Finite Group Databasebeta

← #16022769

Subgroups — #16022769

Order 3328.

3420 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719258C211yesmaximal, characteristic
2C2×#11719227C212yesmaximal, complemented
3#13117900C211yesmaximal, characteristic, complemented
4#13117897C212yesmaximal, complemented
5#13117874C212yesmaximal, complemented
6#13117869C214yesmaximal, complemented
7#13117781C212yesmaximal, complemented
8#13117748C211yesmaximal, characteristic, complemented
9#13117673C212yesmaximal, complemented
10#13117400C212yesmaximal, complemented
11#13117398C211yesmaximal, characteristic, complemented
12#13117348C214yesmaximal, complemented
13#13117342C212yesmaximal, complemented
14C4×#88141C211yesmaximal, characteristic, complemented
15C4×D4×Dic13C211yesmaximal, characteristic, complemented
16C4×#88147C212yesmaximal, complemented
17C13×#2354C211yesmaximal, characteristic, complemented
18C22×#6127C2212yes—
19C2×C4×D4×C13C2211yescharacteristic
20C2×C13×#117C2212yes—
21C2×#88194C2212yes—
22C2×D4×Dic13C2211yescharacteristic
23C2×D4×Dic13C2211yescharacteristic
24C2×#88184C2212yes—
25C22×C4×Dic13C2212yes—
26#11719258C4116yescomplemented
27#11719227—216no—
28C2×#88147C2212yes—
29C2×#88147C2212yes—
30C2×#88147C2212yes—
31C2×#88147C2212yes—
32C2×#88147C2212yes—
33C2×#88141C2211yescharacteristic
34C2×#88141C2212yes—
35C2×#88141C2211yescharacteristic
36C2×#88138C2214yes—
37C2×#88135C2214yes—
38C2×#88135C2214yes—
39C2×#88135C2214yes—
40C2×#88128C2211yescharacteristic
41C2×C4×D52C2212yes—
42C2×#88126C2214yes—
43C2×C42×D13C2214yes—
44C2×C4×Dic26C2211yescharacteristic
45C13×#390C2212yes—
46C13×#388C2214yes—
47C13×#384C2211yescharacteristic
48C13×#380C2212yes—
49C4×C13×C4⋊C4C2211yescharacteristic
50C4×C13×C4⋊C4C2212yes—
51C4×C22⋊Dic13C2212yes—
52#11718649C2212yes—
53#11718649C2212yes—
54#11718649C2212yes—
55#11718649C2212yes—
56#11718637C2212yes—
57C4⋊C4×Dic13C2211yescharacteristic
58C4⋊C4×Dic13C2211yescharacteristic
59C4⋊C4×Dic13C2212yes—
60C4⋊C4×Dic13C2211yescharacteristic
61C4⋊C4×Dic13C2211yescharacteristic
62#11718634C2212yes—
63#11718633C2214yes—
64#11718619C2214yes—
65#11718618C2214yes—
66#11718618C2214yes—
67#11718618C2214yes—
68#11718617C2214yes—
69C22⋊C4×Dic13C2212yes—
70C22⋊C4×Dic13C2212yes—
71#11718601C2214yes—
72#11718600C2212yes—
73C4×#6103C2214yes—
74C4×C4⋊Dic13C2211yescharacteristic
75C4×#6101C2212yes—
76C42×Dic13C2211yescharacteristic
77C42×Dic13C2212yes—
78#11718330C2214yes—
79#11718328C2214yes—
80#11718327C2214yes—
81#11718327C2214yes—
82#11718326C2214yes—
83#11718310C2212yes—
84#11718310C2212yes—
85C22×D4×C13C2311yescharacteristic
86C23×C4×C13C2312yes—
87C22×C22⋊D13C2314yes—
88C22×C22⋊D13C2314yes—
89C23×Dic13C2312yes—
90C23×Dic13C2312yes—
91C2×#6127—28no—
92C2×#6127—28no—
93C2×#6127C2×C4116yescomplemented
94C22×D52C2312yes—
95C22×D52C2312yes—
96C22×D52C2312yes—
97C22×C4×D13C2314yes—
98C22×C4×D13C2314yes—
99C22×C4×D13C2314yes—
100C22×Dic26C2311yescharacteristic
101C4×D4×C13C2×C418yescomplemented
