Finite Group Databasebeta

← #15878423

Subgroups — #15878423

Order 3328.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719257C211yesmaximal, characteristic
2C2×#11718672C211yesmaximal, characteristic, complemented
3C2×#11718627C211yesmaximal, characteristic, complemented
4C22×#88050C211yesmaximal, characteristic, complemented
5#13115768C211yesmaximal, characteristic, complemented
6#13115650C211yesmaximal, characteristic, complemented
7#13115267C211yesmaximal, characteristic, complemented
8#13115262C211yesmaximal, characteristic, complemented
9#13115153C211yesmaximal, characteristic, complemented
10#13115143C211yesmaximal, characteristic, complemented
11#13114838C211yesmaximal, characteristic, complemented
12#13114774C211yesmaximal, characteristic, complemented
13#13114770C211yesmaximal, characteristic, complemented
14#13114669C211yesmaximal, characteristic, complemented
15D4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C2×C4×D4×C13—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C2×#88193—21no—
23C2×#88184C2211yescharacteristic
24C2×#88178C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26C23×#1055C2211yescharacteristic
27#11719257—24no—
28#11719257C418yescomplemented
29C2×#88150—21no—
30C2×#88139—21no—
31C2×#88135—21no—
32C2×#88129C2211yescharacteristic
33C2×C4×Dic26C2211yescharacteristic
34C13×#389—21no—
35C13×#385—21no—
36C13×#385—21no—
37C13×#384C2211yescharacteristic
38C13×#380C2211yescharacteristic
39C13×#380C2211yescharacteristic
40C4×C13×C4⋊C4C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718672—24no—
44C2×#88050—24no—
45C2×#88050C2211yescharacteristic
46C2×#88050C2211yescharacteristic
47C2×#88050C2211yescharacteristic
48C2×#88050C2211yescharacteristic
49C2×#88050C2211yescharacteristic
50C2×#88050C2211yescharacteristic
51C2×#88050C2211yescharacteristic
52C2×#88050C2211yescharacteristic
53#11718627—24no—
54C2×#88049C2211yescharacteristic
55C2×#88049C2211yescharacteristic
56C2×#88049C2211yescharacteristic
57C2×#88049C2211yescharacteristic
58C2×C4⋊#1055C2211yescharacteristic
59C2×#88043C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718121C2211yescharacteristic
63#11718121C2211yescharacteristic
64C22×D4×C13D411yescharacteristic
65C23×C4×C13—21no—
66C23×C4×C13—21no—
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C22×C22⋊D13—21no—
70C22×C22⋊D13—21no—
71C23×Dic13—21no—
72C2×#6127—22no—
73C2×#6127—22no—
74C2×#6127—22no—
75C2×#6127—41no—
76C2×#6127—41no—
77C2×#6127C2×C414yescomplemented
78C22×D52C2311yescharacteristic
79C22×C4×D13—21no—
80C22×Dic26—22no—
81C22×Dic26—22no—
82C22×Dic26—21no—
83C22×Dic26—22no—
84C22×Dic26—41no—
85C22×Dic26—41no—
86C22×Dic26C2×C414yescomplemented
87C22×Dic26C2311yescharacteristic
88C22×Dic26C2311yescharacteristic
89C4×D4×C13—44no—
90C4×D4×C13C2×C414yes—
