Finite Group Databasebeta

← #16021072

Subgroups — #16021072

Order 3328.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127986C211yesmaximal, characteristic, complemented
2#13127974C211yesmaximal, characteristic, complemented
3#13117155C212yesmaximal, complemented
4#13117153C211yesmaximal, characteristic, complemented
5#13117148C211yesmaximal, characteristic, complemented
6#13117147C212yesmaximal, complemented
7#13117144C212yesmaximal, complemented
8C2×#11718041C211yesmaximal, characteristic, complemented
9D13×SD64C212yesmaximal, complemented
10#13117129C211yesmaximal, characteristic, complemented
11C13×#2262C211yesmaximal, characteristic, complemented
12#11719476—21no—
13#11719474—21no—
14C13×#508C2211yescharacteristic
15C13×#508C2211yescharacteristic, complemented
16#11718856—21no—
17#11718854—21no—
18#11718580C2212yes—
19D13×Q32C2212yescomplemented
20#11718576—22no—
21#11718575—22no—
22#11718573C2212yescomplemented
23D13×D16C2212yes—
24C2×Dic104C2211yescharacteristic, complemented
25C2×D208C2211yescharacteristic
26#11718562C2211yescharacteristic
27C13×Q64C2211yescharacteristic, complemented
28C13×SD64C2211yescharacteristic, complemented
29C13×SD64C2211yescharacteristic, complemented
30C13×D32C2211yescharacteristic, complemented
31C2×C13×C32C2211yescharacteristic, complemented
32#11718114C2212yescomplemented
33#11718113C2212yescomplemented
34#11718112C2212yescomplemented
35#11718111C2212yescomplemented
36#11718091C2211yescharacteristic, complemented
37#11718041C2212yescomplemented
38#11718041C2212yescomplemented
39#11718039C2212yescomplemented
40D13×C32C2212yescomplemented
41#88257—41no—
42#88256—41no—
43C13×#135—21no—
44C13×#135—21no—
45#88205—41no—
46#88203—41no—
47#88173—22no—
48Q16×D13—22no—
49#88169—42no—
50#88168—42no—
51#88166—22no—
52D8×D13—22no—
53C2×Dic52—21no—
54C2×D104—21no—
55#88155D411yescharacteristic
56C13×Q32C2311yescharacteristic
57C13×Q32C2311yescharacteristic
58C13×SD32—21no—
59C13×SD32—21no—
60C13×D16C2311yescharacteristic
61C13×D16C2311yescharacteristic
62C2×C13×C16C2311yescharacteristic
63#88069—22no—
64#88068—22no—
65#88067—22no—
66#88066—22no—
67#88052D411yescharacteristic
68Dic104—21no—
69Dic104C2312yes—
70D208—21no—
71D208C2312yes—
72#88038D412yes—
73C16×D13C2312yes—
74C13×C32C2311yescharacteristic
75C13×C32C2311yescharacteristic
76#88034C2312yes—
77#33983—131nomaximal, Sylow
78C13×#41—41no—
79C13×#41—41no—
80#6131—42no—
81Q8×D13—42no—
82#6129—42no—
83#6129—82no—
84D4×D13—42no—
85D4×D13—82no—
86#6127—81no—
87#6127—81no—
88#6127D811yescharacteristic
89C2×D52—41no—
90C2×D52—81no—
91C2×Dic26—41no—
92C2×Dic26—81no—
93C13×Q16—21no—
94C13×Q16—21no—
95C13×SD16—41no—
96C13×SD16—41no—
97C13×D8—21no—
98C13×D8—21no—
99C2×C8×C13C2×D411yescharacteristic
100#6107—42no—
101#6106—42no—
102#6105—42no—
103#6104—42no—
104#6099D811yescharacteristic
105Dic52—22no—
106Dic52—41no—
107D104—22no—
108D104—41no—
109#6094D812yes—
110C8×D13C2×D412yes—
111C13×C16C2×D411yescharacteristic
112C13×C16C2411yescharacteristic
113#6090C2×D412yes—
114#3417—131no—
115#3415—131no—
116#2264—131no—
117#2264—132no—
118#2263—131no—
119#2263—132no—
120#2262—132no—
121#2262D1311yescharacteristic, complemented
122C2×SD64—132no—
123C2×SD64—131no—
124#2258—131no—
125C22×D13—81no—
126C22×D13—82no—
127Q8×C13—41no—
128Q8×C13—41no—
129D4×C13—41no—
130D4×C13—41no—
131D4×C13—81no—
132D4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13C2×D811yescharacteristic
136C22⋊D13—82no—
137C22⋊D13—82no—
138C22⋊D13D1612yes—
139C2×Dic13—81no—
140C2×Dic13—82no—
141D52—42no—
142D52—82no—
143D52—81no—
144D52D1611yescharacteristic
145C4×D13—82no—
146C4×D13—82no—
