Finite Group Databasebeta

← #13124955

Subgroups — #13124955

Order 1664.

424 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 119 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#11719301C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic, complemented
3C13×#480C211yesmaximal, characteristic, complemented
4#11718701C211yesmaximal, characteristic, complemented
5#11718628C211yesmaximal, characteristic, complemented
6#11718550C212yesmaximal, complemented
7#11718536C212yesmaximal, complemented
8#11718423C212yesmaximal, complemented
9#11718418C212yesmaximal, complemented
10#11718399C211yesmaximal, characteristic, complemented
11#11718380C211yesmaximal, characteristic, complemented
12C2×#6129—21no—
13C22×Dic26C2211yescharacteristic
14C13×#121C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16#88194C2211yescharacteristic
17#88193—21no—
18D4×Dic13C2211yescharacteristic
19C2×#6105C2212yes—
20#88184C2211yescharacteristic
21C2×#6101—21no—
22C2×C4×Dic13—21no—
23C2×C4×Dic13C2211yescharacteristic
24C2×#6095C2212yes—
25#88147C2211yescharacteristic
26#88142C2211yescharacteristic
27#88141—21no—
28#88141—21no—
29#88141C2212yes—
30#88141C2212yes—
31#88139—21no—
32#88135—21no—
33C13×#107C2212yes—
34C13×#102C2212yes—
35C13×C22⋊C8C2211yescharacteristic
36C22⋊#1055C2211yescharacteristic
37#88056C2212yes—
38#88055C2212yes—
39#88054C2212yes—
40#88050C2212yes—
41#88049C2212yes—
42#88047C2212yes—
43C2×D4×C13—21no—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48C2×C22⋊D13—21no—
49C2×C22⋊D13—21no—
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13D411yescharacteristic
53C22×Dic13D411yescharacteristic
54#6129—44no—
55C2×D52C2311yescharacteristic
56C2×C4×D13—21no—
57C2×Dic26—21no—
58C2×Dic26—24no—
59C2×Dic26—21no—
60C2×Dic26C2312yes—
61C2×C8×C13C2312yes—
62C13×C4⋊C4—21no—
63C13×C4⋊C4C2312yes—
64C13×C4⋊C4C2311yescharacteristic
65C13×C22⋊C4—21no—
66C22⋊Dic13—21no—
67#6105—24no—
68#6103—21no—
69#6103—21no—
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72#6101—22no—
73#6101—22no—
74C4×Dic13—22no—
75C4×Dic13—22no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C4×Dic13C2311yescharacteristic
80C2×#1055C2312yes—
81#6095—24no—
82#3112—131nomaximal, Sylow
83C23×C13—21no—
84C23×C13C2×D411yescharacteristic
85C22×D13—21no—
86D4×C13—22no—
87D4×C13—42no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—42no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2411yescharacteristic
94C22⋊D13—42no—
95C22⋊D13—42no—
96C22⋊D13—42no—
97C2×Dic13—24no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—21no—
102C2×Dic13—42no—
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106C2×Dic13C2×D411yescharacteristic
107D52—22no—
108C4×D13—42no—
109Dic26—24no—
110Dic26—22no—
111Dic26—42no—
112Dic26#4114yescomplemented
113C8×C13—22no—
114#1055—22no—
115#532—131no—
116C2×C4×Q8—131no—
117#480—131no—
118#480D1311yescharacteristic, complemented
119#477—132no—
120#460—132no—
121#448—131no—
122#448—131no—
123#440—132no—
124#440—132no—
125#432—131no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—41no—
129C22×C13—41no—
130C22×C13—41no—
131C22×C13AGL(1,ℤ/8)12yes—
132C22×C13C22×D411yescharacteristic
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—41no—
136C4×C13—21no—
137C4×C13—41no—
138C4×C13—42no—
