Finite Group Databasebeta

← #15834880

Subgroups — #15834880

Order 3328.

572 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#13123996C211yesmaximal, characteristic
2#13123938C211yesmaximal, characteristic, complemented
3#13113745C211yesmaximal, characteristic, complemented
4#13113727C211yesmaximal, characteristic, complemented
5#13113715C211yesmaximal, characteristic, complemented
6#13113708C211yesmaximal, characteristic, complemented
7#13113687C211yesmaximal, characteristic, complemented
8#13113673C211yesmaximal, characteristic, complemented
9SD16⋊#1055C211yesmaximal, characteristic, complemented
10Q16×#1055C211yesmaximal, characteristic, complemented
11#13113588C211yesmaximal, characteristic, complemented
12#13113244C211yesmaximal, characteristic
13#13113239C211yesmaximal, characteristic, complemented
14#13113133C211yesmaximal, characteristic, complemented
15C13×#3172C211yesmaximal, characteristic
16C13×#533C2211yescharacteristic
17C13×#529C2211yescharacteristic
18C13×#501C411yescharacteristic
19C13×#497C411yescharacteristic
20C13×#491C411yescharacteristic
21C13×#489C411yescharacteristic
22C13×#470C411yescharacteristic
23C13×#470C411yescharacteristic
24C13×#468C411yescharacteristic
25C13×#468C411yescharacteristic
26C4×C13×Q16C2211yescharacteristic
27C4×C13×Q16C2211yescharacteristic
28C4×C13×SD16C2211yescharacteristic
29C4×C13×SD16C2211yescharacteristic
30C4×C13×M16C2211yescharacteristic
31#11718685—21no—
32#11718685C2211yescharacteristic
33#11718685C2211yescharacteristic
34#11718685C2211yescharacteristic
35Q8×#1055—21no—
36Q8×#1055C2211yescharacteristic
37Q8×#1055C2211yescharacteristic
38Q8×#1055C2211yescharacteristic
39#11718673C2211yescharacteristic
40#11718672—21no—
41D4×#1055—21no—
42D4×#1055C2211yescharacteristic
43#11718661—21no—
44#11718661—21no—
45#11718661—21no—
46#11718660—21no—
47#11718586C2211yescharacteristic
48#11718586C2211yescharacteristic
49#11718586C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53Q8⋊#1055C2211yescharacteristic
54Q8⋊#1055C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57D4⋊#1055C2211yescharacteristic
58D4⋊#1055C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×Q16C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×SD16C2×C411yescharacteristic
71C2×C13×M16C2×C411yescharacteristic
72C2×C13×M16C2×C411yescharacteristic
73C13×C4⋊Q8C2×C411yescharacteristic
74C13×C4⋊Q8C2×C411yescharacteristic
75C13×#126—21no—
76C13×#125—21no—
77C13×#125C2×C411yescharacteristic
78C13×#124C2×C411yescharacteristic
79C13×#123—21no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8C2×C411yescharacteristic
82C13×C22⋊Q8C2×C411yescharacteristic
83C13×C22⋊Q8C2×C411yescharacteristic
84C13×#121C2×C411yescharacteristic
85C4×Q8×C13—21no—
86C4×Q8×C13C2311yescharacteristic
87C4×Q8×C13C2311yescharacteristic
88C4×Q8×C13C2311yescharacteristic
89C4×D4×C13—21no—
90C4×D4×C13C2311yescharacteristic
91C13×#117—21no—
92C13×#117—21no—
93C2×C42×C13C2311yescharacteristic
94C2×#6099—21no—
95C22×#1055—21no—
96C22×#1055—21no—
97C13×#107C2×C411yescharacteristic
98C13×#107C2×C411yescharacteristic
99C13×#106C2×C411yescharacteristic
100C13×#106C2×C411yescharacteristic
101C13×#103C2×C411yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×#97C2×C411yescharacteristic
110C13×#97C2×C411yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C22⋊#1055—21no—
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055D411yescharacteristic
118C22⋊#1055D411yescharacteristic
119C4⋊#1055—21no—
120C4⋊#1055—21no—
121C4⋊#1055—21no—
122C4⋊#1055—21no—
123C4⋊#1055—21no—
124C4⋊#1055—21no—
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055D411yescharacteristic
128C4⋊#1055D411yescharacteristic
129C4⋊#1055C2311yescharacteristic
130C4⋊#1055C2311yescharacteristic
131C4⋊#1055C2311yescharacteristic
132C4⋊#1055C2311yescharacteristic
133#88043—21no—
134#88043—21no—
135#88043—21no—
