Finite Group Databasebeta

← #15767014

Subgroups — #15767014

Order 3328.

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

normal subgroups only

This group has 364 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#13114989C211yesmaximal, characteristic
3#13113537C212yesmaximal
4#13113349C212yesmaximal
5C13×#1290C211yesmaximal, characteristic
6#11719175C2212yes—
7C13×#432C2212yes—
8C2×C13×C4⋊C8C2211yescharacteristic
9#11718777—22no—
10C2×#88054—22no—
11#11718593C2211yescharacteristic
12C2×C4⋊#1055C2211yescharacteristic
13#11718511—22no—
14#11718510—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—
39#88054—44no—
40C4⋊#1055—22no—
41#10516—131nomaximal, Sylow
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13C2×D411yescharacteristic
44C22×C4×C13#4111yescharacteristic
45C22×Dic13—22no—
46C2×Dic26—22no—
47C2×Dic26—22no—
48C2×C8×C13—22no—
49C2×C8×C13—42no—
50C2×C8×C13—42no—
51C42×C13C2×D412yes—
52C42×C13#4112yes—
53C22⋊Dic13—42no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4⋊Dic13—22no—
57C4⋊Dic13—22no—
58#6101—42no—
59#6101—42no—
60C4×Dic13—22no—
61C4×Dic13—22no—
62C4×Dic13—42no—
63C2×#1055—42no—
64C2×#1055—41no—
65Dic52—82no—
66#3249—131no—
67#1843—131no—
68#1552—132no—
69#1506—132no—
70#1290D1311yescharacteristic
71C23×C13#12111yescharacteristic
72C2×C4×C13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—41no—
76C2×C4×C13#12011yescharacteristic
77C2×C4×C13#12112yes—
78C2×C4×C13#12312yes—
79C2×C4×C13#12411yescharacteristic
80C2×Dic13—24no—
81C2×Dic13—42no—
82C2×Dic13—42no—
83C2×Dic13—42no—
84C2×Dic13—42no—
85Dic26—42no—
86Dic26—42no—
87Dic26—82no—
88C8×C13—42no—
89C8×C13—82no—
90#1055—81no—
91#533—132no—
92#477—262no—
93#467—262no—
94#462—262no—
95#432C2×D1312yes—
96C2×C4⋊C8—131no—
97C2×C4⋊C8—262no—
98C2×C4⋊C8C2×D1311yescharacteristic
99#376—131no—
100#332—262no—
101#332—262no—
102#328—264no—
103C22×C13—21no—
104C22×C13—21no—
105C22×C13#39411yescharacteristic
106C22×C13#47312yes—
107C4×C13—22no—
108C4×C13—21no—
109C4×C13—22no—
110C4×C13#45311yescharacteristic
111C4×C13#45611yescharacteristic
112Dic13—44no—
113Dic13—82no—
114Dic13—82no—
115C2×Q16—262no—
116C22×C8—261no—
117C22×C8D5212yes—
118C4⋊Q8—132no—
119C4⋊Q8—132no—
120#125—262no—
121C22⋊Q8—262no—
122C22⋊Q8—262no—
123C4×Q8—262no—
124C4×Q8—262no—
125#117—262no—
126C2×C42—261no—
127C2×C42C22×D1311yescharacteristic
128#107—262no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—262no—
132C4⋊C8—524no—
133#103—264no—
134C22⋊C8—22no—
135#97—22no—
136#95—132no—
137#95—261no—
138C2×C13—22no—
139C2×C13#203911yescharacteristic
140C2×C13#204711yescharacteristic
141C2×C13#205311yescharacteristic
142C2×Q8—262no—
143C2×Q8—262no—
144C22×C4—262no—
145C22×C4C2×D5211yescharacteristic
146C22×C4D4×D1311yescharacteristic
147C22×C4#613111yescharacteristic
148Q16—1042no—
149C2×C8—22no—
150C2×C8—42no—
151C2×C8—42no—
152C2×C8—522no—
153C2×C8—521no—
154C4⋊C4—262no—
155C4⋊C4—262no—
156C4⋊C4—262no—
157C4⋊C4—262no—
158C4⋊C4—522no—
159C4⋊C4—522no—
160C22⋊C4—522no—
161C42—262no—
162C42—262no—
163C42—522no—
164C42#612712yes—
165C42D4×D1312yes—
166C13#1051611yescharacteristic, complemented, Sylow
167C23#8814911yescharacteristic
168Q8—522no—
169Q8—522no—
170Q8—1042no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—264no—
176C2×C4—522no—
177C2×C4—522no—
178C2×C4—522no—
179C2×C4—522no—
180C2×C4#8812911yescharacteristic
181C2×C4#8813611yescharacteristic
182C2×C4#8813812yes—
183C2×C4#8814812yes—
184C8—42no—
185C8—82no—
186C8—1041no—
187C22—21no—
188C22—21no—
189C22#1171833311yescharacteristic
190C22#1171855712yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—524no—
195C4—1042no—
196C4—1042no—
197C4#1171840811yescharacteristic
198C4#1171841311yescharacteristic
199C2—22no—
200C2#1311606111yescharacteristic
201C2#1311610511yescharacteristic
202C2#1311614311yescharacteristic
subgroupG/H
centerC22#11718333
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1290C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#1290D13
hypocenterC13#10516
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
166. C13#10516semidirect

Maximal subgroups

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

subgroupindex
#131261812
#131149892
#131135372
#131133492
C13×#12902
#1051613