Finite Group Databasebeta

← #15878399

Subgroups — #15878399

Order 3328.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 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×#88072C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic13C211yesmaximal, characteristic, complemented
5#13115769C211yesmaximal, characteristic, complemented
6#13115653C211yesmaximal, characteristic, complemented
7#13115275C211yesmaximal, characteristic, complemented
8#13115260C211yesmaximal, characteristic, complemented
9#13115154C211yesmaximal, characteristic, complemented
10#13115144C211yesmaximal, characteristic, complemented
11#13114836C211yesmaximal, characteristic, complemented
12#13114776C211yesmaximal, characteristic, complemented
13#13114767C211yesmaximal, characteristic, complemented
14#13114661C211yesmaximal, characteristic, complemented
15C2×C13×#546C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C13×#546—24no—
19C13×#546C418yescomplemented
20C2×C13×#124C2211yescharacteristic
21C2×C13×#123—21no—
22C2×C13×C22⋊Q8C2211yescharacteristic
23C2×C13×#121—21no—
24C2×C13×#121C2211yescharacteristic
25C2×C13×#120—21no—
26C2×C4×D4×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C22×C13×C22⋊C4—21no—
29C2×D4×Dic13—21no—
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic, complemented
32C22×#6099C2211yescharacteristic, complemented
33C23×#1055C2211yescharacteristic
34#11718893—24no—
35C2×#88075C2211yescharacteristic, complemented
36C2×#88075C2211yescharacteristic, complemented
37C2×#88075C2211yescharacteristic, complemented
38C2×#88075C2211yescharacteristic, complemented
39C2×#88072—24no—
40C2×#88072C2211yescharacteristic
41C2×#88072C2211yescharacteristic
42C2×#88072C2211yescharacteristic
43C2×#88072C2211yescharacteristic
44C2×#88072C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48#11718873C2211yescharacteristic
49#11718873C2211yescharacteristic, complemented
50C2×C22⋊#1055C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic, complemented
52#11718672—24no—
53#11718646—21no—
54#11718611—21no—
55#11718611—21no—
56#11718596C2211yescharacteristic, complemented
57C4×C4⋊Dic13C2211yescharacteristic, complemented
58C2×C4⋊#1055C2211yescharacteristic, complemented
59C2×#88043C2211yescharacteristic, complemented
60#11718121C2211yescharacteristic, complemented
61#11718121C2211yescharacteristic, complemented
62#11718121C2211yescharacteristic, complemented
63#11718121C2211yescharacteristic, complemented
64C25×C13—21no—
65C2×C13×#41—22no—
66C2×C13×#41—22no—
67C2×C13×#41—22no—
68C2×C13×#41—41no—
69C2×C13×#41—41no—
70C2×C13×#41C2×C414yescomplemented
71C22×Q8×C13C2311yescharacteristic
72C22×D4×C13—22no—
73C22×D4×C13—22no—
74C22×D4×C13—21no—
75C22×D4×C13—21no—
76C22×D4×C13—21no—
77C22×D4×C13—22no—
78C22×D4×C13—41no—
79C22×D4×C13—41no—
80C22×D4×C13C2×C414yescomplemented
81C22×D4×C13D411yescharacteristic
82C22×D4×C13C2311yescharacteristic
83C22×D4×C13C2311yescharacteristic
84C23×C4×C13—21no—
