Finite Group Databasebeta

← #15760614

Subgroups — #15760614

Order 3328.

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

normal subgroups only

This group has 448 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#13113553C212yesmaximal
3#13113180C211yesmaximal, characteristic
4#13112692C212yesmaximal
5C13×#2567C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#395—21no—
9C13×#395—21no—
10C13×#391C412yes—
11C13×#389—21no—
12C13×#389—21no—
13C13×#384C412yes—
14C4×C13×C4⋊C4C2211yescharacteristic
15#11718685—24no—
16#11718587—21no—
17#11718587C2212yes—
18#11718587C2212yes—
19#11718586—21no—
20#11718139—24no—
21#11718120—21no—
22#11718120—21no—
23C22×Q8×C13—21no—
24C22×Q8×C13C2×C411yescharacteristic
25C13×C4⋊Q8—22no—
26C13×C4⋊Q8—22no—
27C4×Q8×C13—22no—
28C4×Q8×C13—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C42×C13C2×C412yes—
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13C2311yescharacteristic
41C13×#95—22no—
42C13×#95—22no—
43C13×#95—21no—
44C22⋊#1055—22no—
45C22⋊#1055—22no—
46C4⋊#1055—22no—
47C4⋊#1055—22no—
48C4⋊#1055—22no—
49C4⋊#1055D414yes—
50#88043—22no—
51#88043—22no—
52#88043—22no—
53C4×#1055—22no—
54#9454—131nomaximal, Sylow
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13—41no—
58C2×Q8×C13—42no—
59C2×Q8×C13—82no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C13×C4⋊C4—24no—
70C13×C4⋊C4—22no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—82no—
77C13×C4⋊C4—82no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—42no—
83C42×C13C2×D412yes—
84C42×C13#4112yes—
85C2×#1055—24no—
86C2×#1055—42no—
87#2983—131no—
88#2567D1311yescharacteristic
89#1556—132no—
90#1467—131no—
91#1285—132no—
92C23×C13C2×C22⋊C411yescharacteristic
93Q8×C13—44no—
94Q8×C13—84no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—24no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13#10112yes—
115C2×C4×C13C4×D412yes—
116C2×C4×C13#12011yescharacteristic
117C2×C4×C13#12112yes—
118C2×C4×C13#12311yescharacteristic
119#1055—44no—
120#1055—82no—
121C2×C4⋊Q8C2×D1311yescharacteristic
122C2×C4×Q8C2×D1311yescharacteristic
123#446—264no—
124#432—132no—
125#432—132no—
126#432—261no—
127#431—261no—
128#395—21no—
129#395—21no—
130#391Dic1312yes—
131#389—21no—
132#389—21no—
133#384Dic1312yes—
134C4×C4⋊C4C2×D1311yescharacteristic
135#332—264no—
136#324—261no—
137#324—261no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13#38611yescharacteristic
141C22×C13C2×#10111yescharacteristic
142C22×C13#41311yescharacteristic
143C4×C13—21no—
144C4×C13—22no—
145C4×C13—22no—
146C4×C13—22no—
147C4×C13—44no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13—82no—
152C4×C13#45612yes—
153C22×Q8—21no—
154C22×Q8C2×Dic1311yescharacteristic
155C4⋊Q8—22no—
156C4⋊Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4C2×Dic1312yes—
164C2×C4⋊C4C2×Dic1311yescharacteristic
165C2×C4⋊C4C22⋊D1311yescharacteristic
166C2×C4⋊C4C22⋊D1311yescharacteristic
167C2×C42C2×Dic1312yes—
168C2×C42C22⋊D1311yescharacteristic
169C2×C42C22⋊D1311yescharacteristic
170C2×C42C22×D1311yescharacteristic
171C4⋊C8—134no—
172C4⋊C8—262no—
173C4⋊C8—262no—
174C4⋊C8—262no—
175C22⋊C8—262no—
176C22⋊C8—262no—
177#97—262no—
178#97—262no—
179#97—262no—
180C4×C8—262no—
181#95—22no—
182#95—22no—
183#95—21no—
184C2×C13—21no—
185C2×C13—21no—
186C2×C13#188611yescharacteristic
187C2×C13#190111yescharacteristic
188C2×C13#191011yescharacteristic
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—82no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4C22⋊Dic1311yescharacteristic
197C22×C4C22⋊Dic1311yescharacteristic
198C22×C4C22⋊Dic1311yescharacteristic
199C22×C4C22⋊Dic1311yescharacteristic
200C22×C4C22×Dic1311yescharacteristic
201C22×C4C2×C22⋊D1311yescharacteristic
202C22×C4C2×C22⋊D1311yescharacteristic
203C2×C8—264no—
204C2×C8—522no—
205C4⋊C4—24no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—24no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—82no—
213C4⋊C4—82no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—42no—
219C42D4×D1312yes—
220C42#612912yes—
221C13#945411yescharacteristic, complemented, Sylow
222C23C2×C22⋊Dic1311yescharacteristic
223Q8—44no—
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4#8807612yes—
245C2×C4D4×Dic1312yes—
246C2×C4#8818911yescharacteristic
247C2×C4#8819111yescharacteristic
248C2×C4#8819312yes—
249C8—524no—
250C8—1042no—
251C22—21no—
252C22—21no—
253C22#1171888111yescharacteristic
254C22C2×#8807611yescharacteristic
255C22#1171889811yescharacteristic
256C4—21no—
257C4—22no—
258C4—22no—
259C4—22no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4#1171875612yes—
266C2—21no—
267C2—21no—
268C2#1311523011yescharacteristic
269C2#1311530511yescharacteristic
270C2#1311536411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2567C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2567D13
hypocenterC13#9454
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2567

Complements

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

NH ≅ G/Ntype
221. C13#9454semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131135532
#131131802
#131126922
C13×#25672
#945413