91C4×D4×C13D414yes—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4D411yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C22⋊C4—21no—
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4D411yescharacteristic
108C2×C13×C22⋊C4D411yescharacteristic
109C2×C42×C13—21no—
110C2×C42×C13C2311yescharacteristic
111C2×C22⋊Dic13—21no—
112#88193—28no—
113#88184—22no—
114#88184C2×C414yescomplemented
115C2×#6103—21no—
116C2×#6103—21no—
117C2×#6103—21no—
118C2×C4⋊Dic13C2311yescharacteristic
119#88178—22no—
120#88178C2×C414yescomplemented
121C2×#6101—21no—
122C2×#6101—21no—
123C2×C4×Dic13—21no—
124C2×#6099—22no—
125C2×#6099—22no—
126C2×#6099—41no—
127C22×#1055—22no—
128C22×#1055—22no—
129C22×#1055—41no—
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C22×#1055C2311yescharacteristic
133C22×#1055C2311yescharacteristic
134#88150—28no—
135#88139—28no—
136#88135—28no—
137#88129—22no—
138#88129C2×C414yescomplemented
139C4×Dic26—22no—
140C4×Dic26C2×C414yescomplemented
141C13×#95—21no—
142C13×#95—21no—
143C13×#95—21no—
144C22⋊#1055—22no—
145C22⋊#1055—22no—
146#88050—22no—
147#88050—22no—
148#88050—22no—
149#88050—22no—
150#88050—22no—
151#88050—41no—
152#88050—41no—
153#88050D414yescomplemented
154#88049—22no—
155#88049—22no—
156#88049—41no—
157#88049—41no—
158C4⋊#1055—22no—
159#88043—22no—
160#22421—131nomaximal, Sylow
161C24×C13C2×D411yescharacteristic
162C24×C13C2×D411yescharacteristic
163C23×D13—21no—
164C2×D4×C13—22no—
165C2×D4×C13—22no—
166C2×D4×C13C22⋊C414yes—
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—42no—
180C22×C4×C13—42no—
181C22×C4×C13—42no—
182C22×C4×C13—42no—
183C22×C4×C13—81no—
184C22×C4×C13—81no—
185C22×C4×C13C22×C412yes—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C2×D412yes—
188C22×C4×C13C2×D412yes—
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2411yescharacteristic
194C2×C22⋊D13—24no—
195C2×C22⋊D13—24no—
196C2×C22⋊D13—42no—
197C2×C22⋊D13—42no—
198C2×C22⋊D13—42no—
199C2×C22⋊D13—42no—
200C22×Dic13—21no—
201C22×Dic13—24no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—42no—
205C22×Dic13—42no—
206#6127—28no—
207#6127—44no—
208#6127—44no—
209#6127—44no—
210C2×D52—21no—
211C2×D52—21no—
212C2×D52—21no—
213C2×D52—21no—
214C2×D52—21no—
215C2×D52C22×C412yes—
216C2×C4×D13—24no—
217C2×C4×D13—42no—
218C2×C4×D13—42no—
219C2×Dic26—21no—
220C2×Dic26—21no—
221C2×Dic26—21no—
222C2×Dic26—21no—
223C2×Dic26—21no—
224C2×Dic26—21no—
225C2×Dic26—21no—
226C2×Dic26—28no—
227C2×Dic26—24no—
228C2×Dic26—21no—
229C2×Dic26—44no—
230C2×Dic26—44no—
231C2×Dic26—44no—
232C2×Dic26—42no—
233C2×Dic26—42no—
234C2×Dic26C22×C412yes—
235C2×Dic26C22×C412yes—
236C2×Dic26C2×D412yes—
237C2×Dic26#4112yes—
238C13×C4⋊C4—21no—
239C13×C4⋊C4—21no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4—21no—
242C13×C4⋊C4—21no—
243C13×C4⋊C4—21no—
244C13×C4⋊C4—21no—
245C13×C4⋊C4—42no—
