Finite Group Databasebeta

← #15790377

Subgroups — #15790377

Order 3328.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718316C211yesmaximal, characteristic, complemented
2C2×#11718328C211yesmaximal, characteristic
3C2×#11718648C211yesmaximal, characteristic
4#13113102C211yesmaximal, characteristic, complemented
5#13113101C211yesmaximal, characteristic, complemented
6#13113090C211yesmaximal, characteristic, complemented
7#13113082C211yesmaximal, characteristic
8#13113082C211yesmaximal, characteristic
9#13113072C211yesmaximal, characteristic
10#13113072C211yesmaximal, characteristic
11#13113070C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113067C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C13×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
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#11718648—24no—
52#11718328C418yescomplemented
53#11718316—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—22no—
73C22×C4×D13—41no—
74C22×C4×D13—41no—
75C22×C4×D13C2×C414yes—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—41no—
79C2×#6103—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
83C2×#6103—22no—
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×#6103C2×C414yes—
95C2×#6103C2×C414yes—
96C2×#6103Q814yes—
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—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—41no—
109C2×#6101—41no—
110C2×#6101C2×C414yes—
111C2×#6101C2×C414yes—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—41no—
114C2×C4×Dic13—41no—
115C2×C4×Dic13—41no—
116C2×C4×Dic13—41no—
117C2×C4×Dic13—41no—
118C13×#95—22no—
119C13×#95—22no—
120C13×#95—41no—
121C13×#95—41no—
122C13×#95—41no—
123C13×#95C2×C414yes—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071—41no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071C2×C414yes—
137#88071D414yes—
138#14370—131nomaximal, Sylow
139C24×C13C2411yescharacteristic
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×D13—21no—
151C23×D13—21no—
152C23×D13C22×C412yes—
153C23×D13C2×Q812yes—
154C23×D13#4112yes—
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×C13—21no—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C22×C412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2×Q812yes—
202C22×C4×C13#4112yes—
203C22×C4×C13#4112yes—
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×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C22×C412yes—
249C22×Dic13C2×D412yes—
250C22×Dic13C2×D412yes—
251C22×Dic13C2×Q812yes—
252C22×Dic13#4112yes—
253C2×C4×D13—28no—
254C2×C4×D13—28no—
255C2×C4×D13—44no—
256C2×C4×D13—44no—
257C2×C4×D13—44no—
258C2×C4×D13—44no—
259C2×C4×D13—44no—
260C13×C4⋊C4—44no—
261#6103—44no—
262#6103—44no—
263#6103—44no—
264#6103—44no—
265#6103—44no—
266#6103—44no—
267C4⋊Dic13—44no—
268C4⋊Dic13—44no—
269C4⋊Dic13—44no—
270#6101—28no—
271#6101—44no—
272C4×Dic13—44no—
273C4×Dic13—44no—
274C2×#387—131no—
275C2×#380—131no—
276C2×#380—131no—
277#1445—131no—
278#1444—131no—
279#1442D1311yescharacteristic, complemented
280#1441—131no—
281#1439—131no—
282#1439—131no—
283#1437—131no—
284#1437—131no—
285#1436—131no—
286#1436—131no—
287#1436—131no—
288C22⋊#95—131no—
289C23×C13C23×C411yescharacteristic
290C23×C13C22×D411yescharacteristic
291C23×C13C22×Q811yescharacteristic
292C23×C13C2×#4111yescharacteristic
293C23×C13C2×#4111yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C23×C13C2×#4111yescharacteristic
296C23×C13H(5,𝔽2)11yescharacteristic
297C23×C13H(5,𝔽2)11yescharacteristic
