Finite Group Databasebeta

← #15772562

Subgroups — #15772562

Order 3328.

394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 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#13113180C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112770C214yesmaximal
4C13×#2546C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C13×C4⋊Q8C412yes—
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#398—21no—
9C13×#398—21no—
10C13×#391C2212yes—
11C13×#389—21no—
12C13×#389—21no—
13C4×C13×C4⋊C4C411yescharacteristic
14#11718587—21no—
15#11718586—21no—
16#11718120—21no—
17#11718120—21no—
18#11718120C2212yes—
19#11718120C2212yes—
20C22×Q8×C13C2×C412yes—
21C22×Q8×C13C2×C411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C13×C4⋊Q8—44no—
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13C2×C412yes—
37C2×C42×C13D411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—22no—
42C22⋊#1055—22no—
43C22⋊#1055—22no—
44C4⋊#1055—41no—
45C4⋊#1055—41no—
46#88043—41no—
47C4×#1055—41no—
48#11568—131nomaximal, Sylow
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—24no—
52C2×Q8×C13—41no—
53C2×Q8×C13—42no—
54C2×Q8×C13—42no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C13×C4⋊C4—24no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—44no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—44no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—42no—
80C2×#1055—42no—
81C2×#1055—42no—
82#2546D1311yescharacteristic
83#1467—131no—
84#1461—131no—
85#1319—134no—
86C23×C13C2×C22⋊C411yescharacteristic
87Q8×C13—44no—
88Q8×C13—84no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—24no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13#9911yescharacteristic
110C2×C4×C13#9911yescharacteristic
111C2×C4×C13#10012yes—
112C2×C4×C13#13112yes—
113#1055—82no—
114#1055—82no—
115C2×C4⋊Q8Dic1311yescharacteristic
116C2×C4⋊Q8Dic1312yes—
117C2×C4×Q8C2×D1311yescharacteristic
118#432—261no—
119#431—261no—
120#398—21no—
121#398—21no—
122#391C2×D1312yes—
123#389—21no—
124#389—21no—
125C4×C4⋊C4Dic1311yescharacteristic
126#324—132no—
127#324—132no—
128#324—261no—
129#324—261no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13#40811yescharacteristic
133C22×C13C2×#9911yescharacteristic
134C22×C13C2×#10011yescharacteristic
135C4×C13—21no—
136C4×C13—22no—
137C4×C13—22no—
138C4×C13—44no—
139C4×C13—41no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13—82no—
144C4×C13#35612yes—
145C22×Q8C2×Dic1312yes—
146C22×Q8C2×Dic1311yescharacteristic
147C4⋊Q8—41no—
148C4⋊Q8—41no—
149C4⋊Q8—44no—
150C4×Q8—41no—
151C4×Q8—41no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C22⋊D1311yescharacteristic
158C2×C4⋊C4C22⋊D1311yescharacteristic
159C2×C4⋊C4C22×D1311yescharacteristic
160C2×C42C2×Dic1311yescharacteristic
161C2×C42C2×Dic1312yes—
162C2×C42C22⋊D1311yescharacteristic
163C2×C42C22⋊D1311yescharacteristic
164C4⋊C8—521no—
165C4⋊C8—521no—
166C22⋊C8—262no—
167C22⋊C8—262no—
168#97—521no—
169C4×C8—521no—
170#95—21no—
171#95—22no—
172#95—22no—
173C2×C13—21no—
174C2×C13—21no—
175C2×C13#147111yescharacteristic
176C2×C13#212911yescharacteristic
177C2×C13C2×#35611yescharacteristic
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—24no—
181C2×Q8—41no—
182C2×Q8—42no—
183C2×Q8—42no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C22⋊Dic1311yescharacteristic
187C22×C4C22⋊Dic1311yescharacteristic
188C22×C4C22⋊Dic1311yescharacteristic
189C22×C4C22⋊Dic1311yescharacteristic
190C22×C4C22×Dic1311yescharacteristic
191C22×C4C2×C22⋊D1311yescharacteristic
192C22×C4C2×C22⋊D1311yescharacteristic
193C2×C8—522no—
194C2×C8—522no—
195C4⋊C4—24no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—44no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—42no—
211C13#1156811yescharacteristic, complemented, Sylow
212C23C2×C22⋊Dic1311yescharacteristic
213Q8—44no—
214Q8—84no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4#8807312yes—
236C2×C4#8807411yescharacteristic
237C2×C4#8807411yescharacteristic
238C2×C4#8820212yes—
239C8—1042no—
240C8—1042no—
241C22—21no—
242C22—21no—
243C22C2×#8807311yescharacteristic
244C22C2×#8807411yescharacteristic
245C22#1171889511yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—44no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—82no—
255C4#1171814012yes—
256C2—21no—
257C2—21no—
258C2#1311319611yescharacteristic
259C2#1311651111yescharacteristic
260C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2546C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2546D13
hypocenterC13#11568
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
211. C13#11568semidirect

Maximal subgroups

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

subgroupindex
#131131802
#131131602
#131127702
C13×#25462
#1156813