Finite Group Databasebeta

← #15767010

Subgroups — #15767010

Order 3328.

364 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 81 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#13114989C211yesmaximal, characteristic
2#13113536C212yesmaximal
3#13113348C212yesmaximal
4#13112706C211yesmaximal, characteristic
5C13×#3249C211yesmaximal, characteristic
6C13×#533C2212yes—
7C13×#477—22no—
8C13×#467—22no—
9C13×#462—22no—
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×#88054—22no—
12#11718593C2211yescharacteristic
13#11718587C2212yes—
14C2×C4⋊#1055C2211yescharacteristic
15#11718139—22no—
16#11718139—22no—
17#11718130—24no—
18C2×C13×Q16—22no—
19C22×C8×C13D412yes—
20C13×C4⋊Q8D412yes—
21C13×C4⋊Q8D412yes—
22C13×#125—22no—
23C13×C22⋊Q8—22no—
24C13×C22⋊Q8—22no—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C13×#117—22no—
28C2×C42×C13C2311yescharacteristic
29C2×C4×Dic13—21no—
30C22×#1055—21no—
31C13×#107—22no—
32C13×C4⋊C8—22no—
33C13×#103—24no—
34#88071—21no—
35#88071D412yes—
36C22⋊#1055—22no—
37#88054—44no—
38C4⋊#1055—22no—
39C4⋊#1055—22no—
40#88043—22no—
41#10516—131nomaximal, Sylow
42C2×Q8×C13—22no—
43C2×Q8×C13—22no—
44C22×C4×C13C2×D411yescharacteristic
45C22×C4×C13C2×D411yescharacteristic
46C22×C4×C13#4111yescharacteristic
47C22×Dic13—22no—
48C13×Q16—82no—
49C2×C8×C13—22no—
50C2×C8×C13—42no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—42no—
57C13×C22⋊C4—42no—
58C42×C13—42no—
59C42×C13C2×D412yes—
60C42×C13#4112yes—
61C4×Dic13—22no—
62C4×Dic13—22no—
63C2×#1055—42no—
64C2×#1055—41no—
65C2×#1055—42no—
66#3249D1311yescharacteristic
67#1843—131no—
68#1552—132no—
69#1506—132no—
70#1290—131no—
71C23×C13#12111yescharacteristic
72Q8×C13—42no—
73Q8×C13—42no—
74Q8×C13—82no—
75C2×C4×C13—22no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—41no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13#12011yescharacteristic
82C2×C4×C13#12112yes—
83C2×C4×C13#12312yes—
84C2×C4×C13#12411yescharacteristic
85C2×Dic13—24no—
86C2×Dic13—42no—
87C2×Dic13—42no—
88C8×C13—42no—
89#1055—82no—
90#1055—81no—
91#533C2×D1312yes—
92#477—22no—
93#467—22no—
94#462—22no—
95#432—132no—
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—82no—
111C4×C13—82no—
112C4×C13#45311yescharacteristic
113C4×C13#45611yescharacteristic
114Dic13—44no—
115C2×Q16—22no—
116C22×C8—261no—
117C22×C8C22⋊D1312yes—
118C4⋊Q8C22⋊D1312yes—
119C4⋊Q8C22⋊D1312yes—
120#125—22no—
121C22⋊Q8—22no—
122C22⋊Q8—22no—
123C4×Q8—22no—
124C4×Q8—22no—
125#117—22no—
126C2×C42—261no—
127C2×C42C22×D1311yescharacteristic
128#107—22no—
129C4⋊C8—22no—
130C4⋊C8—262no—
131C4⋊C8—262no—
132C4⋊C8—524no—
133#103—24no—
134C22⋊C8—262no—
135#97—262no—
136#95—132no—
137#95—261no—
138C2×C13—22no—
139C2×C13#203911yescharacteristic
140C2×C13#204711yescharacteristic
141C2×C13#205311yescharacteristic
142C2×Q8—22no—
143C2×Q8—22no—
144C22×C4—262no—
145C22×C4D4×D1311yescharacteristic
146C22×C4#612911yescharacteristic
147C22×C4C2×C22⋊D1311yescharacteristic
148Q16—82no—
149C2×C8—22no—
150C2×C8—42no—
151C2×C8—522no—
152C2×C8—522no—
153C2×C8—521no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C22⋊C4—42no—
161C42—42no—
162C42—262no—
163C42—262no—
164C42#612912yes—
165C42C2×C22⋊D1312yes—
166C13#1051611yescharacteristic, complemented, Sylow
167C23#8819211yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—264no—
178C2×C4—522no—
179C2×C4—522no—
180C2×C4#8818912yes—
181C2×C4#8819011yescharacteristic
182C2×C4#8819312yes—
183C2×C4#8820711yescharacteristic
184C8—42no—
185C8—1042no—
186C8—1041no—
187C22—21no—
188C22—21no—
189C22#1171885312yes—
190C22#1171888311yescharacteristic
191C4—21no—
192C4—22no—
193C4—22no—
194C4—82no—
195C4—82no—
196C4—524no—
197C4#1171890211yescharacteristic
198C4#1171890711yescharacteristic
199C2—22no—
200C2#1311605711yescharacteristic
201C2#1311610111yescharacteristic
202C2#1311613911yescharacteristic
subgroupG/H
centerC22#11718883
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3249C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#3249D13
hypocenterC13#10516
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

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
#131149892
#131135362
#131133482
#131127062
C13×#32492
#1051613