Finite Group Databasebeta

← #13121003

Subgroups — #13121003

Order 1664.

434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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×#88152C211yesmaximal, characteristic
2C2×#88144C211yesmaximal, characteristic, complemented
3C13×#400C211yesmaximal, characteristic, complemented
4#11718653C211yesmaximal, characteristic
5#11718644C211yesmaximal, characteristic, complemented
6#11718337C212yesmaximal
7#11718335C211yesmaximal, characteristic
8#11718331C212yesmaximal
9#11718318C212yesmaximal, complemented
10#11718310C211yesmaximal, characteristic, complemented
11#11718308C212yesmaximal, complemented
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×#6103C2211yescharacteristic
15C2×#6103C2211yescharacteristic
16C2×#6103C2211yescharacteristic
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×C4⋊Dic13C2212yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2211yescharacteristic
22C2×#6101C2212yes—
23C2×#6101C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×C4×Dic13C2212yes—
28C2×C4×Dic13C2211yescharacteristic
29#88152—24no—
30#88144—24no—
31C13×#95C2212yes—
32C13×#95C2211yescharacteristic
33C13×#95C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2312yes—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—22no—
50#6103—22no—
51#6103—22no—
52#6103—22no—
53#6103—24no—
54#6103—42no—
55C4⋊Dic13—22no—
56C4⋊Dic13—24no—
57C4⋊Dic13—22no—
58#6101—24no—
59#6101—22no—
60#6101—24no—
61#6101—24no—
62#6101—42no—
63C4×Dic13—42no—
64C4×Dic13D414yes—
65#2664—131nomaximal, Sylow
66C23×C13C2411yescharacteristic
67C22×D13—21no—
68C22×D13—22no—
69C22×D13—21no—
70C22×D13—22no—
71C22×D13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D412yes—
85C2×Dic13—22no—
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13C2×D412yes—
96C2×Dic13C2×D412yes—
97C2×Dic13#4114yes—
98C2×#126—131no—
99C2×#125—131no—
100#400D1311yescharacteristic, complemented
101#399—131no—
102#398—131no—
103#398—132no—
104#397—131no—
105#396—132no—
106#389—132no—
107#388—132no—
108C4×C4⋊C4—131no—
109C22×C13C22×D411yescharacteristic
110C22×C13C2×#4112yes—
111C22×C13H(5,𝔽2)11yescharacteristic
112C22×C132−1+411yescharacteristic
113C22×C132−1+412yes—
114C2×D13—41no—
115C2×D13—41no—
116C2×D13—41no—
117C2×D13—42no—
118C2×D13—42no—
119C4×C13—22no—
120C4×C13—42no—
121C4×C13—41no—
122C4×C13—41no—
123C4×C13—42no—
124Dic13—22no—
125Dic13—22no—
126Dic13—24no—
127Dic13—41no—
128Dic13—42no—
129#126—264no—
130#125—264no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—131no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—131no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4C2×D1311yescharacteristic
140C2×C4⋊C4C2×D1311yescharacteristic
141C2×C22⋊C4—131no—
142C2×C22⋊C4—131no—
143C2×C22⋊C4—131no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4—132no—
146C2×C42—131no—
147C2×C42—132no—
148#95—131no—
149#95—132no—
150#95—132no—
151#95C2×D1311yescharacteristic
152#95C2×D1312yes—
153#95C2×D1312yes—
154C2×C13#53211yescharacteristic
155C2×C13#53611yescharacteristic
156C2×C13#53711yescharacteristic
157C2×C13#53912yes—
158C2×C13#54112yes—
159D13—81no—
160C24—131no—
161C22×C4—132no—
162C22×C4—131no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—132no—
166C22×C4C22×D1311yescharacteristic
167C22×C4C22×D1312yes—
168C22×C4C22×D1311yescharacteristic
169C22×C4C22×D1312yes—
170C22×C4C22×D1311yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—264no—
174C4⋊C4—264no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—264no—
178C4⋊C4—264no—
179C4⋊C4—262no—
180C4⋊C4—522no—
181C22⋊C4—262no—
182C22⋊C4—262no—
183C22⋊C4—264no—
184C22⋊C4—262no—
185C22⋊C4—522no—
186C42—134no—
187C42—522no—
188C13#266411yescharacteristic, complemented, Sylow
189C23—261no—
190C23—261no—
191C23—262no—
192C23—261no—
193C23—262no—
194C23C23×D1311yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—132no—
208C2×C4—132no—
209C2×C4—134no—
210C2×C4—261no—
211C2×C4—262no—
212C2×C4—261no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4D4×D1312yes—
221C22—521no—
222C22—521no—
223C22—521no—
224C22—522no—
225C22—522no—
226C22C2×D4×D1311yescharacteristic
227C22#8825411yescharacteristic
228C22#41×D1312yes—
229C22#8825611yescharacteristic
230C22#8825712yes—
231C4—22no—
232C4—41no—
233C4—41no—
234C4—42no—
235C4—42no—
236C4—262no—
237C4—262no—
238C4—264no—
239C4—522no—
240C4—521no—
241C2—1041no—
242C2#1171933411yescharacteristic
243C2#1171935311yescharacteristic
244C2#1171937311yescharacteristic
245C2#1171940112yes—
246C2#1171941212yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#400C2
prime radicalC23×D13C23
hypercenter#400D13
hypocenterC13#2664
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#88144C2semidirect
3. C13×#400C2semidirect
5. #11718644C2semidirect
9. #11718318C2semidirect
10. #11718310C2semidirect
11. #11718308C2semidirect
100. #400D13semidirect
188. C13#2664semidirect

Maximal subgroups

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

subgroupindex
C2×#881522
C2×#881442
C13×#4002
#117186532
#117186442
#117183372
#117183352
#117183312
#117183182
#117183102
#117183082
#266413