Finite Group Databasebeta

← #15833777

Subgroups — #15833777

Order 3328.

544 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125419C211yesmaximal, characteristic
2#13123932C211yesmaximal, characteristic
3#13123927C211yesmaximal, characteristic
4#13113709C211yesmaximal, characteristic, complemented
5#13113708C211yesmaximal, characteristic, complemented
6#13113706C211yesmaximal, characteristic, complemented
7#13113689C211yesmaximal, characteristic, complemented
8#13113686C211yesmaximal, characteristic, complemented
9#13113684C211yesmaximal, characteristic, complemented
10#13113683C211yesmaximal, characteristic, complemented
11#13113596C211yesmaximal, characteristic
12#13113307C211yesmaximal, characteristic
13#13113307C211yesmaximal, characteristic
14#13113127C211yesmaximal, 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#11718496C2211yescharacteristic
32#11718496C2211yescharacteristic
33#11718492—21no—
34#11718492C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718474C411yescharacteristic
38#11718474C411yescharacteristic
39#11718453C411yescharacteristic
40#11718453C411yescharacteristic
41#11718370—21no—
42#11718362—21no—
43C4×Dic52C2211yescharacteristic
44#11718351—21no—
45#11718346C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48#11718340—21no—
49#11718340C2211yescharacteristic
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#11718047C2211yescharacteristic
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
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×C8×D13C2×C411yescharacteristic
78C2×C8×D13C2×C411yescharacteristic
79#88151C2×C411yescharacteristic
80#88151C2×C411yescharacteristic
81#88150—21no—
82#88150—21no—
83#88143—21no—
84#88143—21no—
85#88142C2×C411yescharacteristic
86#88142C2×C411yescharacteristic
87#88126—21no—
88#88126—21no—
89C42×D13C2311yescharacteristic
90C4×Dic26—21no—
91C4×Dic26—21no—
92C4×Dic26C2311yescharacteristic
93C4×Dic26C2311yescharacteristic
94C13×#107C2×C411yescharacteristic
95C13×C4⋊C8—21no—
96C13×C4⋊C8—21no—
97C13×C4⋊C8C2311yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×#103C2×C411yescharacteristic
100C13×#103C2×C411yescharacteristic
101C13×#97—21no—
102C4×C8×C13—21no—
103C4×C8×C13C2311yescharacteristic
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106#88075C2×C411yescharacteristic
107#88075C2×C411yescharacteristic
108#88060—21no—
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#88055—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124#88054—21no—
125#88054D411yescharacteristic
126#88054D411yescharacteristic
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#17991—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—41no—
170#6107—41no—
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—
202C8×D13—41no—
203C8×D13—41no—
204#3170—131no—
205#2985—131no—
206#2985—131no—
207#1587—131no—
208#1587—131no—
209#1587—131no—
210#1587D1311yescharacteristic, complemented
211#1584—131no—
212#1584—131no—
213#1584—131no—
214#1584—131no—
215#1568—131no—
216#1497—131no—
217#1497—131no—
218#1452—131no—
219C22×D13C4×D411yescharacteristic
220Q8×C13—21no—
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13C23×C411yescharacteristic
229C2×C4×C13C22×D411yescharacteristic
230C2×C4×C13C2×#4111yescharacteristic
231C2×Dic13—21no—
232C2×Dic13—21no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13C4×D411yescharacteristic
236C2×Dic13C4×D411yescharacteristic
237C2×Dic13C4×D411yescharacteristic
238C4×D13—21no—
239C4×D13—21no—
240C4×D13—21no—
241C4×D13—21no—
242C4×D13—41no—
243Dic26—21no—
244Dic26—21no—
245Dic26—21no—
246Dic26—21no—
247Dic26—81no—
248Dic26—81no—
249C8×C13—21no—
250C8×C13—21no—
251C8×C13—21no—
252C8×C13—21no—
253C8×C13—41no—
254C8×C13—41no—
255C8×C13—41no—
256#1055—21no—
257#1055—21no—
258#1055—21no—
259#1055—21no—
260#1055—41no—
261#1055—41no—
262#1055—41no—
263#533—131no—
264#533—131no—
265#500—131no—
266#494—131no—
267#487—131no—
268#487—131no—
269#467—131no—
270#467—131no—
271#467—131no—
272#467—131no—
273#446—131no—
274#446—131no—
275#446—131no—
276#446—261no—
277#446—261no—
278#446—261no—
279#446—261no—
280#446C2×D1311yescharacteristic
281C8×Q8—131no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8C2×D1311yescharacteristic
285C4×Q16—131no—
286C4×Q16—131no—
287C4×Q16—131no—
288C4×Q16C2×D1311yescharacteristic
289#433—261no—
290#433—261no—
291#433—261no—
292#433—261no—
293#432—131no—
294#432—131no—
295#431—131no—
296#431—131no—
297C2×C4×C8—131no—
298#335—131no—
299#335—131no—
300#334—131no—
301#334C2×D1311yescharacteristic
302Q8⋊C8—131no—
303Q8⋊C8—131no—
304Q8⋊C8—131no—
305Q8⋊C8—131no—
306Q8⋊C8—131no—
307Q8⋊C8—131no—
308Q8⋊C8C2×D1311yescharacteristic
