Finite Group Databasebeta

← #13122916

Subgroups — #13122916

Order 1664.

472 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C13×#385C211yesmaximal, characteristic, complemented
2#11718874C212yesmaximal, complemented
3#11718652C212yesmaximal, complemented
4#11718643C212yesmaximal, complemented
5#11718621C211yesmaximal, characteristic
6#11718620C212yesmaximal, complemented
7#11718608C211yesmaximal, characteristic, complemented
8#11718336C212yesmaximal, complemented
9#11718334C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×D52C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×C4⋊C4C2212yes—
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6101C2212yes—
24C13×#95C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2211yescharacteristic
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31C24×C13C2311yescharacteristic
32C23×D13C2312yes—
33C22×C4×C13—41no—
34C22×C4×C13—42no—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C2×C22⋊D13—24no—
40C2×C22⋊D13—42no—
41C2×C22⋊D13—42no—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C2×D52—41no—
46C2×D52—42no—
47C2×Dic26—41no—
48C2×Dic26—42no—
49C13×C4⋊C4—42no—
50C13×C22⋊C4—22no—
51C13×C22⋊C4—41no—
52C22⋊Dic13—42no—
53#6103—42no—
54#6103—42no—
55#6103—42no—
56#6103—42no—
57#6103—42no—
58#6101—42no—
59#2824—131nomaximal, Sylow
60C23×C13—22no—
61C23×C13—21no—
62C23×C13—22no—
63C23×C13—21no—
64C23×C13#4112yes—
65C23×C13C2411yescharacteristic
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—44no—
84C22⋊D13—48no—
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—
95Dic26—44no—
96#400—132no—
97#397—132no—
98#394—132no—
99#394—132no—
100#393—131no—
101#393—132no—
102#392—131no—
103#386—132no—
104#385D1311yescharacteristic, complemented
105C22×C13—24no—
106C22×C13—22no—
107C22×C13—41no—
108C22×C13—41no—
109C22×C13—42no—
110C22×C13C2×#4111yescharacteristic
111C22×C13H(5,𝔽2)12yes—
112C22×C13H(5,𝔽2)11yescharacteristic
113C22×C13H(5,𝔽2)12yes—
114C22×C132−1+411yescharacteristic
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—42no—
118C2×D13—42no—
119C2×D13—42no—
120C2×D13—42no—
121C2×D13—42no—
122C4×C13—42no—
123C4×C13—41no—
124C4×C13—41no—
125C4×C13—42no—
126Dic13—42no—
127Dic13—42no—
128Dic13—42no—
129C22×Q8—131no—
130C22×D4—132no—
131C22×D4—131no—
132C23×C4C2×D1311yescharacteristic
133C2×C4⋊C4—132no—
134C2×C4⋊C4C2×D1312yes—
135C2×C22⋊C4—132no—
136C2×C22⋊C4—132no—
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4C2×D1311yescharacteristic
142C2×C22⋊C4C2×D1311yescharacteristic
143#95—132no—
144#95—132no—
145#95—131no—
146#95—132no—
147#95—132no—
148#95—131no—
149#95C2×D1312yes—
150C2×C13—42no—
151C2×C13#53812yes—
152C2×C13#53911yescharacteristic
153C2×C13#56011yescharacteristic
154C2×C13H(3,𝔽4)11yescharacteristic
155C2×C13#56212yes—
156D13—82no—
157C24—132no—
158C24C22×D1311yescharacteristic
159C2×Q8—521no—
160C2×Q8—522no—
161C2×D4—264no—
162C2×D4—521no—
163C2×D4—522no—
164C2×D4—522no—
165C2×D4—522no—
166C22×C4—41no—
167C22×C4—42no—
168C22×C4—132no—
169C22×C4—132no—
170C22×C4—132no—
171C22×C4C22×D1311yescharacteristic
172C22×C4C22×D1312yes—
173C22×C4C22×D1311yescharacteristic
174C22×C4C22×D1312yes—
175C4⋊C4—42no—
176C4⋊C4—522no—
177C22⋊C4—22no—
178C22⋊C4—41no—
179C22⋊C4—522no—
180C22⋊C4—522no—
181C22⋊C4—522no—
182C22⋊C4—522no—
183C22⋊C4—522no—
184C22⋊C4—522no—
185C13#282411yescharacteristic, complemented, Sylow
186C23—21no—
187C23—22no—
188C23—21no—
189C23—22no—
190C23—262no—
191C23—262no—
192C23—262no—
193C23—262no—
194C23—262no—
195C23—262no—
196C23—262no—
197C23#612712yes—
198C23C23×D1311yescharacteristic
199Q8—524no—
200D4—524no—
201D4—528no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—44no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C22—22no—
223C22—24no—
224C22—41no—
225C22—42no—
226C22—41no—
227C22—522no—
228C22—522no—
229C22—522no—
230C22—522no—
231C22—522no—
232C22—522no—
233C22—522no—
234C22C2×#612711yescharacteristic
235C22#8825111yescharacteristic
236C22#8825112yes—
237C22#8825411yescharacteristic
238C22#8825612yes—
239C4—42no—
240C4—42no—
241C4—41no—
242C4—41no—
243C4—522no—
244C4—522no—
245C4—522no—
246C2—42no—
247C2—1042no—
248C2#1171922011yescharacteristic
249C2#1171926512yes—
250C2#1171929911yescharacteristic
251C2#1171935212yes—
252C2#1171937111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#385C2
prime radical#11718621C2
hypercenter#385D13
hypocenterC13#2824
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C13×#385C2semidirect
2. #11718874C2semidirect
3. #11718652C2semidirect
4. #11718643C2semidirect
6. #11718620C2semidirect
7. #11718608C2semidirect
8. #11718336C2semidirect
9. #11718334C2semidirect
104. #385D13semidirect
185. C13#2824semidirect

Maximal subgroups

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

subgroupindex
C13×#3852
#117188742
#117186522
#117186432
#117186212
#117186202
#117186082
#117183362
#117183342
#282413