Finite Group Databasebeta

← #13127559

Subgroups — #13127559

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#11719437C211yesmaximal, characteristic, complemented
2#11719432C211yesmaximal, characteristic, complemented
3C13×#487C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718744C211yesmaximal, characteristic, complemented
6#11718480C212yesmaximal
7#11718478C212yesmaximal, complemented
8#11718456C212yesmaximal, complemented
9#11718455C212yesmaximal, complemented
10C4×D104C211yesmaximal, characteristic
11#11718340C211yesmaximal, characteristic, complemented
12C2×Q8×D13—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic
15#88201C2212yes—
16#88200—21no—
17Q8×Dic13C2212yes—
18C2×#6106C2212yes—
19C2×D104C2211yescharacteristic
20#88152—22no—
21#88151—21no—
22#88150—22no—
23#88147C2212yes—
24#88146—21no—
25#88142C2212yes—
26C4×D52C2211yescharacteristic
27C4×D52C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#103C2212yes—
30C13×#103C2212yes—
31C4×C8×C13C2211yescharacteristic
32#88075C2212yes—
33#88061C2211yescharacteristic
34#88061C2211yescharacteristic
35#88058C2211yescharacteristic
36#88055C2212yes—
37#88054C2212yes—
38#88049C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2312yes—
43Q8×D13—44no—
44C2×D52C2311yescharacteristic
45C2×D52C2311yescharacteristic
46C2×C4×D13—21no—
47C2×C4×D13—21no—
48C2×C4×D13—22no—
49C2×Dic26—22no—
50C2×Dic26D411yescharacteristic
51C2×C8×C13C2311yescharacteristic
52C2×C8×C13C2311yescharacteristic
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2312yes—
57C42×C13C2311yescharacteristic
58#6106—24no—
59#6103—21no—
60#6103—21no—
61#6103—22no—
62#6103—22no—
63#6103—22no—
64C4⋊Dic13—22no—
65C4⋊Dic13D411yescharacteristic
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68#6101—22no—
69#6101D412yes—
70C4×Dic13—22no—
71C4×Dic13C2312yes—
72C2×#1055C2312yes—
73D104—22no—
74#3367—131nomaximal, Sylow
75C22×D13—21no—
76C22×D13—21no—
77Q8×C13—22no—
78Q8×C13—22no—
79Q8×C13—42no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2411yescharacteristic
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13C2×D412yes—
88C2×Dic13C2×D412yes—
89D52—21no—
90D52—21no—
91D52—21no—
92D52#4112yes—
93C4×D13—44no—
94C4×D13—42no—
95C4×D13—42no—
96Dic26—22no—
97Dic26—44no—
98C8×C13—21no—
99C8×C13—21no—
100#1055—22no—
101#556—131no—
102D4×Q8—131no—
103#489—132no—
104#487D1311yescharacteristic, complemented
105#477—132no—
106#474—131no—
107#463—132no—
108#461—131no—
109#446—131no—
110#440—132no—
111C4×D8—131no—
112C22×C13C22×D411yescharacteristic
113C2×D13—22no—
114C2×D13—41no—
115C2×D13—41no—
116C2×D13—41no—
117C2×D13—41no—
118C2×D13—41no—
119C4×C13—21no—
120C4×C13—42no—
121C4×C13—42no—
122C4×C13AGL(1,ℤ/8)12yes—
123C4×C13C2×#4111yescharacteristic
124C4×C132−1+411yescharacteristic
125Dic13—22no—
126Dic13—22no—
127Dic13—41no—
128Dic13—41no—
129C22×Q8—261no—
130C2×SD16—132no—
131C2×D8—131no—
132C4⋊Q8—132no—
133C4⋊Q8C2×D1311yescharacteristic
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×D4—131no—
145#117—261no—
146#107—131no—
147#107—132no—
148C4⋊C8—132no—
149C4⋊C8—131no—
150#103—132no—
151#103C2×D1312yes—
152#103C2×D1312yes—
153#102—131no—
154#102—131no—
155#102—132no—
156#97—132no—
157C4×C8C2×D1311yescharacteristic
158C2×C13#54811yescharacteristic
159C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
160C2×C13#57811yescharacteristic
161D13—42no—
162D13—81no—
163C2×Q8—21no—
164C2×Q8—131no—
165C2×Q8—262no—
166C2×Q8—524no—
167C2×Q8C22×D1312yes—
168C2×D4—131no—
169C2×D4—131no—
170C22×C4—262no—
171C22×C4—261no—
172C22×C4—261no—
173SD16—264no—
174D8—262no—
175C2×C8—132no—
176C2×C8C22×D1311yescharacteristic
177C2×C8C22×D1311yescharacteristic
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—131no—
182C4⋊C4—132no—
183C4⋊C4—131no—
184C4⋊C4—131no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C4⋊C4C22×D1312yes—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C22⋊C4—262no—
191C22⋊C4—261no—
192C22⋊C4—261no—
193C42—132no—
194C42—262no—
195C42C22×D1311yescharacteristic
196C13#336711yescharacteristic, complemented, Sylow
197C23—261no—
198C23—261no—
199Q8—22no—
200Q8—22no—
201Q8—42no—
202Q8—262no—
203Q8—524no—
204D4—132no—
205D4—261no—
206D4—261no—
207D4—261no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—132no—
211C2×C4—132no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—524no—
215C2×C4—522no—
216C2×C4—522no—
217C2×C4D4×D1311yescharacteristic
218C2×C4D4×D1311yescharacteristic
219C2×C4C23×D1311yescharacteristic
220C8—21no—
221C8—21no—
222C8—262no—
223C22—262no—
224C22—521no—
225C22—521no—
226C22—521no—
227C22—521no—
228C22—521no—
229C22C2×D4×D1311yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—262no—
234C4—262no—
235C4—521no—
236C4—521no—
237C4#8816812yes—
238C4#41×D1311yescharacteristic
239C4#8825711yescharacteristic
240C2—522no—
241C2—1041no—
242C2#1171938211yescharacteristic
243C2C2×#8816811yescharacteristic
244C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radicalC2×D104C22
hypercenter#487D13
hypocenterC13#3367
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #11719437C2semidirect
2. #11719432C2semidirect
3. C13×#487C2semidirect
4. #11718748C2semidirect
5. #11718744C2semidirect
7. #11718478C2semidirect
8. #11718456C2semidirect
9. #11718455C2semidirect
11. #11718340C2semidirect
104. #487D13semidirect
196. C13#3367semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117194322
C13×#4872
#117187482
#117187442
#117184802
#117184782
#117184562
#117184552
C4×D1042
#117183402
#336713