Finite Group Databasebeta

← #15790995

Subgroups — #15790995

Order 3328.

1498 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718601C211yesmaximal, characteristic
2C2×#11718651C211yesmaximal, characteristic
3C2×#11718651C211yesmaximal, characteristic
4C2×#11718639C211yesmaximal, characteristic, complemented
5#13113095C211yesmaximal, characteristic, complemented
6#13113086C211yesmaximal, characteristic, complemented
7#13113078C211yesmaximal, characteristic
8#13113078C211yesmaximal, characteristic
9#13113078C211yesmaximal, characteristic
10#13113078C211yesmaximal, characteristic
11#13113068C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113068C211yesmaximal, characteristic, complemented
14#13113063C211yesmaximal, characteristic, complemented
15C2×C13×#384C211yesmaximal, characteristic, complemented
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C13×#384—24no—
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#11718651—24no—
54#11718639—24no—
55#11718601C418yescomplemented
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
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
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×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C4⋊C4—41no—
85C2×C13×C4⋊C4—41no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4—41no—
88C2×C13×C4⋊C4D414yes—
89C2×C42×C13—22no—
90C2×C42×C13—22no—
91C2×C42×C13C2×C414yes—
92C2×#6103—22no—
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×#6103—41no—
109C2×#6103—41no—
110C2×#6103C2×C414yes—
111C2×#6103C2×C414yes—
112C2×#6103C2×C414yes—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101C2×C414yes—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—41no—
120C2×C4×Dic13—41no—
121C2×C4×Dic13—41no—
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—22no—
132#88071—41no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071C2×C414yes—
138#88071C2×C414yes—
139#88071D414yes—
140#14413—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×D13—21no—
155C23×D13—21no—
156C23×D13C22×C412yes—
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×C13C22×C412yes—
196C22×C4×C13C22×C412yes—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C2×D412yes—
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2×D412yes—
202C22×C4×C13#4112yes—
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×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13C2×D412yes—
255C13×C4⋊C4—44no—
256C13×C4⋊C4—44no—
257C13×C4⋊C4—44no—
258C13×C4⋊C4—44no—
259C13×C4⋊C4—44no—
260C13×C4⋊C4—44no—
261C42×C13—28no—
262#6103—28no—
263#6103—28no—
264#6103—28no—
265#6103—44no—
266#6103—44no—
267#6103—44no—
268#6103—44no—
269#6101—28no—
270C4×Dic13—44no—
271C4×Dic13—44no—
272C2×#388—131no—
273C2×#388—131no—
274C2×#388—131no—
275C2×#387—131no—
276C2×#384D1311yescharacteristic, complemented
277#1442—131no—
278#1441—131no—
279#1439—131no—
280#1439—131no—
281#1439—131no—
282#1439—131no—
283#1436—131no—
284#1436—131no—
285#1436—131no—
286#1434—131no—
287C23×C13C23×C411yescharacteristic
288C23×C13C22×D411yescharacteristic
289C23×C13C22×D411yescharacteristic
290C23×C13C2×#4111yescharacteristic
291C23×C13C2×#4111yescharacteristic
292C23×C13C2×#4111yescharacteristic
293C23×C13C2×#4111yescharacteristic
294C23×C13H(5,𝔽2)11yescharacteristic
295C23×C13H(5,𝔽2)11yescharacteristic
296C23×C13H(5,𝔽2)11yescharacteristic
297C23×C13H(5,𝔽2)11yescharacteristic
298C23×C132−1+411yescharacteristic
299C23×C132−1+411yescharacteristic
300C23×C132−1+411yescharacteristic
301C23×C132−1+411yescharacteristic
302C22×D13—22no—
303C22×D13—22no—
304C22×D13—22no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
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—
333C22×D13—41no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
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—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—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#11714yes—
384C2×C4×C13C4×D414yes—
385C2×C4×C13C4×D414yes—
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—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
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—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C22×C4⋊C4—131no—
436C22×C4⋊C4C2×D1311yescharacteristic
