Finite Group Databasebeta

← #13122891

Subgroups — #13122891

Order 1664.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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×#88201C211yesmaximal, characteristic
2C2×#88143C211yesmaximal, characteristic, complemented
3C13×#395C211yesmaximal, characteristic, complemented
4#11718890C211yesmaximal, characteristic, complemented
5#11718655C212yesmaximal, complemented
6#11718653C212yesmaximal, complemented
7#11718652C211yesmaximal, characteristic
8#11718337C212yesmaximal, complemented
9#11718336C212yesmaximal, complemented
10#11718333C211yesmaximal, characteristic
11#11718311C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16#88201—24no—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2211yescharacteristic
25C2×#6101C2211yescharacteristic
26C2×#6101C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C2×C4×Dic13C2211yescharacteristic
31#88143—24no—
32C13×#95C2211yescharacteristic
33C13×#95C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C23×D13C2312yes—
38C2×Q8×C13—22no—
39C2×Q8×C13—42no—
40C22×C4×C13C2312yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C2×D52—22no—
51C2×D52—42no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—42no—
54#6103—24no—
55#6103—24no—
56#6103—42no—
57#6103—42no—
58#6103—42no—
59#6103—42no—
60C4⋊Dic13—22no—
61#6101—22no—
62#6101—22no—
63#6101—22no—
64#6101—22no—
65#6101—42no—
66#6101—42no—
67C4×Dic13D414yes—
68#2820—131nomaximal, Sylow
69C23×C13C2411yescharacteristic
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—22no—
73C22×D13—22no—
74C22×D13—22no—
75C22×D13—22no—
76C22×D13—22no—
77Q8×C13—44no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13C2×D412yes—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13C2×D412yes—
103C2×Dic13C2×D412yes—
104D52—44no—
105C2×#125—131no—
106C2×#124—131no—
107#399—132no—
108#397—132no—
109#396—132no—
110#396—132no—
111#395—131no—
112#395D1311yescharacteristic, complemented
113#394—131no—
114#394—131no—
115#382—131no—
116C22×C13C22×D411yescharacteristic
117C22×C13H(5,𝔽2)12yes—
118C22×C13H(5,𝔽2)11yescharacteristic
119C22×C132−1+412yes—
120C22×C132−1+411yescharacteristic
121C2×D13—42no—
122C2×D13—42no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13—42no—
127C2×D13—42no—
128C4×C13—22no—
129C4×C13—41no—
130C4×C13—42no—
131C4×C13—41no—
132C4×C13—42no—
133Dic13—22no—
134Dic13—22no—
135Dic13—41no—
136Dic13—41no—
137Dic13—42no—
138C22×Q8C2×D1311yescharacteristic
139C22×D4—131no—
140#125—264no—
141#124—264no—
142C2×C4⋊C4—131no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4—131no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4—132no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4C2×D1311yescharacteristic
150C2×C4⋊C4C2×D1312yes—
151C2×C22⋊C4—132no—
152C2×C22⋊C4—132no—
153C2×C22⋊C4—132no—
154C2×C22⋊C4—132no—
155C2×C22⋊C4—132no—
156C2×C22⋊C4—132no—
157C2×C42—131no—
158#95—131no—
159#95—132no—
160#95—132no—
161#95C2×D1311yescharacteristic
162#95C2×D1312yes—
163C2×C13#53511yescharacteristic
164C2×C13#53611yescharacteristic
165C2×C13#53711yescharacteristic
166C2×C13#56212yes—
167C2×C13#56312yes—
168D13—82no—
169C24—132no—
170C2×Q8—22no—
171C2×Q8—42no—
172C2×D4—262no—
173C2×D4—522no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—132no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4C22×D1312yes—
180C22×C4C22×D1312yes—
181C22×C4C22×D1311yescharacteristic
182C22×C4C22×D1311yescharacteristic
183C22×C4C22×D1311yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—262no—
187C4⋊C4—262no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—522no—
192C4⋊C4—522no—
193C22⋊C4—264no—
194C22⋊C4—264no—
195C22⋊C4—522no—
196C22⋊C4—522no—
197C22⋊C4—522no—
198C22⋊C4—522no—
199C42—134no—
200C13#282011yescharacteristic, complemented, Sylow
201C23—262no—
202C23—262no—
203C23—262no—
204C23—262no—
205C23—262no—
206C23—262no—
207C23—262no—
208C23C23×D1311yescharacteristic
209Q8—44no—
210D4—524no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—132no—
224C2×C4—132no—
225C2×C4—262no—
226C2×C4—261no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—262no—
236C2×C4D4×D1312yes—
237C22—522no—
238C22—522no—
239C22—522no—
240C22—522no—
241C22—522no—
242C22—522no—
243C22—522no—
244C22C2×D4×D1311yescharacteristic
245C22#8825112yes—
246C22#8825412yes—
247C22#8825411yescharacteristic
248C22#8825611yescharacteristic
249C4—22no—
250C4—41no—
251C4—42no—
252C4—41no—
253C4—42no—
254C4—262no—
255C4—262no—
256C4—521no—
257C4—521no—
258C4—522no—
259C2—1042no—
260C2#1171929711yescharacteristic
261C2#1171933411yescharacteristic
262C2#1171935212yes—
263C2#1171942911yescharacteristic
264C2#1171944012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#395C2
prime radicalC22×D52C22
hypercenter#395D13
hypocenterC13#2820
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#88143C2semidirect
3. C13×#395C2semidirect
4. #11718890C2semidirect
5. #11718655C2semidirect
6. #11718653C2semidirect
8. #11718337C2semidirect
9. #11718336C2semidirect
11. #11718311C2semidirect
112. #395D13semidirect
200. C13#2820semidirect

Maximal subgroups

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

subgroupindex
C2×#882012
C2×#881432
C13×#3952
#117188902
#117186552
#117186532
#117186522
#117183372
#117183362
#117183332
#117183112
#282013