Finite Group Databasebeta

← #15925656

Subgroups — #15925656

Order 3328.

904 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×#11718745C211yesmaximal, characteristic, complemented
2C2×#11718656C211yesmaximal, characteristic, complemented
3#13117850C211yesmaximal, characteristic
4#13116360C211yesmaximal, characteristic, complemented
5#13116327C211yesmaximal, characteristic, complemented
6#13116207C211yesmaximal, characteristic, complemented
7#13116166C211yesmaximal, characteristic, complemented
8#13115602C211yesmaximal, characteristic, complemented
9#13115411C211yesmaximal, characteristic, complemented
10#13115272C211yesmaximal, characteristic
11#13115158C211yesmaximal, characteristic
12#13115082C211yesmaximal, characteristic, complemented
13#13115028C211yesmaximal, characteristic, complemented
14#13115021C211yesmaximal, characteristic, complemented
15C13×#2439C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×#88184C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×#88135—21no—
22C2×C4×D52C2211yescharacteristic
23C13×#396—21no—
24C13×#393—21no—
25C13×#391—21no—
26C13×#389C2211yescharacteristic
27C13×#389C2211yescharacteristic
28C13×#387—21no—
29C13×#382C2211yescharacteristic
30C13×#380C2211yescharacteristic
31C4×C13×C22⋊C4C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33#11718745—24no—
34#11718656—24no—
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718619—21no—
46#11718600C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718331—21no—
52#11718329—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13—21no—
62C23×C4×C13C2311yescharacteristic
63C22×C22⋊D13—21no—
64C23×Dic13—21no—
65C22×D52C2311yescharacteristic
66C22×C4×D13—21no—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8—41no—
69C13×#117—22no—
70C13×#117—41no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85#88184—22no—
86#88184Q814yescomplemented
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—41no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×#6099—22no—
100C2×#6099—22no—
101C2×#6099—22no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88135—44no—
107C4×D52—22no—
108C4×D52—41no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95D411yescharacteristic
115C13×#95D411yescharacteristic
116#88071—21no—
117#88071—21no—
118C22⋊#1055—22no—
119#88049—22no—
120#88049—22no—
121#88049—22no—
122#88049—41no—
123#88048—22no—
124#88048—22no—
125#88048—41no—
126#88048D414yescomplemented
127#88047—22no—
128#88047—22no—
129C4⋊#1055—22no—
130C4⋊#1055—22no—
131#26354—131nomaximal, Sylow
132C24×C13C2×D411yescharacteristic
133C23×D13—21no—
134C2×Q8×C13—42no—
135C2×Q8×C13—42no—
136C2×Q8×C13—81no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×Q812yes—
151C22×C4×C13#4112yes—
152C22×C4×C13C2411yescharacteristic
153C2×C22⋊D13—24no—
154C2×C22⋊D13—42no—
155C2×C22⋊D13—42no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—42no—
160C22×Dic13—42no—
161C22×Dic13—81no—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52—21no—
165C2×D52—21no—
166C2×D52—21no—
167C2×D52C2×Q812yes—
168C2×C4×D13—42no—
169C2×C4×D13—42no—
170C2×C4×D13—81no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—42no—
179C13×C4⋊C4—42no—
180C13×C4⋊C4—81no—
181C13×C4⋊C4C2×D412yes—
182C13×C22⋊C4—22no—
183C13×C22⋊C4—41no—
184C13×C22⋊C4—42no—
185C13×C22⋊C4—81no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—42no—
191#6103—24no—
192#6103—42no—
193#6103—42no—
194#6103—81no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—42no—
200C4⋊Dic13C2×D412yes—
201C4⋊Dic13C2×Q812yes—
202#6101—42no—
203C4×Dic13—42no—
204#6099—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×#476—131no—
218C2×#428—131no—
219#2439D1311yescharacteristic, complemented
220#2361—131no—
