Finite Group Databasebeta

← #15878545

Subgroups — #15878545

Order 3328.

1466 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718673C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic, complemented
3C2×#11718886C211yesmaximal, characteristic, complemented
4#13117765C211yesmaximal, characteristic, complemented
5#13115769C211yesmaximal, characteristic, complemented
6#13115648C211yesmaximal, characteristic, complemented
7#13115275C211yesmaximal, characteristic, complemented
8#13115270C211yesmaximal, characteristic, complemented
9#13115159C211yesmaximal, characteristic, complemented
10#13115144C211yesmaximal, characteristic, complemented
11#13114851C211yesmaximal, characteristic, complemented
12#13114776C211yesmaximal, characteristic, complemented
13#13114771C211yesmaximal, characteristic, complemented
14C4×#88075C211yesmaximal, 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×#88180C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6099C2211yescharacteristic
32C22×#6099C2211yescharacteristic
33#11718893—24no—
34#11718886—24no—
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88075C2211yescharacteristic
40C2×#88075C2211yescharacteristic
41C2×#88075C2211yescharacteristic
42C2×#88075C2211yescharacteristic
43#11718881—21no—
44C2×#88072C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48#11718873C2211yescharacteristic
49#11718873C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic
52#11718673—24no—
53#11718642—21no—
54#11718612—21no—
55C22⋊C4×Dic13—21no—
56#11718597C2211yescharacteristic
57C4×C4⋊Dic13C2211yescharacteristic
58C2×C4⋊#1055C2211yescharacteristic
59C2×C4×#1055C2211yescharacteristic
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×C414yes—
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—
88C13×#124—28no—
89C13×#124—22no—
90C13×#124C2×C414yescomplemented
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—28no—
93C13×C22⋊Q8C2×C414yes—
94C13×#121—28no—
95C13×#121—22no—
96C13×#121C2×C414yescomplemented
97C4×Q8×C13—22no—
98C4×Q8×C13C2×C414yescomplemented
99C4×D4×C13—28no—
100C4×D4×C13C2×C414yes—
101C4×D4×C13D414yes—
102C2×C13×C4⋊C4—21no—
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⋊C4D411yescharacteristic
111C2×C13×C22⋊C4D411yescharacteristic
112C2×C42×C13—21no—
113C2×C42×C13C2311yescharacteristic
114C2×C22⋊Dic13—21no—
115C2×C22⋊Dic13—21no—
116C2×C22⋊Dic13—21no—
117#88180—22no—
118#88180—41no—
119C2×C4⋊Dic13—22no—
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13—41no—
122C2×C4⋊Dic13C2311yescharacteristic
123C2×C4⋊Dic13C2311yescharacteristic
124C2×C4⋊Dic13C2311yescharacteristic
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4×Dic13—21no—
127C2×C4×Dic13—21no—
128C2×#6099—22no—
129C2×#6099—22no—
130C2×#6099—22no—
131C2×#6099—22no—
132C2×#6099—41no—
133C2×#6099—41no—
134C22×#1055C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136C22×#1055C2311yescharacteristic
137C22×#1055C2311yescharacteristic
138#88075—22no—
139#88075—22no—
140#88075—22no—
141#88075—22no—
142#88075—22no—
143#88075—41no—
144#88075—41no—
145#88075D414yescomplemented
146#88072—22no—
147#88072—22no—
148#88072—41no—
149#88072—41no—
150#88071—21no—
151#88071—21no—
