Finite Group Databasebeta

← #15832995

Subgroups — #15832995

Order 3328.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124920C211yesmaximal, characteristic
2#13123984C211yesmaximal, characteristic
3#13123915C211yesmaximal, characteristic, complemented
4#13113711C211yesmaximal, characteristic, complemented
5#13113710C211yesmaximal, characteristic, complemented
6#13113687C211yesmaximal, characteristic, complemented
7#13113678C211yesmaximal, characteristic, complemented
8#13113650C211yesmaximal, characteristic, complemented
9C8×#6107C211yesmaximal, characteristic, complemented
10C8×#6106C211yesmaximal, characteristic, complemented
11#13113623C211yesmaximal, characteristic, complemented
12#13113263C211yesmaximal, characteristic, complemented
13#13113243C211yesmaximal, characteristic
14#13113137C211yesmaximal, characteristic, complemented
15C13×#1579C211yesmaximal, characteristic, complemented
16#11719285C2211yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718847C411yescharacteristic
22#11718846C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6106C2211yescharacteristic
25#11718685C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718543C411yescharacteristic
28#11718538C411yescharacteristic
29#11718500—21no—
30#11718499C2211yescharacteristic
31#11718498C2211yescharacteristic
32#11718497—21no—
33#11718494—21no—
34#11718494C2211yescharacteristic
35#11718491—21no—
36#11718491C2211yescharacteristic
37#11718467C411yescharacteristic
38#11718466C411yescharacteristic
39#11718460C411yescharacteristic
40#11718459C411yescharacteristic
41C4×#6095C2211yescharacteristic
42#11718351—21no—
43#11718349—21no—
44C8×D52C2211yescharacteristic
45#11718346—21no—
46#11718346C2211yescharacteristic
47#11718346C2211yescharacteristic
48#11718346C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718050C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71#88201C2×C411yescharacteristic
72#88200C2×C411yescharacteristic
73Q8×Dic13C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76C2×#6095C2×C411yescharacteristic
77C2×#6094—21no—
78C2×#6094—21no—
79C2×C8×D13—21no—
80#88152—21no—
81#88149C2×C411yescharacteristic
82#88148—21no—
83C4⋊C4×D13—21no—
84C4⋊C4×D13C2×C411yescharacteristic
85#88144C2×C411yescharacteristic
86#88141—21no—
87#88141C2×C411yescharacteristic
88C4×D52—21no—
89C4×D52C2311yescharacteristic
90#88126—21no—
91C42×D13—21no—
92C42×D13C2311yescharacteristic
93C4×Dic26—21no—
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
102C4×C8×C13—21no—
103C4×C8×C13—21no—
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107#88075C2×C411yescharacteristic
108#88075C2×C411yescharacteristic
109#88061C2×C411yescharacteristic
110#88060—21no—
111#88060—21no—
112#88060—21no—
113#88060—21no—
114#88060C2×C411yescharacteristic
115#88060C2×C411yescharacteristic
116#88060D411yescharacteristic
117#88060D411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124#88054C2×C411yescharacteristic
125#88054C2×C411yescharacteristic
126#88054D411yescharacteristic
127#88054D411yescharacteristic
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13—21no—
131#88050C2×C411yescharacteristic
132#88049C2×C411yescharacteristic
133#88048C2×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#17919—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147Q8×D13—22no—
148Q8×D13—22no—
149C2×D52—21no—
150C2×D52C22×C411yescharacteristic
151C2×C4×D13—21no—
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13C22×C411yescharacteristic
155C2×C4×D13C2×D411yescharacteristic
156C2×C4×D13#4111yescharacteristic
157C2×Dic26—21no—
158C2×Dic26C22×C411yescharacteristic
159C13×Q16—22no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C42×C13—21no—
172C42×C13—21no—
173C42×C13C2411yescharacteristic
174#6107—22no—
175#6106—22no—
176#6103—21no—
177#6103—21no—
178#6103—21no—
179#6103—21no—
180#6103—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13C22×C411yescharacteristic
184C4⋊Dic13C22×C411yescharacteristic
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13C22×C411yescharacteristic
194C4×Dic13C2×D411yescharacteristic
195C4×Dic13#4111yescharacteristic
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203#6095—22no—
204#6094—81no—
205#6094—81no—
206C8×D13—81no—
207#3108—131no—
208#2993—131no—
209#2982—131no—
210#1588—131no—
211#1587—131no—
212#1584—131no—
213#1583—131no—
214#1579D1311yescharacteristic, complemented
215SD16⋊C8—131no—
216C8×Q16—131no—
217C8×SD16—131no—
218#1574—131no—
219#1487—131no—
220#1482—131no—
221#1454—131no—
222C22×D13—21no—
223C22×D13C4×D411yescharacteristic
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13#13112yes—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13C23×C411yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13C4×D411yescharacteristic
239C2×Dic13C4×D411yescharacteristic
240C2×Dic13C4×D411yescharacteristic
241D52—21no—
242D52—21no—
243D52—81no—
244C4×D13—24no—
245C4×D13—21no—
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—41no—
250C4×D13—41no—
251C4×D13—41no—
252C4×D13—81no—
253Dic26—24no—
254Dic26—21no—
255Dic26#13112yes—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13—41no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#529—131no—
271C2×C4×Q8—131no—
272#483—131no—
273#480—131no—
274#479—131no—
275#479—131no—
276#464—131no—
277#464—131no—
278#451—131no—
279#448—131no—
280#446—131no—
