Finite Group Databasebeta

← #15834285

Subgroups — #15834285

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123925C211yesmaximal, characteristic, complemented
2#13123903C211yesmaximal, characteristic
3#13113739C211yesmaximal, characteristic, complemented
4#13113727C211yesmaximal, characteristic, complemented
5#13113715C211yesmaximal, characteristic, complemented
6#13113694C211yesmaximal, characteristic, complemented
7#13113680C211yesmaximal, characteristic, complemented
8#13113673C211yesmaximal, characteristic, complemented
9SD16⋊#1055C211yesmaximal, characteristic, complemented
10SD16×#1055C211yesmaximal, characteristic, complemented
11#13113616C211yesmaximal, characteristic, complemented
12#13113305C211yesmaximal, characteristic
13#13113231C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#3103C211yesmaximal, characteristic
16C13×#532C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C13×#481C411yescharacteristic
19C13×#481C411yescharacteristic
20C13×#475C411yescharacteristic
21C13×#475C411yescharacteristic
22C13×#460C411yescharacteristic
23C13×#460C411yescharacteristic
24C13×#448C411yescharacteristic
25C13×#448C411yescharacteristic
26C4×C13×SD16C2211yescharacteristic
27C4×C13×SD16C2211yescharacteristic
28C4×C13×SD16C2211yescharacteristic
29C4×C13×SD16C2211yescharacteristic
30C13×#431C2211yescharacteristic
31#11718895—21no—
32#11718895—21no—
33#11718685—21no—
34#11718685—21no—
35#11718685C2211yescharacteristic
36#11718685C2211yescharacteristic
37Q8×#1055C2211yescharacteristic
38Q8×#1055C2211yescharacteristic
39#11718673—21no—
40#11718673C2211yescharacteristic
41#11718673C2211yescharacteristic
42D4×#1055—21no—
43D4×#1055C2211yescharacteristic
44D4×#1055C2211yescharacteristic
45#11718587—21no—
46#11718587C2211yescharacteristic
47#11718586—21no—
48#11718586C2211yescharacteristic
49#11718586C2211yescharacteristic
50#11718586C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53Q8⋊#1055C2211yescharacteristic
54Q8⋊#1055C2211yescharacteristic
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57D4⋊#1055C2211yescharacteristic
58D4⋊#1055C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C22×Q8×C13C2×C411yescharacteristic
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×SD16C2×C411yescharacteristic
71C2×C13×SD16C2×C411yescharacteristic
72C2×C13×SD16C2×C411yescharacteristic
73C13×C4⋊Q8C2×C411yescharacteristic
74C13×#127C2×C411yescharacteristic
75C13×#124—21no—
76C13×#121—21no—
77C13×#121C2×C411yescharacteristic
78C13×#121C2×C411yescharacteristic
79C4×Q8×C13—21no—
80C4×Q8×C13—21no—
81C4×Q8×C13C2×C411yescharacteristic
82C4×Q8×C13C2×C411yescharacteristic
83C4×Q8×C13C2311yescharacteristic
84C4×Q8×C13C2311yescharacteristic
85C4×D4×C13—21no—
86C4×D4×C13C2311yescharacteristic
87C4×D4×C13C2311yescharacteristic
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4C2×C411yescharacteristic
90C2×C42×C13—21no—
91C2×C42×C13C2311yescharacteristic
92C2×#6099—21no—
93C2×#6099—21no—
94C22×#1055—21no—
95C22×#1055—21no—
96C13×#106C2×C411yescharacteristic
97C13×#106C2×C411yescharacteristic
98C13×#106C2×C411yescharacteristic
99C13×#106C2×C411yescharacteristic
100C13×C4⋊C8C2×C411yescharacteristic
101C13×C4⋊C8C2×C411yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#102C2×C411yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×C22⋊C8C2×C411yescharacteristic
111C13×C22⋊C8C2×C411yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055—21no—
118C22⋊#1055—21no—
119C22⋊#1055—21no—
120C22⋊#1055—21no—
121C22⋊#1055D411yescharacteristic
122C22⋊#1055D411yescharacteristic
123C4⋊#1055—21no—
124C4⋊#1055—21no—
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055—21no—
128C4⋊#1055D411yescharacteristic
129C4⋊#1055D411yescharacteristic
130C4⋊#1055C2311yescharacteristic
131C4⋊#1055C2311yescharacteristic
132C4⋊#1055C2311yescharacteristic
133C4⋊#1055C2311yescharacteristic
134#88043—21no—
135#88043—21no—
136#88043—21no—
137C4×#1055—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18030—131nomaximal, Sylow
145C13×#41—81no—
146C13×#41—81no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—22no—
150C2×Q8×C13—41no—
151C2×Q8×C13C22×C411yescharacteristic
152C2×Q8×C13C22×C411yescharacteristic