85C23×C4×C13—21no—
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×Dic13—21no—
89C23×Dic13—21no—
90C13×#124—22no—
91C13×#124C2×C414yescomplemented
92C13×#123—28no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8C2×C414yescomplemented
95C13×#121—22no—
96C13×#121—28no—
97C13×#121C2×C414yescomplemented
98C13×#120—28no—
99C4×D4×C13—22no—
100C4×D4×C13C2×C414yes—
101C4×D4×C13C2×C414yescomplemented
102C4×D4×C13D414yes—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4D411yescharacteristic
105C2×C13×C4⋊C4C2311yescharacteristic
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—28no—
112C2×C13×C22⋊C4D411yescharacteristic
113C2×C13×C22⋊C4D411yescharacteristic
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—41no—
144#88075—41no—
145#88072—22no—
146#88072—22no—
147#88072—22no—
148#88072—22no—
149#88072—22no—
150#88072—41no—
151#88072—41no—
152#88072D414yescomplemented
153#88071—21no—
154#88071—21no—
155#88071—21no—
156C22⋊#1055—22no—
157C22⋊#1055—22no—
158C4⋊#1055—22no—
159#88043—22no—
160#22419—131nomaximal, Sylow
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—24no—
164C24×C13—42no—
165C24×C13—42no—
166C24×C13—42no—
167C24×C13—42no—
168C24×C13—81no—
169C24×C13—81no—
170C24×C13C2×D411yescharacteristic
171C24×C13C2×D411yescharacteristic
172C13×#41—28no—
173C13×#41—44no—
174C13×#41—44no—
175C13×#41—44no—
176C2×Q8×C13—21no—
177C2×Q8×C13—21no—
178C2×Q8×C13—21no—
179C2×Q8×C13—21no—
180C2×Q8×C13—21no—
181C2×Q8×C13C22×C412yes—
182C2×D4×C13—22no—
183C2×D4×C13—22no—
184C2×D4×C13—28no—
185C2×D4×C13—24no—
186C2×D4×C13—24no—
187C2×D4×C13—24no—
188C2×D4×C13—21no—
189C2×D4×C13—21no—
190C2×D4×C13—21no—
191C2×D4×C13—21no—
192C2×D4×C13—21no—
193C2×D4×C13—21no—
194C2×D4×C13—21no—
195C2×D4×C13—21no—
196C2×D4×C13—44no—
197C2×D4×C13—44no—
198C2×D4×C13—44no—
199C2×D4×C13—42no—
200C2×D4×C13—42no—
201C2×D4×C13—42no—
202C2×D4×C13—42no—
203C2×D4×C13—81no—
204C2×D4×C13—81no—
205C2×D4×C13C22⋊C414yes—
206C2×D4×C13C22×C412yes—
207C2×D4×C13C22×C412yes—
208C2×D4×C13C2×D412yes—
209C2×D4×C13#4112yes—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—24no—
221C22×C4×C13—24no—
222C22×C4×C13—42no—
223C22×C4×C13—42no—
224C22×C4×C13—81no—
225C22×C4×C13—81no—
226C22×C4×C13C22×C412yes—
227C22×C4×C13C22×C412yes—
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D412yes—
233C22×C4×C13C2×D412yes—
234C22×C4×C13C2411yescharacteristic
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—42no—
240C22×Dic13—42no—
241C22×Dic13—42no—
242C22×Dic13—42no—
243C22×Dic13—81no—
244C22×Dic13—81no—
245C13×C4⋊C4—24no—
246C13×C4⋊C4—21no—
247C13×C4⋊C4C22⋊C414yes—
248C13×C4⋊C4C22×C412yes—
249C13×C22⋊C4—24no—
250C13×C22⋊C4—24no—
251C13×C22⋊C4—24no—
252C13×C22⋊C4—24no—
253C13×C22⋊C4—24no—
254C13×C22⋊C4C22⋊C414yes—
255C13×C22⋊C4C22⋊C414yes—
256C42×C13C22×C412yes—
257C42×C13C2×D412yes—
258C22⋊Dic13—42no—
259C22⋊Dic13—42no—
260C4⋊Dic13—21no—
261C4⋊Dic13—21no—
262C4⋊Dic13—21no—
263C4⋊Dic13—21no—
264C4⋊Dic13—21no—
