Finite Group Databasebeta

← #15878429

Subgroups — #15878429

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×#11718672C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic, complemented
3C22×#88075C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic13C211yesmaximal, characteristic, complemented
5#13115769C211yesmaximal, characteristic, complemented
6#13115653C211yesmaximal, characteristic, complemented
7#13115270C211yesmaximal, characteristic, complemented
8#13115265C211yesmaximal, characteristic, complemented
9#13115154C211yesmaximal, characteristic, complemented
10#13115144C211yesmaximal, characteristic, complemented
11#13114841C211yesmaximal, characteristic, complemented
12#13114776C211yesmaximal, characteristic, complemented
13#13114771C211yesmaximal, characteristic, complemented
14#13114666C211yesmaximal, characteristic, complemented
15C2×C13×#548C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C23×Q8×C13C2211yescharacteristic
18C13×#548—24no—
19C13×#548C418yescomplemented
20C2×C13×#124—21no—
21C2×C13×#124C2211yescharacteristic
22C2×C13×C22⋊Q8—21no—
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×#121—21no—
25C2×C13×#121C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13—21no—
28C2×C4×D4×C13C2211yescharacteristic
29C2×D4×Dic13—21no—
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×#6099C2211yescharacteristic
33C23×#1055C2211yescharacteristic
34#11718893—24no—
35C2×#88075—24no—
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88075C2211yescharacteristic
40C2×#88075C2211yescharacteristic
41C2×#88075C2211yescharacteristic
42C2×#88075C2211yescharacteristic
43C2×#88075C2211yescharacteristic
44C2×#88072C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48#11718873C2211yescharacteristic
49#11718873C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic
52#11718672—24no—
53#11718646—21no—
54#11718611—21no—
55#11718611—21no—
56#11718596C2211yescharacteristic
57C4×C4⋊Dic13C2211yescharacteristic
58C2×C4⋊#1055C2211yescharacteristic
59C2×#88043C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718121C2211yescharacteristic
63#11718121C2211yescharacteristic
64C2×C13×#41—22no—
65C2×C13×#41—22no—
66C2×C13×#41—22no—
67C2×C13×#41—41no—
68C2×C13×#41—41no—
69C2×C13×#41C2×C414yescomplemented
70C22×Q8×C13—21no—
71C22×Q8×C13—22no—
72C22×Q8×C13—22no—
73C22×Q8×C13—22no—
74C22×Q8×C13—41no—
75C22×Q8×C13—41no—
76C22×Q8×C13C2×C414yescomplemented
77C22×Q8×C13C2311yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13D411yescharacteristic
82C22×D4×C13C2311yescharacteristic
83C23×C4×C13—21no—
84C23×C4×C13—21no—
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×Dic13—21no—
88C23×Dic13—21no—
89C13×#124—28no—
90C13×#124—22no—
91C13×#124C2×C414yescomplemented
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—28no—
94C13×C22⋊Q8C2×C414yescomplemented
95C13×#121—28no—
96C13×#121—22no—
97C13×#121C2×C414yescomplemented
98C4×Q8×C13—22no—
99C4×Q8×C13C2×C414yescomplemented
100C4×D4×C13—28no—
101C4×D4×C13C2×C414yes—
102C4×D4×C13D414yes—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4D411yescharacteristic
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4D411yescharacteristic
