Finite Group Databasebeta

← #15904241

Subgroups — #15904241

Order 3328.

828 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718496C211yesmaximal, characteristic
2#13123183C211yesmaximal, characteristic
3C4×#88200C211yesmaximal, characteristic
4#13116260C212yesmaximal
5#13116031C212yesmaximal
6#13115785C211yesmaximal, characteristic, complemented
7#13115600C211yesmaximal, characteristic, complemented
8#13115577C212yesmaximal, complemented
9#13115523C212yesmaximal, complemented
10#13114841C211yesmaximal, characteristic, complemented
11C2×C13×#477C211yesmaximal, characteristic, complemented
12C2×C13×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C13C2211yescharacteristic
14C2×#88200—21no—
15C2×#88200C2211yescharacteristic
16C2×C42×D13C2211yescharacteristic
17C13×#477—24no—
18C2×C13×#107C2212yes—
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×#103C2212yes—
21#11718891—21no—
22#11718891C2211yescharacteristic
23C2×#88075C2212yes—
24C2×#88060C2212yes—
25C2×#88057C2212yes—
26C2×#88055C2212yes—
27#11718650—21no—
28#11718648—21no—
29#11718648C2211yescharacteristic
30#11718648C2212yes—
31#11718639—21no—
32#11718634—21no—
33#11718634C2212yes—
34#11718634C2211yescharacteristic
35C4×#6103—21no—
36#11718596C2211yescharacteristic
37C4×C4⋊Dic13C2211yescharacteristic
38C4×#6101—21no—
39C2×C4⋊#1055C2211yescharacteristic
40#11718496—24no—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×Q8×C13—21no—
46C22×Q8×C13C2311yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13D411yescharacteristic
49C22×C4×D13C2311yescharacteristic
50C22×C8×C13C2312yes—
51C13×C4⋊Q8—22no—
52C13×C4⋊Q8—22no—
53C4×Q8×C13—22no—
54C4×Q8×C13—22no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C4⋊C4C2311yescharacteristic
59C2×C42×C13—21no—
60C2×C42×C13C2311yescharacteristic
61#88200—22no—
62#88200—22no—
63#88200—44no—
64C2×#6103—21no—
65C2×#6103—22no—
66C2×#6103—21no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13C2312yes—
70C2×C4⋊Dic13C2311yescharacteristic
71C2×C4⋊Dic13C2311yescharacteristic
72C2×#6101—21no—
73C2×#6101—22no—
74C2×#6101—21no—
75C2×C4×Dic13—21no—
76C2×C4×Dic13D411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13C2311yescharacteristic
79C22×#1055C2312yes—
80C42×D13—22no—
81C42×D13—22no—
82C13×#107—24no—
83C13×C4⋊C8D414yes—
84C13×#103—24no—
85#88075—24no—
86#88071—21no—
87#88071—21no—
88#88071—21no—
89#88071—21no—
90#88071—21no—
91#88071—22no—
92#88071—22no—
93#88060—24no—
94#88057—24no—
95#88055—24no—
96C4⋊#1055—22no—
97#24711—131nomaximal, Sylow
98C23×D13C2×D411yescharacteristic
99C2×Q8×C13—21no—
100C2×Q8×C13—21no—
101C2×Q8×C13—21no—
102C2×Q8×C13—21no—
103C2×Q8×C13—21no—
104C2×Q8×C13—42no—
105C2×Q8×C13—42no—
106C2×Q8×C13—42no—
107C2×Q8×C13#4112yes—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2411yescharacteristic
