Finite Group Databasebeta

← #15793660

Subgroups — #15793660

Order 3328.

1326 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×#11718336C211yesmaximal, characteristic
2C2×#11718633C211yesmaximal, characteristic, complemented
3C2×#11718651C211yesmaximal, characteristic
4#13113102C211yesmaximal, characteristic, complemented
5#13113099C211yesmaximal, characteristic, complemented
6#13113099C211yesmaximal, characteristic, complemented
7#13113098C211yesmaximal, characteristic, complemented
8#13113096C211yesmaximal, characteristic, complemented
9#13113080C211yesmaximal, characteristic
10#13113080C211yesmaximal, characteristic
11#13113080C211yesmaximal, characteristic
12#13113078C211yesmaximal, characteristic
13#13113078C211yesmaximal, characteristic
14#13113060C211yesmaximal, characteristic, complemented
15C13×#1444C211yesmaximal, characteristic, complemented
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
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#11718651—24no—
52#11718633—24no—
53#11718336C418yescomplemented
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
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—41no—
72C2×C13×C4⋊C4—41no—
73C2×C13×C4⋊C4—41no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4—41no—
77C2×C13×C4⋊C4—41no—
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×#6103—41no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103—41no—
95C2×#6103—41no—
96C2×#6103C2×C414yes—
97C2×#6103C2×C414yes—
98C2×#6103C2×C414yes—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101—41no—
104C2×#6101—41no—
105C2×#6101—41no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×#6101—41no—
109C2×#6101—41no—
110C2×#6101C2×C414yes—
111C2×C4×Dic13—41no—
112C2×C4×Dic13—41no—
113C2×C4×Dic13D414yes—
114C13×#95—41no—
115C13×#95—41no—
116C13×#95—41no—
117C13×#95C2×C414yes—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—41no—
124#88071—41no—
125#88071—41no—
126#88071—41no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071C2×C414yes—
133#88071C2×C414yes—
134#14630—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×D13—21no—
149C23×D13—21no—
150C23×D13C22×C412yes—
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×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13C22×C412yes—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C2×D412yes—
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×Dic13—21no—
243C22×Dic13C22×C412yes—
244C22×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13C2×D412yes—
247C22×Dic13C2×D412yes—
248C22×Dic13#4112yes—
249C13×C4⋊C4—44no—
250C13×C4⋊C4—44no—
251C13×C4⋊C4—44no—
252#6103—28no—
253#6103—44no—
254#6103—44no—
255#6103—44no—
256#6103—44no—
257#6103—44no—
258#6103—44no—
259#6101—28no—
260#6101—44no—
261#6101—44no—
262#6101—44no—
263C4×Dic13—44no—
264C2×#397—131no—
265C2×#389—131no—
266C2×#388—131no—
267#1445—131no—
268#1444—131no—
269#1444—131no—
270#1444D1311yescharacteristic, complemented
271#1443—131no—
272#1443—131no—
273#1439—131no—
274#1439—131no—
275#1439—131no—
276#1439—131no—
277#1439—131no—
278#1434—131no—
279C23×C13C23×C411yescharacteristic
280C23×C13C22×D411yescharacteristic
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×C13H(5,𝔽2)11yescharacteristic
289C23×C132−1+411yescharacteristic
290C23×C132−1+411yescharacteristic
291C23×C132−1+411yescharacteristic
292C23×C132−1+411yescharacteristic
293C23×C132−1+411yescharacteristic
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—41no—
302C22×D13—41no—
303C22×D13—41no—
304C22×D13—41no—
305C22×D13—41no—
306C22×D13—41no—
307C22×D13—41no—
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—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
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—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×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
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—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
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⋊C4C2×D1311yescharacteristic
432C22×C4⋊C4C2×D1311yescharacteristic
433C22×C4⋊C4C2×D1311yescharacteristic
434C22×C22⋊C4—131no—
