Finite Group Databasebeta

← #15833996

Subgroups — #15833996

Order 3328.

594 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#13124901C211yesmaximal, characteristic
2#13123851C211yesmaximal, characteristic
3#13113743C211yesmaximal, characteristic, complemented
4#13113731C211yesmaximal, characteristic, complemented
5#13113707C211yesmaximal, characteristic, complemented
6#13113691C211yesmaximal, characteristic, complemented
7#13113686C211yesmaximal, characteristic, complemented
8#13113670C211yesmaximal, characteristic, complemented
9#13113646C211yesmaximal, characteristic, complemented
10C8×#6106C211yesmaximal, characteristic, complemented
11#13113619C211yesmaximal, characteristic, complemented
12#13113309C211yesmaximal, characteristic, complemented
13#13113221C211yesmaximal, characteristic
14#13113133C211yesmaximal, characteristic, complemented
15C13×#2962C211yesmaximal, characteristic, complemented
16C13×#533C2211yescharacteristic
17C4×#6127C2211yescharacteristic
18C13×#446—21no—
19C13×#446—21no—
20C13×#446C2211yescharacteristic
21C13×#446C2211yescharacteristic
22C8×Q8×C13C2211yescharacteristic
23C8×Q8×C13C2211yescharacteristic
24C13×#424—21no—
25C2×C13×C4⋊C8C2211yescharacteristic
26C13×#405—21no—
27C4×C13×M16C2211yescharacteristic
28#11718788—21no—
29#11718788—21no—
30#11718755C411yescharacteristic
31#11718751C411yescharacteristic
32#11718748C411yescharacteristic
33#11718744C411yescharacteristic
34#11718708C411yescharacteristic
35#11718708C411yescharacteristic
36#11718706C411yescharacteristic
37#11718706C411yescharacteristic
38C4×#6107C2211yescharacteristic
39C4×#6107C2211yescharacteristic
40C4×#6106C2211yescharacteristic
41C4×#6106C2211yescharacteristic
42#11718587C2211yescharacteristic
43#11718586C2211yescharacteristic
44#11718586C2211yescharacteristic
45#11718366—21no—
46D13×#97—21no—
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718340C2211yescharacteristic
50#11718340C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53Q8⋊#1055C2211yescharacteristic
54Q8⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6127C2×C411yescharacteristic
68C2×C13×M16D411yescharacteristic
69C2×C13×M16D411yescharacteristic
70C22×C8×C13—21no—
71C13×C4⋊Q8C2×C411yescharacteristic
72C13×C4⋊Q8C2×C411yescharacteristic
73C13×#125—21no—
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8C2×C411yescharacteristic
76C13×C22⋊Q8C2×C411yescharacteristic
77C4×Q8×C13—21no—
78C4×Q8×C13C2311yescharacteristic
79C4×Q8×C13C2311yescharacteristic
80C13×#117—21no—
81C2×C42×C13C2311yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×#6107C2×C411yescharacteristic
84C2×#6106C2×C411yescharacteristic
85C2×#6106C2×C411yescharacteristic
86C4×C22⋊D13—21no—
87C4×C22⋊D13—21no—
88#88180C2×C411yescharacteristic
89C2×C8×D13—21no—
90C2×C8×D13—21no—
91C4×D52C2×C411yescharacteristic
92C4×D52C2311yescharacteristic
93#88126—21no—
94C42×D13—21no—
95C4×Dic26C2×C411yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8—21no—
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×#97—21no—
105C13×#97—21no—
106C13×#97D411yescharacteristic
107C13×#97D411yescharacteristic
108C4×C8×C13—21no—
109C4×C8×C13—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112#88075C2×C411yescharacteristic
113#88075C2×C411yescharacteristic
114#88075C2×C411yescharacteristic
115#88075C2×C411yescharacteristic
116C22⋊#1055—21no—
117C22⋊#1055—21no—
118C22⋊#1055C2×C411yescharacteristic
119C22⋊#1055C2×C411yescharacteristic
120#88060—21no—
121#88060—21no—
122#88055—21no—
123#88055—21no—
124#88054—21no—
125#88054—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18009—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13#4111yescharacteristic
151C2×C22⋊D13—21no—
152#6127—22no—
153#6127—41no—
154C2×D52C22×C411yescharacteristic
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×Dic26C22×C411yescharacteristic
159C13×M16—22no—
160C13×M16—41no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—42no—
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13C22×C411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13#4111yescharacteristic
184C42×C13C2411yescharacteristic
185C22⋊Dic13—21no—
186#6107—41no—
187#6107—41no—
188#6106—22no—
189#6106—22no—
190#6103—21no—
191#6103—21no—
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C8×D13—42no—
208C8×D13—42no—
209#3107—131no—
210#2970—131no—
211#2962D1311yescharacteristic, complemented
212#1593—131no—
213#1591—131no—
214#1587—131no—
215#1585—131no—
216#1584—131no—
217#1582—131no—
218SD16⋊C8—131no—
219C8×SD16—131no—
220#1573—131no—
221#1497—131no—
222#1477—131no—
223#1453—131no—
224C23×C13C4×D411yescharacteristic
225C22×D13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13—81no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C22⋊D13—42no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250D52—21no—
251D52#13112yes—
252C4×D13—42no—
253C4×D13—41no—
254C4×D13—41no—
255C4×D13—81no—
256Dic26—21no—
257Dic26—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13#13712yes—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#1055—41no—
272#533C2×D1311yescharacteristic
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—21no—
