Finite Group Databasebeta

← #15878519

Subgroups — #15878519

Order 3328.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 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×#11718876C211yesmaximal, characteristic, complemented
4#13117765C211yesmaximal, characteristic, complemented
5#13115769C211yesmaximal, characteristic, complemented
6#13115648C211yesmaximal, characteristic, complemented
7#13115275C211yesmaximal, characteristic, complemented
8#13115270C211yesmaximal, characteristic, complemented
9#13115154C211yesmaximal, characteristic, complemented
10#13115149C211yesmaximal, characteristic, complemented
11#13114846C211yesmaximal, characteristic, complemented
12#13114776C211yesmaximal, characteristic, complemented
13#13114767C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, 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×#88180C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic, complemented
31C22×#6099C2211yescharacteristic
32C22×#6099C2211yescharacteristic, complemented
33#11718893—24no—
34C2×#88075C2211yescharacteristic, complemented
35C2×#88075C2211yescharacteristic, complemented
36C2×#88075C2211yescharacteristic, complemented
37C2×#88075C2211yescharacteristic, complemented
38#11718881—21no—
39#11718876—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#11718673—24no—
53#11718642—21no—
54#11718612—21no—
55C22⋊C4×Dic13—21no—
56#11718597C2211yescharacteristic, complemented
57C4×C4⋊Dic13C2211yescharacteristic, complemented
58C2×C4⋊#1055C2211yescharacteristic, complemented
59C2×C4×#1055C2211yescharacteristic, 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×C414yes—
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—
89C13×#124—22no—
90C13×#124C2×C414yescomplemented
91C13×#123—28no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8C2×C414yescomplemented
94C13×#121—22no—
95C13×#121—28no—
96C13×#121C2×C414yes—
97C13×#120—28no—
98C4×D4×C13—22no—
99C4×D4×C13C2×C414yes—
100C4×D4×C13C2×C414yescomplemented
101C4×D4×C13D414yes—
102C2×C13×C4⋊C4—21no—
103C2×C13×C4⋊C4D411yescharacteristic
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C22⋊C4—21no—
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—28no—
111C2×C13×C22⋊C4D411yescharacteristic
112C2×C13×C22⋊C4D411yescharacteristic
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—41no—
141#88075—41no—
142#88072—22no—
143#88072—22no—
144#88072—22no—
145#88072—22no—
146#88072—22no—
147#88072—41no—
148#88072—41no—
149#88072D414yescomplemented
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#22427—131nomaximal, Sylow
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—24no—
163C24×C13—42no—
164C24×C13—42no—
165C24×C13—42no—
166C24×C13—42no—
167C24×C13—81no—
168C24×C13—81no—
169C24×C13C2×D411yescharacteristic
170C24×C13C2×D411yescharacteristic
171C13×#41—28no—
172C13×#41—44no—
173C13×#41—44no—
174C13×#41—44no—
175C2×Q8×C13—21no—
176C2×Q8×C13—21no—
177C2×Q8×C13—21no—
178C2×Q8×C13—21no—
179C2×Q8×C13—21no—
180C2×Q8×C13C22×C412yes—
181C2×D4×C13—28no—
182C2×D4×C13—24no—
