Finite Group Databasebeta

← #15834907

Subgroups — #15834907

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125419C211yesmaximal, characteristic
2#13123936C211yesmaximal, characteristic
3#13123934C211yesmaximal, characteristic
4#13113731C211yesmaximal, characteristic, complemented
5#13113730C211yesmaximal, characteristic, complemented
6#13113709C211yesmaximal, characteristic, complemented
7#13113708C211yesmaximal, characteristic, complemented
8#13113706C211yesmaximal, characteristic, complemented
9C8×#6107C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113581C211yesmaximal, characteristic
12#13113255C211yesmaximal, characteristic
13#13113255C211yesmaximal, characteristic
14#13113115C211yesmaximal, characteristic
15C13×#1587C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17#11719283C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718849C411yescharacteristic
22#11718842C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6107C2211yescharacteristic
25#11718685C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718548C411yescharacteristic
28#11718535C411yescharacteristic
29#11718501—21no—
30#11718501—21no—
31#11718494C2211yescharacteristic
32#11718494C2211yescharacteristic
33#11718492C2211yescharacteristic
34#11718491—21no—
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718474C411yescharacteristic
38#11718474C411yescharacteristic
39#11718453C411yescharacteristic
40#11718453C411yescharacteristic
41#11718370—21no—
42#11718362—21no—
43C4×Dic52C2211yescharacteristic
44#11718351—21no—
45C4×#6094C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×Q16C2×C411yescharacteristic
68C4×Q8×C13C2311yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70#88200C2×C411yescharacteristic
71#88200C2×C411yescharacteristic
72#88198C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6107C2×C411yescharacteristic
76C2×Dic52C2×C411yescharacteristic
77C2×#6094—21no—
78C2×C8×D13C2×C411yescharacteristic
79C2×C8×D13C2×C411yescharacteristic
80#88151C2×C411yescharacteristic
81#88151C2×C411yescharacteristic
82#88150—21no—
83#88150—21no—
84#88143—21no—
85#88143—21no—
86#88142C2×C411yescharacteristic
87#88142C2×C411yescharacteristic
88#88126—21no—
89#88126—21no—
90C42×D13C2311yescharacteristic
91C4×Dic26—21no—
92C4×Dic26—21no—
93C4×Dic26C2311yescharacteristic
94C4×Dic26C2311yescharacteristic
95C13×#107C2×C411yescharacteristic
96C13×C4⋊C8—21no—
97C13×C4⋊C8—21no—
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×#103C2×C411yescharacteristic
101C13×#103C2×C411yescharacteristic
102C13×#97—21no—
103C4×C8×C13—21no—
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107#88075C2×C411yescharacteristic
108#88075C2×C411yescharacteristic
109#88060—21no—
110#88060—21no—
111#88060D411yescharacteristic
112#88060D411yescharacteristic
113#88058C2×C411yescharacteristic
114#88056C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88055—21no—
117#88055—21no—
118#88055—21no—
119#88054—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054D411yescharacteristic
124#88054D411yescharacteristic
125C8×Dic13—21no—
126C8×Dic13—21no—
127C8×Dic13—21no—
128C8×Dic13—21no—
129C8×Dic13C2×C411yescharacteristic
130C8×Dic13C2×C411yescharacteristic
131#88050C2×C411yescharacteristic
132#88050C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18086—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147C2×C4×D13C22×C411yescharacteristic
148C2×C4×D13C2×D411yescharacteristic
149C2×C4×D13#4111yescharacteristic
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26C22×C411yescharacteristic
153C2×Dic26C22×C411yescharacteristic
154C13×Q16—41no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13C22×C411yescharacteristic
159C2×C8×C13C22×C411yescharacteristic
160C2×C8×C13C2×D411yescharacteristic
161C2×C8×C13C2×D411yescharacteristic
