Finite Group Databasebeta

← #15790164

Subgroups — #15790164

Order 3328.

1422 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718327C211yesmaximal, characteristic
2#13113098C211yesmaximal, characteristic, complemented
3#13113094C211yesmaximal, characteristic, complemented
4#13113091C211yesmaximal, characteristic, complemented
5#13113084C211yesmaximal, characteristic
6#13113084C211yesmaximal, characteristic
7#13113080C211yesmaximal, characteristic
8#13113080C211yesmaximal, characteristic
9#13113064C211yesmaximal, characteristic, complemented
10#13113062C211yesmaximal, characteristic, complemented
11#13113060C211yesmaximal, characteristic, complemented
12#13113060C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic
14#13113057C211yesmaximal, characteristic
15C13×#1443C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×#6103C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
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#11718327C418yescomplemented
52C24×D13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C22×C4×D13—22no—
68C22×C4×D13—22no—
69C22×C4×D13—41no—
70C22×C4×D13—41no—
71C22×C4×D13—41no—
72C22×C4×D13—41no—
73C22×C4×D13C2×C414yes—
74C2×#6103—22no—
75C2×#6103—22no—
76C2×#6103—22no—
77C2×#6103—22no—
78C2×#6103—22no—
79C2×#6103—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—41no—
83C2×#6103—41no—
84C2×#6103—41no—
85C2×#6103—41no—
86C2×#6103—41no—
87C2×#6103—41no—
88C2×#6103—41no—
89C2×#6103—41no—
90C2×#6103C2×C414yes—
91C2×#6103C2×C414yes—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×#6101—41no—
95C2×#6101—41no—
96C2×#6101—41no—
97C2×#6101—41no—
98C2×C4×Dic13—41no—
99C2×C4×Dic13—41no—
100C2×C4×Dic13—41no—
101C2×C4×Dic13—41no—
102C2×C4×Dic13C2×C414yes—
103C2×C4×Dic13C2×C414yes—
104C13×#95—41no—
105C13×#95—41no—
106C13×#95—41no—
107C13×#95—41no—
108C13×#95—41no—
109C13×#95—41no—
110C13×#95C2×C414yes—
111#88071—22no—
112#88071—22no—
113#88071—22no—
114#88071—22no—
115#88071—22no—
116#88071—22no—
117#88071—41no—
118#88071—41no—
119#88071—41no—
120#88071—41no—
121#88071—41no—
122#88071—41no—
123#88071—41no—
124#88071—41no—
125#88071—41no—
126#88071—41no—
127#88071C2×C414yes—
128#14351—131nomaximal, Sylow
129C24×C13C2411yescharacteristic
130C23×D13—21no—
131C23×D13—21no—
132C23×D13—21no—
133C23×D13—21no—
134C23×D13—21no—
135C23×D13—21no—
136C23×D13—21no—
137C23×D13—21no—
138C23×D13—21no—
139C23×D13—21no—
140C23×D13—21no—
141C23×D13—21no—
142C23×D13C22×C412yes—
143C23×D13#4112yes—
144C23×D13#4112yes—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
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×C13C22×C412yes—
192C22×C4×C13C22×C412yes—
193C22×C4×C13C22×C412yes—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
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×Dic13C22×C412yes—
237C22×Dic13C22×C412yes—
238C22×Dic13C22×C412yes—
239C22×Dic13#4112yes—
240C22×Dic13#4112yes—
241C22×Dic13#4112yes—
242C22×Dic13#4112yes—
243C2×C4×D13—28no—
244C2×C4×D13—44no—
245C2×C4×D13—44no—
246C2×C4×D13—44no—
247C2×C4×D13—44no—
248C2×C4×D13—44no—
249C2×C4×D13—44no—
250#6103—28no—
251#6103—28no—
252#6103—44no—
253#6103—44no—
254#6103—44no—
255#6103—44no—
256#6101—44no—
257#6101—44no—
258C4×Dic13—44no—
259C4×Dic13—44no—
260C2×C4×C22⋊C4—131no—
261#1443—131no—
262#1443D1311yescharacteristic, complemented
263#1442—131no—
264#1442—131no—
265#1440—131no—
266#1440—131no—
267#1439—131no—
268#1439—131no—
269C4⋊#95—131no—
