Finite Group Databasebeta

← #16799527

Subgroups — #16799527

Order 3328.

714 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131517C211yesmaximal, characteristic
2#13131401C211yesmaximal, characteristic
3#13130952C211yesmaximal, characteristic, complemented
4#13130952C211yesmaximal, characteristic, complemented
5#13130951C211yesmaximal, characteristic, complemented
6#13130950C211yesmaximal, characteristic, complemented
7#13130790C211yesmaximal, characteristic
8#13130790C211yesmaximal, characteristic
9#13130789C211yesmaximal, characteristic
10#13130788C211yesmaximal, characteristic
11#13130656C211yesmaximal, characteristic, complemented
12#13130656C211yesmaximal, characteristic, complemented
13C4×#88104C211yesmaximal, characteristic, complemented
14C4×#88103C211yesmaximal, characteristic, complemented
15D13×#433C211yesmaximal, characteristic
16C2×D13⋊M16C2211yescharacteristic
17C22×#6118C2211yescharacteristic
18D13×#117C2211yescharacteristic
19#11719127C2211yescharacteristic
20#11719127C2211yescharacteristic
21C2×#88104C2211yescharacteristic
22C2×#88104C2211yescharacteristic
23C2×#88104C2211yescharacteristic
24C2×#88104C2211yescharacteristic
25C2×#88103C2211yescharacteristic
26C2×#88103C2211yescharacteristic
27C2×#88103C2211yescharacteristic
28C2×#88103C2211yescharacteristic
29#11719077—21no—
30#11719077—21no—
31#11719072—21no—
32#11719072—21no—
33#11719068—21no—
34#11719068—21no—
35#11719062—21no—
36#11719062—21no—
37#11719053C2211yescharacteristic
38#11719052C2211yescharacteristic
39C4×#6118C2211yescharacteristic
40C4×#6118C2211yescharacteristic
41C4×#6118C2211yescharacteristic
42C4×#6118C2211yescharacteristic
43C4×#6118C2211yescharacteristic
44C4×#6118C2211yescharacteristic
45C13×#433C411yescharacteristic
46#11718661C411yescharacteristic
47#11718501C411yescharacteristic
48#11718501C411yescharacteristic
49D13×C4⋊C8C2211yescharacteristic
50D13×C4⋊C8C2211yescharacteristic
51D13×C22⋊C8C2211yescharacteristic
52D13×C22⋊C8C2211yescharacteristic
53#11718381C411yescharacteristic
54#11718381C411yescharacteristic
55#11718370C411yescharacteristic
56D13×#97C2211yescharacteristic
57#11718351C411yescharacteristic
58C4×C8×D13C2211yescharacteristic
59#11718268C2211yescharacteristic
60#11718268C2211yescharacteristic
61#11718268C2211yescharacteristic
62#11718268C2211yescharacteristic
63#11718268C2211yescharacteristic
64#11718268C2211yescharacteristic
65#11718268C2211yescharacteristic
66#11718268C2211yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C2×#6122—21no—
69C22×#1057—21no—
70D13⋊M16—22no—
71D13⋊M16—22no—
72C2×#6118—21no—
73C2×#6118—22no—
74C2×#6118—22no—
75C2×#6118C2311yescharacteristic
76C2×#6118C2311yescharacteristic
77C2×#6118C2311yescharacteristic
78C2×#6118C2311yescharacteristic
79C2×#6118C2311yescharacteristic
80C2×#6118C2311yescharacteristic
81C2×#6118C2311yescharacteristic
82C2×#6118C2311yescharacteristic
83C2×D13⋊C8—21no—
84C13×#117C2×C411yescharacteristic
85#88180C2×C411yescharacteristic
86C2×C8×D13C2311yescharacteristic
87C2×C8×D13C2311yescharacteristic
