Finite Group Databasebeta

← #15834063

Subgroups — #15834063

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#13124905C211yesmaximal, characteristic
2#13123855C211yesmaximal, characteristic
3#13123784C211yesmaximal, characteristic, complemented
4#13113736C211yesmaximal, characteristic, complemented
5#13113725C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113683C211yesmaximal, characteristic, complemented
8#13113676C211yesmaximal, characteristic, complemented
9#13113653C211yesmaximal, characteristic, complemented
10Q16×#1055C211yesmaximal, characteristic, complemented
11#13113618C211yesmaximal, characteristic, complemented
12#13113307C211yesmaximal, characteristic, complemented
13#13113222C211yesmaximal, characteristic
14#13113132C211yesmaximal, characteristic, complemented
15C13×#1587C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×#6131C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718848C411yescharacteristic
22#11718843C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6106C2211yescharacteristic
25Q8×#1055C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718551C411yescharacteristic
28#11718549C411yescharacteristic
29#11718500—21no—
30#11718499—21no—
31#11718499C2211yescharacteristic
32#11718496—21no—
33#11718496C2211yescharacteristic
34D13×C4⋊C8C2211yescharacteristic
35#11718492—21no—
36#11718492C2211yescharacteristic
37#11718479C411yescharacteristic
38#11718476C411yescharacteristic
39#11718471C411yescharacteristic
40#11718452C411yescharacteristic
41#11718369—21no—
42#11718362—21no—
43C4×#6095C2211yescharacteristic
44#11718349—21no—
45#11718349C2211yescharacteristic
46C4×#6094—21no—
47C4×#6094C2211yescharacteristic
48#11718346C2211yescharacteristic
49#11718346C2211yescharacteristic
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#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6131C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71#88200C2×C411yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76C2×#6095C2×C411yescharacteristic
77C2×#6094—21no—
78C2×#6094—21no—
79C2×#6094D411yescharacteristic
80C2×#6094D411yescharacteristic
81C2×C8×D13—21no—
82#88151C2×C411yescharacteristic
83#88150—21no—
84#88147—21no—
85#88147C2×C411yescharacteristic
86#88146—21no—
87#88146C2×C411yescharacteristic
88#88143—21no—
89#88142C2×C411yescharacteristic
90C4×D52—21no—
91C4×D52C2311yescharacteristic
92#88126—21no—
93C42×D13—21no—
94C42×D13C2311yescharacteristic
95C4×Dic26—21no—
96C4×Dic26C2311yescharacteristic
97C13×#107C2×C411yescharacteristic
98C13×C4⋊C8—21no—
99C13×C4⋊C8—21no—
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#97—21no—
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109#88075C2×C411yescharacteristic
110#88075C2×C411yescharacteristic
111#88061C2×C411yescharacteristic
112#88060—21no—
113#88060—21no—
114#88060—21no—
115#88060—21no—
116#88060C2×C411yescharacteristic
117#88060C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88055—21no—
121#88055—21no—
122#88055D411yescharacteristic
123#88055D411yescharacteristic
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128#88054C2×C411yescharacteristic
129#88054C2×C411yescharacteristic
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
139C4×#1055—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18013—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147#6131—22no—
148#6131—41no—
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—41no—
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—41no—
204#6094—22no—
205#6094—41no—
206#6094—42no—
207#6094—42no—
208C8×D13—42no—
209#3107—131no—
210#2971—131no—
211#2962—131no—
212#1592—131no—
213#1590—131no—
214#1588—131no—
215#1587D1311yescharacteristic, complemented
216#1584—131no—
217#1583—131no—
218#1579—131no—
219C8×Q16—131no—
220#1573—131no—
221#1497—131no—
222#1477—131no—
223#1453—131no—
224C22×D13—21no—
225C22×D13C4×D411yescharacteristic
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13#13112yes—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13C23×C411yescharacteristic
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13C4×D411yescharacteristic
241C2×Dic13C4×D411yescharacteristic
242C2×Dic13C4×D411yescharacteristic
243D52—21no—
244D52—21no—
245D52—42no—
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—21no—
250C4×D13—41no—
251C4×D13—42no—
252C4×D13—41no—
253C4×D13—41no—
254C4×D13—81no—
255Dic26—21no—
256Dic26—21no—
257Dic26—81no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#1055#13712yes—
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—261no—
284#446—261no—
285#446C2×D1311yescharacteristic
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8C2×D1311yescharacteristic
290C4×Q16—131no—
291C4×Q16C2×D1311yescharacteristic
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#431—131no—
301#431—131no—
302#424—261no—
303C2×C4⋊C8—131no—
304#405—261no—