298C23×C13H(5,𝔽2)11yescharacteristic
299C23×C13H(5,𝔽2)11yescharacteristic
300C23×C13H(5,𝔽2)11yescharacteristic
301C23×C13H(5,𝔽2)11yescharacteristic
302C23×C132−1+411yescharacteristic
303C23×C132−1+411yescharacteristic
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—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
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—
333C22×D13—41no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
337C22×D13—41no—
338C22×D13C4×Q814yes—
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—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
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×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13#11714yes—
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—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
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—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13C4×D414yes—
437C4×D13—416no—
438C24×C4—131no—
439C22×C4⋊C4—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4C2×D1311yescharacteristic
445C22×C22⋊C4—131no—
446C22×C22⋊C4—131no—
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C42—131no—
452C22×C42—131no—
453#387—264no—
454#380—138no—
455#380—264no—
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×#95—131no—
467C2×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95C2×D1311yescharacteristic
471C2×#95C2×D1311yescharacteristic
472C2×#95C2×D1311yescharacteristic
473C2×#95C2×D1311yescharacteristic
474C2×#95C2×D1311yescharacteristic
475C2×#95C2×D1311yescharacteristic
476C22×C13C2×#11711yescharacteristic
477C22×C13C2×C4×D411yescharacteristic
478C22×C13C2×C4×Q811yescharacteristic
479C22×C13#51811yescharacteristic
480C22×C13#51811yescharacteristic
481C22×C13#52011yescharacteristic
482C22×C13#52011yescharacteristic
483C22×C13#53511yescharacteristic
484C22×C13#53711yescharacteristic
485C22×C13#53811yescharacteristic
486C22×C13#53911yescharacteristic
487C22×C13#54011yescharacteristic
488C22×C13#54011yescharacteristic
489C22×C13#54111yescharacteristic
490C22×C13#54211yescharacteristic
491C22×C13#54211yescharacteristic
492C22×C13#54211yescharacteristic
493C22×C13#54311yescharacteristic
494C22×C13#54411yescharacteristic
495C22×C13#54611yescharacteristic
496C22×C13#54611yescharacteristic
497C22×C13#54611yescharacteristic
498C22×C13D4×Q811yescharacteristic
499C22×C13#55111yescharacteristic
500C22×C13#55111yescharacteristic
501C22×C13#55211yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55411yescharacteristic
505C22×C13#55411yescharacteristic
506C22×C13#55411yescharacteristic
507C22×C13#56011yescharacteristic
508C22×C13#56011yescharacteristic
509C22×C13#56211yescharacteristic
510C22×C13#56211yescharacteristic
511C2×D13—24no—
512C2×D13—24no—
513C2×D13—24no—
514C2×D13—42no—
515C2×D13—42no—
516C2×D13—42no—
517C2×D13—42no—
518C2×D13—42no—
519C2×D13—42no—
520C2×D13—42no—
521C2×D13—42no—
522C2×D13—42no—
523C2×D13—42no—
524C2×D13—42no—
525C2×D13—42no—
526C4×C13—24no—
527C4×C13—42no—
528C4×C13—42no—
529C4×C13—42no—
530C4×C13—42no—
531C4×C13—81no—
532C4×C13—81no—
533Dic13—24no—
534Dic13—42no—
535Dic13—42no—
536Dic13—42no—
537Dic13—42no—
538Dic13—81no—
539Dic13—81no—
540C25—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—134no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—262no—
550C23×C4—262no—
551C23×C4—262no—
552C23×C4—262no—
553C23×C4—521no—
554C23×C4—521no—
555C23×C4C22×D1311yescharacteristic
