Finite Group Databasebeta

← #15790810

Subgroups — #15790810

Order 3328.

1398 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C211yesmaximal, characteristic
2C2×#11718605C211yesmaximal, characteristic
3C2×#11718311C211yesmaximal, characteristic, complemented
4#13113100C211yesmaximal, characteristic, complemented
5#13113091C211yesmaximal, characteristic, complemented
6#13113083C211yesmaximal, characteristic
7#13113081C211yesmaximal, characteristic
8#13113079C211yesmaximal, characteristic
9#13113079C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113069C211yesmaximal, characteristic, complemented
12#13113066C211yesmaximal, characteristic, complemented
13#13113062C211yesmaximal, characteristic, complemented
14#13113062C211yesmaximal, characteristic, complemented
15C13×#1437C211yesmaximal, characteristic
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
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#11718612C418yescomplemented
52#11718605—24no—
53#11718311—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—41no—
75C2×C13×C22⋊C4—41no—
76C2×C13×C22⋊C4—41no—
77C2×C13×C22⋊C4C2×C414yes—
78C2×C42×C13—22no—
79C2×C42×C13—41no—
80C2×C42×C13—41no—
81C2×C22⋊Dic13—22no—
82C2×C22⋊Dic13—22no—
83C2×C22⋊Dic13—22no—
84C2×C22⋊Dic13—41no—
85C2×C22⋊Dic13—41no—
86C2×C22⋊Dic13—41no—
87C2×C22⋊Dic13—41no—
88C2×C22⋊Dic13—41no—
89C2×C22⋊Dic13—41no—
90C2×C22⋊Dic13—41no—
91C2×C22⋊Dic13C2×C414yes—
92C2×C22⋊Dic13C2×C414yes—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—41no—
95C2×C4⋊Dic13—41no—
96C2×C4⋊Dic13—41no—
97C2×C4⋊Dic13—41no—
98C2×C4⋊Dic13C2×C414yes—
99C2×#6101—22no—
100C2×#6101—41no—
101C2×#6101—41no—
102C2×#6101—41no—
103C2×#6101—41no—
104C2×#6101—41no—
105C2×#6101—41no—
106C2×#6101—41no—
107C2×#6101D414yes—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—41no—
113C2×C4×Dic13C2×C414yes—
114C13×#95—22no—
115C13×#95—22no—
116C13×#95—41no—
117#88071—22no—
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—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071C2×C414yes—
133#88071C2×C414yes—
134#14399—131nomaximal, Sylow
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×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13C22×C412yes—
150C24×C13C2411yescharacteristic
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×C13C22×C412yes—
187C22×C4×C13C22×C412yes—
188C22×C4×C13C2×D412yes—
189C22×C4×C13#4112yes—
190C22×C4×C13#4112yes—
191C22×C4×C13#4112yes—
192C22×C4×C13#4112yes—
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×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13C22×C412yes—
243C22×Dic13C22×C412yes—
244C22×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13C2×D412yes—
247C22×Dic13C2×D412yes—
248C22×Dic13#4112yes—
249C13×C22⋊C4—28no—
250C13×C22⋊C4—44no—
251C13×C22⋊C4—44no—
252C42×C13—44no—
253C22⋊Dic13—28no—
254C22⋊Dic13—44no—
255C22⋊Dic13—44no—
256C22⋊Dic13—44no—
257C4⋊Dic13—44no—
258C4⋊Dic13—44no—
259#6101—44no—
260#6101—44no—
261#6101—44no—
262C4×Dic13—28no—
263C4×Dic13—44no—
264C2×#388—131no—
265C2×#388—131no—
266C2×#382—131no—
267#1444—131no—
268#1442—131no—
269#1440—131no—
270#1439—131no—
271#1439—131no—
272#1439—131no—
273#1437D1311yescharacteristic
274#1436—131no—
275#1436—131no—
276C4⋊#95—131no—
277#1434—131no—
278#1434—131no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
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×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13C23×C411yescharacteristic
315C23×C13C22×D411yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13C2×#4111yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C13H(5,𝔽2)11yescharacteristic
324C23×C13H(5,𝔽2)11yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C23×C132−1+411yescharacteristic
327C23×C132−1+411yescharacteristic
328C23×C132−1+411yescharacteristic
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
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—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#11714yes—
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—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—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13C4×D414yes—
