Finite Group Databasebeta

← #13121797

Subgroups — #13121797

Order 1664.

476 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88152C212yesmaximal, complemented
2C13×#389C211yesmaximal, characteristic, complemented
3#11718655C212yesmaximal, complemented
4#11718652C212yesmaximal
5#11718646C212yesmaximal, complemented
6#11718600C211yesmaximal, characteristic
7#11718589C211yesmaximal, characteristic, complemented
8#11718338C212yesmaximal, complemented
9#11718331C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15C2×#6103C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2212yes—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×#6101C2212yes—
27C2×C4×Dic13C2212yes—
28#88152—28no—
29C13×#95C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32C23×D13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C2×D52—22no—
42C2×D52—41no—
43C2×D52—41no—
44C13×C4⋊C4—24no—
45C13×C4⋊C4—41no—
46C13×C4⋊C4D414yescomplemented
47C42×C13—41no—
48#6103—24no—
49#6103—24no—
50#6103—24no—
51#6103—24no—
52#6103—42no—
53#6103—42no—
54C4⋊Dic13—24no—
55C4⋊Dic13—22no—
56C4⋊Dic13—41no—
57C4⋊Dic13—42no—
58C4⋊Dic13—41no—
59#6101—24no—
60C4×Dic13—24no—
61#2727—131nomaximal, Sylow
62C23×C13C2411yescharacteristic
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—22no—
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13C2×D414yes—
82C2×C4×C13C2×D412yes—
83C2×C4×C13#4112yes—
84C2×C4×C13#4112yes—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94D52—44no—
95C2×#126—132no—
96#399—132no—
97#396—132no—
98#394—132no—
99#390—131no—
100#389—132no—
101#389—131no—
102#389D1311yescharacteristic, complemented
103#388—132no—
104C22×C13C22×D411yescharacteristic
105C22×C13C2×#4111yescharacteristic
106C22×C13C2×#4111yescharacteristic
107C22×C13H(5,𝔽2)11yescharacteristic
108C22×C13H(5,𝔽2)11yescharacteristic
109C22×C132−1+411yescharacteristic
110C22×C132−1+411yescharacteristic
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—42no—
114C2×D13—42no—
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—42no—
118C4×C13—22no—
119C4×C13—22no—
120C4×C13—22no—
121C4×C13—24no—
122C4×C13—42no—
123Dic13—42no—
124Dic13—42no—
125Dic13—42no—
126C22×D4—131no—
127#126—268no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4—131no—
131C2×C4⋊C4—131no—
132C2×C4⋊C4—131no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4C2×D1312yes—
135C2×C4⋊C4C2×D1311yescharacteristic
136C2×C4⋊C4C2×D1311yescharacteristic
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4—132no—
142C2×C22⋊C4—132no—
143C2×C42—132no—
144C2×C42C2×D1311yescharacteristic
145#95—132no—
146#95—132no—
147#95C2×D1312yes—
148C2×C13#53711yescharacteristic
149C2×C13#53811yescharacteristic
150C2×C13#53911yescharacteristic
151C2×C13#54711yescharacteristic
152C2×C13#55011yescharacteristic
153C2×C13#55611yescharacteristic
154C2×C13#56311yescharacteristic
155D13—82no—
156C24—132no—
157C2×D4—262no—
158C2×D4—521no—
159C2×D4—521no—
160C22×C4—132no—
161C22×C4—132no—
162C22×C4—132no—
163C22×C4C22×D1312yes—
164C22×C4C22×D1312yes—
165C22×C4C22×D1311yescharacteristic
166C22×C4C22×D1311yescharacteristic
167C22×C4C22×D1311yescharacteristic
168C4⋊C4—24no—
169C4⋊C4—41no—
170C4⋊C4—264no—
171C4⋊C4—264no—
172C4⋊C4—262no—
173C4⋊C4—521no—
174C4⋊C4—521no—
175C4⋊C4—522no—
176C4⋊C4D5214yescomplemented
177C22⋊C4—264no—
178C22⋊C4—264no—
179C22⋊C4—264no—
180C22⋊C4—264no—
181C22⋊C4—522no—
182C22⋊C4—522no—
183C42—41no—
184C42—264no—
185C13#272711yescharacteristic, complemented, Sylow
186C23—262no—
187C23—262no—
188C23—262no—
189C23—262no—
190C23—262no—
191C23—262no—
192C23—262no—
193C23C23×D1311yescharacteristic
194D4—524no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4C2×D5214yes—
216C2×C4C2×D5212yes—
217C2×C4#612912yes—
218C2×C4#613112yes—
219C22—522no—
220C22—522no—
221C22—522no—
222C22—522no—
223C22—522no—
224C22—522no—
225C22—522no—
226C22C22×D5211yescharacteristic
227C22C2×#612911yescharacteristic
228C22#8825111yescharacteristic
229C22C2×#613111yescharacteristic
230C22#8825411yescharacteristic
231C22#8825611yescharacteristic
232C22#8825711yescharacteristic
233C4—22no—
234C4—24no—
235C4—22no—
236C4—22no—
237C4—42no—
238C4—522no—
239C4—522no—
240C4—522no—
241C2—1042no—
242C2#1171921511yescharacteristic
243C2#1171926011yescharacteristic
244C2#1171928211yescharacteristic
245C2#1171932211yescharacteristic
246C2#1171935011yescharacteristic
247C2#1171940411yescharacteristic
248C2#1171943711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
prime radicalC22×D52C22
hypercenter#389D13
hypocenterC13#2727
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#88152C2semidirect
2. C13×#389C2semidirect
3. #11718655C2semidirect
5. #11718646C2semidirect
7. #11718589C2semidirect
8. #11718338C2semidirect
9. #11718331C2semidirect
46. C13×C4⋊C4D4semidirect
102. #389D13semidirect
176. C4⋊C4D52semidirect
185. C13#2727semidirect

Maximal subgroups

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

subgroupindex
C2×#881522
C13×#3892
#117186552
#117186522
#117186462
#117186002
#117185892
#117183382
#117183312
#272713