556C23×C4C22×D1311yescharacteristic
557C23×C4C22×D1311yescharacteristic
558C23×C4C22×D1311yescharacteristic
559C23×C4C22×D1311yescharacteristic
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—134no—
567C2×C4⋊C4—262no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4—262no—
570C2×C4⋊C4—262no—
571C2×C4⋊C4—262no—
572C2×C4⋊C4—521no—
573C2×C4⋊C4—521no—
574C2×C4⋊C4—521no—
575C2×C4⋊C4—521no—
576C2×C4⋊C4—521no—
577C2×C4⋊C4—521no—
578C2×C4⋊C4—521no—
579C2×C4⋊C4—521no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—134no—
583C2×C22⋊C4—262no—
584C2×C22⋊C4—262no—
585C2×C22⋊C4—262no—
586C2×C22⋊C4—262no—
587C2×C22⋊C4—262no—
588C2×C22⋊C4—521no—
589C2×C22⋊C4—521no—
590C2×C22⋊C4—521no—
591C2×C22⋊C4—521no—
592C2×C22⋊C4—521no—
593C2×C22⋊C4—521no—
594C2×C22⋊C4—521no—
595C2×C22⋊C4—521no—
596C2×C22⋊C4—521no—
597C2×C22⋊C4—521no—
598C2×C42—262no—
599C2×C42—521no—
600C2×C42—521no—
601C2×C42—521no—
602C2×C42—521no—
603C2×C42—521no—
604#95—22no—
605#95—22no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95—134no—
610#95—134no—
611#95—262no—
612#95—262no—
613#95—262no—
614#95—262no—
615#95—262no—
616#95—521no—
617#95—521no—
618#95—521no—
619#95—521no—
620#95—521no—
621#95—521no—
622#95—521no—
623#95C4×D1314yes—
624C2×C13#231411yescharacteristic
625C2×C13#232411yescharacteristic
626C2×C13#232911yescharacteristic
627C2×C13#234211yescharacteristic
628C2×C13#234511yescharacteristic
629C2×C13#236011yescharacteristic
630C2×C13#237711yescharacteristic
631C2×C13#269111yescharacteristic
632C2×C13#269211yescharacteristic
633C2×C13#270311yescharacteristic
634C2×C13#270411yescharacteristic
635C2×C13#274111yescharacteristic
636C2×C13#274211yescharacteristic
637C2×C13#274711yescharacteristic
638C2×C13#274811yescharacteristic
639D13—44no—
640C24—132no—
641C24—132no—
642C24—132no—
643C24—261no—
644C24—261no—
645C24—261no—
646C24—261no—
647C24—261no—
648C24—261no—
649C24—261no—
650C24—261no—
651C24—261no—
652C24—261no—
653C24—261no—
654C24—261no—
655C24C23×D1311yescharacteristic
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—132no—
705C22×C4—268no—
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—268no—
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×C4—261no—
748C22×C4—261no—
749C22×C4—524no—
750C22×C4—524no—
751C22×C4—524no—
752C22×C4—524no—
753C22×C4—524no—
754C22×C4C2×C4×D1312yes—
755C22×C4C2×C4×D1312yes—
756C22×C4C2×C4×D1312yes—
757C22×C4D4×D1312yes—
758C22×C4#612912yes—
759C22×C4Q8×D1312yes—
760C22×C4#613112yes—
761C4⋊C4—44no—
762C4⋊C4—268no—
763C4⋊C4—524no—
764C4⋊C4—524no—
765C4⋊C4—524no—
766C4⋊C4—524no—
767C22⋊C4—524no—
768C22⋊C4—524no—
769C22⋊C4—524no—
770C22⋊C4—524no—
771C22⋊C4—524no—
772C22⋊C4—524no—
773C42—524no—
774C42—524no—
775C13#1437011yescharacteristic, complemented, Sylow
776C23—134no—
777C23—262no—
778C23—262no—
779C23—262no—
780C23—262no—
781C23—262no—
782C23—262no—
783C23—262no—
784C23—262no—
785C23—262no—
786C23—262no—
787C23—262no—
788C23—262no—
789C23—262no—
790C23—262no—
791C23—262no—
792C23—262no—
793C23—262no—
794C23—262no—
795C23—521no—
796C23—521no—
797C23—521no—
798C23—521no—
799C23—521no—
800C23—521no—
801C23—521no—
802C23—521no—
803C23—521no—
804C23—521no—
805C23—521no—
806C23—521no—
807C23—521no—
808C23—521no—
809C23—521no—
810C23—521no—
811C23C22×C4×D1311yescharacteristic
812C23C2×D4×D1311yescharacteristic
813C23C2×#612911yescharacteristic
814C23#8825111yescharacteristic
815C23#8825111yescharacteristic
816C23C2×Q8×D1311yescharacteristic
817C23C2×#613111yescharacteristic
