Finite Group Databasebeta

← #15787223

Subgroups — #15787223

Order 3328.

1586 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×#11718330C211yesmaximal, characteristic
2C2×#11718639C211yesmaximal, characteristic, complemented
3C2×#11718327C211yesmaximal, characteristic
4#13113096C211yesmaximal, characteristic, complemented
5#13113084C211yesmaximal, characteristic
6#13113078C211yesmaximal, characteristic
7#13113072C211yesmaximal, characteristic
8#13113067C211yesmaximal, characteristic, complemented
9#13113061C211yesmaximal, characteristic, complemented
10#13113061C211yesmaximal, characteristic, complemented
11#13113060C211yesmaximal, characteristic, complemented
12#13113057C211yesmaximal, characteristic
13#13113057C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic, complemented
15C13×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
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#11718639—24no—
52#11718330C418yescomplemented
53#11718327—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—22no—
73C22×C4×D13—22no—
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—22no—
89C2×#6103—22no—
90C2×#6103—41no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103C2×C414yes—
95C2×#6103C2×C414yes—
96C2×#6103C2×C414yes—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101C2×C414yescomplemented
100C2×C4×Dic13—22no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—41no—
105C2×C4×Dic13—41no—
106C2×C4×Dic13—41no—
107C2×C4×Dic13—41no—
108C2×C4×Dic13—41no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13C2×C414yescomplemented
111C2×C4×Dic13D414yes—
112C13×#95—22no—
113C13×#95—22no—
114C13×#95—22no—
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—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—41no—
132#88071—41no—
133#88071C2×C414yescomplemented
134#14086—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×Dic13C22×C412yes—
240C22×Dic13C22×C412yes—
241C22×Dic13C22×C412yes—
242C22×Dic13C2×D412yes—
243C22×Dic13C2×D412yes—
244C22×Dic13#4112yes—
245C22×Dic13#4112yes—
246C22×Dic13#4112yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C2×C4×D13—28no—
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—28no—
260#6103—44no—
261#6103—44no—
262#6103—44no—
263#6101—28no—
264C4×Dic13—44no—
265C4×Dic13—44no—
266C4×Dic13—44no—
267C4×Dic13—44no—
268C2×#388—131no—
269C2×#387—131no—
270C2×C4×C22⋊C4—131no—
271#1443—131no—
272#1442D1311yescharacteristic, complemented
273#1440—131no—
274#1439—131no—
275#1437—131no—
276#1436—131no—
277#1434—131no—
278#1434—131no—
279#1434—131no—
280C22⋊#95—131no—
281C22⋊#95—131no—
282C4×#95—131no—
283C23×C13C23×C411yescharacteristic
284C23×C13C22×D411yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13C2×#4111yescharacteristic
287C23×C13C2×#4111yescharacteristic
288C23×C13C2×#4111yescharacteristic
289C23×C13C2×#4111yescharacteristic
290C23×C13C2×#4111yescharacteristic
291C23×C13C2×#4111yescharacteristic
292C23×C13C2×#4111yescharacteristic
293C23×C13C2×#4111yescharacteristic
294C23×C13H(5,𝔽2)11yescharacteristic
295C23×C13H(5,𝔽2)11yescharacteristic
296C23×C13H(5,𝔽2)11yescharacteristic
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—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×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—22no—
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×Dic13C4×D414yes—
430C2×Dic13#12414yes—
431C4×D13—416no—
432C24×C4—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4C2×D1311yescharacteristic
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4—131no—
441C22×C42—131no—
442C22×C42—131no—
443C22×C42—131no—
444C22×C42—131no—
445#388—138no—
446#387—264no—
447C4×C22⋊C4—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×C13C4×#4111yescharacteristic
474C22×C13C4×#4111yescharacteristic
475C22×C13#51811yescharacteristic
476C22×C13#52011yescharacteristic
477C22×C13#52511yescharacteristic
478C22×C13#52511yescharacteristic
479C22×C13C2×#12411yescharacteristic
480C22×C13#52911yescharacteristic
481C22×C13#52911yescharacteristic
482C22×C13#52911yescharacteristic
483C22×C13#52911yescharacteristic
484C22×C13#53211yescharacteristic
485C22×C13#53411yescharacteristic
486C22×C13#53711yescharacteristic
487C22×C13#53811yescharacteristic
488C22×C13#53911yescharacteristic
489C22×C13#55111yescharacteristic
490C22×C13#55111yescharacteristic
491C22×C13#55111yescharacteristic
492C22×C13#55111yescharacteristic
493C22×C13#55111yescharacteristic
494C22×C13#55111yescharacteristic
495C22×C13#55211yescharacteristic
496C22×C13#55211yescharacteristic
497C22×C13#55211yescharacteristic
498C22×C13#55311yescharacteristic
499C22×C13#55311yescharacteristic
500C22×C13#55311yescharacteristic
501C22×C13#55311yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55611yescharacteristic
504C22×C13#55911yescharacteristic
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—42no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—42no—
526C4×C13—81no—
527Dic13—24no—
528Dic13—24no—
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—262no—
546C23×C4—262no—
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—262no—
561C2×C4⋊C4—262no—
562C2×C22⋊C4—134no—
563C2×C22⋊C4—134no—
564C2×C22⋊C4—134no—
565C2×C22⋊C4—262no—
566C2×C22⋊C4—262no—
567C2×C22⋊C4—262no—
