Finite Group Databasebeta

← #15830671

Subgroups — #15830671

Order 3328.

938 conjugacy classes of subgroups; only the 395 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 395 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#13123917C211yesmaximal, characteristic
2#13117757C211yesmaximal, characteristic
3#13113400C216yesmaximal
4#13113335C216yesmaximal
5C13×#3502C211yesmaximal, characteristic
6Q82×C13C414yescomplemented
7C13×#557—24no—
8C13×#557C414yescomplemented
9C13×#544—23no—
10C13×#533C2216yes—
11C13×#519—21no—
12C2×C4×Q8×C13C2211yescharacteristic
13C2×Q8×Dic13—21no—
14Q8×#1055—24no—
15#11718646—23no—
16#11718597C2213yes—
17C4×C4⋊Dic13C2213yes—
18#11718586C2216yes—
19#11718130C22112yes—
20#11718130C2214yes—
21C22×Q8×C13D411yescharacteristic
22C13×C4⋊Q8—212no—
23C13×C4⋊Q8C2×C416yes—
24C13×C4⋊Q8C2×C416yes—
25C13×#125—212no—
26C13×#125—26no—
27C13×C22⋊Q8—26no—
28C13×C22⋊Q8C2314yes—
29C4×Q8×C13—24no—
30C4×Q8×C13—24no—
31C4×Q8×C13—26no—
32C4×Q8×C13C2×C4112yes—
33C4×Q8×C13C2×C414yes—
34C4×Q8×C13D414yes—
35C13×#117—26no—
36C2×C13×C4⋊C4D413yes—
37C2×C42×C13C2313yes—
38Q8×Dic13—44no—
39C2×C4⋊Dic13—23no—
40C2×C4⋊Dic13—23no—
41C2×C4×Dic13—23no—
42#88071—23no—
43#88071C2311yescharacteristic
44#88071C2313yes—
45C22⋊#1055C2314yes—
46C4⋊#1055—26no—
47C4×#1055—26no—
48#17619—131nomaximal, Sylow
49C2×Q8×C13—26no—
50C2×Q8×C13C22⋊C414yes—
51C2×Q8×C13SD1614yes—
52C2×Q8×C13Q1614yes—
53C2×Q8×C13C22×C414yes—
54C22×C4×C13C2×D413yes—
55C22×C4×C13C2×D413yes—
56C22×C4×C13C2411yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—23no—
59C13×C4⋊C4—26no—
60C13×C4⋊C4—26no—
61C13×C4⋊C4—26no—
62C13×C4⋊C4—212no—
63C13×C4⋊C4—24no—
64C13×C4⋊C4C22⋊C4112yes—
65C13×C4⋊C4C22×C414yes—
66C13×C22⋊C4—24no—
67C42×C13—212no—
68C42×C13C22×C416yes—
69C42×C13C2×D416yes—
70C4⋊Dic13—46no—
71C4⋊Dic13—46no—
72C4×Dic13—46no—
73C2×#1055—24no—
74#3502D1311yescharacteristic
75#2982—131no—
76#2351—131no—
77#1518—136no—
78#1503—136no—
79C23×C13C22×D411yescharacteristic
80Q8×C13—44no—
81Q8×C13—86no—
82Q8×C13#103116yes—
83C2×C4×C13—24no—
84C2×C4×C13—24no—
85C2×C4×C13—43no—
86C2×C4×C13—41no—
87C2×C4×C13C2×C22⋊C416yes—
88C2×C4×C13C2×C22⋊C416yes—
89C2×C4×C13C2×SD1616yes—
90C2×C4×C13C2×Q1616yes—
91C2×C4×C13C23×C411yescharacteristic
92C2×C4×C13C22×D411yescharacteristic
93C2×Dic13—22no—
94C2×Dic13—41no—
95C2×Dic13—41no—
96C2×Dic13—43no—
97C2×Dic13—43no—
98C2×Dic13—43no—
99#1055—44no—
100Q82Dic1314yescomplemented
101#557—24no—
102#557Dic1314yescomplemented
103#544—23no—
104#533C2×D1316yes—
105#519—21no—
106C2×C4×Q8—261no—
107C2×C4×Q8C2×D1311yescharacteristic
108C8×Q8—264no—
109#431—136no—
110#389—263no—
111#382—133no—
112C4×C4⋊C4—133no—
113#328—134no—
114#328—1312no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13C22×C22⋊C411yescharacteristic
118C22×C13C22×SD1611yescharacteristic
