Finite Group Databasebeta

← #13120406

Subgroups — #13120406

Order 1664.

492 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 139 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×Q8×Dic13C211yesmaximal, characteristic, complemented
2C2×#88131C211yesmaximal, characteristic
3C13×#393C211yesmaximal, characteristic
4#11718890C211yesmaximal, characteristic, complemented
5#11718614C211yesmaximal, characteristic
6#11718611C212yesmaximal
7#11718606C212yesmaximal
8#11718322C211yesmaximal, characteristic, complemented
9#11718316C212yesmaximal, complemented
10#11718315C212yesmaximal, complemented
11#11718312C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C23×Dic13C2211yescharacteristic
14C2×C13×C22⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18Q8×Dic13—24no—
19C2×C4⋊Dic13C2212yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2212yes—
22C2×#6101C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28#88131—24no—
29C13×#95C2211yescharacteristic
30C13×#95C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C2×Q8×C13—22no—
39C2×Q8×C13—24no—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×Dic13—22no—
45C22×Dic13—22no—
46C22×Dic13—22no—
47C22×Dic13C2312yes—
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2312yes—
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C13×C22⋊C4—22no—
54C13×C22⋊C4—24no—
55C22⋊Dic13—24no—
56C22⋊Dic13—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13—24no—
59C4⋊Dic13—24no—
60#6101—22no—
61#6101—24no—
62#6101—22no—
63C4×Dic13—22no—
64C4×Dic13—24no—
65C4×Dic13D414yes—
66#2599—131nomaximal, Sylow
67C23×C13—21no—
68C23×C13—22no—
69C23×C13—21no—
70C23×C13—22no—
71C23×C13#4112yes—
72C23×C13C2411yescharacteristic
73Q8×C13—28no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13C2×D412yes—
83C2×C4×C13#4114yes—
84C2×Dic13—28no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13C2×D412yes—
99C2×Dic13C2×D412yes—
100C2×Dic13#4112yes—
101C2×C4×Q8—131no—
102C2×#117—131no—
103#398—131no—
104#397—131no—
105#395—131no—
106#393D1311yescharacteristic
107#388—132no—
108#387—132no—
109#387—132no—
110#385—132no—
111#383—131no—
112C22×C13—22no—
113C22×C13—24no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—42no—
117C22×C13C22×D411yescharacteristic
118C22×C13C2×#4112yes—
119C22×C13C2×#4111yescharacteristic
120C22×C13C2×#4111yescharacteristic
121C22×C132−1+412yes—
122C4×C13—22no—
123C4×C13—24no—
124C4×C13—41no—
125C4×C13—42no—
126Dic13—22no—
127Dic13—22no—
128Dic13—22no—
129Dic13—41no—
130Dic13—42no—
131Dic13—42no—
132C22×Q8C2×D1311yescharacteristic
133C23×C4—131no—
134C4×Q8—264no—
135#117—264no—
136C2×C4⋊C4—131no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—131no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4—132no—
142C2×C22⋊C4—131no—
143C2×C22⋊C4—132no—
144C2×C22⋊C4C2×D1311yescharacteristic
145C2×C22⋊C4C2×D1312yes—
146C2×C42—131no—
147C2×C42—131no—
148C2×C42—132no—
149#95—132no—
150#95—132no—
151#95—131no—
152#95—132no—
153#95—132no—
154#95—132no—
155#95C2×D1311yescharacteristic
156#95C2×D1312yes—
157C2×C13—42no—
158C2×C13#52511yescharacteristic
159C2×C13#52511yescharacteristic
160C2×C13#53611yescharacteristic
161C2×C13#55212yes—
162C2×C13#55612yes—
163C24C22×D1311yescharacteristic
164C2×Q8—22no—
165C2×Q8—24no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—132no—
170C22×C4—131no—
171C22×C4—132no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4—262no—
175C22×C4C22×D1312yes—
176C22×C4C22×D1311yescharacteristic
177C22×C4C22×D1311yescharacteristic
178C22×C4C22×D1312yes—
179C4⋊C4—262no—
180C4⋊C4—264no—
181C4⋊C4—264no—
182C4⋊C4—262no—
183C4⋊C4—262no—
184C4⋊C4—264no—
185C22⋊C4—22no—
186C22⋊C4—24no—
187C22⋊C4—262no—
188C22⋊C4—264no—
189C42—134no—
190C42—262no—
191C42—264no—
192C13#259911yescharacteristic, complemented, Sylow
193C23—21no—
194C23—22no—
195C23—21no—
196C23—22no—
197C23#613112yes—
198C23C23×D1311yescharacteristic
199Q8—28no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—132no—
209C2×C4—132no—
210C2×C4—132no—
211C2×C4—268no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—262no—
217C2×C4—261no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4D4×D1312yes—
226C2×C4#612914yes—
227C22—22no—
228C22—24no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22C2×D4×D1311yescharacteristic
233C22C2×#612912yes—
234C22C2×#613111yescharacteristic
235C22#41×D1311yescharacteristic
236C22#8825712yes—
237C4—22no—
238C4—24no—
239C4—42no—
240C4—41no—
241C4—262no—
242C4—262no—
243C4—262no—
244C4—521no—
245C4—522no—
246C4—522no—
247C2—42no—
248C2#1171929111yescharacteristic
249C2#1171933211yescharacteristic
250C2#1171934712yes—
251C2#1171937612yes—
252C2#1171938011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC24×C13C23
hypercenter#393D13
hypocenterC13#2599
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic13C2semidirect
4. #11718890C2semidirect
8. #11718322C2semidirect
9. #11718316C2semidirect
10. #11718315C2semidirect
11. #11718312C2semidirect
192. C13#2599semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
C2×#881312
C13×#3932
#117188902
#117186142
#117186112
#117186062
#117183222
#117183162
#117183152
#117183122
#259913