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4C22×C411yescharacteristic
165C13×C4⋊C4C22×C411yescharacteristic
166C42×C13—21no—
167C42×C13—21no—
168C42×C13C2411yescharacteristic
169#6107—22no—
170#6107—22no—
171#6103—21no—
172#6103—21no—
173#6103—21no—
174#6103—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13C22×C411yescharacteristic
178C4⋊Dic13C22×C411yescharacteristic
179#6101—21no—
180#6101—21no—
181#6101—21no—
182#6101—21no—
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13C22×C411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13#4111yescharacteristic
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055C22×C411yescharacteristic
198C2×#1055C22×C411yescharacteristic
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201Dic52—41no—
202#6094—24no—
203C8×D13—22no—
204C8×D13—41no—
205#3170—131no—
206#2986—131no—
207#2986—131no—
208#1591—131no—
209#1591—131no—
210#1587—131no—
211#1587—131no—
212#1587—131no—
213#1587D1311yescharacteristic, complemented
214C8×Q16—131no—
215C8×Q16—131no—
216#1564—131no—
217#1485—131no—
218#1485—131no—
219C8×M16—131no—
220C22×D13C4×D411yescharacteristic
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224Q8×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13C23×C411yescharacteristic
230C2×C4×C13C22×D411yescharacteristic
231C2×C4×C13C2×#4111yescharacteristic
232C2×Dic13—21no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13—21no—
236C2×Dic13C4×D411yescharacteristic
237C2×Dic13C4×D411yescharacteristic
238C2×Dic13C4×D411yescharacteristic
239C4×D13—21no—
240C4×D13—21no—
241C4×D13—21no—
242C4×D13—21no—
243C4×D13—22no—
244Dic26—21no—
245Dic26—21no—
246Dic26—21no—
247Dic26—21no—
248Dic26—42no—
249Dic26—42no—
250C8×C13—22no—
251C8×C13—21no—
252C8×C13—21no—
253C8×C13—21no—
254C8×C13—21no—
255C8×C13—41no—
256C8×C13—41no—
257#1055—22no—
258#1055—21no—
259#1055—21no—
260#1055—21no—
261#1055—41no—
262#1055—41no—
263#1055#13112yes—
264#533—131no—
265#533—131no—
266#500—131no—
267#494—131no—
268#487—131no—
269#487—131no—
270#467—131no—
271#467—131no—
272#467—131no—
273#467—131no—
274#446—131no—
275#446—131no—
276#446—131no—
277#446—261no—
278#446—261no—
279#446C2×D1311yescharacteristic
280C8×Q8—131no—
281C8×Q8—131no—
282C8×Q8—131no—
283C8×Q8—261no—
284C8×Q8—261no—
285C8×Q8C2×D1311yescharacteristic
286C4×Q16—131no—
287C4×Q16—131no—
288C4×Q16—131no—
289C4×Q16C2×D1311yescharacteristic
290#433—261no—
291#433—261no—
292#433—261no—
293#433—261no—
294#431—131no—
295#431—131no—
296#431—131no—
297C4×M16—131no—
298C2×C4×C8—131no—
299#335—131no—
300#335—131no—
301#334—131no—
302#334C2×D1311yescharacteristic
303Q8⋊C8—131no—
304Q8⋊C8—131no—
305Q8⋊C8—131no—
306Q8⋊C8—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8C2×D1311yescharacteristic
310Q8⋊C8C2×D1311yescharacteristic
311#322—131no—
312#322C2×D1311yescharacteristic
313C82—131no—
314C82—131no—
315C22×C13C2×C4×D411yescharacteristic
316C2×D13—21no—
317C2×D13—21no—
318C2×D13—21no—
319C4×C13—21no—
320C4×C13—41no—
321C4×C13—41no—
322C4×C13—41no—
323C4×C13—41no—
324C4×C13C2×#13111yescharacteristic
325C4×C13#56811yescharacteristic
326C4×C13#57811yescharacteristic
327C4×C13#57811yescharacteristic
328Dic13—21no—
329Dic13—21no—
330Dic13—41no—
331Dic13—41no—
332Dic13—41no—
333Dic13—41no—
334Dic13#44312yes—
335C2×Q16—131no—
336C2×Q16—131no—
337C2×Q16—131no—
338C2×Q16C4×D1311yescharacteristic
339C2×M16—261no—
340C22×C8—131no—
341C22×C8—131no—
342C4⋊Q8—131no—
343C4⋊Q8—131no—
344C4⋊Q8—131no—
345C4⋊Q8—131no—
346#125—261no—
347#125—261no—
348C22⋊Q8—131no—
349C22⋊Q8—131no—
350C22⋊Q8—131no—
351C22⋊Q8—131no—
352C22⋊Q8—261no—
353C22⋊Q8—261no—
354C4×Q8—131no—
355C4×Q8—131no—
356C4×Q8—261no—
357C4×Q8—261no—
358C4×Q8C22×D1311yescharacteristic
359C4×Q8C22×D1311yescharacteristic
360#117—261no—
361#117—261no—
362C2×C42—131no—
363#107—131no—
364#107—131no—
365#107—131no—
366#107C4×D1311yescharacteristic
