Finite Group Databasebeta

← #15845461

Subgroups — #15845461

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125350C211yesmaximal, characteristic, complemented
2#13124844C212yesmaximal
3#13114359C212yesmaximal, complemented
4#13114349C212yesmaximal, complemented
5#13114335C214yesmaximal, complemented
6#13113584C211yesmaximal, characteristic, complemented
7#13113494C212yesmaximal, complemented
8C2×C13×#436C211yesmaximal, characteristic
9C22×C13×M16—21no—
10C2×C4×D4×C13C2211yescharacteristic
11#11719175C2212yes—
12C13×#436—21no—
13C13×#436—21no—
14C13×#436C2212yes—
15C13×#436C2212yes—
16C2×C13×C4⋊C8C2211yescharacteristic
17C2×C13×C22⋊C8—21no—
18C2×C4×C8×C13C2211yescharacteristic
19#11718879—22no—
20#11718767—21no—
21#11718767—21no—
22#11718680C2214yes—
23C4×#6105—24no—
24#11718669C2214yes—
25#11718632—22no—
26#11718586C2212yes—
27#11718344—21no—
28#11718344—21no—
29#11718343C2211yescharacteristic, complemented
30#11718343C2211yescharacteristic, complemented
31#11718341C2212yescomplemented
32#11718078C2214yescomplemented
33#11718073C2214yescomplemented
34#11718050C2212yescomplemented
35#11718049C2212yescomplemented
36C22×D4×C13D411yescharacteristic
37C23×C4×C13—21no—
38C2×C13×M16—22no—
39C2×C13×M16—22no—
40C2×C13×M16—44no—
41C22×C8×C13—21no—
42C22×C8×C13D411yescharacteristic
43C22×C8×C13D411yescharacteristic
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13D412yes—
47C4×D4×C13C2312yes—
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C22⋊C4—21no—
50C2×C42×C13C2311yescharacteristic
51C2×#6105—24no—
52#88180—22no—
53#88178—22no—
54#88178—22no—
55#88124—22no—
56#88123C2312yes—
57#88123C2312yes—
58C4×Dic26—22no—
59C4×Dic26—22no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8C2312yes—
62C13×C22⋊C8—22no—
63C13×C22⋊C8—22no—
64C4×C8×C13D411yescharacteristic
65C4×C8×C13D411yescharacteristic
66C4×C8×C13C2311yescharacteristic
67C4×C8×C13C2311yescharacteristic
68#88072—24no—
69C22⋊#1055—22no—
70#88058—21no—
71#88058—21no—
72#88058—21no—
73#88058—21no—
74#88057—22no—
75#88057—22no—
76#88050—24no—
77#88048—24no—
78C4⋊#1055C2314yes—
79C4×#1055—22no—
80#19137—131nomaximal, Sylow
81C24×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—42no—
84C2×D4×C13C2×D412yes—
85C22×C4×C13—21no—
86C22×C4×C13—22no—
87C22×C4×C13—22no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13#4111yescharacteristic
93C2×Dic26—22no—
94C2×Dic26—22no—
95C13×M16—44no—
96C13×M16—44no—
97C2×C8×C13—22no—
98C2×C8×C13—22no—
99C2×C8×C13—42no—
100C2×C8×C13SD1614yescomplemented
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13C2×D411yescharacteristic
104C2×C8×C13C2×D411yescharacteristic
105C13×C4⋊C4—21no—
106C13×C4⋊C4C2×D412yes—
107C13×C22⋊C4—22no—
108C13×C22⋊C4—22no—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13#4111yescharacteristic
112C42×C13C2411yescharacteristic
113C22⋊Dic13—42no—
114#6105—48no—
115C4⋊Dic13—22no—
116C4⋊Dic13—22no—
117C4⋊Dic13—22no—
118C4⋊Dic13—22no—
119#6101—42no—
120#6101—42no—
121C4×Dic13—42no—
122C2×#1055—24no—
123#3160—131no—
124#3101—132no—
125C2×#436D1311yescharacteristic
126#1695—132no—
127#1693—132no—
128#1691—134no—
129#1564—131no—
130#1542—132no—
131C23×C13—22no—
132C23×C13—42no—
133C23×C13—42no—
134C23×C13—42no—
135C23×C13#12111yescharacteristic
136D4×C13—24no—
137D4×C13—42no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—44no—
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13C2×SD1612yes—
149C2×C4×C13#13712yes—
150C2×C4×C13C22×D411yescharacteristic
151C2×C4×C13C22×D411yescharacteristic
152C2×C4×C13C2×#4111yescharacteristic
153C2×Dic13—42no—
154C2×Dic13—42no—
155Dic26—44no—
156Dic26—82no—
157C8×C13—21no—
158C8×C13—21no—
159C8×C13—42no—
160C8×C13C2×SD1612yes—
161C8×C13C2×SD1612yes—
162#1055—44no—
163C22×M16—21no—
164#533—132no—
165C2×C4×D4C2×D1311yescharacteristic
166#500—131no—
167#500—131no—
168#499—261no—
169#499—261no—
170#498—132no—
171#483—262no—
172#476—134no—
173#461—134no—
174#450—262no—
175C4×SD16—264no—
176#436—21no—
177#436—21no—
178#436C2×D1312yes—
179#436C2×D1312yes—
180#431—132no—
181#427—261no—
182#427—261no—
183C2×C4⋊C8C2×D1311yescharacteristic
184C2×C22⋊C8—21no—
185C2×C4×C8C2×D1311yescharacteristic
186#335—132no—
187#334—132no—
188#333—134no—
