Finite Group Databasebeta

← #16795224

Subgroups — #16795224

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131753C211yesmaximal, characteristic, complemented
2#13131683C211yesmaximal, characteristic, complemented
3#13130433C212yesmaximal, complemented
4#13130427C212yesmaximal, complemented
5#13130419C212yesmaximal, complemented
6#13130416C212yesmaximal, complemented
7#13130389C211yesmaximal, characteristic, complemented
8#13130129C211yesmaximal, characteristic, complemented
9C2×D4⋊#1057C211yesmaximal, characteristic, complemented
10M16×#1057C211yesmaximal, characteristic, complemented
11#13123640C211yesmaximal, characteristic
12C2×D4×Dic13C2211yescharacteristic
13C2×#88186C411yescharacteristic
14#11719227C2211yescharacteristic
15C2×C22⋊#1057—22no—
16D4×#1057—21no—
17D4×#1057—21no—
18D4×#1057C2212yes—
19D4×#1057C2212yes—
20#11719119C2211yescharacteristic
21#11719119C2211yescharacteristic
22C2×C4⋊#1057C2211yescharacteristic
23C2×C4×#1057C2211yescharacteristic
24#11719074C2212yescomplemented
25#11719073C2212yescomplemented
26#11719063—22no—
27#11719051—21no—
28D13⋊(C4⋊C8)—21no—
29C13×#418C411yescharacteristic
30#11718794C411yescharacteristic
31M16×Dic13C2211yescharacteristic
32#11718656C411yescharacteristic
33#11718446C412yes—
34#11718419C2212yes—
35#11718418C412yes—
36#11718417C2212yes—
37D4⋊#1057C2212yes—
38D4⋊#1057C2212yes—
39#11718256C2212yescomplemented
40#11718255C2212yescomplemented
41#11718251C2212yescomplemented
42C8×#1057C2212yescomplemented
43#11718244C2211yescharacteristic, complemented
44#11718244C2211yescharacteristic, complemented
45#11718243C2211yescharacteristic, complemented
46#11718243C2211yescharacteristic, complemented
47C22×D4×C13C2×C411yescharacteristic
48C23×Dic13—21no—
49C2×#6127C2×C411yescharacteristic
50C22×#1057—21no—
51C22×#1057—21no—
52C22×#1057—22no—
53C22×#1057—22no—
54C2×D13⋊C8—22no—
55C2×C13×M16C2×C411yescharacteristic
56C13×#117C2×C411yescharacteristic
57C2×C22⋊Dic13—21no—
58D4×Dic13—21no—
59D4×Dic13—21no—
60D4×Dic13C2×C412yes—
61D4×Dic13C2312yes—
62C2×#6105C2×C412yes—
63#88186C818yescomplemented
64C2×#6104C2×C412yes—
65C2×C4⋊Dic13C2×C411yescharacteristic
66C2×C4×Dic13C2311yescharacteristic
67C2×#6099C2×C411yescharacteristic
68#88147C2×C411yescharacteristic
69#88147C2311yescharacteristic
70#88141C2×C411yescharacteristic
71#88141C2311yescharacteristic
72#88135—21no—
73#88135—21no—
74#88126—21no—
75C42×D13—21no—
76C22⋊#1057—21no—
77C22⋊#1057—22no—
78C22⋊#1057—22no—
79C22⋊#1057D412yes—
80#88112—22no—
81#88111—22no—
82C4⋊#1057—21no—
83C4⋊#1057D411yescharacteristic
84C4⋊#1057D411yescharacteristic
85C4⋊#1057C2311yescharacteristic
86C4⋊#1057C2311yescharacteristic
87C4⋊#1057C2312yes—
88C4×#1057—22no—
89C4×#1057—21no—
90C4×#1057—21no—
91C4×#1057C2311yescharacteristic
92C4×#1057C2311yescharacteristic