102C13×#117—28no—
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C4⋊C4C2312yes—
105C2×C13×C4⋊C4C2312yes—
106C2×C13×C4⋊C4C2312yes—
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2312yes—
112C2×C42×C13C2312yes—
113C2×C42×C13C2314yes—
114C2×C42×C13C2311yescharacteristic
115C2×C22⋊Dic13C2312yes—
116C2×C22⋊Dic13C2312yes—
117#88194C2×C4116yescomplemented
118D4×Dic13—24no—
119D4×Dic13—24no—
120#88184C2×C4116yescomplemented
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×C4⋊Dic13C2311yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2311yescharacteristic
131C2×#6101C2314yes—
132C2×#6101C2312yes—
133C2×#6101C2314yes—
134C2×#6101C2312yes—
135C2×#6101C2312yes—
136C2×C4×Dic13—28no—
137C2×C4×Dic13C2312yes—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2312yes—
140C2×C4×Dic13C2312yes—
141C2×C4×Dic13C2312yes—
142C2×C4×Dic13C2312yes—
143C2×C4×Dic13C2311yescharacteristic
144C2×C4×Dic13C2311yescharacteristic
145C2×C4×Dic13C2311yescharacteristic
146C2×C4×Dic13C2311yescharacteristic
147C2×C4×Dic13C2312yes—
148C2×C4×Dic13C2312yes—
149C2×C4×Dic13C2312yes—
150C2×C4×Dic13C2311yescharacteristic
151C2×C4×Dic13C2311yescharacteristic
152#88147—28no—
153#88147—28no—
154#88147—28no—
155#88147—44no—
156#88147C2×C4116yescomplemented
157#88141—28no—
158#88141—24no—
159#88141D418yescomplemented
160#88138C2×C4132yescomplemented
161#88135—216no—
162#88135—216no—
163#88135—48no—
164#88128C2×C418yescomplemented
165C4×D52—28no—
166#88126—216no—
167C42×D13—216no—
168C4×Dic26C2×C418yescomplemented
169C13×#95C2314yes—
170C13×#95C2312yes—
171#88071C2312yes—
172#88071C2312yes—
173#88071C2312yes—
174#88071C2312yes—
175#88071C2314yes—
176#88071C2312yes—
177C4×#550—131nomaximal, Sylow
178C24×C13C2412yes—
179C23×D13C2414yes—
180C2×D4×C13—22no—
181C2×D4×C13—22no—
182C2×D4×C13C22×C414yes—
183C22×C4×C13—24no—
184C22×C4×C13—24no—
185C22×C4×C13C22×C418yes—
186C22×C4×C13C2412yes—
187C22×C4×C13C2414yes—
188C22×C4×C13C2411yescharacteristic
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2411yescharacteristic
192C22×C4×C13C2411yescharacteristic
193C2×C22⋊D13—28no—
194C2×C22⋊D13—28no—
195C2×C22⋊D13—44no—
196C2×C22⋊D13—44no—
197C2×C22⋊D13C22×C4116yes—
198C2×C22⋊D13C22×C4116yes—
199C22×Dic13—24no—
200C22×Dic13—24no—
201C22×Dic13—24no—
202C22×Dic13—24no—
203C22×Dic13—24no—
204C22×Dic13—42no—
205C22×Dic13C2411yescharacteristic
206C22×Dic13C2412yes—
207C22×Dic13C2412yes—
208C22×Dic13C2411yescharacteristic
209C22×Dic13C2412yes—
210C22×Dic13C2411yescharacteristic
211C22×Dic13C2412yes—
212C22×Dic13C2411yescharacteristic
213#6127—264no—
214C2×D52—24no—
215C2×D52—24no—
216C2×D52—24no—
217C2×D52—24no—
218C2×D52—42no—
219C2×D52—42no—
220C2×D52C22×C418yes—
221C2×D52C22×C418yes—
222C2×D52C22×C418yes—
223C2×C4×D13—28no—
224C2×C4×D13—28no—
225C2×C4×D13—28no—
226C2×C4×D13—28no—
227C2×C4×D13—28no—
228C2×C4×D13—28no—
229C2×C4×D13—28no—
230C2×C4×D13—44no—
231C2×C4×D13C22×C4116yes—
232C2×Dic26C22×C414yes—
233C2×Dic26C2×D414yes—
234C2×Dic26#4114yes—
