Finite Group Databasebeta

← #13117598

Subgroups — #13117598

Order 1664.

596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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×#88184C211yesmaximal, characteristic
2C13×#381C211yesmaximal, characteristic, complemented
3C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
4#11718618C212yesmaximal, complemented
5#11718617C212yesmaximal, complemented
6#11718330C212yesmaximal, complemented
7#11718327C212yesmaximal, complemented
8#11718326C212yesmaximal, complemented
9#11718314C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×D52C2211yescharacteristic
13C22×C4×D13C2212yes—
14C2×C13×C22⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17#88184C418yescomplemented
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2212yes—
24C2×C4×Dic13C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27C13×#95C2212yes—
28C13×#95C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32C24×C13C2311yescharacteristic
33C23×D13C2312yes—
34C22×C4×C13—41no—
35C22×C4×C13—41no—
36C22×C4×C13C2×C414yescomplemented
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C2×C22⋊D13—42no—
42C2×C22⋊D13—42no—
43C2×C22⋊D13C2×C418yescomplemented
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C2×D52—41no—
48C2×D52—41no—
49C2×D52C2×C414yes—
50C2×C4×D13—24no—
51C2×C4×D13—42no—
52C2×C4×D13—42no—
53C13×C22⋊C4—41no—
54C13×C22⋊C4—41no—
55C22⋊Dic13—24no—
56#6103—24no—
57#6103—42no—
58#6103—42no—
59#6103C2×C418yescomplemented
60C4⋊Dic13C2×C414yescomplemented
61#6101—42no—
62C4×Dic13—41no—
63C4×Dic13—42no—
64C4×Dic13—41no—
65#2333—131nomaximal, Sylow
66C23×C13—22no—
67C23×C13—21no—
68C23×C13—21no—
69C23×C13—22no—
70C23×C13C22×C412yes—
71C23×C13C2411yescharacteristic
72C22×D13—22no—
73C22×D13—22no—
74C22×D13—22no—
75C22×D13—22no—
76C22×D13—22no—
77C22×D13—22no—
78C22×D13C22×C414yes—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—44no—
90C2×C4×C13C22×C412yes—
91C2×C4×C13C22×C412yes—
92C22⋊D13—48no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13C22×C414yes—
101C2×Dic13#4114yes—
102D52—44no—
103C4×D13—48no—
104C2×#121—131no—
105#390—132no—
106#388—132no—
107#387—132no—
108#386—132no—
109#386—132no—
110#381D1311yescharacteristic, complemented
111C4×C22⋊C4—131no—
112C4×C22⋊C4—132no—
113C22×C13—22no—
114C22×C13—22no—
115C22×C13—22no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13C23×C411yescharacteristic
119C22×C13C2×#4112yes—
120C22×C13H(5,𝔽2)11yescharacteristic
121C22×C13H(5,𝔽2)11yescharacteristic
122C22×C13H(5,𝔽2)12yes—
123C2×D13—24no—
124C2×D13—24no—
125C2×D13—24no—
126C2×D13—42no—
127C2×D13—42no—
128C2×D13—42no—
129C2×D13—42no—
130C4×C13—22no—
131C4×C13—22no—
132C4×C13—42no—
133C4×C13—42no—
134Dic13—24no—
135Dic13—24no—
136Dic13—42no—
137C22×D4—132no—
138C22×D4—131no—
139C23×C4—132no—
140C23×C4C2×D1311yescharacteristic
141#121—138no—
142C2×C4⋊C4—131no—
143C2×C4⋊C4—132no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4—132no—
146C2×C22⋊C4—132no—
147C2×C22⋊C4—132no—
148C2×C22⋊C4—132no—
149C2×C22⋊C4C2×D1311yescharacteristic
150C2×C22⋊C4C2×D1311yescharacteristic
151C2×C42—131no—
152C2×C42—132no—
153C2×C42—131no—
154#95—132no—
155#95—132no—
156#95—132no—
157#95C2×D1312yes—
158#95C2×D1312yes—
159C2×C13—42no—
160C2×C13C4×#4111yescharacteristic
161C2×C13#51811yescharacteristic
162C2×C13#51811yescharacteristic
163C2×C13#53812yes—
164C2×C13#54012yes—
165D13—44no—
166C24—132no—
167C24C22×D1311yescharacteristic
168C2×D4—138no—
169C2×D4—134no—
170C2×D4—521no—
171C2×D4—521no—
172C2×D4—522no—
173C2×D4—522no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—132no—
177C22×C4—132no—
178C22×C4—132no—
179C22×C4—264no—
180C22×C4—522no—
181C22×C4—522no—
182C22×C4C4×D1314yescomplemented
183C22×C4C22×D1312yes—
184C22×C4C22×D1312yes—
185C22×C4C22×D1311yescharacteristic
186C22×C4C22×D1311yescharacteristic
187C4⋊C4—134no—
188C4⋊C4—522no—
189C22⋊C4—41no—
190C22⋊C4—41no—
191C22⋊C4—138no—
192C22⋊C4—264no—
193C22⋊C4—264no—
194C22⋊C4—522no—
195C22⋊C4—522no—
196C42—521no—
197C42—521no—
198C42—522no—
199C13#233311yescharacteristic, complemented, Sylow
200C23—21no—
201C23—21no—
202C23—22no—
203C23—22no—
204C23—134no—
205C23—262no—
206C23—262no—
207C23—262no—
208C23—262no—
209C23—262no—
210C23—262no—
211C23C2×C4×D1312yes—
212C23C23×D1311yescharacteristic
213D4—524no—
214D4—528no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—44no—
226C2×C4—134no—
227C2×C4—134no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—528no—
236C2×C4C2×C4×D1312yes—
237C2×C4C2×C4×D1312yes—
238C22—22no—
239C22—22no—
240C22—22no—
241C22—42no—
242C22—42no—
243C22—264no—
244C22—264no—
245C22—264no—
246C22—522no—
247C22—522no—
248C22—522no—
249C22—522no—
250C22C22×C4×D1311yescharacteristic
251C22#8825111yescharacteristic
252C22#8825111yescharacteristic
253C22#41×D1312yes—
254C22#8825612yes—
255C4—22no—
256C4—22no—
257C4—42no—
258C4—42no—
259C4—264no—
260C4—264no—
261C4—522no—
262C2—42no—
263C2—524no—
264C2#1171919111yescharacteristic
265C2#1171922611yescharacteristic
266C2#1171922711yescharacteristic
267C2#1171936212yes—
268C2#1171936812yes—
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#381C2
socle, cosocleC23×C13C24
prime radicalC2×#88184C2
hypercenter#381D13
hypocenterC13#2333
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C13×#381C2semidirect
3. C4×C22⋊Dic13C2semidirect
4. #11718618C2semidirect
5. #11718617C2semidirect
6. #11718330C2semidirect
7. #11718327C2semidirect
8. #11718326C2semidirect
9. #11718314C2semidirect
17. #88184C4semidirect
36. C22×C4×C13C2×C4semidirect
43. C2×C22⋊D13C2×C4semidirect
59. #6103C2×C4semidirect
60. C4⋊Dic13C2×C4semidirect
110. #381D13semidirect
182. C22×C4C4×D13semidirect
199. C13#2333semidirect

Maximal subgroups

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

subgroupindex
C2×#881842
C13×#3812
C4×C22⋊Dic132
#117186182
#117186172
#117183302
#117183272
#117183262
#117183142
#233313