Finite Group Databasebeta

← #15751179

Subgroups — #15751179

Order 3328.

520 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117379C211yesmaximal, characteristic
2#13114688C212yesmaximal, complemented
3#13112662C211yesmaximal, characteristic, complemented
4#13112656C212yesmaximal
5C13×#1272C211yesmaximal, characteristic, complemented
6C2×#88201C411yescharacteristic
7C2×Q8×Dic13C411yescharacteristic
8C2×#88147C411yescharacteristic
9C13×#391C2211yescharacteristic
10C2×#88055—22no—
11C2×#88054—22no—
12#11718638C411yescharacteristic
13#11718600C2211yescharacteristic
14C42×Dic13C2211yescharacteristic
15#11718331—22no—
16#11718327—22no—
17C13×#336C2212yes—
18#11718116C2212yes—
19C22×Q8×C13C2×C411yescharacteristic
20C22×D52C2×C411yescharacteristic
21C22×C4×D13—21no—
22C22×C8×C13—22no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C42×C13C2311yescharacteristic
25#88201—22no—
26#88201—22no—
27Q8×Dic13—42no—
28C2×#6103—22no—
29C2×#6103—22no—
30C2×#6103—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4×Dic13—21no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D412yes—
37C2×C4×Dic13D412yes—
38C22×#1055—22no—
39#88147—42no—
40C13×#95—22no—
41#88071—22no—
42#88055—44no—
43#88054—28no—
44#7635—131nomaximal, Sylow
45C23×D13—21no—
46C2×Q8×C13—21no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13M1612yes—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13C22×C411yescharacteristic
53C22×C4×C13C2×D412yes—
54C22×Dic13—21no—
55C22×Dic13C22⋊C412yes—
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C22⋊C411yescharacteristic
58C2×D52—21no—
59C2×D52—41no—
60C2×D52—41no—
61C2×D52M1612yes—
62C2×C4×D13—42no—
63C2×C4×D13—44no—
64C2×C8×C13—24no—
65C2×C8×C13—42no—
66C2×C8×C13—42no—
67C13×C4⋊C4—41no—
68C42×C13—41no—
69#6103—28no—
70#6103—42no—
71#6103—42no—
72#6103—42no—
73C4⋊Dic13—42no—
74C4⋊Dic13—41no—
75C4×Dic13—21no—
76C4×Dic13—21no—
77C4×Dic13—22no—
78C4×Dic13—22no—
79C4×Dic13—22no—
80C4×Dic13—24no—
81C4×Dic13—42no—
82C2×#1055—24no—
83C2×#1055—42no—
84C2×#1055—42no—
85C4×#124—131no—
86#1767—132no—
87#1272—131no—
88#1272D1311yescharacteristic, complemented
89#1270—132no—
90C23×C13C2×C22⋊C411yescharacteristic
91C22×D13—22no—
92C22×D13—41no—
93C22×D13—41no—
94C22×D13—42no—
95C22×D13—42no—
96Q8×C13—42no—
97Q8×C13—42no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13C2×M1611yescharacteristic
108C2×C4×C13C2×M1611yescharacteristic
109C2×C4×C13AGL(1,ℤ/8)12yes—
110C2×C4×C13#13712yes—
111C2×Dic13—22no—
112C2×Dic13—21no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—22no—
116C2×Dic13—41no—
117C2×Dic13—42no—
118C2×Dic13#10012yes—
119C2×Dic13#10414yes—
120D52—42no—
121D52—42no—
122C4×D13—84no—
123C8×C13—44no—
124#1055—44no—
125C2×#124—131no—
126C2×C4×Q8—131no—
127C2×C4×D4—131no—
128C2×C4⋊C8—262no—
129C2×#97—262no—
130#391C2×D1311yescharacteristic
131#390—131no—
132#388—262no—
133#382—131no—
134C4×C22⋊C4—262no—
135C43—131no—
136#336—132no—
137#336C2×D1312yes—
138C22×C13#40711yescharacteristic
139C22×C13#41011yescharacteristic
140C22×C13C2×#10011yescharacteristic
141C22×C13#41712yes—