93C4×#1057C2312yes—
94C13×#102C2×C412yes—
95C13×#102C2×C412yes—
96#88061C2×C412yes—
97#88056C2×C412yes—
98#88055C2×C412yes—
99C8×Dic13C2312yes—
100#88048C2×C412yes—
101#88047C2×C412yes—
102#17852—131nomaximal, Sylow
103C24×C13—21no—
104C2×D4×C13—21no—
105C2×D4×C13—22no—
106C2×D4×C13C2×C814yescomplemented
107C2×D4×C13C22×C412yes—
108C22×C4×C13C22×C411yescharacteristic
109C2×C22⋊D13—21no—
110C22×Dic13—21no—
111C22×Dic13—22no—
112C22×Dic13—22no—
113C22×Dic13—81no—
114C22×Dic13—81no—
115C22×Dic13C2×D411yescharacteristic
116C22×Dic13#4111yescharacteristic
117#6127—22no—
118#6127C2×C814yescomplemented
119C2×D52C22×C411yescharacteristic
120C2×C4×D13—21no—
121C2×C4×D13—21no—
122C2×C4×D13—21no—
123C2×Dic26C22×C411yescharacteristic
124C2×#1057—21no—
125C2×#1057—22no—
126C2×#1057—21no—
127C2×#1057—21no—
128C2×#1057—21no—
129C2×#1057—42no—
130C2×#1057—82no—
131C2×#1057—82no—
132C2×#1057—81no—
133C2×#1057C2×D412yes—
134C2×#1057C2×D412yes—
135D13⋊C8—82no—
136C13×M16—22no—
137C2×C8×C13C22×C412yes—
138C13×C4⋊C4C22×C411yescharacteristic
139C13×C4⋊C4C22×C411yescharacteristic
140C13×C22⋊C4—21no—
141C42×C13—21no—
142C22⋊Dic13—22no—
143C22⋊Dic13—22no—
144#6105C2×C818yescomplemented
145#6104C2×C818yescomplemented
146#6103—21no—
147#6103—21no—
148C4⋊Dic13—21no—
149C4⋊Dic13C22×C412yes—
150#6101—21no—
151#6101—21no—
152C4×Dic13—21no—
153C4×Dic13—21no—
154C4×Dic13C22×C411yescharacteristic
155C4×Dic13C2×D411yescharacteristic
156C4×Dic13#4111yescharacteristic
157C4×Dic13C2411yescharacteristic
158#6099C2×C814yescomplemented
159C2×#1055C22×C412yes—
160#2988—131no—
161#2972—131no—
162C4×AGL(1,ℤ/8)—131no—
163#1580—132no—
164SD16⋊C8—132no—
165C8×SD16—132no—
166C8×D8—132no—
167#1565—131no—
168#1476—131no—
169C2×D4⋊C8—131no—
170C8×M16—131no—
171C23×C13—22no—
172C23×C13—24no—
173C23×C13—81no—
174C23×C13—81no—
175C23×C13C4×D411yescharacteristic
176C22×D13—21no—
177D4×C13—22no—
178D4×C13—24no—
179D4×C13C22×C814yes—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13C4×D411yescharacteristic
183C2×C4×C13C22×C812yes—
184C2×C4×C13#13112yes—
185C2×C4×C13C23×C411yescharacteristic
186C22⋊D13—24no—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13—21no—
190C2×Dic13—22no—
191C2×Dic13—41no—
192C2×Dic13—42no—
193C2×Dic13—42no—
194C2×Dic13—82no—
195C2×Dic13—81no—
196C2×Dic13C4×D411yescharacteristic
197C2×Dic13C4×D411yescharacteristic
198C2×Dic13C22×D411yescharacteristic
199C2×Dic13C2×#4111yescharacteristic
200D52—21no—
201D52C22×C812yes—
202C4×D13—24no—
203C4×D13—41no—
204C4×D13—41no—
205C4×D13—81no—
206Dic26—21no—
207Dic26C22×C812yes—
208#1057—22no—
209#1057—22no—
210#1057—22no—
211#1057—41no—
212#1057—42no—
213#1057—41no—
214#1057—41no—
215C8×C13—22no—
216#1055C22×C814yes—
217C2×AGL(1,ℤ/8)—131no—
218C4×#41—131no—
219C2×C4×D4—131no—
220C8×Q8—132no—
221#442—132no—
222#440—132no—