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13C22×C411yescharacteristic
158C2×D4×C13C22×C411yescharacteristic
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13C22×C411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13#4111yescharacteristic
166C13×SD16—22no—
167C13×SD16—22no—
168C13×SD16—41no—
169C13×SD16—41no—
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C4⋊C4C22×C411yescharacteristic
183C13×C4⋊C4C22×C411yescharacteristic
184C13×C22⋊C4—21no—
185C13×C22⋊C4—21no—
186C13×C22⋊C4—21no—
187C13×C22⋊C4—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13C22×C411yescharacteristic
193C42×C13C2×D411yescharacteristic
194C42×C13#4111yescharacteristic
195C42×C13C2411yescharacteristic
196#6099—81no—
197#6099—81no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—81no—
205C2×#1055—81no—
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210#3103D1311yescharacteristic
211#2984—131no—
212#2979—131no—
213#1592—131no—
214#1590—131no—
215#1588—131no—
216#1585—131no—
217#1583—131no—
218#1582—131no—
219SD16⋊C8—131no—
220C8×SD16—131no—
221#1572—131no—
222#1496—131no—
223#1479—131no—
224#1454—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13C4×D411yescharacteristic
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13—21no—
231Q8×C13—42no—
232Q8×C13—81no—
233Q8×C13#13112yes—
234D4×C13—21no—
235D4×C13—21no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—42no—
239D4×C13—81no—
240D4×C13—81no—
241D4×C13—81no—
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—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—41no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13C4×D411yescharacteristic
260C2×C4×C13C4×D411yescharacteristic
261C2×C4×C13C4×D411yescharacteristic
262C2×C4×C13C23×C411yescharacteristic
263C2×C4×C13C22×D411yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C8×C13—21no—
266C8×C13—21no—
267C8×C13—21no—
268C8×C13—21no—
269#1055—21no—
270#1055—21no—
271#1055—21no—
272#1055—21no—
273#1055—41no—
274#1055—41no—
275#1055—41no—
276#1055—41no—
277#1055—41no—
278#1055—41no—
279#532C2×D1311yescharacteristic
280C2×C4×Q8C2×D1311yescharacteristic
281#481Dic1311yescharacteristic
282#481Dic1311yescharacteristic
283#475Dic1311yescharacteristic
284#475Dic1311yescharacteristic
285#460Dic1311yescharacteristic
286#460Dic1311yescharacteristic
287#448Dic1311yescharacteristic
288#448Dic1311yescharacteristic
289#446—131no—
290#446—131no—
291#446—261no—
292#446—261no—
293C8×Q8—131no—
294C8×Q8—131no—
295C4×SD16C2×D1311yescharacteristic
296C4×SD16C2×D1311yescharacteristic
297C4×SD16C2×D1311yescharacteristic
298C4×SD16C2×D1311yescharacteristic
299#436—131no—
300#436—131no—
301#436—261no—
302C8×D4—131no—
303C8×D4—131no—
304C8×D4—261no—
305#432—131no—
306#432—261no—
307#431—131no—
308#431—131no—
309#431—131no—
310#431—261no—
311#431C2×D1311yescharacteristic
312#408—261no—
313#408—261no—
314#335—131no—
315#335—131no—
316#334—131no—
317#334—131no—
318Q8⋊C8—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322D4⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326#322—131no—
327#322—131no—
328#322—131no—
329C82—131no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13C2×C4×D411yescharacteristic
340C4×C13—21no—
341C4×C13—22no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—21no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13C2×#13111yescharacteristic
351C4×C13#56811yescharacteristic
352C4×C13#57711yescharacteristic
353C4×C13#57711yescharacteristic
354C2×#41—21no—
355C22×Q8C2×Dic1311yescharacteristic
356C2×SD16C2×Dic1311yescharacteristic
357C2×SD16C2×Dic1311yescharacteristic
358C2×SD16C2×Dic1311yescharacteristic
359C2×SD16C2×Dic1311yescharacteristic
360C2×M16—261no—
361C2×M16—261no—
362C22×C8—261no—
363C22×C8—261no—
364C4⋊Q8C2×Dic1311yescharacteristic
365#127C2×Dic1311yescharacteristic
366#124—21no—
367#121—21no—
368#121C2×Dic1311yescharacteristic
369#121C2×Dic1311yescharacteristic
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C2×Dic1311yescharacteristic
373C4×Q8C2×Dic1311yescharacteristic
374C4×Q8C22×D1311yescharacteristic
375C4×Q8C22×D1311yescharacteristic
376C4×D4—21no—
377C4×D4C22×D1311yescharacteristic