568C2×C22⋊C4—262no—
569C2×C22⋊C4—262no—
570C2×C22⋊C4—262no—
571C2×C22⋊C4—262no—
572C2×C22⋊C4—262no—
573C2×C22⋊C4—262no—
574C2×C22⋊C4—262no—
575C2×C22⋊C4—262no—
576C2×C22⋊C4—521no—
577C2×C22⋊C4—521no—
578C2×C22⋊C4—521no—
579C2×C22⋊C4—521no—
580C2×C42—134no—
581C2×C42—134no—
582C2×C42—262no—
583C2×C42—262no—
584C2×C42—262no—
585C2×C42—262no—
586C2×C42—521no—
587C2×C42—521no—
588C2×C42—521no—
589C2×C42—521no—
590C2×C42—521no—
591C2×C42—521no—
592#95—22no—
593#95—22no—
594#95—22no—
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—262no—
608#95—262no—
609#95—262no—
610#95—262no—
611#95—521no—
612#95—521no—
613#95C4×D1314yescomplemented
614C2×C13#229011yescharacteristic
615C2×C13C4×#12411yescharacteristic
616C2×C13#232511yescharacteristic
617C2×C13#234311yescharacteristic
618C2×C13#235311yescharacteristic
619C2×C13#237311yescharacteristic
620C2×C13#237411yescharacteristic
621C2×C13#256111yescharacteristic
622C2×C13#256211yescharacteristic
623C2×C13#257511yescharacteristic
624C2×C13#257611yescharacteristic
625C2×C13#257711yescharacteristic
626C2×C13#257811yescharacteristic
627C2×C13#260111yescharacteristic
628C2×C13#260211yescharacteristic
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—132no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—132no—
699C22×C4—268no—
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—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#612912yes—
750C22×C4#613112yes—
751C4⋊C4—44no—
752C4⋊C4—268no—
753C22⋊C4—268no—
754C22⋊C4—268no—
755C22⋊C4—268no—
756C22⋊C4—524no—
757C22⋊C4—524no—
758C22⋊C4—524no—
759C42—524no—
760C42—524no—
761C42—524no—
762C42—524no—
763C13#1408611yescharacteristic, 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
801C23C2×#612911yescharacteristic
802C23#8825111yescharacteristic
803C23#8825111yescharacteristic
804C23C2×#613111yescharacteristic
805C23#8825411yescharacteristic
806C23#41×D1311yescharacteristic
807C23#41×D1311yescharacteristic
808C23#41×D1311yescharacteristic
809C23#41×D1311yescharacteristic
810C23#41×D1311yescharacteristic
811C23#41×D1311yescharacteristic
812C23#41×D1311yescharacteristic
813C23#8825611yescharacteristic
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—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—41no—
863C2×C4—134no—
864C2×C4—134no—
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—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—5216no—
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—521no—
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—
928C22#1171920911yescharacteristic
929C22D13×#11711yescharacteristic
930C22#1171922711yescharacteristic
931C22C4×#612911yescharacteristic
932C22C4×D4×D1311yescharacteristic
933C22#1171925011yescharacteristic
934C22C4×#613111yescharacteristic
935C22#1171929411yescharacteristic
936C22#1171930111yescharacteristic
937C22#1171930611yescharacteristic
938C22#1171931911yescharacteristic
939C22#1171933211yescharacteristic
940C22#1171933411yescharacteristic
941C22#1171934211yescharacteristic
942C22#1171934211yescharacteristic
943C22#1171934311yescharacteristic
944C22#1171935411yescharacteristic
945C22#1171936111yescharacteristic
946C22#1171936211yescharacteristic
947C22#1171936311yescharacteristic
948C22#1171936911yescharacteristic
949C22D13×#12411yescharacteristic
950C22#1171938411yescharacteristic
951C22#1171938411yescharacteristic
952C22#1171938411yescharacteristic
953C22#1171939611yescharacteristic
954C22#1171939811yescharacteristic
955C22#1171939811yescharacteristic
956C22#1171939811yescharacteristic
957C22#1171940011yescharacteristic
958C22#1171941111yescharacteristic
959C22#1171941111yescharacteristic
960C22#1171941411yescharacteristic
961C22#1171941411yescharacteristic
962C22#1171943711yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—81no—
970C4—264no—
971C4—264no—
972C4—522no—
973C4—522no—
974C4—522no—
975C4—522no—
976C4—1041no—
977C2—524no—
978C2#1311727411yescharacteristic
979C2#1311737711yescharacteristic
980C2#1311753311yescharacteristic
981C2#1311768911yescharacteristic
982C2#1311777111yescharacteristic
983C2#1311795911yescharacteristic
984C2#1311796811yescharacteristic
985C2#1311999011yescharacteristic
986C2#1311999811yescharacteristic
987C2#1312012011yescharacteristic
988C2#1312014311yescharacteristic
989C2#1312015811yescharacteristic
990C2#1312016511yescharacteristic
991C2#1312042811yescharacteristic
992C2#1312045111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1442C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1442D13
hypocenterC13#14086
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#11718639C2semidirect
4. #13113096C2semidirect
8. #13113067C2semidirect
9. #13113061C2semidirect
10. #13113061C2semidirect
11. #13113060C2semidirect
14. #95×Dic13C2semidirect
15. C13×#1442C2semidirect
52. #11718330C4semidirect
99. C2×#6101C2×C4semidirect
110. C2×C4×Dic13C2×C4semidirect
117. C13×#95C2×C4semidirect
133. #88071C2×C4semidirect
272. #1442D13semidirect
613. #95C4×D13semidirect
763. C13#14086semidirect

Maximal subgroups

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

subgroupindex
C2×#117183302
C2×#117186392
C2×#117183272
#131130962
#131130842
#131130782
#131130722
#131130672
#131130612
#131130602
#131130572
#95×Dic132
C13×#14422
#1408613