112C2×C13×C22⋊C4D411yescharacteristic
113C2×C42×C13—21no—
114C2×C42×C13C2311yescharacteristic
115C2×C22⋊Dic13—21no—
116C2×C22⋊Dic13—21no—
117D4×Dic13—44no—
118C2×C4⋊Dic13—22no—
119C2×C4⋊Dic13—22no—
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13—21no—
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13—21no—
124C2×C4⋊Dic13—41no—
125C2×C4⋊Dic13—41no—
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2311yescharacteristic
128C2×C4⋊Dic13C2311yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4×Dic13—21no—
131C2×#6099—22no—
132C2×#6099—22no—
133C2×#6099—41no—
134C22×#1055—22no—
135C22×#1055—22no—
136C22×#1055—41no—
137C22×#1055C2311yescharacteristic
138C22×#1055C2311yescharacteristic
139C22×#1055C2311yescharacteristic
140C22×#1055C2311yescharacteristic
141#88075—22no—
142#88075—22no—
143#88075—22no—
144#88075—22no—
145#88075—22no—
146#88075—41no—
147#88075—41no—
148#88075D414yescomplemented
149#88072—22no—
150#88072—22no—
151#88072—41no—
152#88072—41no—
153#88071—21no—
154#88071—21no—
155#88071—21no—
156C22⋊#1055—22no—
157C22⋊#1055—22no—
158C4⋊#1055—22no—
159#88043—22no—
160#22421—131nomaximal, Sylow
161C24×C13—21no—
162C24×C13C2×D411yescharacteristic
163C24×C13C2×D411yescharacteristic
164C13×#41—28no—
165C13×#41—44no—
166C13×#41—44no—
167C13×#41—44no—
168C2×Q8×C13—24no—
169C2×Q8×C13—21no—
170C2×Q8×C13—21no—
171C2×Q8×C13—21no—
172C2×Q8×C13—21no—
173C2×Q8×C13—28no—
174C2×Q8×C13—21no—
175C2×Q8×C13—21no—
176C2×Q8×C13—21no—
177C2×Q8×C13—21no—
178C2×Q8×C13—42no—
179C2×Q8×C13—42no—
180C2×Q8×C13—44no—
181C2×Q8×C13—44no—
182C2×Q8×C13—44no—
183C2×Q8×C13C22×C412yes—
184C2×Q8×C13C22×C412yes—
185C2×Q8×C13C2×D412yes—
186C2×Q8×C13#4112yes—
187C2×D4×C13—22no—
188C2×D4×C13—22no—
189C2×D4×C13—24no—
190C2×D4×C13—24no—
191C2×D4×C13—21no—
192C2×D4×C13—21no—
193C2×D4×C13—21no—
194C2×D4×C13—21no—
195C2×D4×C13—21no—
196C2×D4×C13—42no—
197C2×D4×C13—42no—
198C2×D4×C13—42no—
199C2×D4×C13—42no—
200C2×D4×C13C22⋊C414yes—
201C2×D4×C13C22×C412yes—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—24no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—24no—
215C22×C4×C13—42no—
216C22×C4×C13—42no—
217C22×C4×C13—42no—
218C22×C4×C13—42no—
219C22×C4×C13C22×C412yes—
220C22×C4×C13C22×C412yes—
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D411yescharacteristic
223C22×C4×C13C2×D411yescharacteristic
224C22×C4×C13C2×D411yescharacteristic
225C22×C4×C13C2×D412yes—
226C22×C4×C13C2×D412yes—
227C22×C4×C13C2411yescharacteristic
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—42no—
233C22×Dic13—42no—
234C22×Dic13—42no—
235C22×Dic13—42no—
236C22×Dic13—81no—
237C22×Dic13—81no—
238C13×C4⋊C4—24no—
239C13×C4⋊C4—24no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4C22⋊C414yes—
242C13×C4⋊C4C22×C412yes—
243C13×C22⋊C4—24no—
244C13×C22⋊C4—24no—
245C13×C22⋊C4—24no—
246C13×C22⋊C4—24no—
247C13×C22⋊C4C22⋊C414yes—
248C13×C22⋊C4C22⋊C414yes—
249C42×C13—24no—
250C42×C13C22×C412yes—
251C42×C13C2×D412yes—
252C22⋊Dic13—42no—
253C22⋊Dic13—42no—
254C4⋊Dic13—21no—
255C4⋊Dic13—21no—
256C4⋊Dic13—21no—
257C4⋊Dic13—21no—
258C4⋊Dic13—21no—
259C4⋊Dic13—21no—
260C4⋊Dic13—21no—
261C4⋊Dic13—42no—
