Finite Group Databasebeta

← #15793607

Subgroups — #15793607

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718334C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic, complemented
3C2×#11718651C211yesmaximal, characteristic
4#13113106C211yesmaximal, characteristic, complemented
5#13113100C211yesmaximal, characteristic, complemented
6#13113095C211yesmaximal, characteristic, complemented
7#13113094C211yesmaximal, characteristic, complemented
8#13113093C211yesmaximal, characteristic, complemented
9#13113084C211yesmaximal, characteristic
10#13113084C211yesmaximal, characteristic
11#13113082C211yesmaximal, characteristic
12#13113080C211yesmaximal, characteristic
13#13113080C211yesmaximal, characteristic
14#13113060C211yesmaximal, characteristic, complemented
15C13×#1442C211yesmaximal, characteristic, complemented
16C23×Dic26C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
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#11718334C418yescomplemented
53#11718307—24no—
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
69C22×Dic26—22no—
70C22×Dic26—22no—
71C22×Dic26—41no—
72C22×Dic26—41no—
73C22×Dic26—41no—
74C22×Dic26—41no—
75C22×Dic26C2×C414yes—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4—41no—
79C2×#6103—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
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×#6103—41no—
97C2×#6103C2×C414yes—
98C2×#6103C2×C414yes—
99C2×#6103C2×C414yes—
100C2×C4⋊Dic13—41no—
101C2×C4⋊Dic13—41no—
102C2×C4⋊Dic13—41no—
103C2×#6101—22no—
104C2×#6101—41no—
105C2×#6101—41no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×#6101—41no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13D414yes—
112C13×#95—22no—
113C13×#95—41no—
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—22no—
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#14625—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—
249C2×Dic26—28no—
250C2×Dic26—44no—
251C2×Dic26—44no—
252C2×Dic26—44no—
253C2×Dic26—44no—
254C2×Dic26—44no—
255C2×Dic26—44no—
256C13×C4⋊C4—44no—
257#6103—28no—
258#6103—44no—
259#6103—44no—
260#6103—44no—
261#6103—44no—
262#6103—44no—
263#6103—44no—
264C4⋊Dic13—44no—
265#6101—44no—
266#6101—44no—
267C4×Dic13—44no—
268C2×#393—131no—
269C2×#391—131no—
270C2×#388—131no—
271#1446—131no—
272#1444—131no—
273#1442—131no—
274#1442—131no—
275#1442—131no—
276#1442D1311yescharacteristic, complemented
277#1440—131no—
278#1440—131no—
279#1439—131no—
280#1439—131no—
281#1439—131no—
282#1434—131no—
283C23×C13C23×C411yescharacteristic
284C23×C13C22×D411yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13H(5,𝔽2)11yescharacteristic
287C23×C13H(5,𝔽2)11yescharacteristic
288C23×C13H(5,𝔽2)11yescharacteristic
289C23×C13H(5,𝔽2)11yescharacteristic
290C23×C13H(5,𝔽2)11yescharacteristic
291C23×C13H(5,𝔽2)11yescharacteristic
292C23×C13H(5,𝔽2)11yescharacteristic
293C23×C132−1+411yescharacteristic
294C23×C132−1+411yescharacteristic
295C23×C132−1+411yescharacteristic
296C23×C132−1+411yescharacteristic
297C23×C132−1+411yescharacteristic
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13—22no—
303C22×D13—22no—
304C22×D13—22no—
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—
329C22×D13—41no—
330C22×D13—41no—
331C22×D13—41no—
332C22×D13—41no—
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—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×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
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—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
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×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13C4×D414yes—
431Dic26—416no—
432C23×Q8—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4—131no—
436C22×C4⋊C4C2×D1311yescharacteristic
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4—131no—
441C22×C22⋊C4—131no—
442C22×C22⋊C4—131no—
443C22×C22⋊C4—131no—
444C22×C42—131no—
445#393—138no—
446#391—264no—
447#388—264no—
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×#95—131no—
463C2×#95—131no—
464C2×#95C2×D1311yescharacteristic
465C2×#95C2×D1311yescharacteristic