223C4×SD16—132no—
224C4×D8—132no—
225C8×D4—132no—
226C8×D4—132no—
227C8×D4—132no—
228C8×D4—262no—
229C8×D4—261no—
230C8×D4—261no—
231#431—131no—
232#431—131no—
233#431—261no—
234#428—131no—
235C2×C4⋊C8—131no—
236C2×C4⋊C8—261no—
237#418#26111yescharacteristic
238#417—131no—
239C2×C22⋊C8—262no—
240C4×M16—131no—
241C2×C4×C8—131no—
242#335—132no—
243#334—132no—
244Q8⋊C8—131no—
245Q8⋊C8—131no—
246D4⋊C8—131no—
247D4⋊C8—132no—
248D4⋊C8—132no—
249D4⋊C8—131no—
250#322—132no—
251C82—132no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—24no—
255C22×C13—42no—
256C22×C13—42no—
257C22×C13—84no—
258C22×C13C8×D412yes—
259C22×C13C2×C4×D411yescharacteristic
260C2×D13—22no—
261C2×D13—41no—
262C2×D13—41no—
263C4×C13—41no—
264C4×C13—41no—
265C4×C13C8×D412yes—
266C4×C13C23×C811yescharacteristic
267C4×C13C2×#13111yescharacteristic
268Dic13—22no—
269Dic13—21no—
270Dic13—21no—
271Dic13—21no—
272Dic13—42no—
273Dic13#57611yescharacteristic
274Dic13#57711yescharacteristic
275C2×#41—131no—
276C22×D4C2×#26111yescharacteristic
277C23×C4—261no—
278AGL(1,ℤ/8)—138no—
279C2×SD16—132no—
280C2×D8—132no—
281C2×M16—131no—
282C2×M16C2×#26111yescharacteristic
283C22×C8—262no—
284C22×C8—262no—
285C22×C8—262no—
286C22×C8—261no—
287C22×C8—261no—
288C4×Q8—131no—
289C4×Q8—131no—
290C4×D4—132no—
291C4×D4—132no—
292C4×D4—131no—
293C4×D4—131no—
294C4×D4—261no—
295C4×D4—261no—
296C4×D4—261no—
297C4×D4—261no—
298#117—261no—
299#117C2×#26111yescharacteristic
300C2×C4⋊C4—131no—
301C2×C22⋊C4—261no—
302C2×C42—131no—
303C2×C42—261no—
304#107—132no—
305#106—132no—
306C4⋊C8—131no—
307C4⋊C8—131no—
308C4⋊C8—132no—
309C4⋊C8—131no—
310C4⋊C8—131no—
311C4⋊C8—261no—
312C4⋊C8—262no—
313#103—132no—
314#102—132no—
315#102C2×#26112yes—
316#102C2×#26112yes—
317C22⋊C8—132no—
318C22⋊C8—262no—
319C22⋊C8—262no—
320C22⋊C8—262no—
321C22⋊C8—261no—
322#97—132no—
323C4×C8—132no—
324C4×C8—132no—
325C4×C8—131no—
326C4×C8—131no—
327C4×C8—261no—
328C4×C8—261no—
329C4×C8—262no—
330C2×C13—22no—
331C2×C13—44no—
332C2×C13C2×C8×D411yescharacteristic
333C2×C13#294611yescharacteristic
334C2×C13#295611yescharacteristic
335D13—42no—
336C24—21no—
337#41—134no—
338#41—262no—
339C2×Q8—131no—
340C2×D4—22no—
341C2×D4—21no—
342C2×D4—131no—
343C2×D4—261no—
344C2×D4D13⋊C814yescomplemented
345C2×D4C22×#26112yes—
346C22×C4—131no—
347C22×C4—131no—
348C22×C4—261no—
349C22×C4—261no—
350C22×C4—262no—
351C22×C4—262no—
352C22×C4—261no—
353C22×C4—261no—
354C22×C4—1041no—
355C22×C4—1041no—
356C22×C4C22×#26111yescharacteristic
357SD16—138no—
358D8—138no—
359M16—22no—
360M16—134no—
361C2×C8—132no—
362C2×C8—132no—
363C2×C8—132no—
364C2×C8—261no—
365C2×C8—261no—
366C2×C8—261no—
367C2×C8—261no—
368C2×C8—262no—
369C2×C8—522no—
370C2×C8—1042no—
371C2×C8—1042no—
372C2×C8—1042no—
373C2×C8—1041no—
374C2×C8C22×#26112yes—
375C4⋊C4—132no—
376C4⋊C4—261no—
