Finite Group Databasebeta

← #15845635

Subgroups — #15845635

Order 3328.

596 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125418C211yesmaximal, characteristic, complemented
2#13124624C211yesmaximal, characteristic
3#13123803C211yesmaximal, characteristic
4#13114420C211yesmaximal, characteristic, complemented
5#13114416C211yesmaximal, characteristic, complemented
6#13114413C211yesmaximal, characteristic, complemented
7#13114409C211yesmaximal, characteristic, complemented
8#13114362C211yesmaximal, characteristic, complemented
9#13114357C211yesmaximal, characteristic, complemented
10#13114328C211yesmaximal, characteristic, complemented
11#13114323C211yesmaximal, characteristic, complemented
12C2×#11718072C211yesmaximal, characteristic, complemented
13#13113494C211yesmaximal, characteristic, complemented
14#13113493C211yesmaximal, characteristic, complemented
15C13×#3076C211yesmaximal, characteristic
16C13×#533C2211yescharacteristic
17C4×C13×#41C2211yescharacteristic
18#11719175C2211yescharacteristic
19C13×#479—21no—
20C13×#478—21no—
21C13×#477C2211yescharacteristic
22C13×#476C2211yescharacteristic
23C13×#475C2211yescharacteristic
24C13×#474C2211yescharacteristic
25C13×#427—21no—
26C2×C13×C4⋊C8C2211yescharacteristic
27C13×#416—21no—
28#11718894—21no—
29#11718754C2211yescharacteristic
30#11718753C2211yescharacteristic
31#11718742C2211yescharacteristic
32#11718739C2211yescharacteristic
33#11718712—21no—
34#11718712—21no—
35C4×#6107—21no—
36C4×#6107—21no—
37#11718685C2211yescharacteristic
38#11718685C2211yescharacteristic
39#11718683—21no—
40#11718682C2211yescharacteristic
41#11718681C2211yescharacteristic
42#11718673C2211yescharacteristic
43#11718673C2211yescharacteristic
44#11718672—21no—
45#11718672—21no—
46#11718670—21no—
47#11718669C2211yescharacteristic
48#11718668C2211yescharacteristic
49#11718659—21no—
50#11718586—21no—
51#11718586C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53C4×#6099—21no—
54C2×C4×#1055C2211yescharacteristic
55#11718139C2211yescharacteristic
56#11718139C2211yescharacteristic
57#11718138C2211yescharacteristic
58#11718138C2211yescharacteristic
59#11718078C2211yescharacteristic
60#11718078C2211yescharacteristic
61#11718073C2211yescharacteristic
62#11718073C2211yescharacteristic
63#11718072C2211yescharacteristic
64#11718072C2211yescharacteristic
65#11718072C2211yescharacteristic
66#11718072C2211yescharacteristic
67C2×C13×#41D411yescharacteristic
68C22×C8×C13—21no—
69C13×C4⋊Q8C2311yescharacteristic
70C13×C4⋊Q8C2311yescharacteristic
71C13×#125—21no—
72C13×C22⋊Q8—21no—
73C13×C22⋊Q8—21no—
74C4×Q8×C13—21no—
75C4×Q8×C13—21no—
76C4×Q8×C13D411yescharacteristic
77C4×Q8×C13C2311yescharacteristic
78C4×D4×C13—21no—
79C4×D4×C13—21no—
80C4×D4×C13D411yescharacteristic
81C4×D4×C13C2311yescharacteristic
82C13×#117—21no—
83C13×#117—21no—
84C13×#117D411yescharacteristic
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×#6107—21no—
88C2×#6107—21no—
89#88180—21no—
90#88178—21no—
91#88178—21no—
92C2×#6099—21no—
93C2×#6099—21no—
94C22×#1055—21no—
95C22×#1055D411yescharacteristic
96C22×#1055D411yescharacteristic
97#88124—21no—
98#88123C2311yescharacteristic
99#88123C2311yescharacteristic
100C4×Dic26—21no—
101C4×Dic26—21no—
102C13×#107—21no—
103C13×#107—21no—
104C13×#106—21no—
105C13×#106—21no—
106C13×C4⋊C8—21no—
107C13×C4⋊C8C2311yescharacteristic
108C13×C4⋊C8C2311yescharacteristic
109C13×#103—21no—
110C13×#103—21no—
111C13×#102—21no—
112C13×#102—21no—
113#88075—21no—
114#88075—21no—
115#88075—21no—
116#88075—21no—
117#88072—21no—
118#88072—21no—
119C22⋊#1055—21no—
120C22⋊#1055—21no—
121C22⋊#1055—21no—
122#88050—21no—
123#88050—21no—
124#88048—21no—
125#88048—21no—
126#88047—21no—
127#88047—21no—
128#88047—21no—
129#88047—21no—
130C4⋊#1055—21no—
131C4⋊#1055—21no—
132C4⋊#1055—21no—
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136C4⋊#1055C2311yescharacteristic
137#88043—21no—
138#88043—21no—
139C4×#1055—21no—
140C4×#1055D411yescharacteristic
