Finite Group Databasebeta

← #13130977

Subgroups — #13130977

Order 1664.

408 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 72 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×#88138C211yesmaximal, characteristic
2C2×#88119C212yesmaximal, complemented
3#11719136C211yesmaximal, characteristic, complemented
4C4×C22⋊#261C211yesmaximal, characteristic, complemented
5C2×#88107C212yesmaximal, complemented
6C22×C22⋊D13C411yescharacteristic, complemented
7C22×C22⋊D13C2211yescharacteristic
8C22×D52C2211yescharacteristic
9C22×C4×D13C2211yescharacteristic
10C2×C22⋊#261C2212yes—
11C2×C22⋊#261C2212yes—
12C2×C4⋊#261—21no—
13C2×C4×#261—21no—
14C2×C13×C22⋊C4C411yescharacteristic, complemented
15C2×#6103C411yescharacteristic, complemented
16C2×#6101C411yescharacteristic, complemented
17#88138—21no—
18#88138—21no—
19#88138—21no—
20#88138—21no—
21#88119—24no—
22(C2×#261)⋊C4—21no—
23(C2×#261)⋊C4—21no—
24#88107—24no—
25C24×C13C2×C411yescharacteristic
26C23×D13C2×C411yescharacteristic
27C23×D13C2311yescharacteristic
28C22×#261—22no—
29C22×#261—22no—
30C22×C4×C13C2×C411yescharacteristic
31C22×C4×C13C2×C411yescharacteristic
32C2×C22⋊D13—22no—
33C2×C22⋊D13—21no—
34C2×C22⋊D13—21no—
35C2×C22⋊D13—22no—
36C2×C22⋊D13—21no—
37C2×C22⋊D13—21no—
38C2×C22⋊D13—42no—
39C22×Dic13C2×C411yescharacteristic
40C22×Dic13C2×C411yescharacteristic
41C2×D52—22no—
42C2×D52—21no—
43C2×D52—21no—
44C2×D52—22no—
45C2×C4×D13—42no—
46C2×C4×D13D411yescharacteristic
47C2×C4×D13D411yescharacteristic
48C2×C4×D13D411yescharacteristic
49C2×C4×D13D411yescharacteristic
50C22⋊#261—22no—
51C22⋊#261—22no—
52C22⋊#261—22no—
53C22⋊#261D414yescomplemented
54C4⋊#261—42no—
55C4×#261—42no—
56C13×C22⋊C4—21no—
57C13×C22⋊C4—21no—
58#6103—21no—
59#6103—21no—
60#6101—21no—
61#6101—21no—
62#1964—131nomaximal, Sylow
63C23×C13—21no—
64C23×C13—22no—
65C23×C13—41no—
66C23×C13—41no—
67C23×C13C22×C411yescharacteristic
68C22×D13—21no—
69C22×D13—22no—
70C22×D13—41no—
71C22×D13—41no—
72C22×D13—41no—
73C22×D13—41no—
74C22×D13C2×D411yescharacteristic
75C22×D13C2×D411yescharacteristic
76C22×D13C2×D412yes—
77C22×D13#4112yes—
78C2×#261—24no—
79C2×#261—42no—
80C2×#261—42no—
81C2×#261—42no—
82C2×#261—42no—
83C2×#261—42no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—41no—
87C2×C4×C13C22⋊C411yescharacteristic
88C2×C4×C13C22⋊C411yescharacteristic
89C22⋊D13—42no—
90C22⋊D13—42no—
91C22⋊D13—41no—
92C22⋊D13—41no—
93C22⋊D13—42no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13C22⋊C411yescharacteristic
98C2×Dic13C22⋊C411yescharacteristic
99D52—42no—
100D52—41no—
101D52—41no—
102C4×D13—22no—
103C4×D13—22no—
104C4×D13—41no—
105C4×D13—41no—
106C2×#121—131no—
107C2×#99—132no—
108C2×#99—132no—
109#380—131no—
110C4×C22⋊C4—131no—
111C22×C13—21no—
112C22×C13—21no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—82no—
117C22×C13C2×C22⋊C411yescharacteristic
118C22×C13C4×D412yes—
119C2×D13—21no—
120C2×D13—21no—
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—41no—
126C2×D13—41no—
127C2×D13—41no—
128C2×D13—82no—
129C2×D13#12112yes—
130C2×D13#12411yescharacteristic
131C2×D13#12711yescharacteristic
132#261—44no—
133#261—82no—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—41no—
137Dic13—21no—
