Finite Group Databasebeta

← #13121176

Subgroups — #13121176

Order 1664.

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

normal subgroups only

This group has 568 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×#88150C212yesmaximal, complemented
2C2×#88148C212yesmaximal
3C13×#384C211yesmaximal, characteristic, complemented
4#11718654C212yesmaximal, complemented
5#11718652C211yesmaximal, characteristic
6#11718650C212yesmaximal, complemented
7#11718641C212yesmaximal, complemented
8#11718640C211yesmaximal, characteristic, complemented
9#11718601C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×C4×D13C2212yes—
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2212yes—
14C2×C13×C4⋊C4C2212yes—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C42×C13C2211yescharacteristic
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26#88150—28no—
27#88148—28no—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31#88071C2211yescharacteristic
32#88071C2212yes—
33C23×D13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C2×D52—24no—
43C2×D52—41no—
44C2×C4×D13—24no—
45C2×C4×D13—24no—
46C2×C4×D13—42no—
47C2×Dic26—24no—
48C2×Dic26—41no—
49C13×C4⋊C4—24no—
50C13×C4⋊C4—24no—
51C13×C4⋊C4—41no—
52C13×C4⋊C4—41no—
53C42×C13—22no—
54#6103—24no—
55#6103—24no—
56#6103—24no—
57#6103—24no—
58#6103D418yes—
59#6101—24no—
60#6101—24no—
61#6101—24no—
62#2680—131nomaximal, Sylow
63C23×C13C2411yescharacteristic
64C22×D13—22no—
65C22×D13—22no—
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13C2×D414yes—
71C2×C4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13C2×D414yes—
83C2×C4×C13#4112yes—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13C2×D414yes—
93D52—44no—
94C4×D13—48no—
95Dic26—44no—
96C2×#123—132no—
97C2×C22⋊Q8—132no—
98#398—132no—
99#397—132no—
100#395—131no—
101#394—131no—
102#388—132no—
103#385—132no—
104#384D1311yescharacteristic, complemented
105C22×C13C22×D412yes—
106C22×C13C2×#4111yescharacteristic
107C22×C13H(5,𝔽2)11yescharacteristic
108C22×C132−1+411yescharacteristic
109C22×C132−1+412yes—
110C2×D13—24no—
111C2×D13—24no—
112C2×D13—24no—
113C2×D13—42no—
114C2×D13—42no—
115C2×D13—42no—
116C2×D13—42no—
117C4×C13—22no—
118C4×C13—24no—
119C4×C13—41no—
120C4×C13—42no—
121C4×C13—41no—
122Dic13—24no—
123Dic13—42no—
124Dic13—42no—
125C22×Q8—131no—
126C22×D4—131no—
127C23×C4—132no—
128#123—268no—
129C22⋊Q8—268no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4C2×D1312yes—
134C2×C4⋊C4C2×D1312yes—
135C2×C4⋊C4C2×D1311yescharacteristic
136C2×C4⋊C4C2×D1311yescharacteristic
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4—132no—
142C2×C42C2×D1311yescharacteristic
143#95—132no—
144#95—132no—
145#95—132no—
146#95—131no—
147#95—131no—
148C2×C13#53612yes—
149C2×C13#53911yescharacteristic
150C2×C13D4211yescharacteristic
151C2×C13#54712yes—
152C2×C13#56311yescharacteristic
153D13—44no—
154C24—132no—
155C2×Q8—264no—
156C2×Q8—521no—
157C2×D4—264no—
158C2×D4—521no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4—132no—
162C22×C4—264no—
163C22×C4—264no—
164C22×C4—522no—
165C22×C4C22×D1311yescharacteristic
166C22×C4C22×D1312yes—
167C22×C4C22×D1311yescharacteristic
168C22×C4C22×D1311yescharacteristic
169C22×C4C22×D1312yes—
170C4⋊C4—24no—
171C4⋊C4—24no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—264no—
175C4⋊C4—264no—
176C4⋊C4—264no—
177C22⋊C4—138no—
178C22⋊C4—264no—
179C22⋊C4—264no—
180C22⋊C4—264no—
181C22⋊C4—264no—
182C42—22no—
183C13#268011yescharacteristic, complemented, Sylow
184C23—134no—
185C23—262no—
186C23—262no—
187C23—262no—
188C23—262no—
189C23—262no—
190C23—262no—
191C23C23×D1311yescharacteristic
192Q8—524no—
193D4—524no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—134no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—528no—
215C2×C4#612712yes—
216C2×C4D4×D1314yes—
217C22—264no—
218C22—264no—
219C22—264no—
220C22—522no—
221C22—522no—
222C22—522no—
223C22—522no—
224C22C2×#612711yescharacteristic
225C22C2×D4×D1312yes—
226C22#8825111yescharacteristic
227C22#8825411yescharacteristic
228C22#8825412yes—
229C4—24no—
230C4—22no—
231C4—42no—
232C4—41no—
233C4—41no—
234C4—264no—
235C4—522no—
236C4—522no—
237C2—524no—
238C2#1171921212yes—
239C2#1171922011yescharacteristic
240C2#1171942211yescharacteristic
241C2#1171942912yes—
242C2#1171944011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#384C2
prime radicalC22×D52C22
hypercenter#384D13
hypocenterC13#2680
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#88150C2semidirect
3. C13×#384C2semidirect
4. #11718654C2semidirect
6. #11718650C2semidirect
7. #11718641C2semidirect
8. #11718640C2semidirect
9. #11718601C2semidirect
104. #384D13semidirect
183. C13#2680semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×#881482
C13×#3842
#117186542
#117186522
#117186502
#117186412
#117186402
#117186012
#268013