141C4×#1055D411yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#19158—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—22no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13C2×D411yescharacteristic
150C2×D4×C13—21no—
151C2×D4×C13C2×D411yescharacteristic
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13#4111yescharacteristic
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—42no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—41no—
170C13×C4⋊C4—41no—
171C13×C4⋊C4C2×D411yescharacteristic
172C13×C4⋊C4C2×D411yescharacteristic
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C13×C22⋊C4—41no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—41no—
181C42×C13C2×D411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13#4111yescharacteristic
184C42×C13C2411yescharacteristic
185C22⋊Dic13—41no—
186#6107—42no—
187#6107—42no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192#6101—41no—
193#6101—41no—
194C4×Dic13—41no—
195#6099—42no—
196#6099—42no—
197C2×#1055—22no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—41no—
203C2×#1055—42no—
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#3170—131no—
209#3076—131no—
210#3076D1311yescharacteristic
211#2965—131no—
212#1704—131no—
213#1704—131no—
214#1703—131no—
215#1703—131no—
216#1696—131no—
217#1695—131no—
218#1690—131no—
219#1689—131no—
220C2×#334—131no—
221#1542—131no—
222#1542—131no—
223C23×C13—21no—
224C23×C13#12111yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—41no—
228Q8×C13—41no—
229Q8×C13—81no—
230D4×C13—21no—
231D4×C13—21no—
232D4×C13—42no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—41no—
239C2×C4×C13—42no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—42no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13#12111yescharacteristic
246C2×C4×C13#12111yescharacteristic
247C2×C4×C13#12111yescharacteristic
248C2×C4×C13#13712yes—
249C2×C4×C13#13712yes—
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×Dic13—41no—
254C2×Dic13—41no—
255Dic26—41no—
256Dic26—41no—
257Dic26—81no—
258C8×C13—41no—
259C8×C13—41no—
260#1055—21no—
261#1055—21no—
262#1055—21no—
263#1055—41no—
264#1055—41no—
265#1055—41no—
266#1055—41no—
267#1055#13512yes—
268#533—131no—
269#533C2×D1311yescharacteristic
270C4×#41C2×D1311yescharacteristic
271#500—131no—
272#494—131no—
273#487—131no—
274#487—131no—
275#479—21no—
276#479—261no—
277#478—21no—
278#478—261no—
279#477—131no—
280#477C2×D1311yescharacteristic
281#476—131no—
282#476C2×D1311yescharacteristic
283#475—131no—
284#475C2×D1311yescharacteristic
285#474—131no—
286#474C2×D1311yescharacteristic
287#467—261no—
288#467—261no—
289#446—131no—
290#446—131no—
291C4×Q16—261no—
292C4×Q16—261no—
293#436—131no—
294#436—131no—
295#435—261no—
296#435—261no—
297#431—131no—
298#431—261no—
299#427—21no—
300#427—261no—
301C2×C4⋊C8—131no—
302C2×C4⋊C8C2×D1311yescharacteristic
303#416—21no—
304#416—261no—
305C4×M16—261no—
306C2×C4×C8—131no—
307#334—131no—
308#334—131no—
309#334—131no—
310#334—131no—
311#333—131no—
312#333—131no—
313#333—131no—
314#333—131no—
315#332—131no—
316#332—131no—
317#332—131no—
318#332—131no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13#47012yes—
325C22×C13C2×#12111yescharacteristic
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—81no—
333C4×C13—81no—
334C4×C13#47012yes—
335C4×C13C2×#13511yescharacteristic
336C4×C13C2×#13711yescharacteristic
337C4×C13C2×#13711yescharacteristic
338C4×C13#57511yescharacteristic
339Dic13—81no—
340Dic13—81no—
341C2×#41C22⋊D1311yescharacteristic
342C2×Q16—261no—
343C2×Q16—261no—
344C2×M16—261no—
345C2×M16—261no—
346C22×C8—21no—
347C22×C8—131no—
348C22×C8—131no—
349C22×C8—261no—
350C4⋊Q8—131no—
351C4⋊Q8—131no—
352C4⋊Q8C22×D1311yescharacteristic
353C4⋊Q8C22×D1311yescharacteristic
354#125—21no—
355#125—261no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—261no—
359C22⋊Q8—261no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—261no—
363C4×Q8—261no—
