Finite Group Databasebeta

← #13131314

Subgroups — #13131314

Order 1664.

484 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 162 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
1D13×#117C211yesmaximal, characteristic
2#11719136C212yesmaximal
3#11719082C214yesmaximal, complemented
4#11719071C214yesmaximal
5#11719060C211yesmaximal, characteristic, complemented
6#11719059C211yesmaximal, characteristic, complemented
7C4×C4⋊#261C212yesmaximal, complemented
8C22×C4×D13C2211yescharacteristic
9C2×C22⋊#261C2214yes—
10C2×C4⋊#261C2212yes—
11C2×C4⋊#261C2212yes—
12C2×C4⋊#261C2214yes—
13C2×C4×#261C2214yes—
14C13×#117C411yescharacteristic, complemented
15#88180C411yescharacteristic, complemented
16#88146C412yescomplemented
17C4⋊C4×D13C2212yes—
18C22⋊C4×D13C2212yes—
19#88131C412yescomplemented
20#88126C411yescharacteristic, complemented
21#88126C411yescharacteristic, complemented
22C42×D13C2211yescharacteristic
23C42×D13C2211yescharacteristic
24(C2×#261)⋊C4C2214yes—
25(C2×#261)⋊C4C2214yes—
26(C2×#261)⋊C4C2214yes—
27C23×D13C2311yescharacteristic
28C22×#261C2314yes—
29C22×#261C2314yes—
30C22×C4×C13C2×C411yescharacteristic
31C22×Dic13C2×C411yescharacteristic
32C2×C4×D13—22no—
33C2×C4×D13—22no—
34C2×C4×D13C2×C411yescharacteristic
35C2×C4×D13C2×C411yescharacteristic
36C2×C4×D13C2311yescharacteristic
37C2×C4×D13C2312yes—
38C2×C4×D13C2312yes—
39C2×C4×D13C2311yescharacteristic
40C22⋊#261—44no—
41C4⋊#261—24no—
42C4⋊#261—24no—
43C4⋊#261—44no—
44C4×#261—44no—
45C13×C4⋊C4C2×C412yes—
46C13×C22⋊C4C2×C412yes—
47C42×C13C2×C411yescharacteristic
48C42×C13C2×C411yescharacteristic
49C22⋊Dic13C2×C412yes—
50#6103C2×C412yes—
51#6103C2×C412yes—
52C4⋊Dic13C2×C412yes—
53#6101C2×C412yes—
54#6101C2×C412yes—
55C4×Dic13C2×C411yescharacteristic
56C4×Dic13C2×C411yescharacteristic
57C4×Dic13C2×C412yes—
58C4×Dic13C2×C412yes—
59#2314—131nomaximal, Sylow
60C23×C13C22×C411yescharacteristic
61C22×D13—21no—
62C22×D13—21no—
63C22×D13—22no—
64C22×D13—22no—
65C22×D13C22×C411yescharacteristic
66C22×D13C2411yescharacteristic
67C2×#261—24no—
68C2×#261—24no—
69C2×#261—24no—
70C2×#261—24no—
71C2×#261—24no—
72C2×#261—24no—
73C2×C4×C13—22no—
74C2×C4×C13C22×C412yes—
75C2×C4×C13C22×C412yes—
76C2×C4×C13C22×C411yescharacteristic
77C2×C4×C13C22×C411yescharacteristic
78C2×Dic13—22no—
79C2×Dic13C22×C412yes—
80C2×Dic13C22×C412yes—
81C2×Dic13C22×C411yescharacteristic
82C2×Dic13C22×C411yescharacteristic
83C4×D13—21no—
84C4×D13—21no—
85C4×D13—22no—
86C4×D13—22no—
87C4×D13—22no—
88C4×D13—22no—
89C4×D13—22no—
90C4×D13—22no—
91C4×D13#4112yes—
92C4×D13#4112yes—
93C2×#117—131no—
94#388—134no—
95#387—134no—
96#384—131no—
97#382—131no—
98#380—132no—
99C4×C4⋊C4—132no—
100C22×C13—21no—
101C22×C13—22no—
102C22×C13C23×C411yescharacteristic
103C2×D13—21no—
104C2×D13—22no—
105C2×D13—41no—
106C2×D13—41no—
107C2×D13—42no—
108C2×D13C2×#4111yescharacteristic
109C2×D13C2×#4111yescharacteristic
110C2×D13H(5,𝔽2)12yes—
111C2×D132−1+412yes—
112#261—44no—
113#261—44no—
