Finite Group Databasebeta

← #15750956

Subgroups — #15750956

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114904C211yesmaximal, characteristic
2C4×C22⋊#1055C211yesmaximal, characteristic
3#13112662C212yesmaximal, complemented
4#13112659C212yesmaximal, complemented
5C4×C13×C22⋊Q8C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C2×C4×Q8×C13C411yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C13×#391C2211yescharacteristic
10C13×#389C2211yescharacteristic
11C13×#387—21no—
12C13×#385—21no—
13C13×#380C411yescharacteristic
14C4×C13×C4⋊C4—21no—
15C4×C13×C4⋊C4C411yescharacteristic
16C4×C13×C22⋊C4—21no—
17C2×C22⋊#1055—21no—
18C2×C22⋊#1055—21no—
19C2×C4×#1055—21no—
20#11718116—21no—
21#11718116C2212yes—
22#11718116C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—22no—
28C13×C22⋊Q8C814yescomplemented
29C4×Q8×C13—42no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C42×C13—21no—
39C2×C42×C13—21no—
40C2×C42×C13—42no—
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13C2311yescharacteristic
45C22×#1055—22no—
46C22×#1055—22no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C22⋊#1055—24no—
53C22⋊#1055—42no—
54C4×#1055—42no—
55#7583—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C2×Q8×C13—21no—
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C2×Q8×C13C2×C812yes—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C2×C812yes—
77C22×C4×C13M1612yes—
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C13×C4⋊C4—24no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4C2×C812yes—
88C13×C22⋊C4—24no—
89C13×C22⋊C4—42no—
90C42×C13—22no—
91C42×C13—22no—
92C42×C13—41no—
93C42×C13—41no—
94C42×C13—42no—
95C42×C13—42no—
96C2×#1055—24no—
97C2×#1055—42no—
98C2×#1055—42no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#1055—42no—
102C4×C22⋊Q8D1311yescharacteristic
103#1817—131no—
104C4×C22⋊C8—131no—
105#1272—132no—
106#1271—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13C22⋊C812yes—
114C23×C13C2×C22⋊C411yescharacteristic
115Q8×C13—42no—
116Q8×C13—42no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—44no—
134C2×C4×C13—44no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13C22⋊C812yes—
146C2×C4×C13#9912yes—
147C2×C4×C13#10412yes—
148C2×C4×C13C22×C811yescharacteristic
149C2×C4×C13C2×M1611yescharacteristic
150C2×C4×C13#13512yes—
151C2×C4×C13#13712yes—
152#1055—44no—
153#1055—82no—
154C2×C22⋊Q8Dic1311yescharacteristic
155C2×C4×Q8Dic1311yescharacteristic
156C22×C42C2×D1311yescharacteristic
157C2×C22⋊C8—261no—
158C2×C22⋊C8—261no—
159C2×C4×C8—261no—
160#391C2×D1311yescharacteristic
161#389C2×D1311yescharacteristic
162#387—21no—
163#385—21no—
164#380Dic1311yescharacteristic
165C4×C4⋊C4—21no—
166C4×C4⋊C4Dic1311yescharacteristic
167C4×C22⋊C4—21no—
168#336—132no—
169#336—132no—
170#336—261no—
171C22×C13—22no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13C2×C22⋊C811yescharacteristic
179C22×C13C2×#9911yescharacteristic
180C22×C13#41311yescharacteristic
181C22×C13#41611yescharacteristic
182C22×C13#41911yescharacteristic
183C22×C13C2×#10411yescharacteristic
184C22×C13#42111yescharacteristic
185C4×C13—22no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—22no—
189C4×C13—22no—
190C4×C13—22no—
191C4×C13—22no—
192C4×C13—42no—
193C4×C13—42no—
194C4×C13—81no—
195C4×C13—81no—
196C22×Q8C2×Dic1311yescharacteristic
197C23×C4C2×Dic1311yescharacteristic
198C23×C4C22⋊D1311yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C22×C8—262no—
201C22×C8—262no—
202C22⋊Q8—22no—
203C22⋊Q8#105514yescomplemented
204C4×Q8—42no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4C2×Dic1311yescharacteristic
209C2×C4⋊C4C2×Dic1311yescharacteristic
210C2×C4⋊C4C2×Dic1311yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—42no—
216C2×C42C2×Dic1311yescharacteristic
217C2×C42C22⋊D1311yescharacteristic
218C2×C42C22⋊D1311yescharacteristic
219C2×C42C22×D1311yescharacteristic
220C22⋊C8—264no—
221C22⋊C8—522no—
222C4×C8—522no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228C2×C13—42no—
229C2×C13#145911yescharacteristic
230C2×C13#147611yescharacteristic
231C2×C13#147911yescharacteristic
232C2×C13#150811yescharacteristic
233C2×C13#151611yescharacteristic
234C2×C13#152911yescharacteristic
235C2×C13#155411yescharacteristic
236C24C22⋊Dic1311yescharacteristic
237C2×Q8—21no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8C2×#105512yes—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4C2×#105512yes—
254C22×C4#609912yes—
255C22×C4C22⋊Dic1311yescharacteristic
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22⋊Dic1311yescharacteristic
258C22×C4C22×Dic1311yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261C2×C8—264no—
262C2×C8—522no—
263C2×C8—522no—
264C2×C8—522no—
265C2×C8—522no—
266C2×C8—522no—
267C4⋊C4—24no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4C2×#105512yes—
274C22⋊C4—24no—
275C22⋊C4—42no—
276C42—22no—
277C42—22no—
278C42—41no—
279C42—41no—
280C42—42no—
281C42—42no—
282C13#758311yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C22⋊#105512yes—
290C23C2×C22⋊Dic1311yescharacteristic
291Q8—42no—
292Q8—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4C22⋊#105512yes—
322C2×C4#8807412yes—
323C2×C4#8807712yes—
324C2×C4C22×#105511yescharacteristic
325C2×C4C2×#609911yescharacteristic
326C2×C4#8819612yes—
327C2×C4#8820412yes—
328C8—524no—
329C8—1042no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×C22⋊#105511yescharacteristic
338C22C2×#8807411yescharacteristic
339C22#1171888611yescharacteristic
340C22#1171889411yescharacteristic
341C22C2×#8807711yescharacteristic
342C22#1171889711yescharacteristic
343C22#1171889811yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—22no—
348C4—22no—
349C4—21no—
350C4—21no—
351C4—42no—
352C4—42no—
353C4—81no—
354C4—81no—
355C2—42no—
356C2#1311315411yescharacteristic
357C2#1311321811yescharacteristic
358C2#1311323111yescharacteristic
359C2#1311335611yescharacteristic
360C2#1311339211yescharacteristic
361C2#1311344311yescharacteristic
362C2#1311354611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC4×C13×C22⋊Q8C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenterC4×C22⋊Q8D13
hypocenterC13#7583
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13112662C2semidirect
4. #13112659C2semidirect
28. C13×C22⋊Q8C8semidirect
203. C22⋊Q8#1055semidirect
282. C13#7583semidirect

Maximal subgroups

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

subgroupindex
#131149042
C4×C22⋊#10552
#131126622
#131126592
C4×C13×C22⋊Q82
#758313