364C4×Q8C22⋊D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C22⋊D1311yescharacteristic
369C4×D4C22×D1311yescharacteristic
370#117—21no—
371#117—21no—
372#117—261no—
373#117C22⋊D1311yescharacteristic
374C2×C42—21no—
375C2×C42C22×D1311yescharacteristic
376#107—21no—
377#107—21no—
378#107—261no—
379#107—261no—
380#107—261no—
381#107—261no—
382#106—21no—
383#106—21no—
384#106—261no—
385#106—261no—
386C4⋊C8—21no—
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8C22×D1311yescharacteristic
395C4⋊C8C22×D1311yescharacteristic
396#103—21no—
397#103—21no—
398#103—261no—
399#103—261no—
400#103—261no—
401#103—261no—
402#103—261no—
403#103—261no—
404#102—21no—
405#102—21no—
406#102—261no—
407#102—261no—
408C22⋊C8—261no—
409C22⋊C8—261no—
410C22⋊C8—261no—
411#97—261no—
412#97—261no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—261no—
418C2×C13—22no—
419C2×C13—81no—
420C2×C13#303511yescharacteristic
421C2×C13C2×#47011yescharacteristic
422C2×C13#306711yescharacteristic
423#41—22no—
424#41—22no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—261no—
428C2×Q8—261no—
429C2×Q8C2×C22⋊D1311yescharacteristic
430C2×D4—21no—
431C2×D4C2×C22⋊D1311yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4D4×D1311yescharacteristic
436C22×C4#612911yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438Q16—522no—
439Q16—522no—
440M16—522no—
441M16—522no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—42no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—262no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—521no—
455C2×C8—522no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—521no—
469C4⋊C4—521no—
470C4⋊C4C2×C22⋊D1311yescharacteristic
471C4⋊C4C2×C22⋊D1311yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—521no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—521no—
482C42D4×D1311yescharacteristic
483C42#612911yescharacteristic
484C42C2×C22⋊D1311yescharacteristic
485C42C23×D1311yescharacteristic
486C13#1915811yescharacteristic, complemented, Sylow
487C23—21no—
488C23#8819311yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—81no—
494Q8—521no—
495Q8—521no—
496Q8—1041no—
497D4—21no—
498D4—21no—
499D4—42no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—521no—
513C2×C4—521no—
514C2×C4#8819311yescharacteristic
515C2×C4#8819311yescharacteristic
516C2×C4#8819311yescharacteristic
517C2×C4#8819612yes—
518C2×C4#8820512yes—
519C2×C4C2×D4×D1311yescharacteristic
520C2×C4C2×#612911yescharacteristic
521C2×C4C22×C22⋊D1311yescharacteristic
522C8—41no—
523C8—41no—
524C8—132no—
525C8—261no—
526C8—261no—
527C8—261no—
528C8—521no—
529C8—521no—
530C8—521no—
531C8—521no—
532C22—21no—
533C22—21no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22#1171871312yes—
538C22C2×#8819311yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—1041no—
548C4—1041no—
549C4#1171871312yes—
550C4D13×#13511yescharacteristic
551C4#1171947311yescharacteristic
552C4C2×#8819611yescharacteristic
553C4C2×#8820511yescharacteristic
554C2—22no—
555C2—81no—
556C2#1312428711yescharacteristic
557C2C2×#1171871311yescharacteristic
558C2#1312455311yescharacteristic
subgroupG/H
centerC2×C4#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#3076C2
socleC22×C13C2×#121
prime radicalC2×C13×#41D4
hypercenter#3076D13
hypocenterC13#19158
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #13125418C2semidirect
4. #13114420C2semidirect
5. #13114416C2semidirect
6. #13114413C2semidirect
7. #13114409C2semidirect
8. #13114362C2semidirect
9. #13114357C2semidirect
10. #13114328C2semidirect
11. #13114323C2semidirect
12. C2×#11718072C2semidirect
13. #13113494C2semidirect
14. #13113493C2semidirect
486. C13#19158semidirect

Maximal subgroups

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

subgroupindex
#131254182
#131246242
#131238032
#131144202
#131144162
#131144132
#131144092
#131143622
#131143572
#131143282
#131143232
C2×#117180722
#131134942
#131134932
C13×#30762
#1915813