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—
442#397—138no—
443#389—264no—
444#388—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×#95C2×D1311yescharacteristic
462C2×#95C2×D1311yescharacteristic
463C2×#95C2×D1311yescharacteristic
464C2×#95C2×D1311yescharacteristic
465C22×C13C2×C4×D411yescharacteristic
466C22×C13#51811yescharacteristic
467C22×C13#52011yescharacteristic
468C22×C13#52011yescharacteristic
469C22×C13#52011yescharacteristic
470C22×C13#52011yescharacteristic
471C22×C13#52011yescharacteristic
472C22×C13#53411yescharacteristic
473C22×C13#53511yescharacteristic
474C22×C13#53511yescharacteristic
475C22×C13#53611yescharacteristic
476C22×C13#53611yescharacteristic
477C22×C13#53711yescharacteristic
478C22×C13#53911yescharacteristic
479C22×C13#53911yescharacteristic
480C22×C13#54011yescharacteristic
481C22×C13#54211yescharacteristic
482C22×C13#54211yescharacteristic
483C22×C13#54211yescharacteristic
484C22×C13#56011yescharacteristic
485C22×C13#56011yescharacteristic
486C22×C13#56011yescharacteristic
487C22×C13#56011yescharacteristic
488C22×C13#56211yescharacteristic
489C22×C13#56211yescharacteristic
490C22×C13#56211yescharacteristic
491C22×C13#56211yescharacteristic
492C22×C13#56311yescharacteristic
493C22×C13#56311yescharacteristic
494C22×C13#56311yescharacteristic
495C22×C13#56311yescharacteristic
496C22×C13#56311yescharacteristic
497C22×C13#56311yescharacteristic
498C22×C13#56311yescharacteristic
499C22×C13#56311yescharacteristic
500C2×D13—42no—
501C2×D13—42no—
502C2×D13—42no—
503C2×D13—42no—
504C2×D13—42no—
505C2×D13—42no—
506C2×D13—42no—
507C2×D13—81no—
508C2×D13—81no—
509C2×D13—81no—
510C2×D13—81no—
511C2×D13—81no—
512C2×D13—81no—
513C2×D13—81no—
514C2×D13—81no—
515C4×C13—42no—
516C4×C13—42no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—81no—
520C4×C13—81no—
521C4×C13—81no—
522Dic13—24no—
523Dic13—42no—
524Dic13—42no—
525Dic13—42no—
526Dic13—81no—
527Dic13—81no—
528Dic13—81no—
529C25—131no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4C22×D1311yescharacteristic
538C23×C4C22×D1311yescharacteristic
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—134no—
554C2×C4⋊C4—262no—
555C2×C4⋊C4—262no—
556C2×C4⋊C4—262no—
557C2×C4⋊C4—262no—
558C2×C4⋊C4—521no—
559C2×C4⋊C4—521no—
560C2×C4⋊C4—521no—
561C2×C4⋊C4—521no—
562C2×C4⋊C4—521no—
563C2×C4⋊C4—521no—
564C2×C4⋊C4—521no—
565C2×C22⋊C4—134no—
566C2×C22⋊C4—134no—
567C2×C22⋊C4—134no—
568C2×C22⋊C4—262no—
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⋊C4—521no—
580C2×C22⋊C4—521no—
581C2×C22⋊C4—521no—
582C2×C22⋊C4—521no—
583C2×C22⋊C4—521no—
584C2×C22⋊C4—521no—
585C2×C22⋊C4—521no—
586C2×C42—134no—
587C2×C42—521no—
588C2×C42—521no—
589#95—41no—
590#95—41no—
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—521no—
600#95—521no—
601#95—521no—
602#95—521no—
603#95—521no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95C4×D1314yes—
609C2×C13#232211yescharacteristic
610C2×C13#232411yescharacteristic
611C2×C13#232611yescharacteristic
612C2×C13#237611yescharacteristic
613C2×C13#237611yescharacteristic
614C2×C13#238311yescharacteristic
615C2×C13#238311yescharacteristic
616C2×C13#281411yescharacteristic
617C2×C13#281511yescharacteristic
618C2×C13#282011yescharacteristic
619C2×C13#282111yescharacteristic
620C2×C13#283711yescharacteristic
621C2×C13#283711yescharacteristic
622C2×C13#283811yescharacteristic
623C2×C13#283811yescharacteristic
624D13—82no—
625C24—132no—
626C24—261no—
627C24—261no—
628C24—261no—
629C24—261no—
630C24—261no—
631C24—261no—
632C24—261no—
633C24—261no—
634C24—261no—
635C24—261no—
636C24—261no—
637C24—261no—
638C24—261no—
639C24—261no—
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—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—132no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—132no—
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×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4C2×C4×D1312yes—
736C22×C4C2×C4×D1312yes—
737C22×C4C2×C4×D1312yes—
738C22×C4D4×D1312yes—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—268no—
743C4⋊C4—524no—
744C4⋊C4—524no—
745C4⋊C4—524no—
746C22⋊C4—268no—