235C13×C4⋊C4—24no—
236C13×C4⋊C4—22no—
237C13×C4⋊C4—24no—
238C13×C4⋊C4—42no—
239C13×C4⋊C4C22×C414yes—
240C13×C4⋊C4C2×D414yes—
241C13×C22⋊C4—28no—
242C13×C22⋊C4—44no—
243C13×C22⋊C4C22×C418yes—
244C42×C13—28no—
245C42×C13—24no—
246C42×C13C22×C414yes—
247C22⋊Dic13—24no—
248C22⋊Dic13—24no—
249#6103—28no—
250#6103—28no—
251#6103—28no—
252#6103—28no—
253#6103—44no—
254#6103—44no—
255#6103C22×C4116yes—
256C4⋊Dic13—22no—
257C4⋊Dic13C22×C414yes—
258C4⋊Dic13#4114yescomplemented
259#6101—28no—
260#6101—24no—
261#6101—44no—
262#6101C22×C418yes—
263#6101C2×D418yes—
264C4×Dic13—24no—
265C4×Dic13—22no—
266C4×Dic13—22no—
267C4×Dic13—24no—
268C4×Dic13—28no—
269C4×Dic13—24no—
270C4×Dic13—24no—
271C4×Dic13—24no—
272C4×Dic13—22no—
273C4×Dic13—41no—
274C4×Dic13—42no—
275C4×Dic13C22×C418yes—
276C4×Dic13C2×D418yes—
277C4×Dic13C2×D414yes—
278C4×Dic13#4114yescomplemented
279C2×#550—131no—
280C2×C4×#41—132no—
281#2366—132no—
282#2366—131no—
283#2363—134no—
284#2363—132no—
285#2354—132no—
286#2354D1311yescharacteristic, complemented
287Q8×C4⋊C4—131no—
288#2341—132no—
289C4×#127—132no—
290C4×#127—131no—
291C4×#121—134no—
292C4×#121—132no—
293C42×Q8—131no—
294C42×D4—132no—
295C42×D4—131no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13C23×C414yes—
303C23×C13C2511yescharacteristic
304C22×D13—24no—
305C22×D13—24no—
306C22×D13—24no—
307C22×D13—24no—
308C22×D13—24no—
309C22×D13—24no—
310C22×D13C23×C418yes—
311D4×C13—28no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—21no—
316C2×C4×C13—22no—
317C2×C4×C13—21no—
318C2×C4×C13—216no—
319C2×C4×C13—24no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—24no—
323C2×C4×C13—22no—
324C2×C4×C13—24no—
325C2×C4×C13C23×C412yes—
326C2×C4×C13C23×C414yes—
327C2×C4×C13C23×C412yes—
328C2×C4×C13C23×C412yes—
329C2×C4×C13C22×D414yes—
330C2×C4×C13C22×D412yes—
331C2×C4×C13C2×#4112yes—
332C2×C4×C13C2×#4112yes—
333C2×C4×C13C2×#4112yes—
334C22⋊D13—232no—
335C22⋊D13—416no—
336C2×Dic13—22no—
337C2×Dic13—21no—
338C2×Dic13—21no—
339C2×Dic13—22no—
340C2×Dic13—21no—
341C2×Dic13—21no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—21no—
346C2×Dic13—21no—
347C2×Dic13—22no—
348C2×Dic13—21no—
349C2×Dic13—22no—
350C2×Dic13—48no—
351C2×Dic13—48no—
352C2×Dic13C23×C414yes—
353C2×Dic13C23×C414yes—
354C2×Dic13C22×D412yes—
355C2×Dic13C22×D414yes—
356C2×Dic13C22×D412yes—
357C2×Dic13C2×#4112yes—
358C2×Dic13C2×#4114yes—
359C2×Dic13C2×#4114yes—
360C2×Dic13C2×#4112yes—
361C2×Dic13H(5,𝔽2)12yes—
362D52—216no—
363D52—216no—
364D52—48no—
365C4×D13—232no—
366C4×D13—416no—
367C4×D13—416no—
368Dic26C4×D4116yescomplemented
369C22×#41—132no—
370#550—1316no—
371C2×#127—132no—
372C2×#127—131no—
373C2×#121—132no—
374C2×#121—134no—
375C4×#41—2616no—
376C2×C4×Q8—131no—
377C2×C4×Q8—131no—
378C2×C4×Q8—132no—
379C2×C4×Q8—131no—
380C2×C4×D4—131no—
381C2×C4×D4—131no—
382C2×C4×D4—132no—
383C2×C4×D4—132no—
384C2×C4×D4—132no—
385C2×C4×D4—132no—
386C2×C4×D4—132no—
387C2×C4×D4—134no—
388C2×C4×D4—134no—
389C2×C4×D4—134no—
390C2×C4×D4—132no—
