Finite Group Databasebeta

← #15790155

Subgroups — #15790155

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×C22⋊C4×Dic13C211yesmaximal, characteristic
2#13113097C211yesmaximal, characteristic, complemented
3#13113096C211yesmaximal, characteristic, complemented
4#13113094C211yesmaximal, characteristic, complemented
5#13113091C211yesmaximal, characteristic, complemented
6#13113085C211yesmaximal, characteristic
7#13113079C211yesmaximal, characteristic
8#13113079C211yesmaximal, characteristic
9#13113064C211yesmaximal, characteristic, complemented
10#13113062C211yesmaximal, characteristic, complemented
11#13113060C211yesmaximal, characteristic, complemented
12#13113060C211yesmaximal, 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×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
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
51C22⋊C4×Dic13C418yescomplemented
52C25×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×Dic13—22no—
60C23×Dic13—22no—
61C23×Dic13—41no—
62C23×Dic13—41no—
63C23×Dic13—41no—
64C23×Dic13—41no—
65C23×Dic13C2×C414yes—
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—41no—
79C2×C13×C22⋊C4—41no—
80C2×C13×C22⋊C4—41no—
81C2×C13×C22⋊C4—41no—
82C2×C13×C22⋊C4C2×C414yes—
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⋊Dic13C2×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—
108#88071—22no—
109#88071—22no—
110#88071—22no—
111#88071—22no—
112#88071—22no—
113#88071—22no—
114#88071—41no—
115#88071—41no—
116#88071—41no—
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#88071C2×C414yes—
127#88071C2×C414yes—
128#14351—131nomaximal, Sylow
129C24×C13—21no—
130C24×C13—21no—
131C24×C13—21no—
132C24×C13—21no—
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13C22×C412yes—
142C24×C13#4112yes—
143C24×C13#4112yes—
144C24×C13C2411yescharacteristic
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×C13C22×C412yes—
186C22×C4×C13C22×C412yes—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
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—28no—
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—44no—
237C22×Dic13—44no—
238C22×Dic13—44no—
239C22×Dic13—44no—
240C22×Dic13—44no—
241C22×Dic13—44no—
242C22×Dic13C22×C412yes—
243C22×Dic13C22×C412yes—
244C22×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13#4112yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C22×Dic13#4112yes—
250C13×C22⋊C4—28no—
251C13×C22⋊C4—44no—
252C13×C22⋊C4—44no—
253C22⋊Dic13—28no—
254C22⋊Dic13—44no—
255C22⋊Dic13—44no—
256#6101—44no—
257#6101—44no—
258C4×Dic13—44no—
259C4×Dic13—44no—
260C2×C4×C22⋊C4—131no—
261#1443—131no—
262#1443—131no—
263#1442—131no—
264#1442—131no—
265#1440—131no—
266#1440D1311yescharacteristic
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×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
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—41no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
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#11714yes—
310C23×C13C23×C411yescharacteristic
311C23×C13C2×#4111yescharacteristic
312C23×C13C2×#4111yescharacteristic
313C23×C13C2×#4111yescharacteristic
314C23×C13C2×#4111yescharacteristic
315C23×C13C2×#4111yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13H(5,𝔽2)11yescharacteristic
318C23×C13H(5,𝔽2)11yescharacteristic
319C23×C13H(5,𝔽2)11yescharacteristic
320C23×C13H(5,𝔽2)11yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C132−1+411yescharacteristic
324C23×C132−1+411yescharacteristic
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—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
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×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
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—416no—
386C2×Dic13—41no—