147C4×D13C2×D812yes—
148Dic26—42no—
149Dic26—81no—
150Dic26—82no—
151Dic26D1611yescharacteristic
152C8×C13C2×D811yescharacteristic
153C8×C13C22×D411yescharacteristic
154#1055C2×D812yes—
155#578—261no—
156#576—261no—
157#510—262no—
158#510—261no—
159#509—262no—
160#509—261no—
161#508—132no—
162#508—132no—
163#508C2×D1311yescharacteristic
164#508C2×D1311yescharacteristic, complemented
165C2×Q32—132no—
166C2×Q32—131no—
167C2×D16—132no—
168C2×D16—131no—
169#504—131no—
170Q64—132no—
171Q64C2×D1311yescharacteristic, complemented
172SD64—132no—
173SD64—132no—
174SD64—132no—
175SD64—132no—
176SD64C2×D1311yescharacteristic, complemented
177SD64C2×D1311yescharacteristic, complemented
178D32—132no—
179D32C2×D1311yescharacteristic, complemented
180M64—131no—
181M64—132no—
182C2×C32—132no—
183C2×C32C2×D1311yescharacteristic, complemented
184C22×C13—81no—
185C22×C13—81no—
186C22×C13C2×D1611yescharacteristic
187C2×D13—82no—
188C2×D13—322no—
189C2×D13—321no—
190C2×D13C2×D1612yes—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13C2×D1611yescharacteristic
194C4×C13C22×D811yescharacteristic
195Dic13—82no—
196Dic13C2×D1612yes—
1972−1+4—521no—
198H(5,𝔽2)—521no—
199#137—522no—
200#137—521no—
201AGL(1,ℤ/8)—522no—
202AGL(1,ℤ/8)—521no—
203#135—21no—
204#135—21no—
205#135—262no—
206#135—262no—
207C2×Q16—262no—
208C2×Q16—261no—
209C2×D8—262no—
210C2×D8—261no—
211#131—131no—
212Q32—132no—
213Q32—262no—
214Q32—261no—
215Q32C22×D1311yescharacteristic
216Q32C22×D1311yescharacteristic
217SD32—21no—
218SD32—21no—
219SD32—262no—
220SD32—262no—
221D16—132no—
222D16—262no—
223D16—261no—
224D16C22×D1311yescharacteristic
225D16C22×D1311yescharacteristic
226M32—131no—
227M32—132no—
228C2×C16—132no—
229C2×C16C22×D1311yescharacteristic
230C32—132no—
231C32C22×D1311yescharacteristic
232C32C22×D1311yescharacteristic
233C2×C13—21no—
234C2×C13—161no—
235C2×C13—161no—
236C2×C13C22×D1611yescharacteristic
237D13—22no—
238D13—162no—
239#41—41no—
240#41—41no—
241#41—131no—
242#41—522no—
243#41—522no—
244#41—1041no—
245#41—1041no—
246#41—1042no—
247C2×Q8—522no—
248C2×Q8—521no—
249C2×Q8—1041no—
250C2×D4—522no—
251C2×D4—521no—
252C2×D4—1041no—
253C2×D4—1042no—
254Q16—21no—
255Q16—21no—
256Q16—262no—
257Q16—522no—
258Q16—521no—
259SD16—41no—
260SD16—41no—
261SD16—522no—
262SD16—522no—
263D8—21no—
264D8—21no—
265D8—262no—
266D8—522no—
267D8—521no—
268M16—131no—
269M16—132no—
270C2×C8—132no—
271C2×C8D4×D1311yescharacteristic
272C16—132no—
273C16D4×D1311yescharacteristic
274C16C23×D1311yescharacteristic
275C13#3398311yescharacteristic, complemented, Sylow
276C23—1042no—
277C23—1041no—
278Q8—41no—
279Q8—41no—
280Q8—131no—
281Q8—522no—
282Q8—1042no—
283Q8—1041no—
284D4—41no—
285D4—41no—
286D4—81no—
287D4—81no—
288D4—132no—
289D4—131no—
290D4—522no—
291D4—1042no—
292D4—1042no—
293D4—1042no—
294D4—1041no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—132no—
298C2×C4—1042no—
299C2×C4—1042no—
300C2×C4—1042no—
301C2×C4—1041no—
302C2×C4D8×D1311yescharacteristic
303C8—132no—
304C8D8×D1311yescharacteristic
305C8C2×D4×D1311yescharacteristic
306C22—81no—
307C22—81no—
308C22—132no—
309C22—1042no—
310C22—4161no—
311C22—4162no—
312C22D13×D1611yescharacteristic
313C4—81no—
314C4—81no—
315C4—132no—
316C4—1042no—
317C4D13×D1611yescharacteristic
318C4C2×D8×D1311yescharacteristic
319C2—21no—
320C2—161no—
321C2—161no—
322C2—262no—
323C2—2082no—
324C2C2×D13×D1611yescharacteristic
subgroupG/H
centerC2C2×D13×D16
commutator, cosocleC13×C16C24
FrattiniC16C23×D13
FittingC13×#2262C2
socleC2×C13C22×D16
hypercenter#2262D13
hypocenterC13#33983
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2262