88C2×C8×D13C2311yescharacteristic
89C2×C8×D13C2311yescharacteristic
90#88146D411yescharacteristic
91#88146D411yescharacteristic
92C4⋊C4×D13Q811yescharacteristic
93C4⋊C4×D13Q811yescharacteristic
94C22⋊C4×D13Q811yescharacteristic
95C22⋊C4×D13Q811yescharacteristic
96#88131D411yescharacteristic
97#88131D411yescharacteristic
98#88126C2×C411yescharacteristic
99#88126C2×C411yescharacteristic
100C42×D13C2311yescharacteristic
101C42×D13C2311yescharacteristic
102C22⋊#1057—21no—
103C22⋊#1057—21no—
104#88112—21no—
105#88112—21no—
106#88111—21no—
107#88111—21no—
108#88110—21no—
109#88110—21no—
110#88110—21no—
111#88110—21no—
112#88110—21no—
113#88110—21no—
114C4⋊#1057—21no—
115C4⋊#1057—21no—
116C4×#1057—21no—
117C4×#1057—21no—
118C4×#1057—21no—
119C4×#1057—21no—
120C4×#1057—21no—
121C4×#1057—21no—
122#88104—22no—
123#88104—22no—
124#88104—22no—
125#88104—22no—
126#88103—22no—
127#88103—22no—
128#88103—22no—
129#88103—22no—
130C13×C4⋊C8C2×C411yescharacteristic
131C13×C4⋊C8C2×C411yescharacteristic
132C13×C22⋊C8C2×C411yescharacteristic
133C13×C22⋊C8C2×C411yescharacteristic
134C13×#97C2×C411yescharacteristic
135C4×C8×C13C2×C411yescharacteristic
136C22⋊#1055C2×C411yescharacteristic
137C22⋊#1055C2×C411yescharacteristic
138#88060C2×C411yescharacteristic
139#88060C2×C411yescharacteristic
140#88060C2×C411yescharacteristic
141#88060C2×C411yescharacteristic
142#88055C2×C411yescharacteristic
143#88055C2×C411yescharacteristic
144#88054C2×C411yescharacteristic
145#88054C2×C411yescharacteristic
146#88054C2×C411yescharacteristic
147#88054C2×C411yescharacteristic
148C8×Dic13C2×C411yescharacteristic
149C8×Dic13C2×C411yescharacteristic
150C4⋊#1055C2×C411yescharacteristic
151C4⋊#1055C2×C411yescharacteristic
152#88043C2×C411yescharacteristic
153C4×#1055C2×C411yescharacteristic
154#21372—131nomaximal, Sylow
155C23×D13C2×Q811yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C22×Dic13C2×D411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13C22×C411yescharacteristic
163C2×C4×D13C2×D411yescharacteristic
164C2×C4×D13C2×Q811yescharacteristic
165C2×C4×D13C2×Q811yescharacteristic
166C2×C4×D13C2×Q811yescharacteristic
167C2×C4×D13C2×Q811yescharacteristic
168C2×C4×D13C2×Q811yescharacteristic
169C2×C4×D13C2411yescharacteristic
170#6122—24no—
171C2×#1057—24no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057—21no—
175C2×#1057—21no—
176C2×#1057—21no—
177C2×#1057—21no—
178C2×#1057—21no—
179C2×#1057—21no—
180#6118—24no—
181#6118—21no—
182#6118—21no—
183#6118—21no—
184#6118—21no—
185#6118—21no—
186#6118—21no—
187#6118—21no—
188#6118—21no—
189#6118—21no—
190#6118—21no—
191#6118—21no—
192#6118—21no—
193#6118#4112yes—
194#6118#4112yes—
195#6118#4112yes—
196#6118#4112yes—
197D13⋊C8—24no—
198C2×C8×C13C22×C411yescharacteristic
199C2×C8×C13C22×C411yescharacteristic
200C2×C8×C13C22×C411yescharacteristic
201C2×C8×C13C22×C411yescharacteristic
202C13×C4⋊C4C4⋊C411yescharacteristic
203C13×C4⋊C4C4⋊C411yescharacteristic
204C13×C22⋊C4C4⋊C411yescharacteristic
205C13×C22⋊C4C4⋊C411yescharacteristic
