Finite Group Databasebeta

← #13120662

Subgroups — #13120662

Order 1664.

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

normal subgroups only

This group has 488 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×#88142C211yesmaximal, characteristic, complemented
2C2×#88131C211yesmaximal, characteristic
3C13×#399C211yesmaximal, characteristic
4#11718643C211yesmaximal, characteristic, complemented
5#11718640C212yesmaximal, complemented
6#11718633C212yesmaximal, complemented
7#11718610C211yesmaximal, characteristic
8#11718608C212yesmaximal
9#11718603C212yesmaximal
10#11718320C211yesmaximal, characteristic, complemented
11#11718311C211yesmaximal, characteristic, complemented
12C23×Dic13C2211yescharacteristic
13C22×Dic26C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22C2×#6101C2211yescharacteristic
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28#88142—24no—
29#88131—24no—
30C13×#95C2211yescharacteristic
31#88071C2212yes—
32#88071C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×Dic13—22no—
43C22×Dic13—22no—
44C22×Dic13Q814yescomplemented
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2312yes—
47C22×Dic13C2312yes—
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2311yescharacteristic
51C2×Dic26—24no—
52C2×Dic26—42no—
53C2×Dic26—42no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—42no—
56C13×C22⋊C4—22no—
57C13×C22⋊C4—42no—
58C22⋊Dic13—22no—
59C22⋊Dic13—42no—
60C4⋊Dic13—22no—
61#6101—22no—
62#6101—22no—
63#6101—24no—
64#6101—24no—
65#6101—42no—
66C4×Dic13—22no—
67C4×Dic13D414yes—
68#2628—131nomaximal, Sylow
69C23×C13—21no—
70C23×C13—21no—
71C23×C13—22no—
72C23×C13—22no—
73C23×C13C2×Q812yes—
74C23×C13C2411yescharacteristic
75C2×C4×C13—22no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D412yes—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—28no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13C2×D412yes—
98C2×Dic13C2×D412yes—
99C2×Dic13C2×Q812yes—
100C2×Dic13C2×Q812yes—
101C2×Dic13#4112yes—
102Dic26—48no—
103C2×C4⋊Q8—131no—
104C2×#117—131no—
105#400—131no—
106#400—131no—
107#399—131no—
108#399D1311yescharacteristic
109#395—132no—
110#393—132no—
111#389—132no—
112#382—131no—
113#380—132no—
114C22×C13—22no—
115C22×C13—24no—
116C22×C13—41no—
117C22×C13—41no—
118C22×C13—42no—
119C22×C13C22×D411yescharacteristic
120C22×C13C22×Q811yescharacteristic
121C22×C13C2×#4111yescharacteristic
122C22×C13H(5,𝔽2)12yes—
123C22×C132−1+412yes—
124C4×C13—22no—
125C4×C13—42no—
126C4×C13—41no—
127C4×C13—42no—
128Dic13—22no—
129Dic13—22no—
130Dic13—42no—
131Dic13—41no—
132Dic13—42no—
133Dic13C22⋊Q814yes—
134C22×Q8—132no—
135C23×C4—131no—
136C4⋊Q8—264no—
137#117—264no—
138C2×C4⋊C4—131no—
139C2×C4⋊C4—131no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4—131no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—132no—
144C2×C4⋊C4C2×D1311yescharacteristic
145C2×C4⋊C4C2×D1312yes—
146C2×C22⋊C4—131no—
147C2×C22⋊C4—132no—
148C2×C22⋊C4C2×D1311yescharacteristic
149C2×C22⋊C4C2×D1312yes—
150C2×C42—131no—
151C2×C42—131no—
152#95—132no—
153#95—132no—
154#95—132no—
155#95—131no—
156#95—132no—
157#95—132no—
158#95C2×D1311yescharacteristic
159C2×C13—42no—
160C2×C13C2×C22⋊Q811yescharacteristic
161C2×C13#53511yescharacteristic
162C2×C13#53611yescharacteristic
163C2×C13#54212yes—
164C2×C13#54412yes—
165C24C22×D1311yescharacteristic
166C2×Q8—264no—
167C2×Q8—522no—
168C2×Q8—522no—
169C22×C4—131no—
170C22×C4—134no—
171C22×C4—131no—
172C22×C4—131no—
173C22×C4—131no—
174C22×C4—132no—
175C22×C4—132no—
176C22×C4—262no—
177C22×C4—262no—
178C22×C4C22×D1312yes—
179C22×C4C22×D1312yes—
180C22×C4C22×D1311yescharacteristic
181C22×C4C22×D1311yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—42no—
184C4⋊C4—262no—
185C4⋊C4—264no—
186C4⋊C4—264no—
187C4⋊C4—262no—
188C4⋊C4—262no—
189C4⋊C4—522no—
190C22⋊C4—22no—
191C22⋊C4—42no—
192C22⋊C4—262no—
193C22⋊C4—522no—
194C42—134no—
195C42—262no—
196C13#262811yescharacteristic, complemented, Sylow
197C23—21no—
198C23—22no—
199C23—21no—
200C23—22no—
201C23Q8×D1312yes—
202C23C23×D1311yescharacteristic
203Q8—528no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—132no—
214C2×C4—132no—
215C2×C4—132no—
216C2×C4—132no—
217C2×C4—132no—
218C2×C4—268no—
219C2×C4—261no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4D4×D1312yes—
231C22—24no—
232C22—22no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22C2×D4×D1311yescharacteristic
237C22#8825112yes—
238C22C2×Q8×D1311yescharacteristic
239C22#41×D1311yescharacteristic
240C22#8825712yes—
241C4—22no—
242C4—42no—
243C4—41no—
244C4—42no—
245C4—134no—
246C4—262no—
247C4—262no—
248C4—521no—
249C4—522no—
250C4—522no—
251C2—42no—
252C2#1171932812yes—
253C2D13×C22⋊Q811yescharacteristic
254C2#1171935311yescharacteristic
255C2#1171936712yes—
256C2#1171942011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#399C2
prime radicalC24×C13C23
hypercenter#399D13
hypocenterC13#2628
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#88142C2semidirect
4. #11718643C2semidirect
5. #11718640C2semidirect
6. #11718633C2semidirect
10. #11718320C2semidirect
11. #11718311C2semidirect
44. C22×Dic13Q8semidirect
196. C13#2628semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
C2×#881312
C13×#3992
#117186432
#117186402
#117186332
#117186102
#117186082
#117186032
#117183202
#117183112
#262813