Finite Group Databasebeta

← #15791767

Subgroups — #15791767

Order 3328.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13113104C211yesmaximal, characteristic, complemented
2#13113098C211yesmaximal, characteristic, complemented
3#13113093C211yesmaximal, characteristic, complemented
4#13113089C211yesmaximal, characteristic, complemented
5#13113085C211yesmaximal, characteristic
6#13113081C211yesmaximal, characteristic
7#13113073C211yesmaximal, characteristic
8#13113063C211yesmaximal, characteristic, complemented
9#13113063C211yesmaximal, characteristic, complemented
10#13113061C211yesmaximal, characteristic, complemented
11#13113061C211yesmaximal, characteristic, complemented
12#13113058C211yesmaximal, characteristic
13#13113058C211yesmaximal, characteristic
14#13113058C211yesmaximal, characteristic
15C2×C13×#388C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C13×#388C418yescomplemented
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C25×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×Dic13—22no—
60C23×Dic13—22no—
61C23×Dic13—22no—
62C23×Dic13—41no—
63C23×Dic13—41no—
64C23×Dic13—41no—
65C23×Dic13—41no—
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4C2×C414yescomplemented
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—41no—
80C2×C13×C22⋊C4—41no—
81C2×C13×C22⋊C4—41no—
82C2×C13×C22⋊C4—41no—
83C2×C13×C22⋊C4C2×C414yes—
84C2×C13×C22⋊C4C2×C414yes—
85C2×C13×C22⋊C4C2×C414yes—
86C2×C42×C13—41no—
87C2×C42×C13—41no—
88C2×C42×C13C2×C414yescomplemented
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—41no—
95C2×C22⋊Dic13—41no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C4⋊Dic13—41no—
99C2×C4⋊Dic13—41no—
100C2×C4⋊Dic13—41no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—41no—
104C13×#95C2×C414yescomplemented
105C13×#95C2×C414yescomplemented
106#88071—22no—
107#88071—22no—
108#88071—22no—
109#88071—22no—
110#88071—22no—
111#88071—22no—
112#88071—41no—
113#88071—41no—
114#88071—41no—
115#88071—41no—
116#88071—41no—
117#88071—41no—
118#88071—41no—
119#88071—41no—
120#88071—41no—
121#88071—41no—
122#88071—41no—
123#88071—41no—
124#88071—41no—
125#88071—41no—
126#88071—41no—
127#88071—41no—
128#14479—131nomaximal, Sylow
129C24×C13—21no—
130C24×C13—21no—
131C24×C13—21no—
132C24×C13—21no—
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13C22×C412yes—
142C24×C13#4112yes—
143C24×C13#4112yes—
144C24×C13C2411yescharacteristic
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13C22×C412yes—
182C22×C4×C13C22×C412yes—
183C22×C4×C13C22×C412yes—
184C22×C4×C13C22×C412yes—
185C22×C4×C13C22×C412yes—
186C22×C4×C13C22×C412yes—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—44no—
240C22×Dic13—44no—
241C22×Dic13—44no—
242C22×Dic13—44no—
243C22×Dic13—44no—
244C22×Dic13—44no—
245C22×Dic13—44no—
246C22×Dic13#4112yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C22×Dic13#4112yes—
250C13×C4⋊C4—44no—
251C13×C22⋊C4—28no—
252C13×C22⋊C4—44no—
253C13×C22⋊C4—44no—
254C42×C13—44no—
255C22⋊Dic13—44no—
256C22⋊Dic13—44no—
257C22⋊Dic13—44no—
258C4⋊Dic13—44no—
259C4×Dic13—44no—
260C2×#388D1311yescharacteristic
261#1445—131no—
262#1443—131no—
263#1442—131no—
264#1441—131no—
265#1440—131no—
266#1439—131no—
267#1437—131no—
268#1434—131no—
269#1434—131no—
270#1434—131no—
271#1434—131no—
272C22⋊#95—131no—
273C22⋊#95—131no—
274C22⋊#95—131no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—41no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13#11714yes—
310C23×C13C23×C411yescharacteristic
311C23×C13C2×#4111yescharacteristic
312C23×C13C2×#4111yescharacteristic
313C23×C13C2×#4111yescharacteristic
314C23×C13C2×#4111yescharacteristic
315C23×C13C2×#4111yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13H(5,𝔽2)11yescharacteristic
318C23×C13H(5,𝔽2)11yescharacteristic
319C23×C13H(5,𝔽2)11yescharacteristic
320C23×C13H(5,𝔽2)11yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C132−1+411yescharacteristic
324C23×C132−1+411yescharacteristic
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—416no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—41no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C24×C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4C2×D1311yescharacteristic
427C22×C22⋊C4—131no—