206C42×C13C22×C411yescharacteristic
207C42×C13C22×C411yescharacteristic
208C22⋊Dic13C4⋊C411yescharacteristic
209C22⋊Dic13C4⋊C411yescharacteristic
210#6103C4⋊C411yescharacteristic
211#6103C4⋊C411yescharacteristic
212#6103C4⋊C411yescharacteristic
213#6103C4⋊C411yescharacteristic
214C4⋊Dic13C4⋊C411yescharacteristic
215C4⋊Dic13C4⋊C411yescharacteristic
216#6101C4⋊C411yescharacteristic
217#6101C4⋊C411yescharacteristic
218#6101C4⋊C411yescharacteristic
219#6101C4⋊C411yescharacteristic
220C4×Dic13C22×C411yescharacteristic
221C4×Dic13C22×C411yescharacteristic
222C4×Dic13C2×D411yescharacteristic
223C4×Dic13C2×D411yescharacteristic
224C4×Dic13C2×D411yescharacteristic
225C4×Dic13C2×D411yescharacteristic
226C2×#1055C22×C411yescharacteristic
227C2×#1055C22×C411yescharacteristic
228C2×#1055C22×C411yescharacteristic
229C2×#1055C22×C411yescharacteristic
230C8×D13—21no—
231C8×D13—21no—
232C8×D13—21no—
233C8×D13—21no—
234C8×D13—21no—
235C8×D13—21no—
236C8×D13—21no—
237C8×D13—21no—
238#2921—131no—
239C2×#433—131no—
240#2873—131no—
241#1950—131no—
242#1950—131no—
243#1950—131no—
244#1950—131no—
245#1855—131no—
246#1855—131no—
247#1855—131no—
248#1855—131no—
249#1778—131no—
250#1778—131no—
251C4×#108—131no—
252C4×#108—131no—
253C23×C13C2×C4⋊C411yescharacteristic
254C22×D13—21no—
255C22×D13—21no—
256C22×D13—41no—
257C22×D13—41no—
258C22×D13C2×C4⋊C411yescharacteristic
259C22×D13C22×Q811yescharacteristic
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13C2×C4⋊C411yescharacteristic
263C2×C4×C13C2×C4⋊C411yescharacteristic
264C2×C4×C13C2×C4⋊C411yescharacteristic
265C2×C4×C13C2×C4⋊C411yescharacteristic
266C2×C4×C13C2×C4⋊C411yescharacteristic
267C2×C4×C13C23×C411yescharacteristic
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13C2×C4⋊C411yescharacteristic
271C2×Dic13C2×C4⋊C411yescharacteristic
272C2×Dic13C2×C4⋊C411yescharacteristic
273C2×Dic13C2×C4⋊C411yescharacteristic
274C2×Dic13C2×C4⋊C411yescharacteristic
275C2×Dic13C22×D411yescharacteristic
276C4×D13—21no—
277C4×D13—21no—
278C4×D13—21no—
279C4×D13—21no—
280C4×D13—21no—
281C4×D13—21no—
282C4×D13—41no—
283C4×D13—41no—
284C4×D13—41no—
285C4×D13—41no—
286C4×D13C2×#4111yescharacteristic
287C4×D13C2×#4111yescharacteristic
288C4×D13C2×#4111yescharacteristic
289C4×D13C2×#4111yescharacteristic
290#1057—22no—
291#1057—22no—
292#1057—22no—
293#1057—22no—
294#1057—41no—
295#1057—41no—
296#1057—41no—
297#1057—41no—
298C8×C13—21no—
299C8×C13—21no—
300C8×C13—21no—
301C8×C13—21no—
302#1055—21no—
303#1055—21no—
304#1055—21no—
305#1055—21no—
306C22×M16—131no—
307C22×M16—131no—
308C2×#117—131no—
309#433—131no—
310#433—131no—
311#433—131no—
312#433—131no—
313#433—131no—
314#433—131no—
315#433—131no—
316#433—261no—
317#433—261no—
318#433—261no—
319#433—261no—
320#433#26111yescharacteristic
321C2×#108—131no—
322C2×#108—131no—
323C2×#108—131no—
324C2×#108—131no—
325C2×#108—131no—
326C2×#108—131no—
327C2×#108—131no—
328C2×#108—131no—
329#423—131no—
330#423—131no—
331C2×C4⋊C8—131no—
332C2×C4⋊C8—131no—
333#407—131no—
334#407—131no—
335C2×C22⋊C8—131no—
