Finite Group Databasebeta

← #16795581

Subgroups — #16795581

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×#1057C211yesmaximal, characteristic
2#13131624C211yesmaximal, characteristic, complemented
3#13130449C211yesmaximal, characteristic, complemented
4#13130447C211yesmaximal, characteristic, complemented
5#13130441C211yesmaximal, characteristic, complemented
6#13130439C211yesmaximal, characteristic, complemented
7#13130430C211yesmaximal, characteristic, complemented
8#13130429C211yesmaximal, characteristic, complemented
9#13130427C211yesmaximal, characteristic, complemented
10SD16⋊#1057C211yesmaximal, characteristic, complemented
11#13130412C211yesmaximal, characteristic, complemented
12#13130171C211yesmaximal, characteristic
13#13130158C211yesmaximal, characteristic, complemented
14#13130047C211yesmaximal, characteristic, complemented
15#13124900C211yesmaximal, characteristic
16#41×Dic13C2211yescharacteristic
17#11719327C2211yescharacteristic
18#11719158C2211yescharacteristic
19Q8×#1057C2211yescharacteristic
20Q8×#1057C2211yescharacteristic
21Q8×#1057C2211yescharacteristic
22D4×#1057—21no—
23D4×#1057—21no—
24D4×#1057C2211yescharacteristic
25D4×#1057C2211yescharacteristic
26#11719129C2211yescharacteristic
27C4×#6122C2211yescharacteristic
28#11719119—21no—
29#11719119C2211yescharacteristic
30C2×C4×#1057—21no—
31C2×C4×#1057C2211yescharacteristic
32#11719080C2211yescharacteristic
33#11719078—21no—
34#11719074—21no—
35#11719074C2211yescharacteristic
36#11719067—21no—
37#11719062—21no—
38C13×#452C411yescharacteristic
39#11718900C411yescharacteristic
40Q16×Dic13C2211yescharacteristic
41#11718843C411yescharacteristic
42#11718823C411yescharacteristic
43SD16×Dic13C2211yescharacteristic
44#11718706C411yescharacteristic
45#11718452C411yescharacteristic
46#11718451C2211yescharacteristic
47#11718420C411yescharacteristic
48#11718419C2211yescharacteristic
49#11718384C411yescharacteristic
50#11718379C2211yescharacteristic
51Q8⋊#1057C2211yescharacteristic
52Q8⋊#1057C2211yescharacteristic
53Q8⋊#1057C2211yescharacteristic
54Q8⋊#1057C2211yescharacteristic
55D4⋊#1057C2211yescharacteristic
56D4⋊#1057C2211yescharacteristic
57#11718256C2211yescharacteristic
58#11718255C2211yescharacteristic
59#11718254C2211yescharacteristic
60#11718253C2211yescharacteristic
61#1057⋊C8C2211yescharacteristic
62#1057⋊C8C2211yescharacteristic
63#11718251C2211yescharacteristic
64#11718251C2211yescharacteristic
65#11718244C2211yescharacteristic
66#11718244C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C2×#6122—21no—
69C2×#6122—21no—
70C22×#1057—21no—
71C22×#1057—21no—
72C22×#1057D411yescharacteristic
73C22×#1057D411yescharacteristic
74C2×C13×Q16C2×C411yescharacteristic
75C2×C13×SD16C2×C411yescharacteristic
76C13×C22⋊Q8C2×C411yescharacteristic
77Q8×Dic13C2×C411yescharacteristic
78Q8×Dic13C2311yescharacteristic
79Q8×Dic13C2311yescharacteristic
80#88198C2×C411yescharacteristic
81C2×#6107C2×C411yescharacteristic
82D4×Dic13—21no—
83D4×Dic13—21no—
84D4×Dic13C2×C411yescharacteristic
85D4×Dic13C2311yescharacteristic
86C2×#6105C2×C411yescharacteristic
87#88180—21no—
88#88180C2×C411yescharacteristic
89#88178C2×C411yescharacteristic
90C2×C4×Dic13—21no—
91C2×C4×Dic13C2311yescharacteristic
92#88143—21no—
93#88142C2×C411yescharacteristic
94#88141—21no—
95#88141C2311yescharacteristic
96#88132—21no—
97#88131—21no—
98C22⋊#1057—21no—
99C22⋊#1057—21no—
100C22⋊#1057—21no—
101#88112—21no—
102#88112—21no—
103#88112—21no—
104#88110—21no—
105#88110—21no—
106#88110—21no—
107C4⋊#1057—21no—
108C4⋊#1057—21no—
109C4⋊#1057—21no—
110C4⋊#1057—21no—
111C4⋊#1057C2311yescharacteristic
112C4⋊#1057C2311yescharacteristic
113C4⋊#1057C2311yescharacteristic
114C4⋊#1057C2311yescharacteristic
115C4×#1057—21no—
116C4×#1057—21no—
117C4×#1057—21no—
118C4×#1057—21no—
119C4×#1057—21no—
120C4×#1057D411yescharacteristic
121C4×#1057D411yescharacteristic
122C4×#1057C2311yescharacteristic
123C4×#1057C2311yescharacteristic
124C4×#1057C2311yescharacteristic
125C4×#1057C2311yescharacteristic
126C13×#103C2×C411yescharacteristic
127C13×#102C2×C411yescharacteristic
128C13×C22⋊C8C2×C411yescharacteristic
129#88075C2×C411yescharacteristic
