Finite Group Databasebeta

← #15834041

Subgroups — #15834041

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#13124912C211yesmaximal, characteristic
2M16×Dic26C211yesmaximal, characteristic, complemented
3#13113743C211yesmaximal, characteristic, complemented
4#13113724C211yesmaximal, characteristic, complemented
5#13113705C211yesmaximal, characteristic, complemented
6#13113693C211yesmaximal, characteristic, complemented
7#13113686C211yesmaximal, characteristic, complemented
8#13113677C211yesmaximal, characteristic, complemented
9#13113648C211yesmaximal, characteristic, complemented
10C8×#6107C211yesmaximal, characteristic, complemented
11#13113624C211yesmaximal, characteristic, complemented
12#13113301C211yesmaximal, characteristic
13#13113230C211yesmaximal, characteristic, complemented
14#13113133C211yesmaximal, characteristic, complemented
15C13×#2969C211yesmaximal, characteristic
16C13×#529C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C13×#436—21no—
21C13×#436C2211yescharacteristic
22C13×#435—21no—
23C8×D4×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#431C2211yescharacteristic
26C13×#405—21no—
27C4×C13×M16C2211yescharacteristic
28#11718779—21no—
29M16×Dic13—21no—
30#11718724C411yescharacteristic
31#11718724C411yescharacteristic
32#11718715C411yescharacteristic
33#11718715C411yescharacteristic
34#11718711C411yescharacteristic
35#11718704C411yescharacteristic
36#11718701C411yescharacteristic
37#11718694C411yescharacteristic
38C4×#6107C2211yescharacteristic
39C4×#6107C2211yescharacteristic
40C4×#6105C2211yescharacteristic
41C4×#6105C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718586C2211yescharacteristic
44#11718585C2211yescharacteristic
45#11718362—21no—
46#11718362—21no—
47#11718340C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Dic26C2×C411yescharacteristic
68C2×C13×M16—21no—
69C2×C13×M16D411yescharacteristic
70C2×C13×M16D411yescharacteristic
71C22×C8×C13—21no—
72C13×#126—21no—
73C13×#125C2×C411yescharacteristic
74C13×#124C2×C411yescharacteristic
75C13×#123—21no—
76C13×C22⋊Q8C2×C411yescharacteristic
77C13×#121C2×C411yescharacteristic
78C4×Q8×C13C2311yescharacteristic
79C4×D4×C13—21no—
80C4×D4×C13C2311yescharacteristic
81C13×#117—21no—
82C2×C42×C13C2311yescharacteristic
83C2×#6107C2×C411yescharacteristic
84C2×#6107C2×C411yescharacteristic
85C2×#6105C2×C411yescharacteristic
86C2×#6105C2×C411yescharacteristic
87C2×C4⋊Dic13C2×C411yescharacteristic
88C2×#6101—21no—
89C2×C4×Dic13—21no—
90C2×#6099—21no—
91C4×Dic26—21no—
92C4×Dic26—21no—
93C4×Dic26C2×C411yescharacteristic
94C4×Dic26C2×C411yescharacteristic
95C4×Dic26C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8—21no—
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C22⋊C8—21no—
102C13×C22⋊C8—21no—
103C13×C22⋊C8—21no—
104C13×#97—21no—
105C13×#97D411yescharacteristic
106C13×#97D411yescharacteristic
107C4×C8×C13—21no—
108C4×C8×C13—21no—
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88075C2×C411yescharacteristic
112#88075C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115C22⋊#1055—21no—
116C22⋊#1055C2×C411yescharacteristic
117C22⋊#1055C2×C411yescharacteristic
118#88055—21no—
119#88055—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88050C2×C411yescharacteristic
129#88050C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055—21no—
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2×C411yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18012—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C22×Dic13—21no—
153C22×Dic13—21no—
154C2×Dic26—22no—
155C2×Dic26—21no—
156C2×Dic26—41no—
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C13×M16—22no—
160C13×M16—41no—
161C13×M16—42no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—42no—
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C13×C22⋊C4—21no—
180C42×C13—21no—
181C42×C13C22×C411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13#4111yescharacteristic
184C42×C13C2411yescharacteristic
185#6107—22no—
186#6107—41no—
187#6105—22no—
188#6105—41no—
189C4⋊Dic13—21no—
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200#6099—42no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209#3108—131no—
210#2969D1311yescharacteristic
211Q8×M16—131no—
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×C13—21no—
225C23×C13C4×D411yescharacteristic
226Q8×C13—21no—
227Q8×C13—21no—
228D4×C13—21no—
229D4×C13—21no—
