Finite Group Databasebeta

← #15790555

Subgroups — #15790555

Order 3328.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718651C211yesmaximal, characteristic
2C2×#11718650C211yesmaximal, characteristic
3C2×#11718325C211yesmaximal, characteristic
4C2×#11718648C211yesmaximal, characteristic
5#13113102C211yesmaximal, characteristic, complemented
6#13113095C211yesmaximal, characteristic, complemented
7#13113089C211yesmaximal, characteristic, complemented
8#13113086C211yesmaximal, characteristic, complemented
9#13113084C211yesmaximal, characteristic
10#13113078C211yesmaximal, characteristic
11#13113074C211yesmaximal, characteristic
12#13113070C211yesmaximal, characteristic, complemented
13#13113068C211yesmaximal, characteristic, complemented
14#13113063C211yesmaximal, characteristic, complemented
15C2×C13×#389C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#389—24no—
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
51C2×#88071C2211yescharacteristic
52#11718651—24no—
53#11718650C418yescomplemented
54#11718648—24no—
55#11718325—24no—
56C24×D13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C22×C4×D13—22no—
72C22×C4×D13—22no—
73C22×C4×D13—22no—
74C22×C4×D13—22no—
75C22×C4×D13—41no—
76C22×C4×D13—41no—
77C22×C4×D13C2×C414yes—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4—41no—
88C2×C13×C4⋊C4—41no—
89C2×C13×C4⋊C4C2×C414yes—
90C2×C42×C13—22no—
91C2×C42×C13—22no—
92C2×C42×C13—41no—
93C2×#6103—22no—
94C2×#6103—22no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×#6103—22no—
100C2×#6103—22no—
101C2×#6103—22no—
102C2×#6103—41no—
103C2×#6103—41no—
104C2×#6103—41no—
105C2×#6103—41no—
106C2×#6103—41no—
107C2×#6103—41no—
108C2×#6103C2×C414yes—
109C2×#6103C2×C414yes—
110C2×#6103D414yes—
111C2×C4⋊Dic13—22no—
112C2×C4⋊Dic13—22no—
113C2×C4⋊Dic13—41no—
114C2×#6101—41no—
115C2×#6101—41no—
116C2×#6101C2×C414yes—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13—41no—
120C13×#95—22no—
121C13×#95D414yes—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—41no—
132#88071—41no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071C2×C414yes—
139#88071C2×C414yes—
140#14382—131nomaximal, Sylow
141C24×C13C2411yescharacteristic
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×D13—21no—
153C23×D13—21no—
154C23×D13C22×C412yes—
155C23×D13C2×D412yes—
156C23×D13#4112yes—
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×C4×C13C2×D412yes—
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2×D412yes—
203C22×C4×C13#4112yes—
204C22×C4×C13#4112yes—
205C22×C4×C13#4112yes—
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×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C2×D412yes—
255C2×C4×D13—28no—
256C2×C4×D13—28no—
257C2×C4×D13—44no—
258C2×C4×D13—44no—
259C2×C4×D13—44no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C13×C4⋊C4—28no—
263C13×C4⋊C4—44no—
264C13×C4⋊C4—44no—
265C13×C4⋊C4—44no—
266C42×C13—44no—
267#6103—28no—
268#6103—28no—
269#6103—44no—
270#6103—44no—
271#6103—44no—
272#6103—44no—
273C4⋊Dic13—44no—
274#6101—44no—
275C4×Dic13—44no—
276C2×#389D1311yescharacteristic, complemented
277C2×#388—131no—
278C2×#385—131no—
279C2×#381—131no—
280C2×#380—131no—
281#1445—131no—
282#1442—131no—
283#1441—131no—
284#1441—131no—
285#1440—131no—
286#1439—131no—
287#1437—131no—
288#1436—131no—
289#1436—131no—
290#1434—131no—
291C23×C13C23×C411yescharacteristic
292C23×C13C22×D411yescharacteristic
293C23×C13C22×D411yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C23×C13C2×#4111yescharacteristic
296C23×C13C2×#4111yescharacteristic
297C23×C13C2×#4111yescharacteristic
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
304C23×C132−1+411yescharacteristic
305C23×C132−1+411yescharacteristic
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—22no—
323C22×D13—22no—
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×D13—41no—
339C22×D13—41no—
340C22×D13C4×D414yes—
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—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
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—41no—
388C2×C4×C13#11714yes—
389C2×C4×C13C4×D414yes—
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—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—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C4×D13—416no—
440C24×C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4C2×D1311yescharacteristic
444C22×C4⋊C4C2×D1311yescharacteristic
445C22×C4⋊C4C2×D1311yescharacteristic
446C22×C4⋊C4C2×D1311yescharacteristic
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C42—131no—
