Finite Group Databasebeta

← #13130860

Subgroups — #13130860

Order 1664.

378 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 70 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×#88237C211yesmaximal, characteristic, complemented
2C2×#88148C211yesmaximal, characteristic
3#11719135C211yesmaximal, characteristic, complemented
4C2×#88107C212yesmaximal
5#11718289C212yesmaximal, complemented
6C22×D52C2211yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261C2212yes—
9C2×C22⋊#261C2212yes—
10#88237—24no—
11C2×C4⋊#261—21no—
12C2×C4×#261—21no—
13C2×C13×C4⋊C4C411yescharacteristic, complemented
14C2×#6103C411yescharacteristic, complemented
15C2×#6103C411yescharacteristic, complemented
16C2×#6103C2211yescharacteristic
17C2×#6101C411yescharacteristic, complemented
18#88148—21no—
19#88148—21no—
20#88148—21no—
21#88148—21no—
22(C2×#261)⋊C4—21no—
23(C2×#261)⋊C4—21no—
24#88107—24no—
25C23×D13C2×C411yescharacteristic
26C23×D13C2311yescharacteristic
27C22×#261—22no—
28C22×#261—22no—
29C22×C4×C13C2×C411yescharacteristic
30C22×C4×C13C2×C411yescharacteristic
31C22×C4×C13C2×C411yescharacteristic
32C22×Dic13C2×C411yescharacteristic
33C22×Dic13C2×C411yescharacteristic
34C2×D52—22no—
35C2×D52—21no—
36C2×D52—21no—
37C2×D52—22no—
38C2×C4×D13—22no—
39C2×C4×D13—22no—
40C2×C4×D13D411yescharacteristic
41C2×C4×D13D411yescharacteristic
42C2×C4×D13D411yescharacteristic
43C2×C4×D13D411yescharacteristic
44C22⋊#261—22no—
45C22⋊#261—22no—
46C22⋊#261—22no—
47C22⋊#261D414yes—
48C4⋊#261—24no—
49C4×#261—24no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4—21no—
52#6103—21no—
53#6103—21no—
54#6103—21no—
55#6103—21no—
56#6103—21no—
57#6103—21no—
58#6101—21no—
59#6101—21no—
60#1899—131nomaximal, Sylow
61C23×C13C22×C411yescharacteristic
62C22×D13—21no—
63C22×D13—22no—
64C22×D13—41no—
65C22×D13—41no—
66C22×D13—41no—
67C22×D13—41no—
68C22×D13C2×D411yescharacteristic
69C22×D13C2×D411yescharacteristic
70C22×D13C2×D412yes—
71C22×D13#4112yes—
72C2×#261—24no—
73C2×#261—42no—
74C2×#261—42no—
75C2×#261—42no—
76C2×#261—42no—
77C2×#261—42no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—41no—
83C2×C4×C13C22⋊C411yescharacteristic
84C2×C4×C13C22⋊C411yescharacteristic
85C2×Dic13—22no—
86C2×Dic13—21no—
87C2×Dic13—41no—
88C2×Dic13C22⋊C411yescharacteristic
89C2×Dic13C22⋊C411yescharacteristic
90D52—41no—
91D52—42no—
92D52—41no—
93C4×D13—21no—
94C4×D13—21no—
95C4×D13—22no—
96C4×D13—22no—
97C4×D13—21no—
98C4×D13—21no—
99C2×#123—131no—
100C2×#117—131no—
101C2×#99—132no—
102#381—131no—
103#342—132no—
104C22×C13—21no—
105C22×C13—21no—
106C22×C13C2×C22⋊C411yescharacteristic
107C22×C13C4×D412yes—
108C2×D13—21no—
109C2×D13—21no—
110C2×D13—21no—
111C2×D13—21no—
112C2×D13—42no—
113C2×D13—42no—
114C2×D13—41no—
115C2×D13—41no—
116C2×D13—41no—
117C2×D13—82no—
118C2×D13#12011yescharacteristic
119C2×D13#12112yes—
120C2×D13#12311yescharacteristic
121#261—44no—
122#261—82no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—41no—
126C4×C13—41no—
127Dic13—21no—
128Dic13—21no—
129Dic13—41no—
130C22×D4—131no—
131C23×C4—131no—
132#123—261no—
133#123—261no—
134#123—261no—
135#123—261no—
136#117—264no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—261no—
139C2×C4⋊C4#26111yescharacteristic, complemented
140C2×C22⋊C4—132no—
141C2×C22⋊C4—131no—
142C2×C22⋊C4—131no—
143C2×C22⋊C4—131no—
144C2×C22⋊C4—132no—
145C2×C42—261no—
146#99—264no—
147#95—261no—
148#95—261no—
149C2×C13—22no—
150C2×C13#38611yescharacteristic
151C2×C13#41011yescharacteristic
152C2×C13#41011yescharacteristic
153D13—21no—
154D13—22no—
155D13—21no—
156D13—81no—
157C24—131no—
158C24—131no—
159C2×D4—262no—
160C2×D4—261no—
161C2×D4—261no—
162C2×D4—262no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—262no—
170C22×C4—262no—
171C22×C4—262no—
172C22×C4—262no—
173C22×C4C2×#26111yescharacteristic
174C22×C4C2×#26111yescharacteristic
175C22×C4C2×#26111yescharacteristic
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—261no—
179C4⋊C4—261no—
180C4⋊C4—264no—
181C22⋊C4—134no—
182C22⋊C4—261no—
183C22⋊C4—261no—
184C22⋊C4—261no—
185C22⋊C4—261no—
186C22⋊C4—262no—
187C22⋊C4—261no—
188C22⋊C4—261no—
189C22⋊C4—262no—
190C22⋊C4—262no—
191C42—264no—
192C13#189911yescharacteristic, complemented, Sylow
193C23—131no—
194C23—131no—
195C23—132no—
196C23—132no—
197C23—261no—
198C23—262no—
199C23—521no—
200C23—521no—
201C23—521no—
202C23—521no—
203C23C22×#26111yescharacteristic
204D4—521no—
205D4—522no—
206D4—521no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—131no—
213C2×C4—131no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—261no—
219C2×C4—261no—
220C2×C4—262no—
221C2×C4—264no—
222C2×C4—261no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—521no—
226C2×C4—522no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4C22⋊#26111yescharacteristic
230C2×C4C22⋊#26111yescharacteristic
231C22—21no—
232C22—21no—
233C22—131no—
234C22—132no—
235C22—131no—
236C22—261no—
237C22—261no—
238C22—261no—
239C22—261no—
240C22—522no—
241C22—522no—
242C22—521no—
243C22—521no—
244C22—521no—
245C22—1042no—
246C22D4×#26112yes—
247C22C2×C22⋊#26111yescharacteristic
248C4—21no—
249C4—21no—
250C4—41no—
251C4—41no—
252C4—261no—
253C4—261no—
254C4—524no—
255C4—521no—
256C4—1042no—
257C2—22no—
258C2—261no—
259C2—262no—
260C2—261no—
261C2—1041no—
262C2#1171911611yescharacteristic
263C2#1171915011yescharacteristic
264C2#1171915611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D52C22
cosocleC23×D13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1899
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#88237C2semidirect
3. #11719135C2semidirect
5. #11718289C2semidirect
13. C2×C13×C4⋊C4C4semidirect
14. C2×#6103C4semidirect
15. C2×#6103C4semidirect
17. C2×#6101C4semidirect
139. C2×C4⋊C4#261semidirect
192. C13#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#882372
C2×#881482
#117191352
C2×#881072
#117182892
#189913