Finite Group Databasebeta

← #15925474

Subgroups — #15925474

Order 3328.

882 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718682C211yesmaximal, characteristic, complemented
2C22×#88047C211yesmaximal, characteristic
3#13118538C211yesmaximal, characteristic
4#13116374C211yesmaximal, characteristic, complemented
5#13116332C211yesmaximal, characteristic, complemented
6#13116231C211yesmaximal, characteristic, complemented
7#13116164C211yesmaximal, characteristic, complemented
8#13115594C211yesmaximal, characteristic, complemented
9#13115428C211yesmaximal, characteristic, complemented
10#13115260C211yesmaximal, characteristic
11#13115144C211yesmaximal, characteristic
12#13115090C211yesmaximal, characteristic, complemented
13#13115024C211yesmaximal, characteristic
14#13115016C211yesmaximal, characteristic
15C13×#2360C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88132—21no—
22C2×#88123C2211yescharacteristic
23C13×#391C2211yescharacteristic
24C13×#389—21no—
25C13×#389C2211yescharacteristic
26C13×#387—21no—
27C13×#385—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4—21no—
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35#11718873C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718682—24no—
38C2×#88047—24no—
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718611—21no—
46#11718596C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718322—21no—
52#11718317—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C23×Dic13—21no—
65C22×Dic26—21no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8Q814yescomplemented
68C4×Q8×C13—22no—
69C4×Q8×C13—41no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—21no—
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⋊C4D411yescharacteristic
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13—21no—
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C22⋊Dic13—21no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—41no—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×#6101—21no—
99C22×#1055—22no—
100C22×#1055—22no—
101C22×#1055—22no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88132—44no—
107#88123—22no—
108#88123—41no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95D411yescharacteristic
114C13×#95D411yescharacteristic
115#88075—22no—
116#88075—22no—
117#88075—22no—
118#88075—41no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122C22⋊#1055—22no—
123#88047—22no—
124#88047—22no—
125#88047—22no—
126#88047—22no—
127#88047—41no—
128#88047D414yes—
129C4⋊#1055—22no—
130C4⋊#1055—22no—
131#26342—131nomaximal, Sylow
132C24×C13C2×D411yescharacteristic
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13C2×Q812yes—
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×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—81no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×Q812yes—
156C22×C4×C13#4112yes—
157C22×C4×C13C2411yescharacteristic
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—42no—
163C22×Dic13—42no—
164C22×Dic13—81no—
165C2×Dic26—42no—
166C2×Dic26—42no—
167C2×Dic26—81no—
168C13×C4⋊C4—24no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—81no—
176C13×C4⋊C4C2×D412yes—
177C13×C4⋊C4C2×Q812yes—
178C13×C22⋊C4—24no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4Q1614yes—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—42no—
186C42×C13—81no—
187C22⋊Dic13—42no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—42no—
196C4⋊Dic13—42no—
197C4⋊Dic13—42no—
198C4⋊Dic13—81no—
199C4⋊Dic13C2×D412yes—
200#6101—42no—
201#6101—42no—
202C2×#1055—28no—
203C2×#1055—21no—
204C2×#1055—21no—
