Finite Group Databasebeta

← #15772209

Subgroups — #15772209

Order 3328.

440 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 119 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#13113160C212yesmaximal, complemented
2#13112782C212yesmaximal, complemented
3#13112768C212yesmaximal
4C13×#2326C211yesmaximal, characteristic
5C2×C13×#124C411yescharacteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D4×C13C411yescharacteristic
8C13×#391C411yescharacteristic
9C13×#390C2211yescharacteristic
10C13×#388—22no—
11C13×#385—22no—
12C13×#384C2211yescharacteristic
13C13×#376C411yescharacteristic
14#11718586—22no—
15#11718120—22no—
16#11718120C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C23×C4×C13—21no—
20C13×#124—22no—
21C13×#124C814yescomplemented
22C4×Q8×C13—42no—
23C4×D4×C13—42no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4D412yes—
27C2×C13×C4⋊C4C2311yescharacteristic
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—21no—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13D412yes—
35C13×#95—21no—
36C13×#95—22no—
37C13×#95—21no—
38C22⋊#1055—24no—
39C4⋊#1055—42no—
40C4×#1055—42no—
41#11480—131nomaximal, Sylow
42C24×C13—21no—
43C2×Q8×C13—41no—
44C2×Q8×C13—41no—
45C2×Q8×C13C2×C812yes—
46C2×Q8×C13M1612yes—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13C2×C812yes—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—42no—
55C22×C4×C13—82no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D412yes—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—82no—
65C13×C22⋊C4—28no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—82no—
68C42×C13—22no—
69C42×C13—22no—
70C42×C13—22no—
71C42×C13—21no—
72C42×C13—41no—
73C42×C13C2×C812yes—
74C2×#1055—44no—
75#2326D1311yescharacteristic
76#1461—132no—
77#1325—132no—
78#1318—132no—
79C23×C13—22no—
80C23×C13—42no—
81C23×C13—42no—
82C23×C13—41no—
83C23×C13—41no—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—42no—
86Q8×C13—42no—
87D4×C13—42no—
88D4×C13—42no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—84no—
107C2×C4×C13C22⋊C814yes—
108C2×C4×C13#9912yes—
109C2×C4×C13C22×C811yescharacteristic
110C2×C4×C13C2×M1611yescharacteristic
111#1055—84no—
112C2×#124Dic1311yescharacteristic
113C2×C4×Q8C2×D1311yescharacteristic
114C2×C4×D4Dic1311yescharacteristic
115#431—262no—
116#391Dic1311yescharacteristic
117#390C2×D1311yescharacteristic
118#388—22no—
119#385—22no—
120#384C2×D1311yescharacteristic
121#376Dic1311yescharacteristic
122#324—134no—
123#324—262no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13—44no—
127C22×C13—42no—
128C22×C13—82no—
129C22×C13—81no—
130C22×C13—81no—
131C22×C13C2×C22⋊C811yescharacteristic
132C22×C13C2×#9911yescharacteristic
133C22×C13#41311yescharacteristic
134C4×C13—22no—
135C4×C13—24no—
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13—41no—
141C4×C13—81no—
142C4×C13—81no—
143C22×Q8C2×Dic1311yescharacteristic
144C22×D4C2×Dic1311yescharacteristic
145C23×C4—21no—
146#124—22no—
147#124#105514yescomplemented
148C4×Q8—42no—
149C4×D4—42no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4C2×Dic1311yescharacteristic
152C2×C4⋊C4C22⋊D1312yes—
153C2×C4⋊C4C22×D1311yescharacteristic
154C2×C22⋊C4—22no—
155C2×C22⋊C4—21no—
156C2×C22⋊C4—22no—
157C2×C42C2×Dic1311yescharacteristic
158C2×C42C2×Dic1311yescharacteristic
159C2×C42C2×Dic1311yescharacteristic
160C2×C42C22⋊D1312yes—
161C4⋊C8—522no—
162C22⋊C8—264no—
163C4×C8—522no—
164#95—21no—
165#95—22no—
166#95—21no—
167C2×C13—21no—
168C2×C13—21no—
169C2×C13—82no—
170C2×C13#145911yescharacteristic
171C2×C13#212811yescharacteristic
172C2×C13#213311yescharacteristic
173C24—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8C2×#105512yes—
177C2×Q8#609912yes—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4C2×#105512yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—42no—
186C22×C4—82no—
187C22×C4C22⋊Dic1312yes—
188C22×C4C22⋊Dic1311yescharacteristic
189C22×C4C22⋊Dic1311yescharacteristic
190C22×C4C22×Dic1311yescharacteristic
191C22×C4C2×C22⋊D1312yes—
192C2×C8—524no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—82no—
197C22⋊C4—28no—
198C22⋊C4—42no—
199C22⋊C4—82no—
200C42—22no—
201C42—22no—
202C42—22no—
203C42—21no—
204C42—41no—
205C42C2×#105512yes—
206C13#1148011yescharacteristic, complemented, Sylow
207C23—22no—
208C23—42no—
209C23—42no—
210C23—41no—
211C23—41no—
212C23C2×C22⋊Dic1311yescharacteristic
213Q8—42no—
214Q8—42no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—84no—
235C2×C4C22⋊#105514yes—
236C2×C4#8807412yes—
237C2×C4C22×#105511yescharacteristic
238C2×C4C2×#609911yescharacteristic
239C8—1044no—
240C22—21no—
241C22—21no—
242C22—44no—
243C22—42no—
244C22—82no—
245C22—81no—
246C22—81no—
247C22C2×C22⋊#105511yescharacteristic
248C22C2×#8807411yescharacteristic
249C22#1171889811yescharacteristic
250C4—24no—
251C4—21no—
252C4—21no—
253C4—22no—
254C4—42no—
255C4—42no—
256C4—41no—
257C4—81no—
258C4—81no—
259C2—21no—
260C2—21no—
261C2—82no—
262C2#1311315411yescharacteristic
263C2#1311650811yescharacteristic
264C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2326C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2326D13
hypocenterC13#11480
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2326

Complements

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

NH ≅ G/Ntype
1. #13113160C2semidirect
2. #13112782C2semidirect
21. C13×#124C8semidirect
147. #124#1055semidirect
206. C13#11480semidirect

Maximal subgroups

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

subgroupindex
#131131602
#131127822
#131127682
C13×#23262
#1148013