Finite Group Databasebeta

← #15878474

Subgroups — #15878474

Order 3328.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718672C211yesmaximal, characteristic, complemented
2C2×#11718876C211yesmaximal, characteristic, complemented
3C2×#11718894C211yesmaximal, characteristic, complemented
4#13117785C211yesmaximal, characteristic, complemented
5#13115769C211yesmaximal, characteristic, complemented
6#13115653C211yesmaximal, characteristic, complemented
7#13115270C211yesmaximal, characteristic, complemented
8#13115265C211yesmaximal, characteristic, complemented
9#13115159C211yesmaximal, characteristic, complemented
10#13115149C211yesmaximal, 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×#88180C2211yescharacteristic
30C2×#88180C2211yescharacteristic, complemented
31C22×#6099C2211yescharacteristic
32C23×#1055C2211yescharacteristic, complemented
33#11718894—24no—
34C2×#88075C2211yescharacteristic, complemented
35C2×#88075C2211yescharacteristic, complemented
36C2×#88075C2211yescharacteristic, complemented
37C2×#88075C2211yescharacteristic, complemented
38#11718882—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#11718672—24no—
53C4⋊C4×Dic13—21no—
54#11718612—21no—
55#11718612—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×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×C414yes—
81C22×D4×C13D411yescharacteristic
82C22×D4×C13C2311yescharacteristic
83C22×D4×C13C2311yescharacteristic
84C23×C4×C13—21no—
85C23×C4×C13—21no—
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C13×#124—22no—
89C13×#124C2×C414yes—
90C13×#123—28no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8C2×C414yes—
93C13×#121—22no—
94C13×#121—28no—
95C13×#121C2×C414yes—
96C13×#120—28no—
97C4×D4×C13—22no—
98C4×D4×C13C2×C414yes—
99C4×D4×C13C2×C414yes—
100C4×D4×C13D414yes—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4D411yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C22⋊C4—21no—
105C2×C13×C22⋊C4—21no—
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—28no—
110C2×C13×C22⋊C4D411yescharacteristic
111C2×C13×C22⋊C4D411yescharacteristic
112C2×C42×C13C2311yescharacteristic
113C2×C22⋊Dic13—21no—
114C2×C22⋊Dic13—21no—
115C2×C22⋊Dic13—21no—
116C2×C22⋊Dic13—21no—
117#88180—22no—
118#88180—22no—
119#88180—41no—
120#88180—41no—
121C2×C4⋊Dic13—21no—
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13C2311yescharacteristic
124C2×C4⋊Dic13C2311yescharacteristic
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4×Dic13—21no—
128C2×C4×Dic13—21no—
129C2×C4×Dic13—21no—
130C2×#6099—22no—
131C2×#6099—22no—
132C2×#6099—41no—
133C22×#1055—22no—
134C22×#1055—22no—
135C22×#1055—41no—
136C22×#1055C2311yescharacteristic
137C22×#1055C2311yescharacteristic
138C22×#1055C2311yescharacteristic
139C22×#1055C2311yescharacteristic
140#88075—22no—
141#88075—22no—
142#88075—41no—
143#88075—41no—
144#88072—22no—
145#88072—22no—
146#88072—22no—
147#88072—22no—
148#88072—22no—
149#88072—41no—
150#88072—41no—
151#88072D414yescomplemented
152#88071—21no—
153#88071—21no—
154#88071—21no—
155C22⋊#1055—22no—
156C22⋊#1055—22no—
157C4⋊#1055—22no—
158#88043—22no—
159#22424—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—
238C13×C4⋊C4—24no—
239C13×C4⋊C4—21no—
240C13×C4⋊C4C22⋊C414yes—
241C13×C4⋊C4C22×C412yes—
242C13×C22⋊C4—24no—
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×C13C22×C412yes—
250C42×C13C2×D412yes—
251C22⋊Dic13—42no—
252C22⋊Dic13—42no—
253C22⋊Dic13—81no—
254C22⋊Dic13—81no—
255C4⋊Dic13—21no—
256C4⋊Dic13—21no—
257C4⋊Dic13—21no—
258C4⋊Dic13—21no—
259C4⋊Dic13—21no—
260C4⋊Dic13—21no—
261C4⋊Dic13—21no—
262C4⋊Dic13—42no—
263C4⋊Dic13—81no—
264C4⋊Dic13C2×D412yes—
265C4×Dic13—42no—
266C4×Dic13—42no—
267C4×Dic13—42no—
268#6099—44no—
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—21no—
280C2×#1055—44no—
281C2×#1055C2×D412yes—
282C2×#546D1311yescharacteristic
283C2×#435—131no—
284C2×#418—131no—
285C2×#416—131no—
286#2354—131no—
287#1983—131no—
288#1959—131no—
289#1894—131no—
290#1893—131no—
291#1875—131no—
292#1873—131no—
293#1802—131no—
294#1788—131no—
295#1786—131no—
296#1762—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—
395#1055—22no—