336C2×C22⋊C8—131no—
337#405—261no—
338#405—261no—
339#405—261no—
340#405—261no—
341C4×M16—131no—
342C4×M16—131no—
343C4×M16—131no—
344C4×M16—131no—
345C4×M16—131no—
346C4×M16—131no—
347C2×#97—131no—
348C2×C4×C8—131no—
349#341—131no—
350#341—131no—
351#341—131no—
352#341—131no—
353#341—131no—
354#341—131no—
355#341—131no—
356#341—131no—
357C22×C13—21no—
358C22×C13—21no—
359C22×C13—21no—
360C22×C13C22×C4⋊C411yescharacteristic
361C2×D13—21no—
362C2×D13—21no—
363C2×D13—21no—
364C2×D13—21no—
365C2×D13—21no—
366C2×D13—81no—
367C2×D13—81no—
368C2×D13#53311yescharacteristic
369C2×D13#53311yescharacteristic
370C4×C13—21no—
371C4×C13—21no—
372C4×C13—21no—
373C4×C13—21no—
374C4×C13—21no—
375C4×C13C4×#4111yescharacteristic
376C4×C13C4×#4111yescharacteristic
377Dic13—21no—
378Dic13—21no—
379Dic13—21no—
380Dic13—21no—
381Dic13—21no—
382Dic13#52511yescharacteristic
383Dic13#52511yescharacteristic
384C23×C4—131no—
385C2×M16—131no—
386C2×M16—131no—
387C2×M16—131no—
388C2×M16—131no—
389C2×M16—131no—
390C2×M16—131no—
391C2×M16—131no—
392C2×M16—131no—
393C2×M16—262no—
394C2×M16—262no—
395C2×M16—262no—
396C2×M16—262no—
397C2×M16—261no—
398C2×M16—261no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—261no—
404C22×C8—261no—
405#117—131no—
406#117—131no—
407#117—131no—
408#117—131no—
409#117—131no—
410#117—131no—
411#117—131no—
412#117C2×#26111yescharacteristic
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C22⋊C4—131no—
416C2×C22⋊C4—131no—
417C2×C42—131no—
418C2×C42—131no—
419#108—262no—
420#108—262no—
421#108—262no—
422#108—262no—
423#108—262no—
424#108—262no—
425#108—262no—
426#108—262no—
427C4⋊C8—131no—
428C4⋊C8—131no—
429C4⋊C8—131no—
430C4⋊C8—131no—
431C4⋊C8—131no—
432C4⋊C8—131no—
433C4⋊C8—261no—
434C4⋊C8—261no—
435C4⋊C8—261no—
436C4⋊C8—261no—
437C4⋊C8C2×#26111yescharacteristic
438C4⋊C8C2×#26111yescharacteristic
439C22⋊C8—131no—
440C22⋊C8—131no—
441C22⋊C8—131no—
442C22⋊C8—131no—
443C22⋊C8—131no—
444C22⋊C8—131no—
445C22⋊C8—261no—
446C22⋊C8—261no—
447C22⋊C8—261no—
448C22⋊C8—261no—
449C22⋊C8C2×#26111yescharacteristic
450C22⋊C8C2×#26111yescharacteristic
451#97—131no—
452#97—131no—
453#97—131no—
454#97—261no—
455#97—261no—
456#97—261no—
457#97—261no—
458#97—261no—
459#97—261no—
460#97C2×#26111yescharacteristic
461C4×C8—131no—
462C4×C8—131no—
463C4×C8—131no—
464C4×C8—261no—
465C4×C8—261no—
466C4×C8—261no—
467C4×C8—261no—
468C4×C8—261no—
469C4×C8—261no—
470C4×C8C2×#26111yescharacteristic
471C2×C13—41no—
472C2×C13#229611yescharacteristic
473C2×C13#291611yescharacteristic
474C2×C13#291611yescharacteristic
475D13—21no—
476D13—21no—
477D13—41no—
478C24—131no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—131no—
486C22×C4—131no—
487C22×C4—131no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4C22×#26111yescharacteristic
493M16—132no—
494M16—132no—
495M16—132no—
496M16—132no—
497M16—261no—
498M16—261no—
499M16—261no—
500M16—261no—
501M16—264no—
502M16—264no—
503M16—261no—
504M16—261no—
505M16—261no—
506M16—261no—
507M16—261no—
508M16—261no—
509M16—261no—