454C22×C42C2×D1311yescharacteristic
455#389—24no—
456#388—264no—
457#385—138no—
458#381—264no—
459#380—264no—
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×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95C2×D1311yescharacteristic
479C2×#95C2×D1311yescharacteristic
480C22×C13C2×#11711yescharacteristic
481C22×C13C2×C4×D411yescharacteristic
482C22×C13C2×C4×D411yescharacteristic
483C22×C13#51811yescharacteristic
484C22×C13#51911yescharacteristic
485C22×C13#52011yescharacteristic
486C22×C13#52011yescharacteristic
487C22×C13#53411yescharacteristic
488C22×C13#53611yescharacteristic
489C22×C13#53611yescharacteristic
490C22×C13#53711yescharacteristic
491C22×C13#53911yescharacteristic
492C22×C13#53911yescharacteristic
493C22×C13#54011yescharacteristic
494C22×C13#54011yescharacteristic
495C22×C13#54111yescharacteristic
496C22×C13#54211yescharacteristic
497C22×C13#54211yescharacteristic
498C22×C13#54211yescharacteristic
499C22×C13D4211yescharacteristic
500C22×C13#54611yescharacteristic
501C22×C13#54611yescharacteristic
502C22×C13#54611yescharacteristic
503C22×C13#54711yescharacteristic
504C22×C13#54711yescharacteristic
505C22×C13#54811yescharacteristic
506C22×C13#55111yescharacteristic
507C22×C13#55211yescharacteristic
508C22×C13#55211yescharacteristic
509C22×C13#55211yescharacteristic
510C22×C13#55311yescharacteristic
511C22×C13#56211yescharacteristic
512C22×C13#56211yescharacteristic
513C22×C13#56311yescharacteristic
514C22×C13#56311yescharacteristic
515C2×D13—24no—
516C2×D13—24no—
517C2×D13—24no—
518C2×D13—42no—
519C2×D13—42no—
520C2×D13—42no—
521C2×D13—42no—
522C2×D13—42no—
523C2×D13—42no—
524C2×D13—42no—
525C2×D13—42no—
526C2×D13—42no—
527C2×D13—42no—
528C2×D13—42no—
529C2×D13—42no—
530C4×C13—24no—
531C4×C13—24no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13—81no—
537Dic13—42no—
538Dic13—42no—
539Dic13—42no—
540Dic13—42no—
541Dic13—81no—
542Dic13—81no—
543Dic13—81no—
544C25—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—134no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—262no—
554C23×C4—262no—
555C23×C4—262no—
556C23×C4—262no—
557C23×C4—521no—
558C23×C4—521no—
559C23×C4C22×D1311yescharacteristic
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C23×C4C22×D1311yescharacteristic
564C23×C4C22×D1311yescharacteristic
565C23×C4C22×D1311yescharacteristic
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—134no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—521no—
581C2×C4⋊C4—521no—
582C2×C4⋊C4—521no—
583C2×C4⋊C4C4×D1314yes—
584C2×C22⋊C4—134no—
585C2×C22⋊C4—134no—
586C2×C22⋊C4—134no—
587C2×C22⋊C4—262no—
588C2×C22⋊C4—262no—
589C2×C22⋊C4—262no—
590C2×C22⋊C4—262no—
591C2×C22⋊C4—262no—
592C2×C22⋊C4—262no—
593C2×C22⋊C4—262no—
594C2×C22⋊C4—262no—
595C2×C22⋊C4—262no—
596C2×C22⋊C4—521no—
597C2×C22⋊C4—521no—
598C2×C22⋊C4—521no—
599C2×C22⋊C4—521no—
600C2×C22⋊C4—521no—
601C2×C22⋊C4—521no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—41no—
605C2×C42—262no—
606C2×C42—521no—
607C2×C42—521no—
608#95—22no—
609#95—134no—
610#95—134no—
611#95—262no—
612#95—262no—
613#95—262no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—521no—
621#95—521no—
622#95—521no—
623#95—521no—
624#95—521no—
625#95—521no—
626#95—521no—
627#95C22⋊D1314yes—
628C2×C13#231911yescharacteristic
629C2×C13#232211yescharacteristic
630C2×C13#232311yescharacteristic
631C2×C13#234411yescharacteristic
632C2×C13#235211yescharacteristic
633C2×C13#235811yescharacteristic
634C2×C13#237811yescharacteristic
635C2×C13#267111yescharacteristic
636C2×C13#267411yescharacteristic
637C2×C13#268711yescharacteristic
638C2×C13#269811yescharacteristic
639C2×C13#270111yescharacteristic
640C2×C13#270711yescharacteristic
641C2×C13#273811yescharacteristic
642C2×C13#273911yescharacteristic
643D13—44no—
644C24—132no—
645C24—132no—
646C24—132no—
647C24—261no—
648C24—261no—
649C24—261no—
650C24—261no—
651C24—261no—
652C24—261no—
653C24—261no—
654C24—261no—
655C24—261no—
656C24—261no—
657C24—261no—
658C24—261no—
659C24C23×D1311yescharacteristic
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—21no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—268no—
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—268no—
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×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—524no—
751C22×C4—524no—
752C22×C4—524no—
753C22×C4—524no—
754C22×C4—524no—
755C22×C4C2×C4×D1312yes—
756C22×C4C2×C4×D1312yes—
757C22×C4C2×C4×D1312yes—
758C22×C4#612712yes—
759C22×C4D4×D1312yes—