378C4×D4C22×D1311yescharacteristic
379C2×C4⋊C4—21no—
380C2×C4⋊C4C2×Dic1311yescharacteristic
381C2×C42—21no—
382C2×C42C22×D1311yescharacteristic
383#106C2×Dic1311yescharacteristic
384#106C2×Dic1311yescharacteristic
385#106C2×Dic1311yescharacteristic
386#106C2×Dic1311yescharacteristic
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8C2×Dic1311yescharacteristic
399C4⋊C8C2×Dic1311yescharacteristic
400#103C2×Dic1311yescharacteristic
401#103C2×Dic1311yescharacteristic
402#103C2×Dic1311yescharacteristic
403#103C2×Dic1311yescharacteristic
404#102C2×Dic1311yescharacteristic
405#102C2×Dic1311yescharacteristic
406#102C2×Dic1311yescharacteristic
407#102C2×Dic1311yescharacteristic
408C22⋊C8—131no—
409C22⋊C8—131no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8C2×Dic1311yescharacteristic
418C22⋊C8C2×Dic1311yescharacteristic
419#97—261no—
420#97—261no—
421#97—261no—
422C4×C8—131no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—261no—
427C4×C8—261no—
428C4×C8—261no—
429C4×C8C22×D1311yescharacteristic
430C4×C8C22×D1311yescharacteristic
431C2×C13—41no—
432C2×C13—81no—
433C2×C13—81no—
434C2×C13#293311yescharacteristic
435C2×C13#294911yescharacteristic
436C2×C13#295511yescharacteristic
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8C22×Dic1311yescharacteristic
444C2×Q8C22×Dic1311yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C22×Dic1311yescharacteristic
450C2×D4C22×Dic1311yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4D4×D1311yescharacteristic
456C22×C4#612911yescharacteristic
457C22×C4C22×Dic1311yescharacteristic
458SD16—22no—
459SD16—22no—
460SD16—41no—
461SD16—41no—
462M16—1041no—
463M16—1041no—
464C2×C8—131no—
465C2×C8—131no—
466C2×C8—131no—
467C2×C8—131no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—1041no—
475C2×C8—1041no—
476C2×C8C22×Dic1311yescharacteristic
477C2×C8C22×Dic1311yescharacteristic
478C2×C8C22×Dic1311yescharacteristic
479C2×C8C22×Dic1311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4C22×Dic1311yescharacteristic
487C4⋊C4C22×Dic1311yescharacteristic
488C4⋊C4C22×Dic1311yescharacteristic
489C4⋊C4C22×Dic1311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42D4×D1311yescharacteristic
499C42#612911yescharacteristic
500C42C22×Dic1311yescharacteristic
501C42C23×D1311yescharacteristic
502C13#1803011yescharacteristic, complemented, Sylow
503C23—21no—
504C23—21no—
505C23D4×Dic1311yescharacteristic
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—42no—
510Q8—81no—
511Q8#8820212yes—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—81no—
518D4—81no—
519D4—81no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4D4×Dic1311yescharacteristic
538C2×C4D4×Dic1311yescharacteristic
539C2×C4D4×Dic1311yescharacteristic
540C2×C4C2×D4×D1311yescharacteristic
541C2×C4C2×#612911yescharacteristic
542C2×C4C23×Dic1311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—261no—
548C8—261no—
549C8—261no—
550C8—261no—
551C8—521no—
552C8—521no—
553C8—521no—
554C8—521no—
555C8—521no—
556C8—521no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×D4×Dic1311yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4#1171946711yescharacteristic
578C4#1171946711yescharacteristic
579C4C2×#8820211yescharacteristic
580C4#1171952411yescharacteristic
581C2—41no—
582C2—81no—
583C2—81no—
584C2#1312356311yescharacteristic
585C2#1312369611yescharacteristic
586C2#1312373911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#3103C2
socleC22×C13C2×C4×D4
prime radicalC13×#532C22
cosocleC42×C13C24
hypercenter#3103D13
hypocenterC13#18030
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
1. #13123925C2semidirect
3. #13113739C2semidirect
4. #13113727C2semidirect
5. #13113715C2semidirect
6. #13113694C2semidirect
7. #13113680C2semidirect
8. #13113673C2semidirect
9. SD16⋊#1055C2semidirect
10. SD16×#1055C2semidirect
11. #13113616C2semidirect
13. #13113231C2semidirect
14. #13113136C2semidirect
502. C13#18030semidirect

Maximal subgroups

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

subgroupindex
#131239252
#131239032
#131137392
#131137272
#131137152
#131136942
#131136802
#131136732
SD16⋊#10552
SD16×#10552
#131136162
#131133052
#131132312
#131131362
C13×#31032
#1803013