Finite Group Databasebeta

← #15834621

Subgroups — #15834621

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123870C211yesmaximal, characteristic
2C2×C4×#6106C211yesmaximal, characteristic
3#13113736C212yesmaximal, complemented
4#13113679C212yesmaximal, complemented
5#13113670C212yesmaximal, complemented
6#13113646C212yesmaximal, complemented
7#13113597C211yesmaximal, characteristic, complemented
8#13113283C211yesmaximal, characteristic, complemented
9#13113278C211yesmaximal, characteristic
10#13113126C211yesmaximal, characteristic, complemented
11C13×#2984C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C13C2211yescharacteristic
13C22×#6106C411yescharacteristic
14C2×C4×D52C2211yescharacteristic
15C13×#446—22no—
16C13×#446C2212yescomplemented
17C8×Q8×C13C2212yescomplemented
18C13×#432—21no—
19C13×#432C2211yescharacteristic
20C13×#431—21no—
21C13×#431C2211yescharacteristic
22C2×#88075C411yescharacteristic
23C4×#6106C411yescharacteristic
24C4×#6106C411yescharacteristic
25C4×#6106C411yescharacteristic
26C4×#6106C411yescharacteristic
27C4×#6106C2211yescharacteristic
28C4×#6106C2211yescharacteristic
29C4×#6106C2211yescharacteristic
30C4×#6106C2211yescharacteristic
31C2×#88049C411yescharacteristic
32C2×#88048C411yescharacteristic
33#11718587C2211yescharacteristic
34C4×#6099C2211yescharacteristic
35C2×C4×#1055C2211yescharacteristic
36#11718497—22no—
37#11718387—21no—
38D13×C22⋊C8—21no—
39#11718349C2212yes—
40C8×D52C2212yes—
41Q8⋊#1055C2212yescomplemented
42Q8⋊#1055C2212yescomplemented
43#11718075C2212yes—
44#11718075C2212yes—
45#11718072C2212yescomplemented
46#11718071C2212yescomplemented
47#11718047C2212yescomplemented
48#11718046C2212yescomplemented
49C22×Q8×C13C2×C411yescharacteristic
50C22×D52C2×C411yescharacteristic
51C22×C4×D13—21no—
52C4×Q8×C13—21no—
53C4×Q8×C13—21no—
54C4×Q8×C13C2×C411yescharacteristic
55C4×Q8×C13C2×C411yescharacteristic
56C4×Q8×C13C2311yescharacteristic
57C4×Q8×C13C2311yescharacteristic
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4C2×C411yescharacteristic
60C2×C42×C13—21no—
61C2×C42×C13C2311yescharacteristic
62C2×#6106—24no—
63C2×#6106C2×C411yescharacteristic
64C2×#6106C2×C411yescharacteristic
65C2×#6106C2×C411yescharacteristic
66C2×#6106C2×C411yescharacteristic
67C2×#6103—21no—
68C2×C4⋊Dic13C2×C411yescharacteristic
69C2×#6099—21no—
70C22×#1055C2×C411yescharacteristic
71C22×#1055C2×C411yescharacteristic
72C2×#6094—22no—
73C2×C8×D13—22no—
74C4×D52—21no—
75C4×D52—21no—
76C4×D52C2×C411yescharacteristic
77C4×D52C2×C411yescharacteristic
78C4×D52C2311yescharacteristic
79C4×D52C2311yescharacteristic
80C13×C4⋊C8—22no—
81C13×C4⋊C8—22no—
82C13×C4⋊C8D412yes—
83C13×C4⋊C8C2312yes—
84C13×C22⋊C8—21no—
85C13×C22⋊C8D411yescharacteristic
86C13×C22⋊C8D411yescharacteristic
87C13×#97—22no—
88C13×#97—21no—
89C4×C8×C13—22no—
90C4×C8×C13C2312yes—
91#88075C2×C411yescharacteristic
92#88075C2×C411yescharacteristic
93#88075C2×C411yescharacteristic
94#88075C2×C411yescharacteristic
95C22⋊#1055—21no—
96#88060—22no—
97#88060—22no—
