Finite Group Databasebeta

← #15751206

Subgroups — #15751206

Order 3328.

646 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 121 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
1D13×#391C211yesmaximal, characteristic
2#13114815C212yesmaximal
3#13112662C211yesmaximal, characteristic, complemented
4#13112661C212yesmaximal, complemented
5C13×#1272C211yesmaximal, characteristic, complemented
6C22×Q8×D13C411yescharacteristic
7C2×C4⋊C4×D13C411yescharacteristic
8C2×C42×D13C2211yescharacteristic
9C13×#391C2211yescharacteristic
10#11718891C411yescharacteristic
11C2×#88060—22no—
12C2×#88054—22no—
13#11718635C411yescharacteristic
14#11718590C2211yescharacteristic
15D13×#95—22no—
16#11718307—22no—
17C13×#336C2212yes—
18#11718116C2212yes—
19C22×Q8×C13C2×C411yescharacteristic
20C2×Q8×D13—22no—
21C2×Q8×D13—22no—
22C2×Q8×D13—42no—
23C2×Q8×D13—42no—
24C22×C4×D13—21no—
25C22×C4×D13—21no—
26C22×C4×D13C2×C411yescharacteristic
27C22×C4×D13D412yes—
28C22×Dic26—21no—
29C22×Dic26C2×C411yescharacteristic
30C22×C8×C13—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—21no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D412yes—
37C22×#1055—22no—
38C4⋊C4×D13—42no—
39C42×D13—42no—
40C13×#95—22no—
41#88071—22no—
42#88071—22no—
43#88071—22no—
44#88060—44no—
45#88054—44no—
46#7643—131nomaximal, Sylow
47C23×D13C22⋊C411yescharacteristic
48C2×Q8×C13—21no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13M1612yes—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13C22×C411yescharacteristic
55C22×C4×C13C2×D412yes—
56C22×Dic13—21no—
57C22×Dic13—21no—
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C22⋊C412yes—
60Q8×D13—48no—
61Q8×D13—48no—
62C2×C4×D13—22no—
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×C4×D13—22no—
66C2×C4×D13—24no—
67C2×C4×D13—42no—
68C2×C4×D13—42no—
69C2×C4×D13—42no—
70C2×C4×D13—42no—
71C2×C4×D13—44no—
72C2×C4×D13—42no—
73C2×C4×D13SD1614yes—
74C2×C4×D13Q1614yes—
75C2×Dic26—24no—
76C2×Dic26—21no—
77C2×Dic26—42no—
78C2×Dic26—42no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26M1612yes—
82C2×C8×C13—42no—
83C2×C8×C13—42no—
84C2×C8×C13—42no—
85C13×C4⋊C4—41no—
86C42×C13—41no—
87C4⋊Dic13—41no—
88#6101—42no—
89C4×Dic13—24no—
90C4×Dic13—41no—
91C2×#1055—42no—
92C2×#1055—42no—
93C2×#1055—42no—
94C2×#391—131no—
95#1797—132no—
96#1272—131no—
97#1272—132no—
98#1272D1311yescharacteristic, complemented
99C23×C13C2×C22⋊C411yescharacteristic
100C22×D13—21no—
101C22×D13—21no—
102C22×D13—22no—
103C22×D13#10012yes—
104C22×D13#10314yes—
105Q8×C13—42no—
106Q8×C13—42no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13C2×M1611yescharacteristic
117C2×C4×C13C2×M1611yescharacteristic
118C2×C4×C13C2×SD1612yes—
119C2×C4×C13C2×Q1612yes—
120C2×Dic13—21no—
121C2×Dic13—22no—
122C2×Dic13—21no—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—42no—
129C2×Dic13#9912yes—
130C2×Dic13#10314yes—
131C4×D13—24no—
132C4×D13—24no—
133C4×D13—44no—
134C4×D13—44no—
135C4×D13—48no—
136C4×D13—84no—
137Dic26—48no—
138Dic26—42no—
139Dic26—42no—
140C8×C13—82no—
141#1055—82no—
142C23×Q8—131no—
143C22×C4⋊C4—131no—
144C22×C42—131no—
145C2×C4⋊C8—262no—
146C2×C22⋊C8—262no—
147#391—131no—
148#391—131no—
149#391—131no—
150#391—262no—
151#391C2×D1311yescharacteristic
152C2×#95—262no—
153#336—132no—
154#336C2×D1312yes—
155C22×C13#40711yescharacteristic
