Finite Group Databasebeta

← #15793923

Subgroups — #15793923

Order 3328.

1094 conjugacy classes of subgroups; only the 319 normal subgroups are shown.

normal subgroups only

This group has 1094 conjugacy classes of subgroups — too many to draw. Only its 319 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#13113107C212yesmaximal
2#13113104C213yesmaximal
3#13113098C216yesmaximal
4#13113068C213yesmaximal
5C2×C13×#395C211yesmaximal, characteristic
6C23×Q8×C13C2211yescharacteristic
7C22×C13×C4⋊C4C2213yes—
8C22×C4×Dic13C2211yescharacteristic
9C13×#395C418yescomplemented
10C2×C13×#95C2213yes—
11C2×#88071C2216yes—
12C2×#88071C2213yes—
13C2×#88071C2213yes—
14C2×#88071C2216yes—
15C2×#88071C2216yes—
16C2×#88071C2213yes—
17C22×Q8×C13—43no—
18C22×Q8×C13—43no—
19C22×Q8×C13C2×C414yes—
20C23×C4×C13C2311yescharacteristic
21C23×C4×C13C2313yes—
22C23×C4×C13C2313yes—
23C23×Dic13C2316yes—
24C23×Dic13C2312yes—
25C2×C13×C4⋊C4—43no—
26C2×C13×C4⋊C4—43no—
27C2×C13×C4⋊C4C2×C4112yes—
28C2×C4×Dic13—43no—
29C13×#95C2×C4112yes—
30#88071—212no—
31#88071—46no—
32#88071—43no—
33#88071—43no—
34#88071—43no—
35#88071—46no—
36#14655—131nomaximal, Sylow
37C24×C13C2411yescharacteristic
38C2×Q8×C13—412no—
39C2×Q8×C13—412no—
40C2×Q8×C13—44no—
41C22×C4×C13—26no—
42C22×C4×C13—23no—
43C22×C4×C13—23no—
44C22×C4×C13—23no—
45C22×C4×C13—26no—
46C22×C4×C13—26no—
47C22×C4×C13—23no—
48C22×C4×C13—23no—
49C22×C4×C13—23no—
50C22×C4×C13—26no—
51C22×C4×C13C22×C416yes—
52C22×C4×C13C22×C416yes—
53C22×C4×C13C22×C412yes—
54C22×Dic13—26no—
55C22×Dic13—26no—
56C22×Dic13—26no—
57C22×Dic13—26no—
58C22×Dic13—26no—
59C22×Dic13—26no—
60C22×Dic13—26no—
61C22×Dic13—26no—
62C22×Dic13—26no—
63C22×Dic13#4114yes—
64C13×C4⋊C4—412no—
65C4×Dic13—44no—
66C2×#395D1311yescharacteristic
67#1446—132no—
68#1445—133no—
69#1443—136no—
70#1436—133no—
71C23×C13C23×C411yescharacteristic
72C23×C13C2×#4112yes—
73C23×C13H(5,𝔽2)13yes—
74C23×C13H(5,𝔽2)13yes—
75C23×C132−1+416yes—
76Q8×C13—416no—
77C2×C4×C13—26no—
78C2×C4×C13—26no—
79C2×C4×C13—26no—
80C2×C4×C13—26no—
81C2×C4×C13—212no—
82C2×C4×C13—26no—
83C2×C4×C13—46no—
84C2×C4×C13—46no—
85C2×C4×C13—43no—
86C2×C4×C13—43no—
87C2×C4×C13—46no—
88C2×C4×C13—41no—
89C2×C4×C13—43no—
90C2×Dic13—212no—
91C2×Dic13—42no—
92C2×Dic13—46no—
93C2×Dic13—46no—
94C2×Dic13—46no—
95C2×Dic13—46no—
96C2×Dic13—46no—
97C2×Dic13—46no—
98C2×Dic13—46no—
99C2×Dic13—46no—
100C23×Q8C2×D1311yescharacteristic
101C22×C4⋊C4C2×D1313yes—
102C22×C42—131no—
103#395Dic1318yescomplemented
104C2×#95—136no—
105C2×#95—136no—
106C2×#95—133no—
107C2×#95—133no—
108C2×#95—133no—
109C2×#95—136no—
110C2×#95C2×D1313yes—
111C22×C13C4×#4111yescharacteristic
112C22×C13#51813yes—