265C4⋊Dic13—21no—
266C4⋊Dic13—21no—
267C4⋊Dic13—42no—
268C4⋊Dic13—42no—
269C4⋊Dic13—42no—
270C4⋊Dic13—81no—
271C4⋊Dic13C2×D412yes—
272C4×Dic13—42no—
273#6099—44no—
274C2×#1055—21no—
275C2×#1055—21no—
276C2×#1055—21no—
277C2×#1055—21no—
278C2×#1055—21no—
279C2×#1055—21no—
280C2×#1055—21no—
281C2×#1055—21no—
282C2×#1055—21no—
283C2×#1055—21no—
284C2×#1055—21no—
285C2×#1055—44no—
286C2×#1055C2×D412yes—
287C2×#546D1311yescharacteristic
288C2×#435—131no—
289C2×#417—131no—
290C22×#102—131no—
291D4×C4⋊C4—131no—
292#1983—131no—
293#1959—131no—
294#1895—131no—
295#1892—131no—
296#1874—131no—
297#1872—131no—
298#1802—131no—
299#1788—131no—
300#1786—131no—
301#1762—131no—
302C23×C13—21no—
303C23×C13—21no—
304C23×C13—21no—
305C23×C13—21no—
306C23×C13—22no—
307C23×C13—21no—
308C23×C13—22no—
309C23×C13—21no—
310C23×C13—22no—
311C23×C13—21no—
312C23×C13—21no—
313C23×C13—21no—
314C23×C13—21no—
315C23×C13—22no—
316C23×C13—48no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—48no—
328C23×C13—84no—
329C23×C13—84no—
330C23×C13—84no—
331C23×C13—84no—
332C23×C13—84no—
333C23×C13C2×C22⋊C412yes—
334C23×C13C2×C22⋊C412yes—
335C23×C13AGL(1,ℤ/8)12yes—
336C23×C13#13712yes—
337C23×C13C22×D411yescharacteristic
338Q8×C13—22no—
339Q8×C13—22no—
340Q8×C13—41no—
341Q8×C13—41no—
342D4×C13—28no—
343D4×C13—22no—
344D4×C13—22no—
345D4×C13—22no—
346D4×C13—22no—
347D4×C13—22no—
348D4×C13—48no—
349D4×C13—48no—
350D4×C13—41no—
351D4×C13—41no—
352D4×C13—84no—
353D4×C13C4×D414yescomplemented
354C2×C4×C13—21no—
355C2×C4×C13—21no—
356C2×C4×C13—21no—
357C2×C4×C13—21no—
358C2×C4×C13—21no—
359C2×C4×C13—21no—
360C2×C4×C13—21no—
361C2×C4×C13—21no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—48no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—84no—
378C2×C4×C13C2×C22⋊C412yes—
379C2×C4×C13C2×C22⋊C412yes—
380C2×C4×C13C2×C22⋊C412yes—
381C2×C4×C13C2×C22⋊C412yes—
382C2×C4×C13C23×C411yescharacteristic
383C2×C4×C13C22×D411yescharacteristic
384C2×C4×C13C22×D411yescharacteristic
385C2×C4×C13C2×#4111yescharacteristic
386C2×C4×C13H(5,𝔽2)11yescharacteristic
387C2×C4×C13H(5,𝔽2)11yescharacteristic
388C2×Dic13—22no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—84no—
401C2×Dic13—84no—
402#1055—22no—
403#1055—41no—
404#1055—41no—
405#1055—41no—
406C22×#41C2×D1311yescharacteristic
407C23×D4C2×D1311yescharacteristic
408C22×M16—131no—
409C23×C8—131no—
410#546—24no—
411#546Dic1318yescomplemented
412C2×#124C2×D1311yescharacteristic
413C2×#123—21no—
414C2×C22⋊Q8C2×D1311yescharacteristic
415C2×#121—21no—
416C2×#121C2×D1311yescharacteristic
417C2×#120—21no—
418C2×C4×D4—261no—
419C2×C4×D4C2×D1311yescharacteristic
420C2×C4×D4C2×D1311yescharacteristic
421C22×C4⋊C4—131no—
422C22×C4⋊C4—131no—
423C22×C22⋊C4—21no—
424#435—264no—
425C2×C4⋊C8—131no—
426#417—264no—
427C2×#103—131no—
428C2×#103—131no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#102—131no—
432C2×#102—131no—
433C2×#102—131no—
434C2×#102—131no—
435C2×#102—131no—
436C2×#102—131no—
