Finite Group Databasebeta

← #15790701

Subgroups — #15790701

Order 3328.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718634C211yesmaximal, characteristic, complemented
2C2×#11718611C211yesmaximal, characteristic
3C2×#11718603C211yesmaximal, characteristic
4#13113103C211yesmaximal, characteristic, complemented
5#13113091C211yesmaximal, characteristic, complemented
6#13113088C211yesmaximal, characteristic, complemented
7#13113088C211yesmaximal, characteristic, complemented
8#13113079C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113073C211yesmaximal, characteristic
11#13113071C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113061C211yesmaximal, characteristic, complemented
14#13113058C211yesmaximal, characteristic
15C13×#1439C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
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
51#11718634—24no—
52#11718611C418yescomplemented
53#11718603—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—22no—
62C23×Dic13—22no—
63C23×Dic13—41no—
64C23×Dic13—41no—
65C23×Dic13—41no—
66C23×Dic13—41no—
67C23×Dic13C2×C414yes—
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—41no—
85C2×C13×C22⋊C4—41no—
86C2×C13×C22⋊C4—41no—
87C2×C13×C22⋊C4C2×C414yes—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—41no—
91C2×C22⋊Dic13—41no—
92C2×C22⋊Dic13—41no—
93C2×C22⋊Dic13—41no—
94C2×C22⋊Dic13—41no—
95C2×C22⋊Dic13C2×C414yes—
96C2×C22⋊Dic13Q814yes—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13—41no—
100C2×C4⋊Dic13—41no—
101C2×C4⋊Dic13C2×C414yes—
102C2×C4⋊Dic13C2×C414yes—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—41no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×#6101—41no—
109C2×#6101—41no—
110C2×#6101—41no—
111C2×#6101D414yes—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—41no—
115C2×C4×Dic13—41no—
116C2×C4×Dic13—41no—
117C2×C4×Dic13—41no—
118C13×#95—22no—
119C13×#95—41no—
120C13×#95—41no—
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#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071C2×C414yes—
137#88071C2×C414yes—
138#14392—131nomaximal, Sylow
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13C22×C412yes—
152C24×C13C2×Q812yes—
153C24×C13#4112yes—
154C24×C13C2411yescharacteristic
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×C13C22×C412yes—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C2×D412yes—
195C22×C4×C13#4112yes—
196C22×C4×C13#4112yes—
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—28no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—44no—
246C22×Dic13—44no—
247C22×Dic13—44no—
248C22×Dic13—44no—
249C22×Dic13—44no—
250C22×Dic13—44no—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C22×C412yes—
255C22×Dic13C2×D412yes—
256C22×Dic13C2×D412yes—
257C22×Dic13C2×Q812yes—
258C22×Dic13C2×Q812yes—
259C22×Dic13#4112yes—
260C13×C4⋊C4—44no—
261C13×C22⋊C4—28no—
262C13×C22⋊C4—44no—
263C13×C22⋊C4—44no—
264C22⋊Dic13—44no—
265C22⋊Dic13—44no—
266C22⋊Dic13—44no—
267C4⋊Dic13—28no—
268C4⋊Dic13—44no—
269#6101—44no—
270#6101—44no—
271#6101—44no—
272C4×Dic13—44no—
273C4×Dic13—44no—
274C2×#389—131no—
275C2×#385—131no—
276C2×#380—131no—
277#1445—131no—
278#1442—131no—
279#1441—131no—
280#1441—131no—
281#1439—131no—
282#1439D1311yescharacteristic
283#1437—131no—
284#1437—131no—
285#1436—131no—
286#1436—131no—
287#1434—131no—
288C22⋊#95—131no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13C4×Q814yes—
324C23×C13C23×C411yescharacteristic
325C23×C13C22×D411yescharacteristic
326C23×C13C22×Q811yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13H(5,𝔽2)11yescharacteristic
332C23×C13H(5,𝔽2)11yescharacteristic
333C23×C13H(5,𝔽2)11yescharacteristic
334C23×C13H(5,𝔽2)11yescharacteristic
335C23×C13H(5,𝔽2)11yescharacteristic
336C23×C13H(5,𝔽2)11yescharacteristic
337C23×C132−1+411yescharacteristic
338C23×C132−1+411yescharacteristic
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—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
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#11714yes—
381C2×Dic13—22no—
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—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—416no—
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—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13C4×D414yes—
