Finite Group Databasebeta

← #15790729

Subgroups — #15790729

Order 3328.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718331C211yesmaximal, characteristic
2C2×#11718329C211yesmaximal, characteristic
3C2×#11718638C211yesmaximal, characteristic, complemented
4#13113105C211yesmaximal, characteristic, complemented
5#13113097C211yesmaximal, characteristic, complemented
6#13113088C211yesmaximal, characteristic, complemented
7#13113084C211yesmaximal, characteristic
8#13113078C211yesmaximal, characteristic
9#13113072C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113067C211yesmaximal, characteristic, complemented
12#13113060C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic
14#13113057C211yesmaximal, characteristic
15C13×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
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
51#11718638—24no—
52#11718331C418yescomplemented
53#11718329—24no—
54C24×D13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C22×C4×D13—22no—
70C22×C4×D13—22no—
71C22×C4×D13—22no—
72C22×C4×D13—41no—
73C22×C4×D13—41no—
74C22×C4×D13—41no—
75C22×C4×D13—41no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4—41no—
79C2×#6103—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
83C2×#6103—22no—
84C2×#6103—22no—
85C2×#6103—22no—
86C2×#6103—22no—
87C2×#6103—22no—
88C2×#6103—41no—
89C2×#6103—41no—
90C2×#6103—41no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103C2×C414yes—
95C2×#6103C2×C414yes—
96C2×#6103C2×C414yes—
97C2×C4⋊Dic13—41no—
98C2×C4⋊Dic13—41no—
99C2×C4⋊Dic13—41no—
100C2×C4⋊Dic13—41no—
101C2×C4⋊Dic13C2×C414yescomplemented
102C2×C4⋊Dic13D414yes—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—41no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—41no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13C2×C414yescomplemented
112C13×#95—22no—
113C13×#95—41no—
114C13×#95—41no—
115C13×#95—41no—
116C13×#95—41no—
117C13×#95C2×C414yescomplemented
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071—41no—
133#88071C2×C414yescomplemented
134#14393—131nomaximal, Sylow
135C24×C13C2411yescharacteristic
136C23×D13—21no—
137C23×D13—21no—
138C23×D13—21no—
139C23×D13—21no—
140C23×D13—21no—
141C23×D13—21no—
142C23×D13—21no—
143C23×D13—21no—
144C23×D13—21no—
145C23×D13—21no—
146C23×D13—21no—
147C23×D13—21no—
148C23×D13C22×C412yes—
149C23×D13#4112yes—
150C23×D13#4112yes—
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×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C22×C412yes—
197C22×C4×C13C2×D412yes—
198C22×C4×C13#4112yes—
199C22×C4×C13#4112yes—
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—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13C22×C412yes—
244C22×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13C2×D412yes—
247C22×Dic13C2×D412yes—
248C22×Dic13#4112yes—
249C2×C4×D13—44no—
250C2×C4×D13—44no—
251C2×C4×D13—44no—
252C2×C4×D13—44no—
253C2×C4×D13—44no—
254C2×C4×D13—44no—
255C2×C4×D13—44no—
256C13×C4⋊C4—44no—
257#6103—28no—
258#6103—28no—
259#6103—44no—
260#6103—44no—
261#6103—44no—
262#6103—44no—
263C4⋊Dic13—44no—
264C4⋊Dic13—44no—
265#6101—44no—
266C4×Dic13—28no—
267C4×Dic13—44no—
268C2×#388—131no—
269C2×#385—131no—
270C2×#382—131no—
271#1445—131no—
272#1443—131no—
273#1442D1311yescharacteristic, complemented
274#1441—131no—
275#1440—131no—
276#1439—131no—
277#1437—131no—
278#1436—131no—
279#1436—131no—
280#1434—131no—
281C22⋊#95—131no—
282C22⋊#95—131no—
283C23×C13C23×C411yescharacteristic
