Finite Group Databasebeta

← #13126886

Subgroups — #13126886

Order 1664.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719432C211yesmaximal, characteristic
2#11719399C211yesmaximal, characteristic
3C13×#491C211yesmaximal, characteristic, complemented
4#11718751C211yesmaximal, characteristic, complemented
5#11718724C211yesmaximal, characteristic, complemented
6#11718477C211yesmaximal, characteristic, complemented
7#11718476C211yesmaximal, characteristic, complemented
8#11718474C211yesmaximal, characteristic, complemented
9#11718469C211yesmaximal, characteristic, complemented
10#11718469C211yesmaximal, characteristic, complemented
11#11718466C211yesmaximal, characteristic, complemented
12#11718463C211yesmaximal, characteristic, complemented
13D13×#103C211yesmaximal, characteristic, complemented
14#11718377C211yesmaximal, characteristic, complemented
15#11718367C211yesmaximal, characteristic
16C2×Q8×D13C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C13×#125C2211yescharacteristic
20#88200C2211yescharacteristic
21#88200C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23C2×#6107C2211yescharacteristic
24C2×Dic52C2211yescharacteristic
25C2×#6094C2211yescharacteristic
26C2×C8×D13C2211yescharacteristic
27#88152—21no—
28#88151C2211yescharacteristic
29#88151C2211yescharacteristic
30#88150—21no—
31#88150—21no—
32#88148—21no—
33#88147—21no—
34#88146—21no—
35#88146C2211yescharacteristic
36C4⋊C4×D13C2211yescharacteristic
37#88144—21no—
38#88142—21no—
39C4×D52C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C13×#97C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88060C2211yescharacteristic
50#88060C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61Q8×D13—22no—
62Q8×D13—22no—
63Q8×D13—41no—
64Q8×D13—41no—
65C2×D52D411yescharacteristic
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13C2311yescharacteristic
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26C2311yescharacteristic
74C2×Dic26C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C42×C13C2311yescharacteristic
84#6107—41no—
85#6107—41no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103D411yescharacteristic
92#6103D411yescharacteristic
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13D411yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108Dic52—22no—
109#6094—41no—
110C8×D13—41no—
111#3312—131nomaximal, Sylow
112C22×D13C2×D411yescharacteristic
113C22×D13C2×D411yescharacteristic
114Q8×C13—21no—
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
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×Dic13—21no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131D52—22no—
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—21no—
136C4×D13—42no—
137C4×D13—42no—
138C4×D13—42no—
139Dic26—21no—
140Dic26—21no—
141Dic26—21no—
142Dic26—42no—
143Dic26—42no—
144Dic26#4112yes—
145C8×C13—21no—
146C8×C13—21no—
147#1055—21no—
148#1055—21no—
149#552—131no—
150D4×Q8—131no—
151#491D1311yescharacteristic, complemented
152#485—131no—
153#483—131no—
154#479—131no—
155#470—131no—
156#467—131no—
157#462—131no—
158#451—131no—
159#451—131no—
160#441—131no—
161#435—131no—
162#419—131no—
163C2×#103—131no—
164C22×C13C22×D411yescharacteristic
165C2×D13—21no—
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—21no—
169C2×D13—21no—
170C2×D13#13712yes—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13C2×#4111yescharacteristic
178C4×C13H(5,𝔽2)11yescharacteristic
179Dic13—22no—
180Dic13—21no—
181Dic13—21no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185C22×Q8—131no—
186C22×Q8—131no—
187C2×Q16—131no—
188C2×Q16—131no—
189C2×Q16—131no—
190C2×M16—131no—
191C22×C8—131no—
192C4⋊Q8—261no—
193C4⋊Q8C2×D1311yescharacteristic
194#126—261no—
195#125—261no—
196#125C2×D1311yescharacteristic
197#123—261no—
198C22⋊Q8—131no—
199C22⋊Q8—131no—
200C22⋊Q8—131no—
201C22⋊Q8—131no—
202C22⋊Q8—261no—
203C22⋊Q8—261no—
204C4×Q8—131no—
205C4×Q8—131no—
206C4×D4—131no—
207C4×D4—261no—
208#117—131no—
209#117—261no—
210C2×C4⋊C4—131no—
211#107—131no—
212#106—131no—
213#106—131no—
214C4⋊C8—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103C2×D1311yescharacteristic
222#103C2×D1311yescharacteristic
223#103C2×D1311yescharacteristic
224#103C2×D1311yescharacteristic
225C22⋊C8—131no—
226C22⋊C8—131no—
227#97C2×D1311yescharacteristic
228C2×C13#54611yescharacteristic
229C2×C13C2×#13711yescharacteristic
230C2×C13#57811yescharacteristic
231D13—22no—
232D13—41no—
233C2×Q8—131no—
234C2×Q8—131no—
235C2×Q8—261no—
236C2×Q8—261no—
237C2×Q8—262no—
238C2×Q8—262no—
239C2×Q8—521no—
240C2×Q8—521no—
241C2×Q8C22×D1311yescharacteristic
242C2×Q8C22×D1311yescharacteristic
243C2×D4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249Q16—262no—
250Q16—521no—
251Q16—521no—
252M16—521no—
253C2×C8—131no—
254C2×C8—131no—
255C2×C8—521no—
256C2×C8C22×D1311yescharacteristic
257C2×C8C22×D1311yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—131no—
263C4⋊C4—131no—
264C4⋊C4—131no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4C22×D1311yescharacteristic
273C4⋊C4C22×D1311yescharacteristic
274C22⋊C4—131no—
275C22⋊C4—131no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C42—261no—
282C42—261no—
283C42—261no—
284C42C22×D1311yescharacteristic
285C13#331211yescharacteristic, complemented, Sylow
286C23—131no—
287C23—131no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—132no—
293Q8—261no—
294Q8—261no—
295Q8—261no—
296Q8—522no—
297Q8—522no—
298D4—262no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4—522no—
316C2×C4D4×D1311yescharacteristic
317C2×C4D4×D1311yescharacteristic
318C2×C4C23×D1311yescharacteristic
319C8—21no—
320C8—21no—
321C8—261no—
322C8—261no—
323C22—132no—
324C22—261no—
325C22—261no—
326C22—261no—
327C22—261no—
328C22—261no—
329C22C2×D4×D1311yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—261no—
337C4—261no—
338C4—262no—
339C4—521no—
340C4—521no—
341C4—521no—
342C4#41×D1311yescharacteristic
343C4#8825611yescharacteristic
344C2—262no—
345C2—521no—
346C2#1171938111yescharacteristic
347C2D13×#13711yescharacteristic
348C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#491C2
socleC22×C13C22×D4
prime radicalC2×D52D4
hypercenter#491D13
hypocenterC13#3312
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
3. C13×#491C2semidirect
4. #11718751C2semidirect
5. #11718724C2semidirect
6. #11718477C2semidirect
7. #11718476C2semidirect
8. #11718474C2semidirect
9. #11718469C2semidirect
10. #11718469C2semidirect
11. #11718466C2semidirect
12. #11718463C2semidirect
13. D13×#103C2semidirect
14. #11718377C2semidirect
151. #491D13semidirect
285. C13#3312semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117193992
C13×#4912
#117187512
#117187242
#117184772
#117184762
#117184742
#117184692
#117184662
#117184632
D13×#1032
#117183772
#117183672
#331213