246C13×C4⋊C4—42no—
247C13×C4⋊C4—42no—
248C13×C4⋊C4—81no—
249C13×C4⋊C4C22⋊C414yes—
250C13×C4⋊C4C2×D412yes—
251C13×C22⋊C4—42no—
252C13×C22⋊C4—42no—
253C13×C22⋊C4C22⋊C414yes—
254C13×C22⋊C4C22⋊C414yes—
255C42×C13—42no—
256C42×C13C22×C412yes—
257C42×C13C2×D412yes—
258C22⋊Dic13—24no—
259#6103—24no—
260#6103—24no—
261#6103—24no—
262C4⋊Dic13—21no—
263C4⋊Dic13C22×C412yes—
264#6101—24no—
265#6101—24no—
266C4×Dic13—24no—
267#6099—44no—
268C2×#1055—21no—
269C2×#1055—21no—
270C2×#1055—21no—
271C2×#1055—21no—
272C2×#1055—21no—
273C2×#1055—21no—
274C2×#1055—21no—
275C2×#1055—21no—
276C2×#1055—21no—
277C2×#1055—21no—
278C2×#1055—21no—
279C2×#1055—44no—
280C2×#1055C2×D412yes—
281C2×#548—131no—
282C2×#435—131no—
283C2×#417—131no—
284C22×#103—131no—
285D4×C4⋊C4D1311yescharacteristic, complemented
286#1983—131no—
287#1959—131no—
288#1894—131no—
289#1893—131no—
290#1874—131no—
291#1872—131no—
292#1803—131no—
293#1788—131no—
294#1787—131no—
295#1763—131no—
296C23×C13—21no—
297C23×C13—21no—
298C23×C13—21no—
299C23×C13—21no—
300C23×C13—21no—
301C23×C13—21no—
302C23×C13—21no—
303C23×C13—21no—
304C23×C13—21no—
305C23×C13—21no—
306C23×C13C2×C22⋊C412yes—
307C23×C13C2×C22⋊C412yes—
308C23×C13AGL(1,ℤ/8)12yes—
309C23×C13#13712yes—
310C23×C13C22×D411yescharacteristic
311C22×D13—22no—
312C22×D13—41no—
313C22×D13—41no—
314C22×D13—41no—
315C22×D13—41no—
316C22×D13—41no—
317C22×D13—41no—
318D4×C13—28no—
319C2×C4×C13—21no—
320C2×C4×C13—21no—
321C2×C4×C13—21no—
322C2×C4×C13—21no—
323C2×C4×C13—21no—
324C2×C4×C13—21no—
325C2×C4×C13—21no—
326C2×C4×C13—21no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—84no—
348C2×C4×C13—84no—
349C2×C4×C13C2×C22⋊C412yes—
350C2×C4×C13C2×C22⋊C412yes—
351C2×C4×C13C2×C22⋊C412yes—
352C2×C4×C13C2×C22⋊C412yes—
353C2×C4×C13C23×C411yescharacteristic
354C2×C4×C13C22×D411yescharacteristic
355C2×C4×C13C22×D411yescharacteristic
356C2×C4×C13C2×#4111yescharacteristic
357C2×C4×C13H(5,𝔽2)11yescharacteristic
358C2×C4×C13H(5,𝔽2)11yescharacteristic
359C22⋊D13—48no—
360C22⋊D13—48no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—48no—
367C2×Dic13—41no—
368C2×Dic13—41no—
369C2×Dic13—41no—
370C2×Dic13—41no—
371D52—22no—
372D52—22no—
373D52—41no—
374D52—41no—
375C4×D13—48no—
376Dic26—22no—
377Dic26—22no—
378Dic26—22no—
379Dic26—22no—
380Dic26—22no—
381Dic26—48no—
382Dic26—41no—
383Dic26—41no—
384Dic26C4×D414yescomplemented
385#1055—22no—
386#1055—41no—
387#1055—41no—
388#1055—41no—
389C22×#41—131no—
390C23×Q8—131no—
391C22×M16—131no—
392C23×C8—131no—
393#548—138no—
394#548—264no—
395C2×#124—131no—
396C2×#124—261no—
397C2×C22⋊Q8—131no—
398C2×C22⋊Q8—261no—
399C2×#121—131no—
400C2×#121—261no—
401C2×C4×Q8—131no—
402C2×C4×D4—21no—
403C2×C4×D4—261no—
404C2×C4×D4C2×D1311yescharacteristic
405C22×C4⋊C4C2×D1311yescharacteristic
406C22×C4⋊C4C2×D1311yescharacteristic
407#435—264no—
