Finite Group Databasebeta

← #13126889

Subgroups — #13126889

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#11719246C211yesmaximal, characteristic
2D4×Dic26C211yesmaximal, characteristic
3C13×#435C211yesmaximal, characteristic
4#11718798C211yesmaximal, characteristic, complemented
5#11718781C211yesmaximal, characteristic, complemented
6#11718777C211yesmaximal, characteristic, complemented
7C2×#88056C211yesmaximal, characteristic, complemented
8#11718510C211yesmaximal, characteristic, complemented
9#11718490C211yesmaximal, characteristic, complemented
10#11718400C211yesmaximal, characteristic, complemented
11#11718400C211yesmaximal, characteristic, complemented
12#11718384C211yesmaximal, characteristic, complemented
13#11718382C211yesmaximal, characteristic, complemented
14#11718377C211yesmaximal, characteristic, complemented
15#11718364C211yesmaximal, characteristic, complemented
16C22×Dic26C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C22×C8×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88189—21no—
22D4×Dic13—21no—
23#88180C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25#88178C2211yescharacteristic
26#88178C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic
29C2×Dic52C2211yescharacteristic
30C2×Dic52C2211yescharacteristic
31C2×Dic52C2211yescharacteristic
32#88143—21no—
33#88142—21no—
34#88133—21no—
35#88132—21no—
36#88132—21no—
37#88131—21no—
38#88124C2211yescharacteristic
39#88123C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45C13×#97C2211yescharacteristic
46#88058C2211yescharacteristic
47#88057C2211yescharacteristic
48#88057C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C2×D4×C13D411yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C2×Dic26—22no—
66C2×Dic26—22no—
67C2×Dic26—21no—
68C2×Dic26—21no—
69C2×Dic26—41no—
70C2×Dic26—41no—
71C2×Dic26C2311yescharacteristic
72C2×Dic26C2311yescharacteristic
73C2×Dic26C2311yescharacteristic
74C2×Dic26C2311yescharacteristic
75C13×M16—41no—
76C2×C8×C13—41no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4D411yescharacteristic
82C13×C22⋊C4D411yescharacteristic
83C13×C22⋊C4D411yescharacteristic
84C42×C13C2311yescharacteristic
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108Dic52—22no—
109Dic52—41no—
110Dic52—41no—
111#3312—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114D4×C13—22no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2411yescharacteristic
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135Dic26—21no—
136Dic26—21no—
137Dic26—21no—
138Dic26—21no—
139Dic26—21no—
140Dic26—21no—
141Dic26—21no—
142Dic26—42no—
143Dic26—42no—
144Dic26#4112yes—
145C8×C13—21no—
146C8×C13—21no—
147C8×C13—21no—
148C8×C13—21no—
149#552—131no—
150D4×Q8—131no—
151#491—131no—
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#435D1311yescharacteristic
162#419—131no—
163C2×#103—131no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#13712yes—
170C22×C13C22×D411yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13C2×#4111yescharacteristic
176C4×C13H(5,𝔽2)11yescharacteristic
177Dic13—22no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185C22×Q8—131no—
186C22×Q8—131no—
187C2×Q16—131no—
188C2×Q16—131no—
189C2×Q16—131no—
190C2×M16C2×D1311yescharacteristic
191C22×C8C2×D1311yescharacteristic
192C4⋊Q8—131no—
193C4⋊Q8—261no—
194#126—261no—
195#125—131no—
196#125—261no—
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—261no—
207C4×D4C2×D1311yescharacteristic
208#117—131no—
209#117—261no—
210C2×C4⋊C4—131no—
211#107—131no—
212#106—131no—
213#106—131no—
214C4⋊C8C2×D1311yescharacteristic
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#103—131no—
224#103—131no—
225C22⋊C8C2×D1311yescharacteristic
226C22⋊C8C2×D1311yescharacteristic
227#97C2×D1311yescharacteristic
228C2×C13—22no—
229C2×C13—41no—
230C2×C13#54611yescharacteristic
231C2×C13C2×#13711yescharacteristic
232C2×C13#57811yescharacteristic
233C2×Q8—131no—
234C2×Q8—131no—
235C2×Q8—131no—
236C2×Q8—131no—
237C2×Q8—262no—
238C2×Q8—262no—
239C2×Q8—261no—
240C2×Q8—261no—
241C2×Q8—521no—
242C2×Q8—521no—
243C2×D4D5211yescharacteristic
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4C22×D1311yescharacteristic
248C22×C4C22×D1311yescharacteristic
249Q16—262no—
250Q16—521no—
251Q16—521no—
252M16—41no—
253C2×C8—41no—
254C2×C8C22×D1311yescharacteristic
255C2×C8C22×D1311yescharacteristic
256C2×C8C22×D1311yescharacteristic
257C2×C8C22×D1311yescharacteristic
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—131no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4D5211yescharacteristic
274C22⋊C4—261no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4D5211yescharacteristic
280C22⋊C4D5211yescharacteristic
281C42—261no—
282C42—261no—
283C42—261no—
284C42C22×D1311yescharacteristic
285C13#331211yescharacteristic, complemented, Sylow
286C23C2×D5211yescharacteristic
287C23C2×D5211yescharacteristic
288Q8—132no—
289Q8—261no—
290Q8—261no—
291Q8—261no—
292Q8—261no—
293Q8—261no—
294Q8—261no—
295Q8—261no—
296Q8—522no—
297Q8—522no—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—522no—
312C2×C4—522no—
313C2×C4—522no—
314C2×C4C2×D5211yescharacteristic
315C2×C4C2×D5211yescharacteristic
316C2×C4C2×D5211yescharacteristic
317C2×C4C2×D5211yescharacteristic
318C2×C4C23×D1311yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#8816312yes—
329C22C22×D5211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—262no—
335C4—521no—
336C4—521no—
337C4—521no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4—521no—
342C4#8825111yescharacteristic
343C4#41×D1311yescharacteristic
344C2—22no—
345C2—41no—
346C2#1171925911yescharacteristic
347C2C2×#8816311yescharacteristic
348C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
prime radicalC2×D4×C13D4
hypercenter#435D13
hypocenterC13#3312
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
4. #11718798C2semidirect
5. #11718781C2semidirect
6. #11718777C2semidirect
7. C2×#88056C2semidirect
8. #11718510C2semidirect
9. #11718490C2semidirect
10. #11718400C2semidirect
11. #11718400C2semidirect
12. #11718384C2semidirect
13. #11718382C2semidirect
14. #11718377C2semidirect
15. #11718364C2semidirect
285. C13#3312semidirect

Maximal subgroups

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

subgroupindex
#117192462
D4×Dic262
C13×#4352
#117187982
#117187812
#117187772
C2×#880562
#117185102
#117184902
#117184002
#117183842
#117183822
#117183772
#117183642
#331213