130#88075C2×C411yescharacteristic
131#88075C2×C411yescharacteristic
132#88072C2×C411yescharacteristic
133C22⋊#1055C2×C411yescharacteristic
134#88058C2×C411yescharacteristic
135#88057C2×C411yescharacteristic
136#88056C2×C411yescharacteristic
137#88056C2×C411yescharacteristic
138#88054C2×C411yescharacteristic
139#88054C2×C411yescharacteristic
140C8×Dic13C2311yescharacteristic
141C8×Dic13C2311yescharacteristic
142#88048C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#17916—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—22no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×Q8×C13C22×C411yescharacteristic
149C2×D4×C13—21no—
150C2×D4×C13C22×C411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13C22×C411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13#4111yescharacteristic
157C2×Dic26—21no—
158C2×Dic26C22×C411yescharacteristic
159#6122—42no—
160#6122—42no—
161C2×#1057—22no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057—41no—
169C2×#1057—42no—
170C2×#1057—42no—
171C2×#1057C2×D411yescharacteristic
172C2×#1057C2×D411yescharacteristic
173C2×#1057C2×D411yescharacteristic
174C2×#1057C2×D411yescharacteristic
175C13×Q16—22no—
176C13×SD16—22no—
177C2×C8×C13C22×C411yescharacteristic
178C2×C8×C13C22×C411yescharacteristic
179C13×C4⋊C4—21no—
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C22⋊C4—21no—
182C22⋊Dic13—21no—
183C22⋊Dic13—21no—
184C22⋊Dic13—21no—
185C22⋊Dic13—21no—
186#6107—22no—
187#6105—22no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13C22×C411yescharacteristic
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194#6101—21no—
195#6101—21no—
196#6101—21no—
197#6101—21no—
198#6101—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13C22×C411yescharacteristic
205C4×Dic13C2×D411yescharacteristic
206C4×Dic13#4111yescharacteristic
207C4×Dic13C2411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210#3107—131no—
211C8×#41—131no—
212#2960—131no—
213#1584—131no—
214#1584—131no—
215#1582—131no—
216#1582—131no—
217#1579—131no—
218#1579—131no—
219SD16⋊C8—131no—
220SD16⋊C8—131no—
221#1574—131no—
222#1489—131no—
223#1485—131no—
224#1451—131no—
225C23×C13—21no—
226C23×C13C4×D411yescharacteristic
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13#13112yes—
231D4×C13—24no—
232D4×C13—21no—
233D4×C13#13112yes—
234C2×C4×C13—24no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C23×C411yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—22no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—42no—
252C2×Dic13C4×D411yescharacteristic
253C2×Dic13C4×D411yescharacteristic
254C2×Dic13C22×D411yescharacteristic
255C2×Dic13C2×#4111yescharacteristic
256Dic26—21no—
257Dic26—21no—
258Dic26—42no—
259#1057—21no—
260#1057—21no—
261#1057—21no—
262#1057—41no—
263#1057—41no—
264#1057—41no—
265#1057—41no—
266#1057—41no—
267#1057—41no—
268#1057#13712yes—
269C8×C13—21no—
270C8×C13—21no—
271#1055—21no—
272#1055—21no—
273#533—131no—
274C4×#41—131no—
275#485—131no—
276#485—131no—
277#475—131no—
278#474—131no—
279#462—131no—
280#461—131no—
281#452—131no—
282#452#26111yescharacteristic
283#446—131no—
284#446—131no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8—131no—
290C8×Q8—261no—
291C4×Q16—131no—
292C4×Q16—131no—
293C4×SD16—131no—
294C4×SD16—131no—
295C8×D4—131no—
296C8×D4—131no—
297C8×D4—261no—
298C8×D4—261no—
299#431—131no—
300#431—131no—
301#431—261no—
302#424—261no—
303#423—131no—
304#405—261no—
305C4×M16—131no—
306C2×C4×C8—131no—
307C2×C4×C8—261no—
308#335—131no—
309#335—131no—
310#334—131no—
311#334—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8—131no—
318D4⋊C8—131no—
319D4⋊C8—131no—
320#322—131no—
321#322—131no—
322#322—131no—
323#322—131no—
324C22×C13—21no—
325C22×C13—22no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13C2×C4×D411yescharacteristic
331C4×C13—21no—
332C4×C13—22no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13C2×#13111yescharacteristic
336C4×C13C2×#13111yescharacteristic
337Dic13—21no—
338Dic13—21no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13#44412yes—
344Dic13C2×#13711yescharacteristic
345Dic13#57511yescharacteristic
346C2×#41C2×#26111yescharacteristic