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×#1055C2×D412yes—
214C2×#1055#4112yes—
215C2×#477—131no—
216C22×#107—131no—
217#2440—131no—
218#2360D1311yescharacteristic
219#2095—131no—
220#2087—131no—
221#2068—131no—
222#2057—131no—
223#1947—131no—
224#1921—131no—
225#1892—131no—
226#1872—131no—
227#1863—131no—
228#1852—131no—
229#1850—131no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13C22⋊Q812yes—
235C23×C13C2×Q1612yes—
236C23×C13AGL(1,ℤ/8)12yes—
237C23×C13C22×D411yescharacteristic
238Q8×C13—22no—
239Q8×C13—22no—
240Q8×C13—41no—
241Q8×C13—41no—
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—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—21no—
255C2×C4×C13—22no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—84no—
271C2×C4×C13C22⋊Q812yes—
272C2×C4×C13C2×Q1612yes—
273C2×C4×C13C2×Q1612yes—
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13C22×Q811yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13H(5,𝔽2)11yescharacteristic
279C2×C4×C132−1+411yescharacteristic
280C2×Dic13—22no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—84no—
293Dic26—84no—
294#1055—22no—
295#1055—22no—
296#1055—41no—
297#1055—41no—
298C23×C8—131no—
299C2×C4⋊Q8—131no—
300C2×C22⋊Q8—261no—
301C2×C22⋊Q8C2×D1311yescharacteristic
302C2×C4×Q8C2×D1311yescharacteristic
303C22×C4⋊C4—131no—
304C22×C4⋊C4C2×D1311yescharacteristic
305#477—264no—
306C2×#107—131no—
307C2×#107—131no—
308C2×#107—131no—
309C2×#107—131no—
310C2×#107—131no—
311C2×#107—131no—
312C2×#107—264no—
313C2×C4⋊C8—131no—
314C2×C4⋊C8—131no—
315C2×#103—131no—
316C2×#103—131no—
317C2×#103—131no—
318C2×#103—131no—
319C2×C22⋊C8—131no—
320#398—261no—
321#395—261no—
322#391C2×D1311yescharacteristic
323#389—21no—
324#389—131no—
325#389—131no—
326#389C2×D1311yescharacteristic
327#387—21no—
328#385—21no—
329#385—261no—
330#384—131no—
331#380—131no—
332C4×C4⋊C4C2×D1311yescharacteristic
333C4×C22⋊C4—21no—
334C4×C22⋊C4C2×D1311yescharacteristic
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#336—131no—
342#336—131no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13#47714yescomplemented
350C22×C13C2×C22⋊Q811yescharacteristic
351C22×C13D4211yescharacteristic
352C22×C13#54711yescharacteristic
353C22×C13C22×Q1611yescharacteristic
354C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C13#57611yescharacteristic
356C22×C13#57811yescharacteristic
357C4×C13—22no—
358C4×C13—22no—
359C4×C13—22no—
360C4×C13—42no—
361C4×C13—41no—
362C4×C13—42no—
363C4×C13—41no—
364C4×C13—42no—
365C4×C13—81no—
366C4×C13#52511yescharacteristic
367C4×C13#53911yescharacteristic
368C4×C13D4×Q811yescharacteristic
369C4×C13#55411yescharacteristic
370Dic13—42no—
371Dic13—81no—
372Dic13—81no—
373Dic13—81no—
374C22×Q8—261no—
375C22×Q8C22×D1311yescharacteristic
376C23×C4—21no—
377C23×C4—261no—
378C23×C4C22×D1311yescharacteristic
379C22×C8—131no—
380C22×C8—131no—
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—262no—
384C22×C8—262no—
385C22×C8—262no—
386C4⋊Q8—262no—
387C4⋊Q8—521no—
388C22⋊Q8—22no—
389C22⋊Q8—524no—
390C22⋊Q8Dic2614yescomplemented
391C4×Q8—22no—
392C4×Q8—41no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—262no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—521no—
411C2×C4⋊C4C22×D1311yescharacteristic
412C2×C4⋊C4C22×D1311yescharacteristic
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C22⋊C4C22⋊D1311yescharacteristic
418C2×C42—21no—
419C2×C42—21no—
420C2×C42C22×D1311yescharacteristic
421C2×C42C22×D1311yescharacteristic
422#107—134no—
423#107—262no—
424#107—262no—
425#107—262no—
426#107—262no—
427#107—521no—
428C4⋊C8—262no—
429C4⋊C8—262no—
430#103—262no—
431#103—262no—
432#103—262no—