152#88071—21no—
153#88071—21no—
154#88071—21no—
155C22⋊#1055—22no—
156C22⋊#1055—22no—
157C4⋊#1055—22no—
158C4×#1055—22no—
159#22429—131nomaximal, Sylow
160C24×C13—21no—
161C24×C13C2×D411yescharacteristic
162C24×C13C2×D411yescharacteristic
163C13×#41—28no—
164C13×#41—44no—
165C13×#41—44no—
166C13×#41—44no—
167C2×Q8×C13—24no—
168C2×Q8×C13—21no—
169C2×Q8×C13—21no—
170C2×Q8×C13—21no—
171C2×Q8×C13—21no—
172C2×Q8×C13—28no—
173C2×Q8×C13—21no—
174C2×Q8×C13—21no—
175C2×Q8×C13—21no—
176C2×Q8×C13—21no—
177C2×Q8×C13—42no—
178C2×Q8×C13—42no—
179C2×Q8×C13—44no—
180C2×Q8×C13—44no—
181C2×Q8×C13—44no—
182C2×Q8×C13C22×C412yes—
183C2×Q8×C13C22×C412yes—
184C2×Q8×C13C2×D412yes—
185C2×Q8×C13#4112yes—
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—41no—
194C2×D4×C13—41no—
195C2×D4×C13—42no—
196C2×D4×C13—42no—
197C2×D4×C13—42no—
198C2×D4×C13—42no—
199C2×D4×C13C22⋊C414yes—
200C2×D4×C13C22×C412yes—
201C22×C4×C13—21no—
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—24no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—24no—
214C22×C4×C13—42no—
215C22×C4×C13—42no—
216C22×C4×C13—42no—
217C22×C4×C13—42no—
218C22×C4×C13C22×C412yes—
219C22×C4×C13C22×C412yes—
220C22×C4×C13C2×D411yescharacteristic
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D411yescharacteristic
223C22×C4×C13C2×D411yescharacteristic
224C22×C4×C13C2×D412yes—
225C22×C4×C13C2×D412yes—
226C22×C4×C13C2411yescharacteristic
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—42no—
232C22×Dic13—42no—
233C22×Dic13—81no—
234C13×C4⋊C4—24no—
235C13×C4⋊C4—24no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4C22⋊C414yes—
238C13×C4⋊C4C22×C412yes—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—24no—
241C13×C22⋊C4—24no—
242C13×C22⋊C4—24no—
243C13×C22⋊C4C22⋊C414yes—
244C13×C22⋊C4C22⋊C414yes—
245C42×C13—24no—
246C42×C13C22×C412yes—
247C42×C13C2×D412yes—
248C22⋊Dic13—42no—
249C22⋊Dic13—42no—
250C22⋊Dic13—81no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13—21no—
254C4⋊Dic13—21no—
255C4⋊Dic13—21no—
256C4⋊Dic13—21no—
257C4⋊Dic13—21no—
258C4⋊Dic13—42no—
259C4⋊Dic13C2×D412yes—
260C4×Dic13—42no—
261C4×Dic13—81no—
262#6099—44no—
263#6099—44no—
264C2×#1055—21no—
265C2×#1055—21no—
266C2×#1055—21no—
267C2×#1055—21no—
268C2×#1055—21no—
269C2×#1055—21no—
270C2×#1055—21no—
271C2×#1055—21no—
272C2×#1055—21no—
273C2×#1055—21no—
274C2×#1055—21no—
275C2×#1055C2×D412yes—
276C2×#548D1311yescharacteristic
277C2×#436—131no—
278C2×#417—131no—
279C2×#419—131no—
280#2352—131no—
281#1983—131no—
282#1958—131no—
283#1895—131no—
284#1894—131no—
285#1875—131no—
286#1872—131no—
287#1805—131no—
288#1788—131no—
289#1787—131no—
290C4×#103—131no—
291C23×C13—21no—
292C23×C13—21no—
293C23×C13—21no—
294C23×C13—21no—
295C23×C13—21no—
296C23×C13—21no—
297C23×C13—21no—
298C23×C13—21no—
299C23×C13—21no—
300C23×C13—21no—
301C23×C13—21no—
302C23×C13—21no—
303C23×C13—22no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13C2×C22⋊C412yes—
311C23×C13C2×C22⋊C412yes—
312C23×C13C22×D411yescharacteristic
313Q8×C13—22no—
314Q8×C13—22no—
315Q8×C13—22no—
316Q8×C13—22no—
317Q8×C13—22no—
318Q8×C13—48no—
319Q8×C13—41no—
320Q8×C13—41no—
321Q8×C13C4×D414yes—
322D4×C13—22no—
323D4×C13—22no—
324D4×C13—44no—