396#1055—41no—
397#1055—41no—
398#1055—41no—
399C22×#41C2×D1311yescharacteristic
400C23×D4C2×D1311yescharacteristic
401C22×M16—131no—
402C23×C8—131no—
403#546—24no—
404#546Dic1318yescomplemented
405C2×#124C2×D1311yescharacteristic
406C2×#123—21no—
407C2×C22⋊Q8C2×D1311yescharacteristic
408C2×#121—21no—
409C2×#121C2×D1311yescharacteristic
410C2×#120—21no—
411C2×C4×D4C2×D1311yescharacteristic
412C2×C4×D4C2×D1311yescharacteristic
413C2×#117—131no—
414C2×#117—131no—
415C22×C22⋊C4—21no—
416#435—264no—
417C2×C4⋊C8—131no—
418#418—264no—
419#416—264no—
420C2×#103—131no—
421C2×#103—131no—
422C2×#103—131no—
423C2×#103—131no—
424C2×#102—131no—
425C2×#102—131no—
426C2×#102—131no—
427C2×#102—131no—
428C2×#102—131no—
429C2×#102—131no—
430C2×#102—131no—
431C2×#102—131no—
432C2×C22⋊C8—131no—
433C2×C22⋊C8—131no—
434C2×#97—131no—
435#390—261no—
436#388—261no—
437#388—261no—
438#384—131no—
439#380—131no—
440#380—131no—
441C4×C4⋊C4—131no—
442C4×C4⋊C4—261no—
443#340—131no—
444#340—131no—
445#340—131no—
446#340—131no—
447C22×C13—22no—
448C22×C13—22no—
449C22×C13—24no—
450C22×C13—22no—
451C22×C13—22no—
452C22×C13—22no—
453C22×C13—22no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—41no—
457C22×C13—41no—
458C22×C13—42no—
459C22×C13—41no—
460C22×C13—41no—
461C22×C13—42no—
462C22×C13—41no—
463C22×C13—41no—
464C22×C13—42no—
465C22×C13—41no—
466C22×C13—41no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—816no—
472C22×C13—81no—
473C22×C13—81no—
474C22×C13—81no—
475C22×C13—81no—
476C22×C13C22×C22⋊C411yescharacteristic
477C22×C13D4211yescharacteristic
478C22×C13#54611yescharacteristic
479C22×C13#57511yescharacteristic
480C22×C13#57511yescharacteristic
481C22×C13#57611yescharacteristic
482C22×C13#57711yescharacteristic
483C4×C13—22no—
484C4×C13—22no—
485C4×C13—22no—
486C4×C13—22no—
487C4×C13—42no—
488C4×C13—42no—
489C4×C13C2×C4×D411yescharacteristic
490C4×C13#51811yescharacteristic
491C4×C13D4211yescharacteristic
492C4×C13#54611yescharacteristic
493Dic13—42no—
494Dic13—81no—
495Dic13—81no—
496Dic13—81no—
497C25—21no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41C2×Dic1314yes—
504C22×Q8C22×D1311yescharacteristic
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×Dic1314yes—
514C22×D4C22⋊D1311yescharacteristic
515C22×D4C22×D1311yescharacteristic
516C22×D4C22×D1311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C22×D1311yescharacteristic
520C23×C4C22×D1311yescharacteristic
521C2×M16—262no—
522C2×M16—262no—
523C2×M16—521no—
524C22×C8—131no—
525C22×C8—131no—
526C22×C8—131no—
527C22×C8—131no—
528C22×C8—262no—
529C22×C8—262no—
530C22×C8—521no—
531#124—22no—
532#124C2×Dic1314yes—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8C2×Dic1314yes—
536#121—22no—
537#121—28no—
538#121C2×Dic1314yes—
539#120—28no—
540C4×D4—22no—
541C4×D4C2×Dic1314yes—
542C4×D4C2×Dic1314yes—
543C4×D4C22⋊D1314yes—
544#117—262no—
545#117—262no—
546#117—521no—
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—261no—
554C2×C4⋊C4—261no—
555C2×C4⋊C4C22⋊D1311yescharacteristic
556C2×C4⋊C4C22×D1311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—28no—
563C2×C22⋊C4—261no—
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×C42—261no—
572C2×C42C22×D1311yescharacteristic
573C4⋊C8—262no—
574#103—262no—
575#103—262no—
576#103—521no—
577#103—521no—
578#102—134no—
579#102—262no—
580#102—262no—
581#102—262no—
582#102—262no—
583#102—262no—
584#102—521no—
585#102—521no—
586C22⋊C8—262no—
587C22⋊C8—262no—
588#97—262no—
589#95—261no—
590#95—261no—
591#95—261no—
592C2×C13—42no—
593C2×C13—42no—
594C2×C13—44no—
595C2×C13—82no—
596C2×C13D4×C22⋊C411yescharacteristic
597C2×C13#289611yescharacteristic
598C2×C13#289711yescharacteristic
599C2×C13#326711yescharacteristic
600C2×C13#326811yescharacteristic
601C2×C13#331111yescharacteristic
602C2×C13#331911yescharacteristic
603C24—21no—
604C24—21no—
605C24—24no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—81no—
611C24—81no—
612C24C2×C22⋊D1311yescharacteristic
613C24C2×C22⋊D1311yescharacteristic
614#41—28no—
615#41—44no—
616#41—44no—
617#41—44no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8C22×Dic1312yes—
624C2×D4—28no—
