Finite Group Databasebeta

← #13124200

Subgroups — #13124200

Order 1664.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C2×C13×2−1+4C211yesmaximal, characteristic, complemented
2#11719527C212yesmaximal, complemented
3#11719521C211yesmaximal, characteristic, complemented
4#11718907C214yesmaximal, complemented
5#11718906C214yesmaximal, complemented
6#11718897C212yesmaximal, complemented
7C2×#88076C211yesmaximal, characteristic, complemented
8C13×2−1+4—24no—
9C13×2−1+4—22no—
10C13×2−1+4C2214yes—
11C2×C13×#41—22no—
12C2×C13×#41—22no—
13C2×C13×#41C2212yes—
14C22×Q8×C13—22no—
15C22×Q8×C13C2211yescharacteristic
16C2×#6127C2211yescharacteristic
17#88205C2214yescomplemented
18#88204—24no—
19#88203C2214yescomplemented
20#88201C2212yescomplemented
21#88200—22no—
22#88198C2212yescomplemented
23#88196—22no—
24#88186—22no—
25#88183—22no—
26#88180C2211yescharacteristic
27C2×#6099C2212yes—
28#88077C2218yescomplemented
29#88076C2214yescomplemented
30C13×#41—28no—
31C13×#41—28no—
32C13×#41—28no—
33C13×#41—28no—
34C13×#41—22no—
35C13×#41—22no—
36C13×#41D414yes—
37C13×#41C2314yes—
38C2×Q8×C13—22no—
39C2×Q8×C13—28no—
40C2×Q8×C13—28no—
41C2×Q8×C13—22no—
42C2×Q8×C13—22no—
43C2×Q8×C13D412yes—
44C2×Q8×C13D412yes—
45C2×Q8×C13C2312yes—
46C2×D4×C13—22no—
47C2×D4×C13—22no—
48C2×D4×C13D412yes—
49C22×C4×C13—24no—
50C22×C4×C13—22no—
51C22×C4×C13D412yes—
52C22×C4×C13C2311yescharacteristic
53C2×C22⋊D13—21no—
54#6127—22no—
55#6127—22no—
56C2×D52C2311yescharacteristic
57C2×C4×D13—21no—
58C2×Dic26C2311yescharacteristic
59C22⋊Dic13—21no—
60#6107—24no—
61#6106—24no—
62#6105—24no—
63#6104—24no—
64#6103—24no—
65C4⋊Dic13—21no—
66#6101—24no—
67C4×Dic13C2312yes—
68#6099—22no—
69#6099C2314yes—
70C2×#1055—22no—
71#3020—131nomaximal, Sylow
72C23×C13—22no—
73C23×C13C2×D411yescharacteristic
74C22×D13—21no—
75Q8×C13—28no—
76Q8×C13—22no—
77Q8×C13—24no—
78Q8×C13—24no—
79Q8×C13C2×D414yes—
80D4×C13—28no—
81D4×C13—24no—
82D4×C13—24no—
83D4×C13—22no—
84D4×C13C2×D414yes—
85C2×C4×C13—216no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—24no—
90C2×C4×C13—24no—
91C2×C4×C13C2×D414yes—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D412yes—
94C2×C4×C13C2×D412yes—
95C2×C4×C13C2411yescharacteristic
96C22⋊D13—41no—
97C22⋊D13—41no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100D52—22no—
101C4×D13—42no—
102Dic26—22no—
103#1055—24no—
104C2×2−1+4D1311yescharacteristic, complemented
105#575—132no—
106#536—131no—
107#456—134no—
108#454—134no—
109#421—132no—
110C2×#101—131no—
111C22×C13—24no—
112C22×C13—41no—
113C22×C13—44no—
114C22×C13#12011yescharacteristic
115C22×C13#12011yescharacteristic
116C22×C13C22×D411yescharacteristic
117C2×D13—42no—
118C2×D13—41no—
119C4×C13—24no—
120C4×C13—24no—
121C4×C13#12012yes—
122C4×C13C22×D412yes—
123Dic13—42no—
124Dic13—41no—
1252−1+4—24no—
1262−1+4—22no—