408C2×C4⋊C8—131no—
409#417—264no—
410C2×#103—131no—
411C2×#103—131no—
412C2×#103—131no—
413C2×#103—131no—
414C2×#103—131no—
415C2×#103—131no—
416C2×#103—131no—
417C2×#103—131no—
418C2×#103—264no—
419C2×#102—131no—
420C2×#102—131no—
421C2×#102—131no—
422C2×#102—131no—
423C2×C22⋊C8—131no—
424C2×C22⋊C8—131no—
425C2×#97—131no—
426#389—21no—
427#385—21no—
428#385—21no—
429#384C2×D1311yescharacteristic
430#380C2×D1311yescharacteristic
431#380C2×D1311yescharacteristic
432C4×C4⋊C4C2×D1311yescharacteristic
433#340—131no—
434#340—131no—
435#340—131no—
436#340—131no—
437C22×C13—22no—
438C22×C13—22no—
439C22×C13—22no—
440C22×C13—22no—
441C22×C13—22no—
442C22×C13—22no—
443C22×C13—22no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—41no—
447C22×C13—41no—
448C22×C13—41no—
449C22×C13—41no—
450C22×C13#41714yescomplemented
451C22×C13C22×C22⋊C411yescharacteristic
452C22×C13D4211yescharacteristic
453C22×C13#54611yescharacteristic
454C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C13C2×#13711yescharacteristic
456C22×C13#57711yescharacteristic
457C22×C13#57811yescharacteristic
458C2×D13—42no—
459C2×D13—42no—
460C2×D13—42no—
461C2×D13—81no—
462C2×D13—81no—
463C2×D13—81no—
464C2×D13—81no—
465C4×C13—22no—
466C4×C13—22no—
467C4×C13—22no—
468C4×C13—22no—
469C4×C13—42no—
470C4×C13—81no—
471C4×C13—81no—
472C4×C13—81no—
473C4×C13C2×C4×D411yescharacteristic
474C4×C13#51811yescharacteristic
475C4×C13D4211yescharacteristic
476C4×C13#54611yescharacteristic
477Dic13—24no—
478Dic13—42no—
479Dic13—42no—
480C2×#41—134no—
481C2×#41—262no—
482C2×#41—262no—
483C2×#41—262no—
484C2×#41—521no—
485C2×#41—521no—
486C22×Q8—134no—
487C22×Q8—131no—
488C22×Q8—131no—
489C22×Q8—262no—
490C22×Q8—262no—
491C22×Q8—262no—
492C22×Q8—261no—
493C22×Q8—521no—
494C22×Q8—521no—
495C22×D4—131no—
496C22×D4—261no—
497C22×D4—261no—
498C22×D4C22⋊D1311yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—261no—
502C23×C4—261no—
503C23×C4C22×D1311yescharacteristic
504C23×C4C22×D1311yescharacteristic
505C2×M16—262no—
506C2×M16—262no—
507C2×M16—521no—
508C22×C8—131no—
509C22×C8—131no—
510C22×C8—131no—
511C22×C8—131no—
512C22×C8—262no—
513C22×C8—262no—
514C22×C8—521no—
515#124—134no—
516#124—268no—
517#124—262no—
518C22⋊Q8—134no—
519C22⋊Q8—262no—
520C22⋊Q8—268no—
521#121—134no—
522#121—268no—
523#121—262no—
524C4×Q8—134no—
525C4×Q8—262no—
526C4×D4—44no—
527C4×D4—268no—
528C4×D4C4×D1314yes—
529C4×D4D5214yes—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—131no—
539C2×C4⋊C4—261no—
540C2×C4⋊C4—261no—
541C2×C4⋊C4C22⋊D1311yescharacteristic
542C2×C4⋊C4C22×D1311yescharacteristic
543C2×C4⋊C4C22×D1311yescharacteristic
544C2×C4⋊C4C22×D1311yescharacteristic
545C2×C4⋊C4C22×D1311yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—261no—
549C2×C22⋊C4—261no—
550C2×C22⋊C4—261no—
551C2×C22⋊C4—261no—
552C2×C22⋊C4C22⋊D1311yescharacteristic
