Finite Group Databasebeta

← #13124370

Subgroups — #13124370

Order 1664.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88166C211yesmaximal, characteristic, complemented
2C2×#88165C211yesmaximal, characteristic, complemented
3#11719420C211yesmaximal, characteristic, complemented
4#11719251C211yesmaximal, characteristic, complemented
5C13×#459C211yesmaximal, characteristic, complemented
6#11718814C211yesmaximal, characteristic, complemented
7#11718811C211yesmaximal, characteristic, complemented
8#11718736C211yesmaximal, characteristic, complemented
9#11718677C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718500C211yesmaximal, characteristic, complemented
12#11718432C211yesmaximal, characteristic, complemented
13D13×#102C211yesmaximal, characteristic, complemented
14#11718428C211yesmaximal, characteristic, complemented
15#11718423C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×D4×D13C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic, complemented
21C13×#127C2211yescharacteristic
22C4×D4×C13C2211yescharacteristic, complemented
23#88194C2211yescharacteristic
24#88193—21no—
25#88193—21no—
26#88191—21no—
27#88191—21no—
28#88190C2211yescharacteristic
29D4×Dic13C2211yescharacteristic, complemented
30C2×#6105C2211yescharacteristic
31C2×#6105C2211yescharacteristic, complemented
32C2×#6105C2211yescharacteristic, complemented
33C2×#6104C2211yescharacteristic
34C4×C22⋊D13—21no—
35C2×#6101—21no—
36#88166—24no—
37#88165—24no—
38C2×Dic52C2211yescharacteristic, complemented
39C2×#6095C2211yescharacteristic
40C2×#6094C2211yescharacteristic
41C2×C8×D13C2211yescharacteristic
42C4⋊C4×D13C2211yescharacteristic
43#88141C2211yescharacteristic, complemented
44#88135—21no—
45#88131—21no—
46#88129C2211yescharacteristic
47#88126C2211yescharacteristic
48C4×Dic26C2211yescharacteristic, complemented
49C13×C4⋊C8C2211yescharacteristic, complemented
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic, complemented
52#88072C2211yescharacteristic
53#88072C2211yescharacteristic, complemented
54#88061C2211yescharacteristic
55#88056C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88054C2211yescharacteristic, complemented
58#88050C2211yescharacteristic, complemented
59#88049C2211yescharacteristic
60C4⋊#1055C2211yescharacteristic, complemented
61C23×D13—21no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76#6129—22no—
77#6129—22no—
78#6129—22no—
79#6129D414yescomplemented
80D4×D13—22no—
81D4×D13—22no—
82C2×D52C2311yescharacteristic
83C2×C4×D13—21no—
84C2×C4×D13C2311yescharacteristic
85C2×Dic26C2311yescharacteristic
86C2×Dic26C2311yescharacteristic
87C13×D8—22no—
88C13×D8—22no—
89C2×C8×C13C2311yescharacteristic
90C2×C8×C13C2311yescharacteristic
91C13×C4⋊C4C2311yescharacteristic
92C13×C22⋊C4—21no—
93C42×C13C2311yescharacteristic
94C22⋊Dic13—21no—
95C22⋊Dic13—21no—
96C22⋊Dic13—21no—
97#6105—22no—
98#6105—22no—
99#6105—22no—
100#6104—22no—
101#6103—21no—
102#6103—21no—
103#6103D411yescharacteristic
104#6103D411yescharacteristic
105C4⋊Dic13C2311yescharacteristic
106#6101—21no—
107#6101—21no—
108#6101—21no—
109#6101D411yescharacteristic
110#6101D411yescharacteristic
111C4×Dic13—21no—
112C4×Dic13—21no—
113C4×Dic13C2311yescharacteristic
114C2×#1055C2311yescharacteristic
115C2×#1055C2311yescharacteristic
