Finite Group Databasebeta

← #13120580

Subgroups — #13120580

Order 1664.

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

normal subgroups only

This group has 632 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×C13×#121C211yesmaximal, characteristic
2C2×#88189C212yesmaximal, complemented
3C22×#6101C211yesmaximal, characteristic, complemented
4#11718883C212yesmaximal, complemented
5#11718881C212yesmaximal, complemented
6#11718873C211yesmaximal, characteristic, complemented
7#11718641C212yesmaximal, complemented
8#11718609C214yesmaximal, complemented
9C22×D4×C13C2212yes—
10C22×D4×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C23×Dic13C2211yescharacteristic
13C23×Dic13C2211yescharacteristic
14C13×#121—24no—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C22⋊Dic13C2214yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2214yes—
20#88189—28no—
21C2×C4⋊Dic13C2212yes—
22C2×#6101—24no—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2214yes—
26#88071C2214yes—
27#88071C2212yes—
28C24×C13C2312yes—
29C24×C13C2311yescharacteristic
30C2×D4×C13—24no—
31C2×D4×C13—24no—
32C2×D4×C13—24no—
33C2×D4×C13—22no—
34C2×D4×C13—42no—
35C22×C4×C13—42no—
36C22×C4×C13D414yes—
37C22×C4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×Dic13—22no—
41C22×Dic13—22no—
42C22×Dic13—22no—
43C22×Dic13—42no—
44C22×Dic13D414yescomplemented
45C22×Dic13C2312yes—
46C22×Dic13C2314yes—
47C22×Dic13C2312yes—
48C13×C4⋊C4—22no—
49C13×C22⋊C4—24no—
50C22⋊Dic13—24no—
51C22⋊Dic13—28no—
52C22⋊Dic13—44no—
53C4⋊Dic13—42no—
54#6101—24no—
55#6101—24no—
56#6101—28no—
57#2618—131nomaximal, Sylow
58C23×C13—22no—
59C23×C13—22no—
60C23×C13—22no—
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—24no—
64C23×C13—24no—
65C23×C13C2×D412yes—
66C23×C13C2×D412yes—
67C23×C13#4112yes—
68C23×C13C2411yescharacteristic
69D4×C13—44no—
70D4×C13—48no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—44no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2×D412yes—
79C2×Dic13—28no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—24no—
84C2×Dic13—24no—
85C2×Dic13—24no—
86C2×Dic13—24no—
87C2×Dic13—44no—
88C2×Dic13C2×D414yes—
89C2×#123—132no—
90C2×#121D1311yescharacteristic
91C22×C4⋊C4—131no—
92#398—132no—
93#396—134no—
94#394—132no—
95#386—132no—
96#380—131no—
97C22×C13—22no—
98C22×C13—22no—
99C22×C13—24no—
100C22×C13—24no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—44no—
105C22×C13—44no—
106C22×C13#12114yes—
107C22×C13C22×D411yescharacteristic
108C22×C13C22×D411yescharacteristic
109C22×C13C2×#4111yescharacteristic
110C22×C13H(5,𝔽2)12yes—
111C22×C132−1+412yes—
112C4×C13—22no—
113C4×C13—22no—
114C4×C13—42no—
115Dic13—24no—
116Dic13—42no—
117Dic13—44no—
118C22×D4C2×D1312yes—
119C22×D4C2×D1311yescharacteristic
120C23×C4—131no—
121C23×C4—131no—
122C23×C4C2×D1311yescharacteristic
123#123—268no—
124#121—24no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—134no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—264no—
130C2×C4⋊C4C2×D1311yescharacteristic
131C2×C22⋊C4—132no—
132C2×C22⋊C4—134no—
133C2×C22⋊C4—134no—
134C2×C22⋊C4C2×D1312yes—
135#95—132no—
136#95—134no—
137C2×C13—24no—
138C2×C13—82no—
139C2×C13C2×#12111yescharacteristic
140C2×C13#53411yescharacteristic
141C2×C13#53611yescharacteristic
142C2×C13#53712yes—
143C2×C13#53912yes—
144C24C22×D1312yes—
145C24C22×D1311yescharacteristic
146C2×D4—24no—
147C2×D4—24no—
148C2×D4—24no—
149C2×D4—22no—
150C2×D4—42no—
151C22×C4—42no—
152C22×C4—134no—
153C22×C4—132no—
154C22×C4—134no—
155C22×C4—132no—
156C22×C4—262no—
157C22×C4—262no—
158C22×C4—262no—
159C22×C4—522no—
160C22×C4C22⋊D1314yes—
161C22×C4C22×D1312yes—
162C22×C4C22×D1311yescharacteristic
163C22×C4C22×D1311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—268no—
166C4⋊C4—264no—
167C4⋊C4—264no—
168C4⋊C4—522no—
169C22⋊C4—24no—
170C22⋊C4—268no—
171C22⋊C4—264no—
172C22⋊C4—524no—
173C13#261811yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—24no—
179C23—24no—
180C23—22no—
181C23D4×D1312yes—
182C23#612912yes—
183C23C2×C22⋊D1312yes—
184C23C23×D1311yescharacteristic
185D4—44no—
186D4—48no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—44no—
193C2×C4—134no—
194C2×C4—268no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—264no—
198C2×C4—264no—
199C2×C4—264no—
200C2×C4—264no—
201C2×C4—262no—
202C2×C4—524no—
203C2×C4C2×C22⋊D1312yes—
204C2×C4C2×C22⋊D1312yes—
205C22—22no—
206C22—22no—
207C22—24no—
208C22—24no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—44no—
213C22—44no—
214C22#8819214yes—
215C22C2×D4×D1311yescharacteristic
216C22C2×#612911yescharacteristic
217C22#8825112yes—
218C22#8825712yes—
219C22C22×C22⋊D1311yescharacteristic
220C4—22no—
221C4—22no—
222C4—42no—
223C4—264no—
224C4—522no—
225C4—524no—
226C2—24no—
227C2—82no—
228C2#1171930212yes—
229C2#1171930712yes—
230C2C2×#8819211yescharacteristic
231C2#1171950911yescharacteristic
232C2#1171953011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2618
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#88189C2semidirect
3. C22×#6101C2semidirect
4. #11718883C2semidirect
5. #11718881C2semidirect
6. #11718873C2semidirect
7. #11718641C2semidirect
8. #11718609C2semidirect
44. C22×Dic13D4semidirect
173. C13#2618semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881892
C22×#61012
#117188832
#117188812
#117188732
#117186412
#117186092
#261813