Finite Group Databasebeta

← #13127447

Subgroups — #13127447

Order 1664.

342 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719238C211yesmaximal, characteristic
2#11719216C211yesmaximal, characteristic
3C13×#428C211yesmaximal, characteristic, complemented
4#11718798C211yesmaximal, characteristic, complemented
5#11718789C211yesmaximal, characteristic
6#11718657C211yesmaximal, characteristic, complemented
7#11718632C211yesmaximal, characteristic, complemented
8#11718549C211yesmaximal, characteristic, complemented
9#11718542C211yesmaximal, characteristic, complemented
10#11718536C211yesmaximal, characteristic, complemented
11#11718534C211yesmaximal, characteristic, complemented
12#11718529C211yesmaximal, characteristic, complemented
13#11718523C211yesmaximal, characteristic, complemented
14#11718516C211yesmaximal, characteristic, complemented
15#11718515C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C13×#117C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C4×C22⋊D13—21no—
20C4×C22⋊D13C2211yescharacteristic
21#88178—21no—
22#88178C2211yescharacteristic
23#88178C2211yescharacteristic
24C2×Dic52C2211yescharacteristic
25C2×#6094C2211yescharacteristic
26#88151C2211yescharacteristic
27#88151C2211yescharacteristic
28#88150—21no—
29#88146C2211yescharacteristic
30C4⋊C4×D13C2211yescharacteristic
31#88143—21no—
32#88142C2211yescharacteristic
33#88142C2211yescharacteristic
34#88141C2211yescharacteristic
35#88141C2211yescharacteristic
36#88139—21no—
37#88133—21no—
38#88130—21no—
39C4×Dic26—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88060C2211yescharacteristic
46#88057C2211yescharacteristic
47#88056C2211yescharacteristic
48#88056C2211yescharacteristic
49#88054C2211yescharacteristic
50C8×Dic13C2211yescharacteristic
51#88050C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13D411yescharacteristic
62C2×C4×D13—21no—
63C2×C4×D13C2311yescharacteristic
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×Dic26C2311yescharacteristic
67C2×Dic26C2311yescharacteristic
68C13×M16—22no—
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C42×C13—21no—
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13D411yescharacteristic
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103D411yescharacteristic
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101D411yescharacteristic
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103Dic52—22no—
104#6094—22no—
105#3356—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C22×D13C2×D411yescharacteristic
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—81no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2411yescharacteristic
117C22⋊D13—22no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125C4×D13—21no—
126C4×D13—21no—
127C4×D13—81no—
128Dic26—21no—
129Dic26—21no—
130Dic26—21no—
131Dic26—21no—
132Dic26—42no—
133Dic26—81no—
134C8×C13—21no—
135C8×C13#4112yes—
136#1055—21no—
137#1055—21no—
138#556—131no—
139#554—131no—
140#498—131no—
141#485—131no—
142#485—131no—
143#483—131no—
144#483—131no—
145#477—131no—
146#475—131no—
147#470—131no—
148#470—131no—
149C4×Q16—131no—
150#436—131no—
151#428—131no—
152#428D1311yescharacteristic, complemented
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13C22×D411yescharacteristic
157C2×D13—21no—
158C2×D13—21no—
159C2×D13—21no—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13C2×#4111yescharacteristic
166C4×C132−1+411yescharacteristic
167Dic13—21no—
168Dic13—21no—
169Dic13—41no—
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13#13712yes—
174C2×Q16—131no—
175C2×M16—131no—
176C2×M16C2×D1311yescharacteristic
177C4⋊Q8—131no—
178C4⋊Q8—131no—
179#126—261no—
180#126—261no—
181#125—261no—
182#124—261no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8—131no—
186C22⋊Q8—131no—
187C22⋊Q8—261no—
188C22⋊Q8—261no—
189C4×Q8—131no—
190C4×Q8—131no—
191C4×Q8—261no—
192C4×D4—131no—
193C4×D4—261no—
194#117—131no—
195#117C2×D1311yescharacteristic
196C2×C4⋊C4—131no—
197C2×C4⋊C4C2×D1311yescharacteristic
198#107—131no—
199#107C2×D1311yescharacteristic
200#107C2×D1311yescharacteristic
201#106—131no—
202#106—131no—
203#106—131no—
204#106—131no—
205#106C2×D1311yescharacteristic
206#106C2×D1311yescharacteristic
207C4⋊C8—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214C22⋊C8—131no—
215C22⋊C8—131no—
216C4×C8—131no—
217C2×C13—41no—
218C2×C13#54711yescharacteristic
219C2×C13C2×#13711yescharacteristic
220C2×C13#57711yescharacteristic
221D13—41no—
222C2×Q8—131no—
223C2×Q8—131no—
224C2×Q8—261no—
225C2×Q8—261no—
226C2×D4—131no—
227C22×C4—21no—
228C22×C4—131no—
229C22×C4—261no—
230C22×C4C22×D1311yescharacteristic
231Q16—262no—
232M16—22no—
233M16—262no—
234C2×C8—131no—
235C2×C8—131no—
236C2×C8C22×D1311yescharacteristic
237C2×C8C22×D1311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—131no—
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4C22×D1311yescharacteristic
252C4⋊C4C22×D1311yescharacteristic
253C4⋊C4C22×D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—131no—
257C22⋊C4—131no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C42—21no—
264C42—131no—
265C42—261no—
266C42—261no—
267C42—261no—
268C13#335611yescharacteristic, complemented, Sylow
269C23—131no—
270C23D4×D1311yescharacteristic
271Q8—261no—
272Q8—261no—
273Q8—261no—
274Q8—261no—
275Q8—522no—
276Q8—1041no—
277D4—262no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—1041no—
295C2×C4D4×D1311yescharacteristic
296C2×C4C23×D1311yescharacteristic
297C8—21no—
298C8—261no—
299C8—261no—
300C8#612712yes—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—261no—
305C22—261no—
306C22—261no—
307C22C2×D4×D1311yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—132no—
314C4—261no—
315C4—261no—
316C4—521no—
317C4—521no—
318C4—521no—
319C4—521no—
320C4C2×#612711yescharacteristic
321C4#8825411yescharacteristic
322C2—41no—
323C2—521no—
324C2#1171921211yescharacteristic
325C2#1171948011yescharacteristic
326C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenter#428D13
hypocenterC13#3356
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. C13×#428C2semidirect
4. #11718798C2semidirect
6. #11718657C2semidirect
7. #11718632C2semidirect
8. #11718549C2semidirect
9. #11718542C2semidirect
10. #11718536C2semidirect
11. #11718534C2semidirect
12. #11718529C2semidirect
13. #11718523C2semidirect
14. #11718516C2semidirect
15. #11718515C2semidirect
152. #428D13semidirect
268. C13#3356semidirect

Maximal subgroups

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

subgroupindex
#117192382
#117192162
C13×#4282
#117187982
#117187892
#117186572
#117186322
#117185492
#117185422
#117185362
#117185342
#117185292
#117185232
#117185162
#117185152
#335613