Finite Group Databasebeta

← #15790039

Subgroups — #15790039

Order 3328.

1290 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718613C211yesmaximal, characteristic
2#13113097C211yesmaximal, characteristic, complemented
3#13113097C211yesmaximal, characteristic, complemented
4#13113095C211yesmaximal, characteristic, complemented
5#13113087C211yesmaximal, characteristic, complemented
6#13113083C211yesmaximal, characteristic
7#13113079C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113073C211yesmaximal, characteristic
11#13113071C211yesmaximal, characteristic, complemented
12#13113071C211yesmaximal, characteristic, complemented
13#13113068C211yesmaximal, characteristic, complemented
14#95×Dic13C211yesmaximal, characteristic, complemented
15C13×#1439C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
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
51#11718613C418yescomplemented
52C25×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—41no—
69C2×C13×C4⋊C4—41no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—41no—
73C2×C13×C22⋊C4—41no—
74C2×C13×C22⋊C4—41no—
75C2×C13×C22⋊C4—41no—
76C2×C13×C22⋊C4—41no—
77C2×C13×C22⋊C4—41no—
78C2×C13×C22⋊C4C2×C414yes—
79C2×C22⋊Dic13—22no—
80C2×C22⋊Dic13—22no—
81C2×C22⋊Dic13—22no—
82C2×C22⋊Dic13—22no—
83C2×C22⋊Dic13—41no—
84C2×C22⋊Dic13—41no—
85C2×C22⋊Dic13—41no—
86C2×C22⋊Dic13—41no—
87C2×C22⋊Dic13—41no—
88C2×C22⋊Dic13—41no—
89C2×C22⋊Dic13C2×C414yes—
90C2×C22⋊Dic13C2×C414yes—
91C2×#6101—22no—
92C2×#6101—41no—
93C2×#6101—41no—
94C2×#6101—41no—
95C2×#6101—41no—
96C2×#6101C2×C414yes—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—41no—
101C2×C4×Dic13—41no—
102C2×C4×Dic13—41no—
103C2×C4×Dic13—41no—
104C2×C4×Dic13—41no—
105C2×C4×Dic13—41no—
106C13×#95—22no—
107C13×#95—41no—
108C13×#95—41no—
109#88071—22no—
110#88071—22no—
111#88071—22no—
112#88071—22no—
113#88071—22no—
114#88071—22no—
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#88071C2×C414yes—
126#88071C2×C414yes—
127#88071C2×C414yes—
128#14332—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×C13—21no—
142C24×C13—21no—
143C24×C13C22×C412yes—
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×C13C22×C412yes—
184C22×C4×C13C22×C412yes—
185C22×C4×C13#4112yes—
186C22×C4×C13#4112yes—
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—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×Dic13C22×C412yes—
236C22×Dic13C22×C412yes—
237C22×Dic13C22×C412yes—
238C22×Dic13C22×C412yes—
239C22×Dic13#4112yes—
240C22×Dic13#4112yes—
241C22×Dic13#4112yes—
242C22×Dic13#4112yes—
243C13×C4⋊C4—44no—
244C13×C22⋊C4—44no—
245C13×C22⋊C4—44no—
246C13×C22⋊C4—44no—
247C22⋊Dic13—44no—
248C22⋊Dic13—44no—
249C22⋊Dic13—44no—
250C22⋊Dic13—44no—
251#6101—44no—
252#6101—44no—
253C4×Dic13—44no—
254C4×Dic13—44no—
255C4×Dic13—44no—
256C2×#397—131no—
257#1443—131no—
258#1443—131no—
259#1442—131no—
260#1441—131no—
261#1440—131no—
262#1439—131no—
263#1439D1311yescharacteristic
264#1437—131no—
265#1437—131no—
266#1437—131no—
267#1436—131no—
268#1436—131no—
269#1436—131no—
270C4×#95—131no—
271C23×C13—22no—
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—41no—
279C23×C13—41no—
280C23×C13—41no—
281C23×C13—41no—
282C23×C13—41no—
283C23×C13—41no—
284C23×C13—41no—
285C23×C13—41no—
286C23×C13—41no—
287C23×C13—41no—
288C23×C13—41no—
289C23×C13—41no—
290C23×C13—41no—
291C23×C13—41no—
292C23×C13—41no—
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×C13C23×C411yescharacteristic
307C23×C13C2×#4111yescharacteristic
308C23×C13C2×#4111yescharacteristic
309C23×C13C2×#4111yescharacteristic
310C23×C13C2×#4111yescharacteristic
311C23×C13C2×#4111yescharacteristic
312C23×C13C2×#4111yescharacteristic
313C23×C13H(5,𝔽2)11yescharacteristic
314C23×C13H(5,𝔽2)11yescharacteristic
315C23×C13H(5,𝔽2)11yescharacteristic
316C23×C13H(5,𝔽2)11yescharacteristic
317C23×C13H(5,𝔽2)11yescharacteristic
318C23×C13H(5,𝔽2)11yescharacteristic
319C23×C132−1+411yescharacteristic
320C23×C132−1+411yescharacteristic
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
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—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×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
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—41no—