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—131no—
370C4⋊C8—131no—
371C4⋊C8—131no—
372C4⋊C8—131no—
373C4⋊C8—261no—
374C4⋊C8—261no—
375C4⋊C8—261no—
376C4⋊C8—261no—
377C4⋊C8—261no—
378C4⋊C8—261no—
379C4⋊C8C22×D1311yescharacteristic
380C4⋊C8C22×D1311yescharacteristic
381#103—131no—
382#103—131no—
383#103—131no—
384#103—131no—
385#103—131no—
386#103—131no—
387#103C4×D1311yescharacteristic
388#103C4×D1311yescharacteristic
389C22⋊C8—131no—
390C22⋊C8—131no—
391C22⋊C8—261no—
392C22⋊C8—261no—
393#97—21no—
394#97—261no—
395#97—261no—
396#97—261no—
397#97—261no—
398C4×C8—21no—
399C4×C8—131no—
400C4×C8—131no—
401C4×C8—131no—
402C4×C8—131no—
403C4×C8—131no—
404C4×C8—261no—
405C4×C8—261no—
406C4×C8—261no—
407C4×C8—261no—
408C4×C8—261no—
409C4×C8C22×D1311yescharacteristic
410C4×C8C22×D1311yescharacteristic
411C4×C8C22×D1311yescharacteristic
412C2×C13#293511yescharacteristic
413C2×C13#295011yescharacteristic
414C2×C13C2×#44311yescharacteristic
415D13—41no—
416C2×Q8—131no—
417C2×Q8—131no—
418C2×Q8—261no—
419C2×Q8—261no—
420C2×Q8C2×C4×D1311yescharacteristic
421C2×Q8C2×C4×D1311yescharacteristic
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425Q16—41no—
426Q16—262no—
427Q16—262no—
428Q16—521no—
429M16—264no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—131no—
434C2×C8—131no—
435C2×C8—131no—
436C2×C8—131no—
437C2×C8—262no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—521no—
442C2×C8C2×C4×D1311yescharacteristic
443C2×C8C2×C4×D1311yescharacteristic
444C2×C8D4×D1311yescharacteristic
445C2×C8D4×D1311yescharacteristic
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—131no—
449C4⋊C4—131no—
450C4⋊C4—261no—
451C4⋊C4—261no—
452C4⋊C4—261no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4C2×C4×D1311yescharacteristic
463C4⋊C4C2×C4×D1311yescharacteristic
464C22⋊C4—261no—
465C22⋊C4—261no—
466C22⋊C4—261no—
467C22⋊C4—261no—
468C42—21no—
469C42—21no—
470C42—131no—
471C42—131no—
472C42—131no—
473C42—261no—
474C42—261no—
475C42C23×D1311yescharacteristic
476C13#1808611yescharacteristic, complemented, Sylow
477C23—131no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—261no—
483Q8—261no—
484Q8—261no—
485Q8—261no—
486Q8—522no—
487Q8—522no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—131no—
493C2×C4—131no—
494C2×C4—131no—
495C2×C4—262no—
496C2×C4—261no—
497C2×C4—261no—
498C2×C4—261no—
499C2×C4—261no—
500C2×C4—261no—
501C2×C4—261no—
502C2×C4—261no—
503C2×C4—261no—
504C2×C4C22×C4×D1311yescharacteristic
505C2×C4C2×D4×D1311yescharacteristic
506C2×C4#41×D1311yescharacteristic
507C8—22no—
508C8—21no—
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—132no—
515C8—262no—
516C8—261no—
517C8—261no—
518C8—261no—
519C8—521no—
520C8—521no—
521C22—261no—
522C22—261no—
523C22—261no—
524C22C4×D4×D1311yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—132no—
531C4—261no—
532C4—261no—
533C4—521no—
534C4—521no—
535C4—521no—
536C4—521no—
537C4#1171945011yescharacteristic
538C4D13×#13111yescharacteristic
539C4#1171948411yescharacteristic
540C4#1171948411yescharacteristic
541C2—521no—
542C2#1312357711yescharacteristic
543C2#1312370111yescharacteristic
544C2D13×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1587C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1587D13
hypocenterC13#18086
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #13113731C2semidirect
5. #13113730C2semidirect
6. #13113709C2semidirect
7. #13113708C2semidirect
8. #13113706C2semidirect
9. C8×#6107C2semidirect
10. #13113640C2semidirect
15. C13×#1587C2semidirect
213. #1587D13semidirect
476. C13#18086semidirect

Maximal subgroups

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

subgroupindex
#131254192
#131239362
#131239342
#131137312
#131137302
#131137092
#131137082
#131137062
C8×#61072
#131136402
#131135812
#131132552
#131131152
C13×#15872
#1808613