270#1434—131no—
271#1434—131no—
272#1434—131no—
273C22⋊#95—131no—
274C22⋊#95—131no—
275C23×C13C23×C411yescharacteristic
276C23×C13C2×#4111yescharacteristic
277C23×C13C2×#4111yescharacteristic
278C23×C13C2×#4111yescharacteristic
279C23×C13C2×#4111yescharacteristic
280C23×C13C2×#4111yescharacteristic
281C23×C13C2×#4111yescharacteristic
282C23×C13H(5,𝔽2)11yescharacteristic
283C23×C13H(5,𝔽2)11yescharacteristic
284C23×C13H(5,𝔽2)11yescharacteristic
285C23×C13H(5,𝔽2)11yescharacteristic
286C23×C13H(5,𝔽2)11yescharacteristic
287C23×C13H(5,𝔽2)11yescharacteristic
288C23×C132−1+411yescharacteristic
289C23×C132−1+411yescharacteristic
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13—22no—
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
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—41no—
309C22×D13—41no—
310C22×D13—41no—
311C22×D13—41no—
312C22×D13—41no—
313C22×D13—41no—
314C22×D13—41no—
315C22×D13—41no—
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#11714yes—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
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×Dic13—22no—
375C2×Dic13—22no—
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—22no—
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#11714yes—
422C2×Dic13#11714yes—
423C4×D13—416no—
424C24×C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4—131no—
427C22×C22⋊C4—131no—
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C42—131no—
434C22×C42—131no—
435C4×C22⋊C4—138no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95C2×D1311yescharacteristic
454C2×#95C2×D1311yescharacteristic
455C2×#95C2×D1311yescharacteristic
456C2×#95C2×D1311yescharacteristic
457C2×#95C2×D1311yescharacteristic
458C2×#95C2×D1311yescharacteristic
459C2×#95C2×D1311yescharacteristic
460C22×C13C2×#11711yescharacteristic
461C22×C13C2×#11711yescharacteristic
462C22×C13C2×#11711yescharacteristic
463C22×C13#51811yescharacteristic
464C22×C13#51811yescharacteristic
465C22×C13#52011yescharacteristic
466C22×C13#52011yescharacteristic
467C22×C13#52911yescharacteristic
468C22×C13#52911yescharacteristic
469C22×C13#52911yescharacteristic
470C22×C13#52911yescharacteristic
471C22×C13#53811yescharacteristic
472C22×C13#53811yescharacteristic
473C22×C13#53811yescharacteristic
474C22×C13#53811yescharacteristic
475C22×C13#53811yescharacteristic
476C22×C13#53811yescharacteristic
477C22×C13#53811yescharacteristic
478C22×C13#53811yescharacteristic
479C22×C13#53811yescharacteristic
480C22×C13#53811yescharacteristic
481C22×C13#53911yescharacteristic
482C22×C13#53911yescharacteristic
483C22×C13#53911yescharacteristic
484C22×C13#53911yescharacteristic
485C22×C13#53911yescharacteristic
486C22×C13#53911yescharacteristic
487C22×C13#54011yescharacteristic
488C22×C13#54011yescharacteristic
489C22×C13#54011yescharacteristic
490C22×C13#54111yescharacteristic
491C22×C13#54211yescharacteristic
492C22×C13#54211yescharacteristic
493C22×C13#54211yescharacteristic
494C22×C13#54211yescharacteristic
495C2×D13—24no—
496C2×D13—24no—
497C2×D13—24no—
498C2×D13—42no—
499C2×D13—42no—
500C2×D13—42no—
501C2×D13—42no—
502C2×D13—42no—
503C2×D13—42no—
504C2×D13—42no—
505C2×D13—42no—
506C2×D13—42no—
507C2×D13—42no—
508C2×D13—42no—
509C2×D13—42no—
510C4×C13—42no—
511C4×C13—42no—
512C4×C13—42no—
513C4×C13—81no—
514C4×C13—81no—
515C4×C13—81no—
516C4×C13—81no—
517Dic13—24no—
518Dic13—24no—
519Dic13—42no—
520Dic13—81no—
521Dic13—81no—
522Dic13—81no—
523Dic13—81no—
