Finite Group Databasebeta

← #15790667

Subgroups — #15790667

Order 3328.

1506 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×#11718601C211yesmaximal, characteristic
2C2×#11718650C211yesmaximal, characteristic
3C2×#11718598C211yesmaximal, characteristic, complemented
4#13113102C211yesmaximal, characteristic, complemented
5#13113095C211yesmaximal, characteristic, complemented
6#13113091C211yesmaximal, characteristic, complemented
7#13113087C211yesmaximal, characteristic, complemented
8#13113084C211yesmaximal, characteristic
9#13113078C211yesmaximal, characteristic
10#13113072C211yesmaximal, characteristic
11#13113068C211yesmaximal, characteristic, complemented
12#13113060C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic
14#13113057C211yesmaximal, characteristic
15C13×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
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#11718650—24no—
52#11718601C418yescomplemented
53#11718598—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×C4×D13—22no—
70C22×C4×D13—22no—
71C22×C4×D13—22no—
72C22×C4×D13—41no—
73C22×C4×D13—41no—
74C22×C4×D13—41no—
75C22×C4×D13—41no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—41no—
81C2×C13×C4⋊C4—41no—
82C2×C42×C13—22no—
83C2×C42×C13—22no—
84C2×C42×C13C2×C414yescomplemented
85C2×#6103—22no—
86C2×#6103—22no—
87C2×#6103—22no—
88C2×#6103—22no—
89C2×#6103—22no—
90C2×#6103—22no—
91C2×#6103—22no—
92C2×#6103—22no—
93C2×#6103—22no—
94C2×#6103—41no—
95C2×#6103—41no—
96C2×#6103—41no—
97C2×#6103—41no—
98C2×#6103—41no—
99C2×#6103—41no—
100C2×#6103C2×C414yes—
101C2×#6103C2×C414yes—
102C2×#6103C2×C414yes—
103C2×#6101—22no—
104C2×#6101—41no—
105C2×#6101—41no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×#6101C2×C414yescomplemented
109C2×C4×Dic13—22no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13—41no—
112C13×#95—41no—
113C13×#95—41no—
114C13×#95—41no—
115C13×#95—41no—
116#88071—22no—
117#88071—22no—
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#88071C2×C414yescomplemented
132#88071C2×C414yescomplemented
133#88071D414yes—
134#14389—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×D13C22×C412yes—
149C23×D13#4112yes—
150C23×D13#4112yes—
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×C13C22×C412yes—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13#4112yes—
198C22×C4×C13#4112yes—
199C22×C4×C13#4112yes—
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×Dic13—21no—
244C22×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13C22×C412yes—
247C22×Dic13C2×D412yes—
248C22×Dic13C2×D412yes—
249C2×C4×D13—44no—
250C2×C4×D13—44no—
251C2×C4×D13—44no—
252C2×C4×D13—44no—
253C2×C4×D13—44no—
254C2×C4×D13—44no—
255C2×C4×D13—44no—
256C13×C4⋊C4—44no—
257C13×C4⋊C4—44no—
258C42×C13—28no—
259#6103—28no—
260#6103—28no—
261#6103—44no—
262#6103—44no—
263#6103—44no—
264#6103—44no—
265#6101—44no—
266#6101—44no—
267C4×Dic13—44no—
268C2×#388—131no—
269C2×#385—131no—
270C2×#383—131no—
271#1445—131no—
272#1442—131no—
273#1442—131no—
274#1441—131no—
275#1440—131no—
276#1439—131no—
277#1437—131no—
278#1436—131no—
279C4⋊#95D1311yescharacteristic, complemented
280#1434—131no—
281C22⋊#95—131no—
282C22⋊#95—131no—
283C23×C13C23×C411yescharacteristic
284C23×C13C22×D411yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13C2×#4111yescharacteristic
287C23×C13C2×#4111yescharacteristic
288C23×C13C2×#4111yescharacteristic
289C23×C13C2×#4111yescharacteristic
290C23×C13H(5,𝔽2)11yescharacteristic
291C23×C13H(5,𝔽2)11yescharacteristic
292C23×C13H(5,𝔽2)11yescharacteristic
293C23×C13H(5,𝔽2)11yescharacteristic
294C23×C13H(5,𝔽2)11yescharacteristic
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—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
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#11714yes—
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—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
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×C13C4×D414yes—
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×Dic13—41no—
431C4×D13—416no—
432C24×C4—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4C2×D1311yescharacteristic