466C2×#95C2×D1311yescharacteristic
467C2×#95C2×D1311yescharacteristic
468C2×#95C2×D1311yescharacteristic
469C2×#95C2×D1311yescharacteristic
470C22×C13C2×C4×D411yescharacteristic
471C22×C13#51811yescharacteristic
472C22×C13#51811yescharacteristic
473C22×C13#51911yescharacteristic
474C22×C13#52011yescharacteristic
475C22×C13#52011yescharacteristic
476C22×C13#52011yescharacteristic
477C22×C13#53411yescharacteristic
478C22×C13#53511yescharacteristic
479C22×C13#53511yescharacteristic
480C22×C13#53611yescharacteristic
481C22×C13#53611yescharacteristic
482C22×C13#53711yescharacteristic
483C22×C13#53811yescharacteristic
484C22×C13#53811yescharacteristic
485C22×C13#54111yescharacteristic
486C22×C13#54211yescharacteristic
487C22×C13#54211yescharacteristic
488C22×C13#54211yescharacteristic
489C22×C13H(3,𝔽4)11yescharacteristic
490C22×C13H(3,𝔽4)11yescharacteristic
491C22×C13#56211yescharacteristic
492C22×C13#56211yescharacteristic
493C22×C13#56211yescharacteristic
494C22×C13#56211yescharacteristic
495C22×C13#56211yescharacteristic
496C22×C13#56211yescharacteristic
497C22×C13#56211yescharacteristic
498C22×C13#56211yescharacteristic
499C22×C13#56311yescharacteristic
500C22×C13#56311yescharacteristic
501C22×C13#56311yescharacteristic
502C22×C13#56311yescharacteristic
503C22×C13#56311yescharacteristic
504C22×C13#56311yescharacteristic
505C2×D13—42no—
506C2×D13—42no—
507C2×D13—42no—
508C2×D13—42no—
509C2×D13—42no—
510C2×D13—42no—
511C2×D13—42no—
512C2×D13—81no—
513C2×D13—81no—
514C2×D13—81no—
515C2×D13—81no—
516C2×D13—81no—
517C2×D13—81no—
518C2×D13—81no—
519C2×D13—81no—
520C4×C13—42no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—81no—
525C4×C13—81no—
526C4×C13—81no—
527Dic13—24no—
528Dic13—42no—
529Dic13—42no—
530Dic13—42no—
531Dic13—81no—
532Dic13—81no—
533Dic13—81no—
534C25—131no—
535C22×Q8—134no—
536C22×Q8—262no—
537C22×Q8—262no—
538C22×Q8—521no—
539C22×Q8—521no—
540C22×Q8—521no—
541C22×Q8—521no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C2×C4⋊C4—22no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—521no—
561C2×C4⋊C4—521no—
562C2×C4⋊C4—521no—
563C2×C4⋊C4—521no—
564C2×C4⋊C4—521no—
565C2×C4⋊C4—521no—
566C2×C4⋊C4—521no—
567C2×C4⋊C4—521no—
568C2×C22⋊C4—134no—
569C2×C22⋊C4—134no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—262no—
572C2×C22⋊C4—262no—
573C2×C22⋊C4—262no—
574C2×C22⋊C4—262no—
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×C22⋊C4—521no—
587C2×C22⋊C4—521no—
588C2×C22⋊C4—521no—
589C2×C42—134no—
590C2×C42—521no—
591C2×C42—521no—
592#95—22no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—134no—
598#95—134no—
599#95—262no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—262no—
604#95—262no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95—521no—
609#95—521no—
610#95—521no—
611#95—521no—
612#95—521no—
613#95C4×D1314yes—
614C2×C13#232111yescharacteristic
615C2×C13#232311yescharacteristic
616C2×C13#232611yescharacteristic
617C2×C13#237811yescharacteristic
618C2×C13#237811yescharacteristic
619C2×C13#237911yescharacteristic
620C2×C13#237911yescharacteristic
621C2×C13#281411yescharacteristic
622C2×C13#281611yescharacteristic
623C2×C13#281911yescharacteristic
624C2×C13#282111yescharacteristic
625C2×C13#283111yescharacteristic
626C2×C13#283111yescharacteristic
627C2×C13#283211yescharacteristic
628C2×C13#283211yescharacteristic
629D13—82no—
630C24—132no—
631C24—261no—
632C24—261no—
633C24—261no—
634C24—261no—
635C24—261no—
636C24—261no—
637C24—261no—
638C24—261no—
639C24—261no—
640C24—261no—
641C24—261no—
642C24—261no—
643C24—261no—
644C24—261no—
645C24C23×D1311yescharacteristic
646C2×Q8—268no—
647C2×Q8—524no—
648C2×Q8—524no—
649C2×Q8—524no—
650C2×Q8—524no—
651C2×Q8—524no—
652C2×Q8—524no—
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—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—132no—
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×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4C2×C4×D1312yes—
748C22×C4C2×C4×D1312yes—
749C22×C4C2×C4×D1312yes—
750C22×C4D4×D1312yes—
751C4⋊C4—44no—
752C4⋊C4—524no—
753C4⋊C4—524no—
754C4⋊C4—524no—
755C22⋊C4—268no—
756C22⋊C4—524no—