387C2×Dic13—41no—
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#11714yes—
423C2×Dic13#11714yes—
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⋊C4C2×D1311yescharacteristic
431C22×C22⋊C4C2×D1311yescharacteristic
432C22×C22⋊C4C2×D1311yescharacteristic
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×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95C2×D1311yescharacteristic
457C2×#95C2×D1311yescharacteristic
458C2×#95C2×D1311yescharacteristic
459C2×#95C2×D1311yescharacteristic
460C22×C13—24no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13C2×#11711yescharacteristic
476C22×C13C2×#11711yescharacteristic
477C22×C13C2×#11711yescharacteristic
478C22×C13#51811yescharacteristic
479C22×C13#51811yescharacteristic
480C22×C13#52011yescharacteristic
481C22×C13#52011yescharacteristic
482C22×C13#52911yescharacteristic
483C22×C13#52911yescharacteristic
484C22×C13#52911yescharacteristic
485C22×C13#52911yescharacteristic
486C22×C13#53811yescharacteristic
487C22×C13#53811yescharacteristic
488C22×C13#53811yescharacteristic
489C22×C13#53811yescharacteristic
490C22×C13#53811yescharacteristic
491C22×C13#53811yescharacteristic
492C22×C13#53811yescharacteristic
493C22×C13#53811yescharacteristic
494C22×C13#53811yescharacteristic
495C22×C13#53811yescharacteristic
496C22×C13#53911yescharacteristic
497C22×C13#53911yescharacteristic
498C22×C13#53911yescharacteristic
499C22×C13#53911yescharacteristic
500C22×C13#53911yescharacteristic
501C22×C13#53911yescharacteristic
502C22×C13#54011yescharacteristic
503C22×C13#54011yescharacteristic
504C22×C13#54011yescharacteristic
505C22×C13#54111yescharacteristic
506C22×C13#54211yescharacteristic
507C22×C13#54211yescharacteristic
508C22×C13#54211yescharacteristic
509C22×C13#54211yescharacteristic
510C4×C13—42no—
511C4×C13—42no—
512C4×C13—81no—
513C4×C13—81no—
514C4×C13—81no—
515C4×C13—81no—
516Dic13—24no—
517Dic13—24no—
518Dic13—42no—
519Dic13—42no—
520Dic13—81no—
521Dic13—81no—
522Dic13—81no—
523Dic13—81no—
524C25C22×D1311yescharacteristic
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4—134no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—262no—
535C23×C4—262no—
536C23×C4—521no—
537C23×C4—521no—
538C23×C4—521no—
539C23×C4—521no—
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—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—262no—
562C2×C22⋊C4—262no—
563C2×C22⋊C4—262no—
564C2×C22⋊C4—262no—
565C2×C22⋊C4—521no—
566C2×C22⋊C4—521no—
567C2×C22⋊C4—521no—
568C2×C22⋊C4—521no—
569C2×C22⋊C4C4×D1314yes—
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—134no—
581#95—134no—
582#95—262no—
583#95—262no—
584#95—262no—
585#95—262no—
586#95—262no—
587#95—262no—
588#95—521no—
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#95—521no—
600C2×C13—44no—
601C2×C13#228311yescharacteristic
602C2×C13#231211yescharacteristic
603C2×C13#231411yescharacteristic
604C2×C13#231811yescharacteristic
605C2×C13#231811yescharacteristic
606C2×C13#231811yescharacteristic
607C2×C13#231911yescharacteristic
608C2×C13#264811yescharacteristic
609C2×C13#264811yescharacteristic
610C2×C13#264911yescharacteristic
611C2×C13#264911yescharacteristic
612C2×C13#265211yescharacteristic
613C2×C13#265211yescharacteristic
614C2×C13#265311yescharacteristic
615C2×C13#265311yescharacteristic
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24C2×C4×D1312yes—
629C24#612912yes—
630C24#612912yes—
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—132no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—268no—
681C22×C4—261no—
682C22×C4—261no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
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—261no—
729C22×C4—524no—
730C22×C4—524no—
731C22×C4—524no—
732C22×C4—524no—
733C22×C4—524no—
734C22×C4—524no—
735C22×C4C2×C4×D1312yes—
736C22×C4C2×C4×D1312yes—
