Finite Group Databasebeta

← #13119298

Subgroups — #13119298

Order 1664.

568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 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×#88184C211yesmaximal, characteristic
2C2×#88180C211yesmaximal, characteristic, complemented
3C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
4#11718622C214yesmaximal, complemented
5#11718600C211yesmaximal, characteristic, complemented
6#11718600C211yesmaximal, characteristic, complemented
7#11718597C211yesmaximal, characteristic, complemented
8#11718596C211yesmaximal, characteristic, complemented
9#11718331C214yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×D52C2211yescharacteristic
13C2×C13×C22⋊C4C2212yes—
14C2×C42×C13C2211yescharacteristic
15C2×C42×C13C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17#88184—24no—
18C2×#6103C2212yes—
19C2×#6103C2214yes—
20C2×#6103C2214yes—
21#88180—24no—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2214yes—
26C2×C4×Dic13C2212yes—
27C13×#95C2212yes—
28#88071C2214yes—
29C24×C13C2311yescharacteristic
30C23×D13C2312yes—
31C22×C4×C13—22no—
32C22×C4×C13—22no—
33C22×C4×C13D414yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—24no—
39C2×C22⋊D13—44no—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C2×D52—22no—
44C2×D52—22no—
45C2×D52—22no—
46C13×C22⋊C4—24no—
47C42×C13—22no—
48C42×C13—22no—
49C22⋊Dic13—24no—
50#6103—24no—
51#6103—28no—
52#6103—44no—
53C4⋊Dic13—22no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4⋊Dic13—44no—
57C4×Dic13—24no—
58#2500—131nomaximal, Sylow
59C23×C13—22no—
60C23×C13—21no—
61C23×C13—21no—
62C23×C13—22no—
63C23×C13C2×D412yes—
64C23×C13C2411yescharacteristic
65C22×D13—22no—
66C22×D13—24no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—24no—
70C2×C4×C13—22no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—28no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13C2×D412yes—
79C2×C4×C13C2×D412yes—
80C2×C4×C13#4114yes—
81C2×C4×C13#4112yes—
82C2×C4×C13#4112yes—
83C22⋊D13—48no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—24no—
88C2×Dic13—24no—
89C2×Dic13—24no—
90D52—44no—
91C2×#121—131no—
92C2×#117—131no—
93#394—134no—
94#390—131no—
95#390—131no—
96#388—134no—
97#384—131no—
98#382—131no—
99C4×C22⋊C4D1311yescharacteristic, complemented
100C22×C13—22no—
101C22×C13—22no—
102C22×C13—22no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13C22×D411yescharacteristic
106C22×C13C2×#4112yes—
107C22×C13C2×#4111yescharacteristic
108C22×C13C2×#4111yescharacteristic
109C22×C13H(5,𝔽2)12yes—
110C2×D13—42no—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—44no—
114C2×D13—44no—
115C4×C13—22no—
116C4×C13—24no—
117C4×C13—42no—
118C4×C13#12314yes—
119Dic13—42no—
120Dic13—42no—
121Dic13—42no—
122C22×D4—132no—
123C22×D4—131no—
124C23×C4C2×D1311yescharacteristic
125#121—264no—
126#117—264no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4—134no—
131C2×C22⋊C4—132no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—134no—
134C2×C22⋊C4—134no—
135C2×C22⋊C4C2×D1312yes—
136C2×C42—132no—
137C2×C42C2×D1311yescharacteristic
138C2×C42C2×D1311yescharacteristic
139#95—134no—
140#95C2×D1312yes—
141C2×C13—42no—
142C2×C13C2×#12311yescharacteristic
143C2×C13#53211yescharacteristic
144C2×C13#53511yescharacteristic
145C2×C13#55312yes—
146C2×C13#55512yes—
147D13—82no—
148C24—132no—
149C24C22×D1311yescharacteristic
150C2×D4—264no—
151C2×D4—262no—
152C2×D4—262no—
153C2×D4—262no—
154C2×D4—524no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—132no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4D5214yes—
161C22×C4C22×D1312yes—
162C22×C4C22×D1311yescharacteristic
163C22×C4C22×D1312yes—
164C22×C4C22×D1311yescharacteristic
165C4⋊C4—262no—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C4⋊C4—524no—
169C22⋊C4—24no—
170C22⋊C4—264no—
171C22⋊C4—264no—
172C22⋊C4—268no—
173C22⋊C4—524no—
174C42—22no—
175C42—22no—
176C42—264no—
177C13#250011yescharacteristic, complemented, Sylow
178C23—22no—
179C23—21no—
180C23—21no—
181C23—22no—
182C23—262no—
183C23—264no—
184C23—262no—
185C23—262no—
186C23—264no—
187C23C2×D5212yes—
188C23C23×D1311yescharacteristic
189D4—528no—
190D4—524no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—28no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—264no—
203C2×C4—264no—
204C2×C4—264no—
205C2×C4C2×D5212yes—
206C2×C4C2×D5212yes—
207C2×C4#612714yes—
208C2×C4#612912yes—
209C2×C4#612912yes—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—42no—
214C22—42no—
215C22—522no—
216C22—522no—
217C22—522no—
218C22—524no—
219C22—524no—
220C22C22×D5211yescharacteristic
221C22C2×#612712yes—
222C22C2×#612911yescharacteristic
223C22C2×#612911yescharacteristic
224C22#8825612yes—
225C4—22no—
226C4—24no—
227C4—42no—
228C4—522no—
229C4—522no—
230C4—522no—
231C4#8814014yes—
232C2—42no—
233C2—1042no—
234C2#1171918211yescharacteristic
235C2C2×#8814011yescharacteristic
236C2#1171923011yescharacteristic
237C2#1171926812yes—
238C2#1171927012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC4×C13×C22⋊C4C2
prime radicalC2×#88184C2
hypercenterC4×C22⋊C4D13
hypocenterC13#2500
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#88180C2semidirect
3. C4×C13×C22⋊C4C2semidirect
4. #11718622C2semidirect
5. #11718600C2semidirect
6. #11718600C2semidirect
7. #11718597C2semidirect
8. #11718596C2semidirect
9. #11718331C2semidirect
99. C4×C22⋊C4D13semidirect
177. C13#2500semidirect

Maximal subgroups

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

subgroupindex
C2×#881842
C2×#881802
C4×C13×C22⋊C42
#117186222
#117186002
#117185972
#117185962
#117183312
#250013