377C4⋊C4—261no—
378C4⋊C4—261no—
379C4⋊C4C22×#26111yescharacteristic
380C4⋊C4C22×#26111yescharacteristic
381C22⋊C4—21no—
382C22⋊C4—261no—
383C22⋊C4—261no—
384C22⋊C4—262no—
385C22⋊C4—262no—
386C42—21no—
387C42—131no—
388C42—131no—
389C42—131no—
390C42—131no—
391C42—261no—
392C42—261no—
393C13#1785211yescharacteristic, complemented, Sylow
394C23—22no—
395C23—24no—
396C23—81no—
397C23—81no—
398C23—261no—
399C23D4×#26111yescharacteristic
400Q8—132no—
401Q8—261no—
402D4—24no—
403D4—22no—
404D4—132no—
405D4—264no—
406D4—261no—
407D4C2×D13⋊C814yes—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—131no—
411C2×C4—131no—
412C2×C4—131no—
413C2×C4—131no—
414C2×C4—261no—
415C2×C4—261no—
416C2×C4—261no—
417C2×C4—264no—
418C2×C4—262no—
419C2×C4—521no—
420C2×C4—521no—
421C2×C4—522no—
422C2×C4—522no—
423C2×C4—521no—
424C2×C4—1041no—
425C2×C4—1042no—
426C2×C4—1041no—
427C2×C4C2×D13⋊C812yes—
428C2×C4#8823812yes—
429C2×C4D4×#26111yescharacteristic
430C2×C4C23×#26111yescharacteristic
431C8—22no—
432C8—134no—
433C8—262no—
434C8—262no—
435C8—262no—
436C8—521no—
437C8—522no—
438C8—521no—
439C8—521no—
440C22—21no—
441C22—21no—
442C22—24no—
443C22—42no—
444C22—42no—
445C22—84no—
446C22—262no—
447C22—521no—
448C22—521no—
449C22#1171906312yes—
450C22C2×D4×#26111yescharacteristic
451C4—41no—
452C4—41no—
453C4—131no—
454C4—131no—
455C4—262no—
456C4—261no—
457C4—261no—
458C4—261no—
459C4—522no—
460C4#1171906312yes—
461C4C22×D13⋊C811yescharacteristic
462C4C2×#8823811yescharacteristic
463C2—22no—
464C2—44no—
465C2—522no—
466C2C2×#1171906311yescharacteristic
467C2#1313159311yescharacteristic
468C2#1313161011yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC13×#418C4
socleC22×C13C2×C4×D4
prime radicalC2×#88186C4
cosocleC4×Dic13C24
hypercenter#418#261
hypocenterC13#17852
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #13131753C2semidirect
2. #13131683C2semidirect
3. #13130433C2semidirect
4. #13130427C2semidirect
5. #13130419C2semidirect
6. #13130416C2semidirect
7. #13130389C2semidirect
8. #13130129C2semidirect
9. C2×D4⋊#1057C2semidirect
10. M16×#1057C2semidirect
24. #11719074C22semidirect
25. #11719073C22semidirect
39. #11718256C22semidirect
40. #11718255C22semidirect
41. #11718251C22semidirect
42. C8×#1057C22semidirect
43. #11718244C22semidirect
44. #11718244C22semidirect
45. #11718243C22semidirect
46. #11718243C22semidirect
63. #88186C8semidirect
106. C2×D4×C13C2×C8semidirect
118. #6127C2×C8semidirect
144. #6105C2×C8semidirect
145. #6104C2×C8semidirect
158. #6099C2×C8semidirect
344. C2×D4D13⋊C8semidirect
393. C13#17852semidirect

Maximal subgroups

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

subgroupindex
#131317532
#131316832
#131304332
#131304272
#131304192
#131304162
#131303892
#131301292
C2×D4⋊#10572
M16×#10572
#131236402
#1785213