Finite Group Databasebeta

← #15834045

Subgroups — #15834045

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#13124916C211yesmaximal, characteristic
2#13123840C211yesmaximal, characteristic
3#13113743C211yesmaximal, characteristic, complemented
4#13113726C211yesmaximal, characteristic, complemented
5#13113707C211yesmaximal, characteristic, complemented
6#13113691C211yesmaximal, characteristic, complemented
7#13113684C211yesmaximal, characteristic, complemented
8#13113679C211yesmaximal, characteristic, complemented
9#13113646C211yesmaximal, characteristic, complemented
10C8×#6107C211yesmaximal, characteristic, complemented
11#13113627C211yesmaximal, characteristic, complemented
12#13113299C211yesmaximal, characteristic
13#13113231C211yesmaximal, characteristic, complemented
14#13113133C211yesmaximal, characteristic, complemented
15Q8×C13×M16C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#446—21no—
19C13×#446—21no—
20C13×#446C2211yescharacteristic
21C13×#446C2211yescharacteristic
22C8×Q8×C13C2211yescharacteristic
23C8×Q8×C13C2211yescharacteristic
24C13×#423—21no—
25C13×#423C2211yescharacteristic
26C4×C13×M16—21no—
27C4×C13×M16C2211yescharacteristic
28#11718889C411yescharacteristic
29#11718888C411yescharacteristic
30#11718789—21no—
31#11718788—21no—
32C4×#6107C2211yescharacteristic
33C4×#6107C2211yescharacteristic
34#11718689C411yescharacteristic
35#11718689C411yescharacteristic
36C4×#6106C2211yescharacteristic
37C4×#6106C2211yescharacteristic
38#11718683C411yescharacteristic
39#11718683C411yescharacteristic
40#11718632C411yescharacteristic
41#11718628C411yescharacteristic
42#11718586C2211yescharacteristic
43#11718586C2211yescharacteristic
44#11718586C2211yescharacteristic
45#11718370—21no—
46#11718369—21no—
47#11718349C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
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
67C22×Q8×C13C2×C411yescharacteristic
68C2×C13×M16—21no—
69C2×C13×M16D411yescharacteristic
70C2×C13×M16D411yescharacteristic
71C4×Q8×C13—21no—
72C4×Q8×C13—21no—
73C4×Q8×C13C2×C411yescharacteristic
74C4×Q8×C13C2×C411yescharacteristic
75C4×Q8×C13C2311yescharacteristic
76C4×Q8×C13C2311yescharacteristic
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4C2×C411yescharacteristic
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×#6107C2×C411yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×#6106C2×C411yescharacteristic
84C2×#6106C2×C411yescharacteristic
85#88184C2×C411yescharacteristic
86#88183—21no—
87C4×C22⋊D13—21no—
88#88178C2×C411yescharacteristic
89C2×#6094—21no—
90C2×C8×D13—21no—
91#88130—21no—
92#88129C2×C411yescharacteristic
93C4×D52C2311yescharacteristic
94#88126—21no—
95#88124C2×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#88054—21no—
124#88054—21no—
125C8×Dic13—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
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18012—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—22no—
147C2×Q8×C13—41no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×Q8×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13#4111yescharacteristic
155C2×C22⋊D13—21no—
156C2×D52C22×C411yescharacteristic
157C2×C4×D13—21no—
158C2×Dic26C22×C411yescharacteristic
159C13×M16—22no—
160C13×M16—41no—
161C13×M16—42no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
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⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13C22×C411yescharacteristic
180C42×C13C2×D411yescharacteristic
181C42×C13#4111yescharacteristic
182C42×C13C2411yescharacteristic
183C22⋊Dic13—21no—
184#6107—22no—
185#6107—41no—
186#6106—22no—
187#6106—41no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194#6101—21no—
195#6101—21no—
196#6101—21no—
197#6101—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
207#6094—42no—
208C8×D13—42no—
209#3108—131no—
210#2969—131no—
211Q8×M16D1311yescharacteristic, complemented
212#1593—131no—
213#1590—131no—
214#1587—131no—
215#1585—131no—
216#1584—131no—
217#1583—131no—
218SD16⋊C8—131no—
219C8×Q16—131no—
220#1574—131no—
221#1495—131no—
222#1479—131no—
223#1453—131no—
224C23×C13C4×D411yescharacteristic
225C22×D13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—42no—
230Q8×C13#13112yes—
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×C13—42no—
241C2×C4×C13—81no—
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C23×C411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C22⋊D13—81no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252D52—21no—
