Finite Group Databasebeta

← #15890322

Subgroups — #15890322

Order 3328.

1378 conjugacy classes of subgroups; only the 275 normal subgroups are shown.

normal subgroups only

This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 275 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
1#13117215C213yesmaximal
2#13116002C214yesmaximal, complemented
3#13115999C214yesmaximal
4#13114569C213yesmaximal, complemented
5C13×#3458C211yesmaximal, characteristic, complemented
6C23×C4×D13C2211yescharacteristic
7C13×#544—26no—
8C13×#543C2214yes—
9C13×#533—26no—
10C2×C13×#117C2213yes—
11C2×#88180C2213yes—
12#11718648—26no—
13#11718616C2216yes—
14#11718604C2216yes—
15C4×#6103—26no—
16#11718118C22112yes—
17C24×D13C2311yescharacteristic
18C23×C4×C13C2311yescharacteristic
19C23×Dic13C2311yescharacteristic
20C22×C4×D13—23no—
21C22×C4×D13—23no—
22C22×C4×D13—26no—
23C22×C4×D13Q814yescomplemented
24C13×C4⋊Q8—212no—
25C13×#125—212no—
26C13×C22⋊Q8—224no—
27C4×Q8×C13—28no—
28C13×#117—26no—
29C13×#117—26no—
30C2×C13×C4⋊C4D416yes—
31C2×C13×C22⋊C4C2316yes—
32C2×C42×C13D416yes—
33C2×C22⋊Dic13C2316yes—
34C2×#6103—212no—
35#88180—212no—
36C2×C4⋊Dic13—23no—
37C2×C4×Dic13—23no—
38#88071—212no—
39#23467—131nomaximal, Sylow
40C24×C13C2411yescharacteristic
41C23×D13—23no—
42C23×D13—23no—
43C23×D13—44no—
44C23×D13C2×Q812yes—
45C2×Q8×C13—28no—
46C22×C4×C13C2×D4112yes—
47C22×C4×C13C2×D413yes—
48C22×C4×C13C2×D413yes—
49C22×C4×C13C2×Q812yes—
50C22×C4×C13#4116yes—
51C22×Dic13—23no—
52C22×Dic13—23no—
53C22×Dic13—26no—
54C22×Dic13C2×Q812yes—
55C2×C4×D13—212no—
56C2×C4×D13—212no—
57C2×C4×D13—43no—
58C2×C4×D13—41no—
59C2×C4×D13—46no—
60C2×C4×D13—46no—
61C13×C4⋊C4—224no—
62C13×C4⋊C4—212no—
63C13×C22⋊C4—212no—
64C42×C13—26no—
65C42×C13—26no—
66C22⋊Dic13—212no—
67#6103—424no—
68C4⋊Dic13—46no—
69C4×Dic13—46no—
70#3458D1311yescharacteristic, complemented
71#2280—133no—
72#2030—134no—
73#2029—134no—
74#1740—133no—
75C23×C13—42no—
76C23×C13C22×D413yes—
77C23×C13C22×Q811yescharacteristic
78C23×C13C2×#4113yes—
79C22×D13—212no—
80C22×D13—26no—
81C22×D13—44no—
82C22×D13—412no—
83C22×D13—46no—
84C22×D13—41no—
85C22×D13—43no—
86Q8×C13—88no—
87C2×C4×C13—212no—
88C2×C4×C13—412no—
89C2×C4×C13#12013yes—
90C2×C4×C13#12011yescharacteristic
91C2×C4×C13C22⋊Q816yes—
92C2×C4×C13C22⋊Q816yes—
93C2×C4×C13#12416yes—
94C2×C4×C13#12416yes—
95C2×Dic13—26no—
96C2×Dic13—41no—
97C2×Dic13—43no—
98C2×Dic13—412no—
99C2×Dic13—46no—
100C4×D13—412no—
101C4×D13—44no—
102C24×C4—131no—
103#544—26no—
104#543C2×D1314yes—
105#533—26no—
106C2×#117—133no—
107C2×#117C2×D1313yes—
108#381—136no—
109#380—266no—
110#379—136no—
111C4×C22⋊C4—266no—
112#342—1312no—
113C22×C13—26no—
114C22×C13—41no—
115C22×C13—43no—
116C22×C13C2×#12011yescharacteristic
117C22×C13C2×C22⋊Q813yes—
118C22×C13C2×#12413yes—
