Finite Group Databasebeta

← #15790348

Subgroups — #15790348

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×#11718612C211yesmaximal, characteristic
2C2×#11718873C211yesmaximal, characteristic
3#13113101C211yesmaximal, characteristic, complemented
4#13113098C211yesmaximal, characteristic, complemented
5#13113098C211yesmaximal, characteristic, complemented
6#13113093C211yesmaximal, characteristic, complemented
7#13113085C211yesmaximal, characteristic
8#13113081C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113070C211yesmaximal, characteristic, complemented
12#13113070C211yesmaximal, characteristic, complemented
13#13113070C211yesmaximal, characteristic, complemented
14#13113059C211yesmaximal, characteristic
15C2×C13×#381C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic13C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C13×#381C418yescomplemented
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34#11718873—24no—
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
52C2×#88071C2211yescharacteristic
53#11718612—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—41no—
60C23×C4×C13—41no—
61C23×C4×C13C2×C414yes—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—41no—
79C2×C13×C22⋊C4—41no—
80C2×C13×C22⋊C4C2×C414yes—
81C2×C13×C22⋊C4C2×C414yes—
82C2×C22⋊Dic13—22no—
83C2×C22⋊Dic13—22no—
84C2×C22⋊Dic13—22no—
85C2×C22⋊Dic13—22no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—41no—
88C2×C22⋊Dic13—41no—
89C2×C22⋊Dic13—41no—
90C2×C22⋊Dic13—41no—
91C2×C22⋊Dic13—41no—
92C2×C22⋊Dic13—41no—
93C2×C22⋊Dic13D414yes—
94C2×C4⋊Dic13—22no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—22no—
101C2×C4⋊Dic13—41no—
102C2×C4⋊Dic13—41no—
103C2×C4⋊Dic13—41no—
104C2×C4⋊Dic13—41no—
105C2×C4⋊Dic13—41no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—41no—
108C2×C4×Dic13—41no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13—41no—
112C13×#95C2×C414yes—
113C13×#95C2×C414yes—
114C13×#95C2×C414yes—
115C13×#95C2×C414yes—
116#88071—22no—
117#88071—22no—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—41no—
125#88071—41no—
126#88071—41no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071—41no—
133#88071—41no—
134#14368—131nomaximal, Sylow
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
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×C13C22×C412yes—
148C24×C13C2×D412yes—
149C24×C13#4112yes—
150C24×C13C2411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—28no—
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—28no—
187C22×C4×C13—44no—
188C22×C4×C13—44no—
189C22×C4×C13—44no—
190C22×C4×C13—44no—
191C22×C4×C13—44no—
192C22×C4×C13C22×C412yes—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C22×C412yes—
197C22×C4×C13C22×C412yes—
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×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13C2×D412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13#4112yes—
255C22×Dic13#4112yes—
256C13×C22⋊C4—28no—
257C13×C22⋊C4—44no—
258C22⋊Dic13—44no—
259C22⋊Dic13—44no—
260C22⋊Dic13—44no—
261C22⋊Dic13—44no—
262C4⋊Dic13—44no—
263C4⋊Dic13—44no—
264C4⋊Dic13—44no—
265C4⋊Dic13—44no—
266C4×Dic13—44no—
267C4×Dic13—44no—
268C2×#388—131no—
269C2×#381D1311yescharacteristic
270C2×#380—131no—
271#1444—131no—
272#1443—131no—
273#1443—131no—
274#1442—131no—
275#1440—131no—
276#1439—131no—
277#1437—131no—
278#1436—131no—
279#1436—131no—
280#1436—131no—
281#1436—131no—
282C22⋊#95—131no—
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—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
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—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13C4×D414yes—
318C23×C13C23×C411yescharacteristic
319C23×C13C22×D411yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13C2×#4111yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C23×C13H(5,𝔽2)11yescharacteristic
327C23×C13H(5,𝔽2)11yescharacteristic
328C23×C13H(5,𝔽2)11yescharacteristic
329C23×C13H(5,𝔽2)11yescharacteristic
330C23×C132−1+411yescharacteristic
331C23×C132−1+411yescharacteristic
332C23×C132−1+411yescharacteristic