553C2×C22⋊C4C22⋊D1311yescharacteristic
554C2×C42—21no—
555C2×C42—261no—
556C2×C42C22×D1311yescharacteristic
557C4⋊C8—262no—
558#103—134no—
559#103—262no—
560#103—262no—
561#103—262no—
562#103—262no—
563#103—262no—
564#103—521no—
565#103—521no—
566#102—262no—
567#102—262no—
568#102—521no—
569#102—521no—
570C22⋊C8—262no—
571C22⋊C8—262no—
572#97—262no—
573#95—21no—
574#95—21no—
575#95—21no—
576C2×C13—24no—
577C2×C13—42no—
578C2×C13D4×C22⋊C411yescharacteristic
579C2×C13C2×#41711yescharacteristic
580C2×C13#289811yescharacteristic
581C2×C13#326511yescharacteristic
582C2×C13#327011yescharacteristic
583C2×C13#330811yescharacteristic
584C2×C13#331611yescharacteristic
585D13—82no—
586C24—261no—
587C24C2×C22⋊D1311yescharacteristic
588C24C2×C22⋊D1311yescharacteristic
589#41—268no—
590#41—524no—
591#41—524no—
592#41—524no—
593C2×Q8—132no—
594C2×Q8—132no—
595C2×Q8—132no—
596C2×Q8—132no—
597C2×Q8—268no—
598C2×Q8—264no—
599C2×Q8—261no—
600C2×Q8—261no—
601C2×Q8—261no—
602C2×Q8—261no—
603C2×Q8—261no—
604C2×Q8—261no—
605C2×Q8—261no—
606C2×Q8—261no—
607C2×Q8—522no—
608C2×Q8—522no—
609C2×Q8—524no—
610C2×Q8—524no—
611C2×Q8—524no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—132no—
615C2×D4—264no—
616C2×D4—264no—
617C2×D4—261no—
618C2×D4—261no—
619C2×D4—261no—
620C2×D4—261no—
621C2×D4—261no—
622C2×D4—522no—
623C2×D4—522no—
624C2×D4—522no—
625C2×D4—522no—
626C2×D4#610314yes—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—261no—
646C22×C4—264no—
647C22×C4—261no—
648C22×C4—261no—
649C22×C4—264no—
650C22×C4—522no—
651C22×C4—522no—
652C22×C4—522no—
653C22×C4—522no—
654C22×C4C2×C4×D1312yes—
655C22×C4C2×C4×D1312yes—
656C22×C4C2×D5212yes—
657C22×C4C2×D5212yes—
658C22×C4C2×C22⋊D1311yescharacteristic
659C22×C4C2×C22⋊D1311yescharacteristic
660C22×C4C2×C22⋊D1311yescharacteristic
661C22×C4C2×C22⋊D1311yescharacteristic
662C22×C4C23×D1311yescharacteristic
663M16—524no—
664C2×C8—132no—
665C2×C8—261no—
666C2×C8—261no—
667C2×C8—261no—
668C2×C8—261no—
669C2×C8—261no—
670C2×C8—261no—
671C2×C8—261no—
672C2×C8—261no—
673C2×C8—261no—
674C2×C8—261no—
675C2×C8—261no—
676C2×C8—524no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—81no—
688C4⋊C4—132no—
689C4⋊C4—264no—
690C4⋊C4—264no—
691C4⋊C4—261no—
692C4⋊C4#610314yes—
693C4⋊C4D4×D1312yes—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—264no—
697C22⋊C4—264no—
698C22⋊C4—264no—
699C22⋊C4—264no—
700C22⋊C4#610314yes—
701C22⋊C4#610314yes—
702C42—42no—
703C42—264no—
704C42C2×C4×D1312yes—
705C42C2×D5212yes—
706C13#2242111yescharacteristic, complemented, Sylow
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—262no—
718C23—521no—
719C23—521no—
720C23—521no—
721C23—521no—
722C23—521no—
723C23—521no—
724C23C2×#610312yes—
725C23C2×#610312yes—
726C23#8818612yes—
727C23#8819612yes—
728C23C22×C22⋊D1311yescharacteristic
