Finite Group Databasebeta

← #16782199

Subgroups — #16782199

Order 3328.

514 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 112 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#13130692C212yesmaximal
2#13129714C214yesmaximal, complemented
3#13117239C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8C2×#88112C2214yes—
9#11718638C412yes—
10#11718637C2212yes—
11#11718603—22no—
12C4×#6101—22no—
13#11718290—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13D412yes—
16C22×#1057—24no—
17C13×#117—42no—
18C2×C13×C4⋊C4C2×C412yes—
19C2×C13×C22⋊C4—21no—
20C2×C42×C13—21no—
21C2×C22⋊Dic13—21no—
22#88180—42no—
23C2×C4⋊Dic13C2×C412yes—
24C2×#6101—22no—
25C2×#6101—22no—
26C2×C4×Dic13—24no—
27C2×C4×Dic13—21no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13D412yes—
30C2×C4×Dic13C2311yescharacteristic
31C22⋊#1057—44no—
32#88112—28no—
33#88071—24no—
34#8729—131nomaximal, Sylow
35C24×C13C22⋊C411yescharacteristic
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13C22⋊C411yescharacteristic
41C22×C4×C13C22×C411yescharacteristic
42C22×Dic13—24no—
43C22×Dic13—24no—
44C22×Dic13—22no—
45C22×Dic13—22no—
46C22×Dic13—22no—
47C22×Dic13C22⋊C412yes—
48C22×Dic13C2×D412yes—
49C2×#1057—44no—
50C2×#1057—44no—
51C2×#1057—44no—
52C13×C4⋊C4—42no—
53C13×C22⋊C4—42no—
54C42×C13—42no—
55C22⋊Dic13—42no—
56C4⋊Dic13—42no—
57#6101—44no—
58#6101—42no—
59#6101—42no—
60C4×Dic13—22no—
61C4×Dic13—24no—
62C4×Dic13—42no—
63C4×Dic13#4114yes—
64#2285—131no—
65#1797—132no—
66#1296—134no—
67C23×C13—21no—
68C23×C13—21no—
69C23×C13—22no—
70C23×C13—22no—
71C23×C13#10012yes—
72C23×C13C2×C22⋊C411yescharacteristic
73C2×C4×C13—28no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13#10112yes—
82C2×C4×C13#11712yes—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—44no—
87C2×Dic13—44no—
88C2×Dic13—42no—
89C2×Dic13—42no—
90C2×Dic13—42no—
91C2×Dic13#12314yes—
92C2×Dic13#13514yes—
93C2×Dic13AGL(1,ℤ/8)12yes—
94C2×Dic13#13712yes—
95#1057—84no—
96C2×#117—131no—
97C2×#117#26111yescharacteristic
98C22×C42—131no—
99C2×C4⋊C8—134no—
100C2×C22⋊C8—262no—
101#384—132no—
102#382—132no—
103#380—262no—
104C4×C4⋊C4—262no—
105#336—262no—
106C22×C13—24no—
107C22×C13—22no—
108C22×C13—41no—
109C22×C13—41no—
110C22×C13—42no—
111C22×C13#38111yescharacteristic
112C22×C13C2×#10011yescharacteristic
113C22×C13C2×#10111yescharacteristic
114C22×C13#41612yes—
115C22×C13#41712yes—
116C4×C13—22no—
117C4×C13—22no—
118C4×C13—82no—
119Dic13—42no—
120Dic13—82no—
121Dic13#48214yes—
122Dic13#48514yes—
123C23×C4—132no—
124C23×C4C2×#26111yescharacteristic
125C22×C8—264no—
126#117—42no—
127#117—522no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—262no—
130C2×C4⋊C4—262no—
131C2×C4⋊C4C2×#26112yes—
132C2×C22⋊C4—21no—
133C2×C22⋊C4—261no—
134C2×C42—21no—
135C2×C42—131no—
136C2×C42—132no—
137C2×C42—131no—
138C2×C42—264no—
139C2×C42—261no—
140C4⋊C8—268no—
141C22⋊C8—524no—
142#95—264no—
143C2×C13—42no—
144C2×C13#154411yescharacteristic
145C2×C13#155112yes—
146C2×C13#156111yescharacteristic
147C2×C13#182111yescharacteristic
148C2×C13#182512yes—
149C24C22⋊#26111yescharacteristic
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—132no—
155C22×C4—132no—
156C22×C4—262no—
157C22×C4—264no—
158C22×C4—262no—
159C22×C4—264no—
160C22×C4—262no—
161C22×C4C22⋊#26111yescharacteristic
162C22×C4C22×#26111yescharacteristic
163C2×C8—524no—
164C2×C8—524no—
165C2×C8—524no—
166C4⋊C4—42no—
167C4⋊C4—522no—
168C4⋊C4—522no—
169C4⋊C4—522no—
170C4⋊C4—524no—
171C22⋊C4—42no—
172C22⋊C4—522no—
173C42—42no—
174C42—134no—
175C42—264no—
176C42—262no—
177C42—522no—
178C13#872911yescharacteristic, complemented, Sylow
179C23—21no—
180C23—21no—
181C23—22no—
182C23—22no—
183C23#8812112yes—
184C23C2×C22⋊#26111yescharacteristic
185C2×C4—28no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—134no—
194C2×C4—132no—
195C2×C4—132no—
196C2×C4—134no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—524no—
201C2×C4—524no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4#8811312yes—
206C2×C4#8823712yes—
207C8—1044no—
208C22—24no—
209C22—22no—
210C22—41no—
211C22—41no—
212C22—42no—
213C22C2×#8811311yescharacteristic
214C22#1171913511yescharacteristic
215C22#1171916412yes—
216C22#1171916512yes—
217C22C2×#8812111yescharacteristic
218C4—22no—
219C4—22no—
220C4—82no—
221C4—134no—
222C4—134no—
223C4—522no—
224C4—1042no—
225C2—42no—
226C2#1313034111yescharacteristic
227C2#1313035512yes—
228C2#1313037511yescharacteristic
229C2#1313073511yescharacteristic
230C2#1313074112yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8729
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129714C2semidirect
178. C13#8729semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131297142
#131172392
#872913