Finite Group Databasebeta

← #15925564

Subgroups — #15925564

Order 3328.

922 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic, complemented
2C22×#88048C211yesmaximal, characteristic, complemented
3#13118560C211yesmaximal, characteristic, complemented
4#13116357C211yesmaximal, characteristic, complemented
5#13116338C211yesmaximal, characteristic, complemented
6#13116210C211yesmaximal, characteristic, complemented
7#13116174C211yesmaximal, characteristic, complemented
8#13115604C211yesmaximal, characteristic, complemented
9#13115414C211yesmaximal, characteristic, complemented
10#13115265C211yesmaximal, characteristic
11#13115154C211yesmaximal, characteristic
12#13115097C211yesmaximal, characteristic, complemented
13#13115024C211yesmaximal, characteristic, complemented
14#13115016C211yesmaximal, characteristic, complemented
15C13×#2361C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C2×#88124C2211yescharacteristic
23C13×#390C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#388—21no—
26C13×#386—21no—
27C13×#385—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718670—24no—
37C2×#88048—24no—
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718607—21no—
45#11718603—21no—
46#11718597C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718321—21no—
52#11718318—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C23×C4×C13C2311yescharacteristic
66C23×Dic13—21no—
67C13×#121—22no—
68C13×#121Q814yes—
69C4×D4×C13—22no—
70C4×D4×C13—41no—
71C4×D4×C13—44no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C22⋊Dic13—21no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—41no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C22×#1055—22no—
101C22×#1055—22no—
102C22×#1055—22no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107#88124—22no—
108#88124—41no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113#88072—22no—
114#88072—22no—
115#88072—22no—
116#88072—41no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122C22⋊#1055—22no—
123#88048—22no—
124#88048—22no—
125#88048—22no—
126#88048D414yescomplemented
127#88047—22no—
128#88047—41no—
129C4⋊#1055—22no—
130C4⋊#1055—22no—
131#26348—131nomaximal, Sylow
132C24×C13—21no—
133C24×C13C2×D411yescharacteristic
134C2×D4×C13—24no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—42no—
141C2×D4×C13—42no—
142C2×D4×C13C2×Q812yes—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—42no—
151C22×C4×C13—42no—
152C22×C4×C13—42no—
153C22×C4×C13—42no—
154C22×C4×C13—81no—
155C22×C4×C13—81no—
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×Q812yes—
162C22×C4×C13#4112yes—
163C22×C4×C13C2411yescharacteristic
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—42no—
169C22×Dic13—42no—
170C22×Dic13—81no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4C2×D412yes—
178C13×C4⋊C4C2×Q812yes—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—24no—
182C13×C22⋊C4—42no—
183C13×C22⋊C4—42no—
184C13×C22⋊C4—81no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—42no—
190C22⋊Dic13—42no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—42no—
199C4⋊Dic13C2×D412yes—
200#6101—42no—
201#6101—42no—
202#6101—81no—
203#6101—81no—
204C2×#1055—28no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055C2×D412yes—
216C2×#1055#4112yes—
217C2×#478—131no—
218C22×#106—131no—
219#2442—131no—
220#2361D1311yescharacteristic
221#2092—131no—
222#2088—131no—
223#2065—131no—
224#2059—131no—
225#1949—131no—
226#1919—131no—
227#1893—131no—
228#1874—131no—
229#1864—131no—
230#1852—131no—
231#1850—131no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—22no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13C22⋊Q812yes—
244C23×C13#13512yes—
245C23×C13AGL(1,ℤ/8)12yes—
246C23×C13C22×D411yescharacteristic
247D4×C13—22no—
248D4×C13—22no—
249D4×C13—48no—
250D4×C13—41no—
251D4×C13—41no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—22no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—84no—
280C2×C4×C13—84no—
281C2×C4×C13C22⋊Q812yes—
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13C22×Q811yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13H(5,𝔽2)11yescharacteristic
287C2×C4×C132−1+411yescharacteristic
288C2×Dic13—22no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—84no—
301#1055—22no—
302#1055—22no—
303#1055—41no—
304#1055—41no—
305C23×C8—131no—
306C2×#125—131no—
307C2×#121C2×D1311yescharacteristic
308C2×C4×D4—21no—
309C2×C4×D4C2×D1311yescharacteristic
310C22×C4⋊C4—131no—
311C22×C4⋊C4C2×D1311yescharacteristic
312#478—264no—
313C2×#107—131no—
314C2×#107—131no—
315C2×#106—131no—
316C2×#106—131no—
317C2×#106—131no—
318C2×#106—131no—
319C2×#106—264no—
320C2×C4⋊C8—131no—
321C2×C4⋊C8—131no—
322C2×#102—131no—
323C2×#102—131no—
324C2×#102—131no—
325C2×#102—131no—
326C2×C22⋊C8—131no—
327#400—261no—
328#398—261no—
329#390C2×D1311yescharacteristic
330#389—131no—
331#389—131no—
332#389C2×D1311yescharacteristic
333#388—21no—
334#386—21no—
335#385—21no—
336#385—261no—
337#382—131no—
338#380—131no—
339#380—261no—
340C4×C4⋊C4C2×D1311yescharacteristic
341C4×C22⋊C4C2×D1311yescharacteristic
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#336—131no—
349#336—131no—
350C22×C13—22no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—22no—
354C22×C13—22no—
355C22×C13—22no—
356C22×C13—42no—
357C22×C13—42no—
358C22×C13—42no—
