Finite Group Databasebeta

← #15870469

Subgroups — #15870469

Order 3328.

834 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718685C211yesmaximal, characteristic, complemented
2C2×#11718350C211yesmaximal, characteristic
3#13118106C211yesmaximal, characteristic
4#13115554C211yesmaximal, characteristic, complemented
5#13115403C211yesmaximal, characteristic, complemented
6#13115403C211yesmaximal, characteristic, complemented
7#13115015C211yesmaximal, characteristic
8#13115015C211yesmaximal, characteristic
9#13114817C211yesmaximal, characteristic
10#13114713C211yesmaximal, characteristic, complemented
11#13114709C211yesmaximal, characteristic, complemented
12#13114697C211yesmaximal, characteristic, complemented
13#13114618C211yesmaximal, characteristic
14#13114616C211yesmaximal, characteristic
15C13×#1984C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C22×#6094C2211yescharacteristic
18C22×C8×D13C2211yescharacteristic
19C2×#88126C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C4×C8×C13C2211yescharacteristic
22#11718892C411yescharacteristic
23#11718890C411yescharacteristic
24C2×#88060C2211yescharacteristic
25C2×#88060C2211yescharacteristic
26C2×#88055C2211yescharacteristic
27C2×#88055C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×C8×Dic13C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32#11718685—24no—
33#11718655C411yescharacteristic
34#11718655C411yescharacteristic
35#11718653C411yescharacteristic
36#11718645C411yescharacteristic
37#11718645C411yescharacteristic
38#11718643C411yescharacteristic
39C4×#6103C2211yescharacteristic
40C4×#6103C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42C4×#6101C2211yescharacteristic
43C4×#6101C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×#88043C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718350—24no—
51C13×#336C2211yescharacteristic
52C13×#336C2211yescharacteristic
53C13×#336C2211yescharacteristic
54C13×#336C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61C22×Q8×C13C2×C411yescharacteristic
62C22×C4×D13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C4×Q8×C13—22no—
68C4×Q8×C13—22no—
69C2×C13×C4⋊C4C2×C411yescharacteristic
70C2×C13×C4⋊C4C2×C411yescharacteristic
71C2×C13×C4⋊C4C2×C411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2×C411yescharacteristic
77C2×#6103C2×C411yescharacteristic
78C2×#6103C2×C411yescharacteristic
79C2×#6103C2×C411yescharacteristic
80C2×#6103C2×C411yescharacteristic
81C2×C4⋊Dic13C2×C411yescharacteristic
82C2×C4⋊Dic13C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C2×#6094—22no—
97C2×#6094—22no—
98C2×#6094Q814yescomplemented
99C2×C8×D13—22no—
100C2×C8×D13—22no—
101C2×C8×D13—22no—
102#88126—22no—
103#88126—22no—
104C13×C4⋊C8—22no—
105C4×C8×C13—22no—
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88060—22no—
117#88060—22no—
118#88055—22no—
119#88055—22no—
120#88054—22no—
121#88054—22no—
122C8×Dic13—22no—
123C8×Dic13—22no—
124C4⋊#1055—22no—
125C4⋊#1055—22no—
126C4⋊#1055—22no—
127#88043—22no—
128#88043D414yes—
129C4×#1055—22no—
130#21606—131nomaximal, Sylow
131C23×D13C22×C411yescharacteristic
132C2×Q8×C13—22no—
133C2×Q8×C13—22no—
134C2×Q8×C13—41no—
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C2411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C2×C4×D13—21no—
150C2×C4×D13—21no—
151C2×C4×D13—21no—
152C2×C4×D13—21no—
153C2×C4×D13C2×Q812yes—
154C2×C4×D13#4112yes—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13C2×Q812yes—
166C2×C8×C13#4112yes—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13C2×D412yes—
175C42×C13#4112yes—
176#6103—22no—
177#6103—22no—
178#6103—22no—
179#6103—22no—
180#6103—41no—
181#6103—41no—
182C4⋊Dic13—22no—
183C4⋊Dic13—41no—
184#6101—22no—
185#6101—22no—
186#6101—22no—
187#6101—22no—
188#6101—41no—
189#6101—41no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055C2×D412yes—
205C2×#1055C2×D412yes—
