Finite Group Databasebeta

← #16787531

Subgroups — #16787531

Order 3328.

366 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 92 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#13131194C211yesmaximal, characteristic
2#13130393C211yesmaximal, characteristic
3#13129793C214yesmaximal, complemented
4C2×#11718534C211yesmaximal, characteristic
5C22×Dic52C411yescharacteristic
6C2×#88141—21no—
7#11719129—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#11718257C2212yes—
18#11718256—21no—
19#11718254C2212yes—
20C22×Dic26—21no—
21C2×#6122—41no—
22C22×C8×C13C2×C411yescharacteristic
23C2×C13×C4⋊C4—21no—
24C2×#6101—41no—
25C2×C4×Dic13—41no—
26C2×C4×Dic13D411yescharacteristic
27C22×#1055D411yescharacteristic
28C2×Dic52—21no—
29C2×Dic52—24no—
30C2×Dic52C2×C412yes—
31#88141—22no—
32#88141—22no—
33#88141—41no—
34#88141—41no—
35#88112—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#11658—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—
56#6122—82no—
57C2×#1057—42no—
58C2×C8×C13—22no—
59C2×C8×C13C22⋊C411yescharacteristic
60C2×C8×C13C22×C411yescharacteristic
61C13×C4⋊C4—22no—
62C13×C4⋊C4—41no—
63#6101—42no—
64#6101—42no—
65C4×Dic13—42no—
66C4×Dic13—42no—
67C4×Dic13C22⋊C411yescharacteristic
68C4×Dic13D811yescharacteristic
69C4×Dic13SD1611yescharacteristic
70C4×Dic13C2×D411yescharacteristic
71C2×#1055—41no—
72C2×#1055C22⋊C411yescharacteristic
73C2×#1055C2×D411yescharacteristic
74Dic52—24no—
75Dic52—22no—
76Dic52M1614yescomplemented
77#6092—42no—
78C2×C4×Q16—131no—
79#2162—131no—
80#1567—131no—
81#1332—134no—
82C23×C13#10211yescharacteristic
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—42no—
86C2×C4×C13—82no—
87C2×C4×C13#10211yescharacteristic
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×Dic13—41no—
90C2×Dic13—44no—
91C2×Dic13—42no—
92C2×Dic13#10211yescharacteristic
93C2×Dic13#10211yescharacteristic
94C2×Dic13SD3212yes—
95C2×Dic13Q3212yes—
96C2×Dic13C2×D811yescharacteristic
97C2×Dic13C2×SD1611yescharacteristic
98Dic26—24no—
99Dic26—44no—
100Dic26—42no—
101#1057—82no—
102C8×C13—21no—
103C8×C13C2×M1612yes—
104#1055—21no—
105#1055—21no—
106C22×Q16—131no—
107C2×C4×Q8—261no—
108C4×Q16—132no—
109C4×Q16—132no—
110C4×Q16—261no—
111C4×Q16—261no—
112C2×#107#26111yescharacteristic
113#423—261no—
114C2×#103—261no—
115C2×C4×C8—131no—
116C4⋊C16—261no—
117C22⋊C16—261no—
118C4×C16—132no—
119#335—132no—
120#335—261no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#35812yes—
124C22×C13C2×#10211yescharacteristic
125C4×C13—21no—
126C4×C13—82no—
127C4×C13#40711yescharacteristic
128C4×C13#42111yescharacteristic
129Dic13—21no—
130Dic13—21no—
131Dic13—44no—
132Dic13#35812yes—
133Dic13C2×SD3211yescharacteristic
134Dic13C2×Q3211yescharacteristic
135C22×Q8—261no—
136C2×Q16—132no—
137C2×Q16—264no—
138C2×Q16—261no—
139C2×M16—521no—
140C22×C8—131no—
141C22×C8C2×#26111yescharacteristic
142C4×Q8—262no—
143C4×Q8—262no—
144C4×Q8—521no—
145C4×Q8—521no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—521no—
148C2×C42—131no—
149C2×C42—521no—
150C2×C16—262no—
151#107—21no—
152#107C2×#26112yes—
153C4⋊C8—262no—
154C4⋊C8—521no—
155#103—262no—
156#103—262no—
157C4×C8—131no—
158C4×C8—131no—
159C4×C8—131no—
160C4×C8—131no—
161C2×C13—22no—
162C2×C13#148611yescharacteristic
163C2×C13C2×#35811yescharacteristic
164C2×C13#214311yescharacteristic
165C2×Q8—264no—
166C2×Q8—262no—
167C2×Q8—522no—
168C2×Q8—521no—
169C22×C4—41no—
170C22×C4—131no—
171C22×C4—131no—
172C22×C4—521no—
173C22×C4C22⋊#26111yescharacteristic
174Q16—134no—
175Q16—264no—
176Q16—262no—
177M16—1042no—
178C2×C8—22no—
179C2×C8—131no—
180C2×C8—131no—
181C2×C8—521no—
182C2×C8—522no—
183C2×C8C22⋊#26111yescharacteristic
184C2×C8C22×#26111yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—522no—
188C4⋊C4—522no—
189C42—131no—
190C42—131no—
191C42—131no—
192C42—131no—
193C42—522no—
194C42—522no—
195C16—522no—
196C13#1165811yescharacteristic, complemented, Sylow
197C23#8811511yescharacteristic
198Q8—264no—
199Q8—524no—
200Q8—522no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—82no—
205C2×C4—132no—
206C2×C4—132no—
207C2×C4—131no—
208C2×C4—131no—
209C2×C4—131no—
210C2×C4—131no—
211C2×C4—521no—
212C2×C4—524no—
213C2×C4—522no—
214C2×C4#8811511yescharacteristic
215C2×C4C2×C22⋊#26111yescharacteristic
216C8—21no—
217C8—261no—
218C8—261no—
219C8—1042no—
220C8D13⋊M1612yes—
221C22—21no—
222C22—21no—
223C22#1171828012yes—
224C22C2×#8811511yescharacteristic
225C4—21no—
226C4—82no—
227C4—132no—
228C4—131no—
229C4—131no—
230C4—261no—
231C4—261no—
232C4—524no—
233C4#1171912611yescharacteristic
234C4#1171915511yescharacteristic
235C2—22no—
236C2#1313016311yescharacteristic
237C2C2×#1171828011yescharacteristic
238C2#1313115111yescharacteristic
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#11658
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. #13129793C2semidirect
76. Dic52M16semidirect
196. C13#11658semidirect

Maximal subgroups

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

subgroupindex
#131311942
#131303932
#131297932
C2×#117185342
#1165813