113C22×C13#51913yes—
114C22×C13#53916yes—
115C22×C13#54216yes—
116C22×C13#56013yes—
117C22×C13H(3,𝔽4)11yescharacteristic
118C22×C13#56316yes—
119C22×C13#56313yes—
120C22×C13#56313yes—
121C4×C13—46no—
122C4×C13—42no—
123C4×C13—46no—
124Dic13—44no—
125Dic13—86no—
126C22×Q8—43no—
127C22×Q8—43no—
128C22×Q8C2×Dic1314yes—
129C23×C4—132no—
130C23×C4—136no—
131C23×C4C22×D1311yescharacteristic
132C23×C4C22×D1313yes—
133C23×C4C22×D1313yes—
134C2×C4⋊C4—43no—
135C2×C4⋊C4—43no—
136C2×C4⋊C4C2×Dic13112yes—
137C2×C42—523no—
138#95—2612no—
139#95—523no—
140#95—523no—
141#95—523no—
142#95—526no—
143#95—526no—
144#95C2×Dic13112yes—
145C2×C13#233213yes—
146C2×C13#237511yescharacteristic
147C2×C13#238113yes—
148C2×C13#283512yes—
149C2×C13#283816yes—
150C24C23×D1311yescharacteristic
151C2×Q8—412no—
152C2×Q8—44no—
153C2×Q8—412no—
154C22×C4—23no—
155C22×C4—23no—
156C22×C4—23no—
157C22×C4—26no—
158C22×C4—26no—
159C22×C4—23no—
160C22×C4—23no—
161C22×C4—23no—
162C22×C4—26no—
163C22×C4—26no—
164C22×C4—134no—
165C22×C4—266no—
166C22×C4—266no—
167C22×C4—266no—
168C22×C4—266no—
169C22×C4—266no—
170C22×C4—266no—
171C22×C4—266no—
172C22×C4—266no—
173C22×C4—266no—
174C22×C4C22×Dic1316yes—
175C22×C4C22×Dic1316yes—
176C22×C4C22×Dic1312yes—
177C4⋊C4—412no—
178C42—524no—
179C13#1465511yescharacteristic, complemented, Sylow
180C23#8825113yes—
181C23#8825113yes—
182C23#8825416yes—
183C23#41×D1312yes—
184C23C23×Dic1311yescharacteristic
185Q8—416no—
186C2×C4—26no—
187C2×C4—26no—
188C2×C4—26no—
189C2×C4—212no—
190C2×C4—26no—
191C2×C4—26no—
192C2×C4—41no—
193C2×C4—43no—
194C2×C4—43no—
195C2×C4—46no—
196C2×C4—43no—
197C2×C4—46no—
198C2×C4—46no—
199C2×C4—2612no—
200C2×C4—526no—
201C2×C4—522no—
202C2×C4—526no—
203C2×C4—526no—
204C2×C4—526no—
205C2×C4—526no—
206C2×C4—526no—
207C2×C4—526no—
208C2×C4—526no—
209C22#1171929911yescharacteristic
210C22#1171930013yes—
211C22#1171934316yes—
212C22#1171934516yes—
213C22#1171944016yes—
214C22#1171944013yes—
215C22#1171944013yes—
216C22#1171950313yes—
217C22#1171951713yes—
218C22#41×Dic1311yescharacteristic
219C4—42no—
220C4—46no—
221C4—46no—
222C4—524no—
223C4—1046no—
224C2#1311759413yes—
225C2#1311797711yescharacteristic
226C2#1311801713yes—
227C2#1312302512yes—
228C2#1312306016yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#395C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#395D13
hypocenterC13#14655
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
9. C13×#395C4semidirect
103. #395Dic13semidirect
179. C13#14655semidirect

Maximal subgroups

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

subgroupindex
#131131072
#131131042
#131130982
#131130682
C2×C13×#3952
#1465513