Finite Group Databasebeta

← #13119325

Subgroups — #13119325

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×#88149C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
3C13×#382C211yesmaximal, characteristic, complemented
4#11718649C211yesmaximal, characteristic, complemented
5#11718638C211yesmaximal, characteristic, complemented
6#11718600C211yesmaximal, characteristic, complemented
7C4×#6103C211yesmaximal, characteristic, complemented
8#11718336C214yesmaximal, complemented
9#11718326C214yesmaximal, complemented
10C22×D52C2212yes—
11C22×D52C2211yescharacteristic
12C22×C4×D13C2211yescharacteristic
13C22×C4×D13C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C42×C13C2211yescharacteristic
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2214yes—
20C2×#6103C2214yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×#6101C2212yes—
23C2×C4×Dic13C2211yescharacteristic
24#88149—24no—
25C4⋊C4×D13—24no—
26C13×#95C2214yes—
27#88071C2214yes—
28#88071C2212yes—
29C23×D13C2312yes—
30C23×D13C2311yescharacteristic
31C22×C4×C13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×Dic13C2312yes—
36C22×Dic13C2312yes—
37C22×Dic13C2311yescharacteristic
38C2×D52—24no—
39C2×D52—28no—
40C2×D52—22no—
41C2×D52—22no—
42C2×D52—22no—
43C2×C4×D13—22no—
44C2×C4×D13—22no—
45C2×C4×D13—24no—
46C2×C4×D13—44no—
47C2×C4×D13D414yes—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—22no—
50C42×C13—22no—
51#6103—24no—
52#6103—24no—
53#6103—44no—
54#6103—44no—
55C4⋊Dic13—22no—
56#6101—24no—
57C4×Dic13—22no—
58#2504—131nomaximal, Sylow
59C23×C13C2411yescharacteristic
60C22×D13—21no—
61C22×D13—21no—
62C22×D13—22no—
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—22no—
66C22×D13—24no—
67C22×D13—24no—
68C22×D13C2×D412yes—
69C22×D13#4114yes—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—24no—
75C2×C4×C13—22no—
76C2×C4×C13—24no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13#4112yes—
79C2×C4×C13#4112yes—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—24no—
87C2×Dic13C2×D412yes—
88D52—48no—
89D52—44no—
90C4×D13—28no—
91C4×D13—48no—
92C2×#121—131no—
93C22×C4⋊C4—131no—
94#397—134no—
95#390—131no—
96#390—131no—
97#386—134no—
98#382—131no—
99#382D1311yescharacteristic, complemented
100C4×C22⋊C4—131no—
101C22×C13C22×D411yescharacteristic
102C22×C13C2×#4111yescharacteristic
103C22×C13C2×#4111yescharacteristic
104C22×C13C2×#4112yes—
105C22×C13H(5,𝔽2)12yes—
106C2×D13—22no—
107C2×D13—22no—
108C2×D13—24no—
109C2×D13—24no—
110C2×D13—42no—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—44no—
114C2×D13—44no—
115C2×D13#12414yes—
116C4×C13—42no—
117C4×C13—42no—
118C4×C13—42no—
119C4×C13#12314yes—
120Dic13—22no—
121Dic13—42no—
122Dic13—42no—
123C22×D4—132no—
124C22×D4—131no—
125C23×C4—131no—
126C23×C4—132no—
127#121—264no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4—264no—
131C2×C4⋊C4C2×D1311yescharacteristic
132C2×C4⋊C4C2×D1311yescharacteristic
133C2×C22⋊C4—132no—
134C2×C22⋊C4—132no—
135C2×C22⋊C4—134no—
136C2×C22⋊C4—134no—
137C2×C42—131no—
138C2×C42C2×D1311yescharacteristic
139#95—132no—
140#95—134no—
141#95C2×D1314yes—
142C2×C13C2×#12311yescharacteristic
143C2×C13C2×#12411yescharacteristic
144C2×C13#53511yescharacteristic
145C2×C13#55312yes—
146C2×C13#55312yes—
147D13—24no—
148D13—82no—
149C24—131no—
150C24—132no—
151C2×D4—264no—
152C2×D4—268no—
153C2×D4—262no—
154C2×D4—262no—
155C2×D4—262no—
156C22×C4—131no—
157C22×C4—134no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4—264no—
161C22×C4—262no—
162C22×C4—262no—
163C22×C4—524no—
164C22×C4C22×D1312yes—
165C22×C4C22×D1312yes—
166C22×C4C22×D1312yes—
167C22×C4C22×D1311yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—264no—
171C4⋊C4—262no—
172C22⋊C4—264no—
173C22⋊C4—264no—
174C22⋊C4—524no—
175C22⋊C4—524no—
176C42—22no—
177C42—262no—
178C13#250411yescharacteristic, complemented, Sylow
179C23—132no—
180C23—134no—
181C23—261no—
182C23—261no—
183C23—262no—
184C23—262no—
185C23—262no—
186C23—262no—
187C23—264no—
188C23—264no—
189C23C23×D1311yescharacteristic
190D4—528no—
191D4—524no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—132no—
200C2×C4—261no—
201C2×C4—261no—
202C2×C4—268no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—264no—
208C2×C4—528no—
209C2×C4#612712yes—
210C2×C4D4×D1312yes—
211C2×C4#613112yes—
212C22—134no—
213C22—262no—
214C22—264no—
215C22—262no—
216C22—264no—
217C22—522no—
218C22—524no—
219C22—522no—
220C22—522no—
221C22—524no—
222C22C2×#612711yescharacteristic
223C22C2×D4×D1311yescharacteristic
224C22C2×#613111yescharacteristic
225C22#41×D1312yes—
226C22#8825612yes—
227C4—42no—
228C4—42no—
229C4—42no—
230C4—262no—
231C4—522no—
232C4—522no—
233C4#8814814yes—
234C2—264no—
235C2—1042no—
236C2C2×#8814811yescharacteristic
237C2#1171923512yes—
238C2D13×#12411yescharacteristic
239C2#1171937911yescharacteristic
240C2#1171940012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#382C2
prime radicalC2×#88149C2
hypercenter#382D13
hypocenterC13#2504
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D13C2semidirect
3. C13×#382C2semidirect
4. #11718649C2semidirect
5. #11718638C2semidirect
6. #11718600C2semidirect
7. C4×#6103C2semidirect
8. #11718336C2semidirect
9. #11718326C2semidirect
99. #382D13semidirect
178. C13#2504semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
C2×C4⋊C4×D132
C13×#3822
#117186492
#117186382
#117186002
C4×#61032
#117183362
#117183262
#250413