510M16—261no—
511C2×C8—131no—
512C2×C8—131no—
513C2×C8—131no—
514C2×C8—131no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—264no—
528C2×C8—264no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8C22×#26111yescharacteristic
534C2×C8C22×#26111yescharacteristic
535C2×C8C22×#26111yescharacteristic
536C2×C8C22×#26111yescharacteristic
537C4⋊C4—131no—
538C4⋊C4—131no—
539C4⋊C4—131no—
540C4⋊C4—131no—
541C4⋊C4—131no—
542C4⋊C4—131no—
543C4⋊C4C4⋊#26111yescharacteristic
544C4⋊C4C4⋊#26111yescharacteristic
545C22⋊C4—131no—
546C22⋊C4—131no—
547C22⋊C4—131no—
548C22⋊C4—131no—
549C22⋊C4—131no—
550C22⋊C4—131no—
551C22⋊C4C4⋊#26111yescharacteristic
552C22⋊C4C4⋊#26111yescharacteristic
553C42—131no—
554C42—131no—
555C42—131no—
556C42—131no—
557C42—131no—
558C42—131no—
559C42C22×#26111yescharacteristic
560C42C22×#26111yescharacteristic
561C13#2137211yescharacteristic, complemented, Sylow
562C23—131no—
563C23—131no—
564C23—261no—
565C23—261no—
566C23—521no—
567C23—521no—
568C23C2×C4⋊#26111yescharacteristic
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—131no—
572C2×C4—131no—
573C2×C4—131no—
574C2×C4—131no—
575C2×C4—131no—
576C2×C4—131no—
577C2×C4—131no—
578C2×C4—131no—
579C2×C4—131no—
580C2×C4—131no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—261no—
584C2×C4—261no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4C2×C4⋊#26111yescharacteristic
594C2×C4C2×C4⋊#26111yescharacteristic
595C2×C4C2×C4⋊#26111yescharacteristic
596C2×C4C2×C4⋊#26111yescharacteristic
597C2×C4C2×C4⋊#26111yescharacteristic
598C2×C4C23×#26111yescharacteristic
599C8—21no—
600C8—21no—
601C8—21no—
602C8—21no—
603C8—262no—
604C8—262no—
605C8—262no—
606C8—262no—
607C8—261no—
608C8—261no—
609C8—261no—
610C8—261no—
611C8—521no—
612C8—521no—
613C8—521no—
614C8—521no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—131no—
619C22—131no—
620C22—261no—
621C22—261no—
622C22—261no—
623C22—261no—
624C22—261no—
625C22—1041no—
626C22—1041no—
627C22C22×C4⋊#26111yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—131no—
634C4—131no—
635C4—261no—
636C4—261no—
637C4—261no—
638C4—261no—
639C4—261no—
640C4#41×#26111yescharacteristic
641C4#41×#26111yescharacteristic
642C2—41no—
643C2—261no—
644C2—261no—
645C2—521no—
646C2#1313129611yescharacteristic
647C2#1313149711yescharacteristic
648C2#1313149811yescharacteristic
subgroupG/H
centerC22C22×C4⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#433C4
socleC22×C13C22×C4⋊C4
prime radicalC23×D13C2×Q8
cosocleC2×C4×D13C24
hypercenter#433#261
hypocenterC13#21372
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #13130952C2semidirect
4. #13130952C2semidirect
5. #13130951C2semidirect
6. #13130950C2semidirect
11. #13130656C2semidirect
12. #13130656C2semidirect
13. C4×#88104C2semidirect
14. C4×#88103C2semidirect
561. C13#21372semidirect

Maximal subgroups

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

subgroupindex
#131315172
#131314012
#131309522
#131309512
#131309502
#131307902
#131307892
#131307882
#131306562
C4×#881042
C4×#881032
D13×#4332
#2137213