385C2×Dic13—41no—
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#12614yes—
419C22×C4⋊C4—131no—
420C22×C4⋊C4—131no—
421C22×C4⋊C4C2×D1311yescharacteristic
422C22×C22⋊C4—131no—
423C22×C22⋊C4—131no—
424C22×C22⋊C4—131no—
425C22×C22⋊C4—131no—
426C22×C22⋊C4C2×D1311yescharacteristic
427C22×C22⋊C4C2×D1311yescharacteristic
428C22×C22⋊C4C2×D1311yescharacteristic
429C22×C42—131no—
430C22×C42—131no—
431C22×C42—131no—
432#397—138no—
433C2×#95—131no—
434C2×#95—131no—
435C2×#95—131no—
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×#95C2×D1311yescharacteristic
453C2×#95C2×D1311yescharacteristic
454C2×#95C2×D1311yescharacteristic
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—42no—
462C22×C13—81no—
463C22×C13—81no—
464C22×C13—81no—
465C22×C13—81no—
466C22×C13—81no—
467C22×C13—81no—
468C22×C13—81no—
469C22×C13—81no—
470C22×C13C4×#4111yescharacteristic
471C22×C13C4×#4111yescharacteristic
472C22×C13C4×#4111yescharacteristic
473C22×C13#51811yescharacteristic
474C22×C13#51811yescharacteristic
475C22×C13#52011yescharacteristic
476C22×C13#52011yescharacteristic
477C22×C13C2×#12611yescharacteristic
478C22×C13#52911yescharacteristic
479C22×C13#52911yescharacteristic
480C22×C13#52911yescharacteristic
481C22×C13#53811yescharacteristic
482C22×C13#53811yescharacteristic
483C22×C13#53811yescharacteristic
484C22×C13#53811yescharacteristic
485C22×C13#53811yescharacteristic
486C22×C13#53811yescharacteristic
487C22×C13#53811yescharacteristic
488C22×C13#53811yescharacteristic
489C22×C13#53911yescharacteristic
490C22×C13#53911yescharacteristic
491C22×C13#53911yescharacteristic
492C22×C13#53911yescharacteristic
493C22×C13#54011yescharacteristic
494C22×C13#54011yescharacteristic
495C22×C13#54011yescharacteristic
496C22×C13#54011yescharacteristic
497C22×C13#54011yescharacteristic
498C22×C13#54111yescharacteristic
499C22×C13#54211yescharacteristic
500C22×C13#54211yescharacteristic
501C22×C13#54211yescharacteristic
502C22×C13#54211yescharacteristic
503C22×C13#54211yescharacteristic
504C22×C13#54211yescharacteristic
505C4×C13—42no—
506C4×C13—42no—
507C4×C13—42no—
508C4×C13—42no—
509C4×C13—81no—
510C4×C13—81no—
511Dic13—24no—
512Dic13—42no—
513Dic13—42no—
514Dic13—42no—
515Dic13—42no—
516Dic13—42no—
517Dic13—81no—
518Dic13—81no—
519C25C22×D1311yescharacteristic
520C23×C4—131no—
521C23×C4—131no—
522C23×C4—131no—
523C23×C4—131no—
524C23×C4—131no—
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530C23×C4C22×D1311yescharacteristic
531C23×C4C22×D1311yescharacteristic
532C23×C4C22×D1311yescharacteristic
533C23×C4C22×D1311yescharacteristic
534C2×C4⋊C4—22no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—262no—
539C2×C4⋊C4—521no—
540C2×C4⋊C4—521no—
541C2×C4⋊C4—521no—
542C2×C4⋊C4—521no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—134no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—262no—
554C2×C22⋊C4—262no—
555C2×C22⋊C4—262no—
556C2×C22⋊C4—262no—
557C2×C22⋊C4—521no—
558C2×C22⋊C4—521no—
559C2×C22⋊C4—521no—
560C2×C22⋊C4—521no—
561C2×C22⋊C4—521no—
562C2×C22⋊C4—521no—
563C2×C22⋊C4C4×D1314yes—
564C2×C42—262no—
565C2×C42—262no—
566C2×C42—262no—
567C2×C42—521no—
568C2×C42—521no—
569C2×C42—521no—
570C2×C42—521no—
571C2×C42—521no—
572C2×C42—521no—
573#95—22no—
574#95—41no—
575#95—41no—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—262no—
580#95—262no—
581#95—262no—
582#95—262no—
583#95—262no—
584#95—262no—
585#95—521no—
586#95—521no—
587#95—521no—
588#95—521no—
589#95—521no—
590#95—521no—
591#95—521no—
592#95—521no—
593#95—521no—
594#95—521no—
595C2×C13—82no—
596C2×C13C4×#12611yescharacteristic
597C2×C13#233311yescharacteristic
598C2×C13#233411yescharacteristic
599C2×C13#233511yescharacteristic
600C2×C13#233511yescharacteristic
601C2×C13#233511yescharacteristic
602C2×C13#233711yescharacteristic
603C2×C13#264311yescharacteristic
604C2×C13#264411yescharacteristic
605C2×C13#264811yescharacteristic
606C2×C13#264811yescharacteristic
607C2×C13#265011yescharacteristic
608C2×C13#265111yescharacteristic
609C2×C13#265311yescharacteristic
610C2×C13#265411yescharacteristic
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24C2×C4×D1312yes—
626C24C23×D1311yescharacteristic
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
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—132no—