359C22×C13—81no—
360C22×C13—81no—
361C22×C13—81no—
362C22×C13—81no—
363C22×C13#47814yescomplemented
364C22×C13C2×C22⋊Q811yescharacteristic
365C22×C13D4211yescharacteristic
366C22×C13#54711yescharacteristic
367C22×C13C2×#13511yescharacteristic
368C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C13#57711yescharacteristic
370C22×C13#57711yescharacteristic
371C4×C13—22no—
372C4×C13—42no—
373C4×C13—41no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—42no—
377C4×C13—41no—
378C4×C13—81no—
379C4×C13#52511yescharacteristic
380C4×C13#53911yescharacteristic
381C4×C13D4×Q811yescharacteristic
382C4×C13#55411yescharacteristic
383Dic13—42no—
384Dic13—81no—
385Dic13—81no—
386Dic13—81no—
387C22×D4—21no—
388C22×D4C22×D1311yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—261no—
392C23×C4C22×D1311yescharacteristic
393C22×C8—131no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—262no—
398C22×C8—262no—
399C22×C8—262no—
400#125—262no—
401#125—521no—
402#121—22no—
403#121Dic2614yes—
404C4×D4—22no—
405C4×D4—41no—
406C4×D4—44no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—262no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—521no—
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C4⋊C4C22×D1311yescharacteristic
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—261no—
430C2×C22⋊C4C22⋊D1311yescharacteristic
431C2×C22⋊C4C22⋊D1311yescharacteristic
432C2×C42—21no—
433C2×C42C22×D1311yescharacteristic
434C2×C42C22×D1311yescharacteristic
435#107—262no—
436#107—521no—
437#106—134no—
438#106—262no—
439#106—262no—
440#106—262no—
441C4⋊C8—262no—
442C4⋊C8—262no—
443#102—262no—
444#102—262no—
445#102—262no—
446#102—521no—
447C22⋊C8—262no—
448#95—21no—
449#95—21no—
450#95—261no—
451#95—261no—
452#95—261no—
453#95—261no—
454#95—261no—
455#95C22⋊D1311yescharacteristic
456#95C22⋊D1311yescharacteristic
457C2×C13—24no—
458C2×C13—82no—
459C2×C13#244911yescharacteristic
460C2×C13C2×#47811yescharacteristic
461C2×C13#308411yescharacteristic
462C2×C13#326511yescharacteristic
463C2×C13#328211yescharacteristic
464C2×C13#333711yescharacteristic
465C2×C13#334511yescharacteristic
466C24—21no—
467C24C2×C22⋊D1311yescharacteristic
468C2×D4—24no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4C2×Dic2612yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—522no—
495C22×C4—522no—
496C22×C4—1041no—
497C22×C4C2×Dic2612yes—
498C22×C4#612712yes—
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C2×C22⋊D1311yescharacteristic
503C22×C4C2×C22⋊D1311yescharacteristic
504C22×C4C23×D1311yescharacteristic
505C2×C8—132no—
506C2×C8—132no—
507C2×C8—268no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—132no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—522no—
533C4⋊C4—522no—
534C4⋊C4—522no—
535C4⋊C4—1041no—
536C4⋊C4—1041no—
537C4⋊C4C2×Dic2612yes—
538C4⋊C4D4×D1312yes—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—24no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—81no—
545C22⋊C4—522no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C13#2634811yescharacteristic, complemented, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23#8817812yes—
564C23#8818612yes—
565C23#8820412yes—
566C23C22×C22⋊D1311yescharacteristic
567D4—22no—
568D4—22no—
569D4—48no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—84no—
601C2×C4—262no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—1044no—
614C2×C4#8817812yes—
615C2×C4C22×Dic2611yescharacteristic
616C2×C4C2×#612711yescharacteristic
617C2×C4C2×D4×D1311yescharacteristic
618C2×C4#8825111yescharacteristic
619C2×C4#41×D1311yescharacteristic
620C2×C4#8825711yescharacteristic
621C8—262no—
622C8—262no—
623C8—521no—
624C8—521no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22#1171867014yescomplemented
639C22C2×#8817811yescharacteristic
640C22C2×#8818611yescharacteristic
641C22D4×C22⋊D1311yescharacteristic
642C22C2×#8820411yescharacteristic
643C22#1171952911yescharacteristic
644C22#1171954111yescharacteristic
645C22#1171954211yescharacteristic
646C4—22no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—522no—
655C4—1041no—
656C4—1041no—
657C4—1041no—
658C4D4×Dic2611yescharacteristic
659C4#1171924411yescharacteristic
660C4#1171925211yescharacteristic
661C4#1171926911yescharacteristic
662C2—24no—
663C2—82no—
664C2#1311863911yescharacteristic
665C2C2×#1171867011yescharacteristic
666C2#1312469811yescharacteristic
667C2#1312632711yescharacteristic
668C2#1312654411yescharacteristic
669C2#1312720911yescharacteristic
670C2#1312730611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2361C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2361D13
hypocenterC13#26348
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. C2×#11718670C2semidirect
2. C22×#88048C2semidirect
3. #13118560C2semidirect
4. #13116357C2semidirect
5. #13116338C2semidirect
6. #13116210C2semidirect
7. #13116174C2semidirect
8. #13115604C2semidirect
9. #13115414C2semidirect
12. #13115097C2semidirect
13. #13115024C2semidirect
14. #13115016C2semidirect
126. #88048D4semidirect
363. C22×C13#478semidirect
551. C13#26348semidirect
638. C22#11718670semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C22×#880482
#131185602
#131163572
#131163382
#131162102
#131161742
#131156042
#131154142
#131152652
#131151542
#131150972
#131150242
#131150162
C13×#23612
#2634813