Finite Group Databasebeta

← #15751029

Subgroups — #15751029

Order 3328.

504 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114904C211yesmaximal, characteristic
2#13114816C211yesmaximal, 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—42no—
53C22⋊#1055—42no—
54C4⋊#1055—42no—
55#7600—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—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
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×C13—41no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C2×C812yes—
78C22×C4×C13M1612yes—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C13×C4⋊C4—24no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4C2×C812yes—
90C13×C22⋊C4—24no—
91C13×C22⋊C4—42no—
92C42×C13—22no—
93C42×C13—22no—
94C42×C13—41no—
95C42×C13—41no—
96C42×C13—42no—
97C42×C13—42no—
98C2×#1055—42no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#1055—42no—
102C2×#1055—42no—
103C2×#1055—42no—
104C4×C22⋊Q8D1311yescharacteristic
105#1817—131no—
106#1797—131no—
107#1272—132no—
108#1271—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13C22⋊C812yes—
116C23×C13C2×C22⋊C411yescharacteristic
117Q8×C13—42no—
118Q8×C13—42no—
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—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—44no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
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×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13C22⋊C812yes—
150C2×C4×C13#9912yes—
151C2×C4×C13C22×C811yescharacteristic
152C2×C4×C13C2×M1611yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C13#13711yescharacteristic
155C2×C4×C13#13712yes—
156#1055—82no—
157#1055—82no—
158C2×C22⋊Q8Dic1311yescharacteristic
159C2×C4×Q8Dic1311yescharacteristic
160C22×C42C2×D1311yescharacteristic
161C2×C4⋊C8—261no—
162C2×C22⋊C8—261no—
163C2×C22⋊C8—261no—
164#391C2×D1311yescharacteristic
165#389C2×D1311yescharacteristic
166#387—21no—
167#385—21no—
168#380Dic1311yescharacteristic
169C4×C4⋊C4—21no—
170C4×C4⋊C4Dic1311yescharacteristic
171C4×C22⋊C4—21no—
172#336—132no—
173#336—132no—
174#336—261no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13C2×C22⋊C811yescharacteristic
183C22×C13C2×#9911yescharacteristic
184C22×C13#41311yescharacteristic
185C22×C13#41711yescharacteristic
186C22×C13#41911yescharacteristic
187C22×C13#42111yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—22no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—42no—
197C4×C13—42no—
198C4×C13—41no—
199C4×C13—81no—
200C4×C13—81no—
201C22×Q8C2×Dic1311yescharacteristic
202C23×C4C2×Dic1311yescharacteristic
203C23×C4C22⋊D1311yescharacteristic
204C23×C4C22⋊D1311yescharacteristic
205C22×C8—262no—
206C22×C8—262no—
207C22⋊Q8—22no—
208C22⋊Q8#105514yescomplemented
209C4×Q8—42no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×Dic1311yescharacteristic
214C2×C4⋊C4C2×Dic1311yescharacteristic
215C2×C4⋊C4C2×Dic1311yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—42no—
221C2×C42C2×Dic1311yescharacteristic
222C2×C42C22⋊D1311yescharacteristic
223C2×C42C22⋊D1311yescharacteristic
224C2×C42C22×D1311yescharacteristic
225C4⋊C8—522no—
226C22⋊C8—522no—
227C22⋊C8—522no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233C2×C13—42no—
234C2×C13#145911yescharacteristic
235C2×C13#147711yescharacteristic
236C2×C13#147911yescharacteristic
237C2×C13#151111yescharacteristic
238C2×C13#151311yescharacteristic
239C2×C13#153511yescharacteristic
240C2×C13#155911yescharacteristic
241C24C22⋊Dic1311yescharacteristic
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8C2×#105512yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4C2×#105512yes—
260C22×C4#609912yes—
261C22×C4C22⋊Dic1311yescharacteristic
262C22×C4C22⋊Dic1311yescharacteristic
263C22×C4C22⋊Dic1311yescharacteristic
264C22×C4C22×Dic1311yescharacteristic
265C22×C4C2×C22⋊D1311yescharacteristic
266C22×C4C2×C22⋊D1311yescharacteristic
267C2×C8—522no—
268C2×C8—522no—
269C2×C8—522no—
270C2×C8—522no—
271C2×C8—522no—
272C2×C8—522no—
273C4⋊C4—24no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4C2×#105512yes—
281C22⋊C4—24no—
282C22⋊C4—42no—
283C42—22no—
284C42—22no—
285C42—41no—
286C42—41no—
287C42—42no—
288C42—42no—
289C13#760011yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23C22⋊#105512yes—
297C23C2×C22⋊Dic1311yescharacteristic
298Q8—42no—
299Q8—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4C22⋊#105512yes—
331C2×C4#8807412yes—
332C2×C4C22×#105511yescharacteristic
333C2×C4C2×#609911yescharacteristic
334C2×C4#8819612yes—
335C2×C4#8820311yescharacteristic
336C2×C4#8820511yescharacteristic
337C8—1042no—
338C8—1042no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C2×C22⋊#105511yescharacteristic
347C22C2×#8807411yescharacteristic
348C22#1171888611yescharacteristic
349C22#1171889311yescharacteristic
350C22#1171889711yescharacteristic
351C22#1171889711yescharacteristic
352C22#1171889811yescharacteristic
353C4—22no—
354C4—22no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—42no—
362C4—42no—
363C4—81no—
364C4—81no—
365C2—42no—
366C2#1311315411yescharacteristic
367C2#1311322311yescharacteristic
368C2#1311323111yescharacteristic
369C2#1311336911yescharacteristic
370C2#1311337911yescharacteristic
371C2#1311346711yescharacteristic
372C2#1311356611yescharacteristic
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#7600
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
208. C22⋊Q8#1055semidirect
289. C13#7600semidirect

Maximal subgroups

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

subgroupindex
#131149042
#131148162
#131126622
#131126592
C4×C13×C22⋊Q82
#760013