309Q8⋊C8C2×D1311yescharacteristic
310#322—131no—
311#322—131no—
312#322—131no—
313#322C2×D1311yescharacteristic
314C22×C13C2×C4×D411yescharacteristic
315C2×D13—21no—
316C2×D13—21no—
317C2×D13—21no—
318C4×C13—21no—
319C4×C13—41no—
320C4×C13—41no—
321C4×C13—41no—
322C4×C13—41no—
323C4×C13#56811yescharacteristic
324C4×C13#56811yescharacteristic
325C4×C13#57811yescharacteristic
326C4×C13#57811yescharacteristic
327Dic13—21no—
328Dic13—21no—
329Dic13—21no—
330Dic13—41no—
331Dic13—41no—
332Dic13—41no—
333Dic13—41no—
334C2×Q16—131no—
335C2×Q16—131no—
336C2×Q16—131no—
337C2×Q16C4×D1311yescharacteristic
338C22×C8—131no—
339C22×C8—131no—
340C4⋊Q8—131no—
341C4⋊Q8—131no—
342C4⋊Q8—131no—
343C4⋊Q8—131no—
344#125—261no—
345#125—261no—
346C22⋊Q8—131no—
347C22⋊Q8—131no—
348C22⋊Q8—131no—
349C22⋊Q8—131no—
350C22⋊Q8—261no—
351C22⋊Q8—261no—
352C4×Q8—131no—
353C4×Q8—131no—
354C4×Q8—261no—
355C4×Q8—261no—
356C4×Q8C22×D1311yescharacteristic
357C4×Q8C22×D1311yescharacteristic
358#117—261no—
359#117—261no—
360C2×C42—131no—
361#107—131no—
362#107—131no—
363#107—131no—
364#107C4×D1311yescharacteristic
365C4⋊C8—21no—
366C4⋊C8—21no—
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⋊C8C22×D1311yescharacteristic
379C4⋊C8C22×D1311yescharacteristic
380#103—131no—
381#103—131no—
382#103—131no—
383#103—131no—
384#103—131no—
385#103—131no—
386#103C4×D1311yescharacteristic
387#103C4×D1311yescharacteristic
388C22⋊C8—131no—
389C22⋊C8—131no—
390C22⋊C8—261no—
391C22⋊C8—261no—
392C22⋊C8—261no—
393#97—21no—
394#97—261no—
395#97—261no—
396#97—261no—
397#97—261no—
398#97—261no—
399C4×C8—21no—
400C4×C8—131no—
401C4×C8—131no—
402C4×C8—131no—
403C4×C8—131no—
404C4×C8—131no—
405C4×C8—261no—
406C4×C8—261no—
407C4×C8—261no—
408C4×C8C22×D1311yescharacteristic
409C4×C8C22×D1311yescharacteristic
410C4×C8C22×D1311yescharacteristic
411C2×C13#293211yescharacteristic
412C2×C13#295011yescharacteristic
413C2×C13#295711yescharacteristic
414D13—41no—
415C2×Q8—131no—
416C2×Q8—131no—
417C2×Q8—261no—
418C2×Q8—261no—
419C2×Q8C2×C4×D1311yescharacteristic
420C2×Q8C2×C4×D1311yescharacteristic
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424Q16—41no—
425Q16—521no—
426Q16—521no—
427Q16—521no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—131no—
432C2×C8—131no—
433C2×C8—131no—
434C2×C8—131no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—521no—
439C2×C8—521no—
440C2×C8C2×C4×D1311yescharacteristic
441C2×C8C2×C4×D1311yescharacteristic
442C2×C8D4×D1311yescharacteristic
443C2×C8D4×D1311yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—131no—
447C4⋊C4—131no—
448C4⋊C4—261no—
449C4⋊C4—261no—
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⋊C4C2×C4×D1311yescharacteristic
461C4⋊C4C2×C4×D1311yescharacteristic
462C22⋊C4—261no—
463C22⋊C4—261no—
464C22⋊C4—261no—
465C22⋊C4—261no—
466C42—21no—
467C42—21no—
468C42—131no—
469C42—131no—
470C42—131no—
471C42—261no—
472C42—261no—
473C42C23×D1311yescharacteristic
474C13#1799111yescharacteristic, complemented, Sylow
475C23—131no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—261no—
481Q8—261no—
482Q8—261no—
483Q8—261no—
484Q8—1041no—
485Q8—1041no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—131no—
491C2×C4—131no—
492C2×C4—131no—
493C2×C4—261no—
494C2×C4—261no—
495C2×C4—261no—
496C2×C4—261no—
497C2×C4—261no—
498C2×C4—261no—
499C2×C4—261no—
500C2×C4—261no—
501C2×C4—521no—
502C2×C4C22×C4×D1311yescharacteristic
503C2×C4C2×D4×D1311yescharacteristic
504C2×C4#41×D1311yescharacteristic
505C8—21no—
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—261no—
513C8—261no—
514C8—261no—
515C8—261no—
516C8—521no—
517C8—521no—
518C8—521no—
519C22—261no—
520C22—261no—
521C22—261no—
522C22C4×D4×D1311yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—261no—
529C4—261no—
530C4—261no—
531C4—521no—
532C4—521no—
533C4—521no—
534C4—521no—
535C4#1171945011yescharacteristic
536C4#1171945511yescharacteristic
537C4#1171948411yescharacteristic
538C4#1171948411yescharacteristic
539C2—521no—
540C2#1312355011yescharacteristic
541C2#1312370111yescharacteristic
542C2#1312374811yescharacteristic
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#17991
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. #13113709C2semidirect
5. #13113708C2semidirect
6. #13113706C2semidirect
7. #13113689C2semidirect
8. #13113686C2semidirect
9. #13113684C2semidirect
10. #13113683C2semidirect
15. C13×#1587C2semidirect
210. #1587D13semidirect
474. C13#17991semidirect

Maximal subgroups

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

subgroupindex
#131254192
#131239322
#131239272
#131137092
#131137082
#131137062
#131136892
#131136862
#131136842
#131136832
#131135962
#131133072
#131131272
C13×#15872
#1799113