737C4⋊C4—524no—
738C4⋊C4—524no—
739C22⋊C4—28no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—268no—
743C22⋊C4—524no—
744C22⋊C4—524no—
745C42—524no—
746C42—524no—
747C13#1435111yescharacteristic, complemented, Sylow
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#8813114yes—
783C23C22×C4×D1311yescharacteristic
784C23C2×#612911yescharacteristic
785C23C2×#612911yescharacteristic
786C23#8825111yescharacteristic
787C23#8825111yescharacteristic
788C23#8825111yescharacteristic
789C23#8825111yescharacteristic
790C23#41×D1311yescharacteristic
791C23#41×D1311yescharacteristic
792C23#41×D1311yescharacteristic
793C23#41×D1311yescharacteristic
794C23#8825611yescharacteristic
795C23#8825611yescharacteristic
796C23#8825711yescharacteristic
797C23#8825711yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
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—134no—
841C2×C4—134no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—262no—
846C2×C4—262no—
847C2×C4—262no—
848C2×C4—262no—
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—5216no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
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—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22C2×#8813111yescharacteristic
913C22D13×#11711yescharacteristic
914C22D13×#11711yescharacteristic
915C22#1171925011yescharacteristic
916C22#1171925011yescharacteristic
917C22#1171925111yescharacteristic
918C22#1171925111yescharacteristic
919C22#1171929811yescharacteristic
920C22#1171929811yescharacteristic
921C22#1171930711yescharacteristic
922C22#1171930711yescharacteristic
923C22#1171931811yescharacteristic
924C22#1171931811yescharacteristic
925C22#1171932011yescharacteristic
926C22#1171932011yescharacteristic
927C22#1171932211yescharacteristic
928C22#1171932211yescharacteristic
929C22#1171935411yescharacteristic
930C22#1171935411yescharacteristic
931C22#1171935411yescharacteristic
932C22#1171935411yescharacteristic
933C22#1171936211yescharacteristic
934C22#1171936511yescharacteristic
935C22#1171936711yescharacteristic
936C22#1171936811yescharacteristic
937C22#1171937011yescharacteristic
938C22#1171937011yescharacteristic
939C22#1171937411yescharacteristic
940C22#1171937411yescharacteristic
941C22#1171938311yescharacteristic
942C22#1171938311yescharacteristic
943C22#1171940611yescharacteristic
944C22#1171940911yescharacteristic
945C22#1171941211yescharacteristic
946C22#1171941511yescharacteristic
947C4—42no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4—81no—
952C4—81no—
953C4—264no—
954C4—264no—
955C4—522no—
956C4—522no—
957C4—1041no—
958C4—1041no—
959C4—1041no—
960C4—1041no—
961C2—44no—
962C2#1311722711yescharacteristic
963C2#1311743011yescharacteristic
964C2#1311744011yescharacteristic
965C2#1311746211yescharacteristic
966C2#1311746211yescharacteristic
967C2#1311746611yescharacteristic
968C2#1311747711yescharacteristic
969C2#1312081711yescharacteristic
970C2#1312081911yescharacteristic
971C2#1312083211yescharacteristic
972C2#1312083411yescharacteristic
973C2#1312087711yescharacteristic
974C2#1312087911yescharacteristic
975C2#1312089211yescharacteristic
976C2#1312089411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1440C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1440D13
hypocenterC13#14351
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. #13113097C2semidirect
3. #13113096C2semidirect
4. #13113094C2semidirect
5. #13113091C2semidirect
9. #13113064C2semidirect
10. #13113062C2semidirect
11. #13113060C2semidirect
12. #13113060C2semidirect
51. C22⋊C4×Dic13C4semidirect
747. C13#14351semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×Dic132
#131130972
#131130962
#131130942
#131130912
#131130852
#131130792
#131130642
#131130622
#131130602
#131130582
C13×#14402
#1435113