438C24×C4—131no—
439C22×C4⋊C4—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4C2×D1311yescharacteristic
445C22×C22⋊C4—131no—
446C22×C22⋊C4—131no—
447C22×C22⋊C4—131no—
448C22×C22⋊C4C2×D1311yescharacteristic
449C22×C22⋊C4C2×D1311yescharacteristic
450C22×C22⋊C4C2×D1311yescharacteristic
451C22×C42—131no—
452C22×C42—131no—
453#389—264no—
454#385—138no—
455#380—264no—
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×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95C2×D1311yescharacteristic
474C2×#95C2×D1311yescharacteristic
475C2×#95C2×D1311yescharacteristic
476C22×C13—24no—
477C22×C13—24no—
478C22×C13—24no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13C2×#11711yescharacteristic
492C22×C13C2×C4×D411yescharacteristic
493C22×C13C2×C4×Q811yescharacteristic
494C22×C13#51811yescharacteristic
495C22×C13#51811yescharacteristic
496C22×C13#52011yescharacteristic
497C22×C13#52011yescharacteristic
498C22×C13#53411yescharacteristic
499C22×C13#53511yescharacteristic
500C22×C13#53811yescharacteristic
501C22×C13#53811yescharacteristic
502C22×C13#53811yescharacteristic
503C22×C13#53911yescharacteristic
504C22×C13#54011yescharacteristic
505C22×C13#54011yescharacteristic
506C22×C13#54211yescharacteristic
507C22×C13#54211yescharacteristic
508C22×C13#54311yescharacteristic
509C22×C13#54411yescharacteristic
510C22×C13#54611yescharacteristic
511C22×C13#54611yescharacteristic
512C22×C13#54811yescharacteristic
513C22×C13D4×Q811yescharacteristic
514C22×C13#55211yescharacteristic
515C22×C13#55211yescharacteristic
516C22×C13#55311yescharacteristic
517C22×C13#55311yescharacteristic
518C22×C13#55311yescharacteristic
519C22×C13#55411yescharacteristic
520C22×C13#55411yescharacteristic
521C22×C13#55411yescharacteristic
522C22×C13#56011yescharacteristic
523C22×C13#56211yescharacteristic
524C22×C13#56211yescharacteristic
525C22×C13#56311yescharacteristic
526C4×C13—24no—
527C4×C13—42no—
528C4×C13—42no—
529C4×C13—81no—
530C4×C13—81no—
531C4×C13—81no—
532Dic13—24no—
533Dic13—42no—
534Dic13—42no—
535Dic13—42no—
536Dic13—42no—
537Dic13—42no—
538Dic13—42no—
539Dic13—81no—
540C25C22×D1311yescharacteristic
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—134no—
549C23×C4—131no—
550C23×C4—262no—
551C23×C4—262no—
552C23×C4—521no—
553C23×C4—521no—
554C23×C4—521no—
555C23×C4—521no—
556C23×C4C22×D1311yescharacteristic
557C23×C4C22×D1311yescharacteristic
558C23×C4C22×D1311yescharacteristic
559C23×C4C22×D1311yescharacteristic
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—134no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4—262no—
570C2×C4⋊C4—262no—
571C2×C4⋊C4—262no—
572C2×C4⋊C4—521no—
573C2×C4⋊C4—521no—
574C2×C4⋊C4—521no—
575C2×C4⋊C4—521no—
576C2×C4⋊C4—521no—
577C2×C4⋊C4—521no—
578C2×C4⋊C4—521no—
579C2×C4⋊C4—521no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—134no—
589C2×C22⋊C4—134no—
590C2×C22⋊C4—262no—
591C2×C22⋊C4—262no—
592C2×C22⋊C4—521no—
593C2×C22⋊C4—521no—
594C2×C22⋊C4—521no—
595C2×C22⋊C4—521no—
596C2×C22⋊C4—521no—
597C2×C22⋊C4C4×D1314yes—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—521no—
601C2×C42—521no—
602C2×C42—521no—
603C2×C42—521no—
604#95—22no—
605#95—41no—
606#95—41no—
607#95—134no—
608#95—134no—
609#95—262no—
610#95—262no—
611#95—262no—
612#95—262no—
613#95—262no—
614#95—262no—
615#95—521no—
616#95—521no—
617#95—521no—
618#95—521no—
619#95—521no—
620#95—521no—
621#95—521no—
622#95—521no—
623#95—521no—
624C2×C13—44no—
625C2×C13#231911yescharacteristic
626C2×C13#232111yescharacteristic
627C2×C13#232911yescharacteristic
628C2×C13#234511yescharacteristic
629C2×C13#235211yescharacteristic
630C2×C13#236011yescharacteristic
631C2×C13#237611yescharacteristic
632C2×C13#268811yescharacteristic
633C2×C13#269211yescharacteristic
634C2×C13#271111yescharacteristic
635C2×C13#272911yescharacteristic
636C2×C13#276811yescharacteristic
637C2×C13#277011yescharacteristic
638C2×C13#277911yescharacteristic
639C2×C13#278011yescharacteristic
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24C2×C4×D1312yes—
653C24#612912yes—
654C24Q8×D1312yes—
655C24C23×D1311yescharacteristic
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—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—132no—