283#446—21no—
284#446—131no—
285#446—131no—
286#446C2×D1311yescharacteristic
287#446C2×D1311yescharacteristic
288C8×Q8C2×D1311yescharacteristic
289C8×Q8C2×D1311yescharacteristic
290C4×Q16—131no—
291C4×Q16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294#435—261no—
295#435—261no—
296C8×D4—131no—
297C8×D4—131no—
298#432—131no—
299#432—261no—
300#431—131no—
301#431—131no—
302#424—21no—
303C2×C4⋊C8C2×D1311yescharacteristic
304#405—21no—
305C4×M16C2×D1311yescharacteristic
306C2×#97—261no—
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#322—131no—
320#322—131no—
321#322—131no—
322C82—131no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13C2×C4×D411yescharacteristic
327C2×D13—22no—
328C2×D13—41no—
329C2×D13—41no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13C2×#13111yescharacteristic
339C4×C13#56811yescharacteristic
340C4×C13C2×#13711yescharacteristic
341C4×C13#57511yescharacteristic
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C2×#41—131no—
346C2×Q16—131no—
347C2×Q16—131no—
348C2×SD16—131no—
349C2×SD16—131no—
350C2×M16C22⋊D1311yescharacteristic
351C2×M16C22⋊D1311yescharacteristic
352C22×C8—21no—
353C22×C8—261no—
354C22×C8—261no—
355C4⋊Q8C4×D1311yescharacteristic
356C4⋊Q8C4×D1311yescharacteristic
357#125—21no—
358C22⋊Q8—21no—
359C22⋊Q8C4×D1311yescharacteristic
360C22⋊Q8C4×D1311yescharacteristic
361C4×Q8—21no—
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8C22×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366C4×D4—131no—
367C4×D4—131no—
368C4×D4—261no—
369C4×D4—261no—
370#117—21no—
371#117—131no—
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—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—131no—
385C4⋊C8—131no—
386C4⋊C8—131no—
387C4⋊C8—131no—
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#103—131no—
398#103—131no—
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—21no—
409#97—261no—
410#97—261no—
411#97—261no—
412#97C22⋊D1311yescharacteristic
413#97C22⋊D1311yescharacteristic
414C4×C8—21no—
415C4×C8—21no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C2×C13—41no—
423C2×C13#293311yescharacteristic
424C2×C13C4×#13711yescharacteristic
425C2×C13#295711yescharacteristic
426D13—42no—
427#41—262no—
428#41—521no—
429C2×Q8—21no—
430C2×Q8—131no—
431C2×Q8C2×C4×D1311yescharacteristic
432C2×Q8C2×C4×D1311yescharacteristic
433C2×D4—131no—
434C2×D4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4#612711yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441Q16—521no—
442Q16—521no—
443SD16—262no—
444SD16—262no—
445M16—22no—
446M16—41no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—42no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—522no—
459C2×C8—522no—
460C2×C8C2×C22⋊D1311yescharacteristic
461C2×C8C2×C22⋊D1311yescharacteristic
462C2×C8C2×C22⋊D1311yescharacteristic
463C2×C8C2×C22⋊D1311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—131no—
472C4⋊C4—131no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4C2×C4×D1311yescharacteristic
476C4⋊C4C2×C4×D1311yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C42—21no—
483C42—21no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42#612711yescharacteristic
489C42C2×C22⋊D1311yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1800911yescharacteristic, complemented, Sylow
492C23—261no—
493C23C4×C22⋊D1311yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—261no—
500Q8—261no—
501D4—132no—
502D4—261no—
503D4—522no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—522no—
517C2×C4—521no—
518C2×C4—521no—
519C2×C4—1041no—
520C2×C4C4×C22⋊D1311yescharacteristic
521C2×C4C4×C22⋊D1311yescharacteristic
522C2×C4C4×C22⋊D1311yescharacteristic
523C2×C4C22×C4×D1311yescharacteristic
524C2×C4C2×#612711yescharacteristic
525C2×C4C22×C22⋊D1311yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—521no—
536C8—521no—
537C8—521no—
538C8—521no—
539C8#8819612yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—262no—
544C22—521no—
545C22—521no—
546C22C2×C4×C22⋊D1311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—521no—
556C4—521no—
557C4—521no—
558C4D13×#13111yescharacteristic
559C4#1171945511yescharacteristic
560C4C2×#8819611yescharacteristic
561C4#1171952711yescharacteristic
562C2—41no—
563C2—522no—
564C2#1312355811yescharacteristic
565C2C4×#8819611yescharacteristic
566C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2962C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C2×C4
cosocleC42×C13C24
hypercenter#2962D13
hypocenterC13#18009
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #13113743C2semidirect
4. #13113731C2semidirect
5. #13113707C2semidirect
6. #13113691C2semidirect
7. #13113686C2semidirect
8. #13113670C2semidirect
9. #13113646C2semidirect
10. C8×#6106C2semidirect
11. #13113619C2semidirect
12. #13113309C2semidirect
14. #13113133C2semidirect
15. C13×#2962C2semidirect
211. #2962D13semidirect
491. C13#18009semidirect

Maximal subgroups

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

subgroupindex
#131249012
#131238512
#131137432
#131137312
#131137072
#131136912
#131136862
#131136702
#131136462
C8×#61062
#131136192
#131133092
#131132212
#131131332
C13×#29622
#1800913