98#88049C2×C411yescharacteristic
99#88049C2×C411yescharacteristic
100#88049C2×C411yescharacteristic
101#88049C2×C411yescharacteristic
102#88048C2×C411yescharacteristic
103#88048C2×C411yescharacteristic
104#88048C2×C411yescharacteristic
105#88048C2×C411yescharacteristic
106C4⋊#1055C2312yes—
107#88043—21no—
108#88043—21no—
109C4×#1055C2×C411yescharacteristic
110C4×#1055C2×C411yescharacteristic
111C4×#1055C2312yes—
112C4×#1055C2311yescharacteristic
113C4×#1055C2311yescharacteristic
114#18060—131nomaximal, Sylow
115C23×D13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13—22no—
118C2×Q8×C13—41no—
119C2×Q8×C13C22×C411yescharacteristic
120C2×Q8×C13C22×C411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13#4111yescharacteristic
126C22×Dic13—21no—
127C2×D52—22no—
128C2×D52—21no—
129C2×D52—41no—
130C2×D52C22×C411yescharacteristic
131C2×D52C22×C411yescharacteristic
132C2×C4×D13—21no—
133C2×C4×D13—21no—
134C2×C4×D13—21no—
135C2×C4×D13—21no—
136C2×C4×D13—82no—
137C2×C8×C13—22no—
138C2×C8×C13C2×D412yes—
139C2×C8×C13C2×D412yes—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4C22×C411yescharacteristic
146C13×C4⋊C4C22×C411yescharacteristic
147C42×C13—21no—
148C42×C13—21no—
149C42×C13—21no—
150C42×C13—21no—
151C42×C13C22×C411yescharacteristic
152C42×C13C2×D411yescharacteristic
153C42×C13#4111yescharacteristic
154C42×C13C2411yescharacteristic
155#6106—22no—
156#6106—22no—
157#6106—22no—
158#6106M1614yescomplemented
159#6103—21no—
160#6103—21no—
161#6103—21no—
162#6103—21no—
163C4⋊Dic13—21no—
164C4⋊Dic13C22×C411yescharacteristic
165C4⋊Dic13C22×C411yescharacteristic
166#6099—42no—
167C2×#1055—22no—
168C2×#1055—22no—
169C2×#1055—22no—
170C2×#1055—41no—
171C2×#1055C22×C411yescharacteristic
172C2×#1055C22×C411yescharacteristic
173C2×#1055C22×C411yescharacteristic
174C2×#1055C22×C411yescharacteristic
175#6094—82no—
176C8×D13—82no—
177#2984D1311yescharacteristic, complemented
178#2974—131no—
179C2×C4×SD16—131no—
180#1592—132no—
181#1583—132no—
182#1582—132no—
183SD16⋊C8—132no—
184#1568—131no—
185#1491—131no—
186#1490—131no—
187#1451—131no—
188C23×C13C4×D411yescharacteristic
189C22×D13—21no—
190C22×D13—21no—
191C22×D13—42no—
192C22×D13—42no—
193C22×D13—81no—
194Q8×C13—21no—
195Q8×C13—21no—
196Q8×C13—21no—
197Q8×C13—42no—
198Q8×C13C2×M1612yes—
199C2×C4×C13—21no—
200C2×C4×C13—22no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—22no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13C4×D411yescharacteristic
210C2×C4×C13C4×D411yescharacteristic
211C2×C4×C13C4×D411yescharacteristic
212C2×C4×C13C23×C411yescharacteristic
213C2×C4×C13C22×D411yescharacteristic
214C2×C4×C13C2×#4111yescharacteristic
215C2×Dic13—21no—
216C2×Dic13—21no—
217C2×Dic13—81no—
218D52—21no—
219D52—21no—
220D52—21no—
221D52—42no—
222D52C2×M1612yes—
223C4×D13—42no—
224C4×D13—42no—
225C4×D13—81no—
226C4×D13—81no—
227C8×C13—22no—
228C8×C13—22no—
229C8×C13—42no—
230#1055—21no—
231#1055—21no—
232#1055—21no—
233#1055—42no—
234#1055—42no—
235#1055C2×M1612yes—
236C22×SD16—131no—
