Finite Group Databasebeta

← #15834315

Subgroups — #15834315

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123938C211yesmaximal, characteristic
2#13123925C211yesmaximal, characteristic
3#13113745C211yesmaximal, characteristic, complemented
4#13113733C211yesmaximal, characteristic, complemented
5#13113708C211yesmaximal, characteristic, complemented
6#13113708C211yesmaximal, characteristic, complemented
7#13113687C211yesmaximal, characteristic, complemented
8#13113687C211yesmaximal, characteristic, complemented
9#13113655C211yesmaximal, characteristic, complemented
10Q16×#1055C211yesmaximal, characteristic, complemented
11#13113616C211yesmaximal, characteristic
12#13113309C211yesmaximal, characteristic
13#13113231C211yesmaximal, characteristic
14#13113136C211yesmaximal, characteristic
15C13×#3104C211yesmaximal, characteristic
16C13×#533C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C13×#484C411yescharacteristic
19C13×#484C411yescharacteristic
20C13×#477C411yescharacteristic
21C13×#477C411yescharacteristic
22C13×#462C411yescharacteristic
23C13×#462C411yescharacteristic
24C13×#451C411yescharacteristic
25C13×#451C411yescharacteristic
26C4×C13×Q16C2211yescharacteristic
27C4×C13×Q16C2211yescharacteristic
28C4×C13×Q16C2211yescharacteristic
29C4×C13×Q16C2211yescharacteristic
30C13×#431C2211yescharacteristic
31#11718685—21no—
32#11718685—21no—
33#11718685—21no—
34#11718685C2211yescharacteristic
35#11718685C2211yescharacteristic
36#11718685C2211yescharacteristic
37#11718685C2211yescharacteristic
38Q8×#1055—21no—
39Q8×#1055C2211yescharacteristic
40Q8×#1055C2211yescharacteristic
41Q8×#1055C2211yescharacteristic
42Q8×#1055C2211yescharacteristic
43#11718661—21no—
44#11718661—21no—
45#11718587—21no—
46#11718587C2211yescharacteristic
47#11718586—21no—
48#11718586C2211yescharacteristic
49#11718586C2211yescharacteristic
50#11718586C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53Q8⋊#1055C2211yescharacteristic
54Q8⋊#1055C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57Q8⋊#1055C2211yescharacteristic
58Q8⋊#1055C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Q8×C13C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C2×C13×Q16C2×C411yescharacteristic
70C2×C13×Q16C2×C411yescharacteristic
71C2×C13×Q16C2×C411yescharacteristic
72C13×C4⋊Q8C2×C411yescharacteristic
73C13×C4⋊Q8C2×C411yescharacteristic
74C13×#125—21no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8C2×C411yescharacteristic
77C13×C22⋊Q8C2×C411yescharacteristic
78C4×Q8×C13—21no—
79C4×Q8×C13—21no—
80C4×Q8×C13—21no—
81C4×Q8×C13C2×C411yescharacteristic
82C4×Q8×C13C2×C411yescharacteristic
83C4×Q8×C13C2311yescharacteristic
84C4×Q8×C13C2311yescharacteristic
85C4×Q8×C13C2311yescharacteristic
86C4×Q8×C13C2311yescharacteristic
87C13×#117—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4C2×C411yescharacteristic
90C2×C42×C13—21no—
91C2×C42×C13C2311yescharacteristic
92C13×#107C2×C411yescharacteristic
93C13×#107C2×C411yescharacteristic
94C13×#107C2×C411yescharacteristic
95C13×#107C2×C411yescharacteristic
96C13×C4⋊C8C2×C411yescharacteristic
97C13×C4⋊C8C2×C411yescharacteristic
98C13×#103C2×C411yescharacteristic
99C13×#103C2×C411yescharacteristic
100C13×#103C2×C411yescharacteristic
101C13×#103C2×C411yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×C22⋊C8C2×C411yescharacteristic
107C13×C22⋊C8C2×C411yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C22⋊#1055—21no—
111C22⋊#1055—21no—
112C22⋊#1055—21no—
113C22⋊#1055D411yescharacteristic
114C22⋊#1055D411yescharacteristic
115C4⋊#1055—21no—
116C4⋊#1055—21no—
117C4⋊#1055—21no—
118C4⋊#1055—21no—
119C4⋊#1055—21no—
120C4⋊#1055—21no—
121C4⋊#1055—21no—
122C4⋊#1055—21no—
123C4⋊#1055—21no—
124C4⋊#1055D411yescharacteristic
125C4⋊#1055D411yescharacteristic
126C4⋊#1055C2311yescharacteristic
127C4⋊#1055C2311yescharacteristic
128C4⋊#1055C2311yescharacteristic
129C4⋊#1055C2311yescharacteristic
130#88043—21no—
131#88043—21no—