189#332—134no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—84no—
196C22×C13#46112yes—
197C22×C13C2×#12111yescharacteristic
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—42no—
202C4×C13#46112yes—
203C4×C13C22×SD1611yescharacteristic
204C4×C13C2×#13711yescharacteristic
205C4×C13#57512yes—
206Dic13—82no—
207Dic13—82no—
208C22×D4D5211yescharacteristic
209C23×C4—21no—
210C2×SD16—264no—
211C2×M16—22no—
212C2×M16—22no—
213C2×M16—44no—
214C22×C8—21no—
215C22×C8C22⋊D1311yescharacteristic
216C22×C8C22⋊D1311yescharacteristic
217C4⋊Q8—132no—
218C4⋊Q8—132no—
219#125—262no—
220C22⋊Q8—262no—
221C22⋊Q8—262no—
222C4×Q8—262no—
223C4×Q8—262no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4D5212yes—
227C4×D4C22×D1312yes—
228#117—262no—
229C2×C4⋊C4D5211yescharacteristic
230C2×C22⋊C4—21no—
231C2×C42C22×D1311yescharacteristic
232#107—261no—
233#107—261no—
234#107—261no—
235#107—261no—
236#106—262no—
237#106—262no—
238#106—264no—
239C4⋊C8—21no—
240C4⋊C8—134no—
241C4⋊C8C22×D1312yes—
242#103—264no—
243#102—264no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246C22⋊C8—262no—
247C4×C8—262no—
248C4×C8C22⋊D1311yescharacteristic
249C4×C8C22⋊D1311yescharacteristic
250C4×C8C22×D1311yescharacteristic
251C4×C8C22×D1311yescharacteristic
252C2×C13—22no—
253C2×C13—82no—
254C2×C13C2×#46111yescharacteristic
255C2×C13#305411yescharacteristic
256C2×C13#306711yescharacteristic
257C24—21no—
258C2×Q8—262no—
259C2×Q8—262no—
260C2×D4—21no—
261C2×D4—42no—
262C2×D4C2×D5212yes—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4C2×D5211yescharacteristic
269C22×C4#612711yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271SD16—528no—
272M16—44no—
273M16—44no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—42no—
277C2×C8—264no—
278C2×C8#610514yescomplemented
279C2×C8C2×C22⋊D1311yescharacteristic
280C2×C8C2×C22⋊D1311yescharacteristic
281C2×C8C2×C22⋊D1311yescharacteristic
282C2×C8C2×C22⋊D1311yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—262no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—262no—
288C4⋊C4—522no—
289C4⋊C4—522no—
290C4⋊C4C2×D5212yes—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—522no—
294C42—522no—
295C42C2×D5211yescharacteristic
296C42#612711yescharacteristic
297C42C2×C22⋊D1311yescharacteristic
298C42C23×D1311yescharacteristic
299C13#1913711yescharacteristic, complemented, Sylow
300C23—22no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23#8818411yescharacteristic
305Q8—524no—
306Q8—1042no—
307D4—24no—
308D4—42no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—522no—
317C2×C4—522no—
318C2×C4#8818411yescharacteristic
319C2×C4#8818411yescharacteristic
320C2×C4#8818411yescharacteristic
321C2×C4C2×#610512yes—
322C2×C4#8820512yes—
323C2×C4C22×D5211yescharacteristic
324C2×C4C2×#612711yescharacteristic
325C2×C4C22×C22⋊D1311yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8—524no—
330C8C2×#610512yes—
331C8C2×#610512yes—
332C22—21no—
333C22—21no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—84no—
338C22#1171868012yes—
339C22C2×#8818411yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—42no—
344C4—1042no—
345C4—1042no—
346C4#1171868012yes—
347C4#1171945312yes—
348C4C22×#610511yescharacteristic
349C4C2×#8820511yescharacteristic
350C2—22no—
351C2—82no—
352C2C2×#1171868011yescharacteristic
353C2#1312444511yescharacteristic
354C2#1312455611yescharacteristic
subgroupG/H
centerC2×C4#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#436C2
socleC22×C13C2×#121
prime radicalC22×D4×C13D4
hypercenterC2×#436D13
hypocenterC13#19137
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. #13125350C2semidirect
3. #13114359C2semidirect
4. #13114349C2semidirect
5. #13114335C2semidirect
6. #13113584C2semidirect
7. #13113494C2semidirect
29. #11718343C22semidirect
30. #11718343C22semidirect
31. #11718341C22semidirect
32. #11718078C22semidirect
33. #11718073C22semidirect
34. #11718050C22semidirect
35. #11718049C22semidirect
100. C2×C8×C13SD16semidirect
278. C2×C8#6105semidirect
299. C13#19137semidirect

Maximal subgroups

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

subgroupindex
#131253502
#131248442
#131143592
#131143492
#131143352
#131135842
#131134942
C2×C13×#4362
#1913713