437C2×#102—131no—
438C2×#102—131no—
439C2×#102—264no—
440C2×C22⋊C8—131no—
441C2×C22⋊C8—131no—
442C2×#97—131no—
443#389—261no—
444#385—261no—
445#385—261no—
446#384—131no—
447#380—131no—
448#380—131no—
449C4×C4⋊C4—131no—
450#340—131no—
451#340—131no—
452#340—131no—
453#340—131no—
454C22×C13—22no—
455C22×C13—22no—
456C22×C13—22no—
457C22×C13—22no—
458C22×C13—22no—
459C22×C13—22no—
460C22×C13—22no—
461C22×C13—24no—
462C22×C13—22no—
463C22×C13—22no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—41no—
467C22×C13—42no—
468C22×C13—41no—
469C22×C13—42no—
470C22×C13—41no—
471C22×C13—42no—
472C22×C13—41no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—816no—
478C22×C13—81no—
479C22×C13—81no—
480C22×C13—81no—
481C22×C13—81no—
482C22×C13#41714yescomplemented
483C22×C13C22×C22⋊C411yescharacteristic
484C22×C13D4211yescharacteristic
485C22×C13#54611yescharacteristic
486C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
487C22×C13C2×#13711yescharacteristic
488C22×C13#57611yescharacteristic
489C22×C13#57711yescharacteristic
490C4×C13—22no—
491C4×C13—22no—
492C4×C13—22no—
493C4×C13—22no—
494C4×C13—42no—
495C4×C13—42no—
496C4×C13C2×C4×D411yescharacteristic
497C4×C13#51811yescharacteristic
498C4×C13D4211yescharacteristic
499C4×C13#54611yescharacteristic
500Dic13—42no—
501Dic13—81no—
502Dic13—81no—
503Dic13—81no—
504C25—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41C2×Dic1314yescomplemented
511C22×Q8C22×D1311yescharacteristic
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×Dic1314yescomplemented
521C22×D4C22⋊D1311yescharacteristic
522C22×D4C22×D1311yescharacteristic
523C22×D4C22×D1311yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—261no—
527C23×C4—261no—
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530C2×M16—262no—
531C2×M16—262no—
532C2×M16—521no—
533C22×C8—131no—
534C22×C8—131no—
535C22×C8—131no—
536C22×C8—131no—
537C22×C8—262no—
538C22×C8—262no—
539C22×C8—521no—
540#124—22no—
541#124C2×Dic1314yescomplemented
542#123—28no—
543C22⋊Q8—22no—
544C22⋊Q8C2×Dic1314yescomplemented
545#121—22no—
546#121—28no—
547#121C2×Dic1314yescomplemented
548#120—28no—
549C4×D4—22no—
550C4×D4—524no—
551C4×D4C2×Dic1314yes—
552C4×D4C2×Dic1314yescomplemented
553C4×D4C22⋊D1314yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—131no—
556C2×C4⋊C4—131no—
557C2×C4⋊C4—131no—
558C2×C4⋊C4—131no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
561C2×C4⋊C4—261no—
562C2×C4⋊C4—261no—
563C2×C4⋊C4—261no—
564C2×C4⋊C4—261no—
565C2×C4⋊C4—521no—
566C2×C4⋊C4—521no—
567C2×C4⋊C4C22⋊D1311yescharacteristic
568C2×C4⋊C4C22×D1311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—261no—
576C2×C22⋊C4—261no—
577C2×C22⋊C4C22⋊D1311yescharacteristic
578C2×C22⋊C4C22⋊D1311yescharacteristic
579C2×C42—261no—
580C2×C42C22×D1311yescharacteristic
581C4⋊C8—262no—
582#103—262no—
583#103—262no—
584#103—521no—
585#103—521no—
586#102—134no—
587#102—262no—
588#102—262no—
589#102—262no—
590#102—262no—
