Finite Group Databasebeta

← #15752103

Subgroups — #15752103

Order 3328.

478 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 83 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#13121862C211yesmaximal, characteristic
2#13116240C212yesmaximal, complemented
3#13112662C211yesmaximal, characteristic, complemented
4#13112656C212yesmaximal, complemented
5C13×#2096C211yesmaximal, characteristic, complemented
6C2×#88201—21no—
7C2×C13×#106—21no—
8C2×C13×#103—21no—
9C13×#391C2211yescharacteristic
10C13×#384C2211yescharacteristic
11#11718652—21no—
12C2×#88049—22no—
13#11718600C2212yes—
14#11718332—22no—
15#11718331—22no—
16C13×#336C2211yescharacteristic
17#11718121—22no—
18#11718116C2212yes—
19C22×Q8×C13D411yescharacteristic
20C22×D52—21no—
21C22×D52—21no—
22C22×D52D412yes—
23C22×C8×C13—21no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C42×C13C2311yescharacteristic
28#88201—42no—
29#88201—42no—
30C2×#6103—22no—
31C2×#6103—22no—
32C2×#6103—22no—
33C2×#6103—22no—
34C2×C4⋊Dic13D412yes—
35C2×C4×Dic13—21no—
36C22×#1055—22no—
37C13×#106—42no—
38C13×#103—42no—
39C13×#95—22no—
40#88071—21no—
41#88049—44no—
42#7810—131nomaximal, Sylow
43C23×D13—22no—
44C2×Q8×C13—21no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13SD1612yes—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—41no—
51C22×C4×C13C2×D412yes—
52C22×C4×C13C2×D411yescharacteristic
53C22×Dic13—22no—
54C2×D52—22no—
55C2×D52—22no—
56C2×D52—42no—
57C2×D52—42no—
58C2×D52—42no—
59C2×D52—81no—
60C2×D52—81no—
61C2×D52—81no—
62C2×D52—82no—
63C2×C8×C13—22no—
64C2×C8×C13—41no—
65C2×C8×C13—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C42×C13—41no—
72#6103—44no—
73#6103—42no—
74#6103—42no—
75#6103—42no—
76#6103—42no—
77#6103—82no—
78C4⋊Dic13—42no—
79C4×Dic13—42no—
80C2×#1055—42no—
81C2×#1055—42no—
82C2×#1055—42no—
83#2733—131no—
84#2096D1311yescharacteristic, complemented
85#2071—132no—
86#1272—131no—
87#1270—132no—
88C23×C13#12011yescharacteristic
89C22×D13—42no—
90C22×D13—42no—
91C22×D13—42no—
92C22×D13—42no—
93C22×D13—42no—
94C22×D13—42no—
95C22×D13—42no—
96Q8×C13—42no—
97Q8×C13—81no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—82no—
108C2×C4×C13—81no—
109C2×C4×C13C2×SD1611yescharacteristic
110C2×C4×C13#13512yes—
111C2×C4×C13AGL(1,ℤ/8)12yes—
112C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116D52—44no—
117D52—82no—
118D52—84no—
119D52—84no—
120C8×C13—42no—
121#1055—82no—
122C2×#124—261no—
123C2×#106—21no—
124C2×#103—21no—
125C2×#102—262no—
126#394—261no—
127#392—262no—
128#391C2×D1311yescharacteristic
129#390—132no—
130#388—262no—
131#384C2×D1311yescharacteristic
132#340—262no—
133#336—132no—
134#336C2×D1311yescharacteristic
135C22×C13#44912yes—
136C22×C13#45011yescharacteristic
137C22×C13#45311yescharacteristic
138C22×C13#45512yes—
139C22×C13#45811yescharacteristic
140C2×D13—82no—
141C2×D13—82no—
142C2×D13—82no—
143C2×D13—82no—
144C2×D13—82no—
145C2×D13—82no—
146C2×D13—82no—
147C4×C13—22no—
148C4×C13—22no—
149C4×C13—21no—
150C4×C13—21no—
151C4×C13—42no—
152C4×C13—81no—
153C4×C13—161no—
154Dic13—82no—
155C22×Q8C22⋊D1311yescharacteristic
156C22×D4—132no—
157C22×D4—261no—
158C22×D4—261no—
159C22×C8—21no—
160C22×C8—262no—
161#124—522no—
162#124—522no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4C22⋊D1311yescharacteristic
167C2×C22⋊C4—262no—
168C2×C22⋊C4—262no—
169C2×C22⋊C4—262no—
170C2×C22⋊C4—262no—
171C2×C42—261no—
172C2×C42C22×D1311yescharacteristic
173#106—42no—
174#103—42no—
175#102—524no—
176#95—22no—
177#95—261no—
178C2×C13#161212yes—
179C2×C13#161311yescharacteristic
180C2×C13#162411yescharacteristic
181C2×C13#164212yes—
182C2×C13#165911yescharacteristic
183D13—162no—
184C24—262no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8#610612yes—
189C2×D4—262no—
190C2×D4—262no—
191C2×D4—522no—
192C2×D4—522no—
193C2×D4—522no—
194C2×D4—1041no—
195C2×D4—1041no—
196C2×D4—1041no—
197C2×D4—1042no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4—262no—
202C22×C4D4×D1312yes—
203C22×C4C2×C22⋊D1311yescharacteristic
204C2×C8—22no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—522no—
208C2×C8—522no—
209C2×C8—522no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—522no—
216C22⋊C4—524no—
217C22⋊C4—522no—
218C22⋊C4—522no—
219C22⋊C4—522no—
220C22⋊C4—522no—
221C22⋊C4—1042no—
222C42—41no—
223C42—522no—
224C13#781011yescharacteristic, complemented, Sylow
225C23—522no—
226C23—522no—
227C23—522no—
228C23—522no—
229C23—522no—
230C23—522no—
231C23—522no—
232C23#8819111yescharacteristic
233Q8—42no—
234Q8—81no—
235D4—524no—
236D4—1042no—
237D4—1044no—
238D4—1044no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—81no—
249C2×C4—82no—
250C2×C4—522no—
251C2×C4—522no—
252C2×C4—522no—
253C2×C4#8816812yes—
254C2×C4#8817012yes—
255C2×C4C2×#610611yescharacteristic
256C2×C4#8820311yescharacteristic
257C8—42no—
258C8—1042no—
259C22—1042no—
260C22—1042no—
261C22—1042no—
262C22—1042no—
263C22—1042no—
264C22—1042no—
265C22—1042no—
266C22#1171870711yescharacteristic
267C22#1171871411yescharacteristic
268C22#1171873811yescharacteristic
269C22#1171883312yes—
270C22#1171886312yes—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—81no—
277C4—161no—
278C4—1042no—
279C2—2082no—
280C2#1311384912yes—
281C2#1311385511yescharacteristic
282C2#1311391711yescharacteristic
283C2#1311403512yes—
284C2#1311414011yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2096C2
socleC23×C13#120
prime radical#13121862C2
hypercenter#2096D13
hypocenterC13#7810
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
2. #13116240C2semidirect
3. #13112662C2semidirect
4. #13112656C2semidirect
5. C13×#2096C2semidirect
84. #2096D13semidirect
224. C13#7810semidirect

Maximal subgroups

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

subgroupindex
#131218622
#131162402
#131126622
#131126562
C13×#20962
#781013