Finite Group Databasebeta

← #13120578

Subgroups — #13120578

Order 1664.

632 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×C13×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#88184C211yesmaximal, characteristic
3C2×#88183C212yesmaximal, complemented
4#11718874C212yesmaximal, complemented
5#11718873C211yesmaximal, characteristic, complemented
6#11718655C214yesmaximal, complemented
7#11718652C212yesmaximal, complemented
8#11718644C212yesmaximal, complemented
9C23×C4×C13C2211yescharacteristic
10C23×C4×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C22×C22⋊D13C2212yes—
13C22×D52C2211yescharacteristic
14C2×C13×C4⋊C4—24no—
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C4⋊C4C2212yes—
17C2×C22⋊Dic13C2212yes—
18#88184—24no—
19#88183—28no—
20C2×#6103C2214yes—
21C2×#6103C2212yes—
22C2×#6103C2214yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2212yes—
25C2×#6101C2214yes—
26#88071C2212yes—
27#88071C2214yes—
28C24×C13C2311yescharacteristic
29C23×D13C2312yes—
30C22×C4×C13—22no—
31C22×C4×C13—22no—
32C22×C4×C13—22no—
33C22×C4×C13—42no—
34C22×C4×C13—42no—
35C22×C4×C13D414yes—
36C22×C4×C13D414yescomplemented
37C22×C4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C2×C22⋊D13—24no—
42C2×C22⋊D13—24no—
43C2×C22⋊D13—24no—
44C22×Dic13C2312yes—
45C22×Dic13C2314yes—
46C2×D52—22no—
47C2×D52—42no—
48C13×C4⋊C4—24no—
49C13×C4⋊C4—24no—
50C22⋊Dic13—24no—
51#6103—28no—
52#6103—24no—
53#6103—44no—
54C4⋊Dic13—22no—
55C4⋊Dic13—42no—
56#6101—28no—
57#2618—131nomaximal, Sylow
58C23×C13—22no—
59C23×C13—22no—
60C23×C13C2×D412yes—
61C23×C13C2×D412yes—
62C23×C13#4112yes—
63C23×C13C2411yescharacteristic
64C22×D13—22no—
65C22×D13—22no—
66C22×D13—22no—
67C22×D13—24no—
68C22×D13—24no—
69C2×C4×C13—28no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—24no—
76C2×C4×C13—44no—
77C2×C4×C13—44no—
78C2×C4×C13C2×D414yes—
79C2×C4×C13C2×D412yes—
80C2×C4×C13C2×D412yes—
81C22⋊D13—48no—
82C2×Dic13—22no—
83C2×Dic13—24no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—24no—
87C2×Dic13—24no—
88D52—44no—
89C2×#123—132no—
90C2×#121—131no—
91C22×C4⋊C4D1311yescharacteristic, complemented
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#12114yes—
102C22×C13C22×D411yescharacteristic
103C22×C13C22×D411yescharacteristic
104C22×C13C2×#4111yescharacteristic
105C22×C13H(5,𝔽2)12yes—
106C22×C132−1+412yes—
107C2×D13—42no—
108C2×D13—42no—
109C2×D13—42no—
110C2×D13—44no—
111C2×D13—44no—
112C4×C13—24no—
113C4×C13—22no—
114C4×C13—22no—
115C4×C13—42no—
116Dic13—42no—
117Dic13—44no—
118C22×D4—132no—
119C22×D4—131no—
120C23×C4C2×D1311yescharacteristic
121C23×C4C2×D1311yescharacteristic
122C23×C4C2×D1311yescharacteristic
123#123—268no—
124#121—264no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—131no—
127C2×C4⋊C4—134no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4C2×D1312yes—
130C2×C4⋊C4C2×D1312yes—
131C2×C22⋊C4—132no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—134no—
134C2×C22⋊C4—134no—
135#95—132no—
136#95—134no—
137C2×C13—24no—
138C2×C13C2×#12111yescharacteristic
139C2×C13#53411yescharacteristic
140C2×C13#53611yescharacteristic
141C2×C13#53712yes—
142C2×C13#53912yes—
143D13—82no—
144C24—132no—
145C24C22×D1311yescharacteristic
146C2×D4—264no—
147C2×D4—264no—
148C2×D4—264no—
149C2×D4—262no—
150C2×D4—522no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—134no—
157C22×C4—132no—
158C22×C4D5214yescomplemented
159C22×C4C22⋊D1314yes—
160C22×C4C22×D1312yes—
161C22×C4C22×D1312yes—
162C22×C4C22×D1311yescharacteristic
163C22×C4C22×D1311yescharacteristic
164C4⋊C4—24no—
165C4⋊C4—24no—
166C4⋊C4—268no—
167C4⋊C4—262no—
168C4⋊C4—522no—
169C22⋊C4—264no—
170C22⋊C4—268no—
171C22⋊C4—264no—
172C22⋊C4—524no—
173C13#261811yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23—262no—
177C23—262no—
178C23—264no—
179C23—264no—
180C23—262no—
181C23C2×D5212yes—
182C23#612712yes—
183C23C2×C22⋊D1312yes—
184C23C23×D1311yescharacteristic
185D4—524no—
186D4—528no—
187C2×C4—28no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—44no—
196C2×C4—264no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—264no—
200C2×C4—264no—
201C2×C4—262no—
202C2×C4C2×D5214yes—
203C2×C4C2×C22⋊D1312yes—
204C2×C4C2×C22⋊D1312yes—
205C22—24no—
206C22—24no—
207C22—22no—
208C22—22no—
209C22—524no—
210C22—524no—
211C22—522no—
212C22—522no—
213C22—522no—
214C22#8818414yes—
215C22C22×D5211yescharacteristic
216C22C2×#612711yescharacteristic
217C22#8825112yes—
218C22#8825412yes—
219C22C22×C22⋊D1311yescharacteristic
220C4—24no—
221C4—22no—
222C4—22no—
223C4—42no—
224C4—524no—
225C4—522no—
226C2—24no—
227C2—1042no—
228C2#1171921512yes—
229C2#1171922012yes—
230C2C2×#8818411yescharacteristic
231C2#1171950911yescharacteristic
232C2#1171952111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC22×C13×C4⋊C4C2
prime radicalC2×#88184C2
hypercenterC22×C4⋊C4D13
hypocenterC13#2618
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C13×C4⋊C4C2semidirect
3. C2×#88183C2semidirect
4. #11718874C2semidirect
5. #11718873C2semidirect
6. #11718655C2semidirect
7. #11718652C2semidirect
8. #11718644C2semidirect
36. C22×C4×C13D4semidirect
91. C22×C4⋊C4D13semidirect
158. C22×C4D52semidirect
173. C13#2618semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C4⋊C42
C2×#881842
C2×#881832
#117188742
#117188732
#117186552
#117186522
#117186442
#261813