132#88043—21no—
133#88043—21no—
134#88043—21no—
135C4×#1055—21no—
136C4×#1055—21no—
137C4×#1055—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18032—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—22no—
148C2×Q8×C13—41no—
149C2×Q8×C13C22×C411yescharacteristic
150C2×Q8×C13C22×C411yescharacteristic
151C2×Q8×C13C22×C411yescharacteristic
152C2×Q8×C13C22×C411yescharacteristic
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13C22×C411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13#4111yescharacteristic
158C13×Q16—22no—
159C13×Q16—22no—
160C13×Q16—41no—
161C13×Q16—41no—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
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⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13C22×C411yescharacteristic
191C42×C13C2×D411yescharacteristic
192C42×C13#4111yescharacteristic
193C42×C13C2411yescharacteristic
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204#3104D1311yescharacteristic
205#2986—131no—
206#2984—131no—
207#1593—131no—
208#1591—131no—
209#1587—131no—
210#1587—131no—
211#1584—131no—
212#1584—131no—
213#1579—131no—
214C8×Q16—131no—
215#1572—131no—
216#1497—131no—
217#1479—131no—
218#1454—131no—
219C23×C13C4×D411yescharacteristic
220Q8×C13—21no—
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—42no—
228Q8×C13—42no—
229Q8×C13#13112yes—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
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—41no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C4×D411yescharacteristic
248C2×C4×C13C23×C411yescharacteristic
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C8×C13—21no—
252C8×C13—21no—
253C8×C13—21no—
254C8×C13—21no—
255#1055—21no—
256#1055—21no—
257#1055—21no—
258#1055—21no—
259#1055—41no—
260#1055—41no—
261#1055—41no—
262#1055—41no—
263#1055—41no—
264#1055—41no—
265#533C2×D1311yescharacteristic
266C2×C4×Q8C2×D1311yescharacteristic
267#484Dic1311yescharacteristic
268#484Dic1311yescharacteristic
269#477Dic1311yescharacteristic
270#477Dic1311yescharacteristic
271#462Dic1311yescharacteristic
272#462Dic1311yescharacteristic
273#451Dic1311yescharacteristic
274#451Dic1311yescharacteristic
275#446—131no—
276#446—131no—
277#446—131no—
278#446—131no—
279#446—261no—
280#446—261no—
281#446—261no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—261no—
287C4×Q16C2×D1311yescharacteristic
288C4×Q16C2×D1311yescharacteristic
289C4×Q16C2×D1311yescharacteristic
290C4×Q16C2×D1311yescharacteristic
291#433—261no—
292#433—261no—
293#432—131no—
294#432—261no—
295#431—131no—
296#431—131no—
297#431—131no—
298#431—261no—
299#431C2×D1311yescharacteristic
300#335—131no—
301#335—131no—
302#334—131no—
303#334—131no—
304Q8⋊C8—131no—
305Q8⋊C8—131no—
306Q8⋊C8—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312#322—131no—
313#322—131no—
314#322—131no—
315C82—131no—
316C22×C13—21no—
317C22×C13—21no—
318C22×C13—21no—
319C22×C13C2×C4×D411yescharacteristic
320C4×C13—21no—
321C4×C13—22no—
322C4×C13—21no—
323C4×C13—21no—
324C4×C13—21no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13C2×#13111yescharacteristic
333C4×C13#56811yescharacteristic
334C4×C13#57811yescharacteristic
335C4×C13#57811yescharacteristic
336C22×Q8C2×Dic1311yescharacteristic
337C2×Q16C2×Dic1311yescharacteristic
338C2×Q16C2×Dic1311yescharacteristic
339C2×Q16C2×Dic1311yescharacteristic
340C2×Q16C2×Dic1311yescharacteristic
341C4⋊Q8C2×Dic1311yescharacteristic
342C4⋊Q8C2×Dic1311yescharacteristic
343#125—21no—
344C22⋊Q8—21no—
345C22⋊Q8C2×Dic1311yescharacteristic
346C22⋊Q8C2×Dic1311yescharacteristic
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8C2×Dic1311yescharacteristic
351C4×Q8C2×Dic1311yescharacteristic
352C4×Q8C22×D1311yescharacteristic
353C4×Q8C22×D1311yescharacteristic
354C4×Q8C22×D1311yescharacteristic
355C4×Q8C22×D1311yescharacteristic
356#117—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C2×Dic1311yescharacteristic
359C2×C42—21no—