281C8×Q8—131no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—261no—
285C8×Q8—261no—
286C8×Q8C2×D1311yescharacteristic
287C8×Q8C2×D1311yescharacteristic
288C4×Q16—131no—
289C4×Q16C2×D1311yescharacteristic
290C4×SD16—131no—
291C4×SD16—131no—
292#436—131no—
293#436—261no—
294#435—261no—
295C8×D4—131no—
296#433—261no—
297#431—131no—
298#431—131no—
299#431—131no—
300#431—131no—
301#431—261no—
302#431—261no—
303#424—261no—
304#423—131no—
305#335—131no—
306#335—131no—
307#334—131no—
308#334C2×D1311yescharacteristic
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8C2×D1311yescharacteristic
314Q8⋊C8C2×D1311yescharacteristic
315D4⋊C8—131no—
316D4⋊C8—131no—
317#322—131no—
318#322—131no—
319#322C2×D1311yescharacteristic
320C82—131no—
321C22×C13C2×C4×D411yescharacteristic
322C2×D13—21no—
323C2×D13—21no—
324C2×D13—21no—
325C2×D13—41no—
326C2×D13—41no—
327C2×D13—41no—
328C4×C13—22no—
329C4×C13—21no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13C2×#13111yescharacteristic
334C4×C13C2×#13111yescharacteristic
335C4×C13#57711yescharacteristic
336C4×C13#57811yescharacteristic
337Dic13—21no—
338Dic13—22no—
339Dic13—21no—
340Dic13—21no—
341Dic13—41no—
342Dic13—41no—
343C22×Q8—131no—
344C2×Q16—131no—
345C2×Q16C4×D1311yescharacteristic
346C2×SD16—131no—
347C2×SD16—131no—
348C2×M16—261no—
349C2×M16—261no—
350C22×C8—261no—
351#126—261no—
352#125—131no—
353#124—131no—
354#123—261no—
355C22⋊Q8—131no—
356#121—131no—
357C4×Q8—131no—
358C4×Q8—131no—
359C4×Q8—131no—
360C4×Q8—261no—
361C4×Q8—261no—
362C4×Q8C22×D1311yescharacteristic
363C4×Q8C22×D1311yescharacteristic
364C4×D4—131no—
365C4×D4—261no—
366#117—261no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—261no—
369C2×C42—131no—
370C2×C42—261no—
371#107—131no—
372#107C4×D1311yescharacteristic
373#106—131no—
374#106—131no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8C22×D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103C4×D1311yescharacteristic
396#103C4×D1311yescharacteristic
397#102—131no—
398#102—131no—
399C22⋊C8—131no—
400C22⋊C8—131no—
401C22⋊C8—131no—
402C22⋊C8—131no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—261no—
408C4×C8—21no—
409C4×C8—21no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C2×C13#292911yescharacteristic
421C2×C13#294711yescharacteristic
422C2×C13#295711yescharacteristic
423D13—41no—
424D13—81no—
425C2×Q8—131no—
426C2×Q8—261no—
427C2×Q8—262no—
428C2×Q8—262no—
429C2×Q8C2×C4×D1311yescharacteristic
430C2×Q8C2×C4×D1311yescharacteristic
431C2×D4—131no—
432C2×D4—261no—
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—261no—
439Q16—22no—
440Q16—262no—
441SD16—262no—
442SD16—262no—
443M16—1041no—
444M16—1041no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—1041no—
456C2×C8C2×C4×D1311yescharacteristic
457C2×C8C2×C4×D1311yescharacteristic
458C2×C8D4×D1311yescharacteristic
459C2×C8D4×D1311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—131no—
463C4⋊C4—131no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4C2×C4×D1311yescharacteristic
472C4⋊C4C2×C4×D1311yescharacteristic
473C22⋊C4—261no—
474C22⋊C4—261no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C42—21no—
479C42—21no—
480C42—131no—
481C42—131no—
482C42—131no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42C23×D1311yescharacteristic
487C13#1791911yescharacteristic, complemented, Sylow
488C23—131no—
489C23—261no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—132no—
494Q8—264no—
495Q8—261no—
496Q8#8815512yes—
497D4—261no—
498D4—261no—
499D4—1041no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—131no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—264no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—521no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4—1041no—
519C2×C4C22×C4×D1311yescharacteristic
520C2×C4C2×D4×D1311yescharacteristic
521C2×C4#41×D1311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—261no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—521no—
534C8—521no—
535C8—521no—
536C22—261no—
537C22—261no—
538C22—261no—
539C22—521no—
540C22—521no—
541C22—521no—
542C22C4×D4×D1311yescharacteristic
543C4—21no—
544C4—22no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—261no—
549C4—261no—
550C4—261no—
551C4—262no—
552C4—521no—
553C4—521no—
554C4C2×#8815511yescharacteristic
555C4D13×#13111yescharacteristic
556C4#1171948311yescharacteristic
557C4#1171948411yescharacteristic
558C2—521no—
559C2—1041no—
560C2#1312352511yescharacteristic
561C2#1312367811yescharacteristic
562C2#1312375011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1579C2
socleC22×C13C2×C4×D4
prime radical#88149C2×C4
cosocleC42×C13C24
hypercenter#1579D13
hypocenterC13#17919
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
3. #13123915C2semidirect
4. #13113711C2semidirect
5. #13113710C2semidirect
6. #13113687C2semidirect
7. #13113678C2semidirect
8. #13113650C2semidirect
9. C8×#6107C2semidirect
10. C8×#6106C2semidirect
11. #13113623C2semidirect
12. #13113263C2semidirect
14. #13113137C2semidirect
15. C13×#1579C2semidirect
214. #1579D13semidirect
487. C13#17919semidirect

Maximal subgroups

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

subgroupindex
#131249202
#131239842
#131239152
#131137112
#131137102
#131136872
#131136782
#131136502
C8×#61072
C8×#61062
#131136232
#131132632
#131132432
#131131372
C13×#15792
#1791913