694C22×C4—132no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—268no—
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—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—524no—
751C22×C4—524no—
752C22×C4—524no—
753C22×C4—524no—
754C22×C4—524no—
755C22×C4—524no—
756C22×C4C2×C4×D1312yes—
757C22×C4C2×C4×D1312yes—
758C22×C4D4×D1312yes—
759C22×C4#612912yes—
760C22×C4#612912yes—
761C4⋊C4—44no—
762C4⋊C4—268no—
763C4⋊C4—524no—
764C4⋊C4—524no—
765C4⋊C4—524no—
766C4⋊C4—524no—
767C22⋊C4—28no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—524no—
771C22⋊C4—524no—
772C22⋊C4—524no—
773C42—524no—
774C42—524no—
775C13#1439211yescharacteristic, complemented, Sylow
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23#8814114yes—
811C23C22×C4×D1311yescharacteristic
812C23C2×D4×D1311yescharacteristic
813C23C2×#612911yescharacteristic
814C23C2×#612911yescharacteristic
815C23C2×#612911yescharacteristic
816C23#8825111yescharacteristic
817C23#8825111yescharacteristic
818C23#8825111yescharacteristic
819C23C2×Q8×D1311yescharacteristic
820C23#41×D1311yescharacteristic
821C23#8825611yescharacteristic
822C23#8825611yescharacteristic
823C23#8825611yescharacteristic
824C23#8825711yescharacteristic
825C23#8825711yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
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—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—134no—
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—262no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—5216no—
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—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4#8813114yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C2×#8813111yescharacteristic
941C22C2×#8814111yescharacteristic
942C22#1171922611yescharacteristic
943C22C4×D4×D1311yescharacteristic
944C22#1171925011yescharacteristic
945C22#1171925111yescharacteristic
946C22#1171925111yescharacteristic
947C22#1171929611yescharacteristic
948C22#1171929611yescharacteristic
949C22#1171929811yescharacteristic
950C22#1171930311yescharacteristic
951C22#1171930611yescharacteristic
952C22#1171930811yescharacteristic
953C22#1171931011yescharacteristic
954C22#1171932311yescharacteristic
955C22#1171932311yescharacteristic
956C22#1171932411yescharacteristic
957C22#1171932511yescharacteristic
958C22#1171932811yescharacteristic
959C22#1171933711yescharacteristic
960C22#1171933911yescharacteristic
961C22#1171934011yescharacteristic
962C22#1171934011yescharacteristic
963C22#1171934111yescharacteristic
964C22#1171935511yescharacteristic
965C22#1171935511yescharacteristic
966C22#1171936211yescharacteristic
967C22#1171937011yescharacteristic
968C22#1171937211yescharacteristic
969C22#1171937911yescharacteristic
970C22#1171938711yescharacteristic
971C22#1171938911yescharacteristic
972C22#1171940911yescharacteristic
973C22#1171941711yescharacteristic
974C22#1171942411yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—81no—
979C4—81no—
980C4—81no—
981C4—264no—
982C4—522no—
983C4—522no—
984C4—522no—
985C4—522no—
986C4—522no—
987C4—522no—
988C4—1041no—
989C2—44no—
990C2#1311747311yescharacteristic
991C2#1311748911yescharacteristic
992C2#1311756711yescharacteristic
993C2#1311771511yescharacteristic
994C2#1311776311yescharacteristic
995C2#1311783611yescharacteristic
996C2#1311798211yescharacteristic
997C2#1312127111yescharacteristic
998C2#1312133111yescharacteristic
999C2#1312158611yescharacteristic
1000C2#1312181111yescharacteristic
1001C2#1312231811yescharacteristic
1002C2#1312234211yescharacteristic
1003C2#1312246211yescharacteristic
1004C2#1312247711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14392
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#11718634C2semidirect
4. #13113103C2semidirect
5. #13113091C2semidirect
6. #13113088C2semidirect
7. #13113088C2semidirect
11. #13113071C2semidirect
12. #13113068C2semidirect
13. #13113061C2semidirect
52. #11718611C4semidirect
775. C13#14392semidirect

Maximal subgroups

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

subgroupindex
C2×#117186342
C2×#117186112
C2×#117186032
#131131032
#131130912
#131130882
#131130792
#131130732
#131130712
#131130682
#131130612
#131130582
C13×#14392
#1439213