156C22×C13C2×#9911yescharacteristic
157C22×C13C2×#10011yescharacteristic
158C22×C13C2×#10312yes—
159C22×C13#42112yes—
160C2×D13—22no—
161C2×D13—24no—
162C2×D13—24no—
163C2×D13—22no—
164C2×D13#33314yes—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—42no—
170C4×C13—81no—
171Dic13—22no—
172Dic13—24no—
173Dic13—42no—
174Dic13—81no—
175C22×Q8—131no—
176C22×Q8—261no—
177C22×Q8—262no—
178C22×Q8—262no—
179C22×Q8—522no—
180C22×Q8—522no—
181C22×Q8C4×D1311yescharacteristic
182C23×C4—132no—
183C23×C4—131no—
184C23×C4—261no—
185C23×C4—261no—
186C22×C8—22no—
187C22×C8—262no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—522no—
191C2×C4⋊C4C4×D1311yescharacteristic
192C2×C42—132no—
193C2×C42—131no—
194C2×C42—522no—
195C2×C42C22×D1311yescharacteristic
196C4⋊C8—524no—
197C22⋊C8—524no—
198#95—22no—
199#95—262no—
200#95—262no—
201#95—262no—
202C2×C13#146211yescharacteristic
203C2×C13#148712yes—
204C2×C13#152012yes—
205C2×C13#153311yescharacteristic
206C2×C13C2×#33311yescharacteristic
207D13—24no—
208C24—131no—
209C2×Q8—21no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—132no—
213C2×Q8—264no—
214C2×Q8—261no—
215C2×Q8—521no—
216C2×Q8—521no—
217C2×Q8—522no—
218C2×Q8—522no—
219C2×Q8—528no—
220C2×Q8—528no—
221C2×Q8#609412yes—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—132no—
225C22×C4—131no—
226C22×C4—134no—
227C22×C4—134no—
228C22×C4—262no—
229C22×C4—262no—
230C22×C4—264no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—522no—
236C22×C4—522no—
237C22×C4—522no—
238C22×C4—522no—
239C22×C4—522no—
240C22×C4—524no—
241C22×C4C2×C4×D1311yescharacteristic
242C22×C4D4×D1312yes—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—522no—
247C2×C8—522no—
248C2×C8—522no—
249C4⋊C4—41no—
250C4⋊C4—521no—
251C4⋊C4—522no—
252C42—41no—
253C42—264no—
254C42—521no—
255C13#764311yescharacteristic, complemented, Sylow
256C23—132no—
257C23—134no—
258C23—261no—
259C23—262no—
260C23—261no—
261C23C22⋊C4×D1311yescharacteristic
262Q8—42no—
263Q8—42no—
264Q8—522no—
265Q8—522no—
266Q8—528no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—132no—
277C2×C4—134no—
278C2×C4—264no—
279C2×C4—264no—
280C2×C4—262no—
281C2×C4—261no—
282C2×C4—262no—
283C2×C4—261no—
284C2×C4—262no—
285C2×C4—524no—
286C2×C4—524no—
287C2×C4—528no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—522no—
292C2×C4—1044no—
293C2×C4C2×#609411yescharacteristic
294C2×C4M16×D1311yescharacteristic
295C2×C4SD16×D1312yes—
296C2×C4Q16×D1312yes—
297C8—82no—
298C8—1042no—
299C22—134no—
300C22—264no—
301C22—262no—
302C22—262no—
303C22—264no—
304C22#1171838711yescharacteristic
305C22D13×#9911yescharacteristic
306C22D13×#10011yescharacteristic
307C22D13×#10312yes—
308C22#1171848212yes—
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—264no—
316C4—262no—
317C4—522no—
318C4—1041no—
319C2—264no—
320C2#1311316111yescharacteristic
321C2#1311326312yes—
322C2#1311340612yes—
323C2#1311345811yescharacteristic
324C2D13×#33311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1272D13
hypocenterC13#7643
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
3. #13112662C2semidirect
4. #13112661C2semidirect
5. C13×#1272C2semidirect
98. #1272D13semidirect
255. C13#7643semidirect

Maximal subgroups

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

subgroupindex
D13×#3912
#131148152
#131126622
#131126612
C13×#12722
#764313