Finite Group Databasebeta

← #16781980

Subgroups — #16781980

Order 3328.

336 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 88 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#13130393C212yesmaximal
2#13130375C212yesmaximal
3#13129744C212yesmaximal
4#13123769C211yesmaximal, characteristic
5#11719222C2211yescharacteristic
6#11719129C2214yes—
7C13×#424C411yescharacteristic
8#11718783C411yescharacteristic
9#11718779C2211yescharacteristic
10#11718763C411yescharacteristic
11C2×C8×Dic13C2211yescharacteristic
12#11718658C411yescharacteristic
13#11718491—22no—
14#11718489—22no—
15#11718256—22no—
16#11718254—22no—
17#11718245—24no—
18C2×#6122—24no—
19C2×C13×M16C2×C411yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C13×#117C2×C411yescharacteristic
22#88180C2×C411yescharacteristic
23C2×C4×Dic13C2311yescharacteristic
24C2×#6099C2×C411yescharacteristic
25C22×#1055C2×C411yescharacteristic
26#88144Q812yes—
27#88142D412yes—
28#88132—22no—
29C4×Dic26—22no—
30#88112—24no—
31C4⋊#1057—24no—
32C13×C4⋊C8—22no—
33#88055—21no—
34#88054—22no—
35#88054—22no—
36C8×Dic13—21no—
37C8×Dic13D412yes—
38C8×Dic13D412yes—
39#88043—21no—
40C4×#1055—21no—
41#8639—131nomaximal, Sylow
42C22×C4×C13C22×C411yescharacteristic
43C22×Dic13#4112yes—
44C2×Dic26—22no—
45#6122—84no—
46C2×#1057—44no—
47C13×M16—41no—
48C2×C8×C13—21no—
49C2×C8×C13—41no—
50C2×C8×C13C22⋊C412yes—
51C13×C4⋊C4C4⋊C412yes—
52C13×C22⋊C4—21no—
53C42×C13—21no—
54C22⋊Dic13—21no—
55C4⋊Dic13—22no—
56C4⋊Dic13C4⋊C412yes—
57#6101—22no—
58#6101—22no—
59C4×Dic13—21no—
60C4×Dic13C2×D411yescharacteristic
61C4×Dic13C2×D412yes—
62C4×Dic13C2×Q811yescharacteristic
63#6099—41no—
64C2×#1055—22no—
65C2×#1055—21no—
66C2×#1055C22⋊C411yescharacteristic
67C2×#1055C22⋊C411yescharacteristic
68#2960—131no—
69#1567—132no—
70#1561—132no—
71#1309—132no—
72C23×C13#11711yescharacteristic
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13C2×C22⋊C411yescharacteristic
77C2×C4×C13C2×C4⋊C411yescharacteristic
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13#12112yes—
82C2×Dic13C22⋊Q812yes—
83Dic26—42no—
84Dic26—42no—
85#1057—84no—
86C8×C13—22no—
87C8×C13—41no—
88#1055—21no—
89#1055—41no—
90#1055#10112yes—
91#533—131no—
92#446—262no—
93C8×Q8—262no—
94#424—131no—
95#424#26111yescharacteristic
96#423—131no—
97#423—134no—
98#405—131no—
99#405—131no—
100C2×C4×C8—131no—
101#335—262no—
102#335—262no—
103#332—264no—
104C22×C13—21no—
105C22×C13—22no—
106C22×C13#38011yescharacteristic
107C4×C13—21no—
108C4×C13—42no—
109C4×C13C2×#10111yescharacteristic
110C4×C13#41311yescharacteristic
111Dic13—22no—
112Dic13—42no—
113Dic13#47212yes—
114Dic13#47312yes—
115C2×M16—131no—
116C2×M16—264no—
117C2×M16C2×#26111yescharacteristic
118C22×C8—131no—
119C22×C8C2×#26111yescharacteristic
120C4⋊Q8—132no—
121#125—132no—
122C22⋊Q8—262no—
123C4×Q8—262no—
124#117—131no—
125#117C2×#26111yescharacteristic
126C2×C42—131no—
127C4⋊C8—22no—
128C4⋊C8—262no—
129C4⋊C8—264no—
130C4⋊C8—264no—
131C4⋊C8—262no—
132#97—261no—
133#97—261no—
134C4×C8—132no—
135C4×C8—132no—
136C4×C8—261no—
137C4×C8—261no—
138C2×C13—41no—
139C2×C13#180111yescharacteristic
140C2×C13#181612yes—
141C2×Q8—262no—
142C22×C4—132no—
143C22×C4C22×#26111yescharacteristic
144M16—41no—
145M16—521no—
146M16—1044no—
147C2×C8—21no—
148C2×C8—41no—
149C2×C8—131no—
150C2×C8—131no—
151C2×C8—262no—
152C2×C8—261no—
153C2×C8—524no—
154C2×C8C22⋊#26112yes—
155C4⋊C4—132no—
156C4⋊C4—262no—
157C4⋊C4—262no—
158C4⋊C4—262no—
159C4⋊C4C4⋊#26112yes—
160C22⋊C4—21no—
161C22⋊C4—261no—
162C42—21no—
163C42—131no—
164C42—131no—
165C42—132no—
166C42—261no—
167C13#863911yescharacteristic, complemented, Sylow
168C23#8823711yescharacteristic
169Q8—522no—
170Q8—522no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—132no—
175C2×C4—132no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4C2×C4⋊#26111yescharacteristic
180C2×C4C2×C22⋊#26111yescharacteristic
181C8—22no—
182C8—41no—
183C8—132no—
184C8—261no—
185C8—521no—
186C8—1044no—
187C22—21no—
188C22—22no—
189C22#1171913611yescharacteristic
190C4—21no—
191C4—42no—
192C4—132no—
193C4—132no—
194C4—262no—
195C4—522no—
196C4#1171914811yescharacteristic
197C4D13⋊#10111yescharacteristic
198C2—41no—
199C2#1313070311yescharacteristic
200C2#1313072512yes—
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#424C4
socleC22×C13#380
prime radicalC23×C13#117
cosocleC2×C4×Dic13C23
hypercenter#424#261
hypocenterC13#8639
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
167. C13#8639semidirect

Maximal subgroups

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

subgroupindex
#131303932
#131303752
#131297442
#131237692
#863913