591#102—262no—
592#102—521no—
593#102—521no—
594C22⋊C8—262no—
595C22⋊C8—262no—
596#97—262no—
597#95—261no—
598#95—261no—
599#95—261no—
600C2×C13—24no—
601C2×C13—42no—
602C2×C13—44no—
603C2×C13—82no—
604C2×C13D4×C22⋊C411yescharacteristic
605C2×C13C2×#41711yescharacteristic
606C2×C13#289711yescharacteristic
607C2×C13#326411yescharacteristic
608C2×C13#326611yescharacteristic
609C2×C13#330611yescharacteristic
610C2×C13#331411yescharacteristic
611C24—21no—
612C24—21no—
613C24—24no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×C22⋊D1311yescharacteristic
621C24C2×C22⋊D1311yescharacteristic
622#41—28no—
623#41—44no—
624#41—44no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8C22×Dic1312yes—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—28no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—81no—
654C2×D4—81no—
655C2×D4C22⋊Dic1314yes—
656C2×D4D4×D1312yes—
657C2×D4#612912yes—
658C2×D4C22×Dic1312yes—
659C2×D4C22×Dic1312yes—
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—24no—
671C22×C4—24no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4—261no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—522no—
681C22×C4—522no—
682C22×C4—522no—
683C22×C4—522no—
684C22×C4—1041no—
685C22×C4—1041no—
686C22×C4C22×Dic1312yes—
687C22×C4C22×Dic1312yes—
688C22×C4C2×C22⋊D1311yescharacteristic
689C22×C4C2×C22⋊D1311yescharacteristic
690C22×C4C2×C22⋊D1311yescharacteristic
691C22×C4C2×C22⋊D1311yescharacteristic
692C22×C4C2×C22⋊D1312yes—
693C22×C4C2×C22⋊D1312yes—
694C22×C4C23×D1311yescharacteristic
695M16—524no—
696C2×C8—132no—
697C2×C8—261no—
698C2×C8—261no—
699C2×C8—261no—
700C2×C8—261no—
701C2×C8—261no—
702C2×C8—261no—
703C2×C8—261no—
704C2×C8—261no—
705C2×C8—261no—
706C2×C8—261no—
707C2×C8—261no—
708C2×C8—524no—
709C4⋊C4—24no—
710C4⋊C4—21no—
711C4⋊C4—132no—
712C4⋊C4—261no—
713C4⋊C4—261no—
714C4⋊C4—261no—
715C4⋊C4—261no—
716C4⋊C4—261no—
717C4⋊C4—261no—
718C4⋊C4—261no—
719C4⋊C4—522no—
720C4⋊C4—522no—
721C4⋊C4—522no—
722C4⋊C4—1041no—
723C4⋊C4C22⋊Dic1314yes—
724C4⋊C4C22×Dic1312yes—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—522no—
731C22⋊C4—522no—
732C22⋊C4C22⋊Dic1314yes—
733C22⋊C4C22⋊Dic1314yes—
734C42—522no—
735C42C22×Dic1312yes—
736C42C2×C22⋊D1312yes—
737C13#2241911yescharacteristic, complemented, Sylow
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—21no—
745C23—22no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—48no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23#8820312yes—
770C23#8820512yes—
771C23C2×C22⋊Dic1312yes—
772C23C2×C22⋊Dic1312yes—
773C23C22×C22⋊D1311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4D4×Dic1314yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4—262no—
815C2×C4—521no—
816C2×C4—521no—
817C2×C4—521no—
818C2×C4—521no—
819C2×C4—521no—
820C2×C4—521no—
821C2×C4—521no—
822C2×C4—521no—
823C2×C4—521no—
824C2×C4—521no—
825C2×C4—521no—
826C2×C4—1044no—
827C2×C4—1044no—
828C2×C4C2×C22⋊Dic1312yes—
829C2×C4C2×C22⋊Dic1312yes—
