Finite Group Databasebeta

← #15834064

Subgroups — #15834064

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124908C211yesmaximal, characteristic
2#13123854C211yesmaximal, characteristic
3#13123783C211yesmaximal, characteristic, complemented
4#13113740C211yesmaximal, characteristic, complemented
5#13113728C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113709C211yesmaximal, characteristic, complemented
8#13113688C211yesmaximal, characteristic, complemented
9#13113681C211yesmaximal, characteristic, complemented
10#13113656C211yesmaximal, characteristic, complemented
11C8×Dic52C211yesmaximal, characteristic, complemented
12#13113621C211yesmaximal, characteristic, complemented
13#13113310C211yesmaximal, characteristic, complemented
14#13113224C211yesmaximal, characteristic
15C13×#1453C211yesmaximal, characteristic, complemented
16C4×#6127C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21#11718789—21no—
22#11718789—21no—
23#11718783—21no—
24#11718780—21no—
25#11718587C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718512C411yescharacteristic
28#11718510C411yescharacteristic
29#11718507C411yescharacteristic
30#11718502C411yescharacteristic
31#11718394C411yescharacteristic
32#11718394C411yescharacteristic
33#11718384C411yescharacteristic
34#11718384C411yescharacteristic
35#11718368—21no—
36#11718366—21no—
37#11718362—21no—
38#11718362—21no—
39C4×Dic52C2211yescharacteristic
40C4×Dic52C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45#11718340C2211yescharacteristic
46#11718340C2211yescharacteristic
47C8×Dic26C2211yescharacteristic
48C8×Dic26C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C13×#322C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718050C2211yescharacteristic
58#11718050C2211yescharacteristic
59#11718049C2211yescharacteristic
60#11718049C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718048C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C2×#6127C2×C411yescharacteristic
68C2×C13×M16D411yescharacteristic
69C2×C13×M16D411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C4×C22⋊D13—21no—
72C4×C22⋊D13—21no—
73#88180—21no—
74#88180C2×C411yescharacteristic
75#88178—21no—
76#88178C2×C411yescharacteristic
77#88178C2×C411yescharacteristic
78C22×#1055—21no—
79C2×Dic52C2×C411yescharacteristic
80C2×Dic52C2×C411yescharacteristic
81C2×#6095C2×C411yescharacteristic
82C2×#6095C2×C411yescharacteristic
83C2×#6094—21no—
84C2×#6094—21no—
85C4×D52C2×C411yescharacteristic
86C4×D52C2311yescharacteristic
87#88126—21no—
88C42×D13—21no—
89#88124—21no—
90#88123C2×C411yescharacteristic
91#88123C2×C411yescharacteristic
92C4×Dic26—21no—
93C4×Dic26C2×C411yescharacteristic
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8C2×C411yescharacteristic
99C13×C4⋊C8C2×C411yescharacteristic
100C13×C22⋊C8—21no—
101C13×C22⋊C8C2×C411yescharacteristic
102C13×C22⋊C8C2×C411yescharacteristic
103C13×#97D411yescharacteristic
104C13×#97D411yescharacteristic
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C22⋊#1055—21no—
112#88061C2×C411yescharacteristic
113#88061C2×C411yescharacteristic
114#88060—21no—
115#88060—21no—
116#88058C2×C411yescharacteristic
117#88058C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88057C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88056C2×C411yescharacteristic
126#88055—21no—
127#88055—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134C8×Dic13—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C8×Dic13—21no—
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143#88043—21no—
144#18013—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149#6127—22no—
150#6127—41no—
151C2×D52C22×C411yescharacteristic
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13—21no—
155C2×Dic26—21no—
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C13×M16—22no—
160C13×M16—41no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C22×C411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C42×C13C22×C411yescharacteristic
172C42×C13C2×D411yescharacteristic
173C42×C13#4111yescharacteristic
174C42×C13C2411yescharacteristic
175C22⋊Dic13—21no—
176C22⋊Dic13—21no—
177C22⋊Dic13—21no—
178#6103—21no—
179#6103—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13C22×C411yescharacteristic
184C4⋊Dic13C22×C411yescharacteristic
185C4⋊Dic13C22×C411yescharacteristic
186C4⋊Dic13C22×C411yescharacteristic
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—42no—
203Dic52—22no—
204Dic52—22no—
205#6095—41no—
206#6095—41no—
207#6094—42no—
208#6094—42no—
209#3107—131no—
210#2971—131no—
211#2962—131no—
212#1592—131no—
213#1590—131no—
214#1588—131no—
215#1587—131no—
216#1584—131no—
217#1583—131no—
218#1579—131no—
219C8×Q16—131no—
220#1573—131no—
221#1497—131no—
222#1477—131no—
223#1453D1311yescharacteristic, complemented
224C23×C13C4×D411yescharacteristic
225C22×D13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—41no—
231C2×C4×C13C4×D411yescharacteristic
232C2×C4×C13C4×D411yescharacteristic
233C2×C4×C13C4×D411yescharacteristic
234C2×C4×C13C23×C411yescharacteristic
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C22⋊D13—42no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245D52—21no—
246D52—21no—
247C4×D13—42no—
248C4×D13—41no—
249C4×D13—41no—
250C4×D13—81no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—21no—
256Dic26—81no—
257Dic26#13112yes—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—21no—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13#13712yes—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#1055—41no—