524C25—131no—
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4—134no—
529C23×C4—131no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—262no—
534C23×C4—262no—
535C23×C4—521no—
536C23×C4—521no—
537C23×C4—521no—
538C23×C4—521no—
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1311yescharacteristic
546C2×C4⋊C4—262no—
547C2×C4⋊C4—262no—
548C2×C4⋊C4—521no—
549C2×C4⋊C4—521no—
550C2×C4⋊C4—521no—
551C2×C4⋊C4—521no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—262no—
555C2×C22⋊C4—262no—
556C2×C22⋊C4—262no—
557C2×C22⋊C4—262no—
558C2×C22⋊C4—262no—
559C2×C22⋊C4—262no—
560C2×C22⋊C4—262no—
561C2×C22⋊C4—262no—
562C2×C22⋊C4—521no—
563C2×C22⋊C4—521no—
564C2×C22⋊C4—521no—
565C2×C22⋊C4—521no—
566C2×C22⋊C4—521no—
567C2×C22⋊C4—521no—
568C2×C22⋊C4—521no—
569C2×C22⋊C4—521no—
570C2×C42—134no—
571C2×C42—134no—
572C2×C42—521no—
573C2×C42—521no—
574C2×C42—521no—
575C2×C42—521no—
576#95—41no—
577#95—41no—
578#95—41no—
579#95—41no—
580#95—41no—
581#95—41no—
582#95—134no—
583#95—262no—
584#95—262no—
585#95—262no—
586#95—262no—
587#95—262no—
588#95—262no—
589#95—521no—
590#95—521no—
591#95—521no—
592#95—521no—
593#95—521no—
594#95—521no—
595#95—521no—
596#95—521no—
597#95—521no—
598#95—521no—
599#95C4×D1314yes—
600C2×C13#228311yescharacteristic
601C2×C13#231211yescharacteristic
602C2×C13#231411yescharacteristic
603C2×C13#231811yescharacteristic
604C2×C13#231811yescharacteristic
605C2×C13#231811yescharacteristic
606C2×C13#231911yescharacteristic
607C2×C13#264811yescharacteristic
608C2×C13#264811yescharacteristic
609C2×C13#264911yescharacteristic
610C2×C13#264911yescharacteristic
611C2×C13#265211yescharacteristic
612C2×C13#265211yescharacteristic
613C2×C13#265311yescharacteristic
614C2×C13#265311yescharacteristic
615D13—44no—
616C24—132no—
617C24—132no—
618C24—132no—
619C24—261no—
620C24—261no—
621C24—261no—
622C24—261no—
623C24—261no—
624C24—261no—
625C24—261no—
626C24—261no—
627C24—261no—
628C24—261no—
629C24—261no—
630C24—261no—
631C24C23×D1311yescharacteristic
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
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—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—268no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
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—524no—
729C22×C4—524no—
730C22×C4—524no—
731C22×C4—524no—
732C22×C4—524no—
733C22×C4—524no—
734C22×C4C2×C4×D1312yes—
735C22×C4C2×C4×D1312yes—
736C22×C4C2×C4×D1312yes—
737C4⋊C4—524no—
738C4⋊C4—524no—
739C22⋊C4—268no—
740C22⋊C4—268no—
741C22⋊C4—524no—
742C22⋊C4—524no—
743C22⋊C4—524no—
744C22⋊C4—524no—
745C42—524no—
746C42—524no—
747C13#1435111yescharacteristic, complemented, Sylow
748C23—134no—
749C23—262no—
750C23—262no—
751C23—262no—
752C23—262no—
753C23—262no—
754C23—262no—
755C23—262no—
756C23—262no—
757C23—262no—
758C23—262no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—262no—
763C23—262no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—521no—
768C23—521no—
769C23—521no—
770C23—521no—
771C23—521no—
772C23—521no—
773C23—521no—
774C23—521no—
775C23—521no—
776C23—521no—
777C23—521no—
778C23—521no—
779C23—521no—
780C23—521no—
781C23—521no—
782C23—521no—
783C23C22×C4×D1311yescharacteristic
784C23#8825111yescharacteristic
785C23#8825111yescharacteristic
786C23#8825111yescharacteristic
787C23#8825411yescharacteristic
788C23#41×D1311yescharacteristic
789C23#41×D1311yescharacteristic
790C23#41×D1311yescharacteristic
