Finite Group Databasebeta

← #13125505

Subgroups — #13125505

Order 1664.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719348C211yesmaximal, characteristic
2#11719330C211yesmaximal, characteristic, complemented
3C13×#470C211yesmaximal, characteristic, complemented
4#11718851C211yesmaximal, characteristic, complemented
5Q16×Dic13C211yesmaximal, characteristic, complemented
6#11718795C211yesmaximal, characteristic
7#11718783C211yesmaximal, characteristic, complemented
8#11718712C211yesmaximal, characteristic, complemented
9#11718709C211yesmaximal, characteristic
10#11718517C211yesmaximal, characteristic, complemented
11#11718513C211yesmaximal, characteristic, complemented
12#11718478C211yesmaximal, characteristic, complemented
13#11718461C211yesmaximal, characteristic, complemented
14#11718453C211yesmaximal, characteristic, complemented
15#11718450C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×C22⋊Q8C2211yescharacteristic
20#88201C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23#88198C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25C2×#6106C2211yescharacteristic
26#88184C2211yescharacteristic
27#88180C2211yescharacteristic
28#88178C2211yescharacteristic
29C22×#1055C2211yescharacteristic
30C2×#6095C2211yescharacteristic
31#88152—21no—
32#88151—21no—
33#88147C2211yescharacteristic
34#88144—21no—
35#88144C2211yescharacteristic
36#88143—21no—
37#88142C2211yescharacteristic
38#88141C2211yescharacteristic
39#88139—21no—
40#88137—21no—
41#88133—21no—
42#88133—21no—
43C13×#106C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88061C2211yescharacteristic
49#88058C2211yescharacteristic
50#88056C2211yescharacteristic
51#88055C2211yescharacteristic
52#88055C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×Dic26—21no—
66C2×Dic26C2311yescharacteristic
67C13×Q16—22no—
68C13×M16—22no—
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C22⋊C4—21no—
76C13×C22⋊C4—21no—
77C22⋊Dic13—21no—
78C22⋊Dic13D411yescharacteristic
79C22⋊Dic13D411yescharacteristic
80#6107—22no—
81#6106—22no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13D411yescharacteristic
90C4⋊Dic13D411yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055—22no—
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107#6095—22no—
108#3178—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—81no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131D52—21no—
132D52—21no—
133C4×D13—81no—
134Dic26—21no—
135Dic26—21no—
136Dic26—81no—
137C8×C13—21no—
138C8×C13#4112yes—
139#1055—21no—
140#1055#4112yes—
141#542—131no—
142#541—131no—
143#501—131no—
144#497—131no—
145#488—131no—
146#487—131no—
147#470D1311yescharacteristic, complemented
148#468—131no—
149#467—131no—
150#465—131no—
151#441—131no—
152#440—131no—
153C4×Q16—131no—
154C4×SD16—131no—
155#405—131no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13C22×D411yescharacteristic
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
163C4×C13—21no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13C2×#4111yescharacteristic
169C4×C13C2×#4111yescharacteristic
170Dic13—21no—
171Dic13—21no—
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×Q16—131no—
178C2×Q16C2×D1311yescharacteristic
179C2×SD16—131no—
180C2×SD16—131no—
181C2×M16C2×D1311yescharacteristic
182C22×C8—131no—
183C4⋊Q8—131no—
184C4⋊Q8—131no—
185#126—261no—
186#126—261no—
187#126—261no—
188#125—131no—
189#125—261no—
190#125—261no—
191#124—131no—
192#124—261no—
193#123—261no—
194C22⋊Q8—131no—
195C22⋊Q8—261no—
196C22⋊Q8C2×D1311yescharacteristic
197C22⋊Q8C2×D1311yescharacteristic
198#121—131no—
199C4×Q8—131no—
200C4×Q8—131no—
201C4×Q8—131no—
202C4×D4—131no—
203#117—131no—
204#107—131no—
205#107—131no—
206#106—131no—
207#106C2×D1311yescharacteristic
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103C2×D1311yescharacteristic
213#103C2×D1311yescharacteristic
214#102—131no—
215#102—131no—
216#97—131no—
217#97—131no—
218C4×C8—131no—
219C4×C8—131no—
220C2×C13—41no—
221C2×C13#53211yescharacteristic
222C2×C13#57711yescharacteristic
223C2×C13#57811yescharacteristic
224D13—81no—
225C2×Q8—131no—
226C2×Q8—261no—
227C2×Q8C22×D1311yescharacteristic
228C2×Q8C22×D1311yescharacteristic
229C2×D4—131no—
230C2×D4—261no—
231C22×C4—261no—
232C22×C4C22×D1311yescharacteristic
233Q16—22no—
234Q16—262no—
235SD16—262no—
236SD16—262no—
237M16—22no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—262no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—131no—
263C22⋊C4—131no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—131no—
270C42—131no—
271C42—261no—
272C42—261no—
273C42—261no—
274C13#317811yescharacteristic, complemented, Sylow
275C23—261no—
276C23D4×D1311yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—261no—
282Q8—261no—
283Q8—1041no—
284D4—261no—
285D4—261no—
286D4—1041no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—1041no—
301C2×C4D4×D1311yescharacteristic
302C2×C4C23×D1311yescharacteristic
303C8—21no—
304C8—132no—
305C8—261no—
306C8#612912yes—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—521no—
311C22—521no—
312C22—521no—
313C22C2×D4×D1311yescharacteristic
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—261no—
320C4—261no—
321C4—261no—
322C4—261no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4C2×#612911yescharacteristic
327C4#41×D1311yescharacteristic
328C2—41no—
329C2—1041no—
330C2#1171930111yescharacteristic
331C2#1171948311yescharacteristic
332C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#470C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#470D13
hypocenterC13#3178
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
2. #11719330C2semidirect
3. C13×#470C2semidirect
4. #11718851C2semidirect
5. Q16×Dic13C2semidirect
7. #11718783C2semidirect
8. #11718712C2semidirect
10. #11718517C2semidirect
11. #11718513C2semidirect
12. #11718478C2semidirect
13. #11718461C2semidirect
14. #11718453C2semidirect
15. #11718450C2semidirect
147. #470D13semidirect
274. C13#3178semidirect

Maximal subgroups

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

subgroupindex
#117193482
#117193302
C13×#4702
#117188512
Q16×Dic132
#117187952
#117187832
#117187122
#117187092
#117185172
#117185132
#117184782
#117184612
#117184532
#117184502
#317813