1272−1+4C2×D1314yes—
128C2×#41—22no—
129C2×#41—22no—
130C2×#41—131no—
131C2×#41C2×D1312yes—
132C22×Q8—22no—
133C22×Q8C2×D1311yescharacteristic
134#137—134no—
135#137—262no—
136AGL(1,ℤ/8)—134no—
137AGL(1,ℤ/8)—262no—
138#135—264no—
139C2×M16—132no—
140C4⋊Q8—132no—
141#124—132no—
142#123—262no—
143C22⋊Q8—262no—
144#117—131no—
145#104—138no—
146#101—134no—
147C2×C13—21no—
148C2×C13—21no—
149C2×C13—21no—
150C2×C13—44no—
151C2×C13C2×#12011yescharacteristic
152D13—81no—
153#41—28no—
154#41—28no—
155#41—28no—
156#41—28no—
157#41—22no—
158#41—22no—
159#41—262no—
160#41—262no—
161#41C22⋊D1314yes—
162#41C22×D1314yes—
163C2×Q8—22no—
164C2×Q8—28no—
165C2×Q8—28no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—131no—
169C2×Q8C22⋊D1312yes—
170C2×Q8C22⋊D1312yes—
171C2×Q8C22×D1312yes—
172C2×D4—22no—
173C2×D4—22no—
174C2×D4—131no—
175C2×D4—261no—
176C2×D4C22⋊D1312yes—
177C22×C4—24no—
178C22×C4—22no—
179C22×C4—261no—
180C22×C4C22⋊D1312yes—
181C22×C4C22×D1311yescharacteristic
182Q16—264no—
183SD16—264no—
184SD16—264no—
185D8—264no—
186M16—134no—
187M16—262no—
188C2×C8—262no—
189C4⋊C4—261no—
190C4⋊C4—264no—
191C22⋊C4—261no—
192C22⋊C4—264no—
193C42—132no—
194C13#302011yescharacteristic, complemented, Sylow
195C23—22no—
196C23—261no—
197C23C2×C22⋊D1311yescharacteristic
198Q8—28no—
199Q8—22no—
200Q8—24no—
201Q8—24no—
202Q8—262no—
203Q8C2×C22⋊D1314yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—262no—
209D4—521no—
210D4—521no—
211D4C2×C22⋊D1314yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—262no—
219C2×C4—261no—
220C2×C4—522no—
221C2×C4C2×C22⋊D1314yes—
222C2×C4C2×C22⋊D1311yescharacteristic
223C2×C4C2×C22⋊D1312yes—
224C2×C4C2×C22⋊D1312yes—
225C2×C4C23×D1311yescharacteristic
226C8—264no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—522no—
231C22—521no—
232C22#8820711yescharacteristic
233C22#8820711yescharacteristic
234C22C22×C22⋊D1311yescharacteristic
235C4—24no—
236C4—24no—
237C4—522no—
238C4—521no—
239C4#8820712yes—
240C4C22×C22⋊D1312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—1041no—
246C2C2×#8820711yescharacteristic
subgroupG/H
centerC2C2×#88207
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×2−1+4C2
socleC2×C13C2×#120
hypercenterC2×2−1+4D13
hypocenterC13#3020
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C13×2−1+4C2semidirect
2. #11719527C2semidirect
3. #11719521C2semidirect
4. #11718907C2semidirect
5. #11718906C2semidirect
6. #11718897C2semidirect
7. C2×#88076C2semidirect
17. #88205C22semidirect
19. #88203C22semidirect
20. #88201C22semidirect
22. #88198C22semidirect
28. #88077C22semidirect
29. #88076C22semidirect
104. C2×2−1+4D13semidirect
194. C13#3020semidirect

Maximal subgroups

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

subgroupindex
C2×C13×2−1+42
#117195272
#117195212
#117189072
#117189062
#117188972
C2×#880762
#302013