Finite Group Databasebeta

← #15830670

Subgroups — #15830670

Order 3328.

938 conjugacy classes of subgroups; only the 355 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 355 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#13128646C211yesmaximal, characteristic
2#13123917C211yesmaximal, characteristic
3#13113399C216yesmaximal
4#13113334C216yesmaximal
5C13×#2351C211yesmaximal, characteristic
6C2×C4×Q8×C13—21no—
7C2×C4×Q8×C13C2211yescharacteristic
8#11719517—21no—
9#11719275C414yescomplemented
10#11719274—24no—
11Q8×Dic26C414yescomplemented
12#11719205—23no—
13#11719175C2216yes—
14C13×#389—23no—
15C13×#382C2213yes—
16C4×C13×C4⋊C4C2213yes—
17Q8×#1055—24no—
18#11718586C2216yes—
19#11718044C22112yes—
20#11718044C2214yes—
21C22×Q8×C13D411yescharacteristic
22C4×Q8×C13—44no—
23C4×Q8×C13C2×C414yes—
24C4×Q8×C13D414yes—
25C2×C13×C4⋊C4—23no—
26C2×C13×C4⋊C4—23no—
27C2×C13×C4⋊C4D413yes—
28C2×C42×C13—23no—
29C2×C42×C13C2313yes—
30Q8×Dic13—24no—
31Q8×Dic13—24no—
32#88180—26no—
33#88178—26no—
34#88178C2314yes—
35#88144—212no—
36#88142—212no—
37#88124—26no—
38#88123C2×C416yes—
39#88123C2×C416yes—
40C4×Dic26—26no—
41C4×Dic26C2×C4112yes—
42C13×#95—23no—
43C13×#95C2311yescharacteristic
44C13×#95C2313yes—
45C22⋊#1055C2314yes—
46C4⋊#1055—26no—
47C4×#1055—26no—
48#17619—131nomaximal, Sylow
49C2×Q8×C13C22⋊C414yes—
50C2×Q8×C13SD1614yes—
51C2×Q8×C13Q1614yes—
52C22×C4×C13—21no—
53C22×C4×C13—23no—
54C22×C4×C13C2×D413yes—
55C22×C4×C13C2×D413yes—
56C22×C4×C13C2411yescharacteristic
57C2×Dic26—26no—
58C2×Dic26C22×C414yes—
59C13×C4⋊C4—46no—
60C13×C4⋊C4—46no—
61C13×C4⋊C4C22⋊C4112yes—
62C42×C13—46no—
63C42×C13C22×C416yes—
64C42×C13C2×D416yes—
65C22⋊Dic13—24no—
66C4⋊Dic13—26no—
67C4⋊Dic13—26no—
68C4⋊Dic13—26no—
69C4⋊Dic13C22×C414yes—
70#6101—212no—
71#6101—24no—
72C4×Dic13—212no—
73C2×#1055—24no—
74#3502—131no—
75#2982—131no—
76#2351D1311yescharacteristic
77#1518—136no—
78#1503—136no—
79C23×C13C22×D411yescharacteristic
80Q8×C13#103116yes—
81C2×C4×C13—22no—
82C2×C4×C13—43no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13—43no—
87C2×C4×C13—43no—
88C2×C4×C13—43no—
89C2×C4×C13C2×C22⋊C416yes—
90C2×C4×C13C2×C22⋊C416yes—
91C2×C4×C13C2×SD1616yes—
92C2×C4×C13C2×Q1616yes—
93C2×C4×C13C23×C411yescharacteristic
94C2×C4×C13C22×D411yescharacteristic
95C2×Dic13—24no—
96C2×Dic13—24no—
97Dic26—44no—
98Dic26—86no—
99#1055—44no—
100Q82—134no—
101#557—134no—
102#557—264no—
103#544—263no—
104#533—136no—
105#519—261no—
106C2×C4×Q8—21no—
107C2×C4×Q8C2×D1311yescharacteristic
108C8×Q8—264no—
109#431—136no—
110#389—23no—
111#382C2×D1313yes—
112C4×C4⋊C4C2×D1313yes—
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—42no—
124C4×C13—83no—
125C4×C13C2×#103112yes—
126Dic13—44no—
127Dic13—44no—
128C22×Q8C22⋊D1311yescharacteristic
129C4⋊Q8—136no—
130C4⋊Q8—136no—
131C4⋊Q8—2612no—
132#125—2612no—
133#125—266no—
134C22⋊Q8—134no—
135C22⋊Q8—266no—
136C4×Q8—44no—
137C4×Q8—1312no—
138C4×Q8—264no—
139C4×Q8—264no—
140C4×Q8—266no—
141C4×Q8C4×D1314yes—
142C4×Q8D5214yes—
143#117—266no—
144C2×C4⋊C4—23no—
145C2×C4⋊C4—23no—
146C2×C4⋊C4C22⋊D1313yes—
147C2×C42—23no—
148C2×C42C22×D1313yes—
149C4⋊C8—266no—
150C22⋊C8—134no—
151C4×C8—266no—
152#95—23no—
153#95C22×D1311yescharacteristic
154#95C22×D1313yes—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#288411yescharacteristic
158C2×C13C22×#10311yescharacteristic
159C2×C13#290111yescharacteristic
160C2×Q8—134no—
161C2×Q8—266no—
162C2×Q8#610314yes—
163C2×Q8#610514yes—
164C2×Q8#610714yes—
165C22×C4—21no—
166C22×C4—23no—
167C22×C4C2×C22⋊D1313yes—
168C22×C4C2×C22⋊D1313yes—
169C22×C4C23×D1311yescharacteristic
170C2×C8—264no—
171C4⋊C4—46no—
172C4⋊C4—46no—
173C4⋊C4—134no—
174C4⋊C4—266no—
175C4⋊C4—266no—
176C4⋊C4—2612no—
177C4⋊C4—266no—
178C4⋊C4—264no—
179C4⋊C4#6103112yes—
180C22⋊C4—264no—
181C42—46no—
182C42—2612no—
183C42C2×C4×D1316yes—
184C42C2×D5216yes—
185C13#1761911yescharacteristic, complemented, Sylow
186C23C22×C22⋊D1311yescharacteristic
187Q8—524no—
188Q8—1046no—
189Q8#88050116yes—
190C2×C4—22no—
191C2×C4—43no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—43no—
196C2×C4—43no—
197C2×C4—43no—
198C2×C4—264no—
199C2×C4—264no—
200C2×C4C2×#610316yes—
201C2×C4C2×#610316yes—
202C2×C4C2×#610516yes—
203C2×C4C2×#610716yes—
204C2×C4C22×C4×D1311yescharacteristic
205C2×C4C22×D5211yescharacteristic
206C8—524no—
207C22—21no—
208C22—21no—
209C22C22×#610311yescharacteristic
210C22C22×#610511yescharacteristic
211C22C22×#610711yescharacteristic
212C4—26no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—83no—
217C4—524no—
218C4—524no—
219C4C2×#88050112yes—
220C2—21no—
221C2—21no—
222C2#1312329911yescharacteristic
223C2C22×#8805011yescharacteristic
224C2#1312338411yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2351C2
socleC22×C13C22×C22⋊C4
prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenter#2351D13
hypocenterC13#17619
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2351

Complements

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

NH ≅ G/Ntype
9. #11719275C4semidirect
11. Q8×Dic26C4semidirect
185. C13#17619semidirect

Maximal subgroups

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

subgroupindex
#131286462
#131239172
#131133992
#131133342
C13×#23512
#1761913