433#103—521no—
434C22⋊C8—262no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—261no—
440#95—261no—
441#95—261no—
442#95C22⋊D1311yescharacteristic
443#95C22⋊D1311yescharacteristic
444C2×C13—24no—
445C2×C13#244911yescharacteristic
446C2×C13C2×#47711yescharacteristic
447C2×C13#308311yescharacteristic
448C2×C13#326411yescharacteristic
449C2×C13D4×Q1611yescharacteristic
450C2×C13#333811yescharacteristic
451C2×C13#334311yescharacteristic
452C24C2×C22⋊D1311yescharacteristic
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—522no—
459C2×Q8—522no—
460C2×Q8—1041no—
461C2×Q8C2×Dic2612yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—522no—
478C22×C4—522no—
479C22×C4—1041no—
480C22×C4C2×Dic2612yes—
481C22×C4#612712yes—
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C23×D1311yescharacteristic
488C2×C8—132no—
489C2×C8—132no—
490C2×C8—268no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C4⋊C4—24no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—81no—
509C4⋊C4—132no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—522no—
518C4⋊C4—522no—
519C4⋊C4—522no—
520C4⋊C4—522no—
521C4⋊C4—522no—
522C4⋊C4—1041no—
523C4⋊C4C2×Dic2612yes—
524C4⋊C4D4×D1312yes—
525C22⋊C4—24no—
526C22⋊C4—22no—
527C22⋊C4—522no—
528C22⋊C4#610714yes—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—42no—
534C42—81no—
535C13#2634211yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23#8817812yes—
541C23C2×#610712yes—
542C23#8820312yes—
543C23C22×C22⋊D1311yescharacteristic
544Q8—22no—
545Q8—22no—
546Q8—41no—
547Q8—41no—
548Q8—1044no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4—262no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—1044no—
591C2×C4#8817812yes—
592C2×C4C2×#610712yes—
593C2×C4C2×#610712yes—
594C2×C4C22×Dic2611yescharacteristic
595C2×C4C2×#612711yescharacteristic
596C2×C4C2×D4×D1311yescharacteristic
597C2×C4#8825111yescharacteristic
598C2×C4#41×D1311yescharacteristic
599C2×C4#8825711yescharacteristic
600C8—262no—
601C8—262no—
602C8—521no—
603C8—521no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22#1171868214yescomplemented
611C22C2×#8817811yescharacteristic
612C22D4×C22⋊D1311yescharacteristic
613C22C22×#610711yescharacteristic
614C22C2×#8820311yescharacteristic
615C22#1171952911yescharacteristic
616C22#1171954011yescharacteristic
617C22#1171954311yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—42no—
626C4—81no—
627C4—522no—
628C4—1041no—
629C4—1041no—
630C4—1041no—
631C4D4×Dic2611yescharacteristic
632C4#1171924411yescharacteristic
633C4#1171925211yescharacteristic
634C4#1171926911yescharacteristic
635C2—24no—
636C2#1311863911yescharacteristic
637C2C2×#1171868211yescharacteristic
638C2#1312468711yescharacteristic
639C2#1312631711yescharacteristic
640C2D4×#610711yescharacteristic
641C2#1312722411yescharacteristic
642C2#1312727611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2360C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2360D13
hypocenterC13#26342
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
1. C2×#11718682C2semidirect
4. #13116374C2semidirect
5. #13116332C2semidirect
6. #13116231C2semidirect
7. #13116164C2semidirect
8. #13115594C2semidirect
9. #13115428C2semidirect
12. #13115090C2semidirect
67. C13×C22⋊Q8Q8semidirect
349. C22×C13#477semidirect
390. C22⋊Q8Dic26semidirect
535. C13#26342semidirect
610. C22#11718682semidirect

Maximal subgroups

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

subgroupindex
C2×#117186822
C22×#880472
#131185382
#131163742
#131163322
#131162312
#131161642
#131155942
#131154282
#131152602
#131151442
#131150902
#131150242
#131150162
C13×#23602
#2634213