Finite Group Databasebeta

← #16782272

Subgroups — #16782272

Order 3328.

438 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 80 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#13130084C212yesmaximal
2#13129737C214yesmaximal
3#13117452C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C411yescharacteristic
6C22×C4⋊Dic13C2211yescharacteristic
7#11719169C2214yes—
8#11718634—22no—
9#11718603C412yes—
10#11718603C2212yes—
11#11718589—22no—
12#11718285—22no—
13#11718285—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13C2×C411yescharacteristic
16C23×Dic13C2311yescharacteristic
17C2×#6122—24no—
18C13×#117—42no—
19C2×C13×C4⋊C4—21no—
20C2×C13×C22⋊C4C2×C412yes—
21C2×C42×C13—21no—
22C2×C22⋊Dic13C2×C412yes—
23#88180—42no—
24C2×C4⋊Dic13—24no—
25C2×C4⋊Dic13—21no—
26C2×C4⋊Dic13D412yes—
27C2×C4⋊Dic13D412yes—
28C2×#6101—22no—
29C2×#6101—22no—
30C2×C4×Dic13—21no—
31C22⋊#1057—24no—
32C22⋊#1057—24no—
33#88071—22no—
34#88071—22no—
35#8757—131nomaximal, Sylow
36C24×C13C22×C411yescharacteristic
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13C22⋊C411yescharacteristic
42C22×C4×C13C22⋊C411yescharacteristic
43C22×Dic13—22no—
44C22×Dic13—22no—
45C22×Dic13—81no—
46C22×Dic13—81no—
47C22×Dic13C22⋊C412yes—
48C22×Dic13C2×D412yes—
49C22×Dic13#4114yes—
50#6122—84no—
51C2×#1057—44no—
52C13×C4⋊C4—42no—
53C13×C22⋊C4—42no—
54C42×C13—42no—
55C22⋊Dic13—42no—
56C4⋊Dic13—24no—
57C4⋊Dic13—24no—
58C4⋊Dic13—42no—
59#6101—82no—
60#6101—82no—
61C4×Dic13—42no—
62#2316—131no—
63#1463—132no—
64#1305—134no—
65C23×C13—21no—
66C23×C13—21no—
67C23×C13—41no—
68C23×C13—41no—
69C23×C13C2×C22⋊C411yescharacteristic
70C23×C13#11712yes—
71C2×C4×C13—28no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13#10012yes—
80C2×C4×C13#10112yes—
81C2×Dic13—22no—
82C2×Dic13—42no—
83C2×Dic13—44no—
84C2×Dic13—42no—
85C2×Dic13—42no—
86C2×Dic13—42no—
87C2×Dic13—42no—
88C2×Dic13—82no—
89C2×Dic13#12314yes—
90#1057—84no—
91C2×#117—131no—
92C2×#117#26111yescharacteristic
93C22×C4⋊C4—131no—
94#407—134no—
95#389—262no—
96#389—262no—
97#380—132no—
98#380—132no—
99#324—262no—
100#324—262no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—22no—
104C22×C13—22no—
105C22×C13—22no—
106C22×C13—42no—
107C22×C13—42no—
108C22×C13#38111yescharacteristic
109C22×C13C2×#10011yescharacteristic
110C22×C13C2×#10111yescharacteristic
111C4×C13—22no—
112C4×C13—22no—
113C4×C13—82no—
114Dic13—24no—
115Dic13—42no—
116Dic13—82no—
117C23×C4—131no—
118C23×C4—131no—
119C23×C4C2×#26111yescharacteristic
120C2×M16—264no—
121#117—42no—
122#117—522no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—132no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—264no—
127C2×C4⋊C4—261no—
128C2×C4⋊C4—262no—
129C2×C4⋊C4—262no—
130C2×C22⋊C4—132no—
131C2×C22⋊C4C2×#26112yes—
132C2×C42—21no—
133C2×C42—261no—
134C22⋊C8—264no—
135C22⋊C8—264no—
136#95—262no—
137#95—262no—
138C2×C13—21no—
139C2×C13—21no—
140C2×C13—42no—
141C2×C13#182111yescharacteristic
142C2×C13#182811yescharacteristic
143C2×C13#183011yescharacteristic
144C24C22×#26111yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—134no—
150C22×C4—132no—
151C22×C4—132no—
152C22×C4—262no—
153C22×C4—262no—
154C22×C4—1041no—
155C22×C4—1041no—
156C22×C4C22⋊#26111yescharacteristic
157C22×C4C22⋊#26111yescharacteristic
158M16—1044no—
159C2×C8—524no—
160C4⋊C4—42no—
161C4⋊C4—264no—
162C4⋊C4—264no—
163C4⋊C4—522no—
164C4⋊C4—1042no—
165C4⋊C4—1042no—
166C22⋊C4—42no—
167C22⋊C4—522no—
168C42—42no—
169C42—522no—
170C13#875711yescharacteristic, complemented, Sylow
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23#8823712yes—
176C23C2×C22⋊#26111yescharacteristic
177C2×C4—28no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—134no—
186C2×C4—262no—
187C2×C4—522no—
188C2×C4—524no—
189C2×C4—522no—
190C2×C4—522no—
191C2×C4—522no—
192C2×C4—522no—
193C2×C4—1042no—
194C2×C4#8811312yes—
195C2×C4#8812112yes—
196C8—1044no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22C2×#8811311yescharacteristic
205C22#1171913511yescharacteristic
206C22C2×#8812111yescharacteristic
207C4—22no—
208C4—22no—
209C4—82no—
210C4—264no—
211C4—522no—
212C4—1042no—
213C2—21no—
214C2—21no—
215C2—42no—
216C2#1313073511yescharacteristic
217C2#1313074811yescharacteristic
218C2#1313075011yescharacteristic
subgroupG/H
centerC22#11719135
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC2×C13×#117C4
socleC22×C13#381
cosocleC23×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8757
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
170. C13#8757semidirect

Maximal subgroups

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

subgroupindex
#131300842
#131297372
#131174522
#875713