746C22C22×C22⋊Dic1311yescharacteristic
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—524no—
753C4—524no—
754C4—1042no—
755C4—1042no—
756C2—44no—
757C2—44no—
758C2#1311721911yescharacteristic
759C2#1311728111yescharacteristic
760C2#1311746911yescharacteristic
761C2D4×C22⋊Dic1311yescharacteristic
762C2#1311766611yescharacteristic
763C2#1311778511yescharacteristic
764C2#1311780911yescharacteristic
765C2#1311871312yes—
766C2#1311872812yes—
767C2#1311876712yes—
768C2#1311886612yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C4×D4×C13C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×C4×D4D13
hypocenterC13#13886
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11718612C2semidirect
2. C2×#11718872C2semidirect
3. C2×C4×C22⋊Dic13C2semidirect
4. #13113081C2semidirect
6. #13113068C2semidirect
7. #13113066C2semidirect
8. #13113063C2semidirect
9. #13113059C2semidirect
10. #13113059C2semidirect
16. C2×C4×D4×C13C4semidirect
102. #88071D4semidirect
197. C13×C22⋊C4C22⋊C4semidirect
333. C2×C4×D4Dic13semidirect
585. C22⋊C4C22⋊Dic13semidirect
588. C13#13886semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117188722
C2×C4×C22⋊Dic132
#131130812
#131130772
#131130682
#131130662
#131130632
#131130592
C22×C4×D4×C132
#1388613