284C23×C13C22×D411yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13C2×#4111yescharacteristic
287C23×C13C2×#4111yescharacteristic
288C23×C13C2×#4111yescharacteristic
289C23×C13C2×#4111yescharacteristic
290C23×C13H(5,𝔽2)11yescharacteristic
291C23×C13H(5,𝔽2)11yescharacteristic
292C23×C13H(5,𝔽2)11yescharacteristic
293C23×C13H(5,𝔽2)11yescharacteristic
294C23×C13H(5,𝔽2)11yescharacteristic
295C23×C132−1+411yescharacteristic
296C23×C132−1+411yescharacteristic
297C23×C132−1+411yescharacteristic
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13—22no—
303C22×D13—22no—
304C22×D13—22no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—41no—
317C22×D13—41no—
318C22×D13—41no—
319C22×D13—41no—
320C22×D13—41no—
321C22×D13—41no—
322C22×D13—41no—
323C22×D13—41no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
329C22×D13—41no—
330C22×D13—41no—
331C22×D13—41no—
332C22×D13#11714yes—
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—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
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×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13C4×D414yes—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
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—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C4×D13—416no—
432C24×C4—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4—131no—
436C22×C4⋊C4C2×D1311yescharacteristic
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4—131no—
441C22×C22⋊C4—131no—
442C22×C22⋊C4—131no—
443C22×C42—131no—
444C22×C42—131no—
445#388—138no—
446#385—264no—
447#382—264no—
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×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95C2×D1311yescharacteristic
465C2×#95C2×D1311yescharacteristic
466C2×#95C2×D1311yescharacteristic
467C2×#95C2×D1311yescharacteristic
468C2×#95C2×D1311yescharacteristic
469C2×#95C2×D1311yescharacteristic
470C22×C13C2×#11711yescharacteristic
471C22×C13C2×C4×D411yescharacteristic
472C22×C13C4×#4111yescharacteristic
473C22×C13#51811yescharacteristic
474C22×C13#52011yescharacteristic
475C22×C13#52011yescharacteristic
476C22×C13#52011yescharacteristic
477C22×C13#53411yescharacteristic
478C22×C13#53611yescharacteristic
479C22×C13#53811yescharacteristic
480C22×C13#53811yescharacteristic
481C22×C13#53811yescharacteristic
482C22×C13#53911yescharacteristic
483C22×C13#53911yescharacteristic
484C22×C13#53911yescharacteristic
485C22×C13#53911yescharacteristic
486C22×C13#53911yescharacteristic
487C22×C13#54111yescharacteristic
488C22×C13#54211yescharacteristic
489C22×C13#54611yescharacteristic
490C22×C13#54611yescharacteristic
491C22×C13#54811yescharacteristic
492C22×C13#55011yescharacteristic
493C22×C13#55111yescharacteristic
494C22×C13#55111yescharacteristic
495C22×C13#55211yescharacteristic
496C22×C13#55211yescharacteristic
497C22×C13#55211yescharacteristic
498C22×C13#55311yescharacteristic
499C22×C13#55311yescharacteristic
500C22×C13#55511yescharacteristic
501C22×C13H(3,𝔽4)11yescharacteristic
502C22×C13#56211yescharacteristic
503C22×C13#56211yescharacteristic
504C22×C13#56311yescharacteristic
505C2×D13—24no—
506C2×D13—24no—
507C2×D13—24no—
508C2×D13—42no—
509C2×D13—42no—
510C2×D13—42no—
511C2×D13—42no—
512C2×D13—42no—
513C2×D13—42no—
514C2×D13—42no—
515C2×D13—42no—
516C2×D13—42no—
517C2×D13—42no—
518C2×D13—42no—
519C2×D13—42no—
520C4×C13—24no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—81no—
525C4×C13—81no—
526C4×C13—81no—
527Dic13—42no—
528Dic13—42no—
529Dic13—42no—
530Dic13—42no—