347C2×Q16—131no—
348C2×Q16C2×#26111yescharacteristic
349C2×SD16—131no—
350C2×SD16C2×#26111yescharacteristic
351C2×M16—261no—
352C2×M16—261no—
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—261no—
356C22×C8—261no—
357C4⋊Q8—131no—
358C4⋊Q8—131no—
359#125—261no—
360C22⋊Q8—131no—
361C22⋊Q8—261no—
362C22⋊Q8C2×#26111yescharacteristic
363C4×Q8—131no—
364C4×Q8—131no—
365C4×Q8—131no—
366C4×Q8—131no—
367C4×Q8—261no—
368C4×D4—131no—
369C4×D4—131no—
370C4×D4—261no—
371C4×D4—261no—
372#117—131no—
373#117—261no—
374#117—261no—
375C2×C42—131no—
376C2×C42—261no—
377#107—131no—
378#107—131no—
379#106—131no—
380#106—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—131no—
385C4⋊C8—131no—
386C4⋊C8—131no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#103—131no—
399#103C2×#26111yescharacteristic
400#102—131no—
401#102C2×#26111yescharacteristic
402C22⋊C8—131no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8C2×#26111yescharacteristic
407#97—261no—
408#97—261no—
409#97—261no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8—261no—
421C4×C8—261no—
422C4×C8—261no—
423C2×C13—41no—
424C2×C13—42no—
425C2×C13#292911yescharacteristic
426C2×C13C4×#13711yescharacteristic
427C2×C13C2×#44411yescharacteristic
428#41—22no—
429#41—22no—
430C2×Q8—131no—
431C2×Q8—261no—
432C2×Q8C22×#26111yescharacteristic
433C2×Q8C22×#26111yescharacteristic
434C2×D4—21no—
435C2×D4C22×#26111yescharacteristic
436C22×C4—21no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4C22×#26111yescharacteristic
442Q16—22no—
443Q16—262no—
444SD16—22no—
445SD16—262no—
446M16—522no—
447M16—522no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—262no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—522no—
462C2×C8—521no—
463C2×C8—522no—
464C2×C8C22×#26111yescharacteristic
465C2×C8C22×#26111yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—131no—
468C4⋊C4—131no—
469C4⋊C4—131no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4C22×#26111yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C22⋊C4—261no—
483C22⋊C4—261no—
484C42—131no—
485C42—131no—
486C42—131no—
487C42—131no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42—261no—
492C42—261no—
493C13#1791611yescharacteristic, complemented, Sylow
494C23—21no—
495C23D4×#26111yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—261no—
500Q8—261no—
501Q8—522no—
502Q8#8823812yes—
503D4—24no—
504D4—21no—
505D4#8823812yes—
506C2×C4—24no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—131no—
513C2×C4—131no—
514C2×C4—131no—
515C2×C4—131no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—262no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4—522no—
526C2×C4D4×#26111yescharacteristic
527C2×C4C23×#26111yescharacteristic
528C8—21no—
529C8—21no—
530C8—132no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—521no—
537C8—521no—
538C8—521no—
539C8—521no—
540C8—521no—
541C8—521no—
542C22—21no—
543C22—22no—
544C22—21no—
545C22—21no—
546C22—41no—
547C22—41no—
548C22C2×D4×#26111yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—131no—
554C4—131no—
555C4—132no—
556C4—261no—
557C4—261no—
558C4—521no—
559C4—521no—
560C4—521no—
561C4—521no—
562C4C2×#8823811yescharacteristic
563C4C2×#8823811yescharacteristic
564C2—41no—
565C2—42no—
566C2#1313155111yescharacteristic
567C2#137×#26111yescharacteristic
568C2D13⋊#44411yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#452C4
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C2×C4
cosocleC4×Dic13C24
hypercenter#452#261
hypocenterC13#17916
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #13131624C2semidirect
3. #13130449C2semidirect
4. #13130447C2semidirect
5. #13130441C2semidirect
6. #13130439C2semidirect
7. #13130430C2semidirect
8. #13130429C2semidirect
9. #13130427C2semidirect
10. SD16⋊#1057C2semidirect
11. #13130412C2semidirect
13. #13130158C2semidirect
14. #13130047C2semidirect
493. C13#17916semidirect

Maximal subgroups

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

subgroupindex
#41×#10572
#131316242
#131304492
#131304472
#131304412
#131304392
#131304302
#131304292
#131304272
SD16⋊#10572
#131304122
#131301712
#131301582
#131300472
#131249002
#1791613