325D4×C13—48no—
326D4×C13—48no—
327D4×C13—41no—
328D4×C13—41no—
329C2×C4×C13—22no—
330C2×C4×C13—21no—
331C2×C4×C13—21no—
332C2×C4×C13—22no—
333C2×C4×C13—21no—
334C2×C4×C13—21no—
335C2×C4×C13—22no—
336C2×C4×C13—21no—
337C2×C4×C13—21no—
338C2×C4×C13—21no—
339C2×C4×C13—21no—
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—48no—
351C2×C4×C13—48no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13C2×C22⋊C412yes—
357C2×C4×C13C2×C22⋊C412yes—
358C2×C4×C13C2×C22⋊C412yes—
359C2×C4×C13C2×C22⋊C412yes—
360C2×C4×C13C23×C411yescharacteristic
361C2×C4×C13C22×D411yescharacteristic
362C2×C4×C13C22×D411yescharacteristic
363C2×C4×C13C2×#4111yescharacteristic
364C2×C4×C13H(5,𝔽2)11yescharacteristic
365C2×C4×C13H(5,𝔽2)11yescharacteristic
366C2×Dic13—22no—
367C2×Dic13—41no—
368C2×Dic13—41no—
369C2×Dic13—41no—
370C2×Dic13—41no—
371C2×Dic13—41no—
372C2×Dic13—41no—
373C2×Dic13—41no—
374C2×Dic13—41no—
375C2×Dic13—41no—
376C2×Dic13—41no—
377C2×Dic13—41no—
378C2×Dic13—84no—
379#1055—22no—
380#1055—41no—
381#1055—41no—
382#1055—41no—
383C22×#41C2×D1311yescharacteristic
384C23×Q8C2×D1311yescharacteristic
385C22×M16—131no—
386C22×M16—131no—
387#548—24no—
388#548Dic1318yescomplemented
389C2×#124—21no—
390C2×#124C2×D1311yescharacteristic
391C2×C22⋊Q8—21no—
392C2×C22⋊Q8C2×D1311yescharacteristic
393C2×#121—21no—
394C2×#121C2×D1311yescharacteristic
395C2×C4×Q8C2×D1311yescharacteristic
396C2×C4×D4—21no—
397C2×C4×D4C2×D1311yescharacteristic
398C2×#117—131no—
399C22×C4⋊C4—131no—
400#436—264no—
401C2×C4⋊C8—131no—
402#419—264no—
403#417—264no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103—131no—
409C2×#103—131no—
410C2×#103—131no—
411C2×#103—131no—
412C2×#102—131no—
413C2×#102—131no—
414C2×#102—131no—
415C2×#102—131no—
416C2×C22⋊C8—131no—
417C2×C22⋊C8—131no—
418C2×C4×C8—131no—
419#388—261no—
420#387—261no—
421#386—261no—
422#382—131no—
423#380—131no—
424#380—131no—
425C4×C4⋊C4—131no—
426C4×C22⋊C4—261no—
427#340—131no—
428#340—131no—
429#340—131no—
430#340—131no—
431C22×C13—22no—
432C22×C13—22no—
433C22×C13—22no—
434C22×C13—22no—
435C22×C13—22no—
436C22×C13—22no—
437C22×C13—41no—
438C22×C13—41no—
439C22×C13—41no—
440C22×C13—41no—
441C22×C13—41no—
442C22×C13—41no—
443C22×C13—41no—
444C22×C13—41no—
445C22×C13—42no—
446C22×C13—42no—
447C22×C13—42no—
448C22×C13—81no—
449C22×C13—81no—
450C22×C13—81no—
451C22×C13—81no—
452C22×C13C22×C22⋊C411yescharacteristic
453C22×C13D4211yescharacteristic
454C22×C13#54611yescharacteristic
455C22×C13#57511yescharacteristic
456C22×C13#57511yescharacteristic
457C22×C13#57711yescharacteristic
458C22×C13#57811yescharacteristic
459C4×C13—22no—
460C4×C13—22no—
461C4×C13—24no—
462C4×C13—22no—
463C4×C13—22no—
464C4×C13—42no—
465C4×C13—42no—
466C4×C13C2×C4×D411yescharacteristic
467C4×C13#51811yescharacteristic
468C4×C13D4211yescharacteristic
469C4×C13#54611yescharacteristic
470Dic13—42no—
471Dic13—81no—
472Dic13—81no—
473Dic13—81no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41C2×Dic1314yes—
480C22×Q8—21no—
481C22×Q8—22no—
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—41no—
485C22×Q8—41no—
486C22×Q8C2×Dic1314yescomplemented
487C22×Q8C22×D1311yescharacteristic