791C23#41×D1311yescharacteristic
792C23#41×D1311yescharacteristic
793C23#41×D1311yescharacteristic
794C23#8825611yescharacteristic
795C23#8825611yescharacteristic
796C23#8825611yescharacteristic
797C23#8825711yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
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—134no—
848C2×C4—134no—
849C2×C4—262no—
850C2×C4—262no—
851C2×C4—262no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
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—5216no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4—521no—
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—
897C22—264no—
898C22—264no—
899C22—264no—
900C22—522no—
901C22—522no—
902C22—522no—
903C22—522no—
904C22—522no—
905C22—522no—
906C22—522no—
907C22—522no—
908C22—522no—
909C22—522no—
910C22—522no—
911C22—522no—
912C22D13×#11711yescharacteristic
913C22D13×#11711yescharacteristic
914C22D13×#11711yescharacteristic
915C22#1171925011yescharacteristic
916C22#1171925011yescharacteristic
917C22#1171925111yescharacteristic
918C22#1171927911yescharacteristic
919C22#1171931811yescharacteristic
920C22#1171931811yescharacteristic
921C22#1171932011yescharacteristic
922C22#1171934311yescharacteristic
923C22#1171934311yescharacteristic
924C22#1171934511yescharacteristic
925C22#1171936211yescharacteristic
926C22#1171936211yescharacteristic
927C22#1171936211yescharacteristic
928C22#1171936511yescharacteristic
929C22#1171936811yescharacteristic
930C22#1171936811yescharacteristic
931C22#1171937411yescharacteristic
932C22#1171938311yescharacteristic
933C22#1171938311yescharacteristic
934C22#1171939711yescharacteristic
935C22#1171939711yescharacteristic
936C22#1171940111yescharacteristic
937C22#1171940911yescharacteristic
938C22#1171940911yescharacteristic
939C22#1171940911yescharacteristic
940C22#1171941111yescharacteristic
941C22#1171941111yescharacteristic
942C22#1171941111yescharacteristic
943C22#1171941111yescharacteristic
944C22#1171941211yescharacteristic
945C22#1171941511yescharacteristic
946C22#1171941511yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—81no—
951C4—81no—
952C4—81no—
953C4—81no—
954C4—264no—
955C4—264no—
956C4—522no—
957C4—1041no—
958C4—1041no—
959C4—1041no—
960C4—1041no—
961C2—524no—
962C2#1311723311yescharacteristic
963C2#1311743011yescharacteristic
964C2#1311744211yescharacteristic
965C2#1311746611yescharacteristic
966C2#1311746811yescharacteristic
967C2#1311746811yescharacteristic
968C2#1311747711yescharacteristic
969C2#1312082911yescharacteristic
970C2#1312083111yescharacteristic
971C2#1312084411yescharacteristic
972C2#1312084611yescharacteristic
973C2#1312088911yescharacteristic
974C2#1312089111yescharacteristic
975C2#1312090411yescharacteristic
976C2#1312090611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1443C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1443D13
hypocenterC13#14351
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. #13113098C2semidirect
3. #13113094C2semidirect
4. #13113091C2semidirect
9. #13113064C2semidirect
10. #13113062C2semidirect
11. #13113060C2semidirect
12. #13113060C2semidirect
15. C13×#1443C2semidirect
51. #11718327C4semidirect
262. #1443D13semidirect
747. C13#14351semidirect

Maximal subgroups

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

subgroupindex
C2×#117183272
#131130982
#131130942
#131130912
#131130842
#131130802
#131130642
#131130622
#131130602
#131130572
C13×#14432
#1435113