Finite Group Databasebeta

← #15791724

Subgroups — #15791724

Order 3328.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88133C211yesmaximal, characteristic
2C2×#11718606C211yesmaximal, characteristic
3C2×#11718607C211yesmaximal, characteristic
4#13113102C211yesmaximal, characteristic, complemented
5#13113088C211yesmaximal, characteristic, complemented
6#13113087C211yesmaximal, characteristic, complemented
7#13113087C211yesmaximal, characteristic, complemented
8#13113083C211yesmaximal, characteristic
9#13113070C211yesmaximal, characteristic, complemented
10#13113064C211yesmaximal, characteristic, complemented
11#13113064C211yesmaximal, characteristic, complemented
12#13113062C211yesmaximal, characteristic, complemented
13#13113058C211yesmaximal, characteristic
14#13113058C211yesmaximal, characteristic
15C13×#1440C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×#88133—24no—
32C2×#88133—24no—
33C2×#88133C418yescomplemented
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
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
53C2×#88071C2211yescharacteristic
54#11718607—24no—
55#11718606—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13—22no—
64C23×Dic13—22no—
65C23×Dic13—22no—
66C23×Dic13—41no—
67C23×Dic13—41no—
68C23×Dic13—41no—
69C23×Dic13—41no—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—41no—
84C2×C13×C22⋊C4—41no—
85C2×C13×C22⋊C4—41no—
86C2×C13×C22⋊C4C2×C414yes—
87C2×C22⋊Dic13—22no—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—41no—
92C2×C22⋊Dic13C2×C414yes—
93C2×C22⋊Dic13C2×C414yes—
94C2×C22⋊Dic13D414yes—
95C2×C22⋊Dic13D414yes—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13C2×C414yescomplemented
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—41no—
110C2×#6101—41no—
111C2×#6101—41no—
112C2×#6101C2×C414yescomplemented
113C2×#6101C2×C414yescomplemented
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13C2×C414yescomplemented
120#88133—232no—
121C13×#95—22no—
122C13×#95—41no—
123C13×#95—41no—
124C13×#95—41no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—41no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#14475—131nomaximal, Sylow
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×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13C22×C412yes—
155C24×C13C2×D412yes—
156C24×C13C2×D412yes—
157C24×C13C2411yescharacteristic
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×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C22×C412yes—
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—44no—
246C22×Dic13—44no—
247C22×Dic13—44no—
248C22×Dic13—44no—
249C22×Dic13—44no—
250C22×Dic13—44no—
251C22×Dic13—44no—
252C22×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C2×D412yes—
257C22×Dic13C2×D412yes—
258C22×Dic13C2×D412yes—
259C22×Dic13C2×D412yes—
260C22×Dic13#4112yes—
261C22×Dic13#4112yes—
262C22×Dic13#4112yes—
263C13×C22⋊C4—28no—
264C13×C22⋊C4—44no—
265C13×C22⋊C4—44no—
266C22⋊Dic13—28no—
267C22⋊Dic13—44no—
268C22⋊Dic13C22⋊C4116yes—
269C4⋊Dic13—28no—
270#6101—28no—
271#6101—28no—
272#6101—44no—
273#6101—44no—
274#6101—44no—
275C4×Dic13—28no—
276C4×Dic13—44no—
277C22×#126—131no—
278C2×#388—131no—
279C2×#385—131no—
280#1445—131no—
281#1441—131no—
282#1441—131no—
283#1441—131no—
284#1440—131no—
285#1440D1311yescharacteristic
286#1436—131no—
287C4⋊#95—131no—
288C4⋊#95—131no—
289#1434—131no—
290C22⋊#95—131no—
291C22⋊#95—131no—
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—22no—
308C23×C13—22no—
309C23×C13—22no—
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×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13C2×C22⋊C414yes—
327C23×C13C23×C411yescharacteristic
328C23×C13C22×D411yescharacteristic
329C23×C13C22×D411yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13H(5,𝔽2)11yescharacteristic
335C23×C13H(5,𝔽2)11yescharacteristic
336C23×C13H(5,𝔽2)11yescharacteristic
337C23×C13H(5,𝔽2)11yescharacteristic
338C23×C132−1+411yescharacteristic
339C23×C132−1+411yescharacteristic
340C23×C132−1+411yescharacteristic
341C23×C132−1+411yescharacteristic
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—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
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—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—416no—
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×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13C2×C22⋊C414yes—
