Finite Group Databasebeta

← #15751493

Subgroups — #15751493

Order 3328.

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

normal subgroups only

This group has 500 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#13114904C211yesmaximal, characteristic
2#13114598C211yesmaximal, characteristic
3#13112662C214yesmaximal, complemented
4C13×#2857C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C13×C22⋊Q8C412yes—
7C22×C42×C13C2211yescharacteristic
8C13×#391C2212yes—
9C13×#389—21no—
10C13×#389—21no—
11C13×#384C411yescharacteristic
12C13×#380—21no—
13C13×#380—21no—
14C2×C22⋊#1055—21no—
15C2×C22⋊#1055—21no—
16C2×#88043—21no—
17#11718116—21no—
18#11718116C2212yes—
19#11718116C2212yes—
20C22×Q8×C13C2×C412yes—
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C13×C4⋊Q8—42no—
25C13×C22⋊Q8—44no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C22⋊C4—22no—
33C2×C42×C13—42no—
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C42×C13C2311yescharacteristic
38C22×#1055—22no—
39C22×#1055—22no—
40C13×#95—22no—
41C13×#95—22no—
42C22⋊#1055—24no—
43C22⋊#1055—42no—
44#88043—42no—
45#7707—131nomaximal, Sylow
46C24×C13C22⋊C411yescharacteristic
47C2×Q8×C13—24no—
48C2×Q8×C13—42no—
49C2×Q8×C13—42no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—44no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C22⋊C4—44no—
74C42×C13—22no—
75C42×C13—22no—
76C42×C13—41no—
77C42×C13—41no—
78C2×#1055—24no—
79C2×#1055—42no—
80C2×#1055—42no—
81C2×#1055—42no—
82C2×#1055—42no—
83C2×#1055—42no—
84#2857D1311yescharacteristic
85#1817—131no—
86#1749—131no—
87#1272—134no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13#10012yes—
95C23×C13C2×C22⋊C411yescharacteristic
96Q8×C13—84no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—44no—
111C2×C4×C13—44no—
112C2×C4×C13—44no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13#9912yes—
120C2×C4×C13#10412yes—
121C2×C4×C13#13112yes—
122C2×C4×C13#13712yes—
123C2×C4×C13#13712yes—
124#1055—44no—
125#1055—82no—
126C2×C4⋊Q8Dic1311yescharacteristic
127C2×C22⋊Q8Dic1312yes—
128C22×C42C2×D1311yescharacteristic
129C2×C22⋊C8—261no—
130C2×C22⋊C8—261no—
131C2×#97—261no—
132#391C2×D1312yes—
133#389—21no—
134#389—21no—
135#384Dic1311yescharacteristic
136#380—21no—
137#380—21no—
138#336—132no—
139#336—132no—
140#336—261no—
141C22×C13—22no—
142C22×C13—22no—
143C22×C13—22no—
144C22×C13—41no—
145C22×C13—41no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13#40811yescharacteristic
149C22×C13C2×#9911yescharacteristic
150C22×C13C2×#10011yescharacteristic
151C22×C13#41911yescharacteristic
152C22×C13#41911yescharacteristic
153C22×C13C2×#10411yescharacteristic
154C22×C13#42111yescharacteristic
155C4×C13—22no—
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—41no—
161C4×C13—82no—
162C4×C13—82no—
163C22×Q8C2×Dic1312yes—
164C23×C4C2×Dic1311yescharacteristic
165C23×C4C22⋊D1311yescharacteristic
166C23×C4C22⋊D1311yescharacteristic
167C22×C8—262no—
168C22×C8—262no—
169C4⋊Q8—42no—
170C22⋊Q8—44no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4C2×Dic1312yes—
177C2×C22⋊C4—22no—
178C2×C42—42no—
179C2×C42C2×Dic1311yescharacteristic
180C2×C42C22⋊D1311yescharacteristic
181C2×C42C22⋊D1311yescharacteristic
182C2×C42C22×D1311yescharacteristic
183C22⋊C8—264no—
184C22⋊C8—522no—
185#97—522no—
186#95—22no—
187#95—22no—
188C2×C13—42no—
189C2×C13#147111yescharacteristic
190C2×C13#148511yescharacteristic
191C2×C13#149711yescharacteristic
192C2×C13#150811yescharacteristic
193C2×C13#151111yescharacteristic
194C2×C13#153011yescharacteristic
195C2×C13#155811yescharacteristic
196C24C22⋊Dic1311yescharacteristic
197C2×Q8—24no—
198C2×Q8—42no—
199C2×Q8—42no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4C22⋊Dic1311yescharacteristic
212C22×C4C22⋊Dic1311yescharacteristic
213C22×C4C22⋊Dic1311yescharacteristic
214C22×C4C22×Dic1311yescharacteristic
215C22×C4C2×C22⋊D1311yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217C2×C8—264no—
218C2×C8—522no—
219C2×C8—522no—
220C2×C8—522no—
221C2×C8—522no—
222C2×C8—522no—
223C4⋊C4—42no—
224C4⋊C4—44no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C22⋊C4—44no—
230C42—22no—
231C42—22no—
232C42—41no—
233C42—41no—
234C13#770711yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23#8807312yes—
242C23C2×C22⋊Dic1311yescharacteristic
243Q8—84no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4#8807412yes—
267C2×C4#8807712yes—
268C2×C4#8819612yes—
269C2×C4#8819612yes—
270C2×C4#8820212yes—
271C8—524no—
272C8—1042no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22C2×#8807311yescharacteristic
281C22C2×#8807411yescharacteristic
282C22#1171888611yescharacteristic
283C22#1171888611yescharacteristic
284C22#1171889511yescharacteristic
285C22C2×#8807711yescharacteristic
286C22#1171889711yescharacteristic
287C4—22no—
288C4—22no—
289C4—22no—
290C4—22no—
291C4—22no—
292C4—41no—
293C4—82no—
294C4—82no—
295C2—42no—
296C2#1311319611yescharacteristic
297C2#1311325711yescharacteristic
298C2#1311330911yescharacteristic
299C2#1311335611yescharacteristic
300C2#1311336911yescharacteristic
301C2#1311344711yescharacteristic
302C2#1311356211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2857C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2857D13
hypocenterC13#7707
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
3. #13112662C2semidirect
234. C13#7707semidirect

Maximal subgroups

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

subgroupindex
#131149042
#131145982
#131126622
C13×#28572
#770713