391C2×C4×D4C2×D1311yescharacteristic
392C2×#117—134no—
393C2×#117C2×D1312yes—
394C22×C42—132no—
395C22×C42—134no—
396#390—132no—
397#390—132no—
398#390—132no—
399#390—132no—
400#390—134no—
401#390—134no—
402#390—134no—
403#390—132no—
404#390C2×D1312yes—
405#389—134no—
406#389—132no—
407#388—134no—
408#388—134no—
409#388C2×D1314yes—
410#386—134no—
411#386—134no—
412#386—134no—
413#384—132no—
414#384C2×D1311yescharacteristic
415#380—134no—
416#380C2×D1312yes—
417C4×C4⋊C4—132no—
418C4×C4⋊C4—131no—
419C4×C4⋊C4—131no—
420C4×C4⋊C4—131no—
421C4×C4⋊C4—131no—
422C4×C4⋊C4—131no—
423C4×C4⋊C4—132no—
424C4×C4⋊C4—132no—
425C4×C4⋊C4—132no—
426C4×C4⋊C4C2×D1312yes—
427C4×C4⋊C4C2×D1311yescharacteristic
428C4×C22⋊C4—132no—
429C4×C22⋊C4—132no—
430C4×C22⋊C4—132no—
431C4×C22⋊C4—134no—
432C4×C22⋊C4—134no—
433C4×C22⋊C4—134no—
434C43—132no—
435C43—131no—
436C22×C13—24no—
437C22×C13—24no—
438C22×C13—24no—
439C22×C13—42no—
440C22×C13—42no—
441C22×C13—42no—
442C22×C13—42no—
443C22×C13C24×C411yescharacteristic
444C22×C13C23×D411yescharacteristic
445C22×C13C22×#4111yescharacteristic
446C22×C13C22×#4111yescharacteristic
447C22×C13C22×#4111yescharacteristic
448C22×C13C2×H(5,𝔽2)11yescharacteristic
449C22×C13#58511yescharacteristic
450C2×D13—28no—
451C2×D13—28no—
452C2×D13—28no—
453C2×D13—44no—
454C2×D13—44no—
455C2×D13—44no—
456C2×D13—44no—
457C4×C13—24no—
458C4×C13—22no—
459C4×C13—24no—
460C4×C13—44no—
461C4×C13—42no—
462C4×C13C2×C4×D414yes—
463C4×C13C4×#4114yescomplemented
464Dic13—24no—
465Dic13—24no—
466Dic13—22no—
467Dic13—22no—
468Dic13—42no—
469Dic13—41no—
470Dic13C2×C4×D418yes—
471Dic13#55014yescomplemented
472C2×#41—1316no—
473C2×#41—268no—
474C2×#41—268no—
475C22×Q8—131no—
476C22×D4—134no—
477C22×D4—134no—
478C22×D4—132no—
479C22×D4—132no—
480C22×D4—132no—
481C22×D4C22×D1311yescharacteristic
482C23×C4—134no—
483C23×C4—132no—
484C23×C4—132no—
485C23×C4—134no—
486C23×C4—134no—
487C23×C4C22×D1312yes—
488#127—1316no—
489#127—138no—
490#121—1316no—
491#121—1332no—
492C4×Q8—138no—
493C4×Q8—138no—
494C4×Q8—268no—
495C4×Q8—264no—
496C4×D4—1316no—
497C4×D4—268no—
498C4×D4—2616no—
499C4×D4—268no—
500C4×D4—268no—
501C4×D4—264no—
502C4×D4—2616no—
503C4×D4—264no—
504C4×D4—268no—
505C4×D4—528no—
506C4×D4—524no—
507C4×D4C4×D1318yescomplemented
508#117—28no—
509#117—2616no—
510C2×C4⋊C4—132no—
511C2×C4⋊C4—131no—
512C2×C4⋊C4—132no—
513C2×C4⋊C4—131no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—131no—
516C2×C4⋊C4—132no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4C22×D1312yes—
519C2×C4⋊C4C22×D1312yes—
520C2×C4⋊C4C22×D1311yescharacteristic
521C2×C4⋊C4C22×D1312yes—
522C2×C4⋊C4C22×D1311yescharacteristic
523C2×C4⋊C4C22×D1311yescharacteristic
524C2×C22⋊C4—134no—
525C2×C22⋊C4—132no—
526C2×C22⋊C4—132no—
527C2×C22⋊C4—134no—
528C2×C22⋊C4—134no—
529C2×C22⋊C4—134no—
530C2×C22⋊C4—134no—
531C2×C22⋊C4—134no—
532C2×C22⋊C4—134no—
533C2×C22⋊C4C22×D1314yes—
534C2×C22⋊C4C22×D1314yes—
535C2×C22⋊C4C22×D1312yes—
536C2×C42—131no—
537C2×C42—132no—
