Finite Group Databasebeta

← #13120648

Subgroups — #13120648

Order 1664.

508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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×#88200C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic
3C13×#395C211yesmaximal, characteristic, complemented
4#11718890C211yesmaximal, characteristic, complemented
5#11718650C212yesmaximal
6#11718647C211yesmaximal, characteristic, complemented
7#11718641C212yesmaximal, complemented
8#11718328C211yesmaximal, characteristic
9#11718325C212yesmaximal
10#11718320C211yesmaximal, characteristic, complemented
11#11718318C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2212yes—
18#88200—24no—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2211yescharacteristic
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×#6101C2212yes—
28C4⋊C4×D13—24no—
29C13×#95C2212yes—
30C13×#95C2211yescharacteristic
31#88071C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C2×Q8×C13—22no—
39C2×Q8×C13—42no—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C2×C4×D13—22no—
51C2×C4×D13—22no—
52C2×C4×D13—22no—
53C2×C4×D13—42no—
54C2×C4×D13—42no—
55C2×C4×D13D414yes—
56C2×C4×D13Q814yescomplemented
57C13×C4⋊C4—22no—
58C13×C4⋊C4—42no—
59#6103—24no—
60#6103—24no—
61C4⋊Dic13—22no—
62C4⋊Dic13—22no—
63#6101—22no—
64#6101—22no—
65#6101—24no—
66#6101—42no—
67#6101—42no—
68#2627—131nomaximal, Sylow
69C23×C13C2411yescharacteristic
70C22×D13—22no—
71C22×D13—22no—
72C22×D13C2×D412yes—
73C22×D13C2×Q812yes—
74C22×D13#4112yes—
75Q8×C13—44no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×Q812yes—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—24no—
98C2×Dic13—22no—
99C2×Dic13C2×D412yes—
100C2×Dic13C2×Q812yes—
101C4×D13—28no—
102C4×D13—44no—
103C4×D13—44no—
104C2×C22⋊Q8—131no—
105C22×C4⋊C4—131no—
106#400—131no—
107#400—131no—
108#398—132no—
109#398—132no—
110#395—131no—
111#395D1311yescharacteristic, complemented
112#385—132no—
113#381—132no—
114#380—131no—
115C22×C13C22×D411yescharacteristic
116C22×C13C22×Q811yescharacteristic
117C22×C13C2×#4111yescharacteristic
118C22×C13H(5,𝔽2)12yes—
119C22×C132−1+412yes—
120C2×D13—22no—
121C2×D13—22no—
122C2×D13—24no—
123C2×D13—24no—
124C2×D13C22⋊Q814yes—
125C4×C13—22no—
126C4×C13—22no—
127C4×C13—41no—
128C4×C13—42no—
129C4×C13—42no—
130Dic13—22no—
131Dic13—22no—
132Dic13—41no—
133Dic13—42no—
134Dic13—42no—
135C22×Q8C2×D1311yescharacteristic
136C23×C4—131no—
137C23×C4—131no—
138C23×C4—131no—
139C22⋊Q8—264no—
140C2×C4⋊C4—131no—
141C2×C4⋊C4—131no—
142C2×C4⋊C4—131no—
143C2×C4⋊C4—132no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4—132no—
146C2×C4⋊C4—132no—
147C2×C4⋊C4—264no—
148C2×C4⋊C4C2×D1311yescharacteristic
149C2×C4⋊C4C2×D1312yes—
150C2×C22⋊C4—132no—
151C2×C22⋊C4—132no—
152#95—131no—
153#95—132no—
154#95—132no—
155#95—132no—
156#95—132no—
157#95—132no—
158#95C2×D1311yescharacteristic
159#95C2×D1312yes—
160C2×C13C2×C22⋊Q811yescharacteristic
161C2×C13#53411yescharacteristic
162C2×C13#53611yescharacteristic
163C2×C13#53912yes—
164C2×C13#54412yes—
165D13—24no—
166C24—131no—
167C2×Q8—22no—
168C2×Q8—42no—
169C22×C4—131no—
170C22×C4—131no—
171C22×C4—134no—
172C22×C4—134no—
173C22×C4—132no—
174C22×C4—132no—
175C22×C4—131no—
176C22×C4—262no—
177C22×C4—262no—
178C22×C4—262no—
179C22×C4—522no—
180C22×C4—522no—
181C22×C4C22×D1312yes—
182C22×C4C22×D1311yescharacteristic
183C22×C4C22×D1312yes—
184C22×C4C22×D1311yescharacteristic
185C22×C4C22×D1311yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—42no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—264no—
191C4⋊C4—262no—
192C4⋊C4—262no—
193C4⋊C4—522no—
194C4⋊C4—522no—
195C22⋊C4—264no—
196C22⋊C4—264no—
197C13#262711yescharacteristic, complemented, Sylow
198C23—132no—
199C23—132no—
200C23—132no—
201C23—262no—
202C23—262no—
203C23C23×D1311yescharacteristic
204Q8—44no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—132no—
217C2×C4—132no—
218C2×C4—268no—
219C2×C4—261no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4—262no—
223C2×C4—261no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—264no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—524no—
230C2×C4—524no—
231C2×C4D4×D1312yes—
232C2×C4Q8×D1312yes—
233C22—134no—
234C22—262no—
235C22—264no—
236C22—262no—
237C22—264no—
238C22C2×D4×D1311yescharacteristic
239C22#8825112yes—
240C22C2×Q8×D1311yescharacteristic
241C22#8825412yes—
242C22#41×D1311yescharacteristic
243C4—22no—
244C4—22no—
245C4—41no—
246C4—42no—
247C4—42no—
248C4—262no—
249C4—262no—
250C4—522no—
251C4—521no—
252C4—522no—
253C2—264no—
254C2#1171929411yescharacteristic
255C2D13×C22⋊Q811yescharacteristic
256C2#1171934312yes—
257C2#1171942911yescharacteristic
258C2#1171943412yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#395C2
prime radicalC23×D13C23
hypercenter#395D13
hypocenterC13#2627
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. C13×#395C2semidirect
4. #11718890C2semidirect
6. #11718647C2semidirect
7. #11718641C2semidirect
10. #11718320C2semidirect
11. #11718318C2semidirect
56. C2×C4×D13Q8semidirect
111. #395D13semidirect
197. C13#2627semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
C2×C4⋊C4×D132
C13×#3952
#117188902
#117186502
#117186472
#117186412
#117183282
#117183252
#117183202
#117183182
#262713