Finite Group Databasebeta

← #13119327

Subgroups — #13119327

Order 1664.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88192C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
3C13×#390C211yesmaximal, characteristic, complemented
4#11718882C211yesmaximal, characteristic, complemented
5#11718638C211yesmaximal, characteristic, complemented
6#11718617C214yesmaximal, complemented
7#11718613C214yesmaximal, complemented
8C4×#6103C211yesmaximal, characteristic, complemented
9#11718597C211yesmaximal, characteristic, complemented
10C22×D4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×C4×D13C2211yescharacteristic
13C22×C4×D13C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2214yes—
16C2×C42×C13C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2214yes—
19#88192—24no—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2212yes—
24C2×C4×Dic13C2211yescharacteristic
25C4⋊C4×D13—24no—
26#88071C2214yes—
27#88071C2212yes—
28#88071C2214yes—
29C24×C13C2312yes—
30C23×D13C2311yescharacteristic
31C2×D4×C13—22no—
32C2×D4×C13—22no—
33C2×D4×C13—22no—
34C22×C4×C13C2312yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C2×C22⋊D13—24no—
38C2×C22⋊D13—28no—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2311yescharacteristic
43C2×C4×D13—22no—
44C2×C4×D13—22no—
45C2×C4×D13—24no—
46C2×C4×D13—44no—
47C2×C4×D13D414yes—
48C13×C4⋊C4—22no—
49C13×C22⋊C4—44no—
50C42×C13—22no—
51C22⋊Dic13—24no—
52C22⋊Dic13—44no—
53#6103—24no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56#6101—24no—
57C4×Dic13—22no—
58#2504—131nomaximal, Sylow
59C23×C13—22no—
60C23×C13—24no—
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—24no—
64C23×C13C2411yescharacteristic
65C22×D13—21no—
66C22×D13—21no—
67C22×D13—22no—
68C22×D13C2×D412yes—
69C22×D13#4114yes—
70D4×C13—44no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—24no—
76C2×C4×C13C2×D412yes—
77C2×C4×C13#4112yes—
78C2×C4×C13#4112yes—
79C22⋊D13—48no—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—24no—
87C2×Dic13—22no—
88C2×Dic13—24no—
89C2×Dic13C2×D412yes—
90C4×D13—28no—
91C4×D13—48no—
92C2×#121—131no—
93C22×C4⋊C4—131no—
94#397—134no—
95#390—131no—
96#390D1311yescharacteristic, complemented
97#386—134no—
98#382—131no—
99#382—131no—
100C4×C22⋊C4—131no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—44no—
105C22×C13—44no—
106C22×C13C22×D411yescharacteristic
107C22×C13C2×#4111yescharacteristic
108C22×C13C2×#4111yescharacteristic
109C22×C13C2×#4112yes—
110C22×C13H(5,𝔽2)12yes—
111C2×D13—22no—
112C2×D13—22no—
113C2×D13—24no—
114C2×D13—24no—
115C2×D13#12414yes—
116C4×C13—42no—
117C4×C13—42no—
118C4×C13#12314yes—
119Dic13—22no—
120Dic13—42no—
121Dic13—42no—
122Dic13—42no—
123C22×D4—132no—
124C22×D4C2×D1311yescharacteristic
125C23×C4—131no—
126C23×C4—132no—
127#121—264no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4—131no—
131C2×C4⋊C4—264no—
132C2×C4⋊C4C2×D1311yescharacteristic
133C2×C22⋊C4—132no—
134C2×C22⋊C4—132no—
135C2×C22⋊C4—134no—
136C2×C22⋊C4C2×D1314yes—
137C2×C42—131no—
138C2×C42C2×D1311yescharacteristic
139#95—132no—
140#95—134no—
141#95—134no—
142C2×C13—82no—
143C2×C13C2×#12311yescharacteristic
144C2×C13C2×#12411yescharacteristic
145C2×C13#53511yescharacteristic
146C2×C13#55312yes—
147C2×C13#55312yes—
148D13—24no—
149C24—131no—
150C24C22×D1312yes—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—264no—
155C2×D4—268no—
156C22×C4—131no—
157C22×C4—134no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4—264no—
162C22×C4—262no—
163C22×C4—262no—
164C22×C4—524no—
165C22×C4C22×D1312yes—
166C22×C4C22×D1312yes—
167C22×C4C22×D1311yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—264no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C22⋊C4—44no—
173C22⋊C4—264no—
174C22⋊C4—264no—
175C22⋊C4—524no—
176C42—22no—
177C42—262no—
178C13#250411yescharacteristic, complemented, Sylow
179C23—22no—
180C23—22no—
181C23—22no—
182C23—24no—
183C23—24no—
184C23—132no—
185C23—134no—
186C23—261no—
187C23—261no—
188C23—262no—
189C23C23×D1311yescharacteristic
190D4—44no—
191D4—528no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—132no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—268no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—264no—
206C2×C4—262no—
207C2×C4—264no—
208C2×C4—528no—
209C2×C4#612712yes—
210C2×C4D4×D1312yes—
211C2×C4#612912yes—
212C22—42no—
213C22—44no—
214C22—44no—
215C22—42no—
216C22—42no—
217C22—134no—
218C22—262no—
219C22—264no—
220C22—264no—
221C22—262no—
222C22C2×#612711yescharacteristic
223C22C2×D4×D1311yescharacteristic
224C22C2×#612911yescharacteristic
225C22#8825112yes—
226C22#41×D1312yes—
227C4—42no—
228C4—42no—
229C4—262no—
230C4—522no—
231C4—522no—
232C4—522no—
233C4#8813714yes—
234C2—82no—
235C2—264no—
236C2C2×#8813711yescharacteristic
237C2#1171926312yes—
238C2#1171931912yes—
239C2D13×#12411yescharacteristic
240C2#1171942011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC2×#88192C2
hypercenter#390D13
hypocenterC13#2504
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D13C2semidirect
3. C13×#390C2semidirect
4. #11718882C2semidirect
5. #11718638C2semidirect
6. #11718617C2semidirect
7. #11718613C2semidirect
8. C4×#6103C2semidirect
9. #11718597C2semidirect
96. #390D13semidirect
178. C13#2504semidirect

Maximal subgroups

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

subgroupindex
C2×#881922
C2×C4⋊C4×D132
C13×#3902
#117188822
#117186382
#117186172
#117186132
C4×#61032
#117185972
#250413