206C2×#1055C2×Q812yes—
207C2×#1055#4112yes—
208#6094—28no—
209C8×D13—28no—
210C2×#446—131no—
211C2×#405—131no—
212#2396—131no—
213#1984D1311yescharacteristic, complemented
214#1939—131no—
215#1917—131no—
216#1917—131no—
217#1850—131no—
218#1850—131no—
219#1798—131no—
220#1771—131no—
221#1771—131no—
222C8×C4⋊C4—131no—
223#1753—131no—
224#1753—131no—
225C23×C13C23×C411yescharacteristic
226C22×D13—21no—
227C22×D13—21no—
228C22×D13—21no—
229C22×D13—21no—
230C22×D13—21no—
231C22×D13—21no—
232C22×D13C4×Q812yes—
233Q8×C13—44no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13C4×D412yes—
250C2×C4×C13C4×D412yes—
251C2×C4×C13#13112yes—
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C22×Q811yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13C4×Q812yes—
278C2×Dic13#13112yes—
279C4×D13—22no—
280C4×D13—22no—
281C4×D13—22no—
282C4×D13—22no—
283C8×C13—22no—
284C8×C13—22no—
285C8×C13—41no—
286C8×C13—41no—
287#1055—22no—
288#1055—41no—
289#1055—41no—
290#1055C22⋊Q814yes—
291C22×M16—131no—
292C23×C8—131no—
293C2×C4×Q8C2×D1311yescharacteristic
294C2×#117—131no—
295#446—264no—
296C2×C4⋊C8—131no—
297C2×C4⋊C8—131no—
298C2×C4⋊C8—131no—
299C2×C4⋊C8—131no—
300C2×C4⋊C8—131no—
301C2×C4⋊C8C2×D1311yescharacteristic
302C2×C22⋊C8—131no—
303C2×C22⋊C8—131no—
304#405—264no—
305C2×#97—131no—
306C2×#97—131no—
307C2×#97—131no—
308C2×#97—131no—
309C2×C4×C8—131no—
310C2×C4×C8—131no—
311C2×C4×C8—131no—
312C2×C4×C8C2×D1311yescharacteristic
313#400—131no—
314#399—131no—
315#398—131no—
316#398—131no—
317#396—131no—
318#396—131no—
319#395—131no—
320#393—131no—
321C4×C4⋊C4—131no—
322C4×C4⋊C4—131no—
323C4×C4⋊C4—131no—
324C4×C22⋊C4—131no—
325C4×C22⋊C4—131no—
326#336—131no—
327#336—131no—
328#336—131no—
329#336—131no—
330#336—131no—
331#336—131no—
332#336C2×D1311yescharacteristic
333#336C2×D1311yescharacteristic
334#336C2×D1311yescharacteristic
335#336C2×D1311yescharacteristic
336C22×C13C2×C4×D411yescharacteristic
337C22×C13C2×C4×Q811yescharacteristic
338C22×C13C4×#4111yescharacteristic
339C22×C13C2×#13111yescharacteristic
340C22×C13C2×#13111yescharacteristic
341C22×C13#56811yescharacteristic
342C22×C13#56811yescharacteristic
343C2×D13—22no—
344C2×D13—22no—
345C2×D13—22no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C4×C13—22no—
351C4×C13—22no—
352C4×C13—22no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13C2×C22⋊Q811yescharacteristic
357C4×C13#52511yescharacteristic
358C4×C13#52911yescharacteristic
359C4×C13#53311yescharacteristic
360Dic13—22no—
361Dic13—22no—
362Dic13—41no—
363Dic13—41no—
364Dic13—41no—
365Dic13—41no—
366Dic13—41no—
367C22×Q8C4×D1311yescharacteristic
368C23×C4—131no—
369C2×M16—134no—
370C2×M16—262no—
371C2×M16—262no—
372C22×C8—131no—
373C22×C8—131no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—262no—
377C22×C8—262no—
378C22×C8—262no—
379C22×C8C22×D1311yescharacteristic
380C22×C8C22×D1311yescharacteristic
381C22×C8C22×D1311yescharacteristic
382C22×C8C22×D1311yescharacteristic
383C4×Q8—22no—
384C4×Q8—22no—
385#117—262no—
386#117—262no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4C4×D1311yescharacteristic
396C2×C4⋊C4C4×D1311yescharacteristic
397C2×C4⋊C4C4×D1311yescharacteristic
398C2×C22⋊C4—131no—
399C2×C22⋊C4—131no—
400C2×C22⋊C4—131no—
401C2×C22⋊C4—131no—
402C2×C22⋊C4—131no—
403C2×C22⋊C4—131no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—131no—
407C2×C42C22×D1311yescharacteristic
408C2×C42C22×D1311yescharacteristic
409C2×C42C22×D1311yescharacteristic
410C4⋊C8—22no—
411C4⋊C8—262no—
412C4⋊C8—262no—
413C4⋊C8—262no—
414C4⋊C8—262no—
415C4⋊C8—262no—
416C22⋊C8—262no—
417C22⋊C8—262no—
418#97—134no—
419#97—262no—
420#97—262no—
421#97—262no—
422C4×C8—22no—
423C4×C8—262no—
424C4×C8—262no—
425C4×C8—262no—
426#95—131no—
427#95—131no—
428#95—131no—
429#95—131no—
430#95—131no—
431#95—131no—
432#95—131no—
433#95—131no—
434#95—131no—
435#95—131no—
436C2×C13C4×C22⋊Q811yescharacteristic