538C2×C42—131no—
539C2×C42—132no—
540C2×C42—132no—
541C2×C42—132no—
542C2×C42—131no—
543C2×C42—134no—
544C2×C42—132no—
545C2×C42—131no—
546C2×C42—132no—
547C2×C42—131no—
548C2×C42—132no—
549C2×C42—132no—
550C2×C42—131no—
551C2×C42—2616no—
552C2×C42—268no—
553C2×C42C22×D1314yes—
554C2×C42C22×D1312yes—
555C2×C42C22×D1311yescharacteristic
556#95—132no—
557#95—132no—
558#95—134no—
559#95—132no—
560#95—132no—
561#95—132no—
562#95C22×D1314yes—
563#95C22×D1312yes—
564C2×C13—44no—
565C2×C13C22×C4×D411yescharacteristic
566C2×C13C2×C4×#4111yescharacteristic
567C2×C13C4×H(5,𝔽2)11yescharacteristic
568C2×C13C2×#55011yescharacteristic
569C2×C13D4×#4111yescharacteristic
570C2×C13#348011yescharacteristic
571C2×C13#348311yescharacteristic
572D13—48no—
573C24—134no—
574C24C23×D1312yes—
575#41—2664no—
576C2×Q8—134no—
577C2×Q8—134no—
578C2×Q8—134no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—1316no—
582C2×D4—1316no—
583C2×D4—138no—
584C2×D4—138no—
585C2×D4—138no—
586C2×D4—268no—
587C2×D4—268no—
588C2×D4—264no—
589C2×D4—264no—
590C2×D4—264no—
591C2×D4—264no—
592C2×D4—522no—
593C2×D4—522no—
594C2×D4—524no—
595C2×D4—524no—
596C2×D4C2×C4×D1314yes—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—131no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—131no—
604C22×C4—131no—
605C22×C4—1316no—
606C22×C4—131no—
607C22×C4—132no—
608C22×C4—268no—
609C22×C4—268no—
610C22×C4—268no—
611C22×C4—268no—
612C22×C4—268no—
613C22×C4—268no—
614C22×C4—264no—
615C22×C4—264no—
616C22×C4—264no—
617C22×C4—264no—
618C22×C4—264no—
619C22×C4—268no—
620C22×C4—524no—
621C22×C4—522no—
622C22×C4C2×C4×D1318yes—
623C22×C4C23×D1312yes—
624C22×C4C23×D1314yes—
625C22×C4C23×D1312yes—
626C22×C4C23×D1311yescharacteristic
627C22×C4C23×D1312yes—
628C22×C4C23×D1311yescharacteristic
629C22×C4C23×D1311yescharacteristic
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—42no—
634C4⋊C4—138no—
635C4⋊C4—134no—
636C4⋊C4—138no—
637C4⋊C4—134no—
638C4⋊C4—268no—
639C4⋊C4—264no—
640C4⋊C4—262no—
641C4⋊C4—524no—
642C4⋊C4C2×C4×D1314yes—
643C4⋊C4D4×D1314yes—
644C22⋊C4—28no—
645C22⋊C4—44no—
646C22⋊C4—1316no—
647C22⋊C4—268no—
648C22⋊C4—268no—
649C22⋊C4—268no—
650C22⋊C4—264no—
651C22⋊C4—264no—
652C22⋊C4—268no—
653C22⋊C4—524no—
654C22⋊C4—524no—
655C22⋊C4C2×C4×D1318yes—
656C42—28no—
657C42—24no—
658C42—138no—
659C42—138no—
660C42—134no—
661C42—134no—
662C42—264no—
663C42—264no—
664C42—268no—
665C42—262no—
666C42—264no—
667C42—264no—
668C42—264no—
669C42—262no—
670C42—262no—
671C42—522no—
672C42—521no—
673C42C2×C4×D1314yes—
674C13C4×#55011yescharacteristic, complemented, Sylow
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—138no—
682C23—264no—
683C23—264no—
684C23—264no—
685C23—264no—
686C23—264no—
687C23—264no—
688C23C22×C4×D1314yes—
689C23C24×D1311yescharacteristic
690Q8—1316no—
691D4—28no—
692D4—2632no—
693D4—2616no—
694D4—2616no—
695D4—528no—
696D4—5216no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—216no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—134no—