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
430C22×C22⋊C4C2×D1311yescharacteristic
431C22×C22⋊C4C2×D1311yescharacteristic
432C22×C22⋊C4C2×D1311yescharacteristic
433C22×C42—131no—
434C22×C42C2×D1311yescharacteristic
435#388Dic1318yescomplemented
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95C2×D1311yescharacteristic
459C2×#95C2×D1311yescharacteristic
460C22×C13—24no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13C2×#11711yescharacteristic
476C22×C13C4×#4111yescharacteristic
477C22×C13C4×#4111yescharacteristic
478C22×C13#51811yescharacteristic
479C22×C13#51811yescharacteristic
480C22×C13#52011yescharacteristic
481C22×C13#52011yescharacteristic
482C22×C13#53811yescharacteristic
483C22×C13#53811yescharacteristic
484C22×C13#53811yescharacteristic
485C22×C13#53811yescharacteristic
486C22×C13#53911yescharacteristic
487C22×C13#53911yescharacteristic
488C22×C13#53911yescharacteristic
489C22×C13#53911yescharacteristic
490C22×C13#54011yescharacteristic
491C22×C13#54111yescharacteristic
492C22×C13#54211yescharacteristic
493C22×C13#54211yescharacteristic
494C22×C13#55111yescharacteristic
495C22×C13#55111yescharacteristic
496C22×C13#55111yescharacteristic
497C22×C13#55111yescharacteristic
498C22×C13#55111yescharacteristic
499C22×C13#55111yescharacteristic
500C22×C13#55211yescharacteristic
501C22×C13#55211yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55511yescharacteristic
505C22×C13#55511yescharacteristic
506C22×C13#56011yescharacteristic
507C22×C13#56011yescharacteristic
508C22×C13#56211yescharacteristic
509C22×C13#56211yescharacteristic
510C4×C13—42no—
511C4×C13—42no—
512C4×C13—42no—
513C4×C13—42no—
514C4×C13—42no—
515C4×C13—42no—
516Dic13—42no—
517Dic13—42no—
518Dic13—42no—
519Dic13—42no—
520Dic13—81no—
521Dic13—81no—
522Dic13—81no—
523Dic13—81no—
524C25C22×D1311yescharacteristic
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4—131no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—262no—
534C23×C4—262no—
535C23×C4—262no—
536C23×C4—521no—
537C23×C4—521no—
538C23×C4—521no—
539C23×C4—521no—
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1311yescharacteristic
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—521no—
549C2×C4⋊C4—521no—
550C2×C4⋊C4—521no—
551C2×C4⋊C4C2×Dic1314yescomplemented
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4—41no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—262no—
559C2×C22⋊C4—262no—
560C2×C22⋊C4—262no—
561C2×C22⋊C4—262no—
562C2×C22⋊C4—262no—
563C2×C22⋊C4—521no—
564C2×C22⋊C4—521no—
565C2×C22⋊C4—521no—
566C2×C22⋊C4—521no—
567C2×C22⋊C4C2×Dic1314yes—
568C2×C22⋊C4C2×Dic1314yes—
569C2×C22⋊C4C2×Dic1314yes—
570C2×C42—41no—
571C2×C42—41no—
572C2×C42—262no—
573C2×C42—262no—
574C2×C42—521no—
575C2×C42C2×Dic1314yescomplemented
576#95—262no—
577#95—262no—
578#95—262no—
579#95—262no—
580#95—262no—
581#95—262no—
582#95—521no—
583#95—521no—
584#95—521no—
585#95—521no—
586#95—521no—
587#95—521no—
588#95—521no—
589#95—521no—
590#95—521no—
591#95—521no—
592#95—521no—
593#95—521no—
594#95—521no—
595#95—521no—
596#95—521no—
597#95—521no—
598#95C2×Dic1314yescomplemented
599#95C2×Dic1314yescomplemented
600C2×C13—44no—
601C2×C13#231811yescharacteristic
602C2×C13#233411yescharacteristic
603C2×C13#233511yescharacteristic
604C2×C13#234311yescharacteristic
605C2×C13#235311yescharacteristic
606C2×C13#237211yescharacteristic
607C2×C13#237711yescharacteristic
608C2×C13#273511yescharacteristic
609C2×C13#273711yescharacteristic
610C2×C13#274311yescharacteristic
611C2×C13#274411yescharacteristic
612C2×C13#274611yescharacteristic
613C2×C13#274711yescharacteristic
614C2×C13#275611yescharacteristic
615C2×C13#278111yescharacteristic
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24#612712yes—
629C24#612712yes—
630C24C22×Dic1312yes—
631C24C23×D1311yescharacteristic
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—132no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—132no—
672C22×C4—261no—
673C22×C4—261no—
674C22×C4—261no—
675C22×C4—261no—
676C22×C4—261no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—261no—
681C22×C4—261no—
682C22×C4—261no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—524no—
725C22×C4—524no—
726C22×C4—524no—
727C22×C4—524no—
728C22×C4—524no—
729C22×C4—524no—
730C22×C4—524no—