221#2092—131no—
222#2086—131no—
223#2065—131no—
224#2058—131no—
225#1949—131no—
226#1919—131no—
227#1895—131no—
228#1875—131no—
229#1862—131no—
230#1853—131no—
231#1851—131no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13C22⋊Q812yes—
239C23×C13C22×D411yescharacteristic
240C22×D13—22no—
241C22×D13—41no—
242C22×D13—41no—
243C22×D13—41no—
244C22×D13—41no—
245C22×D13—41no—
246C22×D13—41no—
247Q8×C13—84no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—21no—
257C2×C4×C13—22no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13C22⋊Q812yes—
278C2×C4×C13AGL(1,ℤ/8)12yes—
279C2×C4×C13C22×D411yescharacteristic
280C2×C4×C13C22×Q811yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13H(5,𝔽2)11yescharacteristic
284C2×C4×C132−1+411yescharacteristic
285C22⋊D13—48no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—84no—
296D52—22no—
297D52—22no—
298D52—41no—
299D52—41no—
300C4×D13—84no—
301#1055—22no—
302#1055—22no—
303#1055—41no—
304#1055—41no—
305C22×M16—131no—
306C2×C4⋊Q8C2×D1311yescharacteristic
307C2×#121—131no—
308C2×C4×D4—131no—
309C2×C4×D4—261no—
310C2×#117C2×D1311yescharacteristic
311C22×C4⋊C4—131no—
312#476—264no—
313#428—264no—
314C2×#107—131no—
315C2×#107—131no—
316C2×#106—131no—
317C2×#106—131no—
318C2×#106—131no—
319C2×#106—131no—
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#396—21no—
328#393—21no—
329#391—21no—
330#390—131no—
331#389—131no—
332#389C2×D1311yescharacteristic
333#389C2×D1311yescharacteristic
334#388—261no—
335#387—21no—
336#386—261no—
337#385—261no—
338#382C2×D1311yescharacteristic
339#380C2×D1311yescharacteristic
340C4×C4⋊C4—131no—
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—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13C2×C22⋊Q811yescharacteristic
358C22×C13D4211yescharacteristic
359C22×C13#54711yescharacteristic
360C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C13#57511yescharacteristic
362C22×C13#57711yescharacteristic
363C22×C13#57711yescharacteristic
364C2×D13—42no—
365C2×D13—42no—
366C2×D13—42no—
367C2×D13—81no—
368C2×D13—81no—
369C2×D13—81no—
370C2×D13—81no—
371C4×C13—22no—
372C4×C13—22no—
373C4×C13—41no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—42no—
377C4×C13—81no—
378C4×C13—81no—
379C4×C13—81no—
380C4×C13#52511yescharacteristic
381C4×C13#53911yescharacteristic
382C4×C13D4×Q811yescharacteristic
383C4×C13#55411yescharacteristic
384Dic13—42no—
385Dic13—42no—
386Dic13—81no—
387C22×Q8—21no—
388C22×D4—131no—
389C22×D4—261no—
390C23×C4—261no—
391C23×C4—261no—
392C23×C4C22×D1311yescharacteristic
393C2×M16—262no—
394C2×M16—262no—
395C2×M16—262no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—131no—
400C4⋊Q8—22no—
401C4⋊Q8—41no—
402#121—134no—
403#121—262no—
404C4×D4—262no—
405C4×D4—521no—
406C4×D4—524no—
407#117—22no—
408#117—41no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
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—521no—
419C2×C4⋊C4C22×D1311yescharacteristic
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—261no—
426C2×C22⋊C4—261no—
427C2×C22⋊C4—261no—
428C2×C22⋊C4—261no—
429C2×C22⋊C4C22⋊D1311yescharacteristic
430C2×C22⋊C4C22⋊D1311yescharacteristic
431C2×C42—21no—
432C2×C42—261no—
433C2×C42C22×D1311yescharacteristic
434C2×C42C22×D1311yescharacteristic
435#107—262no—
436#107—262no—
437#106—134no—
438#106—262no—
439#106—262no—
440#106—521no—
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—21no—
451#95—21no—
452#95—21no—
453#95—261no—
454#95—261no—
455#95C22⋊D1311yescharacteristic
456#95C22⋊D1311yescharacteristic
457C2×C13—42no—
458C2×C13#244911yescharacteristic
459C2×C13#307711yescharacteristic
460C2×C13#308411yescharacteristic
461C2×C13#326511yescharacteristic
462C2×C13#327511yescharacteristic