818C23#41×D1311yescharacteristic
819C23#41×D1311yescharacteristic
820C23#8825611yescharacteristic
821C23#8825611yescharacteristic
822C23#8825611yescharacteristic
823C23#8825611yescharacteristic
824C23#8825711yescharacteristic
825C23#8825711yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
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—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—134no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—262no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—5216no—
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—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4#8814614yes—
925C22—264no—
926C22—264no—
927C22—264no—
928C22—522no—
929C22—522no—
930C22—522no—
931C22—522no—
932C22—522no—
933C22—522no—
934C22—522no—
935C22—522no—
936C22—522no—
937C22—522no—
938C22—522no—
939C22—522no—
940C22C2×#8814611yescharacteristic
941C22#1171922811yescharacteristic
942C22#1171922811yescharacteristic
943C22C4×D4×D1311yescharacteristic
944C22#1171925011yescharacteristic
945C22#1171925011yescharacteristic
946C22C4×Q8×D1311yescharacteristic
947C22#1171929611yescharacteristic
948C22#1171930211yescharacteristic
949C22#1171931911yescharacteristic
950C22#1171932511yescharacteristic
951C22#1171933511yescharacteristic
952C22#1171933711yescharacteristic
953C22#1171933911yescharacteristic
954C22#1171934011yescharacteristic
955C22#1171934211yescharacteristic
956C22#1171935911yescharacteristic
957C22#1171936311yescharacteristic
958C22#1171936511yescharacteristic
959C22#1171936811yescharacteristic
960C22#1171937211yescharacteristic
961C22#1171937911yescharacteristic
962C22#1171938711yescharacteristic
963C22#1171938711yescharacteristic
964C22#1171938911yescharacteristic
965C22#1171939411yescharacteristic
966C22#1171939511yescharacteristic
967C22#1171940011yescharacteristic
968C22#1171940211yescharacteristic
969C22#1171940311yescharacteristic
970C22#1171940911yescharacteristic
971C22#1171941311yescharacteristic
972C22#1171941511yescharacteristic
973C22#1171941611yescharacteristic
974C22#1171943511yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—81no—
981C4—81no—
982C4—264no—
983C4—522no—
984C4—522no—
985C4—522no—
986C4—522no—
987C4—1041no—
988C4—1041no—
989C2—524no—
990C2#1311744611yescharacteristic
991C2#1311752411yescharacteristic
992C2#1311756311yescharacteristic
993C2#1311768311yescharacteristic
994C2#1311771211yescharacteristic
995C2#1311784411yescharacteristic
996C2#1311798911yescharacteristic
997C2#1312131611yescharacteristic
998C2#1312133111yescharacteristic
999C2#1312147811yescharacteristic
1000C2#1312149311yescharacteristic
1001C2#1312195311yescharacteristic
1002C2#1312196411yescharacteristic
1003C2#1312204111yescharacteristic
1004C2#1312204811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1442C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1442D13
hypocenterC13#14370
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×#11718316C2semidirect
4. #13113102C2semidirect
5. #13113101C2semidirect
6. #13113090C2semidirect
11. #13113070C2semidirect
12. #13113068C2semidirect
13. #13113067C2semidirect
15. C13×#1442C2semidirect
52. #11718328C4semidirect
279. #1442D13semidirect
775. C13#14370semidirect

Maximal subgroups

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

subgroupindex
C2×#117183162
C2×#117183282
C2×#117186482
#131131022
#131131012
#131130902
#131130822
#131130722
#131130702
#131130682
#131130672
#131130572
C13×#14422
#1437013