Finite Group Databasebeta

← #13120639

Subgroups — #13120639

Order 1664.

464 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88150C211yesmaximal, characteristic
2C2×#88146C211yesmaximal, characteristic
3C13×#398C211yesmaximal, characteristic, complemented
4#11718654C212yesmaximal
5#11718647C211yesmaximal, characteristic, complemented
6#11718641C211yesmaximal, characteristic, complemented
7#11718633C212yesmaximal, complemented
8#11718336C212yesmaximal
9#11718328C211yesmaximal, characteristic
10#11718320C211yesmaximal, characteristic, complemented
11#11718307C212yesmaximal, complemented
12C22×C4×D13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2211yescharacteristic
19C2×#6103C2211yescharacteristic
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×#6101C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2212yes—
27#88150—24no—
28#88146—24no—
29C13×#95C2212yes—
30C13×#95C2211yescharacteristic
31#88071C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C2×C4×D13—24no—
49C2×C4×D13D414yes—
50C2×Dic26—22no—
51C2×Dic26—24no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—42no—
55#6103—24no—
56#6103—22no—
57#6103—22no—
58#6103—42no—
59C4⋊Dic13—22no—
60#6101—22no—
61#6101—22no—
62#6101—24no—
63#6101—42no—
64C4×Dic13—24no—
65#2625—131nomaximal, Sylow
66C23×C13C2411yescharacteristic
67C22×D13—22no—
68C22×D13—21no—
69C22×D13—22no—
70C22×D13—21no—
71C22×D13C2×D412yes—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D412yes—
85C2×Dic13—22no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—24no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13C2×D412yes—
96C2×Dic13#4114yes—
97C4×D13—28no—
98Dic26—44no—
99C2×C22⋊Q8—131no—
100C2×#117—131no—
101#400—131no—
102#400—131no—
103#398—131no—
104#398D1311yescharacteristic, complemented
105#397—132no—
106#397—132no—
107#391—132no—
108#389—132no—
109#380—131no—
110C22×C13C22×D411yescharacteristic
111C22×C13C2×#4112yes—
112C22×C13H(5,𝔽2)11yescharacteristic
113C22×C132−1+412yes—
114C22×C132−1+411yescharacteristic
115C2×D13—22no—
116C2×D13—22no—
117C2×D13—22no—
118C2×D13—42no—
119C2×D13—42no—
120C4×C13—22no—
121C4×C13—41no—
122C4×C13—42no—
123C4×C13—41no—
124C4×C13—42no—
125Dic13—41no—
126Dic13—42no—
127Dic13—41no—
128Dic13—42no—
129Dic13#12314yes—
130C22×Q8—131no—
131C23×C4—131no—
132C22⋊Q8—264no—
133#117—264no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—131no—
136C2×C4⋊C4—131no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4C2×D1311yescharacteristic
140C2×C4⋊C4C2×D1311yescharacteristic
141C2×C4⋊C4C2×D1312yes—
142C2×C22⋊C4—132no—
143C2×C22⋊C4—131no—
144C2×C22⋊C4—131no—
145C2×C22⋊C4—132no—
146C2×C42—132no—
147#95—131no—
148#95—132no—
149#95—132no—
150#95—132no—
151#95—132no—
152#95—132no—
153#95C2×D1311yescharacteristic
154#95C2×D1312yes—
155C2×C13C2×#12311yescharacteristic
156C2×C13#53611yescharacteristic
157C2×C13#53711yescharacteristic
158C2×C13#54112yes—
159C2×C13#54212yes—
160D13—42no—
161C24—131no—
162C2×Q8—262no—
163C2×Q8—264no—
164C22×C4—131no—
165C22×C4—134no—
166C22×C4—132no—
167C22×C4—132no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—264no—
171C22×C4C22×D1312yes—
172C22×C4C22×D1311yescharacteristic
173C22×C4C22×D1311yescharacteristic
174C22×C4C22×D1312yes—
175C22×C4C22×D1311yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—262no—
180C4⋊C4—264no—
181C4⋊C4—262no—
182C4⋊C4—262no—
183C4⋊C4—522no—
184C22⋊C4—264no—
185C22⋊C4—262no—
186C22⋊C4—262no—
187C22⋊C4—522no—
188C42—264no—
189C13#262511yescharacteristic, complemented, Sylow
190C23—132no—
191C23—261no—
192C23—262no—
193C23—262no—
194C23—261no—
195C23C23×D1311yescharacteristic
196Q8—524no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—132no—
210C2×C4—134no—
211C2×C4—268no—
212C2×C4—262no—
213C2×C4—261no—
214C2×C4—261no—
215C2×C4—262no—
216C2×C4—261no—
217C2×C4—264no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4D4×D1312yes—
223C22—262no—
224C22—262no—
225C22—262no—
226C22—522no—
227C22—522no—
228C22C2×D4×D1311yescharacteristic
229C22#8825111yescharacteristic
230C22#8825412yes—
231C22#41×D1312yes—
232C22#8825711yescharacteristic
233C4—22no—
234C4—42no—
235C4—41no—
236C4—42no—
237C4—41no—
238C4—134no—
239C4—522no—
240C4—521no—
241C4—522no—
242C4—521no—
243C2—522no—
244C2#1171931311yescharacteristic
245C2#1171934512yes—
246C2D13×#12311yescharacteristic
247C2#1171940112yes—
248C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC23×D13C23
hypercenter#398D13
hypocenterC13#2625
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C13×#398C2semidirect
5. #11718647C2semidirect
6. #11718641C2semidirect
7. #11718633C2semidirect
10. #11718320C2semidirect
11. #11718307C2semidirect
104. #398D13semidirect
189. C13#2625semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×#881462
C13×#3982
#117186542
#117186472
#117186412
#117186332
#117183362
#117183282
#117183202
#117183072
#262513