183C2×D4×C13—24no—
184C2×D4×C13—24no—
185C2×D4×C13—21no—
186C2×D4×C13—21no—
187C2×D4×C13—21no—
188C2×D4×C13—21no—
189C2×D4×C13—21no—
190C2×D4×C13—21no—
191C2×D4×C13—21no—
192C2×D4×C13—21no—
193C2×D4×C13—44no—
194C2×D4×C13—44no—
195C2×D4×C13—44no—
196C2×D4×C13—41no—
197C2×D4×C13—41no—
198C2×D4×C13—42no—
199C2×D4×C13—42no—
200C2×D4×C13—42no—
201C2×D4×C13—42no—
202C2×D4×C13—81no—
203C2×D4×C13—81no—
204C2×D4×C13C22⋊C414yes—
205C2×D4×C13C22×C412yes—
206C2×D4×C13C22×C412yes—
207C2×D4×C13C2×D412yes—
208C2×D4×C13#4112yes—
209C22×C4×C13—21no—
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—24no—
220C22×C4×C13—24no—
221C22×C4×C13—42no—
222C22×C4×C13—42no—
223C22×C4×C13—81no—
224C22×C4×C13—81no—
225C22×C4×C13C22×C412yes—
226C22×C4×C13C22×C412yes—
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D412yes—
232C22×C4×C13C2×D412yes—
233C22×C4×C13C2411yescharacteristic
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—42no—
239C22×Dic13—42no—
240C22×Dic13—81no—
241C13×C4⋊C4—24no—
242C13×C4⋊C4—21no—
243C13×C4⋊C4C22⋊C414yes—
244C13×C4⋊C4C22×C412yes—
245C13×C22⋊C4—24no—
246C13×C22⋊C4—24no—
247C13×C22⋊C4—24no—
248C13×C22⋊C4—24no—
249C13×C22⋊C4—24no—
250C13×C22⋊C4C22⋊C414yes—
251C13×C22⋊C4C22⋊C414yes—
252C42×C13C22×C412yes—
253C42×C13C2×D412yes—
254C22⋊Dic13—42no—
255C22⋊Dic13—42no—
256C22⋊Dic13—81no—
257C4⋊Dic13—21no—
258C4⋊Dic13—21no—
259C4⋊Dic13—21no—
260C4⋊Dic13—21no—
261C4⋊Dic13—21no—
262C4⋊Dic13—21no—
263C4⋊Dic13—21no—
264C4⋊Dic13—42no—
265C4⋊Dic13C2×D412yes—
266C4×Dic13—42no—
267C4×Dic13—81no—
268#6099—44no—
269#6099—44no—
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—21no—
280C2×#1055—21no—
281C2×#1055C2×D412yes—
282C2×#546D1311yescharacteristic
283C2×#436—131no—
284C2×#417—131no—
285C2×#418—131no—
286#2352—131no—
287#1983—131no—
288#1958—131no—
289#1895—131no—
290#1894—131no—
291#1874—131no—
292#1873—131no—
293#1804—131no—
294#1788—131no—
295#1786—131no—
296C4×#102—131no—
297C23×C13—22no—
298C23×C13—21no—
299C23×C13—21no—
300C23×C13—22no—
301C23×C13—21no—
302C23×C13—21no—
303C23×C13—22no—
304C23×C13—21no—
305C23×C13—21no—
306C23×C13—21no—
307C23×C13—21no—
308C23×C13—21no—
309C23×C13—21no—
310C23×C13—21no—
311C23×C13—21no—
312C23×C13—22no—
313C23×C13—48no—
314C23×C13—48no—
315C23×C13—41no—
316C23×C13—41no—
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—84no—
326C23×C13—84no—
327C23×C13—84no—
328C23×C13—84no—
329C23×C13—84no—
330C23×C13C2×C22⋊C412yes—
331C23×C13C2×C22⋊C412yes—
332C23×C13C22×D411yescharacteristic
333Q8×C13—22no—
334Q8×C13—22no—
335Q8×C13—41no—
336Q8×C13—41no—
337D4×C13—22no—
338D4×C13—22no—
339D4×C13—22no—
340D4×C13—22no—
341D4×C13—22no—
342D4×C13—44no—
343D4×C13—48no—
344D4×C13—48no—
345D4×C13—41no—
346D4×C13—41no—
347D4×C13—84no—
348D4×C13C4×D414yes—
349C2×C4×C13—21no—
350C2×C4×C13—21no—
351C2×C4×C13—21no—
352C2×C4×C13—21no—
353C2×C4×C13—21no—
354C2×C4×C13—21no—
355C2×C4×C13—21no—
356C2×C4×C13—21no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—48no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—84no—