136C4×#1055—21no—
137C4×#1055—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18083—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13C22×C411yescharacteristic
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×C4×C13C2×D411yescharacteristic
154C22×C4×C13#4111yescharacteristic
155C13×Q16—22no—
156C13×Q16—41no—
157C13×SD16—22no—
158C13×SD16—41no—
159C13×M16—22no—
160C13×M16—41no—
161C2×C8×C13C22×C411yescharacteristic
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C13×C22⋊C4—21no—
186C13×C22⋊C4—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13C22×C411yescharacteristic
191C42×C13C2×D411yescharacteristic
192C42×C13#4111yescharacteristic
193C42×C13C2411yescharacteristic
194#6099—81no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—81no—
202C2×#1055—81no—
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207#3172D1311yescharacteristic
208#2994—131no—
209#2986—131no—
210#1593—131no—
211#1590—131no—
212#1588—131no—
213#1587—131no—
214#1584—131no—
215#1582—131no—
216SD16⋊C8—131no—
217C8×Q16—131no—
218#1565—131no—
219#1482—131no—
220#1481—131no—
221#1453—131no—
222C23×C13—21no—
223C23×C13C4×D411yescharacteristic
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13—42no—
231D4×C13—21no—
232D4×C13—21no—
233D4×C13—42no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13C4×D411yescharacteristic
249C2×C4×C13C4×D411yescharacteristic
250C2×C4×C13C4×D411yescharacteristic
251C2×C4×C13C23×C411yescharacteristic
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C8×C13—21no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13#13112yes—
258#1055—21no—
259#1055—21no—
260#1055—21no—
261#1055—21no—
262#1055—41no—
263#1055—41no—
264#1055—41no—
265#1055—41no—
266#1055—41no—
267#1055—41no—
268#533C2×D1311yescharacteristic
269#529C2×D1311yescharacteristic
270#501Dic1311yescharacteristic
271#497Dic1311yescharacteristic
272#491Dic1311yescharacteristic
273#489Dic1311yescharacteristic
274#470Dic1311yescharacteristic
275#470Dic1311yescharacteristic
276#468Dic1311yescharacteristic
277#468Dic1311yescharacteristic
278#446—131no—
279#446—131no—
280#446—131no—
281#446—261no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8—261no—
286C4×Q16C2×D1311yescharacteristic
287C4×Q16C2×D1311yescharacteristic
288C4×SD16C2×D1311yescharacteristic
289C4×SD16C2×D1311yescharacteristic
290#436—131no—
291#435—261no—
292C8×D4—131no—
293C8×D4—261no—
294#433—261no—
295#433—261no—
296#433—261no—
297#431—131no—
298#431—131no—
299#431—131no—
300#424—261no—
301C2×C4⋊C8—131no—
302C4×M16C2×D1311yescharacteristic
303#335—131no—
304#335—131no—
305#334—131no—
306#334—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313D4⋊C8—131no—
314D4⋊C8—131no—
315#322—131no—
316#322—131no—
317#322—131no—
318C82—131no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13C2×C4×D411yescharacteristic
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13C2×#13111yescharacteristic
338C4×C13#56811yescharacteristic
339C4×C13#57711yescharacteristic
340C4×C13#57811yescharacteristic
341C2×Q16C2×Dic1311yescharacteristic
342C2×Q16C2×Dic1311yescharacteristic
343C2×SD16C2×Dic1311yescharacteristic
344C2×SD16C2×Dic1311yescharacteristic
345C2×M16—261no—
346C2×M16C2×Dic1311yescharacteristic
347C2×M16C2×Dic1311yescharacteristic
348C22×C8—261no—
349C22×C8—261no—
350C4⋊Q8C2×Dic1311yescharacteristic
351C4⋊Q8C2×Dic1311yescharacteristic
352#126—21no—
353#125—21no—
354#125C2×Dic1311yescharacteristic
355#124C2×Dic1311yescharacteristic
356#123—21no—
357C22⋊Q8—21no—
358C22⋊Q8C2×Dic1311yescharacteristic
359C22⋊Q8C2×Dic1311yescharacteristic
360C22⋊Q8C2×Dic1311yescharacteristic
361#121C2×Dic1311yescharacteristic
362C4×Q8—21no—
363C4×Q8C22×D1311yescharacteristic
364C4×Q8C22×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366C4×D4—21no—
367C4×D4C22×D1311yescharacteristic
368#117—21no—
369#117—21no—
370C2×C42C22×D1311yescharacteristic
