Finite Group Databasebeta

← #13115865

Subgroups — #13115865

Order 1664.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#124C211yesmaximal, characteristic, complemented
2C2×#88196C211yesmaximal, characteristic, complemented
3#11719510C211yesmaximal, characteristic
4#11718886C211yesmaximal, characteristic, complemented
5C2×#88073C211yesmaximal, characteristic, complemented
6C2×#88045C211yesmaximal, characteristic, complemented
7#11718115C211yesmaximal, characteristic, complemented
8C22×Q8×C13C2211yescharacteristic
9C22×D4×C13C2211yescharacteristic
10C2×#6127C2211yescharacteristic
11C13×#124—22no—
12C13×#124—22no—
13C2×C13×C22⋊C4—22no—
14C2×C42×C13C2211yescharacteristic
15#88207—22no—
16C2×#6107—21no—
17#88196—22no—
18#88196—22no—
19C2×#6106—21no—
20#88194—21no—
21#88192—22no—
22#88190—21no—
23#88180C2211yescharacteristic
24C2×#6099C2211yescharacteristic
25C2×#6099C2211yescharacteristic
26#88075—22no—
27#88073—22no—
28#88045—22no—
29C24×C13D412yes—
30C2×Q8×C13—21no—
31C2×Q8×C13—21no—
32C2×Q8×C13—21no—
33C2×Q8×C13—21no—
34C2×Q8×C13—21no—
35C2×Q8×C13D412yescomplemented
36C2×D4×C13—21no—
37C2×D4×C13—21no—
38C2×D4×C13—21no—
39C2×D4×C13—21no—
40C2×D4×C13—21no—
41C2×D4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—21no—
46C2×C22⋊D13—24no—
47#6127—21no—
48#6127—21no—
49#6127—21no—
50#6127—21no—
51C2×D52D411yescharacteristic
52C2×C4×D13—21no—
53C2×Dic26D411yescharacteristic
54C13×C22⋊C4—28no—
55C42×C13—21no—
56C42×C13D412yescomplemented
57C22⋊Dic13—24no—
58C22⋊Dic13—21no—
59#6107—24no—
60#6106—24no—
61C4⋊Dic13D412yes—
62C4×Dic13—21no—
63#6099—21no—
64#6099—21no—
65#6099—21no—
66#6099D412yescomplemented
67C2×#1055—21no—
68C2×#1055—21no—
69#2004—131nomaximal, Sylow
70C23×C13—22no—
71C23×C13—22no—
72C23×C13—22no—
73C23×C13—44no—
74C23×C13C2×D411yescharacteristic
75C22×D13—21no—
76Q8×C13—22no—
77Q8×C13—22no—
78Q8×C13—41no—
79Q8×C13—41no—
80D4×C13—41no—
81D4×C13—41no—
82D4×C13—41no—
83D4×C13—41no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—42no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13#4111yescharacteristic
95C22⋊D13—41no—
96C22⋊D13—41no—
97C22⋊D13—84no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100D52—21no—
101D52—21no—
102C4×D13—41no—
103C4×D13—41no—
104Dic26—21no—
105Dic26—21no—
106#1055—22no—
107#1055—41no—
108C2×#137—131no—
109#535—131no—
110C2×#124D1311yescharacteristic, complemented
111C2×#104—131no—
112#419—131no—
113C2×#100—131no—
114#339—131no—
115C22×C13—22no—
116C22×C13—44no—
117C22×C13—42no—
118C22×C13—44no—
119C22×C13—82no—
120C22×C13#12011yescharacteristic
121C22×C13#12011yescharacteristic
122C22×C13#12111yescharacteristic
123C2×D13—41no—
124C2×D13—42no—
125C4×C13—42no—
126C4×C13—42no—
127C4×C13#12011yescharacteristic
128C4×C13#12111yescharacteristic
129C4×C13#12111yescharacteristic
130C4×C13#12711yescharacteristic
131Dic13—41no—
132Dic13—42no—
133C2×#41—131no—
134C22×Q8C2×D1311yescharacteristic
135C22×D4C2×D1311yescharacteristic
136#137—262no—
137#137—262no—
138C2×Q16—261no—
139C2×SD16—261no—
140C2×M16—131no—
141C2×M16—131no—
142#127—261no—
143#124—22no—
144#124—22no—
145#124—261no—
146#121—262no—
147#120—262no—
148#117—131no—
149C2×C22⋊C4—22no—
150C2×C42C2×D1311yescharacteristic
151#104—262no—
152#103—262no—
153#100—262no—
154C2×C13—21no—
155C2×C13—21no—
156C2×C13—82no—
157C2×C13#39211yescharacteristic
158C2×C13#45512yes—
159D13—81no—
160C24C22⋊D1312yes—
161#41—261no—
162#41—261no—
163#41—261no—
164#41—261no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—131no—
171C2×Q8C22⋊D1312yescomplemented
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—131no—
179C2×D4—261no—
180C2×D4—264no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—261no—
184C22×C4C22×D1311yescharacteristic
185Q16—264no—
186SD16—264no—
187M16—132no—
188M16—261no—
189M16—261no—
190M16—261no—
191C2×C8—261no—
192C2×C8—261no—
193C4⋊C4—132no—
194C22⋊C4—28no—
195C22⋊C4—264no—
196C22⋊C4—261no—
197C42—21no—
198C42—261no—
199C42C22⋊D1312yescomplemented
200C13#200411yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—261no—
206C23C2×C22⋊D1311yescharacteristic
207Q8—22no—
208Q8—22no—
209Q8—41no—
210Q8—41no—
211Q8—261no—
212Q8—261no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—261no—
218D4—261no—
219D4—521no—
220D4—521no—
221D4—1044no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—262no—
228C2×C4—261no—
229C2×C4—521no—
230C2×C4—521no—
231C2×C4D4×D1311yescharacteristic
232C2×C4D4×D1311yescharacteristic
233C2×C4D4×D1311yescharacteristic
234C2×C4#612911yescharacteristic
235C2×C4C2×C22⋊D1311yescharacteristic
236C2×C4C2×C22⋊D1311yescharacteristic
237C8—262no—
238C8—521no—
239C22—22no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—82no—
244C22—522no—
245C22—521no—
246C22#8819111yescharacteristic
247C22#8819311yescharacteristic
248C22#8820711yescharacteristic
249C4—42no—
250C4—42no—
251C4—522no—
252C4—521no—
253C4#8819111yescharacteristic
254C4#8819211yescharacteristic
255C4#8819311yescharacteristic
256C4#8819411yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—1041no—
261C2#1171872212yes—
262C2#1171888411yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC2×C13×#124C2
socleC22×C13#120
prime radical#11719510C2
hypercenterC2×#124D13
hypocenterC13#2004
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C13×#124C2semidirect
2. C2×#88196C2semidirect
4. #11718886C2semidirect
5. C2×#88073C2semidirect
6. C2×#88045C2semidirect
7. #11718115C2semidirect
35. C2×Q8×C13D4semidirect
56. C42×C13D4semidirect
66. #6099D4semidirect
110. C2×#124D13semidirect
171. C2×Q8C22⋊D13semidirect
199. C42C22⋊D13semidirect
200. C13#2004semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1242
C2×#881962
#117195102
#117188862
C2×#880732
C2×#880452
#117181152
#200413