437C22×C4⋊C4C2×D1311yescharacteristic
438C22×C4⋊C4C2×D1311yescharacteristic
439C22×C4⋊C4C2×D1311yescharacteristic
440C22×C4⋊C4C2×D1311yescharacteristic
441C22×C4⋊C4C2×D1311yescharacteristic
442C22×C22⋊C4—131no—
443C22×C22⋊C4—131no—
444C22×C22⋊C4—131no—
445C22×C22⋊C4—131no—
446C22×C22⋊C4—131no—
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C42—131no—
450C22×C42—131no—
451C22×C42C2×D1311yescharacteristic
452#388—138no—
453#388—264no—
454#388—264no—
455#387—264no—
456#384—24no—
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×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C22×C13C2×#11711yescharacteristic
476C22×C13C2×C4×D411yescharacteristic
477C22×C13C2×C4×D411yescharacteristic
478C22×C13#52011yescharacteristic
479C22×C13#52011yescharacteristic
480C22×C13#52011yescharacteristic
481C22×C13#52011yescharacteristic
482C22×C13#53411yescharacteristic
483C22×C13#53511yescharacteristic
484C22×C13#53611yescharacteristic
485C22×C13#53611yescharacteristic
486C22×C13#53911yescharacteristic
487C22×C13#53911yescharacteristic
488C22×C13#54011yescharacteristic
489C22×C13#54111yescharacteristic
490C22×C13#54211yescharacteristic
491C22×C13#54211yescharacteristic
492C22×C13#54211yescharacteristic
493C22×C13#54211yescharacteristic
494C22×C13D4211yescharacteristic
495C22×C13#54611yescharacteristic
496C22×C13#54711yescharacteristic
497C22×C13#54711yescharacteristic
498C22×C13#54811yescharacteristic
499C22×C13#54811yescharacteristic
500C22×C13#55011yescharacteristic
501C22×C13#55211yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55511yescharacteristic
505C22×C13#55611yescharacteristic
506C22×C13#56011yescharacteristic
507C22×C13#56311yescharacteristic
508C22×C13#56311yescharacteristic
509C22×C13#56311yescharacteristic
510C2×D13—42no—
511C2×D13—42no—
512C2×D13—42no—
513C2×D13—42no—
514C2×D13—42no—
515C2×D13—42no—
516C2×D13—42no—
517C2×D13—81no—
518C2×D13—81no—
519C2×D13—81no—
520C2×D13—81no—
521C2×D13—81no—
522C2×D13—81no—
523C2×D13—81no—
524C2×D13—81no—
525C4×C13—24no—
526C4×C13—24no—
527C4×C13—24no—
528C4×C13—42no—
529C4×C13—42no—
530C4×C13—81no—
531C4×C13—81no—
532Dic13—42no—
533Dic13—42no—
534Dic13—42no—
535Dic13—42no—
536Dic13—42no—
537Dic13—81no—
538Dic13—81no—
539C25—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—134no—
572C2×C4⋊C4—262no—
573C2×C4⋊C4—262no—
574C2×C4⋊C4C22⋊D1314yes—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—262no—
580C2×C22⋊C4—262no—
581C2×C22⋊C4—262no—
582C2×C22⋊C4—262no—
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×C42—22no—
597C2×C42—22no—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—262no—
601C2×C42—521no—
602C2×C42—521no—
603C2×C42—521no—
604C2×C42C4×D1314yes—
605#95—134no—
606#95—134no—
607#95—134no—
608#95—262no—
609#95—262no—
610#95—262no—
611#95—262no—
612#95—262no—
613#95—262no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—521no—
619#95—521no—
620#95—521no—
621#95—521no—
622#95—521no—
623C2×C13#231411yescharacteristic
624C2×C13#232211yescharacteristic
625C2×C13#232611yescharacteristic
626C2×C13#235211yescharacteristic
627C2×C13#235411yescharacteristic
628C2×C13#236111yescharacteristic
629C2×C13#238311yescharacteristic
630C2×C13#267311yescharacteristic
631C2×C13#267411yescharacteristic
632C2×C13#271611yescharacteristic
633C2×C13#271811yescharacteristic
634C2×C13#272111yescharacteristic
635C2×C13#273111yescharacteristic
636C2×C13#279311yescharacteristic
637C2×C13#279511yescharacteristic
638D13—82no—
639C24—132no—
640C24—261no—
641C24—261no—
642C24—261no—
643C24—261no—
644C24—261no—
645C24—261no—
646C24—261no—
647C24—261no—
648C24—261no—
649C24—261no—
650C24—261no—
651C24—261no—
652C24—261no—
653C24—261no—
654C24C23×D1311yescharacteristic
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—132no—
694C22×C4—132no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—132no—
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—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4C2×C4×D1312yes—
743C22×C4C2×C4×D1312yes—
744C22×C4C2×C4×D1312yes—
745C22×C4#612712yes—
746C22×C4D4×D1312yes—
747C22×C4#612912yes—
748C22×C4#613112yes—
749C22×C4#613112yes—
750C22×C4C2×C22⋊D1312yes—
751C22×C4C2×C22⋊D1312yes—
752C22×C4C2×C22⋊D1312yes—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—268no—