116Dic52—22no—
117#6095—22no—
118#6094—22no—
119C8×D13—22no—
120#3045—131nomaximal, Sylow
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C22×D13—21no—
125C22×D13—42no—
126C22×D13—81no—
127C22×D13—81no—
128C22×D13C2×D411yescharacteristic
129D4×C13—21no—
130D4×C13—21no—
131D4×C13—21no—
132D4×C13—21no—
133D4×C13—21no—
134D4×C13—81no—
135D4×C13—81no—
136D4×C13C2×D412yes—
137C2×C4×C13—21no—
138C2×C4×C13—81no—
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2411yescharacteristic
142C22⋊D13—24no—
143C22⋊D13—42no—
144C22⋊D13—42no—
145C22⋊D13—81no—
146C22⋊D13—81no—
147C2×Dic13—21no—
148C2×Dic13—24no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—42no—
152C2×Dic13—81no—
153C2×Dic13C2×D411yescharacteristic
154C2×Dic13C2×D411yescharacteristic
155C2×Dic13C2×D411yescharacteristic
156D52—21no—
157D52—21no—
158C4×D13—81no—
159C4×D13C2×D412yes—
160C4×D13#4112yes—
161Dic26—21no—
162Dic26—21no—
163Dic26—21no—
164Dic26C2×D412yes—
165C8×C13—21no—
166C8×C13—21no—
167#1055—21no—
168#1055—21no—
169C2×AGL(1,ℤ/8)—131no—
170C2×#135—131no—
171#535—131no—
172#520—131no—
173#464—131no—
174#464—131no—
175#463—131no—
176#463—131no—
177#460—131no—
178#460—131no—
179#459—131no—
180#459D1311yescharacteristic, complemented
181#424—131no—
182#417—131no—
183C2×#102—131no—
184C22×C13—22no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13C22×D411yescharacteristic
194C2×D13—21no—
195C2×D13—21no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C2×D13—84no—
200C2×D13#12112yes—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—41no—
204C4×C13C22×D411yescharacteristic
205C4×C13C2×#4111yescharacteristic
206Dic13—22no—
207Dic13—21no—
208Dic13—21no—
209Dic13—41no—
210Dic13—41no—
211Dic13#12112yes—
212C2×#41—131no—
213C2×#41—131no—
214C22×D4—131no—
215AGL(1,ℤ/8)—264no—
216#135—264no—
217C2×Q16—131no—
218C2×SD16—131no—
219C2×SD16—131no—
220C2×SD16—131no—
221C2×SD16—131no—
222C2×D8—131no—
223C2×D8C2×D1311yescharacteristic
224C2×D8C2×D1311yescharacteristic, complemented
225C2×M16—131no—
226C22×C8—131no—
227#127—131no—
228#127C2×D1311yescharacteristic
229#124—131no—
230#124—131no—
231#121—261no—
232#121—261no—
233#120—261no—
234#120—261no—
235C4×Q8—131no—
236C4×Q8—131no—
237C4×D4—131no—
238C4×D4—261no—
239C4×D4—261no—
240C4×D4C2×D1311yescharacteristic, complemented
241#117—131no—
242#117—261no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—261no—
245C4⋊C8—131no—
246C4⋊C8—131no—
247C4⋊C8—131no—
248C4⋊C8C2×D1311yescharacteristic, complemented
249#103—131no—
250#103—131no—
251#102—131no—
252#102—131no—
253#102—131no—
254#102—131no—
255#102C2×D1311yescharacteristic
256#102C2×D1311yescharacteristic, complemented
257C2×C13—42no—
258C2×C13—81no—
259C2×C13—81no—
260C2×C13C2×#12111yescharacteristic
261C2×C13#57611yescharacteristic
262C2×C13#57711yescharacteristic
263D13—22no—
264D13—81no—
265C24—261no—
266#41—134no—
267#41—262no—
268#41—262no—
269#41—262no—
270C2×Q8—131no—
271C2×Q8—131no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—131no—
275C2×D4—262no—
276C2×D4—262no—
277C2×D4—261no—
278C2×D4—261no—
279C2×D4—261no—
280C2×D4—261no—
281C2×D4—261no—
282C2×D4C22×D1311yescharacteristic
283C2×D4C22×D1311yescharacteristic
284C2×D4C22×D1311yescharacteristic
285C22×C4—21no—
286C22×C4—131no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—261no—