230D4×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—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—42no—
252C2×Dic13—81no—
253Dic26—21no—
254Dic26—21no—
255Dic26—21no—
256Dic26—42no—
257Dic26#13112yes—
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#529C2×D1311yescharacteristic
273C2×C4×Q8—131no—
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—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286#446C2×D1311yescharacteristic
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8C2×D1311yescharacteristic
290C4×Q16—131no—
291C4×Q16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294#436—21no—
295#436C2×D1311yescharacteristic
296#435—21no—
297C8×D4C2×D1311yescharacteristic
298#433—21no—
299#431—131no—
300#431—131no—
301#431C2×D1311yescharacteristic
302#423—131no—
303#423—261no—
304#405—21no—
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#322—131no—
320#322—131no—
321#322—131no—
322C82—131no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13C2×C4×D411yescharacteristic
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13C2×#13111yescharacteristic
338C4×C13#56811yescharacteristic
339C4×C13C2×#13711yescharacteristic
340C4×C13#57511yescharacteristic
341Dic13—22no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C22×Q8—131no—
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—21no—
355#126—21no—
356#125C4×D1311yescharacteristic
357#124C4×D1311yescharacteristic
358#123—21no—
359C22⋊Q8C4×D1311yescharacteristic
360#121C4×D1311yescharacteristic
361C4×Q8—131no—
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8—131no—
365C4×Q8—261no—
366C4×Q8—261no—
367C4×Q8C22×D1311yescharacteristic
368C4×D4—21no—
369C4×D4C22×D1311yescharacteristic
370#117—21no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—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—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#103—131no—
398#103—131no—
399#102—131no—
400#102—131no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—131no—
405C22⋊C8—131no—
406C22⋊C8—261no—
407#97—21no—
408#97—261no—
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—81no—
424C2×C13#293311yescharacteristic
425C2×C13C4×#13711yescharacteristic
426C2×C13#295711yescharacteristic
427C2×Q8—131no—
428C2×Q8—131no—
429C2×Q8—262no—
430C2×Q8—261no—
431C2×Q8—521no—
432C2×Q8C2×C4×D1311yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D1311yescharacteristic
435C22×C4—21no—
436C22×C4—261no—
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—42no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
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—131no—
469C4⋊C4—131no—
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—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C42—21no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42#612711yescharacteristic
489C42C2×C22⋊D1311yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1801211yescharacteristic, complemented, Sylow
492C23—21no—
493C23C4×C22⋊D1311yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—132no—
497Q8—261no—
498Q8—261no—
499Q8—261no—
500Q8—522no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—522no—
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#8820512yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×C4×C22⋊D1311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—262no—
555C4—521no—
556C4—521no—
557C4—521no—
558C4D13×#13111yescharacteristic
559C4#1171945511yescharacteristic
560C4#1171952711yescharacteristic
561C4C2×#8820511yescharacteristic
562C2—41no—
563C2—81no—
564C2#1312355811yescharacteristic
565C2C4×#8820511yescharacteristic
566C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2969C2
socleC22×C13C2×C4×D4
prime radicalC13×#121C2×C4
cosocleC42×C13C24
hypercenter#2969D13
hypocenterC13#18012
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. M16×Dic26C2semidirect
3. #13113743C2semidirect
4. #13113724C2semidirect
5. #13113705C2semidirect
6. #13113693C2semidirect
7. #13113686C2semidirect
8. #13113677C2semidirect
9. #13113648C2semidirect
10. C8×#6107C2semidirect
11. #13113624C2semidirect
13. #13113230C2semidirect
14. #13113133C2semidirect
491. C13#18012semidirect

Maximal subgroups

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

subgroupindex
#131249122
M16×Dic262
#131137432
#131137242
#131137052
#131136932
#131136862
#131136772
#131136482
C8×#61072
#131136242
#131133012
#131132302
#131131332
C13×#29692
#1801213