757C22⋊C4—524no—
758C22⋊C4—524no—
759C22⋊C4—524no—
760C22⋊C4—524no—
761C22⋊C4—524no—
762C42—524no—
763C13#1462511yescharacteristic, complemented, Sylow
764C23—262no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
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—
790C23—521no—
791C23—521no—
792C23—521no—
793C23—521no—
794C23—521no—
795C23—521no—
796C23—521no—
797C23—521no—
798C23—521no—
799C23C22×C4×D1311yescharacteristic
800C23C2×D4×D1311yescharacteristic
801C23#8825111yescharacteristic
802C23#8825111yescharacteristic
803C23#8825111yescharacteristic
804C23#8825411yescharacteristic
805C23#8825411yescharacteristic
806C23#41×D1311yescharacteristic
807C23#8825611yescharacteristic
808C23#8825611yescharacteristic
809C23#8825611yescharacteristic
810C23#8825611yescharacteristic
811C23#8825711yescharacteristic
812C23#8825711yescharacteristic
813C23#8825711yescharacteristic
814Q8—5216no—
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—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
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—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—134no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
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—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C22—522no—
914C22—522no—
915C22—522no—
916C22—522no—
917C22—522no—
918C22—522no—
919C22—522no—
920C22—1041no—
921C22—1041no—
922C22—1041no—
923C22—1041no—
924C22—1041no—
925C22—1041no—
926C22—1041no—
927C22—1041no—
928C22#1171920911yescharacteristic
929C22#1171922611yescharacteristic
930C22#1171922811yescharacteristic
931C22C4×D4×D1311yescharacteristic
932C22#1171925011yescharacteristic
933C22#1171925111yescharacteristic
934C22#1171927711yescharacteristic
935C22#1171929711yescharacteristic
936C22#1171931011yescharacteristic
937C22#1171932611yescharacteristic
938C22#1171932611yescharacteristic
939C22#1171933311yescharacteristic
940C22#1171933411yescharacteristic
941C22#1171934511yescharacteristic
942C22#1171935211yescharacteristic
943C22#1171935211yescharacteristic
944C22#1171935311yescharacteristic
945C22#1171936211yescharacteristic
946C22#1171936711yescharacteristic
947C22#1171937211yescharacteristic
948C22#1171937211yescharacteristic
949C22#1171937911yescharacteristic
950C22#1171938811yescharacteristic
951C22#1171938811yescharacteristic
952C22#1171938911yescharacteristic
953C22#1171940111yescharacteristic
954C22#1171940411yescharacteristic
955C22#1171940411yescharacteristic
956C22#1171940411yescharacteristic
957C22#1171940511yescharacteristic
958C22#1171940911yescharacteristic
959C22#1171941511yescharacteristic
960C22#1171941711yescharacteristic
961C22#1171941711yescharacteristic
962C22#1171944011yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—81no—
968C4—81no—
969C4—81no—
970C4—264no—
971C4—522no—
972C4—522no—
973C4—522no—
974C4—1041no—
975C4—1041no—
976C4—1041no—
977C2—1042no—
978C2#1311748911yescharacteristic
979C2#1311751711yescharacteristic
980C2#1311754211yescharacteristic
981C2#1311799811yescharacteristic
982C2#1311800011yescharacteristic
983C2#1311800511yescharacteristic
984C2#1311800711yescharacteristic
985C2#1312285611yescharacteristic
986C2#1312286811yescharacteristic
987C2#1312288411yescharacteristic
988C2#1312290111yescharacteristic
989C2#1312299711yescharacteristic
990C2#1312299911yescharacteristic
991C2#1312300011yescharacteristic
992C2#1312300511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1442C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1442D13
hypocenterC13#14625
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#11718307C2semidirect
4. #13113106C2semidirect
5. #13113100C2semidirect
6. #13113095C2semidirect
7. #13113094C2semidirect
8. #13113093C2semidirect
14. #13113060C2semidirect
15. C13×#1442C2semidirect
52. #11718334C4semidirect
276. #1442D13semidirect
763. C13#14625semidirect

Maximal subgroups

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

subgroupindex
C2×#117183342
C2×#117183072
C2×#117186512
#131131062
#131131002
#131130952
#131130942
#131130932
#131130842
#131130822
#131130802
#131130602
C13×#14422
#1462513