488C22×Q8C22×D1311yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C22⋊D1311yescharacteristic
492C22×D4C22×D1311yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—261no—
496C23×C4C22×D1311yescharacteristic
497C23×C4C22×D1311yescharacteristic
498C2×M16—262no—
499C2×M16—262no—
500C2×M16—262no—
501C2×M16—262no—
502C2×M16—521no—
503C2×M16—521no—
504C22×C8—131no—
505C22×C8—131no—
506C22×C8—131no—
507C22×C8—131no—
508#124—28no—
509#124—22no—
510#124C2×Dic1314yescomplemented
511C22⋊Q8—22no—
512C22⋊Q8—28no—
513C22⋊Q8C2×Dic1314yes—
514#121—28no—
515#121—22no—
516#121C2×Dic1314yescomplemented
517C4×Q8—22no—
518C4×Q8C2×Dic1314yescomplemented
519C4×D4—28no—
520C4×D4C2×Dic1314yes—
521C4×D4C22⋊D1314yes—
522#117—262no—
523#117—521no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—131no—
527C2×C4⋊C4—131no—
528C2×C4⋊C4—131no—
529C2×C4⋊C4—131no—
530C2×C4⋊C4—262no—
531C2×C4⋊C4—261no—
532C2×C4⋊C4—521no—
533C2×C4⋊C4C22⋊D1311yescharacteristic
534C2×C4⋊C4C22×D1311yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—261no—
540C2×C22⋊C4—261no—
541C2×C22⋊C4—261no—
542C2×C22⋊C4C22⋊D1311yescharacteristic
543C2×C22⋊C4C22⋊D1311yescharacteristic
544C2×C42—21no—
545C2×C42—261no—
546C2×C42—261no—
547C2×C42C22×D1311yescharacteristic
548C4⋊C8—262no—
549#103—134no—
550#103—262no—
551#103—262no—
552#103—262no—
553#103—262no—
554#103—262no—
555#103—521no—
556#103—521no—
557#102—262no—
558#102—262no—
559#102—521no—
560#102—521no—
561C22⋊C8—262no—
562C22⋊C8—262no—
563C4×C8—262no—
564#95—261no—
565#95—261no—
566#95—261no—
567#95—261no—
568#95—261no—
569C2×C13—42no—
570C2×C13—42no—
571C2×C13—82no—
572C2×C13D4×C22⋊C411yescharacteristic
573C2×C13#289611yescharacteristic
574C2×C13#289811yescharacteristic
575C2×C13#327511yescharacteristic
576C2×C13#327711yescharacteristic
577C2×C13#332611yescharacteristic
578C2×C13#332711yescharacteristic
579C24—21no—
580C24C2×C22⋊D1311yescharacteristic
581C24C2×C22⋊D1311yescharacteristic
582#41—28no—
583#41—44no—
584#41—44no—
585#41—44no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—28no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—42no—
597C2×Q8—42no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8D4×D1312yes—
602C2×Q8#612912yes—
603C2×Q8C22×Dic1312yes—
604C2×Q8C22×Dic1312yes—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4C22⋊Dic1314yes—
619C2×D4C22×Dic1312yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—261no—
638C22×C4—261no—
639C22×C4—261no—
640C22×C4—261no—
641C22×C4—522no—
642C22×C4—522no—
643C22×C4—1041no—
644C22×C4C22×Dic1312yes—
645C22×C4C22×Dic1312yes—
646C22×C4C2×C22⋊D1311yescharacteristic
647C22×C4C2×C22⋊D1311yescharacteristic
648C22×C4C2×C22⋊D1311yescharacteristic
649C22×C4C2×C22⋊D1311yescharacteristic
650C22×C4C2×C22⋊D1312yes—
651C22×C4C2×C22⋊D1312yes—
652C22×C4C23×D1311yescharacteristic
653M16—524no—
654M16—524no—
655C2×C8—132no—
656C2×C8—261no—
657C2×C8—261no—
658C2×C8—261no—
659C2×C8—261no—
660C2×C8—261no—
661C2×C8—261no—
662C2×C8—261no—
663C2×C8—261no—
664C2×C8—261no—
665C2×C8—261no—
666C2×C8—261no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—132no—
671C4⋊C4—261no—
672C4⋊C4—261no—
673C4⋊C4—261no—
674C4⋊C4—261no—
675C4⋊C4—261no—
676C4⋊C4—261no—
677C4⋊C4—261no—
678C4⋊C4—522no—