272#533—131no—
273C4×#41—131no—
274#485—131no—
275#485—131no—
276#475—131no—
277#474—131no—
278#462—131no—
279#461—131no—
280#452—131no—
281#452—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8—131no—
290C4×Q16—131no—
291C4×Q16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294#436—131no—
295#436—131no—
296#436—261no—
297#436—261no—
298#432—131no—
299#432—261no—
300#431C2×D1311yescharacteristic
301#431C2×D1311yescharacteristic
302#424—261no—
303C2×C4⋊C8—131no—
304#405—261no—
305C4×M16—261no—
306C4×M16C2×D1311yescharacteristic
307#335—131no—
308#335—131no—
309#334—131no—
310#334—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317D4⋊C8—131no—
318D4⋊C8—131no—
319#322C2×D1311yescharacteristic
320#322C2×D1311yescharacteristic
321#322C2×D1311yescharacteristic
322C82C2×D1311yescharacteristic
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13C2×C4×D411yescharacteristic
327C2×D13—41no—
328C2×D13—41no—
329C2×D13—41no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13C2×#13111yescharacteristic
335C4×C13#56811yescharacteristic
336C4×C13C2×#13711yescharacteristic
337C4×C13#57511yescharacteristic
338Dic13—22no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C2×#41—131no—
346C2×Q16—131no—
347C2×Q16—131no—
348C2×SD16—131no—
349C2×SD16—131no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16D5211yescharacteristic
353C2×M16D5211yescharacteristic
354C22×C8—261no—
355C4⋊Q8—131no—
356C4⋊Q8—131no—
357#125—261no—
358C22⋊Q8—131no—
359C22⋊Q8—131no—
360C22⋊Q8—261no—
361C4×Q8—131no—
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8—131no—
365C4×Q8—261no—
366C4×D4—131no—
367C4×D4—131no—
368C4×D4—261no—
369C4×D4—261no—
370#117—131no—
371#117—261no—
372#117—261no—
373C2×C42—261no—
374C2×C42C22×D1311yescharacteristic
375#107—131no—
376#107—131no—
377#106—131no—
378#106—131no—
379C4⋊C8—21no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8C4×D1311yescharacteristic
392C4⋊C8C4×D1311yescharacteristic
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#103—131no—
399#102—131no—
400#102—131no—
401C22⋊C8—21no—
402C22⋊C8—261no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8C4×D1311yescharacteristic
406C22⋊C8C4×D1311yescharacteristic
407#97—261no—
408#97—261no—
409#97—261no—
410#97D5211yescharacteristic
411#97D5211yescharacteristic
412C4×C8—261no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C2×C13—41no—
423C2×C13#293311yescharacteristic
424C2×C13C4×#13711yescharacteristic
425C2×C13#295711yescharacteristic
426D13—81no—
427#41—262no—
428#41—521no—
429C2×Q8—131no—
430C2×Q8—131no—
431C2×Q8—131no—
432C2×Q8—261no—
433C2×D4—131no—
434C2×D4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4C2×D5211yescharacteristic
440C22×C4#612711yescharacteristic
441Q16—262no—
442Q16—262no—
443SD16—521no—
444SD16—521no—
445M16—22no—
446M16—41no—
447M16—522no—
448M16—522no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—522no—
456C2×C8C2×C4×D1311yescharacteristic
457C2×C8C2×C4×D1311yescharacteristic
458C2×C8C2×C4×D1311yescharacteristic
459C2×C8C2×C4×D1311yescharacteristic
460C2×C8C2×D5211yescharacteristic
461C2×C8C2×D5211yescharacteristic
462C2×C8C2×D5211yescharacteristic
463C2×C8C2×D5211yescharacteristic
464C4⋊C4—131no—
465C4⋊C4—131no—
466C4⋊C4—131no—
467C4⋊C4—131no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42C2×D5211yescharacteristic
489C42#612711yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1801311yescharacteristic, complemented, Sylow
492C23—261no—
493C23C4×D5211yescharacteristic
494Q8—132no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—261no—
499Q8—261no—
500Q8—1041no—
501D4—261no—
502D4—261no—
503D4—522no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—522no—
517C2×C4—521no—
518C2×C4—521no—
519C2×C4—1041no—
520C2×C4C4×D5211yescharacteristic
521C2×C4C4×D5211yescharacteristic
522C2×C4C4×D5211yescharacteristic
523C2×C4C22×C4×D1311yescharacteristic
524C2×C4C22×D5211yescharacteristic
525C2×C4C2×#612711yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—521no—
536C8—521no—
537C8—521no—
538C8—521no—
539C8#8816312yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—521no—
544C22—521no—
545C22—521no—
546C22C2×C4×D5211yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—262no—
552C4—521no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4—521no—
557C4—521no—
558C4C2×#8816311yescharacteristic
559C4#1171945311yescharacteristic
560C4D13×#13111yescharacteristic
561C4#1171945511yescharacteristic
562C2—41no—
563C2—1041no—
564C2#1312356411yescharacteristic
565C2C4×#8816311yescharacteristic
566C2#1312375411yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1453C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C2×C4
cosocleC42×C13C24
hypercenter#1453D13
hypocenterC13#18013
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. #13123783C2semidirect
4. #13113740C2semidirect
5. #13113728C2semidirect
6. #13113716C2semidirect
7. #13113709C2semidirect
8. #13113688C2semidirect
9. #13113681C2semidirect
10. #13113656C2semidirect
11. C8×Dic52C2semidirect
12. #13113621C2semidirect
13. #13113310C2semidirect
15. C13×#1453C2semidirect
223. #1453D13semidirect
491. C13#18013semidirect

Maximal subgroups

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

subgroupindex
#131249082
#131238542
#131237832
#131137402
#131137282
#131137162
#131137092
#131136882
#131136812
#131136562
C8×Dic522
#131136212
#131133102
#131132242
C13×#14532
#1801313