373C2×C4×C13C2×C22⋊C412yes—
374C2×C4×C13C2×C22⋊C412yes—
375C2×C4×C13C2×C22⋊C412yes—
376C2×C4×C13C2×C22⋊C412yes—
377C2×C4×C13C23×C411yescharacteristic
378C2×C4×C13C22×D411yescharacteristic
379C2×C4×C13C22×D411yescharacteristic
380C2×C4×C13C2×#4111yescharacteristic
381C2×C4×C13H(5,𝔽2)11yescharacteristic
382C2×C4×C13H(5,𝔽2)11yescharacteristic
383C2×Dic13—22no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—84no—
396#1055—22no—
397#1055—41no—
398#1055—41no—
399#1055—41no—
400C22×#41C2×D1311yescharacteristic
401C23×D4C2×D1311yescharacteristic
402C22×M16—131no—
403C22×M16—131no—
404#546—24no—
405#546Dic1318yescomplemented
406C2×#124C2×D1311yescharacteristic
407C2×#123—21no—
408C2×C22⋊Q8C2×D1311yescharacteristic
409C2×#121—21no—
410C2×#121C2×D1311yescharacteristic
411C2×#120—21no—
412C2×C4×D4C2×D1311yescharacteristic
413C2×C4×D4C2×D1311yescharacteristic
414C2×#117—131no—
415C22×C4⋊C4—131no—
416C22×C22⋊C4—21no—
417#436—264no—
418C2×C4⋊C8—131no—
419#418—264no—
420#417—264no—
421C2×#103—131no—
422C2×#103—131no—
423C2×#103—131no—
424C2×#103—131no—
425C2×#102—131no—
426C2×#102—131no—
427C2×#102—131no—
428C2×#102—131no—
429C2×#102—131no—
430C2×#102—131no—
431C2×#102—131no—
432C2×#102—131no—
433C2×C22⋊C8—131no—
434C2×C22⋊C8—131no—
435C2×C4×C8—131no—
436#388—261no—
437#387—261no—
438#386—261no—
439#382—131no—
440#380—131no—
441#380—131no—
442C4×C4⋊C4—131no—
443C4×C22⋊C4—261no—
444#340—131no—
445#340—131no—
446#340—131no—
447#340—131no—
448C22×C13—22no—
449C22×C13—22no—
450C22×C13—24no—
451C22×C13—22no—
452C22×C13—22no—
453C22×C13—22no—
454C22×C13—22no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—41no—
458C22×C13—41no—
459C22×C13—42no—
460C22×C13—41no—
461C22×C13—41no—
462C22×C13—42no—
463C22×C13—41no—
464C22×C13—41no—
465C22×C13—42no—
466C22×C13—41no—
467C22×C13—41no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—816no—
473C22×C13—81no—
474C22×C13—81no—
475C22×C13—81no—
476C22×C13—81no—
477C22×C13C22×C22⋊C411yescharacteristic
478C22×C13D4211yescharacteristic
479C22×C13#54611yescharacteristic
480C22×C13#57511yescharacteristic
481C22×C13#57511yescharacteristic
482C22×C13#57611yescharacteristic
483C22×C13#57711yescharacteristic
484C4×C13—22no—
485C4×C13—22no—
486C4×C13—22no—
487C4×C13—22no—
488C4×C13—42no—
489C4×C13—42no—
490C4×C13C2×C4×D411yescharacteristic
491C4×C13#51811yescharacteristic
492C4×C13D4211yescharacteristic
493C4×C13#54611yescharacteristic
494Dic13—42no—
495Dic13—81no—
496Dic13—81no—
497Dic13—81no—
498C25—21no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41C2×Dic1314yes—
505C22×Q8C22×D1311yescharacteristic
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×Dic1314yescomplemented
515C22×D4C22⋊D1311yescharacteristic
516C22×D4C22×D1311yescharacteristic
517C22×D4C22×D1311yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—261no—
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C2×M16—262no—
524C2×M16—262no—
525C2×M16—262no—
526C2×M16—262no—
527C2×M16—521no—
528C2×M16—521no—
529C22×C8—131no—
530C22×C8—131no—
531C22×C8—131no—
532C22×C8—131no—