679C4⋊C4C22⋊Dic1314yes—
680C4⋊C4C22×Dic1312yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—522no—
686C22⋊C4—522no—
687C22⋊C4—1041no—
688C22⋊C4C22⋊Dic1314yes—
689C22⋊C4C22⋊Dic1314yes—
690C42—24no—
691C42—522no—
692C42—1041no—
693C42C22×Dic1312yes—
694C42C2×C22⋊D1312yes—
695C13#2242911yescharacteristic, complemented, Sylow
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊Dic1312yes—
716C23C2×C22⋊Dic1312yes—
717C23C22×C22⋊D1311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—48no—
724Q8—41no—
725Q8—41no—
726Q8D4×Dic1314yes—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4—41no—
733D4—41no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—262no—
762C2×C4—521no—
763C2×C4—521no—
764C2×C4—521no—
765C2×C4—521no—
766C2×C4—521no—
767C2×C4—521no—
768C2×C4—521no—
769C2×C4—521no—
770C2×C4—521no—
771C2×C4—521no—
772C2×C4—521no—
773C2×C4—1044no—
774C2×C4C2×C22⋊Dic1312yes—
775C2×C4C2×C22⋊Dic1312yes—
776C2×C4C2×C22⋊Dic1312yes—
777C2×C4C2×C22⋊Dic1312yes—
778C2×C4C2×D4×D1311yescharacteristic
779C2×C4C2×#612911yescharacteristic
780C2×C4#8825111yescharacteristic
781C2×C4#8825111yescharacteristic
782C2×C4C23×Dic1311yescharacteristic
783C2×C4C22×C22⋊D1311yescharacteristic
784C8—262no—
785C8—521no—
786C8—521no—
787C8—521no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22D4×C22⋊D1311yescharacteristic
810C22#1171951111yescharacteristic
811C22#1171952711yescharacteristic
812C22#1171952711yescharacteristic
813C22#1171954211yescharacteristic
814C22#1171954311yescharacteristic
815C22C22×C22⋊Dic1311yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—24no—
821C4—42no—
822C4—42no—
823C4—522no—
824C4—1041no—
825C4—1041no—
826C4—1041no—
827C4C2×D4×Dic1311yescharacteristic
828C4#1171950311yescharacteristic
829C4D4×C22⋊D1311yescharacteristic
830C4#1171951111yescharacteristic
831C2—42no—
832C2—42no—
833C2—82no—
834C2D4×C22⋊Dic1311yescharacteristic
835C2#1312335511yescharacteristic
836C2#1312336911yescharacteristic
837C2#1312646811yescharacteristic
838C2#1312648911yescharacteristic
839C2#1312708911yescharacteristic
840C2#1312710411yescharacteristic
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#22429
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×#11718673C2semidirect
2. C2×#11718893C2semidirect
3. C2×#11718886C2semidirect
4. #13117765C2semidirect
5. #13115769C2semidirect
6. #13115648C2semidirect
7. #13115275C2semidirect
8. #13115270C2semidirect
9. #13115159C2semidirect
10. #13115144C2semidirect
11. #13114851C2semidirect
12. #13114776C2semidirect
13. #13114771C2semidirect
14. C4×#88075C2semidirect
19. C13×#548C4semidirect
76. C22×Q8×C13C2×C4semidirect
90. C13×#124C2×C4semidirect
96. C13×#121C2×C4semidirect
98. C4×Q8×C13C2×C4semidirect
145. #88075D4semidirect
388. #548Dic13semidirect
486. C22×Q8C2×Dic13semidirect
510. #124C2×Dic13semidirect
516. #121C2×Dic13semidirect
518. C4×Q8C2×Dic13semidirect
695. C13#22429semidirect

Maximal subgroups

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

subgroupindex
C2×#117186732
C2×#117188932
C2×#117188862
#131177652
#131157692
#131156482
#131152752
#131152702
#131151592
#131151442
#131148512
#131147762
#131147712
C4×#880752
C2×C13×#5482
#2242913