262C4⋊Dic13—42no—
263C4⋊Dic13—42no—
264C4⋊Dic13—81no—
265C4⋊Dic13C2×D412yes—
266C4×Dic13—42no—
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×#548D1311yescharacteristic
282C2×#435—131no—
283C2×#417—131no—
284C22×#103—131no—
285D4×C4⋊C4—131no—
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×C13—22no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13C2×C22⋊C412yes—
314C23×C13C2×C22⋊C412yes—
315C23×C13AGL(1,ℤ/8)12yes—
316C23×C13#13712yes—
317C23×C13C22×D411yescharacteristic
318Q8×C13—22no—
319Q8×C13—22no—
320Q8×C13—22no—
321Q8×C13—22no—
322Q8×C13—22no—
323Q8×C13—48no—
324Q8×C13—41no—
325Q8×C13—41no—
326Q8×C13C4×D414yescomplemented
327D4×C13—28no—
328D4×C13—22no—
329D4×C13—22no—
330D4×C13—48no—
331D4×C13—48no—
332D4×C13—41no—
333D4×C13—41no—
334C2×C4×C13—22no—
335C2×C4×C13—21no—
336C2×C4×C13—21no—
337C2×C4×C13—22no—
338C2×C4×C13—21no—
339C2×C4×C13—21no—
340C2×C4×C13—22no—
341C2×C4×C13—21no—
342C2×C4×C13—21no—
343C2×C4×C13—21no—
344C2×C4×C13—21no—
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—48no—
356C2×C4×C13—48no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13C2×C22⋊C412yes—
362C2×C4×C13C2×C22⋊C412yes—
363C2×C4×C13C2×C22⋊C412yes—
364C2×C4×C13C2×C22⋊C412yes—
365C2×C4×C13C23×C411yescharacteristic
366C2×C4×C13C22×D411yescharacteristic
367C2×C4×C13C22×D411yescharacteristic
368C2×C4×C13C2×#4111yescharacteristic
369C2×C4×C13H(5,𝔽2)11yescharacteristic
370C2×C4×C13H(5,𝔽2)11yescharacteristic
371C2×Dic13—22no—
372C2×Dic13—41no—
373C2×Dic13—41no—
374C2×Dic13—41no—
375C2×Dic13—41no—
376C2×Dic13—41no—
377C2×Dic13—41no—
378C2×Dic13—41no—
379C2×Dic13—41no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—41no—
383C2×Dic13—84no—
384C2×Dic13—84no—
385#1055—22no—
386#1055—41no—
387#1055—41no—
388#1055—41no—
389C22×#41C2×D1311yescharacteristic
390C23×Q8C2×D1311yescharacteristic
391C22×M16—131no—
392C23×C8—131no—
393#548—24no—
394#548Dic1318yescomplemented
395C2×#124—21no—
396C2×#124C2×D1311yescharacteristic
397C2×C22⋊Q8—21no—
398C2×C22⋊Q8C2×D1311yescharacteristic
399C2×#121—21no—
400C2×#121C2×D1311yescharacteristic
401C2×C4×Q8C2×D1311yescharacteristic
402C2×C4×D4—21no—
403C2×C4×D4—261no—
404C2×C4×D4C2×D1311yescharacteristic
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
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—261no—
427#385—261no—
428#385—261no—
429#384—131no—
430#380—131no—
431#380—131no—
432C4×C4⋊C4—131no—
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—42no—
451C22×C13—42no—
452C22×C13—42no—
453C22×C13—81no—
454C22×C13—81no—
455C22×C13—81no—
456C22×C13—81no—
457C22×C13#41714yescomplemented
458C22×C13C22×C22⋊C411yescharacteristic
459C22×C13D4211yescharacteristic
460C22×C13#54611yescharacteristic
461C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C13C2×#13711yescharacteristic
463C22×C13#57711yescharacteristic
464C22×C13#57811yescharacteristic
465C4×C13—22no—
466C4×C13—22no—
467C4×C13—24no—
468C4×C13—22no—
469C4×C13—22no—
470C4×C13—42no—
471C4×C13—42no—
472C4×C13C2×C4×D411yescharacteristic
473C4×C13#51811yescharacteristic
474C4×C13D4211yescharacteristic
475C4×C13#54611yescharacteristic
476Dic13—42no—
477Dic13—81no—
478Dic13—81no—
