Finite Group Databasebeta

← #15772588

Subgroups — #15772588

Order 3328.

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

normal subgroups only

This group has 374 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#13112782C214yesmaximal
4C13×#2567C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C13×#395—21no—
8C13×#395—21no—
9C13×#391C412yes—
10C13×#389—21no—
11C13×#389—21no—
12C13×#384C2212yes—
13C4×C13×C4⋊C4C411yescharacteristic
14#11718587—21no—
15#11718586—21no—
16#11718120—21no—
17#11718120—21no—
18#11718120C2212yes—
19#11718120C2212yes—
20C22×Q8×C13—21no—
21C22×Q8×C13C2×C411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C42×C13C2×C412yes—
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C13×#95—21no—
39C13×#95—22no—
40C13×#95—22no—
41C22⋊#1055—22no—
42C22⋊#1055—22no—
43C4⋊#1055—41no—
44C4⋊#1055—41no—
45#88043—41no—
46C4×#1055—41no—
47#11574—131nomaximal, Sylow
48C2×Q8×C13—22no—
49C2×Q8×C13—22no—
50C2×Q8×C13—41no—
51C2×Q8×C13—42no—
52C2×Q8×C13—82no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C13×C4⋊C4—24no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—82no—
70C13×C4⋊C4—82no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—24no—
78C2×#1055—42no—
79C2×#1055—42no—
80#2567D1311yescharacteristic
81#1467—131no—
82#1461—131no—
83#1325—134no—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—44no—
86Q8×C13—84no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—24no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13#9911yescharacteristic
108C2×C4×C13#9911yescharacteristic
109C2×C4×C13#10112yes—
110C2×C4×C13#13112yes—
111#1055—82no—
112#1055—82no—
113C2×C4⋊Q8Dic1311yescharacteristic
114C2×C4×Q8C2×D1311yescharacteristic
115#432—261no—
116#431—261no—
117#395—21no—
118#395—21no—
119#391Dic1312yes—
120#389—21no—
121#389—21no—
122#384C2×D1312yes—
123C4×C4⋊C4Dic1311yescharacteristic
124#324—132no—
125#324—132no—
126#324—261no—
127#324—261no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13#40811yescharacteristic
131C22×C13C2×#9911yescharacteristic
132C22×C13C2×#10111yescharacteristic
133C4×C13—21no—
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—44no—
137C4×C13—41no—
138C4×C13—41no—
139C4×C13—41no—
140C4×C13—41no—
141C4×C13—82no—
142C4×C13#35612yes—
143C22×Q8—21no—
144C22×Q8C2×Dic1311yescharacteristic
145C4⋊Q8—41no—
146C4⋊Q8—41no—
147C4×Q8—41no—
148C4×Q8—41no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4C2×Dic1312yes—
154C2×C4⋊C4C22⋊D1311yescharacteristic
155C2×C4⋊C4C22⋊D1311yescharacteristic
156C2×C4⋊C4C22×D1311yescharacteristic
157C2×C42C2×Dic1312yes—
158C2×C42C2×Dic1311yescharacteristic
159C2×C42C22⋊D1311yescharacteristic
160C2×C42C22⋊D1311yescharacteristic
161C4⋊C8—521no—
162C4⋊C8—521no—
163C22⋊C8—262no—
164C22⋊C8—262no—
165#97—521no—
166C4×C8—521no—
167#95—21no—
168#95—22no—
169#95—22no—
170C2×C13—21no—
171C2×C13—21no—
172C2×C13#147211yescharacteristic
173C2×C13#212811yescharacteristic
174C2×C13C2×#35611yescharacteristic
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—41no—
178C2×Q8—42no—
179C2×Q8—82no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C22⋊Dic1311yescharacteristic
183C22×C4C22⋊Dic1311yescharacteristic
184C22×C4C22⋊Dic1311yescharacteristic
185C22×C4C22⋊Dic1311yescharacteristic
186C22×C4C22×Dic1311yescharacteristic
187C22×C4C2×C22⋊D1311yescharacteristic
188C22×C4C2×C22⋊D1311yescharacteristic
189C2×C8—522no—
190C2×C8—522no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—82no—
199C4⋊C4—82no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—24no—
207C13#1157411yescharacteristic, complemented, Sylow
208C23C2×C22⋊Dic1311yescharacteristic
209Q8—44no—
210Q8—84no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4#8807411yescharacteristic
232C2×C4#8807411yescharacteristic
233C2×C4#8807612yes—
234C2×C4#8820212yes—
235C8—1042no—
236C8—1042no—
237C22—21no—
238C22—21no—
239C22C2×#8807411yescharacteristic
240C22C2×#8807611yescharacteristic
241C22#1171889511yescharacteristic
242C4—21no—
243C4—22no—
244C4—22no—
245C4—44no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4#1171814012yes—
252C2—21no—
253C2—21no—
254C2#1311320011yescharacteristic
255C2#1311650811yescharacteristic
256C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2567C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2567D13
hypocenterC13#11574
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
207. C13#11574semidirect

Maximal subgroups

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

subgroupindex
#131131802
#131131602
#131127822
C13×#25672
#1157413