360C2×C42C22×D1311yescharacteristic
361#107C2×Dic1311yescharacteristic
362#107C2×Dic1311yescharacteristic
363#107C2×Dic1311yescharacteristic
364#107C2×Dic1311yescharacteristic
365C4⋊C8—131no—
366C4⋊C8—131no—
367C4⋊C8—131no—
368C4⋊C8—131no—
369C4⋊C8—131no—
370C4⋊C8—131no—
371C4⋊C8—261no—
372C4⋊C8—261no—
373C4⋊C8—261no—
374C4⋊C8—261no—
375C4⋊C8—261no—
376C4⋊C8—261no—
377C4⋊C8—261no—
378C4⋊C8—261no—
379C4⋊C8—261no—
380C4⋊C8C2×Dic1311yescharacteristic
381C4⋊C8C2×Dic1311yescharacteristic
382#103C2×Dic1311yescharacteristic
383#103C2×Dic1311yescharacteristic
384#103C2×Dic1311yescharacteristic
385#103C2×Dic1311yescharacteristic
386#103C2×Dic1311yescharacteristic
387#103C2×Dic1311yescharacteristic
388#103C2×Dic1311yescharacteristic
389#103C2×Dic1311yescharacteristic
390C22⋊C8—131no—
391C22⋊C8—131no—
392C22⋊C8—261no—
393C22⋊C8—261no—
394C22⋊C8—261no—
395C22⋊C8C2×Dic1311yescharacteristic
396C22⋊C8C2×Dic1311yescharacteristic
397#97—261no—
398#97—261no—
399#97—261no—
400#97—261no—
401#97—261no—
402C4×C8—131no—
403C4×C8—131no—
404C4×C8—131no—
405C4×C8—131no—
406C4×C8—261no—
407C4×C8—261no—
408C4×C8—261no—
409C4×C8—261no—
410C4×C8—261no—
411C4×C8C22×D1311yescharacteristic
412C4×C8C22×D1311yescharacteristic
413C2×C13—41no—
414C2×C13#293311yescharacteristic
415C2×C13#295011yescharacteristic
416C2×C13#295511yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—41no—
421C2×Q8C22×Dic1311yescharacteristic
422C2×Q8C22×Dic1311yescharacteristic
423C2×Q8C22×Dic1311yescharacteristic
424C2×Q8C22×Dic1311yescharacteristic
425C22×C4—21no—
426C22×C4—21no—
427C22×C4D4×D1311yescharacteristic
428C22×C4#612911yescharacteristic
429C22×C4C22×Dic1311yescharacteristic
430Q16—22no—
431Q16—22no—
432Q16—41no—
433Q16—41no—
434C2×C8—131no—
435C2×C8—131no—
436C2×C8—131no—
437C2×C8—131no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8C22×Dic1311yescharacteristic
445C2×C8C22×Dic1311yescharacteristic
446C2×C8C22×Dic1311yescharacteristic
447C2×C8C22×Dic1311yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4C22×Dic1311yescharacteristic
461C4⋊C4C22×Dic1311yescharacteristic
462C4⋊C4C22×Dic1311yescharacteristic
463C4⋊C4C22×Dic1311yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42D4×D1311yescharacteristic
473C42#612911yescharacteristic
474C42C22×Dic1311yescharacteristic
475C42C23×D1311yescharacteristic
476C13#1803211yescharacteristic, complemented, Sylow
477C23D4×Dic1311yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—42no—
486Q8—42no—
487Q8#8820212yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4D4×Dic1311yescharacteristic
504C2×C4D4×Dic1311yescharacteristic
505C2×C4D4×Dic1311yescharacteristic
506C2×C4C2×D4×D1311yescharacteristic
507C2×C4C2×#612911yescharacteristic
508C2×C4C23×Dic1311yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—261no—
514C8—261no—
515C8—261no—
516C8—261no—
517C8—521no—
518C8—521no—
519C8—521no—
520C8—521no—
521C8—521no—
522C8—521no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×D4×Dic1311yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4#1171947111yescharacteristic
540C4#1171947111yescharacteristic
541C4C2×#8820211yescharacteristic
542C4#1171952411yescharacteristic
543C2—41no—
544C2#1312356311yescharacteristic
545C2#1312370411yescharacteristic
546C2#1312373911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#3104C2
socleC22×C13C2×C4×D4
prime radicalC23×C13C4×D4
cosocleC42×C13C24
hypercenter#3104D13
hypocenterC13#18032
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #13113745C2semidirect
4. #13113733C2semidirect
5. #13113708C2semidirect
6. #13113708C2semidirect
7. #13113687C2semidirect
8. #13113687C2semidirect
9. #13113655C2semidirect
10. Q16×#1055C2semidirect
476. C13#18032semidirect

Maximal subgroups

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

subgroupindex
#131239382
#131239252
#131137452
#131137332
#131137082
#131136872
#131136552
Q16×#10552
#131136162
#131133092
#131132312
#131131362
C13×#31042
#1803213