427C22×C4⋊C4—131no—
428C22×C4⋊C4—131no—
429C22×C4⋊C4—131no—
430C22×C4⋊C4—131no—
431C22×C4⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4C2×D1311yescharacteristic
437C22×C22⋊C4C2×D1311yescharacteristic
438C22×C22⋊C4C2×D1311yescharacteristic
439C22×C42—131no—
440C22×C42—131no—
441C22×C42C2×D1311yescharacteristic
442#388—138no—
443#388—264no—
444#382—264no—
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×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95C2×D1311yescharacteristic
463C2×#95C2×D1311yescharacteristic
464C2×#95C2×D1311yescharacteristic
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—81no—
473C22×C13—81no—
474C22×C13—81no—
475C22×C13—81no—
476C22×C13—81no—
477C22×C13—81no—
478C22×C13—81no—
479C22×C13—81no—
480C22×C13C2×#11711yescharacteristic
481C22×C13C2×C4×D411yescharacteristic
482C22×C13C4×#4111yescharacteristic
483C22×C13#51811yescharacteristic
484C22×C13#52011yescharacteristic
485C22×C13#52011yescharacteristic
486C22×C13#52011yescharacteristic
487C22×C13#53411yescharacteristic
488C22×C13#53611yescharacteristic
489C22×C13#53811yescharacteristic
490C22×C13#53811yescharacteristic
491C22×C13#53811yescharacteristic
492C22×C13#53911yescharacteristic
493C22×C13#53911yescharacteristic
494C22×C13#53911yescharacteristic
495C22×C13#53911yescharacteristic
496C22×C13#53911yescharacteristic
497C22×C13#54111yescharacteristic
498C22×C13#54211yescharacteristic
499C22×C13#54611yescharacteristic
500C22×C13#54711yescharacteristic
501C22×C13#55011yescharacteristic
502C22×C13#55011yescharacteristic
503C22×C13#55211yescharacteristic
504C22×C13#55211yescharacteristic
505C22×C13#55311yescharacteristic
506C22×C13#55511yescharacteristic
507C22×C13#55511yescharacteristic
508C22×C13#55511yescharacteristic
509C22×C13#55511yescharacteristic
510C22×C13#55611yescharacteristic
511C22×C13H(3,𝔽4)11yescharacteristic
512C22×C13#56211yescharacteristic
513C22×C13#56211yescharacteristic
514C22×C13#56311yescharacteristic
515C4×C13—24no—
516C4×C13—42no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—81no—
521Dic13—24no—
522Dic13—42no—
523Dic13—42no—
524Dic13—42no—
525Dic13—42no—
526Dic13—81no—
527Dic13—81no—
528Dic13—81no—
529C25C22×D1311yescharacteristic
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4C22×D1311yescharacteristic
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C2×C4⋊C4—134no—
545C2×C4⋊C4—134no—
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×C4⋊C4—521no—
553C2×C4⋊C4—521no—
554C2×C4⋊C4—521no—
555C2×C4⋊C4—521no—
556C2×C4⋊C4—521no—
557C2×C4⋊C4—521no—
558C2×C4⋊C4—521no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—134no—
568C2×C22⋊C4—134no—
569C2×C22⋊C4—262no—
570C2×C22⋊C4—262no—
571C2×C22⋊C4—262no—
572C2×C22⋊C4—521no—
573C2×C22⋊C4—521no—
574C2×C22⋊C4—521no—
575C2×C22⋊C4—521no—
576C2×C22⋊C4—521no—
577C2×C22⋊C4—521no—
578C2×C22⋊C4—521no—
579C2×C22⋊C4C4×D1314yes—
580C2×C42—22no—
581C2×C42—41no—
582C2×C42—41no—
583C2×C42—134no—
584C2×C42—262no—
585C2×C42—262no—
586C2×C42—262no—
587C2×C42—262no—
588C2×C42—521no—
589#95—22no—
590#95—22no—
591#95—41no—
592#95—134no—
593#95—134no—
594#95—262no—
595#95—262no—
596#95—262no—
597#95—262no—
598#95—262no—
599#95—262no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—262no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95—521no—
609C2×C13—82no—
610C2×C13#231811yescharacteristic
611C2×C13#232211yescharacteristic
612C2×C13#233411yescharacteristic
613C2×C13#234611yescharacteristic
614C2×C13#235411yescharacteristic
615C2×C13#236311yescharacteristic
616C2×C13#237911yescharacteristic
617C2×C13#268611yescharacteristic
618C2×C13#269411yescharacteristic
619C2×C13#272111yescharacteristic
620C2×C13#273311yescharacteristic
621C2×C13#277511yescharacteristic
622C2×C13#278111yescharacteristic
623C2×C13#278311yescharacteristic
624C2×C13#278511yescharacteristic
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C2×C4×D1312yes—
640C24C23×D1311yescharacteristic
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—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