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—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—416no—
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#11714yes—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
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—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C24×C4C2×D1311yescharacteristic
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4—131no—
436C22×C4⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4—131no—
441C22×C22⋊C4C2×D1311yescharacteristic
442C22×C22⋊C4C2×D1311yescharacteristic
443C22×C42—131no—
444C22×C42—131no—
445#388—264no—
446#381Dic1318yescomplemented
447#380—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×#95—131no—
465C2×#95—131no—
466C2×#95C2×D1311yescharacteristic
467C2×#95C2×D1311yescharacteristic
468C2×#95C2×D1311yescharacteristic
469C2×#95C2×D1311yescharacteristic
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—24no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13C2×#11711yescharacteristic
486C22×C13C2×C4×D411yescharacteristic
487C22×C13C4×#4111yescharacteristic
488C22×C13#51811yescharacteristic
489C22×C13#52011yescharacteristic
490C22×C13#52011yescharacteristic
491C22×C13#52011yescharacteristic
492C22×C13#53411yescharacteristic
493C22×C13#53611yescharacteristic
494C22×C13#53811yescharacteristic
495C22×C13#53911yescharacteristic
496C22×C13#53911yescharacteristic
497C22×C13#53911yescharacteristic
498C22×C13#54011yescharacteristic
499C22×C13#54011yescharacteristic
500C22×C13#54111yescharacteristic
501C22×C13#54211yescharacteristic
502C22×C13#54211yescharacteristic
503C22×C13#54211yescharacteristic
504C22×C13#54611yescharacteristic
505C22×C13#54611yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54711yescharacteristic
508C22×C13#55111yescharacteristic
509C22×C13#55111yescharacteristic
510C22×C13#55111yescharacteristic
511C22×C13#55211yescharacteristic
512C22×C13#55311yescharacteristic
513C22×C13#55311yescharacteristic
514C22×C13#55611yescharacteristic
515C22×C13#55611yescharacteristic
516C22×C13#56011yescharacteristic
517C22×C13#56211yescharacteristic
518C22×C13#56211yescharacteristic
519C22×C13#56311yescharacteristic
520C4×C13—24no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—42no—
526Dic13—42no—
527Dic13—42no—
528Dic13—42no—
529Dic13—42no—
530Dic13—81no—
531Dic13—81no—
532Dic13—81no—
533Dic13—81no—
534C25C22×D1311yescharacteristic
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—22no—
539C23×C4—41no—
540C23×C4—41no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4C2×Dic1314yes—
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C2×C4⋊C4—262no—
557C2×C4⋊C4—262no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
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—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—262no—
574C2×C22⋊C4—262no—
575C2×C22⋊C4—262no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—521no—
579C2×C22⋊C4—521no—
580C2×C22⋊C4—521no—
581C2×C22⋊C4—521no—
582C2×C22⋊C4—521no—
583C2×C22⋊C4—521no—
584C2×C22⋊C4C2×Dic1314yes—
585C2×C22⋊C4C2×Dic1314yes—
586C2×C42—262no—
587C2×C42—521no—
588C2×C42—521no—
589C2×C42—521no—
590C2×C42—521no—
591C2×C42—521no—
592#95—262no—
593#95—262no—
594#95—262no—
595#95—262no—
596#95—262no—
597#95—262no—
598#95—262no—
599#95—262no—
600#95—521no—
601#95—521no—
602#95—521no—
603#95—521no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95—521no—
609#95—521no—
610#95C2×Dic1314yes—
611#95C2×Dic1314yes—
612#95C2×Dic1314yes—
613#95C2×Dic1314yes—
614C2×C13—44no—
615C2×C13#231411yescharacteristic
616C2×C13#232211yescharacteristic
617C2×C13#233511yescharacteristic
618C2×C13#234211yescharacteristic
619C2×C13#234711yescharacteristic
620C2×C13#235911yescharacteristic
621C2×C13#237611yescharacteristic
622C2×C13#268811yescharacteristic
623C2×C13#268911yescharacteristic
624C2×C13#270011yescharacteristic
625C2×C13#270111yescharacteristic
626C2×C13#273911yescharacteristic
627C2×C13#274011yescharacteristic
628C2×C13#274511yescharacteristic
629C2×C13#274611yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24D4×D1312yes—
643C24#612912yes—
644C24C22×Dic1312yes—
645C24C23×D1311yescharacteristic