760C22×C4#612912yes—
761C22×C4#613112yes—
762C22×C4C2×C22⋊D1312yes—
763C22×C4C2×C22⋊D1312yes—
764C22×C4C2×C22⋊D1312yes—
765C4⋊C4—28no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—524no—
770C4⋊C4—524no—
771C22⋊C4—268no—
772C22⋊C4—268no—
773C22⋊C4—524no—
774C22⋊C4—524no—
775C22⋊C4—524no—
776C22⋊C4—524no—
777C42—44no—
778C42—524no—
779C13#1438211yescharacteristic, complemented, Sylow
780C23—134no—
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—262no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—521no—
800C23—521no—
801C23—521no—
802C23—521no—
803C23—521no—
804C23—521no—
805C23—521no—
806C23—521no—
807C23—521no—
808C23—521no—
809C23—521no—
810C23—521no—
811C23—521no—
812C23—521no—
813C23—521no—
814C23—521no—
815C23C22×C4×D1311yescharacteristic
816C23C2×#612711yescharacteristic
817C23C2×D4×D1311yescharacteristic
818C23C2×#612911yescharacteristic
819C23#8825111yescharacteristic
820C23#8825111yescharacteristic
821C23C2×#613111yescharacteristic
822C23#8825411yescharacteristic
823C23#8825411yescharacteristic
824C23#8825411yescharacteristic
825C23#41×D1311yescharacteristic
826C23#8825611yescharacteristic
827C23#8825611yescharacteristic
828C23#8825711yescharacteristic
829C23C22×C22⋊D1311yescharacteristic
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—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
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—41no—
875C2×C4—41no—
876C2×C4—41no—
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—5216no—
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—
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—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4#8814614yes—
928C2×C4C4×C22⋊D1314yes—
929C22—264no—
930C22—264no—
931C22—264no—
932C22—522no—
933C22—522no—
934C22—522no—
935C22—522no—
936C22—522no—
937C22—522no—
938C22—522no—
939C22—522no—
940C22—522no—
941C22—522no—
942C22—522no—
943C22—522no—
944C22C2×#8814611yescharacteristic
945C22#1171920911yescharacteristic
946C22#1171921811yescharacteristic
947C22#1171921911yescharacteristic
948C22C4×D4×D1311yescharacteristic
949C22#1171925011yescharacteristic
950C22#1171925511yescharacteristic
951C22#1171926111yescharacteristic
952C22#1171927711yescharacteristic
953C22#1171927911yescharacteristic
954C22#1171928711yescharacteristic
955C22#1171928811yescharacteristic
956C22#1171931011yescharacteristic
957C22#1171931611yescharacteristic
958C22#1171932411yescharacteristic
959C22#1171932611yescharacteristic
960C22#1171934311yescharacteristic
961C22#1171934411yescharacteristic
962C22#1171934811yescharacteristic
963C22#1171935211yescharacteristic
964C22#1171939711yescharacteristic
965C22#1171939911yescharacteristic
966C22#1171940311yescharacteristic
967C22#1171940411yescharacteristic
968C22#1171942911yescharacteristic
969C22#1171943111yescharacteristic
970C22#1171943811yescharacteristic
971C22#1171944011yescharacteristic
972C22C2×C4×C22⋊D1311yescharacteristic
973C22D4×C22⋊D1311yescharacteristic
974C22#1171951111yescharacteristic
975C22#1171952111yescharacteristic
976C22#1171952211yescharacteristic
977C22#1171953411yescharacteristic
978C22#1171953811yescharacteristic
979C4—24no—
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—522no—
987C4—522no—
988C4—522no—
989C4—522no—
990C4—1041no—
991C4—1041no—
992C4—1041no—
993C2—524no—
994C2#1311747511yescharacteristic
995C2#1311750011yescharacteristic
996C2#1311751211yescharacteristic
997C2#1311770411yescharacteristic
998C2#1311776111yescharacteristic
999C2#1311781311yescharacteristic
1000C2#1311799811yescharacteristic
1001C2#1312106711yescharacteristic
1002C2#1312111211yescharacteristic
1003C2#1312125311yescharacteristic
1004C2#1312140511yescharacteristic
1005C2#1312144411yescharacteristic
1006C2#1312153311yescharacteristic
1007C2#1312190911yescharacteristic
1008C2#1312192411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13#14382
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
5. #13113102C2semidirect
6. #13113095C2semidirect
7. #13113089C2semidirect
8. #13113086C2semidirect
12. #13113070C2semidirect
13. #13113068C2semidirect
14. #13113063C2semidirect
15. C2×C13×#389C2semidirect
53. #11718650C4semidirect
276. C2×#389D13semidirect
779. C13#14382semidirect

Maximal subgroups

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

subgroupindex
C2×#117186512
C2×#117186502
C2×#117183252
C2×#117186482
#131131022
#131130952
#131130892
#131130862
#131130842
#131130782
#131130742
#131130702
#131130682
#131130632
C2×C13×#3892
#1438213