Finite Group Databasebeta

← #13127114

Subgroups — #13127114

Order 1664.

374 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#11719346C211yesmaximal, characteristic
2#11719337C211yesmaximal, characteristic
3C13×#470C211yesmaximal, characteristic, complemented
4#11718847C211yesmaximal, characteristic, complemented
5#11718843C211yesmaximal, characteristic, complemented
6#11718789C211yesmaximal, characteristic
7#11718781C211yesmaximal, characteristic, complemented
8#11718711C211yesmaximal, characteristic, complemented
9#11718706C211yesmaximal, characteristic, complemented
10#11718528C211yesmaximal, characteristic, complemented
11#11718515C211yesmaximal, characteristic, complemented
12#11718477C211yesmaximal, characteristic, complemented
13#11718463C211yesmaximal, characteristic, complemented
14#11718453C211yesmaximal, characteristic, complemented
15#11718451C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic
19C2×C13×M16C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22#88200C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24#88198C2211yescharacteristic
25C2×#6107C2211yescharacteristic
26C2×#6107C2211yescharacteristic
27C4×C22⋊D13C2211yescharacteristic
28#88180C2211yescharacteristic
29C2×#6094C2211yescharacteristic
30#88152—21no—
31#88151C2211yescharacteristic
32#88150—21no—
33#88146C2211yescharacteristic
34#88142—21no—
35#88142C2211yescharacteristic
36#88141—21no—
37#88141C2211yescharacteristic
38#88139—21no—
39#88135—21no—
40#88133—21no—
41#88132—21no—
42C13×#106C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88054C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13D411yescharacteristic
63C22×Dic13—21no—
64Q8×D13—22no—
65Q8×D13—41no—
66C2×C4×D13—21no—
67C2×C4×D13C2311yescharacteristic
68C2×Dic26—22no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—41no—
73C2×Dic26C2311yescharacteristic
74C2×Dic26C2311yescharacteristic
75C13×Q16—41no—
76C13×M16—41no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13D411yescharacteristic
87#6107—22no—
88#6107—41no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103D411yescharacteristic
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101D411yescharacteristic
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6094—41no—
111#3328—131nomaximal, Sylow
112C23×C13C2×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×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C22⋊D13—22no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—42no—
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C4×D13—21no—
136C4×D13—21no—
137C4×D13—42no—
138Dic26—21no—
139Dic26—21no—
140Dic26—21no—
141Dic26—42no—
142Dic26—42no—
143Dic26—42no—
144Dic26#4112yes—
145C8×C13—21no—
146C8×C13—21no—
147#1055—21no—
148#1055—21no—
149#556—131no—
150D4×Q8—131no—
151#487—131no—
152#485—131no—
153#485—131no—
154#475—131no—
155#470—131no—
156#470D1311yescharacteristic, complemented
157#462—131no—
158#451—131no—
159#451—131no—
160C4×Q16—131no—
161#436—131no—
162#419—131no—
163#419—131no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13C22×D411yescharacteristic
168C2×D13—21no—
169C2×D13—21no—
170C2×D13—21no—
171C4×C13—21no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13C2×#4111yescharacteristic
177C4×C13H(5,𝔽2)11yescharacteristic
178Dic13—22no—
179Dic13—21no—
180Dic13—21no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184Dic13#13712yes—
185C22×Q8—131no—
186C22×Q8—131no—
187C2×Q16—131no—
188C2×Q16—131no—
189C2×Q16C2×D1311yescharacteristic
190C2×M16—131no—
191C2×M16C2×D1311yescharacteristic
192C4⋊Q8—131no—
193C4⋊Q8—131no—
194C4⋊Q8—261no—
195#126—261no—
196#126—261no—
197#124—261no—
198C22⋊Q8—131no—
199C22⋊Q8—131no—
200C22⋊Q8—261no—
201C22⋊Q8—261no—
202C22⋊Q8C2×D1311yescharacteristic
203C22⋊Q8C2×D1311yescharacteristic
204C4×Q8—131no—
205C4×Q8—131no—
206C4×Q8—261no—
207C4×D4—131no—
208C4×D4—261no—
209#117—131no—
210#117—131no—
211#107—131no—
212#106—131no—
213#106C2×D1311yescharacteristic
214C4⋊C8—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103C2×D1311yescharacteristic
224#103C2×D1311yescharacteristic
225C22⋊C8—131no—
226C22⋊C8—131no—
227C4×C8—131no—
228C2×C13—41no—
229C2×C13#54611yescharacteristic
230C2×C13C2×#13711yescharacteristic
231C2×C13#57811yescharacteristic
232D13—41no—
233C2×Q8—131no—
234C2×Q8—131no—
235C2×Q8—261no—
236C2×Q8—261no—
237C2×Q8—262no—
238C2×Q8—261no—
239C2×Q8—262no—
240C2×Q8—521no—
241C2×Q8—521no—
242C2×Q8C22×D1311yescharacteristic
243C2×Q8C22×D1311yescharacteristic
244C2×D4—131no—
245C22×C4—131no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4C22×D1311yescharacteristic
249Q16—41no—
250Q16—262no—
251Q16—521no—
252M16—41no—
253M16—521no—
254C2×C8—131no—
255C2×C8—131no—
256C2×C8C22×D1311yescharacteristic
257C2×C8C22×D1311yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—131no—
261C4⋊C4—131no—
262C4⋊C4—131no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4C22×D1311yescharacteristic
271C4⋊C4C22×D1311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—131no—
275C22⋊C4—131no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C42—131no—
281C42—261no—
282C42—261no—
283C42—261no—
284C42—261no—
285C13#332811yescharacteristic, complemented, Sylow
286C23—131no—
287C23D4×D1311yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—132no—
293Q8—261no—
294Q8—261no—
295Q8—261no—
296Q8—522no—
297Q8—522no—
298Q8—522no—
299D4—262no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—131no—
307C2×C4—131no—
308C2×C4—131no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—522no—
316C2×C4—522no—
317C2×C4D4×D1311yescharacteristic
318C2×C4C23×D1311yescharacteristic
319C8—21no—
320C8—21no—
321C8—261no—
322C8—261no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—261no—
327C22—261no—
328C22—261no—
329C22C2×D4×D1311yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—132no—
336C4—261no—
337C4—261no—
338C4—262no—
339C4—521no—
340C4—521no—
341C4—521no—
342C4#8825111yescharacteristic
343C4#41×D1311yescharacteristic
344C2—41no—
345C2—521no—
346C2#1171931511yescharacteristic
347C2D13×#13711yescharacteristic
348C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#470C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenter#470D13
hypocenterC13#3328
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
3. C13×#470C2semidirect
4. #11718847C2semidirect
5. #11718843C2semidirect
7. #11718781C2semidirect
8. #11718711C2semidirect
9. #11718706C2semidirect
10. #11718528C2semidirect
11. #11718515C2semidirect
12. #11718477C2semidirect
13. #11718463C2semidirect
14. #11718453C2semidirect
15. #11718451C2semidirect
156. #470D13semidirect
285. C13#3328semidirect

Maximal subgroups

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

subgroupindex
#117193462
#117193372
C13×#4702
#117188472
#117188432
#117187892
#117187812
#117187112
#117187062
#117185282
#117185152
#117184772
#117184632
#117184532
#117184512
#332813