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×C42—131no—
444C22×C42C2×D1311yescharacteristic
445#388—138no—
446#385—264no—
447#383—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×#95—131no—
465C2×#95—131no—
466C2×#95C2×D1311yescharacteristic
467C2×#95C2×D1311yescharacteristic
468C2×#95C2×D1311yescharacteristic
469C2×#95C2×D1311yescharacteristic
470C22×C13C2×#11711yescharacteristic
471C22×C13C2×C4×D411yescharacteristic
472C22×C13C4×#4111yescharacteristic
473C22×C13#51811yescharacteristic
474C22×C13#52011yescharacteristic
475C22×C13#52011yescharacteristic
476C22×C13#52011yescharacteristic
477C22×C13#53511yescharacteristic
478C22×C13#53711yescharacteristic
479C22×C13#53811yescharacteristic
480C22×C13#53811yescharacteristic
481C22×C13#53811yescharacteristic
482C22×C13#53811yescharacteristic
483C22×C13#53911yescharacteristic
484C22×C13#53911yescharacteristic
485C22×C13#54011yescharacteristic
486C22×C13#54211yescharacteristic
487C22×C13#54211yescharacteristic
488C22×C13#54211yescharacteristic
489C22×C13#54611yescharacteristic
490C22×C13#54611yescharacteristic
491C22×C13#54711yescharacteristic
492C22×C13#54811yescharacteristic
493C22×C13#55111yescharacteristic
494C22×C13#55111yescharacteristic
495C22×C13#55111yescharacteristic
496C22×C13#55211yescharacteristic
497C22×C13#55211yescharacteristic
498C22×C13#55211yescharacteristic
499C22×C13#55211yescharacteristic
500C22×C13#55311yescharacteristic
501C22×C13#56011yescharacteristic
502C22×C13#56311yescharacteristic
503C22×C13#56311yescharacteristic
504C22×C13#56311yescharacteristic
505C2×D13—24no—
506C2×D13—24no—
507C2×D13—24no—
508C2×D13—42no—
509C2×D13—42no—
510C2×D13—42no—
511C2×D13—42no—
512C2×D13—42no—
513C2×D13—42no—
514C2×D13—42no—
515C2×D13—42no—
516C2×D13—42no—
517C2×D13—42no—
518C2×D13—42no—
519C2×D13—42no—
520C4×C13—24no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—81no—
526C4×C13—81no—
527Dic13—42no—
528Dic13—42no—
529Dic13—42no—
530Dic13—42no—
531Dic13—42no—
532Dic13—81no—
533Dic13—81no—
534C25—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—262no—
543C23×C4—262no—
544C23×C4—262no—
545C23×C4—521no—
546C23×C4—521no—
547C23×C4—521no—
548C23×C4—521no—
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—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—134no—
563C2×C4⋊C4—262no—
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—262no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—262no—
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—22no—
587C2×C42—22no—
588C2×C42—262no—
589C2×C42—521no—
590C2×C42—521no—
591C2×C42C4×D1314yescomplemented
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—134no—
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—262no—
606#95—521no—
607#95—521no—
608#95—521no—
609#95—521no—
610#95—521no—
611#95—521no—
612#95—521no—
613#95—521no—
614C2×C13#231811yescharacteristic
615C2×C13#232411yescharacteristic
616C2×C13#233711yescharacteristic
617C2×C13#234311yescharacteristic
618C2×C13#235211yescharacteristic
619C2×C13#235911yescharacteristic
620C2×C13#238311yescharacteristic
621C2×C13#268511yescharacteristic
622C2×C13#269511yescharacteristic
623C2×C13#270211yescharacteristic
624C2×C13#272311yescharacteristic
625C2×C13#273811yescharacteristic
626C2×C13#274911yescharacteristic
627C2×C13#276411yescharacteristic
628C2×C13#277011yescharacteristic
629D13—44no—
630C24—132no—
631C24—132no—
632C24—132no—
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
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—21no—
687C22×C4—21no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—132no—
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×C4—261no—
736C22×C4—261no—
737C22×C4—524no—
738C22×C4—524no—
739C22×C4—524no—
740C22×C4—524no—
741C22×C4—524no—
742C22×C4—524no—
743C22×C4—524no—
744C22×C4C2×C4×D1312yes—
745C22×C4C2×C4×D1312yes—
746C22×C4C2×C4×D1312yes—
747C22×C4#612712yes—
748C22×C4#612712yes—
749C22×C4D4×D1312yes—
750C22×C4#612912yes—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—524no—
754C4⋊C4—524no—
755C22⋊C4—268no—
756C22⋊C4—268no—
757C22⋊C4—524no—