114C22×Dic13—21no—
115C22×Dic13—21no—
116C22×Dic13—22no—
117C22×Dic13C2×D411yescharacteristic
118C22×Dic13C2×D411yescharacteristic
119C22×Dic13C2×D411yescharacteristic
120C2×C4×D13—22no—
121C2×C4×D13—22no—
122C2×C4×D13—22no—
123C2×C4×D13—22no—
124C2×C4×D13—22no—
125C2×C4×D13—21no—
126C2×C4×D13—21no—
127C2×C4×D13—21no—
128C2×C4×D13—21no—
129C2×C4×D13—21no—
130C2×C4×D13—21no—
131C2×C4×D13—41no—
132C2×C8×C13—22no—
133C2×C8×C13—22no—
134C2×C8×C13C2×D414yes—
135C13×C4⋊C4—22no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—22no—
139C13×C4⋊C4—42no—
140C13×C4⋊C4—42no—
141C42×C13—42no—
142C42×C13C2×D412yes—
143C42×C13#4112yes—
144#6103—24no—
145#6103—42no—
146#6103—44no—
147C4⋊Dic13—21no—
148C4⋊Dic13—22no—
149C4⋊Dic13—22no—
150C4⋊Dic13—21no—
151C4⋊Dic13—21no—
152C4⋊Dic13—42no—
153C4⋊Dic13—42no—
154C4⋊Dic13#4112yes—
155#6101—24no—
156#6101—42no—
157#6101—44no—
158C4×Dic13—22no—
159C4×Dic13—22no—
160C4×Dic13—21no—
161C4×Dic13—21no—
162C4×Dic13—42no—
163C2×#1055—22no—
164C2×#1055—22no—
165C2×#1055—22no—
166C2×#477D1311yescharacteristic, complemented
167C2×#432—131no—
168#2857—131no—
169C4×C22⋊Q8—131no—
170#2075—132no—
171#2035—132no—
172#1987—131no—
173#1948—131no—
174#1944—132no—
175#1935—132no—
176#1803—131no—
177C23×C13C22×D411yescharacteristic
178C22×D13—21no—
179C22×D13—21no—
180C22×D13—21no—
181C22×D13—21no—
182C22×D13—21no—
183C22×D13—21no—
184C22×D13AGL(1,ℤ/8)12yes—
185Q8×C13—22no—
186Q8×C13—22no—
187Q8×C13—41no—
188Q8×C13—41no—
189Q8×C13—84no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—22no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13#12112yes—
202C2×C4×C13#12112yes—
203C2×C4×C13#13712yes—
204C2×C4×C13#13712yes—
205C2×C4×C13C22×D411yescharacteristic
206C2×C4×C13C2×#4111yescharacteristic
207C2×C4×C13C2×#4111yescharacteristic
208C2×C4×C13C2×#4111yescharacteristic
209C2×C4×C132−1+411yescharacteristic
210C2×C4×C132−1+411yescharacteristic
211C2×Dic13—21no—
212C2×Dic13—21no—
213C2×Dic13—21no—
214C2×Dic13—21no—
215C2×Dic13—22no—
216C2×Dic13—21no—
217C2×Dic13—21no—
218C2×Dic13—21no—
219C2×Dic13—21no—
220C2×Dic13—21no—
221C2×Dic13—41no—
222C2×Dic13—41no—
223C2×Dic13—42no—
224C2×Dic13—41no—
225C2×Dic13—42no—
226C2×Dic13—41no—
227C2×Dic13—41no—
228C2×Dic13—42no—
229C4×D13—44no—
230C4×D13—41no—
231C4×D13—41no—
232C4×D13—41no—
233C4×D13—41no—
234C4×D13—44no—
235C8×C13—24no—
236#1055—42no—
237C2×C4⋊Q8C2×D1311yescharacteristic
238C2×C22⋊Q8—131no—
239C2×C22⋊Q8—261no—
240C2×C4×Q8C2×D1311yescharacteristic
241C22×C42—131no—
242#477—24no—
243#432—264no—
244C2×#107C2×D1312yes—
245C2×#106—132no—
246C2×C4⋊C8—131no—
247C2×C4⋊C8C2×D1311yescharacteristic
248C2×#103—132no—
249C2×#103C2×D1312yes—
250C2×C22⋊C8—132no—
251C2×#97—132no—
252#391—131no—
253#391—261no—
254#389—132no—
255#389—131no—
256#389—261no—
257#387—261no—
258#385—261no—
259#384—131no—