625C2×D4—24no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—41no—
640C2×D4—41no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C22⋊Dic1314yes—
648C2×D4D4×D1312yes—
649C2×D4#612912yes—
650C2×D4C22×Dic1312yes—
651C2×D4C22×Dic1312yes—
652C22×C4—21no—
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—24no—
663C22×C4—24no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—81no—
667C22×C4—81no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4C22×Dic1312yes—
673C22×C4C22×Dic1312yes—
674C22×C4C2×C22⋊D1311yescharacteristic
675C22×C4C2×C22⋊D1311yescharacteristic
676C22×C4C2×C22⋊D1311yescharacteristic
677C22×C4C2×C22⋊D1311yescharacteristic
678C22×C4C2×C22⋊D1312yes—
679C22×C4C2×C22⋊D1312yes—
680C22×C4C23×D1311yescharacteristic
681M16—524no—
682C2×C8—132no—
683C2×C8—261no—
684C2×C8—261no—
685C2×C8—261no—
686C2×C8—261no—
687C2×C8—261no—
688C2×C8—261no—
689C2×C8—261no—
690C2×C8—261no—
691C2×C8—261no—
692C2×C8—261no—
693C2×C8—261no—
694C2×C8—524no—
695C4⋊C4—24no—
696C4⋊C4—21no—
697C4⋊C4—132no—
698C4⋊C4—261no—
699C4⋊C4—261no—
700C4⋊C4—261no—
701C4⋊C4—261no—
702C4⋊C4—261no—
703C4⋊C4—261no—
704C4⋊C4—261no—
705C4⋊C4—522no—
706C4⋊C4—1041no—
707C4⋊C4C22⋊Dic1314yes—
708C4⋊C4C22×Dic1312yes—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—522no—
715C22⋊C4—522no—
716C22⋊C4—1041no—
717C22⋊C4—1041no—
718C22⋊C4C22⋊Dic1314yes—
719C22⋊C4C22⋊Dic1314yes—
720C42—522no—
721C42—522no—
722C42—522no—
723C42C22×Dic1312yes—
724C42C2×C22⋊D1312yes—
725C13#2242411yescharacteristic, complemented, Sylow
726C23—21no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊Dic1312yes—
760C23C2×C22⋊Dic1312yes—
761C23C22×C22⋊D1311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4D4×Dic1314yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
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—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—262no—
803C2×C4—521no—
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×C4C2×C22⋊Dic1312yes—
815C2×C4C2×C22⋊Dic1312yes—
816C2×C4C2×C22⋊Dic1312yes—
817C2×C4C2×C22⋊Dic1312yes—
818C2×C4C2×D4×D1311yescharacteristic
819C2×C4C2×#612911yescharacteristic
820C2×C4#8825111yescharacteristic
821C2×C4#8825111yescharacteristic
822C2×C4C23×Dic1311yescharacteristic
823C2×C4C22×C22⋊D1311yescharacteristic
824C8—262no—
825C8—521no—
826C8—521no—
827C8—521no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—24no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22D4×C22⋊D1311yescharacteristic
858C22#1171951111yescharacteristic
859C22#1171952711yescharacteristic
860C22#1171952711yescharacteristic
861C22#1171954011yescharacteristic
862C22#1171954111yescharacteristic
863C22C22×C22⋊Dic1311yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—522no—
871C4—1041no—
872C4—1041no—
873C4—1041no—
874C4C2×D4×Dic1311yescharacteristic
875C4#1171950311yescharacteristic
876C4D4×C22⋊D1311yescharacteristic
877C4#1171951111yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊Dic1311yescharacteristic
883C2#1312335511yescharacteristic
884C2#1312336211yescharacteristic
885C2#1312635711yescharacteristic
886C2#1312637211yescharacteristic
887C2#1312687211yescharacteristic
888C2#1312699211yescharacteristic
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#22424
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×#11718876C2semidirect
3. C2×#11718894C2semidirect
4. #13117785C2semidirect
5. #13115769C2semidirect
6. #13115653C2semidirect
7. #13115270C2semidirect
8. #13115265C2semidirect
9. #13115159C2semidirect
10. #13115149C2semidirect
11. #13114836C2semidirect
12. #13114776C2semidirect
13. #13114767C2semidirect
14. #13114661C2semidirect
19. C13×#546C4semidirect
30. C2×#88180C22semidirect
32. C23×#1055C22semidirect
34. C2×#88075C22semidirect
35. C2×#88075C22semidirect
36. C2×#88075C22semidirect
37. 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
151. #88072D4semidirect
404. #546Dic13semidirect
725. C13#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#117186722
C2×#117188762
C2×#117188942
#131177852
#131157692
#131156532
#131152702
#131152652
#131151592
#131151492
#131148362
#131147762
#131147672
#131146612
C2×C13×#5462
#2242413