440C2×Dic13C2×C22⋊C414yes—
441C24×C4—131no—
442C2×#126—138no—
443C2×#126—264no—
444C2×#126—264no—
445C22×C4⋊C4—131no—
446C22×C4⋊C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4C2×D1311yescharacteristic
455C22×C22⋊C4C2×D1311yescharacteristic
456C22×C22⋊C4C2×D1311yescharacteristic
457C22×C42—131no—
458C22×C42—131no—
459#388—264no—
460#385—264no—
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×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95C2×D1311yescharacteristic
478C2×#95C2×D1311yescharacteristic
479C2×#95C2×D1311yescharacteristic
480C2×#95C2×D1311yescharacteristic
481C22×C13—24no—
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13C22×C22⋊C411yescharacteristic
497C22×C13C4×#4111yescharacteristic
498C22×C13C4×#4111yescharacteristic
499C22×C13#52011yescharacteristic
500C22×C13#52011yescharacteristic
501C22×C13#52011yescharacteristic
502C22×C13#52011yescharacteristic
503C22×C13#53511yescharacteristic
504C22×C13#53611yescharacteristic
505C22×C13#53711yescharacteristic
506C22×C13#53711yescharacteristic
507C22×C13#53811yescharacteristic
508C22×C13#53811yescharacteristic
509C22×C13#53911yescharacteristic
510C22×C13#53911yescharacteristic
511C22×C13#54111yescharacteristic
512C22×C13#54111yescharacteristic
513C22×C13#54211yescharacteristic
514C22×C13#54211yescharacteristic
515C22×C13#54611yescharacteristic
516C22×C13#54611yescharacteristic
517C22×C13#54611yescharacteristic
518C22×C13#54611yescharacteristic
519C22×C13#54711yescharacteristic
520C22×C13#54711yescharacteristic
521C22×C13#54711yescharacteristic
522C22×C13#54711yescharacteristic
523C22×C13#55111yescharacteristic
524C22×C13#55211yescharacteristic
525C22×C13#55311yescharacteristic
526C22×C13#55611yescharacteristic
527C22×C13#56011yescharacteristic
528C22×C13#56311yescharacteristic
529C22×C13#56311yescharacteristic
530C22×C13#56311yescharacteristic
531C4×C13—42no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—81no—
535C4×C13—81no—
536C4×C13—81no—
537Dic13—24no—
538Dic13—24no—
539Dic13—42no—
540Dic13—42no—
541Dic13—42no—
542Dic13—42no—
543Dic13—42no—
544Dic13—81no—
545C25C22×D1311yescharacteristic
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—262no—
555C23×C4—262no—
556C23×C4—262no—
557C23×C4—521no—
558C23×C4—521no—
559C23×C4—521no—
560C23×C4—521no—
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C23×C4C22×D1311yescharacteristic
564C23×C4C22×D1311yescharacteristic
565C23×C4C22×D1311yescharacteristic
566C23×C4C22×D1311yescharacteristic
567#126—2632no—
568C2×C4⋊C4—134no—
569C2×C4⋊C4—134no—
570C2×C4⋊C4—134no—
571C2×C4⋊C4—262no—
572C2×C4⋊C4—262no—
573C2×C4⋊C4—262no—
574C2×C4⋊C4—262no—
575C2×C4⋊C4—262no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—262no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—521no—
584C2×C4⋊C4—521no—
585C2×C4⋊C4—521no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—134no—
595C2×C22⋊C4—134no—
596C2×C22⋊C4—134no—
597C2×C22⋊C4—134no—
598C2×C22⋊C4—262no—
599C2×C22⋊C4—262no—
600C2×C22⋊C4—262no—
601C2×C22⋊C4—262no—
602C2×C22⋊C4—521no—
603C2×C22⋊C4C4×D1314yes—
604C2×C42—134no—
605C2×C42—262no—
606C2×C42—262no—
607C2×C42—262no—
608C2×C42—262no—
609C2×C42—521no—
610#95—22no—
611#95—41no—
612#95—41no—
613#95—41no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—521no—
622#95—521no—
623#95—521no—
624#95—521no—
625#95—521no—
626#95—521no—
627#95—521no—
628#95—521no—
629#95—521no—
630C2×C13—44no—
631C2×C13#231111yescharacteristic
632C2×C13#233411yescharacteristic
633C2×C13#233411yescharacteristic
634C2×C13#233911yescharacteristic
635C2×C13#233911yescharacteristic
636C2×C13#237311yescharacteristic
637C2×C13#238311yescharacteristic
638C2×C13#268511yescharacteristic
639C2×C13#268911yescharacteristic
640C2×C13#269111yescharacteristic
641C2×C13#269511yescharacteristic
642C2×C13#269811yescharacteristic
643C2×C13#271511yescharacteristic
644C2×C13#271811yescharacteristic
645C2×C13#272211yescharacteristic
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24C2×C4×D1312yes—
659C24D4×D1312yes—
660C24D4×D1312yes—
661C24C23×D1311yescharacteristic
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—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—132no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