437C2×C13#293311yescharacteristic
438C2×C13#293511yescharacteristic
439C2×C13#296211yescharacteristic
440C2×C13#296211yescharacteristic
441C2×C13#296611yescharacteristic
442C2×C13#296711yescharacteristic
443D13—42no—
444C24—131no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—41no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—132no—
451C22×C4—132no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4C2×C4×D1311yescharacteristic
462C22×C4C2×C4×D1311yescharacteristic
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4C2×C4×D1311yescharacteristic
466C22×C4C2×C4×D1311yescharacteristic
467C22×C4C23×D1311yescharacteristic
468M16—268no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—132no—
480C2×C8—132no—
481C2×C8—132no—
482C2×C8—132no—
483C2×C8—268no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8Q8×D1312yes—
493C2×C8#613112yes—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—262no—
498C4⋊C4—262no—
499C4⋊C4—262no—
500C4⋊C4—262no—
501C4⋊C4—262no—
502C4⋊C4—521no—
503C4⋊C4—521no—
504C4⋊C4—521no—
505C22⋊C4—262no—
506C22⋊C4—262no—
507C22⋊C4—262no—
508C22⋊C4—262no—
509C22⋊C4—521no—
510C22⋊C4—521no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—261no—
516C42—261no—
517C42—261no—
518C42—261no—
519C42—261no—
520C42—261no—
521C42D4×D1312yes—
522C42#612912yes—
523C13#2160611yescharacteristic, complemented, Sylow
524C23—132no—
525C23—261no—
526C23—261no—
527C23—261no—
528C23—261no—
529C23—261no—
530C23—261no—
531C23C22×C4×D1311yescharacteristic
532Q8—44no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—132no—
549C2×C4—132no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—262no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—261no—
566C2×C4—261no—
567C2×C4—261no—
568C2×C4—261no—
569C2×C4—261no—
570C2×C4—261no—
571C2×C4—261no—
572C2×C4—261no—
573C2×C4#8813512yes—
574C2×C4#8813512yes—
575C2×C4#8815512yes—
576C2×C4C2×D4×D1311yescharacteristic
577C2×C4C2×#612911yescharacteristic
578C2×C4C2×Q8×D1311yescharacteristic
579C2×C4C2×#613111yescharacteristic
580C2×C4#41×D1311yescharacteristic
581C2×C4#41×D1311yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C8—134no—
587C8—262no—
588C8—521no—
589C8—521no—
590C22—262no—
591C22—262no—
592C22—262no—
593C22—521no—
594C22—521no—
595C22—521no—
596C22—521no—
597C22C2×#8813511yescharacteristic
598C22C4×Q8×D1311yescharacteristic
599C22C4×#613111yescharacteristic
600C22C2×#8815511yescharacteristic
601C22#1171945011yescharacteristic
602C22D13×#13111yescharacteristic
603C22#1171945511yescharacteristic
604C4—22no—
605C4—22no—
606C4—22no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—262no—
611C4—262no—
612C4—521no—
613C4—521no—
614C4—521no—
615C4—521no—
616C4—521no—
617C4D13×C22⋊Q811yescharacteristic
618C4#1171933211yescharacteristic
619C4#1171938511yescharacteristic
620C4#1171943311yescharacteristic
621C2—522no—
622C2#1311737411yescharacteristic
623C2#1312355711yescharacteristic
624C2#1312357611yescharacteristic
625C2#1312377811yescharacteristic
626C2#1312378111yescharacteristic
627C2#1312381311yescharacteristic
628C2#1312382011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1984C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1984D13
hypocenterC13#21606
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1984

Complements

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

NH ≅ G/Ntype
1. C2×#11718685C2semidirect
4. #13115554C2semidirect
5. #13115403C2semidirect
6. #13115403C2semidirect
10. #13114713C2semidirect
11. #13114709C2semidirect
12. #13114697C2semidirect
15. C13×#1984C2semidirect
98. C2×#6094Q8semidirect
213. #1984D13semidirect
523. C13#21606semidirect

Maximal subgroups

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

subgroupindex
C2×#117186852
C2×#117183502
#131181062
#131155542
#131154032
#131150152
#131148172
#131147132
#131147092
#131146972
#131146182
#131146162
C13×#19842
#2160613