371#107C2×Dic1311yescharacteristic
372#107C2×Dic1311yescharacteristic
373#106C2×Dic1311yescharacteristic
374#106C2×Dic1311yescharacteristic
375C4⋊C8—131no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389#103C2×Dic1311yescharacteristic
390#103C2×Dic1311yescharacteristic
391#103C2×Dic1311yescharacteristic
392#103C2×Dic1311yescharacteristic
393#103C2×Dic1311yescharacteristic
394#103C2×Dic1311yescharacteristic
395#102C2×Dic1311yescharacteristic
396#102C2×Dic1311yescharacteristic
397C22⋊C8—131no—
398C22⋊C8—131no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—261no—
404#97—261no—
405#97—261no—
406#97C2×Dic1311yescharacteristic
407#97C2×Dic1311yescharacteristic
408C4×C8—131no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—261no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C2×C13—41no—
419C2×C13—81no—
420C2×C13#293511yescharacteristic
421C2×C13#294711yescharacteristic
422C2×C13#295511yescharacteristic
423C2×Q8—21no—
424C2×Q8C22×Dic1311yescharacteristic
425C2×Q8C22×Dic1311yescharacteristic
426C2×Q8C22×Dic1311yescharacteristic
427C2×D4—21no—
428C2×D4C22×Dic1311yescharacteristic
429C22×C4—21no—
430C22×C4D4×D1311yescharacteristic
431C22×C4#612911yescharacteristic
432C22×C4C22×Dic1311yescharacteristic
433Q16—22no—
434Q16—41no—
435SD16—22no—
436SD16—41no—
437M16—22no—
438M16—41no—
439M16—1041no—
440C2×C8—131no—
441C2×C8—131no—
442C2×C8—131no—
443C2×C8—131no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—1041no—
451C2×C8—1041no—
452C2×C8C22×Dic1311yescharacteristic
453C2×C8C22×Dic1311yescharacteristic
454C2×C8C22×Dic1311yescharacteristic
455C2×C8C22×Dic1311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4C22×Dic1311yescharacteristic
468C4⋊C4C22×Dic1311yescharacteristic
469C4⋊C4C22×Dic1311yescharacteristic
470C4⋊C4C22×Dic1311yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42D4×D1311yescharacteristic
482C42#612911yescharacteristic
483C42C22×Dic1311yescharacteristic
484C42C23×D1311yescharacteristic
485C13#1808311yescharacteristic, complemented, Sylow
486C23—21no—
487C23D4×Dic1311yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—42no—
495D4—21no—
496D4—21no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4D4×Dic1311yescharacteristic
513C2×C4D4×Dic1311yescharacteristic
514C2×C4D4×Dic1311yescharacteristic
515C2×C4C2×D4×D1311yescharacteristic
516C2×C4C2×#612911yescharacteristic
517C2×C4C23×Dic1311yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—261no—
522C8—261no—
523C8—261no—
524C8—261no—
525C8—521no—
526C8—521no—
527C8—521no—
528C8—521no—
529C8—521no—
530C8—521no—
531C8#8820212yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×D4×Dic1311yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4#1171948311yescharacteristic
551C4#1171948411yescharacteristic
552C4C2×#8820211yescharacteristic
553C4#1171952411yescharacteristic
554C2—41no—
555C2—81no—
556C2#1312358011yescharacteristic
557C2#1312368011yescharacteristic
558C2#1312373911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#3172C2
socleC22×C13C2×C4×D4
prime radicalC13×#121C2×C4
cosocleC42×C13C24
hypercenter#3172D13
hypocenterC13#18083
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3172

Complements

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

NH ≅ G/Ntype
2. #13123938C2semidirect
3. #13113745C2semidirect
4. #13113727C2semidirect
5. #13113715C2semidirect
6. #13113708C2semidirect
7. #13113687C2semidirect
8. #13113673C2semidirect
9. SD16⋊#1055C2semidirect
10. Q16×#1055C2semidirect
11. #13113588C2semidirect
13. #13113239C2semidirect
14. #13113133C2semidirect
485. C13#18083semidirect

Maximal subgroups

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

subgroupindex
#131239962
#131239382
#131137452
#131137272
#131137152
#131137082
#131136872
#131136732
SD16⋊#10552
Q16×#10552
#131135882
#131132442
#131132392
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