531Dic13—42no—
532Dic13—42no—
533Dic13—81no—
534C25—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—262no—
543C23×C4—262no—
544C23×C4—262no—
545C23×C4—521no—
546C23×C4—521no—
547C23×C4—521no—
548C23×C4—521no—
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C2×C4⋊C4—22no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—134no—
560C2×C4⋊C4—134no—
561C2×C4⋊C4—262no—
562C2×C4⋊C4—262no—
563C2×C4⋊C4—521no—
564C2×C4⋊C4—521no—
565C2×C4⋊C4—521no—
566C2×C4⋊C4—521no—
567C2×C4⋊C4—521no—
568C2×C22⋊C4—134no—
569C2×C22⋊C4—134no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—262no—
572C2×C22⋊C4—262no—
573C2×C22⋊C4—262no—
574C2×C22⋊C4—262no—
575C2×C22⋊C4—262no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—262no—
580C2×C22⋊C4—521no—
581C2×C22⋊C4—521no—
582C2×C22⋊C4—521no—
583C2×C22⋊C4—521no—
584C2×C22⋊C4—521no—
585C2×C22⋊C4—521no—
586C2×C42—134no—
587C2×C42—262no—
588C2×C42—262no—
589C2×C42—521no—
590C2×C42—521no—
591C2×C42—521no—
592#95—22no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—134no—
598#95—262no—
599#95—262no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—262no—
604#95—262no—
605#95—262no—
606#95—262no—
607#95—521no—
608#95—521no—
609#95—521no—
610#95—521no—
611#95—521no—
612#95—521no—
613#95C4×D1314yescomplemented
614C2×C13#231811yescharacteristic
615C2×C13#232211yescharacteristic
616C2×C13#233411yescharacteristic
617C2×C13#234311yescharacteristic
618C2×C13#235211yescharacteristic
619C2×C13#236311yescharacteristic
620C2×C13#237911yescharacteristic
621C2×C13#268411yescharacteristic
622C2×C13#269011yescharacteristic
623C2×C13#269411yescharacteristic
624C2×C13#273011yescharacteristic
625C2×C13#274411yescharacteristic
626C2×C13#276511yescharacteristic
627C2×C13#278111yescharacteristic
628C2×C13#278211yescharacteristic
629D13—44no—
630C24—132no—
631C24—132no—
632C24—132no—
633C24—261no—
634C24—261no—
635C24—261no—
636C24—261no—
637C24—261no—
638C24—261no—
639C24—261no—
640C24—261no—
641C24—261no—
642C24—261no—
643C24—261no—
644C24—261no—
645C24C23×D1311yescharacteristic
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—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—132no—
693C22×C4—132no—
694C22×C4—132no—
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—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—524no—
739C22×C4—524no—
740C22×C4—524no—
741C22×C4—524no—
742C22×C4—524no—
743C22×C4—524no—
744C22×C4—524no—
745C22×C4C2×C4×D1312yes—
746C22×C4C2×C4×D1312yes—
747C22×C4C2×C4×D1312yes—
748C22×C4D4×D1312yes—
749C22×C4#613112yes—
750C22×C4#613112yes—
751C4⋊C4—44no—
752C4⋊C4—524no—
753C4⋊C4—524no—
754C4⋊C4—524no—
755C22⋊C4—268no—
756C22⋊C4—268no—
757C22⋊C4—524no—
758C22⋊C4—524no—
759C22⋊C4—524no—
760C22⋊C4—524no—
761C42—268no—
762C42—524no—
763C13#1439311yescharacteristic, complemented, Sylow
764C23—134no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—262no—
775C23—262no—
776C23—262no—
777C23—262no—
778C23—262no—
779C23—262no—
780C23—262no—
781C23—262no—
782C23—262no—
783C23—521no—
784C23—521no—
785C23—521no—
786C23—521no—
787C23—521no—
788C23—521no—
789C23—521no—
790C23—521no—
791C23—521no—
792C23—521no—
793C23—521no—
794C23—521no—
795C23—521no—
796C23—521no—
797C23—521no—
798C23—521no—
799C23C22×C4×D1311yescharacteristic
800C23C2×D4×D1311yescharacteristic
801C23#8825111yescharacteristic
802C23#8825111yescharacteristic
803C23#8825111yescharacteristic
804C23C2×#613111yescharacteristic
805C23C2×#613111yescharacteristic
806C23#41×D1311yescharacteristic
