Finite Group Databasebeta

← #15760604

Subgroups — #15760604

Order 3328.

468 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123921C211yesmaximal, characteristic
2#13113562C212yesmaximal
3#13113180C211yesmaximal, characteristic
4#13112692C212yesmaximal
5C13×#2546C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C412yes—
7C2×C13×C4⋊Q8C2211yescharacteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C13×#398—21no—
10C13×#398—21no—
11C13×#391C412yes—
12C13×#389—21no—
13C13×#389—21no—
14C4×C13×C4⋊C4C2211yescharacteristic
15#11718685—24no—
16#11718587—21no—
17#11718587C2212yes—
18#11718587C2212yes—
19#11718586—21no—
20#11718138—24no—
21#11718120—21no—
22#11718120—21no—
23C22×Q8×C13C2×C412yes—
24C22×Q8×C13C2×C411yescharacteristic
25C13×C4⋊Q8—22no—
26C13×C4⋊Q8—22no—
27C13×C4⋊Q8—44no—
28C4×Q8×C13—22no—
29C4×Q8×C13—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C42×C13C2×C412yes—
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C42×C13C2311yescharacteristic
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—21no—
45C22⋊#1055—22no—
46C22⋊#1055—22no—
47C4⋊#1055—22no—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50C4⋊#1055D414yes—
51#88043—22no—
52#88043—22no—
53#88043—22no—
54C4×#1055—22no—
55#9452—131nomaximal, Sylow
56C2×Q8×C13—22no—
57C2×Q8×C13—22no—
58C2×Q8×C13—24no—
59C2×Q8×C13—41no—
60C2×Q8×C13—42no—
61C2×Q8×C13—42no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C13×C4⋊C4—24no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—44no—
76C13×C4⋊C4—44no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—41no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—42no—
85C42×C13C2×D412yes—
86C42×C13#4112yes—
87C2×#1055—24no—
88C2×#1055—42no—
89#2983—131no—
90#2546D1311yescharacteristic
91#1558—132no—
92#1467—131no—
93#1285—132no—
94C23×C13C2×C22⋊C411yescharacteristic
95Q8×C13—44no—
96Q8×C13—84no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—24no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13#10012yes—
117C2×C4×C13C4×D412yes—
118C2×C4×C13#12011yescharacteristic
119C2×C4×C13#12112yes—
120C2×C4×C13#12311yescharacteristic
121#1055—44no—
122#1055—82no—
123C2×C4⋊Q8Dic1312yes—
124C2×C4⋊Q8C2×D1311yescharacteristic
125C2×C4×Q8C2×D1311yescharacteristic
126#446—264no—
127#432—132no—
128#432—132no—
129#432—261no—
130#431—261no—
131#398—21no—
132#398—21no—
133#391Dic1312yes—
134#389—21no—
135#389—21no—
136C4×C4⋊C4C2×D1311yescharacteristic
137#333—264no—
138#324—261no—
139#324—261no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13#38611yescharacteristic
143C22×C13C2×#10011yescharacteristic
144C22×C13#41311yescharacteristic
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—22no—
148C4×C13—22no—
149C4×C13—44no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13—41no—
153C4×C13—82no—
154C4×C13#45612yes—
155C22×Q8C2×Dic1312yes—
156C22×Q8C2×Dic1311yescharacteristic
157C4⋊Q8—22no—
158C4⋊Q8—22no—
159C4⋊Q8—44no—
160C4×Q8—22no—
161C4×Q8—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4C2×Dic1311yescharacteristic
168C2×C4⋊C4C22⋊D1311yescharacteristic
169C2×C4⋊C4C22⋊D1311yescharacteristic
170C2×C42C2×Dic1312yes—
171C2×C42C22⋊D1311yescharacteristic
172C2×C42C22⋊D1311yescharacteristic
173C2×C42C22×D1311yescharacteristic
174C4⋊C8—134no—
175C4⋊C8—262no—
176C4⋊C8—262no—
177C4⋊C8—262no—
178C22⋊C8—262no—
179C22⋊C8—262no—
180#97—262no—
181#97—262no—
182#97—262no—
183C4×C8—262no—
184#95—22no—
185#95—22no—
186#95—21no—
187C2×C13—21no—
188C2×C13—21no—
189C2×C13#188611yescharacteristic
190C2×C13#190011yescharacteristic
191C2×C13#190911yescharacteristic
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—24no—
195C2×Q8—41no—
196C2×Q8—42no—
197C2×Q8—42no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4C22⋊Dic1311yescharacteristic
201C22×C4C22⋊Dic1311yescharacteristic
202C22×C4C22⋊Dic1311yescharacteristic
203C22×C4C22⋊Dic1311yescharacteristic
204C22×C4C22×Dic1311yescharacteristic
205C22×C4C2×C22⋊D1311yescharacteristic
206C22×C4C2×C22⋊D1311yescharacteristic
207C2×C8—264no—
208C2×C8—522no—
209C4⋊C4—24no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—44no—
214C4⋊C4—44no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—42no—
223C42D4×D1312yes—
224C42#612912yes—
225C13#945211yescharacteristic, complemented, Sylow
226C23C2×C22⋊Dic1311yescharacteristic
227Q8—44no—
228Q8—84no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4#8807312yes—
249C2×C4D4×Dic1312yes—
250C2×C4#8818911yescharacteristic
251C2×C4#8819111yescharacteristic
252C2×C4#8819312yes—
253C8—524no—
254C8—1042no—
255C22—21no—
256C22—21no—
257C22C2×#8807311yescharacteristic
258C22#1171888111yescharacteristic
259C22#1171889811yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4#1171875612yes—
270C2—21no—
271C2—21no—
272C2#1311523011yescharacteristic
273C2#1311530011yescharacteristic
274C2#1311535911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2546C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2546D13
hypocenterC13#9452
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
225. C13#9452semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131135622
#131131802
#131126922
C13×#25462
#945213