260#380—131no—
261#380—132no—
262#380—261no—
263C4×C4⋊C4—131no—
264C4×C4⋊C4—261no—
265C4×C22⋊C4—261no—
266#340—132no—
267#340—132no—
268#340—132no—
269#340—132no—
270C22×C13C2×#12111yescharacteristic
271C22×C13#52511yescharacteristic
272C22×C13#53611yescharacteristic
273C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C13C2×#13711yescharacteristic
275C22×C13C2×#13711yescharacteristic
276C22×C13#57511yescharacteristic
277C2×D13—22no—
278C2×D13—22no—
279C2×D13—22no—
280C2×D13—41no—
281C2×D13—41no—
282C2×D13—41no—
283C2×D13—41no—
284C4×C13—22no—
285C4×C13—42no—
286C4×C13—81no—
287C4×C13—82no—
288C4×C13#47014yes—
289C4×C13#54711yescharacteristic
290C4×C13#54811yescharacteristic
291C4×C13#55211yescharacteristic
292C4×C13#55611yescharacteristic
293Dic13—42no—
294Dic13—41no—
295Dic13—41no—
296Dic13—41no—
297Dic13—82no—
298Dic13—81no—
299C22×Q8—21no—
300C22×Q8C22×D1311yescharacteristic
301C23×C4—131no—
302C23×C4—131no—
303C23×C4—131no—
304C22×C8—132no—
305C22×C8C22×D1312yes—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C22⋊Q8—262no—
309C22⋊Q8—262no—
310C22⋊Q8—524no—
311C4×Q8—22no—
312C4×Q8—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—131no—
316C2×C4⋊C4—131no—
317C2×C4⋊C4—132no—
318C2×C4⋊C4—261no—
319C2×C4⋊C4—262no—
320C2×C4⋊C4—261no—
321C2×C4⋊C4—261no—
322C2×C4⋊C4—261no—
323C2×C4⋊C4C22×D1311yescharacteristic
324C2×C4⋊C4C22×D1312yes—
325C2×C22⋊C4—261no—
326C2×C22⋊C4—262no—
327C2×C22⋊C4—261no—
328C2×C42—21no—
329C2×C42—131no—
330C2×C42—131no—
331C2×C42—131no—
332C2×C42—262no—
333C2×C42—262no—
334C2×C42—261no—
335C2×C42C22×D1311yescharacteristic
336#107—24no—
337#106—264no—
338C4⋊C8—262no—
339C4⋊C8C22⋊D1314yes—
340#103—24no—
341#103—264no—
342C22⋊C8—264no—
343#97—264no—
344#95—261no—
345#95—261no—
346#95—261no—
347#95—261no—
348#95—262no—
349#95—262no—
350#95—261no—
351C2×C13#241511yescharacteristic
352C2×C13C2×#47011yescharacteristic
353C2×C13#305511yescharacteristic
354C2×C13#311211yescharacteristic
355C2×C13#311611yescharacteristic
356C2×C13#323711yescharacteristic
357C2×C13#323811yescharacteristic
358D13—42no—
359C24—131no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8#613112yes—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—131no—
373C22×C4—131no—
374C22×C4—131no—
375C22×C4—262no—
376C22×C4—261no—
377C22×C4—262no—
378C22×C4—262no—
379C22×C4—262no—
380C22×C4—262no—
381C22×C4—261no—
382C22×C4—261no—
383C22×C4—261no—
384C22×C4—261no—
385C22×C4—261no—
386C22×C4—261no—
387C22×C4—261no—
388C22×C4—262no—
389C22×C4—521no—
390C22×C4D4×D1311yescharacteristic
391C22×C4D4×D1311yescharacteristic
392C22×C4C23×D1311yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—262no—
396C2×C8—262no—
397C2×C8—262no—
398C2×C8C2×C22⋊D1314yes—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—132no—
406C4⋊C4—264no—
407C4⋊C4—261no—
408C4⋊C4—262no—
