Finite Group Databasebeta

← #15758640

Subgroups — #15758640

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊Dic13C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic
3C2×#11718130C212yesmaximal
4#13112714C212yesmaximal
5C13×#2855C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2211yescharacteristic
7C22×C42×C13C2211yescharacteristic
8C22×C4⋊Dic13—21no—
9C22×C4×Dic13—21no—
10C13×#391C412yescomplemented
11C13×#389C412yescomplemented
12C13×#387—22no—
13C13×#385—21no—
14C13×#381—21no—
15C13×#380C2211yescharacteristic
16C2×#88071C2212yes—
17C2×C22⋊#1055C2212yes—
18C4×C4⋊Dic13—24no—
19#11718130—24no—
20#11718116—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C23×Dic13—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C42×C13—22no—
35C2×C42×C13—22no—
36C2×C42×C13C2×C412yes—
37C2×C42×C13D412yes—
38C2×C4⋊Dic13—28no—
39C2×C4⋊Dic13—24no—
40C2×C4×Dic13—24no—
41C2×C4×Dic13—42no—
42C2×C4×Dic13—42no—
43C22×#1055—22no—
44C13×#95—22no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95—21no—
48#88071—22no—
49#88071D414yes—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52#9144—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
54C2×Q8×C13—22no—
55C2×Q8×C13—42no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—24no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—42no—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22⋊C412yes—
69C22×C4×C13SD1612yes—
70C22×C4×C13Q1612yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4112yes—
75C22×Dic13—28no—
76C22×Dic13—24no—
77C22×Dic13—44no—
78C22×Dic13—42no—
79C22×Dic13—42no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—44no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C42×C13—24no—
89C42×C13—24no—
90C4⋊Dic13—216no—
91C4×Dic13—48no—
92C2×#1055—44no—
93C2×#1055—42no—
94#2855D1311yescharacteristic
95C2×C4×C4⋊C4—131no—
96#1817—131no—
97C2×#328—132no—
98#1294—132no—
99C23×C13—22no—
100C23×C13—22no—
101C23×C13C2×C22⋊C411yescharacteristic
102C23×C13#12011yescharacteristic
103C23×C13#12311yescharacteristic
104C23×C13C2×SD1611yescharacteristic
105C23×C13C2×Q1611yescharacteristic
106C23×C13AGL(1,ℤ/8)11yescharacteristic
107C23×C13#13711yescharacteristic
108Q8×C13—82no—
109C2×C4×C13—24no—
110C2×C4×C13—24no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13#10314yes—
131C2×C4×C13#10414yes—
132C2×C4×C13C4×D412yes—
133C2×C4×C13#12112yes—
134C2×Dic13—28no—
135C2×Dic13—44no—
136C2×Dic13—48no—
137C2×Dic13—48no—
138C2×Dic13—44no—
139#1055—82no—
140C2×C22⋊Q8C2×D1311yescharacteristic
141C22×C4⋊C4—261no—
142C22×C42—261no—
143C22×C42C2×D1311yescharacteristic
144C2×C22⋊C8—132no—
145#391Dic1312yescomplemented
146#389Dic1312yescomplemented
147#387—22no—
148#385—21no—
149#381—21no—
150#380C2×D1311yescharacteristic
151C4×C4⋊C4—264no—
152C2×#95—132no—
153#336—262no—
154#328—264no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13#38611yescharacteristic
164C22×C13#41012yes—
165C22×C13C2×#10311yescharacteristic
166C22×C13#41711yescharacteristic
167C22×C13C2×#10412yes—
168C22×C13#45011yescharacteristic
169C22×C13#45111yescharacteristic
170C22×C13#48311yescharacteristic
171C22×C13#48411yescharacteristic
172C4×C13—24no—
173C4×C13—24no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13—82no—
179Dic13—48no—
180C22×Q8C2×Dic1311yescharacteristic
181C23×C4—262no—
182C23×C4C22⋊D1311yescharacteristic
183C23×C4C22⋊D1311yescharacteristic
184C23×C4C22×D1311yescharacteristic
185C22×C8—262no—
186C22⋊Q8—22no—
187C22⋊Q8—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—268no—
191C2×C4⋊C4—264no—
192C2×C4⋊C4C2×Dic1311yescharacteristic
193C2×C4⋊C4C2×Dic1312yes—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—264no—
199C2×C42—522no—
200C2×C42—522no—
201C2×C42C2×Dic1312yes—
202C2×C42C22⋊D1312yes—
203C22⋊C8—262no—
204C22⋊C8—262no—
205#95—22no—
206#95—22no—
207#95—22no—
208#95—21no—
209#95—134no—
210#95—262no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13#150312yes—
216C2×C13#150912yes—
217C2×C13#187211yescharacteristic
218C2×C13#189611yescharacteristic
219C2×C13#189911yescharacteristic
220C24C2×C22⋊D1311yescharacteristic
221C2×Q8—22no—
222C2×Q8—42no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—268no—
235C22×C4—264no—
236C22×C4—524no—
237C22×C4—522no—
238C22×C4—522no—
239C22×C4#610612yes—
240C22×C4#610712yes—
241C22×C4C22⋊Dic1312yes—
242C22×C4C22⋊Dic1312yes—
243C22×C4D4×D1312yes—
244C22×C4#612912yes—
245C22×C4C22×Dic1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247C2×C8—524no—
248C2×C8—522no—
249C4⋊C4—22no—
250C4⋊C4—42no—
251C4⋊C4—44no—
252C4⋊C4—42no—
253C4⋊C4—2616no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C42—24no—
259C42—24no—
260C42—528no—
261C13#914411yescharacteristic, complemented, Sylow
262C23—22no—
263C23—22no—
264C23#8818911yescharacteristic
265C23#8819111yescharacteristic
266C23C2×#610611yescharacteristic
267C23C2×#610711yescharacteristic
268C23#8820311yescharacteristic
269C23#8820511yescharacteristic
270C23C2×C22⋊Dic1311yescharacteristic
271Q8—82no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—268no—
294C2×C4—528no—
295C2×C4—524no—
296C2×C4—528no—
297C2×C4—524no—
298C2×C4#8807514yes—
299C2×C4#8807714yes—
300C2×C4D4×Dic1312yes—
301C2×C4#8819312yes—
302C8—1042no—
303C22—22no—
304C22—22no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—22no—
311C22#1171870411yescharacteristic
312C22#1171870511yescharacteristic
313C22#1171870711yescharacteristic
314C22#1171871111yescharacteristic
315C22#1171888111yescharacteristic
316C22C2×#8807511yescharacteristic
317C22#1171889311yescharacteristic
318C22C2×#8807712yes—
319C22#1171890112yes—
320C4—24no—
321C4—24no—
322C4—22no—
323C4—22no—
324C4—82no—
325C4—81no—
326C4—81no—
327C4—528no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#1311333512yes—
333C2#1311336112yes—
334C2#1311514411yescharacteristic
335C2#1311528011yescharacteristic
336C2#1311529511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2855C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2855D13
hypocenterC13#9144
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
10. C13×#391C4semidirect
11. C13×#389C4semidirect
145. #391Dic13semidirect
146. #389Dic13semidirect
261. C13#9144semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊Dic132
#131149042
C2×#117181302
#131127142
C13×#28552
#914413