Complements

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

NH ≅ G/Ntype
1. #13127986C2semidirect
2. #13127974C2semidirect
3. #13117155C2semidirect
4. #13117153C2semidirect
5. #13117148C2semidirect
6. #13117147C2semidirect
7. #13117144C2semidirect
8. C2×#11718041C2semidirect
9. D13×SD64C2semidirect
10. #13117129C2semidirect
11. C13×#2262C2semidirect
15. C13×#508C22semidirect
19. D13×Q32C22semidirect
22. #11718573C22semidirect
24. C2×Dic104C22semidirect
27. C13×Q64C22semidirect
28. C13×SD64C22semidirect
29. C13×SD64C22semidirect
30. C13×D32C22semidirect
31. C2×C13×C32C22semidirect
32. #11718114C22semidirect
33. #11718113C22semidirect
34. #11718112C22semidirect
35. #11718111C22semidirect
36. #11718091C22semidirect
37. #11718041C22semidirect
38. #11718041C22semidirect
39. #11718039C22semidirect
40. D13×C32C22semidirect
121. #2262D13semidirect
164. #508C2×D13semidirect
171. Q64C2×D13semidirect
176. SD64C2×D13semidirect
177. SD64C2×D13semidirect
179. D32C2×D13semidirect
183. C2×C32C2×D13semidirect
275. C13#33983semidirect

Maximal subgroups

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

subgroupindex
#131279862
#131279742
#131171552
#131171532
#131171482
#131171472
#131171442
C2×#117180412
D13×SD642
#131171292
C13×#22622
#3398313