139C4×C13C2×#4112yes—
140Dic13—24no—
141Dic13—21no—
142Dic13—21no—
143Dic13—21no—
144Dic13—41no—
145Dic13#13712yes—
146C2×#41—261no—
147C22×Q8—131no—
148C2×SD16—132no—
149C2×SD16—132no—
150C4⋊Q8—131no—
151#127—131no—
152#124—261no—
153#121—131no—
154#121—261no—
155#121C2×D1311yescharacteristic
156C4×Q8—132no—
157C4×Q8—132no—
158C4×Q8—261no—
159C4×Q8—261no—
160C4×D4—131no—
161C4×D4—131no—
162C4×D4—261no—
163C2×C4⋊C4—261no—
164C2×C4⋊C4C2×D1311yescharacteristic
165C2×C42—131no—
166C2×C42—261no—
167#107—132no—
168#107C2×D1312yes—
169C4⋊C8—132no—
170#103—132no—
171#103—132no—
172#102—132no—
173#102C2×D1312yes—
174C22⋊C8—131no—
175C22⋊C8C2×D1311yescharacteristic
176#97—132no—
177C2×C13—22no—
178C2×C13—81no—
179C2×C13#52511yescharacteristic
180C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C13C2×#13711yescharacteristic
182D13—81no—
183#41—524no—
184C2×Q8—132no—
185C2×Q8—261no—
186C2×Q8—264no—
187C2×Q8—261no—
188C2×D4—21no—
189C2×D4—131no—
190C2×D4—261no—
191C2×D4—261no—
192C2×D4—261no—
193C2×D4C22×D1311yescharacteristic
194C22×C4—21no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—261no—
198C22×C4—261no—
199C22×C4—261no—
200C22×C4C22×D1311yescharacteristic
201SD16—264no—
202SD16—264no—
203C2×C8—132no—
204C2×C8C22×D1312yes—
205C4⋊C4—21no—
206C4⋊C4—131no—
207C4⋊C4—262no—
208C4⋊C4—262no—
209C4⋊C4—261no—
210C4⋊C4C22×D1312yes—
211C4⋊C4C22×D1311yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—261no—
214C22⋊C4—261no—
215C22⋊C4—261no—
216C42—131no—
217C42—131no—
218C42—131no—
219C42—131no—
220C42—262no—
221C42—262no—
222C13#311211yescharacteristic, complemented, Sylow
223C23—21no—
224C23—261no—
225C23D4×D1311yescharacteristic
226Q8—134no—
227Q8—264no—
228Q8—262no—
229Q8—522no—
230D4—22no—
231D4—42no—
232D4—262no—
233D4—522no—
234D4—522no—
235D4—522no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—131no—
241C2×C4—131no—
242C2×C4—131no—
243C2×C4—131no—
244C2×C4—262no—
245C2×C4—264no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—261no—
249C2×C4—522no—
250C2×C4—522no—
251C2×C4D4×D1311yescharacteristic
252C2×C4C23×D1311yescharacteristic
253C8—22no—
254C8—262no—
255C22—21no—
256C22—21no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—521no—
261C22—521no—
262C22—521no—
263C22#8816512yes—
264C22C2×D4×D1311yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—132no—
269C4—261no—
270C4—261no—
271C4—261no—
272C4—264no—
273C4—521no—
274C4#41×D1312yes—
275C2—22no—
276C2—81no—
277C2—1041no—
278C2#1171936111yescharacteristic
279C2C2×#8816511yescharacteristic
280C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#480C2
socleC22×C13C22×D4
prime radical#11719301C2
hypercenter#480D13
hypocenterC13#3112
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#88141C2semidirect
3. C13×#480C2semidirect
4. #11718701C2semidirect
5. #11718628C2semidirect
6. #11718550C2semidirect
7. #11718536C2semidirect
8. #11718423C2semidirect
9. #11718418C2semidirect
10. #11718399C2semidirect
11. #11718380C2semidirect
112. Dic26#41semidirect
118. #480D13semidirect
222. C13#3112semidirect

Maximal subgroups

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

subgroupindex
#117193012
C2×#881412
C13×#4802
#117187012
#117186282
#117185502
#117185362
#117184232
#117184182
#117183992
#117183802
#311213