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—28no—
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—28no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
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—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#612712yes—
744C22×C4#612712yes—
745C22×C4C22×Dic1312yes—
746C22×C4C22×Dic1312yes—
747C22×C4C22×Dic1312yes—
748C22×C4C22×Dic1312yes—
749C22×C4C22×Dic1312yes—
750C22×C4C22×Dic1312yes—
751C4⋊C4—524no—
752C4⋊C4—524no—
753C4⋊C4—524no—
754C4⋊C4—524no—
755C22⋊C4—28no—
756C22⋊C4—44no—
757C22⋊C4—524no—
758C22⋊C4—524no—
759C22⋊C4—524no—
760C22⋊C4—524no—
761C42—524no—
762C42—524no—
763C13#1436811yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23D4×Dic1314yes—
799C23C2×#612711yescharacteristic
800C23C2×#612711yescharacteristic
801C23C2×D4×D1311yescharacteristic
802C23C2×#612911yescharacteristic
803C23#8825111yescharacteristic
804C23#8825111yescharacteristic
805C23#41×D1311yescharacteristic
806C23#41×D1311yescharacteristic
807C23#8825611yescharacteristic
808C23#8825611yescharacteristic
809C23#8825611yescharacteristic
810C23#8825711yescharacteristic
811C23#8825711yescharacteristic
812C23#8825711yescharacteristic
813C23C23×Dic1311yescharacteristic
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—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—416no—
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—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
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—
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#8818014yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22#1171919511yescharacteristic
929C22#1171919511yescharacteristic
930C22#1171920011yescharacteristic
931C22#1171920011yescharacteristic
932C22#1171922311yescharacteristic
933C22#1171923511yescharacteristic
934C22#1171923511yescharacteristic
935C22#1171923811yescharacteristic
936C22#1171923811yescharacteristic
937C22#1171923911yescharacteristic
938C22#1171923911yescharacteristic
939C22#1171924011yescharacteristic
940C22#1171935311yescharacteristic
941C22#1171935511yescharacteristic
942C22#1171935611yescharacteristic
943C22#1171935811yescharacteristic
944C22#1171935911yescharacteristic
945C22#1171936011yescharacteristic
946C22#1171936211yescharacteristic
947C22#1171936311yescharacteristic
948C22#1171936511yescharacteristic
949C22#1171936711yescharacteristic
950C22#1171936811yescharacteristic
951C22#1171937011yescharacteristic
952C22#1171937011yescharacteristic
953C22#1171937111yescharacteristic
954C22#1171937211yescharacteristic
955C22#1171937211yescharacteristic
956C22C2×#8818011yescharacteristic
957C22C2×D4×Dic1311yescharacteristic
958C22#1171950311yescharacteristic
959C22#41×Dic1311yescharacteristic
960C22#1171953211yescharacteristic
961C22#1171953211yescharacteristic
962C22#1171953211yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—522no—
970C4—522no—
971C4—522no—
972C4—522no—
973C4—1041no—
974C4—1041no—
975C4—1041no—
976C4—1041no—
977C2—44no—
978C2#1311744511yescharacteristic
979C2#1311750811yescharacteristic
980C2#1311763011yescharacteristic
981C2#1311768511yescharacteristic
982C2#1311772911yescharacteristic
983C2#1311783211yescharacteristic
984C2#1311798411yescharacteristic
985C2#1312127211yescharacteristic
986C2#1312128711yescharacteristic
987C2#1312143411yescharacteristic
988C2#1312144911yescharacteristic
989C2#1312192111yescharacteristic
990C2#1312193611yescharacteristic
991C2#1312200511yescharacteristic
992C2#1312202011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#381C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#381D13
hypocenterC13#14368
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #13113101C2semidirect
4. #13113098C2semidirect
5. #13113098C2semidirect
6. #13113093C2semidirect
10. #13113070C2semidirect
11. #13113070C2semidirect
12. #13113070C2semidirect
13. #13113070C2semidirect
29. C13×#381C4semidirect
446. #381Dic13semidirect
763. C13#14368semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117188732
#131131012
#131130982
#131130932
#131130852
#131130812
#131130732
#131130702
#131130592
C2×C13×#3812
#1436813