114C4×C13—21no—
115C4×C13—22no—
116C4×C13—22no—
117C4×C13#11712yes—
118Dic13—21no—
119Dic13—22no—
120Dic13—22no—
121Dic13#11712yes—
122C23×C4—131no—
123#117—131no—
124#117—132no—
125#117—132no—
126#117—131no—
127#117—131no—
128#117#26111yescharacteristic, complemented
129C2×C4⋊C4—132no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—134no—
133C2×C22⋊C4—132no—
134C2×C22⋊C4—134no—
135C2×C42—131no—
136C2×C42—131no—
137C2×C42—134no—
138#95—134no—
139#95—134no—
140#95—134no—
141C2×C13—41no—
142C2×C13C2×#11711yescharacteristic
143C2×C13#52012yes—
144D13—41no—
145D13#54011yescharacteristic
146D13#54111yescharacteristic
147D13#54212yes—
148C24—131no—
149C22×C4—131no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—132no—
153C22×C4—132no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—134no—
157C22×C4—134no—
158C22×C4—262no—
159C22×C4—262no—
160C22×C4C2×#26111yescharacteristic
161C4⋊C4—132no—
162C4⋊C4—132no—
163C4⋊C4—132no—
164C4⋊C4—264no—
165C4⋊C4—264no—
166C4⋊C4—524no—
167C4⋊C4C2×#26112yes—
168C22⋊C4—132no—
169C22⋊C4—132no—
170C22⋊C4—132no—
171C22⋊C4—524no—
172C22⋊C4C2×#26112yes—
173C42—132no—
174C42—132no—
175C42—131no—
176C42—131no—
177C42—524no—
178C42C2×#26111yescharacteristic
179C42C2×#26111yescharacteristic
180C13#231411yescharacteristic, complemented, Sylow
181C23—131no—
182C23—131no—
183C23—262no—
184C23—261no—
185C23—261no—
186C23—262no—
187C23C22×#26111yescharacteristic
188C2×C4—22no—
189C2×C4—131no—
190C2×C4—132no—
191C2×C4—132no—
192C2×C4—132no—
193C2×C4—132no—
194C2×C4—131no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—261no—
201C2×C4—261no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—264no—
205C2×C4—264no—
206C2×C4—264no—
207C2×C4—264no—
208C2×C4—264no—
209C2×C4—264no—
210C2×C4C22×#26112yes—
211C2×C4C22×#26112yes—
212C2×C4C22×#26111yescharacteristic
213C2×C4C22×#26111yescharacteristic
214C22—21no—
215C22—22no—
216C22—131no—
217C22—131no—
218C22—132no—
219C22—132no—
220C22—261no—
221C22—262no—
222C22—521no—
223C22—522no—
224C22—521no—
225C22C23×#26111yescharacteristic
226C4—21no—
227C4—22no—
228C4—22no—
229C4—132no—
230C4—261no—
231C4—262no—
232C4—262no—
233C4—524no—
234C4—524no—
235C4#8823712yes—
236C2—41no—
237C2—131no—
238C2—132no—
239C2—131no—
240C2—521no—
241C2C2×#8823711yescharacteristic
242C2#1171963112yes—
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC13×#117C4
prime radicalC23×D13C23
cosocleC22×D13C24
hypercenter#117#261
hypocenterC13#2314
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #11719082C2semidirect
5. #11719060C2semidirect
6. #11719059C2semidirect
7. C4×C4⋊#261C2semidirect
14. C13×#117C4semidirect
15. #88180C4semidirect
16. #88146C4semidirect
19. #88131C4semidirect
20. #88126C4semidirect
21. #88126C4semidirect
128. #117#261semidirect
180. C13#2314semidirect

Maximal subgroups

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

subgroupindex
D13×#1172
#117191362
#117190822
#117190712
#117190602
#117190592
C4×C4⋊#2612
#231413