Finite Group Databasebeta

← #13127667

Subgroups — #13127667

Order 1664.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719376C211yesmaximal, characteristic, complemented
2#11719244C211yesmaximal, characteristic, complemented
3C13×#463C211yesmaximal, characteristic
4#11718825C211yesmaximal, characteristic, complemented
5#11718823C211yesmaximal, characteristic, complemented
6#11718814C211yesmaximal, characteristic
7#11718813C211yesmaximal, characteristic
8#11718717C211yesmaximal, characteristic, complemented
9C4×#6105C211yesmaximal, characteristic, complemented
10#11718492C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718458C211yesmaximal, characteristic, complemented
13#11718452C211yesmaximal, characteristic, complemented
14#11718427C211yesmaximal, characteristic, complemented
15#11718426C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×D8C2211yescharacteristic
18C13×#124C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21#88198C2211yescharacteristic
22#88190C2211yescharacteristic
23D4×Dic13C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25D4×Dic13C2211yescharacteristic
26C2×#6105C2211yescharacteristic
27#88178—21no—
28C2×#6101—21no—
29#88144C2211yescharacteristic
30#88142C2211yescharacteristic
31#88133—21no—
32#88133—21no—
33#88132—21no—
34#88132—21no—
35#88132—21no—
36#88131—21no—
37#88124C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88058C2211yescharacteristic
49#88057C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88055C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56#88050C2211yescharacteristic
57#88048C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C2×Dic26—21no—
67C2×Dic26D411yescharacteristic
68C2×Dic26C2311yescharacteristic
69C13×SD16—22no—
70C13×D8—22no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C13×C22⋊C4—21no—
76C13×C22⋊C4—21no—
77C42×C13C2311yescharacteristic
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83#6105—22no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13D411yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3376—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108Q8×C13—21no—
109Q8×C13—21no—
110D4×C13—21no—
111D4×C13—21no—
112D4×C13—21no—
113D4×C13#4112yes—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—81no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—81no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131Dic26—21no—
132Dic26—21no—
133Dic26—41no—
134Dic26—81no—
135C8×C13—21no—
136C8×C13—21no—
137#1055—21no—
138#1055—21no—
139#556—131no—
140#554—131no—
141#491—131no—
142#489—131no—
143#488—131no—
144#479—131no—
145#478—131no—
146#475—131no—
147#463—131no—
148#463D1311yescharacteristic
149#461—131no—
150#446—131no—
151#442—131no—
152#440—131no—
153C4×SD16—131no—
154C22×C13—22no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13C22×D411yescharacteristic
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13C2×#4111yescharacteristic
166C4×C132−1+411yescharacteristic
167Dic13—21no—
168Dic13—21no—
169Dic13—21no—
170Dic13—21no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175C2×SD16—131no—
176C2×SD16C2×D1311yescharacteristic
177C2×D8C2×D1311yescharacteristic
178C4⋊Q8—131no—
179C4⋊Q8—131no—
180#126—261no—
181#126—261no—
182#125—131no—
183#125—131no—
184#124—131no—
185#124C2×D1311yescharacteristic
186C22⋊Q8—261no—
187C22⋊Q8—261no—
188C22⋊Q8—261no—
189C22⋊Q8—261no—
190C4×Q8—131no—
191C4×Q8—131no—
192C4×Q8—131no—
193C4×D4—131no—
194C4×D4—131no—
195C4×D4—131no—
196C4×D4C2×D1311yescharacteristic
197#117—261no—
198C2×C4⋊C4—261no—
199#107—131no—
200#106—131no—
201#106—131no—
202C4⋊C8—131no—
203C4⋊C8—131no—
204C4⋊C8C2×D1311yescharacteristic
205#103—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103C2×D1311yescharacteristic
211#102—131no—
212#102—131no—
213#102—131no—
214#102C2×D1311yescharacteristic
215#97—131no—
216#97—131no—
217C4×C8—131no—
218C2×C13—42no—
219C2×C13—81no—
220C2×C13#54811yescharacteristic
221C2×C13#57511yescharacteristic
222C2×C13#57711yescharacteristic
223C2×Q8—131no—
224C2×Q8—131no—
225C2×Q8—261no—
226C2×Q8C22×D1311yescharacteristic
227C2×D4C22×D1311yescharacteristic
228C2×D4C22×D1311yescharacteristic
229C22×C4—21no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4—261no—
233SD16—22no—
234SD16—262no—
235D8—22no—
236C2×C8—131no—
237C2×C8—131no—
238C2×C8C22×D1311yescharacteristic
239C2×C8C22×D1311yescharacteristic
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4C22×D1311yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—131no—
265C42—131no—
266C42—261no—
267C42—261no—
268C42C22×D1311yescharacteristic
269C13#337611yescharacteristic, complemented, Sylow
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—261no—
275Q8—261no—
276Q8—521no—
277Q8—1041no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4#612912yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—131no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—522no—
294C2×C4—522no—
295C2×C4—1041no—
296C2×C4D4×D1311yescharacteristic
297C2×C4D4×D1311yescharacteristic
298C2×C4C23×D1311yescharacteristic
299C8—21no—
300C8—21no—
301C8—261no—
302C8—261no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D1311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—261no—
315C4—261no—
316C4—261no—
317C4—261no—
318C4—521no—
319C4—521no—
320C4—521no—
321C4—521no—
322C4C2×#612911yescharacteristic
323C4#8825711yescharacteristic
324C2—42no—
325C2—81no—
326C2#1171930311yescharacteristic
327C2#1171947311yescharacteristic
328C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#463C2
socleC22×C13C22×D4
prime radicalC2×C13×D8C22
hypercenter#463D13
hypocenterC13#3376
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #11719376C2semidirect
2. #11719244C2semidirect
4. #11718825C2semidirect
5. #11718823C2semidirect
8. #11718717C2semidirect
9. C4×#6105C2semidirect
10. #11718492C2semidirect
11. #11718490C2semidirect
12. #11718458C2semidirect
13. #11718452C2semidirect
14. #11718427C2semidirect
15. #11718426C2semidirect
269. C13#3376semidirect

Maximal subgroups

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

subgroupindex
#117193762
#117192442
C13×#4632
#117188252
#117188232
#117188142
#117188132
#117187172
C4×#61052
#117184922
#117184902
#117184582
#117184522
#117184272
#117184262
#337613