Finite Group Databasebeta

← #13124963

Subgroups — #13124963

Order 1664.

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

normal subgroups only

This group has 380 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#11719327C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic
3C13×#483C211yesmaximal, characteristic
4#11718711C211yesmaximal, characteristic
5#11718632C211yesmaximal, characteristic
6#11718515C212yesmaximal, complemented
7#11718514C212yesmaximal, complemented
8#11718454C212yesmaximal, complemented
9#11718450C212yesmaximal, complemented
10#11718400C211yesmaximal, characteristic
11#11718380C211yesmaximal, characteristic
12C22×Dic26C2211yescharacteristic
13C13×C22⋊Q8C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15Q8×Dic13C2211yescharacteristic
16#88198C2211yescharacteristic
17C2×#6107C2212yes—
18#88178C2211yescharacteristic
19C2×#6101—21no—
20C2×C4×Dic13—21no—
21C2×C4×Dic13C2211yescharacteristic
22C2×Dic52C2212yes—
23#88143—21no—
24#88142C2211yescharacteristic
25#88141—21no—
26#88141—21no—
27#88141—21no—
28#88141C2212yes—
29#88141C2212yes—
30#88141C2211yescharacteristic
31#88132—21no—
32#88131—21no—
33C13×#106C2212yes—
34C13×#103C2212yes—
35C13×C22⋊C8C2211yescharacteristic
36C22⋊#1055C2211yescharacteristic
37#88056C2212yes—
38#88055C2212yes—
39#88054C2212yes—
40#88050C2212yes—
41#88050C2212yes—
42#88048C2212yes—
43C2×Q8×C13C2311yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13C2311yescharacteristic
46C22×Dic13—21no—
47C22×Dic13D411yescharacteristic
48C22×Dic13D411yescharacteristic
49C2×Dic26—21no—
50C2×Dic26—24no—
51C2×Dic26—21no—
52C2×Dic26C2311yescharacteristic
53C2×Dic26C2312yes—
54C2×C8×C13C2312yes—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2312yes—
58C13×C4⋊C4C2311yescharacteristic
59C13×C22⋊C4—21no—
60C22⋊Dic13—21no—
61#6107—24no—
62C4⋊Dic13—21no—
63C4⋊Dic13C2311yescharacteristic
64#6101—21no—
65#6101—21no—
66#6101—21no—
67#6101—21no—
68#6101—21no—
69#6101—22no—
70#6101—22no—
71C4×Dic13—21no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75C4×Dic13D411yescharacteristic
76C4×Dic13D411yescharacteristic
77C4×Dic13C2311yescharacteristic
78C4×Dic13C2311yescharacteristic
79C2×#1055C2312yes—
80Dic52—24no—
81#3113—131nomaximal, Sylow
82C23×C13C2×D411yescharacteristic
83Q8×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—42no—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2411yescharacteristic
91C2×Dic13—24no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13C2×D411yescharacteristic
98C2×Dic13C2×D411yescharacteristic
99C2×Dic13C2×D411yescharacteristic
100C2×Dic13C2×D411yescharacteristic
101Dic26—24no—
102Dic26—22no—
103Dic26—22no—
104Dic26—42no—
105Dic26#4114yes—
106C8×C13—22no—
107#1055—22no—
108#533—131no—
109C2×C4×Q8—131no—
110#483—131no—
111#483D1311yescharacteristic
112#475—132no—
113#462—132no—
114#451—131no—
115#451—131no—
116#441—132no—
117#441—132no—
118#432—131no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13#13712yes—
122C22×C13C22×D411yescharacteristic
123C4×C13—21no—
124C4×C13—41no—
125C4×C13—41no—
126C4×C13—42no—
127C4×C13C2×#4112yes—
128Dic13—24no—
129Dic13—21no—
130Dic13—21no—
131Dic13—21no—
132Dic13—41no—
133Dic13—41no—
134Dic13#13712yes—
135C22×Q8—131no—
136C2×Q16—132no—
137C2×Q16—132no—
138C4⋊Q8—131no—
139C4⋊Q8—131no—
140#125—261no—
141C22⋊Q8—131no—
142C22⋊Q8—261no—
143C22⋊Q8C2×D1311yescharacteristic
144C4×Q8—131no—
145C4×Q8—132no—
146C4×Q8—132no—
147C4×Q8—131no—
148C4×Q8—261no—
149C4×Q8—261no—
150C4×Q8—261no—
151#117—261no—
152C2×C4⋊C4—261no—
153C2×C4⋊C4C2×D1311yescharacteristic
154C2×C42—131no—
155C2×C42—261no—
156#106—132no—
157#106C2×D1312yes—
158C4⋊C8—132no—
159#103—132no—
160#103—132no—
161#103—132no—
162#103C2×D1312yes—
163C22⋊C8—131no—
164C22⋊C8C2×D1311yescharacteristic
165#97—132no—
166C2×C13—22no—
167C2×C13#52511yescharacteristic
168C2×C13C2×#13711yescharacteristic
169C2×C13C2×#13711yescharacteristic
170C2×Q8—132no—
171C2×Q8—131no—
172C2×Q8—261no—
173C2×Q8—264no—
174C2×Q8—261no—
175C2×Q8C22×D1311yescharacteristic
176C22×C4—21no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—261no—
180C22×C4C22×D1311yescharacteristic
181Q16—264no—
182Q16—264no—
183C2×C8—132no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—131no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4C22×D1311yescharacteristic
197C4⋊C4C22×D1312yes—
198C22⋊C4—21no—
199C22⋊C4—261no—
200C42—131no—
201C42—131no—
202C42—131no—
203C42—131no—
204C42—262no—
205C42—262no—
206C42—261no—
207C42—261no—
208C13#311311yescharacteristic, complemented, Sylow
209C23D4×D1311yescharacteristic
210Q8—22no—
211Q8—134no—
212Q8—264no—
213Q8—262no—
214Q8—262no—
215Q8—522no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—131no—
222C2×C4—131no—
223C2×C4—131no—
224C2×C4—131no—
225C2×C4—262no—
226C2×C4—264no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4D4×D1311yescharacteristic
232C2×C4C23×D1311yescharacteristic
233C8—22no—
234C8—262no—
235C22—21no—
236C22—21no—
237C22#8816912yes—
238C22C2×D4×D1311yescharacteristic
239C4—21no—
240C4—42no—
241C4—41no—
242C4—41no—
243C4—132no—
244C4—261no—
245C4—261no—
246C4—261no—
247C4—264no—
248C4—521no—
249C4—521no—
250C4#41×D1312yes—
251C2—22no—
252C2#1171936111yescharacteristic
253C2C2×#8816911yescharacteristic
254C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#483C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#483D13
hypocenterC13#3113
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
6. #11718515C2semidirect
7. #11718514C2semidirect
8. #11718454C2semidirect
9. #11718450C2semidirect
208. C13#3113semidirect

Maximal subgroups

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

subgroupindex
#117193272
C2×#881412
C13×#4832
#117187112
#117186322
#117185152
#117185142
#117184542
#117184502
#117184002
#117183802
#311313