409C4⋊C4—261no—
410C4⋊C4—262no—
411C4⋊C4—261no—
412C4⋊C4—522no—
413C4⋊C4—524no—
414C4⋊C4—522no—
415C4⋊C4—522no—
416C22⋊C4—264no—
417C22⋊C4—524no—
418C22⋊C4—522no—
419C42—42no—
420C42—262no—
421C42—262no—
422C42—261no—
423C42—261no—
424C42—522no—
425C42#612912yes—
426C42C2×C22⋊D1312yes—
427C13#2471111yescharacteristic, complemented, Sylow
428C23—132no—
429C23—261no—
430C23—261no—
431C23—261no—
432C23—261no—
433C23—261no—
434C23—261no—
435C23C2×D4×D1311yescharacteristic
436Q8—22no—
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—84no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—261no—
453C2×C4—261no—
454C2×C4—261no—
455C2×C4—261no—
456C2×C4—261no—
457C2×C4—261no—
458C2×C4—261no—
459C2×C4—262no—
460C2×C4—261no—
461C2×C4—261no—
462C2×C4—524no—
463C2×C4—521no—
464C2×C4—521no—
465C2×C4—521no—
466C2×C4—521no—
467C2×C4—521no—
468C2×C4—521no—
469C2×C4—524no—
470C2×C4—521no—
471C2×C4—522no—
472C2×C4—522no—
473C2×C4—521no—
474C2×C4—522no—
475C2×C4—521no—
476C2×C4#8817212yes—
477C2×C4#8817212yes—
478C2×C4#8819212yes—
479C2×C4#8819212yes—
480C2×C4C2×#612911yescharacteristic
481C2×C4C2×#613111yescharacteristic
482C2×C4#8825411yescharacteristic
483C2×C4#41×D1311yescharacteristic
484C2×C4#8825711yescharacteristic
485C2×C4C22×C22⋊D1311yescharacteristic
486C8—24no—
487C8—522no—
488C22—262no—
489C22—262no—
490C22—262no—
491C22—521no—
492C22—521no—
493C22—521no—
494C22—521no—
495C22#1171933211yescharacteristic
496C22#1171933311yescharacteristic
497C22C2×#8817211yescharacteristic
498C22C2×#8817211yescharacteristic
499C22D13×AGL(1,ℤ/8)11yescharacteristic
500C22#1171947811yescharacteristic
501C22C2×#8819211yescharacteristic
502C4—22no—
503C4—42no—
504C4—81no—
505C4—82no—
506C4—521no—
507C4—521no—
508C4—521no—
509C4—522no—
510C4—1042no—
511C4—1041no—
512C4#1171885014yes—
513C4#1171934611yescharacteristic
514C4#1171934711yescharacteristic
515C4#1171952211yescharacteristic
516C4#1171952911yescharacteristic
517C2—522no—
518C2#1311826111yescharacteristic
519C2C2×#1171885011yescharacteristic
520C2#1312444911yescharacteristic
521C2#1312496011yescharacteristic
522C2#1312500111yescharacteristic
523C2#1312604811yescharacteristic
524C2#1312606111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#477C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#477D13
hypocenterC13#24711
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
6. #13115785C2semidirect
7. #13115600C2semidirect
8. #13115577C2semidirect
9. #13115523C2semidirect
10. #13114841C2semidirect
11. C2×C13×#477C2semidirect
166. C2×#477D13semidirect
427. C13#24711semidirect

Maximal subgroups

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

subgroupindex
C2×#117184962
#131231832
C4×#882002
#131162602
#131160312
#131157852
#131156002
#131155772
#131155232
#131148412
C2×C13×#4772
#2471113