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—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—524no—
758C22×C4—524no—
759C22×C4—524no—
760C22×C4—524no—
761C22×C4—524no—
762C22×C4—524no—
763C22×C4—524no—
764C22×C4C2×C4×D1312yes—
765C22×C4C2×C4×D1312yes—
766C22×C4#612912yes—
767C4⋊C4—268no—
768C4⋊C4—268no—
769C4⋊C4—268no—
770C4⋊C4—524no—
771C4⋊C4—524no—
772C4⋊C4—524no—
773C22⋊C4—28no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—1316no—
777C22⋊C4—268no—
778C22⋊C4—524no—
779C42—268no—
780C42—524no—
781C13#1447511yescharacteristic, complemented, Sylow
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—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23C22⋊C4×D1314yes—
817C23C22×C4×D1311yescharacteristic
818C23C2×D4×D1311yescharacteristic
819C23C2×D4×D1311yescharacteristic
820C23C2×#612911yescharacteristic
821C23#8825111yescharacteristic
822C23#8825111yescharacteristic
823C23#8825111yescharacteristic
824C23#41×D1311yescharacteristic
825C23#41×D1311yescharacteristic
826C23#41×D1311yescharacteristic
827C23#8825611yescharacteristic
828C23#8825711yescharacteristic
829C23#8825711yescharacteristic
830C23#8825711yescharacteristic
831C23#8825711yescharacteristic
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
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—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—134no—
875C2×C4—134no—
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—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—5216no—
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—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22C2×C22⋊C4×D1311yescharacteristic
947C22#1171922711yescharacteristic
948C22#1171922811yescharacteristic
949C22C4×#612911yescharacteristic
950C22#1171925111yescharacteristic
951C22#1171925111yescharacteristic
952C22#1171925111yescharacteristic
953C22#1171929611yescharacteristic
954C22#1171929711yescharacteristic
955C22#1171930211yescharacteristic
956C22#1171930211yescharacteristic
957C22#1171930611yescharacteristic
958C22#1171930811yescharacteristic
959C22#1171931511yescharacteristic
960C22#1171931611yescharacteristic
961C22#1171931811yescharacteristic
962C22#1171932511yescharacteristic
963C22#1171935311yescharacteristic
964C22#1171935611yescharacteristic
965C22#1171935911yescharacteristic
966C22#1171935911yescharacteristic
967C22#1171936011yescharacteristic
968C22#1171936011yescharacteristic
969C22#1171936011yescharacteristic
970C22#1171936411yescharacteristic
971C22#1171936511yescharacteristic
972C22#1171937011yescharacteristic
973C22#1171937411yescharacteristic
974C22#1171937611yescharacteristic
975C22#1171937711yescharacteristic
976C22#1171938311yescharacteristic
977C22#1171940611yescharacteristic
978C22#1171940611yescharacteristic
979C22#1171941311yescharacteristic
980C22#1171941711yescharacteristic
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—81no—
986C4—81no—
987C4—264no—
988C4—264no—
989C4—522no—
990C4—522no—
991C4—522no—
992C4—522no—
993C4—522no—
994C4—1041no—
995C2—44no—
996C2#1311742311yescharacteristic
997C2#1311760911yescharacteristic
998C2#1311761811yescharacteristic
999C2#1311766011yescharacteristic
1000C2#1311766211yescharacteristic
1001C2#1311795411yescharacteristic
1002C2#1311802311yescharacteristic
1003C2#1312122911yescharacteristic
1004C2#1312128911yescharacteristic
1005C2#1312131011yescharacteristic
1006C2#1312136411yescharacteristic
1007C2#1312141611yescharacteristic
1008C2#1312164011yescharacteristic
1009C2#1312168811yescharacteristic
1010C2#1312173911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1440C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1440D13
hypocenterC13#14475
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
4. #13113102C2semidirect
5. #13113088C2semidirect
6. #13113087C2semidirect
7. #13113087C2semidirect
9. #13113070C2semidirect
10. #13113064C2semidirect
11. #13113064C2semidirect
12. #13113062C2semidirect
33. C2×#88133C4semidirect
98. C2×C4⋊Dic13C2×C4semidirect
112. C2×#6101C2×C4semidirect
113. C2×#6101C2×C4semidirect
119. C2×C4×Dic13C2×C4semidirect
781. C13#14475semidirect

Maximal subgroups

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

subgroupindex
C22×#881332
C2×#117186062
C2×#117186072
#131131022
#131130882
#131130872
#131130832
#131130702
#131130642
#131130622
#131130582
C13×#14402
#1447513