731C22×C4C22×Dic1312yes—
732C22×C4C22×Dic1312yes—
733C22×C4C22×Dic1312yes—
734C22×C4C22×Dic1312yes—
735C22×C4C22×Dic1312yes—
736C22×C4C22×Dic1312yes—
737C4⋊C4—44no—
738C4⋊C4—524no—
739C22⋊C4—28no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—524no—
743C22⋊C4—524no—
744C22⋊C4—524no—
745C42—44no—
746C42—524no—
747C13#1447911yescharacteristic, complemented, Sylow
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#8818014yes—
783C23C2×#612711yescharacteristic
784C23C2×#612711yescharacteristic
785C23#8825111yescharacteristic
786C23#8825111yescharacteristic
787C23#8825111yescharacteristic
788C23#8825111yescharacteristic
789C23#41×D1311yescharacteristic
790C23#41×D1311yescharacteristic
791C23#41×D1311yescharacteristic
792C23#41×D1311yescharacteristic
793C23#8825611yescharacteristic
794C23#8825611yescharacteristic
795C23#8825711yescharacteristic
796C23#8825711yescharacteristic
797C23C23×Dic1311yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—262no—
841C2×C4—262no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—262no—
846C2×C4—262no—
847C2×C4—262no—
848C2×C4—262no—
849C2×C4—262no—
850C2×C4—262no—
851C2×C4—262no—
852C2×C4—5216no—
853C2×C4—521no—
854C2×C4—521no—
855C2×C4—521no—
856C2×C4—521no—
857C2×C4—521no—
858C2×C4—521no—
859C2×C4—521no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4—521no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
886C2×C4—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22#1171923211yescharacteristic
913C22#1171923211yescharacteristic
914C22#1171923611yescharacteristic
915C22#1171923611yescharacteristic
916C22#1171924511yescharacteristic
917C22#1171924511yescharacteristic
918C22#1171926111yescharacteristic
919C22#1171926111yescharacteristic
920C22#1171926511yescharacteristic
921C22#1171926511yescharacteristic
922C22#1171926911yescharacteristic
923C22#1171926911yescharacteristic
924C22#1171932511yescharacteristic
925C22#1171932511yescharacteristic
926C22#1171932611yescharacteristic
927C22#1171932611yescharacteristic
928C22#1171936211yescharacteristic
929C22#1171936511yescharacteristic
930C22#1171936711yescharacteristic
931C22#1171936811yescharacteristic
932C22#1171937511yescharacteristic
933C22#1171937511yescharacteristic
934C22#1171938411yescharacteristic
935C22#1171938411yescharacteristic
936C22#1171940611yescharacteristic
937C22#1171940911yescharacteristic
938C22#1171941211yescharacteristic
939C22#1171941511yescharacteristic
940C22C2×#8818011yescharacteristic
941C22#1171950311yescharacteristic
942C22#1171950311yescharacteristic
943C22#41×Dic1311yescharacteristic
944C22#41×Dic1311yescharacteristic
945C22#1171953211yescharacteristic
946C22#1171953211yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—522no—
954C4—522no—
955C4—522no—
956C4—522no—
957C4—1041no—
958C4—1041no—
959C4—1041no—
960C4—1041no—
961C2—44no—
962C2#1311746911yescharacteristic
963C2#1311761511yescharacteristic
964C2#1311763011yescharacteristic
965C2#1311769611yescharacteristic
966C2#1311777611yescharacteristic
967C2#1311794811yescharacteristic
968C2#1311799311yescharacteristic
969C2#1312187211yescharacteristic
970C2#1312188511yescharacteristic
971C2#1312197611yescharacteristic
972C2#1312198811yescharacteristic
973C2#1312202111yescharacteristic
974C2#1312203611yescharacteristic
975C2#1312215311yescharacteristic
976C2#1312249411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#388C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#388D13
hypocenterC13#14479
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #13113104C2semidirect
2. #13113098C2semidirect
3. #13113093C2semidirect
4. #13113089C2semidirect
8. #13113063C2semidirect
9. #13113063C2semidirect
10. #13113061C2semidirect
11. #13113061C2semidirect
27. C13×#388C4semidirect
76. C2×C13×C4⋊C4C2×C4semidirect
88. C2×C42×C13C2×C4semidirect
104. C13×#95C2×C4semidirect
105. C13×#95C2×C4semidirect
435. #388Dic13semidirect
551. C2×C4⋊C4C2×Dic13semidirect
575. C2×C42C2×Dic13semidirect
598. #95C2×Dic13semidirect
599. #95C2×Dic13semidirect
747. C13#14479semidirect

Maximal subgroups

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

subgroupindex
#131131042
#131130982
#131130932
#131130892
#131130852
#131130812
#131130732
#131130632
#131130612
#131130582
C2×C13×#3882
#1447913