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—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4C2×C4×D1312yes—
733C22×C4C2×C4×D1312yes—
734C22×C4#612712yes—
735C22×C4#612712yes—
736C22×C4D4×D1312yes—
737C22×C4#612912yes—
738C22×C4#612912yes—
739C4⋊C4—524no—
740C4⋊C4—524no—
741C4⋊C4—524no—
742C4⋊C4—524no—
743C4⋊C4—524no—
744C22⋊C4—28no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—268no—
748C22⋊C4—524no—
749C22⋊C4—524no—
750C22⋊C4—524no—
751C42—44no—
752C42—268no—
753C42—524no—
754C13#1439911yescharacteristic, complemented, Sylow
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
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—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C22×C4×D1311yescharacteristic
791C23C2×#612711yescharacteristic
792C23C2×#612711yescharacteristic
793C23C2×D4×D1311yescharacteristic
794C23C2×#612911yescharacteristic
795C23C2×#612911yescharacteristic
796C23#8825111yescharacteristic
797C23#8825111yescharacteristic
798C23#8825111yescharacteristic
799C23#41×D1311yescharacteristic
800C23#8825611yescharacteristic
801C23#8825611yescharacteristic
802C23#8825711yescharacteristic
803C23#8825711yescharacteristic
804C23#8825711yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
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—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—134no—
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—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
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—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4#8813114yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22C4×#612711yescharacteristic
919C22C2×#8813111yescharacteristic
920C22#1171919511yescharacteristic
921C22#1171919911yescharacteristic
922C22#1171922311yescharacteristic
923C22#1171922811yescharacteristic
924C22#1171923711yescharacteristic
925C22#1171924511yescharacteristic
926C22#1171924611yescharacteristic
927C22#1171924611yescharacteristic
928C22C4×D4×D1311yescharacteristic
929C22#1171925011yescharacteristic
930C22#1171925111yescharacteristic
931C22#1171925111yescharacteristic
932C22#1171925811yescharacteristic
933C22#1171926611yescharacteristic
934C22#1171926811yescharacteristic
935C22#1171926811yescharacteristic
936C22#1171926911yescharacteristic
937C22#1171929811yescharacteristic
938C22#1171930711yescharacteristic
939C22#1171931011yescharacteristic
940C22#1171931611yescharacteristic
941C22#1171932111yescharacteristic
942C22#1171932211yescharacteristic
943C22#1171932611yescharacteristic
944C22#1171936511yescharacteristic
945C22#1171937011yescharacteristic
946C22#1171937211yescharacteristic
947C22#1171937611yescharacteristic
948C22#1171938011yescharacteristic
949C22#1171938811yescharacteristic
950C22#1171941211yescharacteristic
951C22#1171941711yescharacteristic
952C22#1171942311yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—81no—
959C4—264no—
960C4—522no—
961C4—522no—
962C4—522no—
963C4—522no—
964C4—1041no—
965C4—1041no—
966C4—1041no—
967C2—82no—
968C2#1311746211yescharacteristic
969C2#1311750611yescharacteristic
970C2#1311761311yescharacteristic
971C2#1311771911yescharacteristic
972C2#1311778411yescharacteristic
973C2#1311787511yescharacteristic
974C2#1311800511yescharacteristic
975C2#1312123711yescharacteristic
976C2#1312135111yescharacteristic
977C2#1312172811yescharacteristic
978C2#1312186111yescharacteristic
979C2#1312240711yescharacteristic
980C2#1312250211yescharacteristic
981C2#1312252611yescharacteristic
982C2#1312254111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1437D13
hypocenterC13#14399
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#11718311C2semidirect
4. #13113100C2semidirect
5. #13113091C2semidirect
10. #13113070C2semidirect
11. #13113069C2semidirect
12. #13113066C2semidirect
13. #13113062C2semidirect
14. #13113062C2semidirect
51. #11718612C4semidirect
754. C13#14399semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117186052
C2×#117183112
#131131002
#131130912
#131130832
#131130812
#131130792
#131130702
#131130692
#131130662
#131130622
C13×#14372
#1439913