Finite Group Databasebeta

← #13120780

Subgroups — #13120780

Order 1664.

584 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88194C211yesmaximal, characteristic
2C2×#88144C211yesmaximal, characteristic, complemented
3C13×#390C211yesmaximal, characteristic, complemented
4#11718882C211yesmaximal, characteristic, complemented
5#11718649C211yesmaximal, characteristic, complemented
6#11718622C214yesmaximal, complemented
7#11718620C214yesmaximal, complemented
8#11718600C211yesmaximal, characteristic, complemented
9#11718593C211yesmaximal, characteristic, complemented
10C22×D4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×C22⋊D13C2212yes—
13C22×D52C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2214yes—
16C2×C42×C13C2211yescharacteristic
17C2×C22⋊Dic13C2214yes—
18#88194—24no—
19C2×#6103C2214yes—
20C2×#6103C2214yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2212yes—
23C2×#6101C2212yes—
24C2×C4×Dic13C2211yescharacteristic
25C2×C4×Dic13C2211yescharacteristic
26#88144—24no—
27#88071C2212yes—
28#88071C2212yes—
29C24×C13C2312yes—
30C23×D13C2312yes—
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—24no—
39C2×C22⋊D13—44no—
40C2×C22⋊D13—44no—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C2×D52—22no—
46C2×D52—22no—
47C2×D52—22no—
48C13×C4⋊C4—22no—
49C13×C22⋊C4—44no—
50C42×C13—22no—
51C22⋊Dic13—44no—
52#6103—44no—
53#6103—44no—
54C4⋊Dic13—22no—
55C4⋊Dic13—24no—
56#6101—24no—
57C4×Dic13—22no—
58C4×Dic13D414yes—
59#2641—131nomaximal, Sylow
60C23×C13—22no—
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—24no—
64C23×C13—24no—
65C23×C13C2411yescharacteristic
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—24no—
70C22×D13—24no—
71D4×C13—44no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—24no—
76C2×C4×C13—22no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13#4112yes—
79C2×C4×C13#4112yes—
80C22⋊D13—48no—
81C22⋊D13—48no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—24no—
88C2×Dic13—22no—
89C2×Dic13C2×D412yes—
90C2×Dic13C2×D412yes—
91D52—44no—
92C2×#127—131no—
93C2×#125—131no—
94#394—134no—
95#394—134no—
96#390—131no—
97#390—131no—
98#390—131no—
99#390D1311yescharacteristic, complemented
100#376—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×C13H(5,𝔽2)12yes—
110C22×C13H(5,𝔽2)12yes—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—42no—
114C2×D13—44no—
115C2×D13—44no—
116C4×C13—42no—
117C4×C13—42no—
118C4×C13#12414yes—
119Dic13—22no—
120Dic13—22no—
121Dic13—42no—
122Dic13—42no—
123C22×D4—132no—
124C22×D4—132no—
125C22×D4—131no—
126C22×D4C2×D1311yescharacteristic
127#127—264no—
128#125—264no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4—131no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4C2×D1311yescharacteristic
133C2×C22⋊C4—134no—
134C2×C22⋊C4—134no—
135C2×C22⋊C4—134no—
136C2×C22⋊C4C2×D1314yes—
137C2×C42—131no—
138C2×C42—131no—
139C2×C42C2×D1311yescharacteristic
140#95—132no—
141#95—132no—
142C2×C13—82no—
143C2×C13C2×#12411yescharacteristic
144C2×C13#53511yescharacteristic
145C2×C13#53511yescharacteristic
146C2×C13#54012yes—
147C2×C13#54012yes—
148D13—82no—
149C24—132no—
150C24C22×D1312yes—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—264no—
155C2×D4—264no—
156C2×D4—262no—
157C2×D4—262no—
158C2×D4—262no—
159C2×D4—524no—
160C2×D4—524no—
161C22×C4—131no—
162C22×C4—131no—
163C22×C4—132no—
164C22×C4—132no—
165C22×C4C22×D1312yes—
166C22×C4C22×D1312yes—
167C22×C4C22×D1311yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—264no—
170C4⋊C4—264no—
171C4⋊C4—262no—
172C22⋊C4—44no—
173C22⋊C4—524no—
174C22⋊C4—524no—
175C22⋊C4—524no—
176C42—22no—
177C42—134no—
178C42—262no—
179C13#264111yescharacteristic, complemented, Sylow
180C23—22no—
181C23—22no—
182C23—22no—
183C23—24no—
184C23—24no—
185C23—262no—
186C23—262no—
187C23—262no—
188C23—264no—
189C23—264no—
190C23C23×D1311yescharacteristic
191D4—44no—
192D4—528no—
193D4—528no—
194D4—524no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—132no—
201C2×C4—132no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—264no—
209C2×C4#612712yes—
210C2×C4D4×D1312yes—
211C2×C4#612912yes—
212C22—42no—
213C22—44no—
214C22—44no—
215C22—42no—
216C22—42no—
217C22—522no—
218C22—524no—
219C22—524no—
220C22—522no—
221C22—522no—
222C22C2×#612711yescharacteristic
223C22C2×D4×D1311yescharacteristic
224C22C2×#612911yescharacteristic
225C22#8825112yes—
226C22#8825612yes—
227C4—42no—
228C4—42no—
229C4—262no—
230C4—262no—
231C4—522no—
232C4—522no—
233C4#8813914yes—
234C2—82no—
235C2—1042no—
236C2C2×#8813911yescharacteristic
237C2#1171926712yes—
238C2#1171932412yes—
239C2#1171937911yescharacteristic
240C2#1171942011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC2×#88194C2
hypercenter#390D13
hypocenterC13#2641
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#88144C2semidirect
3. C13×#390C2semidirect
4. #11718882C2semidirect
5. #11718649C2semidirect
6. #11718622C2semidirect
7. #11718620C2semidirect
8. #11718600C2semidirect
9. #11718593C2semidirect
99. #390D13semidirect
179. C13#2641semidirect

Maximal subgroups

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

subgroupindex
C2×#881942
C2×#881442
C13×#3902
#117188822
#117186492
#117186222
#117186202
#117186002
#117185932
#264113