760C22⋊C4—268no—
761C22⋊C4—268no—
762C22⋊C4—268no—
763C22⋊C4—524no—
764C22⋊C4—524no—
765C22⋊C4—524no—
766C22⋊C4—524no—
767C42—28no—
768C42—524no—
769C42—524no—
770C13#1441311yescharacteristic, complemented, Sylow
771C23—262no—
772C23—262no—
773C23—262no—
774C23—262no—
775C23—262no—
776C23—262no—
777C23—262no—
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—
799C23—521no—
800C23—521no—
801C23—521no—
802C23—521no—
803C23—521no—
804C23—521no—
805C23—521no—
806C23C22×C4×D1311yescharacteristic
807C23C2×#612711yescharacteristic
808C23C2×D4×D1311yescharacteristic
809C23C2×#612911yescharacteristic
810C23#8825111yescharacteristic
811C23#8825111yescharacteristic
812C23#8825111yescharacteristic
813C23#8825111yescharacteristic
814C23C2×#613111yescharacteristic
815C23C2×#613111yescharacteristic
816C23#8825411yescharacteristic
817C23#8825411yescharacteristic
818C23#8825411yescharacteristic
819C23#8825411yescharacteristic
820C23C22×C22⋊D1311yescharacteristic
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—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—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—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—262no—
881C2×C4—262no—
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—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4#8814614yes—
917C2×C4#8814714yes—
918C2×C4C4×C22⋊D1314yes—
919C22—522no—
920C22—522no—
921C22—522no—
922C22—522no—
923C22—522no—
924C22—522no—
925C22—522no—
926C22—1041no—
927C22—1041no—
928C22—1041no—
929C22—1041no—
930C22—1041no—
931C22—1041no—
932C22—1041no—
933C22—1041no—
934C22C2×#8814611yescharacteristic
935C22C2×#8814711yescharacteristic
936C22#1171920911yescharacteristic
937C22#1171920911yescharacteristic
938C22#1171920911yescharacteristic
939C22#1171920911yescharacteristic
940C22#1171921211yescharacteristic
941C22#1171921811yescharacteristic
942C22#1171921911yescharacteristic
943C22#1171921911yescharacteristic
944C22#1171922011yescharacteristic
945C22#1171922011yescharacteristic
946C22#1171942011yescharacteristic
947C22#1171942311yescharacteristic
948C22#1171942411yescharacteristic
949C22#1171942511yescharacteristic
950C22#1171942911yescharacteristic
951C22#1171943111yescharacteristic
952C22#1171943611yescharacteristic
953C22#1171943711yescharacteristic
954C22#1171943811yescharacteristic
955C22#1171943811yescharacteristic
956C22#1171943811yescharacteristic
957C22#1171943811yescharacteristic
958C22#1171943911yescharacteristic
959C22#1171944011yescharacteristic
960C22#1171944011yescharacteristic
961C22#1171944011yescharacteristic
962C22C2×C4×C22⋊D1311yescharacteristic
963C22D4×C22⋊D1311yescharacteristic
964C22#1171950911yescharacteristic
965C22#1171951111yescharacteristic
966C22#1171952111yescharacteristic
967C22#1171952211yescharacteristic
968C22#1171952211yescharacteristic
969C4—24no—
970C4—24no—
971C4—24no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—81no—
976C4—522no—
977C4—522no—
978C4—522no—
979C4—522no—
980C4—522no—
981C4—1041no—
982C4—1041no—
983C2—1042no—
984C2#1311744411yescharacteristic
985C2#1311750511yescharacteristic
986C2#1311754411yescharacteristic
987C2#1311776111yescharacteristic
988C2#1311778711yescharacteristic
989C2#1311785211yescharacteristic
990C2#1311802911yescharacteristic
991C2#1312109611yescharacteristic
992C2#1312111211yescharacteristic
993C2#1312165611yescharacteristic
994C2#1312168111yescharacteristic
995C2#1312172611yescharacteristic
996C2#1312184211yescharacteristic
997C2#1312264111yescharacteristic
998C2#1312266511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#384C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#384D13
hypocenterC13#14413
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
4. C2×#11718639C2semidirect
5. #13113095C2semidirect
6. #13113086C2semidirect
11. #13113068C2semidirect
12. #13113068C2semidirect
13. #13113068C2semidirect
14. #13113063C2semidirect
15. C2×C13×#384C2semidirect
55. #11718601C4semidirect
276. C2×#384D13semidirect
770. C13#14413semidirect

Maximal subgroups

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

subgroupindex
C2×#117186012
C2×#117186512
C2×#117186392
#131130952
#131130862
#131130782
#131130682
#131130632
C2×C13×#3842
#1441313