533#124—22no—
534#124C2×Dic1314yescomplemented
535#123—28no—
536C22⋊Q8—22no—
537C22⋊Q8C2×Dic1314yescomplemented
538#121—22no—
539#121—28no—
540#121C2×Dic1314yes—
541#120—28no—
542C4×D4—22no—
543C4×D4C2×Dic1314yes—
544C4×D4C2×Dic1314yescomplemented
545C4×D4C22⋊D1314yes—
546#117—262no—
547#117—521no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—131no—
550C2×C4⋊C4—131no—
551C2×C4⋊C4—131no—
552C2×C4⋊C4—131no—
553C2×C4⋊C4—262no—
554C2×C4⋊C4—261no—
555C2×C4⋊C4—521no—
556C2×C4⋊C4C22⋊D1311yescharacteristic
557C2×C4⋊C4C22×D1311yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—28no—
564C2×C22⋊C4—261no—
565C2×C22⋊C4—261no—
566C2×C22⋊C4—261no—
567C2×C22⋊C4C22⋊D1311yescharacteristic
568C2×C22⋊C4C22⋊D1311yescharacteristic
569C2×C42—261no—
570C2×C42—261no—
571C2×C42C22×D1311yescharacteristic
572C4⋊C8—262no—
573#103—262no—
574#103—262no—
575#103—521no—
576#103—521no—
577#102—134no—
578#102—262no—
579#102—262no—
580#102—262no—
581#102—262no—
582#102—262no—
583#102—521no—
584#102—521no—
585C22⋊C8—262no—
586C22⋊C8—262no—
587C4×C8—262no—
588#95—261no—
589#95—261no—
590#95—261no—
591#95—261no—
592#95—261no—
593C2×C13—42no—
594C2×C13—42no—
595C2×C13—44no—
596C2×C13—82no—
597C2×C13D4×C22⋊C411yescharacteristic
598C2×C13#289611yescharacteristic
599C2×C13#289711yescharacteristic
600C2×C13#327311yescharacteristic
601C2×C13#327511yescharacteristic
602C2×C13#332211yescharacteristic
603C2×C13#332311yescharacteristic
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×C22⋊D1311yescharacteristic
614C24C2×C22⋊D1311yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×Dic1312yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic1314yes—
649C2×D4D4×D1312yes—
650C2×D4#612912yes—
651C2×D4C22×Dic1312yes—
652C2×D4C22×Dic1312yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—81no—
669C22×C4—261no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—261no—
673C22×C4—522no—
674C22×C4—522no—
675C22×C4—1041no—
676C22×C4C22×Dic1312yes—
677C22×C4C22×Dic1312yes—
678C22×C4C2×C22⋊D1311yescharacteristic
679C22×C4C2×C22⋊D1311yescharacteristic
680C22×C4C2×C22⋊D1311yescharacteristic
681C22×C4C2×C22⋊D1311yescharacteristic
682C22×C4C2×C22⋊D1312yes—
683C22×C4C2×C22⋊D1312yes—
684C22×C4C23×D1311yescharacteristic
685M16—524no—
686M16—524no—
687C2×C8—132no—
688C2×C8—261no—
689C2×C8—261no—
690C2×C8—261no—
691C2×C8—261no—
692C2×C8—261no—
693C2×C8—261no—
694C2×C8—261no—
695C2×C8—261no—
696C2×C8—261no—
697C2×C8—261no—
698C2×C8—261no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—132no—
702C4⋊C4—261no—
703C4⋊C4—261no—
704C4⋊C4—261no—
705C4⋊C4—261no—
706C4⋊C4—261no—
707C4⋊C4—261no—
708C4⋊C4—261no—
709C4⋊C4—522no—
710C4⋊C4C22⋊Dic1314yes—
711C4⋊C4C22×Dic1312yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—522no—
718C22⋊C4—522no—
719C22⋊C4—1041no—
720C22⋊C4C22⋊Dic1314yes—
721C22⋊C4C22⋊Dic1314yes—
722C42—522no—
723C42—1041no—
724C42C22×Dic1312yes—
725C42C2×C22⋊D1312yes—
726C13#2242711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊Dic1312yes—
761C23C2×C22⋊Dic1312yes—