253D52—21no—
254C4×D13—41no—
255C4×D13—41no—
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#529—131no—
273C2×C4×Q8C2×D1311yescharacteristic
274#483—131no—
275#480—131no—
276#479—131no—
277#479—131no—
278#464—131no—
279#464—131no—
280#451—131no—
281#448—131no—
282#446—21no—
283#446—21no—
284#446—131no—
285#446C2×D1311yescharacteristic
286#446C2×D1311yescharacteristic
287C8×Q8—131no—
288C8×Q8C2×D1311yescharacteristic
289C8×Q8C2×D1311yescharacteristic
290C4×Q16—131no—
291C4×Q16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294#436—131no—
295#436—261no—
296#435—261no—
297C8×D4—131no—
298#433—261no—
299#431—131no—
300#431—131no—
301#431—131no—
302#423—21no—
303#423C2×D1311yescharacteristic
304#405—261no—
305C4×M16—21no—
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#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—41no—
328C2×D13—41no—
329C2×D13—41no—
330C4×C13—21no—
331C4×C13—22no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
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—
345C22×Q8C4×D1311yescharacteristic
346C2×Q16—131no—
347C2×Q16—131no—
348C2×SD16—131no—
349C2×SD16—131no—
350C2×M16—21no—
351C2×M16—261no—
352C2×M16C22⋊D1311yescharacteristic
353C2×M16C22⋊D1311yescharacteristic
354C22×C8—261no—
355#126—261no—
356#125—131no—
357#124—131no—
358#123—261no—
359C22⋊Q8—131no—
360#121—131no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—131no—
364C4×Q8C4×D1311yescharacteristic
365C4×Q8C4×D1311yescharacteristic
366C4×Q8C22×D1311yescharacteristic
367C4×Q8C22×D1311yescharacteristic
368C4×D4—131no—
369C4×D4—261no—
370#117—261no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4C4×D1311yescharacteristic
373C2×C42—21no—
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#97C22⋊D1311yescharacteristic
411#97C22⋊D1311yescharacteristic
412C4×C8—21no—
413C4×C8—21no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C2×C13—41no—
423C2×C13#293311yescharacteristic
424C2×C13C4×#13711yescharacteristic
425C2×C13#295711yescharacteristic
426D13—81no—
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—131no—
431C2×Q8C2×C4×D1311yescharacteristic
432C2×Q8C2×C4×D1311yescharacteristic
433C2×D4—131no—
434C2×D4—261no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—261no—
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4#612711yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441Q16—262no—
442Q16—521no—
443SD16—262no—
444SD16—521no—
445M16—22no—
446M16—41no—
447M16—42no—
448M16—522no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
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—131no—
470C4⋊C4—131no—
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—21no—
485C42—21no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42#612711yescharacteristic
489C42C2×C22⋊D1311yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1801211yescharacteristic, complemented, Sylow
492C23—261no—
493C23C4×C22⋊D1311yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8—261no—
499Q8—261no—
500Q8#8816112yes—
501D4—261no—
502D4—261no—
503D4—1041no—
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—42no—
514C2×C4—81no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—521no—
519C2×C4—521no—
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—521no—
544C22—521no—
545C22—521no—
546C22C2×C4×C22⋊D1311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—22no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—521no—
556C4—521no—
557C4—521no—
558C4C2×#8816111yescharacteristic
559C4#1171945011yescharacteristic
560C4C2×#8819611yescharacteristic
561C4#1171952711yescharacteristic
562C2—41no—
563C2—1041no—
564C2#1312356111yescharacteristic
565C2C4×#8819611yescharacteristic
566C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingQ8×C13×M16C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenterQ8×M16D13
hypocenterC13#18012
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
3. #13113743C2semidirect
4. #13113726C2semidirect
5. #13113707C2semidirect
6. #13113691C2semidirect
7. #13113684C2semidirect
8. #13113679C2semidirect
9. #13113646C2semidirect
10. C8×#6107C2semidirect
11. #13113627C2semidirect
13. #13113231C2semidirect
14. #13113133C2semidirect
15. Q8×C13×M16C2semidirect
211. Q8×M16D13semidirect
491. C13#18012semidirect

Maximal subgroups

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

subgroupindex
#131249162
#131238402
#131137432
#131137262
#131137072
#131136912
#131136842
#131136792
#131136462
C8×#61072
#131136272
#131132992
#131132312
#131131332
Q8×C13×M162
#1801213