758C22⋊C4—524no—
759C22⋊C4—524no—
760C22⋊C4—524no—
761C42—28no—
762C42—524no—
763C13#1438911yescharacteristic, complemented, Sylow
764C23—134no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—262no—
775C23—262no—
776C23—262no—
777C23—262no—
778C23—262no—
779C23—262no—
780C23—262no—
781C23—262no—
782C23—262no—
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×#612711yescharacteristic
801C23C2×#612711yescharacteristic
802C23C2×D4×D1311yescharacteristic
803C23C2×#612911yescharacteristic
804C23#8825111yescharacteristic
805C23#8825111yescharacteristic
806C23#8825111yescharacteristic
807C23#8825411yescharacteristic
808C23#8825411yescharacteristic
809C23#8825411yescharacteristic
810C23#41×D1311yescharacteristic
811C23#41×D1311yescharacteristic
812C23#8825611yescharacteristic
813C23#8825611yescharacteristic
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—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
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—262no—
863C2×C4—262no—
864C2×C4—262no—
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—5216no—
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—
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#8813514yes—
913C22—264no—
914C22—264no—
915C22—264no—
916C22—522no—
917C22—522no—
918C22—522no—
919C22—522no—
920C22—522no—
921C22—522no—
922C22—522no—
923C22—522no—
924C22—522no—
925C22—522no—
926C22—522no—
927C22—522no—
928C22C4×#612711yescharacteristic
929C22C2×#8813511yescharacteristic
930C22#1171919511yescharacteristic
931C22#1171920011yescharacteristic
932C22#1171920911yescharacteristic
933C22#1171920911yescharacteristic
934C22#1171920911yescharacteristic
935C22#1171921211yescharacteristic
936C22#1171921811yescharacteristic
937C22D13×#11711yescharacteristic
938C22#1171922611yescharacteristic
939C22#1171926111yescharacteristic
940C22#1171926111yescharacteristic
941C22#1171926511yescharacteristic
942C22#1171926511yescharacteristic
943C22#1171928611yescharacteristic
944C22#1171928611yescharacteristic
945C22#1171928711yescharacteristic
946C22#1171928711yescharacteristic
947C22#1171931211yescharacteristic
948C22#1171931711yescharacteristic
949C22#1171931911yescharacteristic
950C22#1171932411yescharacteristic
951C22#1171933411yescharacteristic
952C22#1171933811yescharacteristic
953C22#1171934411yescharacteristic
954C22#1171934811yescharacteristic
955C22#1171938311yescharacteristic
956C22#1171938311yescharacteristic
957C22#1171939711yescharacteristic
958C22#1171939711yescharacteristic
959C22#1171942511yescharacteristic
960C22#1171944011yescharacteristic
961C22#1171944011yescharacteristic
962C22#1171944011yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—81no—
969C4—81no—
970C4—522no—
971C4—522no—
972C4—522no—
973C4—522no—
974C4—522no—
975C4—1041no—
976C4—1041no—
977C2—524no—
978C2#1311747211yescharacteristic
979C2#1311752511yescharacteristic
980C2#1311764911yescharacteristic
981C2#1311769911yescharacteristic
982C2#1311775811yescharacteristic
983C2#1311782411yescharacteristic
984C2#1311802911yescharacteristic
985C2#1312122811yescharacteristic
986C2#1312137211yescharacteristic
987C2#1312146711yescharacteristic
988C2#1312175511yescharacteristic
989C2#1312190911yescharacteristic
990C2#1312205711yescharacteristic
991C2#1312225611yescharacteristic
992C2#1312234011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#14389
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#11718598C2semidirect
4. #13113102C2semidirect
5. #13113095C2semidirect
6. #13113091C2semidirect
7. #13113087C2semidirect
11. #13113068C2semidirect
12. #13113060C2semidirect
15. C13×C4⋊#95C2semidirect
52. #11718601C4semidirect
84. C2×C42×C13C2×C4semidirect
108. C2×#6101C2×C4semidirect
131. #88071C2×C4semidirect
132. #88071C2×C4semidirect
279. C4⋊#95D13semidirect
591. C2×C42C4×D13semidirect
763. C13#14389semidirect

Maximal subgroups

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

subgroupindex
C2×#117186012
C2×#117186502
C2×#117185982
#131131022
#131130952
#131130912
#131130872
#131130842
#131130782
#131130722
#131130682
#131130602
#131130572
C13×C4⋊#952
#1438913