830C2×C4C2×C22⋊Dic1312yes—
831C2×C4C2×C22⋊Dic1312yes—
832C2×C4C2×D4×D1311yescharacteristic
833C2×C4C2×#612911yescharacteristic
834C2×C4#8825111yescharacteristic
835C2×C4#8825111yescharacteristic
836C2×C4C23×Dic1311yescharacteristic
837C2×C4C22×C22⋊D1311yescharacteristic
838C8—262no—
839C8—521no—
840C8—521no—
841C8—521no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—24no—
852C22—41no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#1171889314yescomplemented
871C22D4×C22⋊D1311yescharacteristic
872C22#1171951111yescharacteristic
873C22C2×#8820311yescharacteristic
874C22C2×#8820511yescharacteristic
875C22#1171954011yescharacteristic
876C22#1171954111yescharacteristic
877C22C22×C22⋊Dic1311yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—522no—
885C4—1041no—
886C4—1041no—
887C4—1041no—
888C4C2×D4×Dic1311yescharacteristic
889C4#1171950311yescharacteristic
890C4D4×C22⋊D1311yescharacteristic
891C4#1171951111yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊Dic1311yescharacteristic
897C2C2×#1171889311yescharacteristic
898C2#1312336211yescharacteristic
899C2#1312631711yescharacteristic
900C2#1312634211yescharacteristic
901C2#1312679711yescharacteristic
902C2#1312691711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#546C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#546D13
hypocenterC13#22419
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#11718672C2semidirect
2. C2×#11718893C2semidirect
3. C22×#88072C2semidirect
4. D4×C4⋊Dic13C2semidirect
5. #13115769C2semidirect
6. #13115653C2semidirect
7. #13115275C2semidirect
8. #13115260C2semidirect
9. #13115154C2semidirect
10. #13115144C2semidirect
11. #13114836C2semidirect
12. #13114776C2semidirect
13. #13114767C2semidirect
14. #13114661C2semidirect
19. C13×#546C4semidirect
31. C22×C4⋊Dic13C22semidirect
32. C22×#6099C22semidirect
35. C2×#88075C22semidirect
36. C2×#88075C22semidirect
37. C2×#88075C22semidirect
38. C2×#88075C22semidirect
49. #11718873C22semidirect
51. C2×C22⋊#1055C22semidirect
56. #11718596C22semidirect
57. C4×C4⋊Dic13C22semidirect
58. C2×C4⋊#1055C22semidirect
59. C2×#88043C22semidirect
60. #11718121C22semidirect
61. #11718121C22semidirect
62. #11718121C22semidirect
63. #11718121C22semidirect
70. C2×C13×#41C2×C4semidirect
80. C22×D4×C13C2×C4semidirect
91. C13×#124C2×C4semidirect
94. C13×C22⋊Q8C2×C4semidirect
97. C13×#121C2×C4semidirect
101. C4×D4×C13C2×C4semidirect
152. #88072D4semidirect
353. D4×C13C4×D4semidirect
411. #546Dic13semidirect
482. C22×C13#417semidirect
510. C2×#41C2×Dic13semidirect
520. C22×D4C2×Dic13semidirect
541. #124C2×Dic13semidirect
544. C22⋊Q8C2×Dic13semidirect
547. #121C2×Dic13semidirect
552. C4×D4C2×Dic13semidirect
737. C13#22419semidirect
789. D4D4×Dic13semidirect
870. 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×#880722
D4×C4⋊Dic132
#131157692
#131156532
#131152752
#131152602
#131151542
#131151442
#131148362
#131147762
#131147672
#131146612
C2×C13×#5462
#2241913