Finite Group Databasebeta

← #13127285

Subgroups — #13127285

Order 1664.

344 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
1C13×#554C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic
3#11718755C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718713C211yesmaximal, characteristic, complemented
6#11718712C211yesmaximal, characteristic, complemented
7#11718706C211yesmaximal, characteristic, complemented
8#11718704C211yesmaximal, characteristic, complemented
9#11718691C211yesmaximal, characteristic, complemented
10#11718683C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic
12#11718632C211yesmaximal, characteristic, complemented
13#11718631C211yesmaximal, characteristic, complemented
14#11718625C211yesmaximal, characteristic, complemented
15C2×#88048C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#125—21no—
18C13×C22⋊Q8—21no—
19C13×C22⋊Q8—21no—
20C13×C22⋊Q8C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22C4×Q8×C13C2211yescharacteristic
23C4×D4×C13—21no—
24C4×D4×C13C2211yescharacteristic
25C2×C13×C4⋊C4C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28#88189—21no—
29#88180C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31#88178C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88143—21no—
36#88133—21no—
37#88131—21no—
38#88124C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40#88075C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88050C2211yescharacteristic
46#88050C2211yescharacteristic
47#88050C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88048C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13D411yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×Dic13—21no—
67C2×Dic26C2311yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4D411yescharacteristic
81C13×C22⋊C4D411yescharacteristic
82C42×C13—21no—
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87#6107—22no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99#6099—22no—
100C2×#1055—22no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3344—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C23×C13C2×D411yescharacteristic
108Q8×C13—21no—
109Q8×C13—21no—
110Q8×C13—81no—
111D4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×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—81no—
121C2×C4×C13—81no—
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—42no—
132Dic26—21no—
133Dic26—21no—
134#1055—21no—
135#1055—21no—
136#1055—21no—
137#1055#4112yes—
138#554D1311yescharacteristic
139#552—131no—
140#501—131no—
141#485—131no—
142#484—131no—
143#483—131no—
144#483—131no—
145#479—131no—
146#475—131no—
147#470—131no—
148#467—131no—
149#441—131no—
150#435—131no—
151#428—131no—
152C2×#106—131no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13#13712yes—
159C22×C13C22×D411yescharacteristic
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13C2×#4111yescharacteristic
169C4×C132−1+411yescharacteristic
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174C2×Q16—131no—
175C2×M16—131no—
176C22×C8—131no—
177C4⋊Q8C2×D1311yescharacteristic
178#126—261no—
179#125—21no—
180#125—131no—
181#125—261no—
182#123—261no—
183C22⋊Q8—21no—
184C22⋊Q8—21no—
185C22⋊Q8—131no—
186C22⋊Q8—131no—
187C22⋊Q8C2×D1311yescharacteristic
188C22⋊Q8C2×D1311yescharacteristic
189C4×Q8—131no—
190C4×Q8C2×D1311yescharacteristic
191C4×D4—21no—
192C4×D4C2×D1311yescharacteristic
193#117—131no—
194#117—261no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4C2×D1311yescharacteristic
197C2×C4⋊C4C2×D1311yescharacteristic
198#107—131no—
199#107—131no—
200#107—131no—
201#106—131no—
202#106—131no—
203#106—131no—
204#106—131no—
205#106—131no—
206#106—131no—
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—
216#97—131no—
217C2×C13—22no—
218C2×C13—41no—
219C2×C13#54711yescharacteristic
220C2×C13C2×#13711yescharacteristic
221C2×C13#57711yescharacteristic
222C2×Q8—21no—
223C2×Q8—131no—
224C2×Q8C22×D1311yescharacteristic
225C2×D4C22⋊D1311yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—261no—
229C22×C4C22×D1311yescharacteristic
230C22×C4C22×D1311yescharacteristic
231Q16—262no—
232M16—262no—
233C2×C8—131no—
234C2×C8—131no—
235C2×C8—131no—
236C2×C8—131no—
237C2×C8—262no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4C22⋊D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4C22⋊D1311yescharacteristic
263C22⋊C4C22⋊D1311yescharacteristic
264C42—21no—
265C42—261no—
266C42—261no—
267C42C22×D1311yescharacteristic
268C13#334411yescharacteristic, complemented, Sylow
269C23C2×C22⋊D1311yescharacteristic
270C23C2×C22⋊D1311yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—81no—
274Q8—261no—
275Q8—261no—
276D4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—522no—
292C2×C4C2×C22⋊D1311yescharacteristic
293C2×C4C2×C22⋊D1311yescharacteristic
294C2×C4C2×C22⋊D1311yescharacteristic
295C2×C4C2×C22⋊D1311yescharacteristic
296C2×C4C23×D1311yescharacteristic
297C8—132no—
298C8—261no—
299C8—261no—
300C8—261no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#8819612yes—
307C22C22×C22⋊D1311yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—521no—
317C4—521no—
318C4—521no—
319C4—521no—
320C4#41×D1311yescharacteristic
321C4#8825711yescharacteristic
322C2—22no—
323C2—41no—
324C2C2×#8819611yescharacteristic
325C2#1171952911yescharacteristic
326C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#554C2
socleC22×C13C22×D4
prime radicalC2×D4×C13D4
hypercenter#554D13
hypocenterC13#3344
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
3. #11718755C2semidirect
4. #11718741C2semidirect
5. #11718713C2semidirect
6. #11718712C2semidirect
7. #11718706C2semidirect
8. #11718704C2semidirect
9. #11718691C2semidirect
10. #11718683C2semidirect
12. #11718632C2semidirect
13. #11718631C2semidirect
14. #11718625C2semidirect
15. C2×#88048C2semidirect
268. C13#3344semidirect

Maximal subgroups

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

subgroupindex
C13×#5542
#117192462
#117187552
#117187412
#117187132
#117187122
#117187062
#117187042
#117186912
#117186832
#117186722
#117186322
#117186312
#117186252
C2×#880482
#334413