Finite Group Databasebeta

← #15767015

Subgroups — #15767015

Order 3328.

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

normal subgroups only

This group has 344 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#13114955C211yesmaximal, 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
11#11718593C2211yescharacteristic
12#11718587C2212yes—
13C2×C4⋊#1055C2211yescharacteristic
14#11718142—22no—
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—
37C4⋊#1055—22no—
38C4⋊#1055—22no—
39#88043—22no—
40#10517—131nomaximal, Sylow
41C2×Q8×C13—22no—
42C2×Q8×C13—22no—
43C22×C4×C13C2×D411yescharacteristic
44C22×C4×C13C2×D411yescharacteristic
45C22×C4×C13#4111yescharacteristic
46C22×Dic13—22no—
47C13×Q16—82no—
48C2×C8×C13—22no—
49C2×C8×C13—42no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—42no—
56C13×C22⋊C4—42no—
57C42×C13—42no—
58C42×C13C2×D412yes—
59C42×C13#4112yes—
60C4×Dic13—41no—
61C4×Dic13—41no—
62C2×#1055—42no—
63C2×#1055—41no—
64C2×#1055—42no—
65#3249D1311yescharacteristic
66#1832—131no—
67#1552—132no—
68#1506—132no—
69#1290—131no—
70C23×C13#12111yescharacteristic
71Q8×C13—42no—
72Q8×C13—42no—
73Q8×C13—82no—
74C2×C4×C13—22no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—41no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13#12011yescharacteristic
81C2×C4×C13#12112yes—
82C2×C4×C13#12312yes—
83C2×C4×C13#12411yescharacteristic
84C2×Dic13—42no—
85C2×Dic13—42no—
86C2×Dic13—42no—
87C8×C13—42no—
88#1055—82no—
89#1055—81no—
90#533C2×D1312yes—
91#477—22no—
92#467—22no—
93#462—22no—
94#432—132no—
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—82no—
110C4×C13—82no—
111C4×C13#45411yescharacteristic
112C4×C13#45511yescharacteristic
113Dic13—82no—
114C2×Q16—22no—
115C22×C8—261no—
116C22×C8C22⋊D1312yes—
117C4⋊Q8C22⋊D1312yes—
118C4⋊Q8C22⋊D1312yes—
119#125—22no—
120C22⋊Q8—22no—
121C22⋊Q8—22no—
122C4×Q8—22no—
123C4×Q8—22no—
124#117—22no—
125C2×C42—261no—
126C2×C42C22×D1311yescharacteristic
127#107—22no—
128C4⋊C8—22no—
129C4⋊C8—262no—
130C4⋊C8—262no—
131#103—24no—
132C22⋊C8—262no—
133#97—262no—
134#95—132no—
135#95—261no—
136C2×C13—22no—
137C2×C13#204011yescharacteristic
138C2×C13#204711yescharacteristic
139C2×C13#205311yescharacteristic
140C2×Q8—22no—
141C2×Q8—22no—
142C22×C4—262no—
143C22×C4D4×D1311yescharacteristic
144C22×C4#612911yescharacteristic
145C22×C4C2×C22⋊D1311yescharacteristic
146Q16—82no—
147C2×C8—22no—
148C2×C8—42no—
149C2×C8—522no—
150C2×C8—522no—
151C2×C8—521no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C22⋊C4—42no—
159C42—42no—
160C42—521no—
161C42—521no—
162C42#612912yes—
163C42C2×C22⋊D1312yes—
164C13#1051711yescharacteristic, complemented, Sylow
165C23#8819211yescharacteristic
166Q8—42no—
167Q8—42no—
168Q8—82no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—522no—
176C2×C4—522no—
177C2×C4—522no—
178C2×C4#8818912yes—
179C2×C4#8819011yescharacteristic
180C2×C4#8819312yes—
181C2×C4#8820711yescharacteristic
182C8—42no—
183C8—1042no—
184C8—1041no—
185C22—21no—
186C22—21no—
187C22#1171885312yes—
188C22#1171888311yescharacteristic
189C4—21no—
190C4—22no—
191C4—22no—
192C4—82no—
193C4—82no—
194C4—1042no—
195C4#1171890311yescharacteristic
196C4#1171890611yescharacteristic
197C2—22no—
198C2#1311606211yescharacteristic
199C2#1311610111yescharacteristic
200C2#1311613911yescharacteristic
subgroupG/H
centerC22#11718883
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3249C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#3249D13
hypocenterC13#10517
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
164. C13#10517semidirect

Maximal subgroups

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

subgroupindex
#131149552
#131135362
#131133482
#131127062
C13×#32492
#1051713