762C23C22×C22⋊D1311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4D4×Dic1314yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—262no—
804C2×C4—521no—
805C2×C4—521no—
806C2×C4—521no—
807C2×C4—521no—
808C2×C4—521no—
809C2×C4—521no—
810C2×C4—521no—
811C2×C4—521no—
812C2×C4—521no—
813C2×C4—521no—
814C2×C4—521no—
815C2×C4—1044no—
816C2×C4C2×C22⋊Dic1312yes—
817C2×C4C2×C22⋊Dic1312yes—
818C2×C4C2×C22⋊Dic1312yes—
819C2×C4C2×C22⋊Dic1312yes—
820C2×C4C2×D4×D1311yescharacteristic
821C2×C4C2×#612911yescharacteristic
822C2×C4#8825111yescharacteristic
823C2×C4#8825111yescharacteristic
824C2×C4C23×Dic1311yescharacteristic
825C2×C4C22×C22⋊D1311yescharacteristic
826C8—262no—
827C8—521no—
828C8—521no—
829C8—521no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—24no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22D4×C22⋊D1311yescharacteristic
860C22#1171951111yescharacteristic
861C22#1171952711yescharacteristic
862C22#1171952711yescharacteristic
863C22#1171954011yescharacteristic
864C22#1171954111yescharacteristic
865C22C22×C22⋊Dic1311yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—522no—
873C4—1041no—
874C4—1041no—
875C4—1041no—
876C4C2×D4×Dic1311yescharacteristic
877C4#1171950311yescharacteristic
878C4D4×C22⋊D1311yescharacteristic
879C4#1171951111yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊Dic1311yescharacteristic
885C2#1312335511yescharacteristic
886C2#1312336211yescharacteristic
887C2#1312644311yescharacteristic
888C2#1312646311yescharacteristic
889C2#1312703711yescharacteristic
890C2#1312705211yescharacteristic
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#22427
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×#11718673C2semidirect
2. C2×#11718893C2semidirect
3. C2×#11718876C2semidirect
4. #13117765C2semidirect
5. #13115769C2semidirect
6. #13115648C2semidirect
7. #13115275C2semidirect
8. #13115270C2semidirect
9. #13115154C2semidirect
10. #13115149C2semidirect
11. #13114846C2semidirect
12. #13114776C2semidirect
13. #13114767C2semidirect
14. C4×#88072C2semidirect
19. C13×#546C4semidirect
30. C22×C4⋊Dic13C22semidirect
32. C22×#6099C22semidirect
34. C2×#88075C22semidirect
35. C2×#88075C22semidirect
36. C2×#88075C22semidirect
37. C2×#88075C22semidirect
49. #11718873C22semidirect
51. C2×C22⋊#1055C22semidirect
56. #11718597C22semidirect
57. C4×C4⋊Dic13C22semidirect
58. C2×C4⋊#1055C22semidirect
59. C2×C4×#1055C22semidirect
60. #11718121C22semidirect
61. #11718121C22semidirect
62. #11718121C22semidirect
63. #11718121C22semidirect
80. C22×D4×C13C2×C4semidirect
90. C13×#124C2×C4semidirect
93. C13×C22⋊Q8C2×C4semidirect
100. C4×D4×C13C2×C4semidirect
149. #88072D4semidirect
405. #546Dic13semidirect
514. C22×D4C2×Dic13semidirect
534. #124C2×Dic13semidirect
537. C22⋊Q8C2×Dic13semidirect
544. C4×D4C2×Dic13semidirect
726. C13#22427semidirect

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×#117188762
#131177652
#131157692
#131156482
#131152752
#131152702
#131151542
#131151492
#131148462
#131147762
#131147672
C4×#880722
C2×C13×#5462
#2242713