711C2×C4—132no—
712C2×C4—134no—
713C2×C4—132no—
714C2×C4—134no—
715C2×C4—132no—
716C2×C4—134no—
717C2×C4—132no—
718C2×C4—132no—
719C2×C4—134no—
720C2×C4—2632no—
721C2×C4—262no—
722C2×C4—261no—
723C2×C4—261no—
724C2×C4—262no—
725C2×C4—261no—
726C2×C4—261no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—261no—
731C2×C4—261no—
732C2×C4—262no—
733C2×C4—261no—
734C2×C4—262no—
735C2×C4—5216no—
736C2×C4—5216no—
737C2×C4—528no—
738C2×C4—528no—
739C2×C4C22×C4×D1312yes—
740C2×C4C22×C4×D1314yes—
741C2×C4C22×C4×D1312yes—
742C2×C4C22×C4×D1312yes—
743C2×C4C2×D4×D1314yes—
744C2×C4C2×D4×D1312yes—
745C2×C4#41×D1312yes—
746C2×C4#41×D1312yes—
747C2×C4#41×D1312yes—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—268no—
756C22—268no—
757C22—268no—
758C22—524no—
759C22—524no—
760C22—524no—
761C22—524no—
762C22C23×C4×D1311yescharacteristic
763C22C22×D4×D1311yescharacteristic
764C22C2×#41×D1311yescharacteristic
765C22C2×#41×D1311yescharacteristic
766C22C2×#41×D1311yescharacteristic
767C22D13×H(5,𝔽2)11yescharacteristic
768C22#1171965211yescharacteristic
769C4—24no—
770C4—22no—
771C4—24no—
772C4—42no—
773C4—44no—
774C4—138no—
775C4—134no—
776C4—264no—
777C4—262no—
778C4—264no—
779C4—262no—
780C4—521no—
781C4—522no—
782C4#1171922714yescomplemented
783C4C4×D4×D1314yes—
784C2—44no—
785C2—528no—
786C2C2×C4×D4×D1311yescharacteristic
787C2C2×#1171922711yescharacteristic
788C2#1312804211yescharacteristic
789C2D13×#55011yescharacteristic
790C2#1312832311yescharacteristic
791C2#1312842811yescharacteristic
792C2#1312846111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2354C2
socle, cosocleC23×C13C25
prime radicalC2×#11719258C2
hypercenter#2354D13
hypocenterC13C4×#550
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×#11719227C2semidirect
3. #13117900C2semidirect
4. #13117897C2semidirect
5. #13117874C2semidirect
6. #13117869C2semidirect
7. #13117781C2semidirect
8. #13117748C2semidirect
9. #13117673C2semidirect
10. #13117400C2semidirect
11. #13117398C2semidirect
12. #13117348C2semidirect
13. #13117342C2semidirect
14. C4×#88141C2semidirect
15. C4×D4×Dic13C2semidirect
16. C4×#88147C2semidirect
17. C13×#2354C2semidirect
26. #11719258C4semidirect
93. C2×#6127C2×C4semidirect
101. C4×D4×C13C2×C4semidirect
117. #88194C2×C4semidirect
120. #88184C2×C4semidirect
156. #88147C2×C4semidirect
159. #88141D4semidirect
160. #88138C2×C4semidirect
164. #88128C2×C4semidirect
168. C4×Dic26C2×C4semidirect
258. C4⋊Dic13#41semidirect
278. C4×Dic13#41semidirect
286. #2354D13semidirect
368. Dic26C4×D4semidirect
463. C4×C13C4×#41semidirect
471. Dic13#550semidirect
507. C4×D4C4×D13semidirect
674. C13C4×#550semidirect
782. C4#11719227semidirect

Maximal subgroups

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

subgroupindex
C2×#117192582
C2×#117192272
#131179002
#131178972
#131178742
#131178692
#131177812
#131177482
#131176732
#131174002
#131173982
#131173482
#131173422
C4×#881412
C4×D4×Dic132
C4×#881472
C13×#23542
C4×#55013