Finite Group Databasebeta

← #13126949

Subgroups — #13126949

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719257C211yesmaximal, characteristic
2#11719248C211yesmaximal, characteristic, complemented
3C13×#435C211yesmaximal, characteristic, complemented
4#11718798C211yesmaximal, characteristic, complemented
5#11718794C211yesmaximal, characteristic, complemented
6#11718775C211yesmaximal, characteristic, complemented
7C2×#88056C211yesmaximal, characteristic, complemented
8#11718512C211yesmaximal, characteristic, complemented
9#11718506C211yesmaximal, characteristic, complemented
10#11718400C211yesmaximal, characteristic, complemented
11#11718396C211yesmaximal, characteristic, complemented
12#11718394C211yesmaximal, characteristic, complemented
13#11718382C211yesmaximal, characteristic, complemented
14#11718377C211yesmaximal, characteristic, complemented
15#11718375C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C22×C8×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88193—21no—
22D4×Dic13—21no—
23#88184C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26#88178C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic
29C2×Dic52C2211yescharacteristic
30C2×Dic52C2211yescharacteristic
31C2×#6095C2211yescharacteristic
32#88150—21no—
33#88144—21no—
34#88139—21no—
35#88135—21no—
36#88132—21no—
37#88132—21no—
38#88129C2211yescharacteristic
39#88123C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45C13×#97C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88057C2211yescharacteristic
50#88057C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C2×D4×C13D411yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67#6127—22no—
68#6127—41no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×Dic26—22no—
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×Dic26—41no—
75C2×Dic26C2311yescharacteristic
76C2×Dic26C2311yescharacteristic
77C2×Dic26C2311yescharacteristic
78C13×M16—41no—
79C2×C8×C13—41no—
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C2×C8×C13C2311yescharacteristic
84C13×C4⋊C4D411yescharacteristic
85C13×C22⋊C4D411yescharacteristic
86C13×C22⋊C4D411yescharacteristic
87C42×C13C2311yescharacteristic
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108Dic52—22no—
109Dic52—41no—
110#6095—41no—
111#3316—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115D4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C22⋊D13—42no—
126C22⋊D13—42no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—42no—
135C2×Dic13—81no—
136C2×Dic13—81no—
137D52—21no—
138D52—21no—
139C4×D13—42no—
140Dic26—21no—
141Dic26—21no—
142Dic26—21no—
143Dic26—21no—
144Dic26—21no—
145Dic26—42no—
146Dic26—81no—
147Dic26#4112yes—
148C8×C13—21no—
149C8×C13—21no—
150C8×C13—21no—
151C8×C13—21no—
152#554—131no—
153#548—131no—
154#489—131no—
155#483—131no—
156#481—131no—
157#475—131no—
158#470—131no—
159#465—131no—
160#464—131no—
161#452—131no—
162#451—131no—
163#441—131no—
164#435D1311yescharacteristic, complemented
165#417—131no—
166C2×#103—131no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13#13712yes—
173C22×C13C22×D411yescharacteristic
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13C2×#4111yescharacteristic
182C4×C13H(5,𝔽2)11yescharacteristic
183Dic13—22no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190C2×#41—131no—
191C22×Q8—131no—
192C2×Q16—131no—
193C2×Q16—131no—
194C2×SD16—131no—
195C2×M16C2×D1311yescharacteristic
196C22×C8C2×D1311yescharacteristic
197C4⋊Q8—131no—
198#125—261no—
199#124—131no—
200#124—261no—
201C22⋊Q8—131no—
202C22⋊Q8—131no—
203C22⋊Q8—131no—
204C22⋊Q8—261no—
205C22⋊Q8—261no—
206C22⋊Q8—261no—
207#121—131no—
208#121—261no—
209C4×Q8—131no—
210C4×Q8—131no—
211C4×D4—261no—
212C4×D4—261no—
213C4×D4C2×D1311yescharacteristic
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216#106—131no—
217#106—131no—
218#106—131no—
219C4⋊C8C2×D1311yescharacteristic
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#102—131no—
228#102—131no—
229#102—131no—
230C22⋊C8C2×D1311yescharacteristic
231C22⋊C8C2×D1311yescharacteristic
232#97C2×D1311yescharacteristic
233C2×C13—22no—
234C2×C13—41no—
235C2×C13#54611yescharacteristic
236C2×C13C2×#13711yescharacteristic
237C2×C13#57711yescharacteristic
238D13—81no—
239#41—262no—
240#41—521no—
241C2×Q8—131no—
242C2×Q8—131no—
243C2×Q8—131no—
244C2×Q8—262no—
245C2×Q8—261no—
246C2×Q8—261no—
247C2×Q8—521no—
248C2×D4—131no—
249C2×D4—261no—
250C2×D4—261no—
251C2×D4D5211yescharacteristic
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4C22×D1311yescharacteristic
257C22×C4C22×D1311yescharacteristic
258Q16—262no—
259Q16—521no—
260SD16—521no—
261M16—41no—
262C2×C8—41no—
263C2×C8C22×D1311yescharacteristic
264C2×C8C22×D1311yescharacteristic
265C2×C8C22×D1311yescharacteristic
266C2×C8C22×D1311yescharacteristic
267C4⋊C4—131no—
268C4⋊C4—131no—
269C4⋊C4—131no—
270C4⋊C4—131no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4D5211yescharacteristic
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4D5211yescharacteristic
287C22⋊C4D5211yescharacteristic
288C42—261no—
289C42—261no—
290C42C22×D1311yescharacteristic
291C13#331611yescharacteristic, complemented, Sylow
292C23—261no—
293C23C2×D5211yescharacteristic
294C23C2×D5211yescharacteristic
295Q8—132no—
296Q8—261no—
297Q8—261no—
298Q8—261no—
299Q8—261no—
300Q8—261no—
301Q8—522no—
302Q8—1041no—
303D4—22no—
304D4—261no—
305D4—261no—
306D4—522no—
307D4—522no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4C2×D5211yescharacteristic
324C2×C4C2×D5211yescharacteristic
325C2×C4C2×D5211yescharacteristic
326C2×C4C2×D5211yescharacteristic
327C2×C4C23×D1311yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—521no—
338C22—521no—
339C22—521no—
340C22#8816312yes—
341C22C22×D5211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—262no—
347C4—521no—
348C4—521no—
349C4—521no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4#8825111yescharacteristic
354C4#41×D1311yescharacteristic
355C2—22no—
356C2—41no—
357C2—1041no—
358C2#1171925911yescharacteristic
359C2C2×#8816311yescharacteristic
360C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
prime radical#11719257C2
hypercenter#435D13
hypocenterC13#3316
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #11719248C2semidirect
3. C13×#435C2semidirect
4. #11718798C2semidirect
5. #11718794C2semidirect
6. #11718775C2semidirect
7. C2×#88056C2semidirect
8. #11718512C2semidirect
9. #11718506C2semidirect
10. #11718400C2semidirect
11. #11718396C2semidirect
12. #11718394C2semidirect
13. #11718382C2semidirect
14. #11718377C2semidirect
15. #11718375C2semidirect
164. #435D13semidirect
291. C13#3316semidirect

Maximal subgroups

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

subgroupindex
#117192572
#117192482
C13×#4352
#117187982
#117187942
#117187752
C2×#880562
#117185122
#117185062
#117184002
#117183962
#117183942
#117183822
#117183772
#117183752
#331613