305C4×M16—131no—
306C4×M16—261no—
307#335—131no—
308#335—131no—
309#334—131no—
310#334C2×D1311yescharacteristic
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8C2×D1311yescharacteristic
316Q8⋊C8C2×D1311yescharacteristic
317D4⋊C8—131no—
318D4⋊C8—131no—
319#322—131no—
320#322—131no—
321#322C2×D1311yescharacteristic
322C82—131no—
323C22×C13C2×C4×D411yescharacteristic
324C2×D13—21no—
325C2×D13—21no—
326C2×D13—21no—
327C2×D13—41no—
328C2×D13—41no—
329C2×D13—41no—
330C4×C13—22no—
331C4×C13—21no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13C2×#13111yescharacteristic
336C4×C13#56811yescharacteristic
337C4×C13C2×#13711yescharacteristic
338C4×C13#57511yescharacteristic
339Dic13—21no—
340Dic13—21no—
341Dic13—21no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C2×#41—131no—
346C2×Q16—131no—
347C2×Q16C4×D1311yescharacteristic
348C2×SD16—131no—
349C2×SD16—131no—
350C2×M16—131no—
351C2×M16—131no—
352C2×M16—261no—
353C2×M16—261no—
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—261no—
364C4×Q8C22×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366C4×D4—131no—
367C4×D4—131no—
368C4×D4—261no—
369C4×D4—261no—
370#117—131no—
371#117—261no—
372#117—261no—
373C2×C42—131no—
374C2×C42—261no—
375#107—131no—
376#107C4×D1311yescharacteristic
377#106—131no—
378#106—131no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—131no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8C22×D1311yescharacteristic
392C4⋊C8C22×D1311yescharacteristic
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103C4×D1311yescharacteristic
398#103C4×D1311yescharacteristic
399#102—131no—
400#102—131no—
401C22⋊C8—131no—
402C22⋊C8—131no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—21no—
408#97—131no—
409#97—131no—
410#97—261no—
411#97—261no—
412C4×C8—21no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C2×C13#293311yescharacteristic
423C2×C13C4×#13711yescharacteristic
424C2×C13#295711yescharacteristic
425D13—41no—
426D13—81no—
427#41—262no—
428#41—521no—
429C2×Q8—131no—
430C2×Q8—261no—
431C2×Q8C2×C4×D1311yescharacteristic
432C2×Q8C2×C4×D1311yescharacteristic
433C2×D4—131no—
434C2×D4—261no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441Q16—22no—
442Q16—262no—
443SD16—521no—
444SD16—521no—
445M16—262no—
446M16—521no—
447M16—522no—
448M16—522no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—522no—
460C2×C8C2×C4×D1311yescharacteristic
461C2×C8C2×C4×D1311yescharacteristic
462C2×C8D4×D1311yescharacteristic
463C2×C8D4×D1311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
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⋊C4C2×C4×D1311yescharacteristic
476C4⋊C4C2×C4×D1311yescharacteristic
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C42—21no—
483C42—21no—
484C42—131no—
485C42—131no—
486C42—131no—
487C42—261no—
488C42—261no—
489C42—261no—
490C42C23×D1311yescharacteristic
491C13#1801311yescharacteristic, complemented, Sylow
492C23—131no—
493C23—261no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—261no—
498Q8—261no—
499Q8—1041no—
500Q8#8816112yes—
501D4—261no—
502D4—261no—
503D4—522no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—131no—
509C2×C4—131no—
510C2×C4—131no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—521no—
519C2×C4—522no—
520C2×C4—521no—
521C2×C4—521no—
522C2×C4—1041no—
523C2×C4C22×C4×D1311yescharacteristic
524C2×C4C2×D4×D1311yescharacteristic
525C2×C4#41×D1311yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—132no—
534C8—261no—
535C8—261no—
536C8—261no—
537C8—521no—
538C8—521no—
539C8—521no—
540C22—261no—
541C22—261no—
542C22—261no—
543C22—521no—
544C22—521no—
545C22—521no—
546C22C4×D4×D1311yescharacteristic
547C4—21no—
548C4—22no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—261no—
553C4—261no—
554C4—261no—
555C4—521no—
556C4—521no—
557C4—521no—
558C4C2×#8816111yescharacteristic
559C4#1171945511yescharacteristic
560C4D13×#13711yescharacteristic
561C4#1171948211yescharacteristic
562C2—521no—
563C2—1041no—
564C2#1312356211yescharacteristic
565C2#1312365211yescharacteristic
566C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1587C2
socleC22×C13C2×C4×D4
prime radicalC2×#6131C2×C4
cosocleC42×C13C24
hypercenter#1587D13
hypocenterC13#18013
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
3. #13123784C2semidirect
4. #13113736C2semidirect
5. #13113725C2semidirect
6. #13113716C2semidirect
7. #13113683C2semidirect
8. #13113676C2semidirect
9. #13113653C2semidirect
10. Q16×#1055C2semidirect
11. #13113618C2semidirect
12. #13113307C2semidirect
14. #13113132C2semidirect
15. C13×#1587C2semidirect
215. #1587D13semidirect
491. C13#18013semidirect

Maximal subgroups

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

subgroupindex
#131249052
#131238552
#131237842
#131137362
#131137252
#131137162
#131136832
#131136762
#131136532
Q16×#10552
#131136182
#131133072
#131132222
#131131322
C13×#15872
#1801313