119C2×D13—212no—
120C2×D13—412no—
121C2×D13—46no—
122C2×D13—42no—
123C2×D13—44no—
124C4×C13—412no—
125C4×C13#39316yes—
126C4×C13#39312yes—
127Dic13—42no—
128Dic13—86no—
129C25—131no—
130C23×C4—131no—
131C23×C4—134no—
132C23×C4—266no—
133C23×C4—263no—
134C23×C4—263no—
135C23×C4C22×D1311yescharacteristic
136C4⋊Q8—212no—
137#125—212no—
138C22⋊Q8—224no—
139C4×Q8—28no—
140#117—26no—
141#117—26no—
142#117—2612no—
143C2×C4⋊C4—263no—
144C2×C4⋊C4C22⋊D1316yes—
145C2×C22⋊C4—136no—
146C2×C22⋊C4—2612no—
147C2×C22⋊C4C22×D1316yes—
148C2×C42—263no—
149C2×C42C22⋊D1316yes—
150#95—2612no—
151C2×C13—23no—
152C2×C13—23no—
153C2×C13C2×#39311yescharacteristic
154C2×C13#302512yes—
155D13—44no—
156C24—132no—
157C24—263no—
158C24—263no—
159C24—524no—
160C24C23×D1311yescharacteristic
161C2×Q8—28no—
162C22×C4—132no—
163C22×C4—263no—
164C22×C4—263no—
165C22×C4—2612no—
166C22×C4—2612no—
167C22×C4—266no—
168C22×C4—526no—
169C22×C4—526no—
170C22×C4—523no—
171C22×C4—521no—
172C22×C4Q8×D1312yes—
173C22×C4#613116yes—
174C22×C4C2×C22⋊D13112yes—
175C22×C4C2×C22⋊D1313yes—
176C22×C4C2×C22⋊D1313yes—
177C4⋊C4—224no—
178C4⋊C4—212no—
179C4⋊C4—526no—
180C22⋊C4—212no—
181C22⋊C4—2612no—
182C22⋊C4—5224no—
183C42—26no—
184C42—26no—
185C42—526no—
186C13#2346711yescharacteristic, complemented, Sylow
187C23—42no—
188C23—2612no—
189C23—266no—
190C23—526no—
191C23—524no—
192C23—5212no—
193C23—523no—
194C23—521no—
195C23C2×Q8×D1311yescharacteristic
196C23C2×#613113yes—
197C23C22×C22⋊D1313yes—
198Q8—88no—
199C2×C4—212no—
200C2×C4—412no—
201C2×C4—266no—
202C2×C4—523no—
203C2×C4—521no—
204C2×C4—5212no—
205C2×C4—524no—
206C2×C4—5212no—
207C2×C4—526no—
208C2×C4#8820016yes—
209C2×C4#8820016yes—
210C2×C4#8820116yes—
211C2×C4#8820116yes—
212C2×C4#8820713yes—
213C2×C4#8820711yescharacteristic
214C22—26no—
215C22—41no—
216C22—43no—
217C22—2612no—
218C22—5212no—
219C22—526no—
220C22—522no—
221C22—524no—
222C22C2×#8820013yes—
223C22C2×#8820113yes—
224C22C2×#8820711yescharacteristic
225C4—412no—
226C4—522no—
227C4—1046no—
228C4#1171889216yes—
229C4#1171889212yes—
230C2—23no—
231C2—23no—
232C2—524no—
233C2C2×#1171889211yescharacteristic
234C2#1312422812yes—
subgroupG/H
centerC2×C4#88207
commutator, cosocleC24×C13C24
FrattiniC24C23×D13
FittingC13×#3458C2
socleC22×C13C2×#120
prime radicalC24×D13C23
hypercenter#3458D13
hypocenterC13#23467
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3458

Complements

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

NH ≅ G/Ntype
2. #13116002C2semidirect
4. #13114569C2semidirect
5. C13×#3458C2semidirect
23. C22×C4×D13Q8semidirect
70. #3458D13semidirect
186. C13#23467semidirect

Maximal subgroups

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

subgroupindex
#131172152
#131160022
#131159992
#131145692
C13×#34582
#2346713