Finite Group Databasebeta

← #15767019

Subgroups — #15767019

Order 3328.

344 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 77 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#13126181C211yesmaximal, characteristic
2#13114955C211yesmaximal, characteristic
3#13113537C212yesmaximal
4#13113349C212yesmaximal
5C13×#1290C211yesmaximal, characteristic
6#11719175C2212yes—
7C13×#432C2212yes—
8C2×C13×C4⋊C8C2211yescharacteristic
9#11718777—22no—
10#11718593C2211yescharacteristic
11C2×C4⋊#1055C2211yescharacteristic
12#11718511—22no—
13#11718510—22no—
14#11718142—22no—
15#11718078—22no—
16#11718074—22no—
17#11718059—24no—
18C22×C8×C13D412yes—
19C2×C42×C13C2311yescharacteristic
20#88180—22no—
21#88178—22no—
22#88178—22no—
23C2×C4×Dic13—21no—
24C22×#1055—21no—
25C2×Dic52—22no—
26#88124—22no—
27#88123D412yes—
28#88123D412yes—
29C4×Dic26—22no—
30C4×Dic26—22no—
31C13×C4⋊C8—22no—
32C13×C4⋊C8—22no—
33C13×C22⋊C8—22no—
34C13×#97—22no—
35#88071—21no—
36#88071D412yes—
37#88058—22no—
38#88056—24no—
39C4⋊#1055—22no—
40#10517—131nomaximal, Sylow
41C22×C4×C13C2×D411yescharacteristic
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13#4111yescharacteristic
44C22×Dic13—22no—
45C2×Dic26—22no—
46C2×Dic26—22no—
47C2×C8×C13—22no—
48C2×C8×C13—42no—
49C2×C8×C13—42no—
50C42×C13C2×D412yes—
51C42×C13#4112yes—
52C22⋊Dic13—42no—
53C4⋊Dic13—22no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4⋊Dic13—22no—
57#6101—42no—
58#6101—42no—
59C4×Dic13—41no—
60C4×Dic13—41no—
61C4×Dic13—42no—
62C2×#1055—42no—
63C2×#1055—41no—
64Dic52—82no—
65#3249—131no—
66#1832—131no—
67#1552—132no—
68#1506—132no—
69#1290D1311yescharacteristic
70C23×C13#12111yescharacteristic
71C2×C4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—41no—
75C2×C4×C13#12011yescharacteristic
76C2×C4×C13#12112yes—
77C2×C4×C13#12312yes—
78C2×C4×C13#12411yescharacteristic
79C2×Dic13—42no—
80C2×Dic13—42no—
81C2×Dic13—42no—
82C2×Dic13—42no—
83C2×Dic13—42no—
84Dic26—42no—
85Dic26—42no—
86Dic26—82no—
87C8×C13—42no—
88C8×C13—82no—
89#1055—81no—
90#533—132no—
91#477—262no—
92#467—262no—
93#462—262no—
94#432C2×D1312yes—
95C2×C4⋊C8—131no—
96C2×C4⋊C8C2×D1311yescharacteristic
97#376—131no—
98#336—262no—
99#332—262no—
100#332—262no—
101#328—264no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13#39411yescharacteristic
105C22×C13#47312yes—
106C4×C13—22no—
107C4×C13—21no—
108C4×C13—22no—
109C4×C13#45411yescharacteristic
110C4×C13#45511yescharacteristic
111Dic13—82no—
112Dic13—82no—
113Dic13—82no—
114C2×Q16—262no—
115C22×C8—261no—
116C22×C8D5212yes—
117C4⋊Q8—132no—
118C4⋊Q8—132no—
119#125—262no—
120C22⋊Q8—262no—
121C22⋊Q8—262no—
122C4×Q8—262no—
123C4×Q8—262no—
124#117—262no—
125C2×C42—261no—
126C2×C42C22×D1311yescharacteristic
127#107—262no—
128C4⋊C8—22no—
129C4⋊C8—22no—
130C4⋊C8—262no—
131#103—264no—
132C22⋊C8—22no—
133#97—22no—
134#95—132no—
135#95—261no—
136C2×C13—22no—
137C2×C13#204011yescharacteristic
138C2×C13#204711yescharacteristic
139C2×C13#205311yescharacteristic
140C2×Q8—262no—
141C2×Q8—262no—
142C22×C4—262no—
143C22×C4C2×D5211yescharacteristic
144C22×C4D4×D1311yescharacteristic
145C22×C4#613111yescharacteristic
146Q16—1042no—
147C2×C8—22no—
148C2×C8—42no—
149C2×C8—42no—
150C2×C8—522no—
151C2×C8—521no—
152C4⋊C4—262no—
153C4⋊C4—262no—
154C4⋊C4—262no—
155C4⋊C4—262no—
156C4⋊C4—522no—
157C4⋊C4—522no—
158C22⋊C4—522no—
159C42—521no—
160C42—521no—
161C42—522no—
162C42#612712yes—
163C42D4×D1312yes—
164C13#1051711yescharacteristic, complemented, Sylow
165C23#8814911yescharacteristic
166Q8—522no—
167Q8—522no—
168Q8—1042no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—522no—
174C2×C4—522no—
175C2×C4—522no—
176C2×C4—522no—
177C2×C4—522no—
178C2×C4#8812911yescharacteristic
179C2×C4#8813611yescharacteristic
180C2×C4#8813812yes—
181C2×C4#8814812yes—
182C8—42no—
183C8—82no—
184C8—1041no—
185C22—21no—
186C22—21no—
187C22#1171833311yescharacteristic
188C22#1171855712yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—1042no—
193C4—1042no—
194C4—1042no—
195C4#1171840711yescharacteristic
196C4#1171841411yescharacteristic
197C2—22no—
198C2#1311606611yescharacteristic
199C2#1311610511yescharacteristic
200C2#1311614311yescharacteristic
subgroupG/H
centerC22#11718333
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1290C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#1290D13
hypocenterC13#10517
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
164. C13#10517semidirect

Maximal subgroups

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

subgroupindex
#131261812
#131149552
#131135372
#131133492
C13×#12902
#1051713