Finite Group Databasebeta

← #13126104

Subgroups — #13126104

Order 1664.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#544C211yesmaximal, characteristic
2#11719223C211yesmaximal, characteristic
3#11718755C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5#11718752C211yesmaximal, characteristic, complemented
6#11718741C211yesmaximal, characteristic, complemented
7#11718730C211yesmaximal, characteristic, complemented
8#11718725C211yesmaximal, characteristic, complemented
9#11718724C211yesmaximal, characteristic, complemented
10#11718724C211yesmaximal, characteristic, complemented
11#11718661C211yesmaximal, characteristic
12#11718657C211yesmaximal, characteristic
13#11718657C211yesmaximal, characteristic
14#11718632C211yesmaximal, characteristic
15#11718631C211yesmaximal, characteristic
16C13×C4⋊Q8—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C13×#125—21no—
20C13×#125C2211yescharacteristic
21C13×#125C2211yescharacteristic
22C13×C22⋊Q8—21no—
23C13×C22⋊Q8—21no—
24C13×#117C2211yescharacteristic
25C13×#117C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic
29#88143—21no—
30#88143—21no—
31#88133—21no—
32#88133—21no—
33#88124C2211yescharacteristic
34#88123C2211yescharacteristic
35C4×Dic26C2211yescharacteristic
36C4×Dic26C2211yescharacteristic
37C22⋊#1055C2211yescharacteristic
38C22⋊#1055C2211yescharacteristic
39#88050C2211yescharacteristic
40#88050C2211yescharacteristic
41#88050C2211yescharacteristic
42#88050C2211yescharacteristic
43#88050C2211yescharacteristic
44#88050C2211yescharacteristic
45#88050C2211yescharacteristic
46#88050C2211yescharacteristic
47#88048C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88047C2211yescharacteristic
52#88047C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56C4⋊#1055C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C2×Dic26C2311yescharacteristic
64C2×Dic26C2311yescharacteristic
65C13×C4⋊C4—21no—
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4D411yescharacteristic
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C13×C22⋊C4D411yescharacteristic
80C13×C22⋊C4D411yescharacteristic
81C42×C13—21no—
82C42×C13C2311yescharacteristic
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C2×#1055C2311yescharacteristic
99C2×#1055C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3242—131nomaximal, Sylow
103C23×C13C2×D411yescharacteristic
104Q8×C13—81no—
105Q8×C13—81no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—81no—
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123Dic26—21no—
124Dic26—21no—
125Dic26—21no—
126Dic26—21no—
127#1055—21no—
128#1055—21no—
129#1055—21no—
130#1055—21no—
131#544D1311yescharacteristic
132#541—131no—
133#501—131no—
134#499—131no—
135#491—131no—
136#487—131no—
137#485—131no—
138#485—131no—
139#484—131no—
140#483—131no—
141#479—131no—
142#479—131no—
143#477—131no—
144#475—131no—
145#433—131no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13C22×D411yescharacteristic
150C4×C13—21no—
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C132−1+411yescharacteristic
160C4×C132−1+411yescharacteristic
161Dic13—41no—
162Dic13—41no—
163Dic13—41no—
164Dic13—41no—
165C4⋊Q8—21no—
166C4⋊Q8—131no—
167C4⋊Q8C2×D1311yescharacteristic
168C4⋊Q8C2×D1311yescharacteristic
169#126—261no—
170#126—261no—
171#125—21no—
172#125—131no—
173#125—261no—
174#125—261no—
175#125C2×D1311yescharacteristic
176#125C2×D1311yescharacteristic
177C22⋊Q8—21no—
178C22⋊Q8—21no—
179C22⋊Q8—131no—
180C22⋊Q8—131no—
181C4×Q8—131no—
182C4×Q8—131no—
183#117C2×D1311yescharacteristic
184#117C2×D1311yescharacteristic
185C2×C4⋊C4C2×D1311yescharacteristic
186#107—131no—
187#107—131no—
188#107—131no—
189#107—131no—
190#106—131no—
191#106—131no—
192#106—131no—
193#106—131no—
194C4⋊C8—131no—
195C4⋊C8—131no—
196#103—131no—
197#103—131no—
198#103—131no—
199#103—131no—
200#103—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204C22⋊C8—131no—
205C22⋊C8—131no—
206#97—131no—
207C4×C8—131no—
208C2×C13—41no—
209C2×C13#53611yescharacteristic
210C2×C13#57711yescharacteristic
211C2×C13#57811yescharacteristic
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—131no—
215C2×Q8—131no—
216C22×C4—21no—
217C22×C4C22×D1311yescharacteristic
218C2×C8—131no—
219C2×C8—131no—
220C2×C8—131no—
221C2×C8—131no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—131no—
230C4⋊C4—131no—
231C4⋊C4—261no—
232C4⋊C4—261no—
233C4⋊C4—261no—
234C4⋊C4—261no—
235C4⋊C4—261no—
236C4⋊C4—261no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4C22⋊D1311yescharacteristic
240C4⋊C4C22⋊D1311yescharacteristic
241C4⋊C4C22×D1311yescharacteristic
242C4⋊C4C22×D1311yescharacteristic
243C4⋊C4C22×D1311yescharacteristic
244C4⋊C4C22×D1311yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—261no—
247C22⋊C4—261no—
248C22⋊C4C22⋊D1311yescharacteristic
249C22⋊C4C22⋊D1311yescharacteristic
250C42—21no—
251C42—261no—
252C42—261no—
253C42C22×D1311yescharacteristic
254C42C22×D1311yescharacteristic
255C13#324211yescharacteristic, complemented, Sylow
256C23C2×C22⋊D1311yescharacteristic
257Q8—81no—
258Q8—81no—
259Q8—261no—
260Q8—261no—
261Q8—261no—
262Q8—261no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—81no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4C2×C22⋊D1311yescharacteristic
275C2×C4C2×C22⋊D1311yescharacteristic
276C2×C4C2×C22⋊D1311yescharacteristic
277C2×C4C2×C22⋊D1311yescharacteristic
278C2×C4C2×C22⋊D1311yescharacteristic
279C2×C4C23×D1311yescharacteristic
280C8—261no—
281C8—261no—
282C8—261no—
283C8—261no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×C22⋊D1311yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—521no—
298C4—521no—
299C4—521no—
300C4—521no—
301C4#8825411yescharacteristic
302C4#8825411yescharacteristic
303C2—41no—
304C2#1171952111yescharacteristic
305C2#1171954111yescharacteristic
306C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#544C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#544D13
hypocenterC13#3242
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #11718755C2semidirect
4. #11718754C2semidirect
5. #11718752C2semidirect
6. #11718741C2semidirect
7. #11718730C2semidirect
8. #11718725C2semidirect
9. #11718724C2semidirect
10. #11718724C2semidirect
255. C13#3242semidirect

Maximal subgroups

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

subgroupindex
C13×#5442
#117192232
#117187552
#117187542
#117187522
#117187412
#117187302
#117187252
#117187242
#117186612
#117186572
#117186322
#117186312
#324213