291Q16—262no—
292SD16—262no—
293SD16—262no—
294SD16—262no—
295SD16—262no—
296D8—22no—
297D8—22no—
298D8—262no—
299M16—262no—
300C2×C8—131no—
301C2×C8—131no—
302C2×C8—262no—
303C2×C8C22×D1311yescharacteristic
304C2×C8C22×D1311yescharacteristic
305C4⋊C4—131no—
306C4⋊C4—131no—
307C4⋊C4—131no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—261no—
311C4⋊C4C22×D1311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—131no—
314C22⋊C4—131no—
315C22⋊C4—261no—
316C22⋊C4—261no—
317C22⋊C4—261no—
318C22⋊C4—261no—
319C22⋊C4—261no—
320C42—131no—
321C42—261no—
322C42—261no—
323C42C22×D1311yescharacteristic
324C13#304511yescharacteristic, complemented, Sylow
325C23—21no—
326C23—21no—
327C23—21no—
328C23—131no—
329C23—261no—
330C23—522no—
331C23—1041no—
332C23—1041no—
333Q8—132no—
334Q8—261no—
335Q8—261no—
336Q8—261no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—81no—
343D4—81no—
344D4—264no—
345D4—261no—
346D4—261no—
347D4—522no—
348D4—522no—
349D4—1041no—
350D4—1041no—
351D4D4×D1312yes—
352C2×C4—21no—
353C2×C4—81no—
354C2×C4—131no—
355C2×C4—132no—
356C2×C4—132no—
357C2×C4—131no—
358C2×C4—131no—
359C2×C4—264no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—522no—
364C2×C4—1041no—
365C2×C4—1041no—
366C2×C4D4×D1311yescharacteristic
367C2×C4D4×D1311yescharacteristic
368C2×C4C23×D1311yescharacteristic
369C8—21no—
370C8—21no—
371C8—261no—
372C8—261no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—132no—
383C22—261no—
384C22—261no—
385C22—521no—
386C22—521no—
387C22—521no—
388C22—1044no—
389C22C2×D4×D1311yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—132no—
394C4—261no—
395C4—261no—
396C4—262no—
397C4—521no—
398C4—521no—
399C4C2×D4×D1311yescharacteristic
400C4#41×D1311yescharacteristic
401C2—42no—
402C2—81no—
403C2—81no—
404C2—262no—
405C2—1041no—
406C2D13×#12111yescharacteristic
407C2#1171946211yescharacteristic
408C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#459C2
socleC22×C13C22×D4
hypercenter#459D13
hypocenterC13#3045
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#88166C2semidirect
2. C2×#88165C2semidirect
3. #11719420C2semidirect
4. #11719251C2semidirect
5. C13×#459C2semidirect
6. #11718814C2semidirect
7. #11718811C2semidirect
8. #11718736C2semidirect
9. #11718677C2semidirect
10. #11718506C2semidirect
11. #11718500C2semidirect
12. #11718432C2semidirect
13. D13×#102C2semidirect
14. #11718428C2semidirect
15. #11718423C2semidirect
20. C2×C13×D8C22semidirect
22. C4×D4×C13C22semidirect
29. D4×Dic13C22semidirect
31. C2×#6105C22semidirect
32. C2×#6105C22semidirect
38. C2×Dic52C22semidirect
43. #88141C22semidirect
48. C4×Dic26C22semidirect
49. C13×C4⋊C8C22semidirect
51. C13×#102C22semidirect
53. #88072C22semidirect
55. #88056C22semidirect
56. #88054C22semidirect
57. #88054C22semidirect
58. #88050C22semidirect
60. C4⋊#1055C22semidirect
79. #6129D4semidirect
180. #459D13semidirect
224. C2×D8C2×D13semidirect
240. C4×D4C2×D13semidirect
248. C4⋊C8C2×D13semidirect
256. #102C2×D13semidirect
324. C13#3045semidirect

Maximal subgroups

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

subgroupindex
C2×#881662
C2×#881652
#117194202
#117192512
C13×#4592
#117188142
#117188112
#117187362
#117186772
#117185062
#117185002
#117184322
D13×#1022
#117184282
#117184232
#304513