Finite Group Databasebeta

← #13126039

Subgroups — #13126039

Order 1664.

324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 113 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×#88144C211yesmaximal, characteristic
3C13×#483C211yesmaximal, characteristic
4#11718705C211yesmaximal, characteristic
5#11718632C211yesmaximal, characteristic
6#11718518C212yesmaximal, complemented
7#11718517C212yesmaximal, complemented
8#11718458C212yesmaximal, complemented
9#11718457C212yesmaximal, complemented
10#11718383C211yesmaximal, characteristic
11#11718380C211yesmaximal, characteristic
12C13×C22⋊Q8C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14Q8×Dic13C2211yescharacteristic
15#88198C2211yescharacteristic
16C2×C4⋊Dic13—21no—
17C2×C4⋊Dic13C2211yescharacteristic
18#88178C2211yescharacteristic
19C2×#6101—21no—
20C2×C4×Dic13C2211yescharacteristic
21#88144—21no—
22#88144—21no—
23#88144C2212yes—
24#88144C2212yes—
25#88143—21no—
26#88142C2211yescharacteristic
27#88141—21no—
28#88141C2211yescharacteristic
29#88132—21no—
30#88131—21no—
31C13×#106C2212yes—
32C13×#103C2212yes—
33C13×C22⋊C8C2211yescharacteristic
34#88075C2212yes—
35C22⋊#1055C2211yescharacteristic
36#88058C2212yes—
37#88056C2212yes—
38#88055C2212yes—
39#88054C2212yes—
40#88050C2212yes—
41#88048C2212yes—
42#88047C2212yes—
43C2×Q8×C13C2311yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13C2311yescharacteristic
46C22×Dic13—21no—
47C22×Dic13D411yescharacteristic
48C22×Dic13D411yescharacteristic
49C2×Dic26—21no—
50C2×Dic26C2311yescharacteristic
51C2×C8×C13C2312yes—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C13×C4⋊C4C2311yescharacteristic
56C13×C22⋊C4—21no—
57C22⋊Dic13—21no—
58C4⋊Dic13—21no—
59C4⋊Dic13—21no—
60C4⋊Dic13—22no—
61C4⋊Dic13—22no—
62C4⋊Dic13C2312yes—
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×Dic13D411yescharacteristic
74C4×Dic13D411yescharacteristic
75C4×Dic13C2311yescharacteristic
76C4×Dic13C2311yescharacteristic
77C2×#1055C2312yes—
78#3236—131nomaximal, Sylow
79C23×C13C2×D411yescharacteristic
80Q8×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—42no—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—41no—
93C2×Dic13—42no—
94C2×Dic13C2×D411yescharacteristic
95C2×Dic13C2×D411yescharacteristic
96C2×Dic13C2×D411yescharacteristic
97C2×Dic13C2×D411yescharacteristic
98Dic26—22no—
99Dic26—42no—
100C8×C13—22no—
101#1055—22no—
102#533—131no—
103C2×#125—131no—
104#501—132no—
105#491—132no—
106#484—131no—
107#484—131no—
108#483—131no—
109#483D1311yescharacteristic
110#479—132no—
111#479—132no—
112#432—131no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13#13712yes—
116C22×C13C22×D411yescharacteristic
117C4×C13—21no—
118C4×C13—41no—
119C4×C13—42no—
120C4×C13—41no—
121C4×C132−1+412yes—
122Dic13—21no—
123Dic13—21no—
124Dic13—21no—
125Dic13—21no—
126Dic13—41no—
127Dic13—41no—
128Dic13—42no—
129C4⋊Q8—131no—
130C4⋊Q8—131no—
131#125—132no—
132#125—132no—
133#125—261no—
134#125—261no—
135#125—261no—
136C22⋊Q8—131no—
137C22⋊Q8—261no—
138C22⋊Q8C2×D1311yescharacteristic
139C4×Q8—131no—
140C4×Q8—131no—
141C4×Q8—261no—
142#117—261no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—261no—
145C2×C4⋊C4—261no—
146C2×C4⋊C4C2×D1311yescharacteristic
147C2×C42—131no—
148#107—132no—
149#107—132no—
150#106—132no—
151#106C2×D1312yes—
152C4⋊C8—132no—
153#103—132no—
154#103—132no—
155#103—132no—
156#103C2×D1312yes—
157C22⋊C8—131no—
158C22⋊C8C2×D1311yescharacteristic
159#97—132no—
160C2×C13—22no—
161C2×C13#53611yescharacteristic
162C2×C13C2×#13711yescharacteristic
163C2×C13#57511yescharacteristic
164C2×Q8—131no—
165C2×Q8—261no—
166C2×Q8C22×D1311yescharacteristic
167C22×C4—21no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—261no—
171C22×C4C22×D1311yescharacteristic
172C2×C8—132no—
173C2×C8C22×D1312yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—132no—
177C4⋊C4—131no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4—262no—
181C4⋊C4—262no—
182C4⋊C4—261no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4—261no—
186C4⋊C4—261no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4C22×D1312yes—
190C4⋊C4C22×D1311yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—261no—
193C42—131no—
194C42—131no—
195C42—131no—
196C42—131no—
197C42—261no—
198C42—261no—
199C13#323611yescharacteristic, complemented, Sylow
200C23D4×D1311yescharacteristic
201Q8—22no—
202Q8—262no—
203Q8—522no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—131no—
210C2×C4—131no—
211C2×C4—131no—
212C2×C4—131no—
213C2×C4—262no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—262no—
217C2×C4—521no—
218C2×C4—522no—
219C2×C4D4×D1311yescharacteristic
220C2×C4C23×D1311yescharacteristic
221C8—22no—
222C8—262no—
223C22—21no—
224C22—21no—
225C22#8816912yes—
226C22C2×D4×D1311yescharacteristic
227C4—21no—
228C4—42no—
229C4—41no—
230C4—41no—
231C4—261no—
232C4—261no—
233C4—261no—
234C4—261no—
235C4—522no—
236C4—521no—
237C4—521no—
238C4#8825712yes—
239C2—22no—
240C2#1171935311yescharacteristic
241C2C2×#8816911yescharacteristic
242C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#483C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#483D13
hypocenterC13#3236
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. #11718518C2semidirect
7. #11718517C2semidirect
8. #11718458C2semidirect
9. #11718457C2semidirect
199. C13#3236semidirect

Maximal subgroups

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

subgroupindex
#117193272
C2×#881442
C13×#4832
#117187052
#117186322
#117185182
#117185172
#117184582
#117184572
#117183832
#117183802
#323613