Finite Group Databasebeta

← #15751175

Subgroups — #15751175

Order 3328.

556 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114598C211yesmaximal, characteristic
2#13114530C211yesmaximal, characteristic
3#13112662C212yesmaximal, complemented
4#13112659C212yesmaximal, complemented
5C4×C13×C22⋊Q8C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C2×C4×Q8×C13C411yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C22×#6099—21no—
10C13×#391C2211yescharacteristic
11C13×#389C2211yescharacteristic
12C13×#387—21no—
13C13×#385—21no—
14C13×#380C411yescharacteristic
15C4×C13×C4⋊C4—21no—
16C4×C13×C4⋊C4C411yescharacteristic
17C4×C13×C22⋊C4—21no—
18C2×C22⋊#1055—21no—
19C2×#88043—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⋊Q8—22no—
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
45C2×#6099—24no—
46C2×#6099—42no—
47C2×#6099—42no—
48C22×#1055—22no—
49C22×#1055—22no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C22⋊#1055—24no—
56#88043—42no—
57#7634—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13M1612yescomplemented
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C13×C4⋊C4—24no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4M1612yescomplemented
92C13×C22⋊C4—24no—
93C13×C22⋊C4—42no—
94C42×C13—22no—
95C42×C13—22no—
96C42×C13—41no—
97C42×C13—41no—
98C42×C13—42no—
99C42×C13—42no—
100#6099—48no—
101C2×#1055—24no—
102C2×#1055—24no—
103C2×#1055—42no—
104C2×#1055—42no—
105C2×#1055—42no—
106C2×#1055—42no—
107C4×C22⋊Q8D1311yescharacteristic
108#1749—131no—
109#1728—131no—
110#1272—132no—
111#1271—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13#10412yes—
119C23×C13C2×C22⋊C411yescharacteristic
120Q8×C13—42no—
121Q8×C13—42no—
122C2×C4×C13—24no—
123C2×C4×C13—24no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—44no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
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×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13#9912yes—
153C2×C4×C13#10412yes—
154C2×C4×C13C2×M1611yescharacteristic
155C2×C4×C13C2×M1611yescharacteristic
156C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C13#13711yescharacteristic
158C2×C4×C13#13712yes—
159#1055—44no—
160#1055—44no—
161C22×M16—261no—
162C2×C22⋊Q8Dic1311yescharacteristic
163C2×C4×Q8Dic1311yescharacteristic
164C22×C42C2×D1311yescharacteristic
165C2×C22⋊C8—261no—
166C2×#97—261no—
167#391C2×D1311yescharacteristic
168#389C2×D1311yescharacteristic
169#387—21no—
170#385—21no—
171#380Dic1311yescharacteristic
172C4×C4⋊C4—21no—
173C4×C4⋊C4Dic1311yescharacteristic
174C4×C22⋊C4—21no—
175#336—132no—
176#336—132no—
177#336—261no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13#40711yescharacteristic
186C22×C13C2×#9911yescharacteristic
187C22×C13#41311yescharacteristic
188C22×C13#41711yescharacteristic
189C22×C13#41911yescharacteristic
190C22×C13C2×#10411yescharacteristic
191C22×C13C2×#10411yescharacteristic
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—22no—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—22no—
199C4×C13—41no—
200C4×C13—42no—
201C4×C13—42no—
202C4×C13—81no—
203C4×C13—81no—
204C22×Q8C2×Dic1311yescharacteristic
205C23×C4C2×Dic1311yescharacteristic
206C23×C4C22⋊D1311yescharacteristic
207C23×C4C22⋊D1311yescharacteristic
208C2×M16—264no—
209C2×M16—522no—
210C2×M16—522no—
211C22×C8—262no—
212C22×C8—262no—
213C22⋊Q8—22no—
214C22⋊Q8—22no—
215C4×Q8—42no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C2×Dic1311yescharacteristic
220C2×C4⋊C4C2×Dic1311yescharacteristic
221C2×C4⋊C4C2×Dic1311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—42no—
227C2×C42C2×Dic1311yescharacteristic
228C2×C42C22⋊D1311yescharacteristic
229C2×C42C22⋊D1311yescharacteristic
230C2×C42C22×D1311yescharacteristic
231C22⋊C8—264no—
232#97—522no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238C2×C13—42no—
239C2×C13#146511yescharacteristic
240C2×C13#148911yescharacteristic
241C2×C13#149111yescharacteristic
242C2×C13#150411yescharacteristic
243C2×C13#150811yescharacteristic
244C2×C13#152411yescharacteristic
245C2×C13#155911yescharacteristic
246C24C22⋊Dic1311yescharacteristic
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8#609912yescomplemented
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C22⋊Dic1311yescharacteristic
267C22×C4C22⋊Dic1311yescharacteristic
268C22×C4C22⋊Dic1311yescharacteristic
269C22×C4C22×Dic1311yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271C22×C4C2×C22⋊D1311yescharacteristic
272M16—528no—
273C2×C8—264no—
274C2×C8—264no—
275C2×C8—522no—
276C2×C8—522no—
277C2×C8—522no—
278C2×C8—522no—
279C4⋊C4—24no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4#609912yescomplemented
287C22⋊C4—24no—
288C22⋊C4—42no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—41no—
293C42—42no—
294C42—42no—
295C13#763411yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#8807712yes—
303C23C2×C22⋊Dic1311yescharacteristic
304Q8—42no—
305Q8—42no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4#8807412yes—
337C2×C4#8807712yes—
338C2×C4C2×#609911yescharacteristic
339C2×C4C2×#609911yescharacteristic
340C2×C4#8819612yes—
341C2×C4#8820311yescharacteristic
342C2×C4#8820511yescharacteristic
343C8—524no—
344C8—524no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22#1171886811yescharacteristic
353C22C2×#8807411yescharacteristic
354C22#1171888611yescharacteristic
355C22#1171889311yescharacteristic
356C22C2×#8807711yescharacteristic
357C22C2×#8807711yescharacteristic
358C22#1171889811yescharacteristic
359C4—22no—
360C4—22no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—41no—
367C4—42no—
368C4—42no—
369C4—81no—
370C4—81no—
371C2—42no—
372C2#1311317411yescharacteristic
373C2#1311327511yescharacteristic
374C2#1311328311yescharacteristic
375C2#1311334011yescharacteristic
376C2#1311335611yescharacteristic
377C2#1311342411yescharacteristic
378C2#1311356611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×C22⋊Q8C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenterC4×C22⋊Q8D13
hypocenterC13#7634
LCSG ▷ C22×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
62. C2×Q8×C13M16semidirect
91. C13×C4⋊C4M16semidirect
250. C2×Q8#6099semidirect
286. C4⋊C4#6099semidirect
295. C13#7634semidirect

Maximal subgroups

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

subgroupindex
#131145982
#131145302
#131126622
#131126592
C4×C13×C22⋊Q82
#763413