807C23#41×D1311yescharacteristic
808C23#41×D1311yescharacteristic
809C23#8825611yescharacteristic
810C23#8825611yescharacteristic
811C23#8825711yescharacteristic
812C23#8825711yescharacteristic
813C23#8825711yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
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—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—5216no—
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—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4#8814714yes—
913C22—264no—
914C22—264no—
915C22—264no—
916C22—522no—
917C22—522no—
918C22—522no—
919C22—522no—
920C22—522no—
921C22—522no—
922C22—522no—
923C22—522no—
924C22—522no—
925C22—522no—
926C22—522no—
927C22—522no—
928C22C2×#8814711yescharacteristic
929C22D13×#11711yescharacteristic
930C22#1171922811yescharacteristic
931C22#1171925011yescharacteristic
932C22#1171925111yescharacteristic
933C22#1171925111yescharacteristic
934C22C4×#613111yescharacteristic
935C22#1171929411yescharacteristic
936C22#1171930411yescharacteristic
937C22#1171931811yescharacteristic
938C22#1171932611yescharacteristic
939C22#1171933511yescharacteristic
940C22#1171934211yescharacteristic
941C22#1171934911yescharacteristic
942C22#1171935011yescharacteristic
943C22#1171935011yescharacteristic
944C22#1171935311yescharacteristic
945C22#1171936411yescharacteristic
946C22#1171936511yescharacteristic
947C22#1171936711yescharacteristic
948C22#1171937211yescharacteristic
949C22#1171938111yescharacteristic
950C22#1171938211yescharacteristic
951C22#1171938311yescharacteristic
952C22#1171938811yescharacteristic
953C22#1171939911yescharacteristic
954C22#1171939911yescharacteristic
955C22#1171940011yescharacteristic
956C22#1171940011yescharacteristic
957C22#1171940211yescharacteristic
958C22#1171941211yescharacteristic
959C22#1171941211yescharacteristic
960C22#1171941311yescharacteristic
961C22#1171941711yescharacteristic
962C22#1171943911yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—81no—
968C4—81no—
969C4—81no—
970C4—522no—
971C4—522no—
972C4—522no—
973C4—522no—
974C4—522no—
975C4—522no—
976C4—1041no—
977C2—524no—
978C2#1311746611yescharacteristic
979C2#1311750411yescharacteristic
980C2#1311761411yescharacteristic
981C2#1311769511yescharacteristic
982C2#1311776211yescharacteristic
983C2#1311787311yescharacteristic
984C2#1311800511yescharacteristic
985C2#1312121911yescharacteristic
986C2#1312130911yescharacteristic
987C2#1312136111yescharacteristic
988C2#1312183911yescharacteristic
989C2#1312198911yescharacteristic
990C2#1312227611yescharacteristic
991C2#1312250511yescharacteristic
992C2#1312251511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1442C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1442D13
hypocenterC13#14393
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
3. C2×#11718638C2semidirect
4. #13113105C2semidirect
5. #13113097C2semidirect
6. #13113088C2semidirect
10. #13113070C2semidirect
11. #13113067C2semidirect
12. #13113060C2semidirect
15. C13×#1442C2semidirect
52. #11718331C4semidirect
101. C2×C4⋊Dic13C2×C4semidirect
111. C2×C4×Dic13C2×C4semidirect
117. C13×#95C2×C4semidirect
133. #88071C2×C4semidirect
273. #1442D13semidirect
613. #95C4×D13semidirect
763. C13#14393semidirect

Maximal subgroups

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

subgroupindex
C2×#117183312
C2×#117183292
C2×#117186382
#131131052
#131130972
#131130882
#131130842
#131130782
#131130722
#131130702
#131130672
#131130602
#131130572
C13×#14422
#1439313