142C22×C13C2×#10412yes—
143C2×D13—42no—
144C2×D13—44no—
145C2×D13—81no—
146C2×D13—82no—
147C2×D13—81no—
148C4×C13—21no—
149C4×C13—21no—
150C4×C13—22no—
151C4×C13—22no—
152C4×C13—42no—
153C4×C13—81no—
154Dic13—41no—
155Dic13—42no—
156Dic13—81no—
157Dic13#32914yes—
158C22×Q8C4×D1311yescharacteristic
159C22×D4—131no—
160C23×C4—261no—
161C22×C8—22no—
162C22×C8—262no—
163#124—262no—
164#124—262no—
165C4×Q8—522no—
166C4×D4—522no—
167C2×C4⋊C4—131no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4C4×D1311yescharacteristic
170C2×C22⋊C4—262no—
171C2×C22⋊C4—261no—
172C2×C22⋊C4—262no—
173C2×C42—131no—
174C2×C42—131no—
175C2×C42—132no—
176C2×C42—132no—
177C2×C42—261no—
178C2×C42C22×D1311yescharacteristic
179C4⋊C8—268no—
180#97—524no—
181#95—22no—
182#95—262no—
183C2×C13#146611yescharacteristic
184C2×C13#148912yes—
185C2×C13#150912yes—
186C2×C13C2×#32911yescharacteristic
187C2×C13#156011yescharacteristic
188D13—82no—
189C24—261no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8#609412yes—
194C2×D4—132no—
195C2×D4—261no—
196C2×D4—521no—
197C2×D4—521no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—131no—
201C22×C4—132no—
202C22×C4—131no—
203C22×C4—261no—
204C22×C4—522no—
205C22×C4—524no—
206C22×C4C2×C4×D1311yescharacteristic
207C22×C4D4×D1312yes—
208C2×C8—24no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—264no—
212C2×C8—522no—
213C2×C8—522no—
214C4⋊C4—41no—
215C4⋊C4—521no—
216C4⋊C4—522no—
217C22⋊C4—268no—
218C22⋊C4—522no—
219C22⋊C4—522no—
220C22⋊C4—522no—
221C42—41no—
222C42—264no—
223C42—262no—
224C42—261no—
225C42—261no—
226C42—262no—
227C42—262no—
228C42—522no—
229C13#763511yescharacteristic, complemented, Sylow
230C23—262no—
231C23—521no—
232C23—521no—
233C23—522no—
234C23—522no—
235C23C22⋊C4×D1311yescharacteristic
236Q8—42no—
237Q8—42no—
238D4—522no—
239D4—522no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—132no—
250C2×C4—134no—
251C2×C4—261no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—262no—
256C2×C4—521no—
257C2×C4—522no—
258C2×C4—1044no—
259C2×C4C2×#609411yescharacteristic
260C2×C4M16×D1311yescharacteristic
261C2×C4#8816812yes—
262C2×C4#8817212yes—
263C8—44no—
264C8—524no—
265C22—522no—
266C22—524no—
267C22—1042no—
268C22—1041no—
269C22—1041no—
270C22#1171838711yescharacteristic
271C22#1171840111yescharacteristic
272C22D13×#10011yescharacteristic
273C22#1171846412yes—
274C22D13×#10412yes—
275C4—22no—
276C4—22no—
277C4—21no—
278C4—21no—
279C4—42no—
280C4—81no—
281C4—134no—
282C4—522no—
283C4—521no—
284C4—1041no—
285C2—1042no—
286C2#1311317511yescharacteristic
287C2#1311327412yes—
288C2#1311336012yes—
289C2D13×#32911yescharacteristic
290C2#1311357011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1272D13
hypocenterC13#7635
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #13114688C2semidirect
3. #13112662C2semidirect
5. C13×#1272C2semidirect
88. #1272D13semidirect
229. C13#7635semidirect

Maximal subgroups

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

subgroupindex
#131173792
#131146882
#131126622
#131126562
C13×#12722
#763513