Finite Group Databasebeta

← #13126003

Subgroups — #13126003

Order 1664.

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

normal subgroups only

This group has 334 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#11719305C211yesmaximal, characteristic
2C2×#88144C211yesmaximal, characteristic, complemented
3C13×#481C211yesmaximal, characteristic
4#11718694C211yesmaximal, characteristic
5#11718631C211yesmaximal, characteristic, complemented
6#11718519C212yesmaximal, complemented
7#11718518C212yesmaximal, complemented
8#11718429C212yesmaximal, complemented
9#11718424C212yesmaximal, complemented
10#11718382C211yesmaximal, characteristic, complemented
11#11718379C211yesmaximal, characteristic, complemented
12C13×#121C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14#88190C2211yescharacteristic
15#88189—21no—
16D4×Dic13—21no—
17D4×Dic13C2211yescharacteristic
18C2×C4⋊Dic13—21no—
19C2×C4⋊Dic13C2211yescharacteristic
20#88178C2211yescharacteristic
21C2×#6101—21no—
22C2×C4×Dic13C2211yescharacteristic
23#88144—21no—
24#88144—21no—
25#88144C2212yes—
26#88144C2212yes—
27#88144C2211yescharacteristic
28#88141C2211yescharacteristic
29#88133—21no—
30#88131—21no—
31C13×#106C2212yes—
32C13×#102C2212yes—
33C13×C22⋊C8C2211yescharacteristic
34#88072C2212yes—
35C22⋊#1055C2211yescharacteristic
36#88057C2212yes—
37#88056C2212yes—
38#88054C2212yes—
39C8×Dic13C2212yes—
40#88050C2212yes—
41#88047C2212yes—
42#88047C2212yes—
43C2×D4×C13—21no—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C22×Dic13—21no—
48C22×Dic13—21no—
49C22×Dic13D411yescharacteristic
50C22×Dic13D411yescharacteristic
51C2×Dic26C2311yescharacteristic
52C2×C8×C13C2312yes—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C13×C4⋊C4C2311yescharacteristic
56C13×C22⋊C4—21no—
57C22⋊Dic13—21no—
58C22⋊Dic13—21no—
59C22⋊Dic13—21no—
60C22⋊Dic13—21no—
61C4⋊Dic13—21no—
62C4⋊Dic13—21no—
63C4⋊Dic13—22no—
64C4⋊Dic13—22no—
65C4⋊Dic13C2312yes—
66C4⋊Dic13C2311yescharacteristic
67#6101—21no—
68#6101—21no—
69#6101—21no—
70#6101—22no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13D411yescharacteristic
74C4×Dic13D411yescharacteristic
75C4×Dic13C2311yescharacteristic
76C4×Dic13C2311yescharacteristic
77C2×#1055C2312yes—
78#3232—131nomaximal, Sylow
79C23×C13—21no—
80C23×C13C2×D411yescharacteristic
81D4×C13—22no—
82D4×C13—42no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—42no—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—22no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—41no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13C2×D411yescharacteristic
97C2×Dic13C2×D411yescharacteristic
98C2×Dic13C2×D411yescharacteristic
99C2×Dic13C2×D411yescharacteristic
100Dic26—22no—
101C8×C13—22no—
102#1055—22no—
103#529—131no—
104C2×#125—131no—
105#499—132no—
106#488—132no—
107#484—131no—
108#483—131no—
109#481D1311yescharacteristic
110#480—131no—
111#479—132no—
112#478—132no—
113#431—131no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13—41no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13#13512yes—
120C22×C13C22×D411yescharacteristic
121C4×C13—21no—
122C4×C13—41no—
123C4×C13—42no—
124C4×C132−1+412yes—
125Dic13—21no—
126Dic13—21no—
127Dic13—21no—
128Dic13—21no—
129Dic13—41no—
130Dic13—42no—
131Dic13—41no—
132#126—261no—
133#125—132no—
134#125—132no—
135#125—131no—
136#125—261no—
137#125—261no—
138#124—131no—
139#123—261no—
140C22⋊Q8—131no—
141#121C2×D1311yescharacteristic
142C4×Q8—131no—
143C4×D4—131no—
144C4×D4—261no—
145#117—261no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4—261no—
148C2×C4⋊C4—261no—
149C2×C4⋊C4C2×D1311yescharacteristic
150C2×C42—131no—
151#107—132no—
152#107—132no—
153#106—132no—
154#106C2×D1312yes—
155C4⋊C8—132no—
156#103—132no—
157#103—132no—
158#102—132no—
159#102C2×D1312yes—
160C22⋊C8—131no—
161C22⋊C8C2×D1311yescharacteristic
162C4×C8—132no—
163C2×C13—22no—
164C2×C13—81no—
165C2×C13#53611yescharacteristic
166C2×C13C2×#13511yescharacteristic
167C2×C13#57511yescharacteristic
168C2×Q8—131no—
169C2×D4—21no—
170C2×D4C22×D1311yescharacteristic
171C22×C4—21no—
172C22×C4—131no—
173C22×C4—131no—
174C22×C4—261no—
175C22×C4—261no—
176C22×C4C22×D1311yescharacteristic
177C2×C8—132no—
178C2×C8C22×D1312yes—
179C4⋊C4—21no—
180C4⋊C4—132no—
181C4⋊C4—131no—
182C4⋊C4—262no—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—261no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4C22×D1312yes—
192C4⋊C4C22×D1311yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—261no—
195C22⋊C4—261no—
196C22⋊C4—261no—
197C22⋊C4—261no—
198C42—131no—
199C42—131no—
200C42—131no—
201C42—131no—
202C42—261no—
203C13#323211yescharacteristic, complemented, Sylow
204C23—21no—
205C23D4×D1311yescharacteristic
206Q8—262no—
207D4—22no—
208D4—42no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—42no—
213C2×C4—131no—
214C2×C4—131no—
215C2×C4—131no—
216C2×C4—131no—
217C2×C4—262no—
218C2×C4—261no—
219C2×C4—261no—
220C2×C4—262no—
221C2×C4—521no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4D4×D1311yescharacteristic
225C2×C4C23×D1311yescharacteristic
226C8—22no—
227C8—262no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22#8817012yes—
234C22C2×D4×D1311yescharacteristic
235C4—21no—
236C4—41no—
237C4—42no—
238C4—261no—
239C4—261no—
240C4—261no—
241C4—261no—
242C4—522no—
243C4—521no—
244C4—521no—
245C4#8825712yes—
246C2—22no—
247C2—81no—
248C2#1171935311yescharacteristic
249C2C2×#8817011yescharacteristic
250C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#481C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#481D13
hypocenterC13#3232
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#88144C2semidirect
5. #11718631C2semidirect
6. #11718519C2semidirect
7. #11718518C2semidirect
8. #11718429C2semidirect
9. #11718424C2semidirect
10. #11718382C2semidirect
11. #11718379C2semidirect
203. C13#3232semidirect

Maximal subgroups

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

subgroupindex
#117193052
C2×#881442
C13×#4812
#117186942
#117186312
#117185192
#117185182
#117184292
#117184242
#117183822
#117183792
#323213