463C2×C13#335011yescharacteristic
464C2×C13#335411yescharacteristic
465D13—82no—
466C24—261no—
467C24C2×C22⋊D1311yescharacteristic
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—81no—
471C2×D4—132no—
472C2×D4—264no—
473C2×D4—261no—
474C2×D4—261no—
475C2×D4—261no—
476C2×D4—261no—
477C2×D4—261no—
478C2×D4—522no—
479C2×D4—522no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—522no—
492C22×C4—522no—
493C22×C4—522no—
494C22×C4—522no—
495C22×C4—1041no—
496C22×C4—1041no—
497C22×C4Q8×D1312yes—
498C22×C4#613112yes—
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C2×C22⋊D1311yescharacteristic
503C22×C4C2×C22⋊D1311yescharacteristic
504C22×C4C23×D1311yescharacteristic
505M16—268no—
506C2×C8—132no—
507C2×C8—132no—
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—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—81no—
528C4⋊C4—132no—
529C4⋊C4—132no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—522no—
535C4⋊C4—522no—
536C4⋊C4D4×D1312yes—
537C22⋊C4—22no—
538C22⋊C4—41no—
539C22⋊C4—42no—
540C22⋊C4—81no—
541C22⋊C4—264no—
542C22⋊C4—522no—
543C22⋊C4—522no—
544C22⋊C4—1041no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—42no—
550C42—522no—
551C13#2635411yescharacteristic, complemented, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—262no—
559C23—521no—
560C23—521no—
561C23—521no—
562C23—521no—
563C23—521no—
564C23—521no—
565C23#8820012yes—
566C23C22×C22⋊D1311yescharacteristic
567Q8—84no—
568D4—262no—
569D4—262no—
570D4—528no—
571D4—521no—
572D4—521no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—1044no—
612C2×C4—1044no—
613C2×C4#8820012yes—
614C2×C4#8820312yes—
615C2×C4C2×D4×D1311yescharacteristic
616C2×C4#8825111yescharacteristic
617C2×C4C2×Q8×D1311yescharacteristic
618C2×C4C2×#613111yescharacteristic
619C2×C4#41×D1311yescharacteristic
620C2×C4#8825711yescharacteristic
621C8—262no—
622C8—262no—
623C8—521no—
624C8—521no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—522no—
633C22—522no—
634C22—522no—
635C22—1041no—
636C22—1041no—
637C22—1041no—
638C22—1041no—
639C22D4×C22⋊D1311yescharacteristic
640C22C2×#8820011yescharacteristic
641C22C2×#8820311yescharacteristic
642C22#1171952711yescharacteristic
643C22#1171952911yescharacteristic
644C22#1171954111yescharacteristic
645C22#1171954211yescharacteristic
646C4—22no—
647C4—22no—
648C4—41no—
649C4—41no—
650C4—42no—
651C4—41no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—522no—
656C4—522no—
657C4—1041no—
658C4#1171933211yescharacteristic
659C4#1171933711yescharacteristic
660C4#1171934111yescharacteristic
661C4#1171935011yescharacteristic
662C2—42no—
663C2—1042no—
664C2#1311864111yescharacteristic
665C2#1312462911yescharacteristic
666C2#1312469411yescharacteristic
667C2#1312633211yescharacteristic
668C2#1312646311yescharacteristic
669C2#1312738111yescharacteristic
670C2#1312742511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2439C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2439D13
hypocenterC13#26354
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2439

Complements

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

NH ≅ G/Ntype
1. C2×#11718745C2semidirect
2. C2×#11718656C2semidirect
4. #13116360C2semidirect
5. #13116327C2semidirect
6. #13116207C2semidirect
7. #13116166C2semidirect
8. #13115602C2semidirect
9. #13115411C2semidirect
12. #13115082C2semidirect
13. #13115028C2semidirect
14. #13115021C2semidirect
15. C13×#2439C2semidirect
86. #88184Q8semidirect
126. #88048D4semidirect
219. #2439D13semidirect
551. C13#26354semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
C2×#117186562
#131178502
#131163602
#131163272
#131162072
#131161662
#131156022
#131154112
#131152722
#131151582
#131150822
#131150282
#131150212
C13×#24392
#2635413