138Dic13—41no—
139Dic13#9912yescomplemented
140C22×D4—131no—
141C22×D4—131no—
142C22×D4—131no—
143C23×C4—131no—
144#121—261no—
145#121—261no—
146#121—261no—
147#121—261no—
148C2×C4⋊C4—131no—
149C2×C4⋊C4—261no—
150C2×C22⋊C4—132no—
151C2×C22⋊C4—131no—
152C2×C22⋊C4—132no—
153C2×C22⋊C4#26111yescharacteristic, complemented
154C2×C42—261no—
155#99—264no—
156#99—264no—
157#95—261no—
158#95—261no—
159C2×C13—22no—
160C2×C13—81no—
161C2×C13#39011yescharacteristic
162C2×C13C2×#9911yescharacteristic
163C2×C13#41011yescharacteristic
164D13—22no—
165D13—21no—
166D13—21no—
167D13—81no—
168C24—131no—
169C24—131no—
170C24C2×#26111yescharacteristic
171C2×D4—262no—
172C2×D4—261no—
173C2×D4—261no—
174C2×D4—262no—
175C2×D4—261no—
176C2×D4—261no—
177C2×D4—262no—
178C2×D4—261no—
179C2×D4—261no—
180C2×D4—262no—
181C2×D4—522no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—131no—
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—522no—
191C22×C4C2×#26111yescharacteristic
192C22×C4C2×#26111yescharacteristic
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4—522no—
196C22⋊C4—21no—
197C22⋊C4—21no—
198C22⋊C4—134no—
199C22⋊C4—262no—
200C22⋊C4—261no—
201C22⋊C4—261no—
202C22⋊C4—262no—
203C22⋊C4—262no—
204C42—522no—
205C13#196411yescharacteristic, complemented, Sylow
206C23—21no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—131no—
211C23—131no—
212C23—132no—
213C23—132no—
214C23—261no—
215C23—262no—
216C23—521no—
217C23—521no—
218C23—521no—
219C23—521no—
220C23C22×#26111yescharacteristic
221D4—522no—
222D4—521no—
223D4—521no—
224D4—522no—
225D4—522no—
226D4—522no—
227D4—521no—
228D4—521no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—131no—
233C2×C4—131no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—264no—
238C2×C4—262no—
239C2×C4—261no—
240C2×C4—521no—
241C2×C4—521no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4C22⋊#26111yescharacteristic
248C2×C4C22⋊#26111yescharacteristic
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—82no—
255C22—132no—
256C22—131no—
257C22—131no—
258C22—261no—
259C22—261no—
260C22—261no—
261C22—261no—
262C22—522no—
263C22—522no—
264C22—521no—
265C22—521no—
266C22—521no—
267C22—1042no—
268C22D4×#26112yes—
269C22C2×C22⋊#26111yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—132no—
274C4—261no—
275C4—524no—
276C4—521no—
277C4—1042no—
278C2—22no—
279C2—81no—
280C2—262no—
281C2—261no—
282C2—261no—
283C2—1041no—
284C2#1171911611yescharacteristic
285C2D13⋊#9911yescharacteristic
286C2#1171915111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C22⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC2×#88138C2
cosocleC23×D13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#1964
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#88119C2semidirect
3. #11719136C2semidirect
4. C4×C22⋊#261C2semidirect
5. C2×#88107C2semidirect
6. C22×C22⋊D13C4semidirect
14. C2×C13×C22⋊C4C4semidirect
15. C2×#6103C4semidirect
16. C2×#6101C4semidirect
53. C22⋊#261D4semidirect
139. Dic13#99semidirect
153. C2×C22⋊C4#261semidirect
205. C13#1964semidirect

Maximal subgroups

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

subgroupindex
C2×#881382
C2×#881192
#117191362
C4×C22⋊#2612
C2×#881072
#196413