479Dic13—81no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41C2×Dic1314yescomplemented
486C22×Q8—21no—
487C22×Q8—22no—
488C22×Q8—22no—
489C22×Q8—22no—
490C22×Q8—41no—
491C22×Q8—41no—
492C22×Q8C2×Dic1314yescomplemented
493C22×Q8C22×D1311yescharacteristic
494C22×Q8C22×D1311yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4C22⋊D1311yescharacteristic
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—28no—
516#124—22no—
517#124C2×Dic1314yescomplemented
518C22⋊Q8—22no—
519C22⋊Q8—28no—
520C22⋊Q8C2×Dic1314yescomplemented
521#121—28no—
522#121—22no—
523#121C2×Dic1314yescomplemented
524C4×Q8—22no—
525C4×Q8C2×Dic1314yescomplemented
526C4×D4—28no—
527C4×D4—524no—
528C4×D4C2×Dic1314yes—
529C4×D4C22⋊D1314yes—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—131no—
533C2×C4⋊C4—131no—
534C2×C4⋊C4—131no—
535C2×C4⋊C4—131no—
536C2×C4⋊C4—262no—
537C2×C4⋊C4—262no—
538C2×C4⋊C4—261no—
539C2×C4⋊C4—261no—
540C2×C4⋊C4—261no—
541C2×C4⋊C4—261no—
542C2×C4⋊C4—521no—
543C2×C4⋊C4—521no—
544C2×C4⋊C4C22⋊D1311yescharacteristic
545C2×C4⋊C4C22×D1311yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
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—261no—
574#95—261no—
575#95—261no—
576C2×C13—24no—
577C2×C13—42no—
578C2×C13—82no—
579C2×C13D4×C22⋊C411yescharacteristic
580C2×C13C2×#41711yescharacteristic
581C2×C13#289811yescharacteristic
582C2×C13#326511yescharacteristic
583C2×C13#327011yescharacteristic
584C2×C13#330811yescharacteristic
585C2×C13#331611yescharacteristic
586C24—21no—
587C24C2×C22⋊D1311yescharacteristic
588C24C2×C22⋊D1311yescharacteristic
589#41—28no—
590#41—44no—
591#41—44no—
592#41—44no—
593C2×Q8—24no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—28no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8D4×D1312yes—
609C2×Q8#612912yes—
610C2×Q8C22×Dic1312yes—
611C2×Q8C22×Dic1312yes—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4C22⋊Dic1314yes—
626C2×D4C22×Dic1312yes—
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—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—261no—
645C22×C4—261no—
646C22×C4—261no—
647C22×C4—261no—
648C22×C4—522no—
649C22×C4—522no—
650C22×C4—522no—
651C22×C4—522no—
652C22×C4—1041no—
653C22×C4—1041no—
654C22×C4C22×Dic1312yes—
655C22×C4C22×Dic1312yes—
656C22×C4C2×C22⋊D1311yescharacteristic
657C22×C4C2×C22⋊D1311yescharacteristic
658C22×C4C2×C22⋊D1311yescharacteristic
659C22×C4C2×C22⋊D1311yescharacteristic
660C22×C4C2×C22⋊D1312yes—
661C22×C4C2×C22⋊D1312yes—
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—24no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—132no—
681C4⋊C4—261no—
682C4⋊C4—261no—
683C4⋊C4—261no—
684C4⋊C4—261no—
685C4⋊C4—261no—
686C4⋊C4—261no—
687C4⋊C4—261no—
688C4⋊C4—522no—
689C4⋊C4—522no—
690C4⋊C4—522no—
691C4⋊C4—1041no—
692C4⋊C4C22⋊Dic1314yes—
693C4⋊C4C22×Dic1312yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—522no—
699C22⋊C4—522no—
700C22⋊C4C22⋊Dic1314yes—
701C22⋊C4C22⋊Dic1314yes—
702C42—24no—
703C42—522no—
704C42C22×Dic1312yes—
705C42C2×C22⋊D1312yes—
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—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23#8820312yes—
725C23#8820512yes—
