Finite Group Databasebeta

← #16782224

Subgroups — #16782224

Order 3328.

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

normal subgroups only

This group has 418 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
1C2×#11718286C212yesmaximal
2#13129679C214yesmaximal
3#13117438C211yesmaximal, characteristic
4C22×#6101C2211yescharacteristic
5C2×C22⋊#1057C2214yes—
6C13×#380C411yescharacteristic
7#11718873C411yescharacteristic
8#11718639—22no—
9#11718604C412yes—
10C22⋊C4×Dic13C2212yes—
11#11718316—22no—
12#11718286—22no—
13#11718286—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13C2×C411yescharacteristic
16C23×Dic13C2311yescharacteristic
17C22×#1057—24no—
18C2×C13×C4⋊C4—21no—
19C2×C13×C22⋊C4C2×C412yes—
20C2×C22⋊Dic13C2×C412yes—
21C2×C4⋊Dic13—21no—
22C2×#6101—24no—
23C2×#6101D412yes—
24C2×#6101D412yes—
25C2×C4×Dic13—22no—
26C22⋊#1057—24no—
27C22⋊#1057—24no—
28C13×#95—21no—
29#88071—21no—
30#88071—24no—
31#88071—22no—
32#8737—131nomaximal, Sylow
33C24×C13C22×C411yescharacteristic
34C22×C4×C13—22no—
35C22×C4×C13—22no—
36C22×C4×C13—81no—
37C22×C4×C13C22⋊C411yescharacteristic
38C22×C4×C13C22⋊C411yescharacteristic
39C22×Dic13—22no—
40C22×Dic13—22no—
41C22×Dic13—22no—
42C22×Dic13—22no—
43C22×Dic13—81no—
44C22×Dic13C22⋊C412yes—
45C22×Dic13C2×D412yes—
46C22×Dic13#4114yes—
47C2×#1057—44no—
48C2×#1057—84no—
49C13×C4⋊C4—81no—
50C13×C22⋊C4—24no—
51C22⋊Dic13—24no—
52C4⋊Dic13—81no—
53#6101—24no—
54#6101—24no—
55C4×Dic13—82no—
56#2313—131no—
57C2×#324—132no—
58#1282—134no—
59C23×C13—41no—
60C23×C13—41no—
61C23×C13C2×C22⋊C411yescharacteristic
62C23×C13#11712yes—
63C23×C13#13112yes—
64C23×C13#13112yes—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—41no—
68C2×C4×C13—41no—
69C2×C4×C13—42no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13—82no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—42no—
77C2×Dic13—44no—
78C2×Dic13—44no—
79C2×Dic13—42no—
80C2×Dic13—42no—
81C2×Dic13—42no—
82C2×Dic13#12314yes—
83#1057—84no—
84C22×C4⋊C4—131no—
85C2×C22⋊C8—134no—
86#387—262no—
87#387—262no—
88#381—132no—
89#380—131no—
90#380#26111yescharacteristic
91C4×C22⋊C4—132no—
92#324—262no—
93#324—262no—
94C22×C13—21no—
95C22×C13—22no—
96C22×C13—21no—
97C22×C13—22no—
98C22×C13—42no—
99C22×C13—42no—
100C22×C13#38111yescharacteristic
101C22×C13#40811yescharacteristic
102C22×C13#40811yescharacteristic
103C22×C13#43314yes—
104C4×C13—41no—
105C4×C13—41no—
106C4×C13—82no—
107Dic13—24no—
108Dic13—42no—
109Dic13—82no—
110C23×C4—131no—
111C23×C4—131no—
112C23×C4C2×#26111yescharacteristic
113C22×C8—264no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4—264no—
118C2×C4⋊C4—261no—
119C2×C22⋊C4—132no—
120C2×C22⋊C4C2×#26112yes—
121C2×C42—262no—
122C22⋊C8—264no—
123C22⋊C8—264no—
124#95—21no—
125#95—262no—
126#95—264no—
127#95—261no—
128C2×C13—21no—
129C2×C13—21no—
130C2×C13—24no—
131C2×C13#181811yescharacteristic
132C2×C13#182811yescharacteristic
133C2×C13#183011yescharacteristic
134C24C22×#26111yescharacteristic
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—81no—
138C22×C4—134no—
139C22×C4—132no—
140C22×C4—132no—
141C22×C4—262no—
142C22×C4—262no—
143C22×C4—262no—
144C22×C4—262no—
145C22×C4—1041no—
146C22×C4C22⋊#26111yescharacteristic
147C22×C4C22⋊#26111yescharacteristic
148C2×C8—524no—
149C2×C8—1044no—
150C4⋊C4—81no—
151C4⋊C4—264no—
152C4⋊C4—264no—
153C4⋊C4—1041no—
154C22⋊C4—24no—
155C22⋊C4—264no—
156C42—1042no—
157C13#873711yescharacteristic, complemented, Sylow
158C23—41no—
159C23—41no—
160C23#8823712yes—
161C23#8823812yes—
162C23#8824012yes—
163C23C2×C22⋊#26111yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—82no—
172C2×C4—134no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—522no—
177C2×C4—524no—
178C2×C4—524no—
179C2×C4—522no—
180C2×C4—522no—
181C2×C4—522no—
182C8—1044no—
183C22—21no—
184C22—22no—
185C22—21no—
186C22—22no—
187C22—42no—
188C22—42no—
189C22#1171907714yes—
190C22#1171913511yescharacteristic
191C22#1171914711yescharacteristic
192C22#1171915911yescharacteristic
193C4—41no—
194C4—41no—
195C4—82no—
196C4—264no—
197C4—522no—
198C4—1042no—
199C2—21no—
200C2—21no—
201C2—24no—
202C2#1313073011yescharacteristic
203C2#1313074711yescharacteristic
204C2#1313075011yescharacteristic
subgroupG/H
centerC22#11719135
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC13×#380C4
socleC22×C13#381
cosocleC23×Dic13C23
hypercenter#380#261
hypocenterC13#8737
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #380

Complements

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

NH ≅ G/Ntype
157. C13#8737semidirect

Maximal subgroups

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

subgroupindex
C2×#117182862
#131296792
#131174382
#873713