Finite Group Databasebeta

← #16787565

Subgroups — #16787565

Order 3328.

354 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 84 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#13131198C211yesmaximal, characteristic
2#13130396C211yesmaximal, characteristic
3#13129797C214yesmaximal, complemented
4C2×#11718534C211yesmaximal, characteristic
5C22×Dic52C411yescharacteristic
6C2×#88141—21no—
7#11719130—21no—
8C2×C13×#107C411yescharacteristic
9C2×C8×Dic13C2211yescharacteristic
10C2×#88050—21no—
11#11718534—21no—
12#11718534—21no—
13#11718534C412yes—
14#11718534C2212yes—
15C22⋊#6092—21no—
16#11718260—21no—
17#11718258C2212yes—
18#11718256—21no—
19#11718253C2212yes—
20C22×Dic26—21no—
21C22×C8×C13C2×C411yescharacteristic
22C2×C13×C4⋊C4—21no—
23C2×#6101—41no—
24C2×C4×Dic13—41no—
25C2×C4×Dic13D411yescharacteristic
26C22×#1055D411yescharacteristic
27C2×Dic52—21no—
28C2×Dic52—24no—
29C2×Dic52C2×C412yes—
30#88141—22no—
31#88141—22no—
32#88141—41no—
33#88141—41no—
34C22⋊#1057—41no—
35#88110—41no—
36C4⋊#1057—22no—
37C2×#6092—22no—
38C13×#107—21no—
39C13×#107C2×C412yes—
40C8×Dic13C2×C411yescharacteristic
41C8×Dic13D411yescharacteristic
42C8×Dic13D411yescharacteristic
43C8×Dic13C2311yescharacteristic
44#88050—22no—
45#88050—22no—
46#11668—131nomaximal, Sylow
47C22×C4×C13—41no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×Dic13—41no—
50C22×Dic13D811yescharacteristic
51C22×Dic13SD1611yescharacteristic
52C2×Dic26—24no—
53C2×Dic26—22no—
54C2×Dic26—42no—
55C2×Dic26—41no—
56C2×#1057—42no—
57C2×C8×C13—22no—
58C2×C8×C13C22⋊C411yescharacteristic
59C2×C8×C13C22×C411yescharacteristic
60C13×C4⋊C4—22no—
61C13×C4⋊C4—41no—
62#6101—42no—
63#6101—42no—
64C4×Dic13—42no—
65C4×Dic13—42no—
66C4×Dic13C22⋊C411yescharacteristic
67C4×Dic13D811yescharacteristic
68C4×Dic13SD1611yescharacteristic
69C4×Dic13C2×D411yescharacteristic
70C2×#1055—41no—
71C2×#1055C22⋊C411yescharacteristic
72C2×#1055C2×D411yescharacteristic
73Dic52—24no—
74Dic52—22no—
75Dic52M1614yes—
76#6092—42no—
77C2×C4×Q16—131no—
78#2163—131no—
79#1568—131no—
80#1334—134no—
81C23×C13#10211yescharacteristic
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—42no—
85C2×C4×C13—82no—
86C2×C4×C13#10211yescharacteristic
87C2×C4×C13C2×C22⋊C411yescharacteristic
88C2×Dic13—22no—
89C2×Dic13—41no—
90C2×Dic13—44no—
91C2×Dic13—42no—
92C2×Dic13#10211yescharacteristic
93C2×Dic13#10211yescharacteristic
94C2×Dic13C2×D811yescharacteristic
95C2×Dic13C2×SD1611yescharacteristic
96Dic26—24no—
97Dic26—44no—
98Dic26—42no—
99#1057—82no—
100C8×C13—21no—
101C8×C13C2×M1612yes—
102#1055—21no—
103#1055—21no—
104C22×Q16—131no—
105C2×C4×Q8—261no—
106C4×Q16—132no—
107C4×Q16—132no—
108C4×Q16—261no—
109C4×Q16—261no—
110#432—261no—
111C2×#107#26111yescharacteristic
112C2×#103—261no—
113C2×C4×C8—131no—
114C4⋊C16—261no—
115C22⋊C16—261no—
116#346—132no—
117#335—261no—
118#334—132no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13#36212yes—
122C22×C13C2×#10211yescharacteristic
123C4×C13—21no—
124C4×C13—82no—
125C4×C13#40711yescharacteristic
126C4×C13#42111yescharacteristic
127Dic13—21no—
128Dic13—21no—
129Dic13—21no—
130Dic13—21no—
131Dic13—44no—
132C22×Q8—261no—
133C2×Q16—132no—
134C2×Q16—264no—
135C2×Q16—261no—
136C22×C8—131no—
137C22×C8C2×#26111yescharacteristic
138C4×Q8—262no—
139C4×Q8—262no—
140C4×Q8—521no—
141C4×Q8—521no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—521no—
144C2×C42—131no—
145C2×C42—521no—
146C2×C16—262no—
147#107—21no—
148#107C2×#26112yes—
149C4⋊C8—262no—
150#103—262no—
151#103—262no—
152C22⋊C8—521no—
153#97—521no—
154C4×C8—131no—
155C4×C8—131no—
156C4×C8—131no—
157C4×C8—131no—
158C2×C13—22no—
159C2×C13#148611yescharacteristic
160C2×C13#214511yescharacteristic
161C2×C13C2×#36211yescharacteristic
162C2×Q8—264no—
163C2×Q8—262no—
164C2×Q8—522no—
165C2×Q8—521no—
166C22×C4—41no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—521no—
170C22×C4C22⋊#26111yescharacteristic
171Q16—134no—
172Q16—264no—
173Q16—262no—
174C2×C8—22no—
175C2×C8—131no—
176C2×C8—131no—
177C2×C8—521no—
178C2×C8—522no—
179C2×C8C22⋊#26111yescharacteristic
180C2×C8C22×#26111yescharacteristic
181C4⋊C4—22no—
182C4⋊C4—41no—
183C4⋊C4—522no—
184C4⋊C4—522no—
185C42—131no—
186C42—131no—
187C42—131no—
188C42—131no—
189C42—522no—
190C42—522no—
191C16—522no—
192C13#1166811yescharacteristic, complemented, Sylow
193C23#8811511yescharacteristic
194Q8—264no—
195Q8—524no—
196Q8—522no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—82no—
201C2×C4—131no—
202C2×C4—131no—
203C2×C4—131no—
204C2×C4—131no—
205C2×C4—262no—
206C2×C4—521no—
207C2×C4—524no—
208C2×C4—522no—
209C2×C4#8811511yescharacteristic
210C2×C4C2×C22⋊#26111yescharacteristic
211C8—21no—
212C8—261no—
213C8—261no—
214C8—1042no—
215C8D13⋊M1612yes—
216C22—21no—
217C22—21no—
218C22#1171828212yes—
219C22C2×#8811511yescharacteristic
220C4—21no—
221C4—82no—
222C4—261no—
223C4—261no—
224C4—261no—
225C4—261no—
226C4—524no—
227C4#1171912611yescharacteristic
228C4#1171915511yescharacteristic
229C2—22no—
230C2#1313016311yescharacteristic
231C2#1313115711yescharacteristic
232C2C2×#1171828211yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC2×C13×#107C4
socleC22×C13C2×#102
prime radicalC23×C13#102
cosocleC8×Dic13C23
hypercenterC2×#107#261
hypocenterC13#11668
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #13129797C2semidirect
192. C13#11668semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131303962
#131297972
C2×#117185342
#1166813