726C23C2×C22⋊Dic1312yes—
727C23C2×C22⋊Dic1312yes—
728C23C22×C22⋊D1311yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—41no—
736Q8—41no—
737Q8D4×Dic1314yescomplemented
738D4—28no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—48no—
743D4—41no—
744D4—41no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—262no—
773C2×C4—521no—
774C2×C4—521no—
775C2×C4—521no—
776C2×C4—521no—
777C2×C4—521no—
778C2×C4—521no—
779C2×C4—521no—
780C2×C4—521no—
781C2×C4—521no—
782C2×C4—521no—
783C2×C4—521no—
784C2×C4—1044no—
785C2×C4—1044no—
786C2×C4C2×C22⋊Dic1312yes—
787C2×C4C2×C22⋊Dic1312yes—
788C2×C4C2×C22⋊Dic1312yes—
789C2×C4C2×C22⋊Dic1312yes—
790C2×C4C2×D4×D1311yescharacteristic
791C2×C4C2×#612911yescharacteristic
792C2×C4#8825111yescharacteristic
793C2×C4#8825111yescharacteristic
794C2×C4C23×Dic1311yescharacteristic
795C2×C4C22×C22⋊D1311yescharacteristic
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—42no—
814C22—42no—
815C22—42no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22#1171889314yescomplemented
821C22D4×C22⋊D1311yescharacteristic
822C22#1171951111yescharacteristic
823C22C2×#8820311yescharacteristic
824C22C2×#8820511yescharacteristic
825C22#1171954211yescharacteristic
826C22#1171954311yescharacteristic
827C22C22×C22⋊Dic1311yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—522no—
836C4—1041no—
837C4—1041no—
838C4—1041no—
839C4C2×D4×Dic1311yescharacteristic
840C4#1171950311yescharacteristic
841C4D4×C22⋊D1311yescharacteristic
842C4#1171951111yescharacteristic
843C2—24no—
844C2—42no—
845C2—82no—
846C2D4×C22⋊Dic1311yescharacteristic
847C2C2×#1171889311yescharacteristic
848C2#1312336911yescharacteristic
849C2#1312633211yescharacteristic
850C2#1312640211yescharacteristic
851C2#1312682711yescharacteristic
852C2#1312694711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#548C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#548D13
hypocenterC13#22421
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#11718672C2semidirect
2. C2×#11718893C2semidirect
3. C22×#88075C2semidirect
4. D4×C4⋊Dic13C2semidirect
5. #13115769C2semidirect
6. #13115653C2semidirect
7. #13115270C2semidirect
8. #13115265C2semidirect
9. #13115154C2semidirect
10. #13115144C2semidirect
11. #13114841C2semidirect
12. #13114776C2semidirect
13. #13114771C2semidirect
14. #13114666C2semidirect
19. C13×#548C4semidirect
69. C2×C13×#41C2×C4semidirect
76. C22×Q8×C13C2×C4semidirect
91. C13×#124C2×C4semidirect
94. C13×C22⋊Q8C2×C4semidirect
97. C13×#121C2×C4semidirect
99. C4×Q8×C13C2×C4semidirect
148. #88075D4semidirect
326. Q8×C13C4×D4semidirect
394. #548Dic13semidirect
457. C22×C13#417semidirect
485. C2×#41C2×Dic13semidirect
492. C22×Q8C2×Dic13semidirect
517. #124C2×Dic13semidirect
520. C22⋊Q8C2×Dic13semidirect
523. #121C2×Dic13semidirect
525. C4×Q8C2×Dic13semidirect
706. C13#22421semidirect
737. Q8D4×Dic13semidirect
820. C22#11718893semidirect

Maximal subgroups

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

subgroupindex
C2×#117186722
C2×#117188932
C22×#880752
D4×C4⋊Dic132
#131157692
#131156532
#131152702
#131152652
#131151542
#131151442
#131148412
#131147762
#131147712
#131146662
C2×C13×#5482
#2242113