Finite Group Databasebeta

← #13118096

Subgroups — #13118096

Order 1664.

560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4×C22⋊D13C211yesmaximal, characteristic
2C2×#88180C211yesmaximal, characteristic, complemented
3C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
4#11718622C212yesmaximal
5#11718614C212yesmaximal, complemented
6C4×#6103C212yesmaximal, complemented
7C4×C4⋊Dic13C212yesmaximal, complemented
8#11718338C211yesmaximal, characteristic, complemented
9#11718335C211yesmaximal, characteristic, complemented
10#11718322C211yesmaximal, characteristic, complemented
11#11718320C211yesmaximal, characteristic, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C42×C13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2211yescharacteristic
19C4×C22⋊D13—24no—
20C2×#6103C2211yescharacteristic
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23#88180—24no—
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2212yes—
27C2×C4⋊Dic13C2212yes—
28C2×#6101C2211yescharacteristic
29C2×C4×Dic13C2212yes—
30C2×C4×Dic13C2211yescharacteristic
31C13×#95C2211yescharacteristic
32C13×#95C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13—24no—
40C22×C4×C13D414yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2312yes—
50C22×Dic13C2312yes—
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C2×C4×D13—22no—
54C2×C4×D13—24no—
55C13×C22⋊C4—24no—
56C42×C13—24no—
57C22⋊Dic13—24no—
58C22⋊Dic13—22no—
59#6103—24no—
60#6103—22no—
61#6103—24no—
62C4⋊Dic13—22no—
63C4⋊Dic13—22no—
64C4⋊Dic13—24no—
65C4⋊Dic13—24no—
66#6101—22no—
67C4×Dic13—24no—
68C4×Dic13—22no—
69#2395—131nomaximal, Sylow
70C23×C13—22no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—22no—
74C23×C13C2×D412yes—
75C23×C13C2411yescharacteristic
76C22×D13—21no—
77C22×D13—22no—
78C22×D13—22no—
79C22×D13—21no—
80C22×D13#4112yes—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—28no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13C2×D412yes—
89C2×C4×C13C2×D412yes—
90C2×C4×C13#4114yes—
91C2×C4×C13#4114yes—
92C22⋊D13—28no—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13#4112yes—
106C4×D13—44no—
107C2×C4×D4—131no—
108C2×#117—131no—
109#400—131no—
110#399—131no—
111#398—131no—
112#397—132no—
113#397—131no—
114#394—132no—
115C4×C4⋊C4—132no—
116C4×C22⋊C4—132no—
117C4×C22⋊C4D1311yescharacteristic, complemented
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—42no—
122C22×C13—42no—
123C22×C13C22×D411yescharacteristic
124C22×C13C2×#4112yes—
125C22×C13C2×#4112yes—
126C22×C13C2×#4111yescharacteristic
127C22×C13C2×#4111yescharacteristic
128C2×D13—22no—
129C2×D13—24no—
130C2×D13—41no—
131C2×D13—42no—
132C2×D13—41no—
133C4×C13—22no—
134C4×C13—24no—
135C4×C13—42no—
136C4×C13#12314yes—
137Dic13—22no—
138Dic13—41no—
139Dic13—42no—
140Dic13—42no—
141Dic13—41no—
142C22×D4—131no—
143C23×C4—131no—
144C23×C4C2×D1311yescharacteristic
145C4×D4—264no—
146#117—264no—
147C2×C4⋊C4—131no—
148C2×C4⋊C4—131no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—132no—
152C2×C22⋊C4—132no—
153C2×C22⋊C4—131no—
154C2×C22⋊C4—131no—
155C2×C22⋊C4—132no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4C2×D1312yes—
158C2×C42—132no—
159C2×C42—131no—
160C2×C42C2×D1312yes—
161#95—132no—
162#95—132no—
163#95—132no—
164#95—132no—
165#95C2×D1311yescharacteristic
166#95C2×D1311yescharacteristic
167C2×C13—42no—
168C2×C13C2×#12311yescharacteristic
169C2×C13#52511yescharacteristic
170C2×C13#52912yes—
171C2×C13#52912yes—
172C2×C13#53211yescharacteristic
173D13—42no—
174C24—131no—
175C24C22×D1311yescharacteristic
176C2×D4—262no—
177C2×D4—262no—
178C2×D4—262no—
179C22×C4—24no—
180C22×C4—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—132no—
184C22×C4—132no—
185C22×C4—262no—
186C22×C4—264no—
187C22×C4D5214yes—
188C22×C4C22×D1312yes—
189C22×C4C22×D1311yescharacteristic
190C22×C4C22×D1312yes—
191C22×C4C22×D1311yescharacteristic
192C4⋊C4—264no—
193C4⋊C4—262no—
194C4⋊C4—262no—
195C4⋊C4—262no—
196C4⋊C4—264no—
197C22⋊C4—24no—
198C22⋊C4—264no—
199C22⋊C4—264no—
200C22⋊C4—262no—
201C22⋊C4—262no—
202C22⋊C4—264no—
203C42—24no—
204C42—264no—
205C42—262no—
206C13#239511yescharacteristic, complemented, Sylow
207C23—22no—
208C23—22no—
209C23—21no—
210C23—21no—
211C23—132no—
212C23—261no—
213C23—262no—
214C23—262no—
215C23—261no—
216C23C2×D5212yes—
217C23C23×D1311yescharacteristic
218D4—268no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—28no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—132no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—524no—
240C2×C4C2×D5212yes—
241C2×C4C2×D5212yes—
242C2×C4#612714yes—
243C2×C4#612914yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—262no—
250C22—264no—
251C22—521no—
252C22—521no—
253C22—522no—
254C22C22×D5211yescharacteristic
255C22C2×#612712yes—
256C22C2×#612912yes—
257C22#41×D1311yescharacteristic
258C22#41×D1311yescharacteristic
259C4—22no—
260C4—24no—
261C4—42no—
262C4—262no—
263C4—521no—
264C4—522no—
265C4—521no—
266C4—522no—
267C4#8814014yes—
268C2—42no—
269C2—522no—
270C2#1171918211yescharacteristic
271C2C2×#8814011yescharacteristic
272C2#1171922911yescharacteristic
273C2#1171924312yes—
274C2#1171926212yes—
subgroupG/H
centerC22×C4C22×D13
commutator, socle, cosocleC23×C13C24
FrattiniC23C23×D13
FittingC4×C13×C22⋊C4C2
prime radicalC22×C22⋊D13C22
hypercenterC4×C22⋊C4D13
hypocenterC13#2395
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#88180C2semidirect
3. C4×C13×C22⋊C4C2semidirect
5. #11718614C2semidirect
6. C4×#6103C2semidirect
7. C4×C4⋊Dic13C2semidirect
8. #11718338C2semidirect
9. #11718335C2semidirect
10. #11718322C2semidirect
11. #11718320C2semidirect
117. C4×C22⋊C4D13semidirect
206. C13#2395semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D132
C2×#881802
C4×C13×C22⋊C42
#117186222
#117186142
C4×#61032
C4×C4⋊Dic132
#117183382
#117183352
#117183222
#117183202
#239513