Finite Group Databasebeta

← #13126940

Subgroups — #13126940

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#11719536C211yesmaximal, characteristic
2#11719340C211yesmaximal, characteristic, complemented
3C13×#452C211yesmaximal, characteristic, complemented
4#11718893C211yesmaximal, characteristic, complemented
5#11718847C211yesmaximal, characteristic, complemented
6#11718845C211yesmaximal, characteristic, complemented
7#11718832C211yesmaximal, characteristic, complemented
8#11718827C211yesmaximal, characteristic, complemented
9#11718713C211yesmaximal, characteristic, complemented
10D13×#103C211yesmaximal, characteristic, complemented
11#11718452C211yesmaximal, characteristic, complemented
12#11718438C211yesmaximal, characteristic, complemented
13#11718426C211yesmaximal, characteristic, complemented
14#11718389C211yesmaximal, characteristic, complemented
15#11718382C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21#88200C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25#88192—21no—
26#88192C2211yescharacteristic
27#88190—21no—
28#88190C2211yescharacteristic
29C4×C22⋊D13—21no—
30C4×C22⋊D13C2211yescharacteristic
31C2×C4⋊Dic13C2211yescharacteristic
32#88178—21no—
33#88178C2211yescharacteristic
34C2×#6099C2211yescharacteristic
35C2×C8×D13C2211yescharacteristic
36#88151—21no—
37C4⋊C4×D13C2211yescharacteristic
38#88143—21no—
39#88142C2211yescharacteristic
40#88135—21no—
41#88132—21no—
42C13×#103C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88060C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88055C2211yescharacteristic
56#88054C2211yescharacteristic
57#88050C2211yescharacteristic
58#88048C2211yescharacteristic
59C13×#41—22no—
60C13×#41—41no—
61C2×Q8×C13C2311yescharacteristic
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13D411yescharacteristic
69C22×Dic13—21no—
70Q8×D13—22no—
71Q8×D13—41no—
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13C2311yescharacteristic
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26C2311yescharacteristic
78C13×Q16—22no—
79C13×SD16—41no—
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13D411yescharacteristic
90#6107—41no—
91#6103—21no—
92#6103D411yescharacteristic
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107#6099—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C8×D13—41no—
111#3316—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13#4112yes—
119D4×C13—21no—
120D4×C13—21no—
121D4×C13—42no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—42no—
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2411yescharacteristic
130C22⋊D13—22no—
131C22⋊D13—42no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—81no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140C4×D13—21no—
141C4×D13—21no—
142C4×D13—42no—
143C4×D13—81no—
144Dic26—21no—
145Dic26—21no—
146Dic26—42no—
147Dic26—81no—
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#475—131no—
158#470—131no—
159#465—131no—
160#464—131no—
161#452D1311yescharacteristic, complemented
162#451—131no—
163#441—131no—
164#435—131no—
165#417—131no—
166C2×#103—131no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13C22×D411yescharacteristic
174C2×D13—21no—
175C2×D13—21no—
176C2×D13#13712yes—
177C4×C13—22no—
178C4×C13—21no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13C2×#4111yescharacteristic
182C4×C13H(5,𝔽2)11yescharacteristic
183Dic13—21no—
184Dic13—21no—
185Dic13—21no—
186Dic13—41no—
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190C2×#41C2×D1311yescharacteristic
191C22×Q8—131no—
192C2×Q16—131no—
193C2×Q16C2×D1311yescharacteristic
194C2×SD16C2×D1311yescharacteristic
195C2×M16—131no—
196C22×C8—131no—
197C4⋊Q8—131no—
198#125—261no—
199#124—131no—
200#124—261no—
201C22⋊Q8—131no—
202C22⋊Q8—131no—
203C22⋊Q8—261no—
204C22⋊Q8—261no—
205C22⋊Q8—261no—
206C22⋊Q8C2×D1311yescharacteristic
207#121—131no—
208#121—261no—
209C4×Q8—131no—
210C4×Q8—131no—
211C4×D4—131no—
212C4×D4—261no—
213C4×D4—261no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216#106—131no—
217#106—131no—
218#106—131no—
219C4⋊C8—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103C2×D1311yescharacteristic
227#102—131no—
228#102—131no—
229#102C2×D1311yescharacteristic
230C22⋊C8—131no—
231C22⋊C8C2×D1311yescharacteristic
232#97—131no—
233C2×C13—41no—
234C2×C13—81no—
235C2×C13#54611yescharacteristic
236C2×C13C2×#13711yescharacteristic
237C2×C13#57711yescharacteristic
238D13—22no—
239#41—22no—
240#41—41no—
241C2×Q8—131no—
242C2×Q8—261no—
243C2×Q8—261no—
244C2×Q8—262no—
245C2×Q8—521no—
246C2×Q8C22×D1311yescharacteristic
247C2×Q8C22×D1311yescharacteristic
248C2×D4—21no—
249C2×D4—131no—
250C2×D4—261no—
251C2×D4C22×D1311yescharacteristic
252C22×C4—21no—
253C22×C4—131no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4C22×D1311yescharacteristic
258Q16—22no—
259Q16—521no—
260SD16—41no—
261M16—521no—
262C2×C8—131no—
263C2×C8—131no—
264C2×C8—521no—
265C2×C8C22×D1311yescharacteristic
266C2×C8C22×D1311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—131no—
269C4⋊C4—131no—
270C4⋊C4—131no—
271C4⋊C4—131no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4C22×D1311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—131no—
282C22⋊C4—131no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C42—131no—
289C42—261no—
290C42—261no—
291C13#331611yescharacteristic, complemented, Sylow
292C23—21no—
293C23—131no—
294C23D4×D1311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—261no—
299Q8—261no—
300Q8—522no—
301Q8—1041no—
302Q8#612912yes—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—262no—
307D4—522no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—131no—
315C2×C4—131no—
316C2×C4—131no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—522no—
324C2×C4—1041no—
325C2×C4—1041no—
326C2×C4D4×D1311yescharacteristic
327C2×C4C23×D1311yescharacteristic
328C8—21no—
329C8—21no—
330C8—261no—
331C8—261no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—132no—
339C22—261no—
340C22—261no—
341C22C2×D4×D1311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—261no—
347C4—261no—
348C4—261no—
349C4—521no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4C2×#612911yescharacteristic
354C4#8825111yescharacteristic
355C2—41no—
356C2—81no—
357C2—262no—
358C2#1171929611yescharacteristic
359C2#1171947511yescharacteristic
360C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#452C2
socleC22×C13C22×D4
prime radical#11719536C2
hypercenter#452D13
hypocenterC13#3316
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #11719340C2semidirect
3. C13×#452C2semidirect
4. #11718893C2semidirect
5. #11718847C2semidirect
6. #11718845C2semidirect
7. #11718832C2semidirect
8. #11718827C2semidirect
9. #11718713C2semidirect
10. D13×#103C2semidirect
11. #11718452C2semidirect
12. #11718438C2semidirect
13. #11718426C2semidirect
14. #11718389C2semidirect
15. #11718382C2semidirect
161. #452D13semidirect
291. C13#3316semidirect

Maximal subgroups

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

subgroupindex
#117195362
#117193402
C13×#4522
#117188932
#117188472
#117188452
#117188322
#117188272
#117187132
D13×#1032
#117184522
#117184382
#117184262
#117183892
#117183822
#331613