237C2×C4×Q8C2×D1311yescharacteristic
238C2×C4×D4—131no—
239#446—22no—
240#446C2×D1312yescomplemented
241C8×Q8C2×D1312yescomplemented
242C4×SD16—131no—
243C4×SD16—131no—
244C4×SD16—131no—
245C4×SD16—131no—
246C4×SD16—131no—
247C4×SD16—131no—
248C4×SD16—131no—
249C4×SD16—131no—
250#436—132no—
251#435—262no—
252C8×D4—132no—
253#432—21no—
254#432—131no—
255#432C2×D1311yescharacteristic
256#431—21no—
257#431C2×D1311yescharacteristic
258C2×#106—131no—
259C2×#103—131no—
260C2×#102—131no—
261#407—261no—
262C2×C22⋊C8—261no—
263C4×M16—131no—
264C2×C4×C8—131no—
265#335—132no—
266#334—132no—
267Q8⋊C8—132no—
268Q8⋊C8—132no—
269D4⋊C8—132no—
270D4⋊C8—132no—
271#322—132no—
272#322—132no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13#44412yes—
276C22×C13C2×C4×D411yescharacteristic
277C2×D13—22no—
278C2×D13—41no—
279C2×D13—41no—
280C2×D13—41no—
281C2×D13—41no—
282C2×D13—41no—
283C2×D13—84no—
284C4×C13—21no—
285C4×C13—22no—
286C4×C13—21no—
287C4×C13—21no—
288C4×C13—21no—
289C4×C13—41no—
290C4×C13—41no—
291C4×C13—41no—
292C4×C13C22×M1611yescharacteristic
293C4×C13#56811yescharacteristic
294C4×C13#57712yes—
295Dic13—41no—
296Dic13—41no—
297C22×Q8C4×D1311yescharacteristic
298C22×D4—131no—
299C23×C4—261no—
300C2×SD16—131no—
301C2×SD16—131no—
302C2×SD16—131no—
303C2×SD16—131no—
304C2×SD16—264no—
305C2×M16—261no—
306C2×M16—262no—
307C22×C8—131no—
308C22×C8—131no—
309C22×C8—262no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8C4×D1311yescharacteristic
313C4×Q8C4×D1311yescharacteristic
314C4×Q8C22×D1311yescharacteristic
315C4×Q8C22×D1311yescharacteristic
316C4×D4—131no—
317C4×D4—131no—
318C4×D4—131no—
319C4×D4—131no—
320C4×D4—261no—
321C4×D4—261no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—131no—
324C2×C4⋊C4C4×D1311yescharacteristic
325C2×C22⋊C4—261no—
326C2×C42—21no—
327C2×C42C22×D1311yescharacteristic
328#106—131no—
329#106—131no—
330#106—131no—
331#106—131no—
332C4⋊C8—22no—
333C4⋊C8—22no—
334C4⋊C8—132no—
335C4⋊C8C22⋊D1312yes—
336C4⋊C8C22×D1312yes—
337#103—131no—
338#103—131no—
339#103—131no—
340#103—131no—
341#102—131no—
342#102—131no—
343#102—131no—
344#102—131no—
345C22⋊C8—21no—
346C22⋊C8—261no—
347C22⋊C8—262no—
348C22⋊C8—262no—
349C22⋊C8C22⋊D1311yescharacteristic
350C22⋊C8C22⋊D1311yescharacteristic
351#97—22no—
352#97—21no—
353#97—261no—
354#97—261no—
355C4×C8—22no—
356C4×C8—131no—
357C4×C8—131no—
358C4×C8—131no—
359C4×C8—131no—
360C4×C8—132no—
361C4×C8C22×D1312yes—
362C2×C13—22no—
363C2×C13D4×M1611yescharacteristic
364C2×C13#294911yescharacteristic
365C2×C13C2×#44411yescharacteristic
366D13—42no—
367D13—81no—
368C24—261no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8—41no—
372C2×Q8C2×C4×D1311yescharacteristic
373C2×Q8C2×C4×D1311yescharacteristic
374C2×D4—131no—
375C2×D4—131no—
376C2×D4—262no—
377C2×D4—261no—
378C2×D4—521no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—261no—
382C22×C4—261no—
383C22×C4—261no—
384C22×C4—261no—
385C22×C4—261no—
386C22×C4—1042no—
387C22×C4C2×C4×D1311yescharacteristic
388C22×C4#612711yescharacteristic