119C22×C13C22×Q1611yescharacteristic
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—26no—
123C4×C13—44no—
124C4×C13—44no—
125C4×C13C2×#103112yes—
126Dic13—42no—
127Dic13—83no—
128C22×Q8C22⋊D1311yescharacteristic
129C4⋊Q8—212no—
130C4⋊Q8C2×Dic1316yes—
131C4⋊Q8C2×Dic1316yes—
132#125—212no—
133#125—26no—
134C22⋊Q8—26no—
135C22⋊Q8C22×D1314yes—
136C4×Q8—24no—
137C4×Q8—24no—
138C4×Q8—26no—
139C4×Q8—524no—
140C4×Q8C2×Dic13112yes—
141C4×Q8C2×Dic1314yes—
142C4×Q8C22⋊D1314yes—
143#117—26no—
144C2×C4⋊C4—263no—
145C2×C4⋊C4—263no—
146C2×C4⋊C4C22⋊D1313yes—
147C2×C42—263no—
148C2×C42C22×D1313yes—
149C4⋊C8—266no—
150C22⋊C8—134no—
151C4×C8—266no—
152#95—131no—
153#95—133no—
154#95—263no—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#288411yescharacteristic
158C2×C13C22×#10311yescharacteristic
159C2×C13#290111yescharacteristic
160C2×Q8—26no—
161C2×Q8#610614yes—
162C2×Q8#610714yes—
163C2×Q8C22⋊Dic1314yes—
164C2×Q8C22×Dic1314yes—
165C22×C4—261no—
166C22×C4—263no—
167C22×C4C2×C22⋊D1313yes—
168C22×C4C2×C22⋊D1313yes—
169C22×C4C23×D1311yescharacteristic
170C2×C8—264no—
171C4⋊C4—26no—
172C4⋊C4—26no—
173C4⋊C4—26no—
174C4⋊C4—212no—
175C4⋊C4—24no—
176C4⋊C4—526no—
177C4⋊C4—526no—
178C4⋊C4C22⋊Dic13112yes—
179C4⋊C4C22×Dic1314yes—
180C22⋊C4—24no—
181C42—212no—
182C42—526no—
183C42C22×Dic1316yes—
184C42C2×C22⋊D1316yes—
185C13#1761911yescharacteristic, complemented, Sylow
186C23C22×C22⋊D1311yescharacteristic
187Q8—44no—
188Q8—86no—
189Q8#88075116yes—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—43no—
193C2×C4—41no—
194C2×C4—262no—
195C2×C4—521no—
196C2×C4—521no—
197C2×C4—523no—
198C2×C4—523no—
199C2×C4—523no—
200C2×C4C2×#610616yes—
201C2×C4C2×#610716yes—
202C2×C4C2×C22⋊Dic1316yes—
203C2×C4C2×C22⋊Dic1316yes—
204C2×C4C23×Dic1311yescharacteristic
205C2×C4C22×C22⋊D1311yescharacteristic
206C8—524no—
207C22—21no—
208C22—21no—
209C22C22×#610611yescharacteristic
210C22C22×#610711yescharacteristic
211C22C22×C22⋊Dic1311yescharacteristic
212C4—26no—
213C4—21no—
214C4—21no—
215C4—44no—
216C4—44no—
217C4—522no—
218C4—1043no—
219C4C2×#88075112yes—
220C2—21no—
221C2—21no—
222C2#1312330011yescharacteristic
223C2C22×#8807511yescharacteristic
224C2#1312338311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#3502C2
socleC22×C13C22×C22⋊C4
prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenter#3502D13
hypocenterC13#17619
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #3502

Complements

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

NH ≅ G/Ntype
6. Q82×C13C4semidirect
8. C13×#557C4semidirect
100. Q82Dic13semidirect
102. #557Dic13semidirect
185. C13#17619semidirect

Maximal subgroups

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

subgroupindex
#131239172
#131177572
#131134002
#131133352
C13×#35022
#1761913