747C22⋊C4—524no—
748C22⋊C4—524no—
749C22⋊C4—524no—
750C22⋊C4—524no—
751C22⋊C4—524no—
752C22⋊C4—524no—
753C42—524no—
754C13#1463011yescharacteristic, complemented, Sylow
755C23—262no—
756C23—262no—
757C23—262no—
758C23—262no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—521no—
763C23—521no—
764C23—521no—
765C23—521no—
766C23—521no—
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—
783C23—521no—
784C23—521no—
785C23—521no—
786C23—521no—
787C23—521no—
788C23—521no—
789C23—521no—
790C23C22×C4×D1311yescharacteristic
791C23C2×D4×D1311yescharacteristic
792C23#8825111yescharacteristic
793C23#8825111yescharacteristic
794C23#8825111yescharacteristic
795C23#8825111yescharacteristic
796C23#8825111yescharacteristic
797C23#8825411yescharacteristic
798C23#8825411yescharacteristic
799C23#8825411yescharacteristic
800C23#8825411yescharacteristic
801C23#41×D1311yescharacteristic
802C23#8825611yescharacteristic
803C23#8825611yescharacteristic
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—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—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—134no—
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—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
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—521no—
903C22—522no—
904C22—522no—
905C22—522no—
906C22—522no—
907C22—522no—
908C22—522no—
909C22—522no—
910C22—1041no—
911C22—1041no—
912C22—1041no—
913C22—1041no—
914C22—1041no—
915C22—1041no—
916C22—1041no—
917C22—1041no—
918C22#1171920911yescharacteristic
919C22#1171920911yescharacteristic
920C22#1171920911yescharacteristic
921C22C4×D4×D1311yescharacteristic
922C22#1171925011yescharacteristic
923C22#1171925111yescharacteristic
924C22#1171927911yescharacteristic
925C22#1171929711yescharacteristic
926C22#1171929711yescharacteristic
927C22#1171930011yescharacteristic
928C22#1171931011yescharacteristic
929C22#1171932511yescharacteristic
930C22#1171932511yescharacteristic
931C22#1171933311yescharacteristic
932C22#1171933411yescharacteristic
933C22#1171934311yescharacteristic
934C22#1171934511yescharacteristic
935C22#1171934511yescharacteristic
936C22#1171935111yescharacteristic
937C22#1171935111yescharacteristic
938C22#1171935211yescharacteristic
939C22#1171935211yescharacteristic
940C22#1171936711yescharacteristic
941C22#1171936811yescharacteristic
942C22#1171937211yescharacteristic
943C22#1171939711yescharacteristic
944C22#1171940411yescharacteristic
945C22#1171940511yescharacteristic
946C22#1171942511yescharacteristic
947C22#1171942911yescharacteristic
948C22#1171944011yescharacteristic
949C22#1171944011yescharacteristic
950C22#1171944011yescharacteristic
951C22#1171944011yescharacteristic
952C22#1171944011yescharacteristic
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—81no—
958C4—81no—
959C4—81no—
960C4—264no—
961C4—522no—
962C4—522no—
963C4—522no—
964C4—1041no—
965C4—1041no—
966C4—1041no—
967C2—1042no—
968C2#1311750011yescharacteristic
969C2#1311752811yescharacteristic
970C2#1311754211yescharacteristic
971C2#1311798111yescharacteristic
972C2#1311798511yescharacteristic
973C2#1311802711yescharacteristic
974C2#1311802911yescharacteristic
975C2#1312285611yescharacteristic
976C2#1312286111yescharacteristic
977C2#1312289111yescharacteristic
978C2#1312290011yescharacteristic
979C2#1312304511yescharacteristic
980C2#1312304711yescharacteristic
981C2#1312306011yescharacteristic
982C2#1312306211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1444C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1444D13
hypocenterC13#14630
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C2×#11718633C2semidirect
4. #13113102C2semidirect
5. #13113099C2semidirect
6. #13113099C2semidirect
7. #13113098C2semidirect
8. #13113096C2semidirect
14. #13113060C2semidirect
15. C13×#1444C2semidirect
53. #11718336C4semidirect
270. #1444D13semidirect
754. C13#14630semidirect

Maximal subgroups

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

subgroupindex
C2×#117183362
C2×#117186332
C2×#117186512
#131131022
#131130992
#131130982
#131130962
#131130802
#131130782
#131130602
C13×#14442
#1463013