666C22×C4—132no—
667C22×C4—132no—
668C22×C4—132no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—132no—
672C22×C4—132no—
673C22×C4—261no—
674C22×C4—261no—
675C22×C4—261no—
676C22×C4—261no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—261no—
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×C4C2×C4×D1312yes—
722C22×C4C2×C4×D1312yes—
723C22×C4#612912yes—
724C22×C4#612912yes—
725C4⋊C4—44no—
726C4⋊C4—524no—
727C4⋊C4—524no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—524no—
732C22⋊C4—524no—
733C22⋊C4—524no—
734C22⋊C4—524no—
735C42—524no—
736C42—524no—
737C42—524no—
738C13#1433211yescharacteristic, complemented, Sylow
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23C22×C4×D1311yescharacteristic
775C23C2×#612911yescharacteristic
776C23C2×#612911yescharacteristic
777C23#8825111yescharacteristic
778C23#8825111yescharacteristic
779C23#8825111yescharacteristic
780C23#8825111yescharacteristic
781C23#8825111yescharacteristic
782C23#8825411yescharacteristic
783C23#41×D1311yescharacteristic
784C23#41×D1311yescharacteristic
785C23#41×D1311yescharacteristic
786C23#41×D1311yescharacteristic
787C23#8825611yescharacteristic
788C23#8825711yescharacteristic
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
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—134no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—262no—
837C2×C4—262no—
838C2×C4—262no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—262no—
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—521no—
854C2×C4—521no—
855C2×C4—521no—
856C2×C4—521no—
857C2×C4—521no—
858C2×C4—521no—
859C2×C4—521no—
860C2×C4—521no—
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—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22#1171919111yescharacteristic
903C22#1171920911yescharacteristic
904C22#1171922711yescharacteristic
905C22C4×#612911yescharacteristic
906C22C4×#612911yescharacteristic
907C22#1171925011yescharacteristic
908C22#1171925111yescharacteristic
909C22#1171929811yescharacteristic
910C22#1171929811yescharacteristic
911C22#1171929811yescharacteristic
912C22#1171930511yescharacteristic
913C22#1171930811yescharacteristic
914C22#1171931811yescharacteristic
915C22#1171932011yescharacteristic
916C22#1171932011yescharacteristic
917C22#1171932011yescharacteristic
918C22#1171932011yescharacteristic
919C22#1171932211yescharacteristic
920C22#1171933011yescharacteristic
921C22#1171934311yescharacteristic
922C22#1171934511yescharacteristic
923C22#1171934511yescharacteristic
924C22#1171934511yescharacteristic
925C22#1171934811yescharacteristic
926C22#1171935411yescharacteristic
927C22#1171936211yescharacteristic
928C22#1171936511yescharacteristic
929C22#1171936511yescharacteristic
930C22#1171936711yescharacteristic
931C22#1171938311yescharacteristic
932C22#1171938311yescharacteristic
933C22#1171938511yescharacteristic
934C22D13×#12611yescharacteristic
935C22#1171941211yescharacteristic
936C22#1171942411yescharacteristic
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4—264no—
944C4—522no—
945C4—522no—
946C4—522no—
947C4—522no—
948C4—522no—
949C4—1041no—
950C4—1041no—
951C2—82no—
952C2#1311739011yescharacteristic
953C2#1311759511yescharacteristic
954C2#1311760611yescharacteristic
955C2#1311762211yescharacteristic
956C2#1311762411yescharacteristic
957C2#1311762711yescharacteristic
958C2#1311765011yescharacteristic
959C2#1312078811yescharacteristic
960C2#1312079811yescharacteristic
961C2#1312081711yescharacteristic
962C2#1312082511yescharacteristic
963C2#1312085511yescharacteristic
964C2#1312086611yescharacteristic
965C2#1312089611yescharacteristic
966C2#1312090911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14332
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #13113097C2semidirect
3. #13113097C2semidirect
4. #13113095C2semidirect
5. #13113087C2semidirect
11. #13113071C2semidirect
12. #13113071C2semidirect
13. #13113068C2semidirect
14. #95×Dic13C2semidirect
51. #11718613C4semidirect
738. C13#14332semidirect

Maximal subgroups

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

subgroupindex
C2×#117186132
#131130972
#131130952
#131130872
#131130832
#131130792
#131130732
#131130712
#131130682
#95×Dic132
C13×#14392
#1433213