Finite Group Databasebeta

← #13126944

Subgroups — #13126944

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#11719435C211yesmaximal, characteristic, complemented
2#11719281C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718691C211yesmaximal, characteristic, complemented
6#11718529C211yesmaximal, characteristic, complemented
7#11718525C211yesmaximal, characteristic, complemented
8#11718524C211yesmaximal, characteristic, complemented
9#11718523C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718497C211yesmaximal, characteristic, complemented
12#11718471C211yesmaximal, characteristic, complemented
13#11718469C211yesmaximal, characteristic, complemented
14#11718464C211yesmaximal, characteristic, complemented
15D13×#103C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20#88200—21no—
21#88200—21no—
22C2×#6107C2211yescharacteristic
23C2×Dic52C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25C2×#6094C2211yescharacteristic
26C2×C8×D13C2211yescharacteristic
27#88151—21no—
28#88151C2211yescharacteristic
29#88151C2211yescharacteristic
30#88151C2211yescharacteristic
31#88149—21no—
32#88149C2211yescharacteristic
33#88147—21no—
34C4⋊C4×D13C2211yescharacteristic
35C4⋊C4×D13C2211yescharacteristic
36#88144—21no—
37#88129—21no—
38#88129C2211yescharacteristic
39C4×D52—21no—
40C4×D52C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×C4⋊C8C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C13×#103C2211yescharacteristic
47#88075C2211yescharacteristic
48#88061C2211yescharacteristic
49#88060C2211yescharacteristic
50#88060C2211yescharacteristic
51#88056C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61#6131—22no—
62#6131—41no—
63Q8×D13—22no—
64Q8×D13—41no—
65C2×D52—21no—
66C2×D52—21no—
67C2×D52D411yescharacteristic
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×C4×D13C2311yescharacteristic
75C2×Dic26—21no—
76C2×Dic26C2311yescharacteristic
77C2×Dic26C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C42×C13—21no—
86C42×C13C2311yescharacteristic
87#6107—22no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103D411yescharacteristic
95#6103D411yescharacteristic
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13D411yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107Dic52—41no—
108#6095—41no—
109#6094—41no—
110C8×D13—41no—
111#3316—131nomaximal, Sylow
112C22×D13—21no—
113C22×D13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—81no—
117Q8×C13#4112yes—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130D52—22no—
131D52—21no—
132D52—21no—
133D52—42no—
134D52—42no—
135C4×D13—21no—
136C4×D13—21no—
137C4×D13—21no—
138C4×D13—21no—
139C4×D13—42no—
140C4×D13—42no—
141C4×D13—81no—
142C4×D13—81no—
143Dic26—21no—
144Dic26—21no—
145Dic26—21no—
146Dic26—21no—
147Dic26—42no—
148C8×C13—21no—
149C8×C13—21no—
150#1055—21no—
151#1055—21no—
152#554—131no—
153#548—131no—
154#489—131no—
155#483—131no—
156#481—131no—
157#475D1311yescharacteristic, complemented
158#470—131no—
159#465—131no—
160#464—131no—
161#452—131no—
162#451—131no—
163#441—131no—
164#435—131no—
165#417—131no—
166C2×#103—131no—
167C22×C13C22×D411yescharacteristic
168C2×D13—21no—
169C2×D13—21no—
170C2×D13—21no—
171C2×D13—21no—
172C2×D13—21no—
173C2×D13—41no—
174C2×D13—41no—
175C2×D13—41no—
176C2×D13#13712yes—
177C4×C13—22no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13C2×#4111yescharacteristic
184C4×C13H(5,𝔽2)11yescharacteristic
185Dic13—21no—
186Dic13—21no—
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190C2×#41—131no—
191C22×Q8—131no—
192C2×Q16—131no—
193C2×Q16—131no—
194C2×SD16—131no—
195C2×M16—131no—
196C22×C8—131no—
197C4⋊Q8C2×D1311yescharacteristic
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×Q8C2×D1311yescharacteristic
211C4×D4—131no—
212C4×D4—261no—
213C4×D4—261no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216#106—131no—
217#106C2×D1311yescharacteristic
218#106C2×D1311yescharacteristic
219C4⋊C8C2×D1311yescharacteristic
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103C2×D1311yescharacteristic
226#103C2×D1311yescharacteristic
227#102—131no—
228#102—131no—
229#102—131no—
230C22⋊C8—131no—
231C22⋊C8—131no—
232#97—131no—
233C2×C13#54611yescharacteristic
234C2×C13C2×#13711yescharacteristic
235C2×C13#57711yescharacteristic
236D13—22no—
237D13—41no—
238D13—81no—
239#41—262no—
240#41—521no—
241C2×Q8—21no—
242C2×Q8—131no—
243C2×Q8—131no—
244C2×Q8—261no—
245C2×Q8—262no—
246C2×Q8—521no—
247C2×Q8C22×D1311yescharacteristic
248C2×D4—131no—
249C2×D4—131no—
250C2×D4—261no—
251C2×D4—261no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258Q16—262no—
259Q16—521no—
260SD16—521no—
261M16—521no—
262C2×C8—131no—
263C2×C8—131no—
264C2×C8—521no—
265C2×C8C22×D1311yescharacteristic
266C2×C8C22×D1311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—21no—
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⋊C4C22×D1311yescharacteristic
278C4⋊C4C22×D1311yescharacteristic
279C4⋊C4C22×D1311yescharacteristic
280C22⋊C4—131no—
281C22⋊C4—131no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C42—21no—
289C42—261no—
290C42C22×D1311yescharacteristic
291C13#331611yescharacteristic, complemented, Sylow
292C23—131no—
293C23—131no—
294C23—261no—
295Q8—21no—
296Q8—81no—
297Q8—261no—
298Q8—261no—
299Q8—261no—
300Q8—261no—
301Q8—522no—
302Q8#613112yes—
303D4—262no—
304D4—261no—
305D4—261no—
306D4—522no—
307D4—522no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—522no—
322C2×C4—522no—
323C2×C4—1041no—
324C2×C4—1041no—
325C2×C4D4×D1311yescharacteristic
326C2×C4D4×D1311yescharacteristic
327C2×C4C23×D1311yescharacteristic
328C8—21no—
329C8—21no—
330C8—261no—
331C8—261no—
332C22—132no—
333C22—261no—
334C22—261no—
335C22—261no—
336C22—261no—
337C22—261no—
338C22—521no—
339C22—521no—
340C22—521no—
341C22C2×D4×D1311yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—261no—
349C4—261no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4C2×#613111yescharacteristic
354C4#8825611yescharacteristic
355C2—262no—
356C2—521no—
357C2—1041no—
358C2#1171933511yescharacteristic
359C2#1171946711yescharacteristic
360C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radical#11719281C2
hypercenter#475D13
hypocenterC13#3316
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
3. C13×#475C2semidirect
4. #11718750C2semidirect
5. #11718691C2semidirect
6. #11718529C2semidirect
7. #11718525C2semidirect
8. #11718524C2semidirect
9. #11718523C2semidirect
10. #11718506C2semidirect
11. #11718497C2semidirect
12. #11718471C2semidirect
13. #11718469C2semidirect
14. #11718464C2semidirect
15. D13×#103C2semidirect
157. #475D13semidirect
291. C13#3316semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117192812
C13×#4752
#117187502
#117186912
#117185292
#117185252
#117185242
#117185232
#117185062
#117184972
#117184712
#117184692
#117184642
D13×#1032
#331613