Finite Group Databasebeta

← #13127553

Subgroups — #13127553

Order 1664.

372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719432C211yesmaximal, characteristic, complemented
2#11719247C211yesmaximal, characteristic, complemented
3C13×#474C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5C4×#6104C211yesmaximal, characteristic
6#11718550C212yesmaximal, complemented
7#11718536C212yesmaximal, complemented
8#11718502C211yesmaximal, characteristic, complemented
9#11718492C211yesmaximal, characteristic, complemented
10#11718448C212yesmaximal
11#11718426C212yesmaximal, complemented
12C2×Q8×D13—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15#88200—21no—
16#88190C2212yes—
17C2×#6104C2211yescharacteristic
18#88180—21no—
19#88178—21no—
20C2×#6095C2212yes—
21#88150—22no—
22#88147C2212yes—
23#88142C2212yes—
24#88141C2212yes—
25#88133—22no—
26C4×D52C2211yescharacteristic
27#88123C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#107C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#102C2212yes—
32#88072C2211yescharacteristic
33#88056C2212yes—
34#88055C2212yes—
35#88054C2212yes—
36#88050C2212yes—
37#88050C2212yes—
38#88049C2211yescharacteristic
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44Q8×D13—44no—
45C2×D52C2311yescharacteristic
46C2×C4×D13—21no—
47C2×C4×D13—22no—
48C2×Dic26—22no—
49C2×Dic26D411yescharacteristic
50C2×Dic26C2312yes—
51C2×C8×C13C2312yes—
52C13×C4⋊C4—21no—
53C13×C4⋊C4C2312yes—
54C13×C4⋊C4C2311yescharacteristic
55C13×C22⋊C4—21no—
56C42×C13C2311yescharacteristic
57C22⋊Dic13—22no—
58C22⋊Dic13—22no—
59#6104—22no—
60#6103—21no—
61#6103—22no—
62C4⋊Dic13—21no—
63C4⋊Dic13—21no—
64C4⋊Dic13D411yescharacteristic
65C4⋊Dic13C2311yescharacteristic
66#6101—22no—
67#6101—22no—
68#6101D412yes—
69C4×Dic13—22no—
70C4×Dic13C2312yes—
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73#6095—24no—
74#3367—131nomaximal, Sylow
75C23×C13—21no—
76C22×D13—21no—
77Q8×C13—42no—
78D4×C13—21no—
79D4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—42no—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2411yescharacteristic
86C2×Dic13—22no—
87C2×Dic13—21no—
88C2×Dic13C2×D412yes—
89C2×Dic13C2×D412yes—
90D52—21no—
91D52#4112yes—
92C4×D13—44no—
93C4×D13—42no—
94Dic26—22no—
95Dic26—22no—
96Dic26—22no—
97Dic26—44no—
98C8×C13—22no—
99#1055—21no—
100#1055—21no—
101#556—131no—
102D4×Q8—131no—
103#489—132no—
104#487—131no—
105#477—132no—
106#474D1311yescharacteristic, complemented
107#463—132no—
108#461—131no—
109#446—131no—
110#440—132no—
111C4×D8—131no—
112C22×C13—41no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13C22×D411yescharacteristic
116C2×D13—22no—
117C2×D13—41no—
118C2×D13—41no—
119C4×C13—21no—
120C4×C13—42no—
121C4×C13—41no—
122C4×C13AGL(1,ℤ/8)12yes—
123C4×C13C2×#4111yescharacteristic
124C4×C132−1+411yescharacteristic
125Dic13—22no—
126Dic13—22no—
127Dic13—42no—
128Dic13—41no—
129C22×Q8—261no—
130C2×SD16—132no—
131C2×D8—131no—
132C4⋊Q8—132no—
133C4⋊Q8—131no—
134C4⋊Q8C2×D1311yescharacteristic
135#126—262no—
136#124—132no—
137C22⋊Q8—262no—
138C22⋊Q8—261no—
139C22⋊Q8—261no—
140C4×Q8—131no—
141C4×Q8—132no—
142C4×D4—132no—
143C4×D4—131no—
144C4×D4C2×D1311yescharacteristic
145#117—261no—
146#107—131no—
147#107C2×D1312yes—
148C4⋊C8—132no—
149C4⋊C8C2×D1311yescharacteristic
150#103—132no—
151#103—132no—
152#103—132no—
153#102—131no—
154#102—131no—
155#102C2×D1312yes—
156#97—132no—
157C4×C8—131no—
158C2×C13—81no—
159C2×C13#54811yescharacteristic
160C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C13#57811yescharacteristic
162D13—42no—
163C2×Q8—21no—
164C2×Q8—131no—
165C2×Q8—132no—
166C2×Q8—262no—
167C2×Q8—524no—
168C2×D4—131no—
169C2×D4C22×D1311yescharacteristic
170C22×C4—21no—
171C22×C4—262no—
172C22×C4—261no—
173SD16—264no—
174D8—262no—
175C2×C8—131no—
176C2×C8—131no—
177C2×C8C22×D1312yes—
178C4⋊C4—21no—
179C4⋊C4—131no—
180C4⋊C4—132no—
181C4⋊C4—131no—
182C4⋊C4—262no—
183C4⋊C4—262no—
184C4⋊C4—261no—
185C4⋊C4—261no—
186C4⋊C4C22×D1311yescharacteristic
187C4⋊C4C22×D1312yes—
188C22⋊C4—21no—
189C22⋊C4—262no—
190C22⋊C4—262no—
191C22⋊C4—262no—
192C22⋊C4—261no—
193C42—132no—
194C42—262no—
195C42C22×D1311yescharacteristic
196C13#336711yescharacteristic, complemented, Sylow
197C23—21no—
198C23—261no—
199Q8—42no—
200Q8—262no—
201Q8—262no—
202Q8—262no—
203Q8—524no—
204D4—21no—
205D4—21no—
206D4—132no—
207D4—261no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—132no—
212C2×C4—132no—
213C2×C4—262no—
214C2×C4—261no—
215C2×C4—524no—
216C2×C4—522no—
217C2×C4D4×D1311yescharacteristic
218C2×C4D4×D1311yescharacteristic
219C2×C4C23×D1311yescharacteristic
220C8—22no—
221C8—261no—
222C8—261no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—262no—
227C22—521no—
228C22—521no—
229C22C2×D4×D1311yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—262no—
234C4—262no—
235C4—521no—
236C4—522no—
237C4#8816512yes—
238C4#8825411yescharacteristic
239C4#41×D1311yescharacteristic
240C2—81no—
241C2—522no—
242C2#1171933811yescharacteristic
243C2C2×#8816511yescharacteristic
244C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#474D13
hypocenterC13#3367
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719432C2semidirect
2. #11719247C2semidirect
3. C13×#474C2semidirect
4. #11718754C2semidirect
6. #11718550C2semidirect
7. #11718536C2semidirect
8. #11718502C2semidirect
9. #11718492C2semidirect
11. #11718426C2semidirect
106. #474D13semidirect
196. C13#3367semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117192472
C13×#4742
#117187542
C4×#61042
#117185502
#117185362
#117185022
#117184922
#117184482
#117184262
#336713