Finite Group Databasebeta

← #13120475

Subgroups — #13120475

Order 1664.

470 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 137 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×#88141C211yesmaximal, characteristic, complemented
2C2×#88133C211yesmaximal, characteristic
3C13×#399C211yesmaximal, characteristic
4#11718643C211yesmaximal, characteristic, complemented
5#11718642C212yesmaximal, complemented
6#11718634C212yesmaximal, complemented
7#11718612C212yesmaximal
8#11718608C211yesmaximal, characteristic
9#11718605C212yesmaximal
10#11718317C211yesmaximal, characteristic, complemented
11#11718309C211yesmaximal, characteristic, complemented
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2212yes—
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C22⋊Dic13C2211yescharacteristic
18C2×C22⋊Dic13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2212yes—
22C2×#6101C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2212yes—
25C2×C4×Dic13C2212yes—
26C2×C4×Dic13C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28#88141—24no—
29#88133—24no—
30C13×#95C2211yescharacteristic
31#88071C2211yescharacteristic
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2312yes—
48C2×Dic26—22no—
49C2×Dic26—24no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—24no—
52C13×C22⋊C4—22no—
53C13×C22⋊C4—24no—
54C22⋊Dic13—22no—
55C22⋊Dic13—22no—
56C22⋊Dic13—24no—
57C4⋊Dic13—22no—
58C4⋊Dic13—24no—
59#6101—22no—
60#6101—22no—
61#6101—24no—
62C4×Dic13—24no—
63C4×Dic13—24no—
64C4×Dic13D414yes—
65#2604—131nomaximal, Sylow
66C23×C13—21no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13—21no—
70C23×C13—21no—
71C23×C13C2411yescharacteristic
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13C2×D412yes—
81C2×C4×C13#4114yes—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13C2×D412yes—
96C2×Dic13C2×D412yes—
97C2×Dic13#4114yes—
98Dic26—28no—
99C2×#126—131no—
100C2×C4×Q8—131no—
101#400—131no—
102#399D1311yescharacteristic
103#395—131no—
104#393—131no—
105#389—132no—
106#388—132no—
107#388—132no—
108#387—132no—
109#376—131no—
110C22×C13—41no—
111C22×C13—41no—
112C22×C13—41no—
113C22×C13—42no—
114C22×C13—42no—
115C22×C13C22×D411yescharacteristic
116C22×C13C2×#4112yes—
117C22×C13C2×#4112yes—
118C22×C132−1+411yescharacteristic
119C22×C132−1+411yescharacteristic
120C4×C13—22no—
121C4×C13—24no—
122C4×C13—42no—
123C4×C13—41no—
124Dic13—24no—
125Dic13—22no—
126Dic13—22no—
127Dic13—41no—
128Dic13—41no—
129Dic13—42no—
130C22×Q8—131no—
131#126—264no—
132C4×Q8—264no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—131no—
136C2×C4⋊C4—131no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4C2×D1311yescharacteristic
139C2×C4⋊C4C2×D1312yes—
140C2×C22⋊C4—131no—
141C2×C22⋊C4—131no—
142C2×C22⋊C4—132no—
143C2×C22⋊C4C2×D1311yescharacteristic
144C2×C22⋊C4C2×D1312yes—
145C2×C42—131no—
146C2×C42—132no—
147C2×C42—132no—
148#95—132no—
149#95—131no—
150#95—132no—
151#95—132no—
152#95—132no—
153#95—132no—
154#95C2×D1311yescharacteristic
155C2×C13—81no—
156C2×C13#52511yescharacteristic
157C2×C13#53211yescharacteristic
158C2×C13#53611yescharacteristic
159C2×C13#55212yes—
160C2×C13#55612yes—
161C24C22×D1311yescharacteristic
162C2×Q8—264no—
163C2×Q8—262no—
164C22×C4—131no—
165C22×C4—132no—
166C22×C4—131no—
167C22×C4—132no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4C22×D1312yes—
171C22×C4C22×D1311yescharacteristic
172C22×C4C22×D1311yescharacteristic
173C22×C4C22×D1312yes—
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—264no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—264no—
180C4⋊C4—262no—
181C22⋊C4—22no—
182C22⋊C4—24no—
183C22⋊C4—262no—
184C22⋊C4—262no—
185C22⋊C4—264no—
186C42—134no—
187C42—264no—
188C42—264no—
189C13#260411yescharacteristic, complemented, Sylow
190C23—21no—
191C23—22no—
192C23—21no—
193C23—22no—
194C23—21no—
195C23C23×D1311yescharacteristic
196Q8—268no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—132no—
206C2×C4—132no—
207C2×C4—134no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—261no—
211C2×C4—262no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—261no—
215C2×C4—262no—
216C2×C4—261no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—261no—
221C2×C4D4×D1312yes—
222C2×C4#612914yes—
223C22—41no—
224C22—42no—
225C22—42no—
226C22—41no—
227C22—41no—
228C22C2×D4×D1311yescharacteristic
229C22C2×#612912yes—
230C22#8825411yescharacteristic
231C22#41×D1312yes—
232C22#8825711yescharacteristic
233C4—24no—
234C4—22no—
235C4—42no—
236C4—41no—
237C4—262no—
238C4—264no—
239C4—262no—
240C4—521no—
241C4—522no—
242C4—521no—
243C2—81no—
244C2#1171933311yescharacteristic
245C2#1171934612yes—
246C2#1171935512yes—
247C2#1171936111yescharacteristic
248C2#1171942111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#399C2
prime radicalC24×C13C23
hypercenter#399D13
hypocenterC13#2604
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#88141C2semidirect
4. #11718643C2semidirect
5. #11718642C2semidirect
6. #11718634C2semidirect
10. #11718317C2semidirect
11. #11718309C2semidirect
189. C13#2604semidirect

Maximal subgroups

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

subgroupindex
C2×#881412
C2×#881332
C13×#3992
#117186432
#117186422
#117186342
#117186122
#117186082
#117186052
#117183172
#117183092
#260413