729Q8—134no—
730Q8—262no—
731Q8—262no—
732Q8—262no—
733Q8—262no—
734Q8—262no—
735Q8—528no—
736Q8—521no—
737Q8—521no—
738D4—28no—
739D4—262no—
740D4—262no—
741D4—528no—
742D4—528no—
743D4—521no—
744D4—521no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—262no—
778C2×C4—262no—
779C2×C4—262no—
780C2×C4—528no—
781C2×C4—528no—
782C2×C4—521no—
783C2×C4—521no—
784C2×C4—521no—
785C2×C4—521no—
786C2×C4C2×#610312yes—
787C2×C4C2×#610312yes—
788C2×C4C2×#610312yes—
789C2×C4C2×#610312yes—
790C2×C4C22×C4×D1311yescharacteristic
791C2×C4C22×D5211yescharacteristic
792C2×C4C2×D4×D1311yescharacteristic
793C2×C4#8825111yescharacteristic
794C2×C4#41×D1311yescharacteristic
795C2×C4#8825611yescharacteristic
796C8—262no—
797C8—521no—
798C8—521no—
799C8—521no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—522no—
814C22—522no—
815C22—522no—
816C22—1041no—
817C22—1041no—
818C22—1041no—
819C22—1041no—
820C22#1171862714yescomplemented
821C22C22×#610311yescharacteristic
822C22C2×#8818611yescharacteristic
823C22D4×C22⋊D1311yescharacteristic
824C22C2×#8819611yescharacteristic
825C22#1171953411yescharacteristic
826C22#1171954111yescharacteristic
827C22#1171954311yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—264no—
837C4—522no—
838C4—522no—
839C4C4×D4×D1311yescharacteristic
840C4#1171925011yescharacteristic
841C4D4×D5211yescharacteristic
842C4#1171925911yescharacteristic
843C2—24no—
844C2—42no—
845C2—1042no—
846C2D4×#610311yescharacteristic
847C2C2×#1171862711yescharacteristic
848C2#1312336611yescharacteristic
849C2#1312632711yescharacteristic
850C2#1312640711yescharacteristic
851C2#1312682111yescharacteristic
852C2#1312694111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC2×#11719257C2
cosocleC22×C4×C13C24
hypercenterD4×C4⋊C4D13
hypocenterC13#22421
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718672C2semidirect
3. C2×#11718627C2semidirect
4. C22×#88050C2semidirect
5. #13115768C2semidirect
6. #13115650C2semidirect
7. #13115267C2semidirect
8. #13115262C2semidirect
9. #13115153C2semidirect
10. #13115143C2semidirect
11. #13114838C2semidirect
12. #13114774C2semidirect
13. #13114770C2semidirect
14. #13114669C2semidirect
15. D4×C13×C4⋊C4C2semidirect
28. #11719257C4semidirect
77. C2×#6127C2×C4semidirect
86. C22×Dic26C2×C4semidirect
114. #88184C2×C4semidirect
120. #88178C2×C4semidirect
138. #88129C2×C4semidirect
140. C4×Dic26C2×C4semidirect
153. #88050D4semidirect
285. D4×C4⋊C4D13semidirect
384. Dic26C4×D4semidirect
450. C22×C13#417semidirect
706. C13#22421semidirect
820. C22#11718627semidirect

Maximal subgroups

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

subgroupindex
C2×#117192572
C2×#117186722
C2×#117186272
C22×#880502
#131157682
#131156502
#131152672
#131152622
#131151532
#131151432
#131148382
#131147742
#131147702
#131146692
D4×C13×C4⋊C42
#2242113