389C22×C4C2×C22⋊D1311yescharacteristic
390SD16—134no—
391SD16—262no—
392SD16—262no—
393SD16—262no—
394M16—522no—
395M16—1042no—
396C2×C8—22no—
397C2×C8—131no—
398C2×C8—131no—
399C2×C8—131no—
400C2×C8—131no—
401C2×C8—262no—
402C2×C8—262no—
403C2×C8—262no—
404C2×C8—521no—
405C2×C8—1042no—
406C2×C8C2×C22⋊D1312yes—
407C2×C8C2×C22⋊D1312yes—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—131no—
414C4⋊C4—131no—
415C4⋊C4—261no—
416C4⋊C4C2×C4×D1311yescharacteristic
417C4⋊C4C2×C4×D1311yescharacteristic
418C22⋊C4—261no—
419C22⋊C4—261no—
420C22⋊C4—261no—
421C22⋊C4—261no—
422C42—21no—
423C42—21no—
424C42—21no—
425C42—21no—
426C42C2×C4×D1311yescharacteristic
427C42#612711yescharacteristic
428C42C2×C22⋊D1311yescharacteristic
429C42C23×D1311yescharacteristic
430C13#1806011yescharacteristic, complemented, Sylow
431C23—261no—
432C23—261no—
433C23—522no—
434C23—522no—
435C23—1041no—
436C23C4×C22⋊D1311yescharacteristic
437Q8—21no—
438Q8—21no—
439Q8—21no—
440Q8—42no—
441Q8M16×D1312yes—
442D4—132no—
443D4—261no—
444D4—261no—
445D4—261no—
446D4—522no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—261no—
458C2×C4—261no—
459C2×C4—522no—
460C2×C4—522no—
461C2×C4—1041no—
462C2×C4—1041no—
463C2×C4—1041no—
464C2×C4C4×C22⋊D1311yescharacteristic
465C2×C4C4×C22⋊D1311yescharacteristic
466C2×C4C4×C22⋊D1311yescharacteristic
467C2×C4C22×C4×D1311yescharacteristic
468C2×C4C2×#612711yescharacteristic
469C2×C4C22×C22⋊D1311yescharacteristic
470C8—22no—
471C8—22no—
472C8—42no—
473C8—132no—
474C8—261no—
475C8—261no—
476C8—261no—
477C8—522no—
478C8—522no—
479C22—21no—
480C22—21no—
481C22—262no—
482C22—521no—
483C22—521no—
484C22—521no—
485C22—521no—
486C22—521no—
487C22—1044no—
488C22#1171880612yes—
489C22C2×C4×C22⋊D1311yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—41no—
498C4—521no—
499C4—521no—
500C4C2×M16×D1311yescharacteristic
501C4#1171945011yescharacteristic
502C4#1171954212yes—
503C2—22no—
504C2—522no—
505C2—1041no—
506C2M16×C22⋊D1311yescharacteristic
507C2#1312369511yescharacteristic
508C2C2×#1171880611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2984C2
socleC22×C13C2×C4×D4
prime radicalC22×D52C2×C4
cosocleC42×C13C24
hypercenter#2984D13
hypocenterC13#18060
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #13113736C2semidirect
4. #13113679C2semidirect
5. #13113670C2semidirect
6. #13113646C2semidirect
7. #13113597C2semidirect
8. #13113283C2semidirect
10. #13113126C2semidirect
11. C13×#2984C2semidirect
16. C13×#446C22semidirect
17. C8×Q8×C13C22semidirect
41. Q8⋊#1055C22semidirect
42. Q8⋊#1055C22semidirect
45. #11718072C22semidirect
46. #11718071C22semidirect
47. #11718047C22semidirect
48. #11718046C22semidirect
158. #6106M16semidirect
177. #2984D13semidirect
240. #446C2×D13semidirect
241. C8×Q8C2×D13semidirect
430. C13#18060semidirect

Maximal subgroups

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

subgroupindex
#131238702
C2×C4×#61062
#131137362
#131136792
#131136702
#131136462
#131135972
#131132832
#131132782
#131131262
C13×#29842
#1806013