Finite Group Databasebeta

← #13126083

Subgroups — #13126083

Order 1664.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#540C211yesmaximal, characteristic
2#11719224C211yesmaximal, characteristic, complemented
3#11718732C211yesmaximal, characteristic, complemented
4#11718731C211yesmaximal, characteristic, complemented
5#11718726C211yesmaximal, characteristic, complemented
6#11718725C211yesmaximal, characteristic, complemented
7#11718696C211yesmaximal, characteristic, complemented
8#11718696C211yesmaximal, characteristic, complemented
9#11718695C211yesmaximal, characteristic, complemented
10#11718694C211yesmaximal, characteristic, complemented
11#11718670C211yesmaximal, characteristic, complemented
12#11718670C211yesmaximal, characteristic, complemented
13#11718669C211yesmaximal, characteristic, complemented
14#11718668C211yesmaximal, characteristic, complemented
15#11718661C211yesmaximal, characteristic, complemented
16C13×#127C2211yescharacteristic
17C13×#125C2211yescharacteristic
18C13×#123—21no—
19C13×#123—21no—
20C13×#121—21no—
21C13×#121—21no—
22C13×#121C2211yescharacteristic
23C13×#121C2211yescharacteristic
24C4×D4×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117C2211yescharacteristic
27#88180C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29#88144—21no—
30#88142—21no—
31#88132—21no—
32#88132—21no—
33#88124C2211yescharacteristic
34#88124C2211yescharacteristic
35#88123C2211yescharacteristic
36#88123C2211yescharacteristic
37#88072C2211yescharacteristic
38#88072C2211yescharacteristic
39#88072C2211yescharacteristic
40#88072C2211yescharacteristic
41#88072C2211yescharacteristic
42#88072C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45C22⋊#1055C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
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×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C22×Dic13—21no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4D411yescharacteristic
82C13×C22⋊C4D411yescharacteristic
83C42×C13C2311yescharacteristic
84C42×C13C2311yescharacteristic
85C22⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C2×#1055C2311yescharacteristic
99C2×#1055C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3241—131nomaximal, Sylow
103C23×C13—21no—
104C23×C13—21no—
105C23×C13C2×D411yescharacteristic
106D4×C13—21no—
107D4×C13—21no—
108D4×C13—21no—
109D4×C13—21no—
110D4×C13—81no—
111D4×C13—81no—
112D4×C13—81no—
113D4×C13—81no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—81no—
131Dic26—81no—
132Dic26—81no—
133#1055—21no—
134#1055—21no—
135#1055—21no—
136#1055—21no—
137#544—131no—
138#540D1311yescharacteristic
139#501—131no—
140#499—131no—
141#490—131no—
142#486—131no—
143#482—131no—
144#482—131no—
145#481—131no—
146#480—131no—
147#478—131no—
148#478—131no—
149#476—131no—
150#474—131no—
151#433—131no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C22×D411yescharacteristic
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C132−1+411yescharacteristic
170C4×C132−1+411yescharacteristic
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175C4⋊Q8—131no—
176C4⋊Q8—131no—
177C4⋊Q8—261no—
178#127C2×D1311yescharacteristic
179#125—131no—
180#125—131no—
181#125—261no—
182#125C2×D1311yescharacteristic
183#123—21no—
184#123—21no—
185C22⋊Q8—261no—
186C22⋊Q8—261no—
187#121—21no—
188#121—21no—
189#121C2×D1311yescharacteristic
190#121C2×D1311yescharacteristic
191C4×D4C2×D1311yescharacteristic
192C4×D4C2×D1311yescharacteristic
193#117—131no—
194#117C2×D1311yescharacteristic
195C2×C4⋊C4—131no—
196#107—131no—
197#107—131no—
198#107—131no—
199#107—131no—
200#106—131no—
201#106—131no—
202#106—131no—
203#106—131no—
204C4⋊C8—131no—
205C4⋊C8—131no—
206#102—131no—
207#102—131no—
208#102—131no—
209#102—131no—
210#102—131no—
211#102—131no—
212#102—131no—
213#102—131no—
214C22⋊C8—131no—
215C22⋊C8—131no—
216#97—131no—
217C4×C8—131no—
218C2×C13—41no—
219C2×C13—81no—
220C2×C13—81no—
221C2×C13#53611yescharacteristic
222C2×C13#57611yescharacteristic
223C2×C13#57711yescharacteristic
224C2×Q8—261no—
225C2×Q8—261no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22×D1311yescharacteristic
231C2×D4C22×D1311yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—261no—
235C22×C4C22×D1311yescharacteristic
236C2×C8—131no—
237C2×C8—131no—
238C2×C8—131no—
239C2×C8—131no—
240C4⋊C4—21no—
241C4⋊C4—21no—
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⋊C4C22⋊D1311yescharacteristic
254C4⋊C4C22⋊D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—261no—
262C22⋊C4C22⋊D1311yescharacteristic
263C22⋊C4C22⋊D1311yescharacteristic
264C42—261no—
265C42C22×D1311yescharacteristic
266C42C22×D1311yescharacteristic
267C13#324111yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23C2×C22⋊D1311yescharacteristic
271Q8—1041no—
272Q8—1041no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
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—1041no—
292C2×C4C2×C22⋊D1311yescharacteristic
293C2×C4C2×C22⋊D1311yescharacteristic
294C2×C4C2×C22⋊D1311yescharacteristic
295C2×C4C2×C22⋊D1311yescharacteristic
296C2×C4C2×C22⋊D1311yescharacteristic
297C2×C4C23×D1311yescharacteristic
298C8—261no—
299C8—261no—
300C8—261no—
301C8—261no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×C22⋊D1311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—521no—
320C4—521no—
321C4—521no—
322C4—521no—
323C4#8825711yescharacteristic
324C4#8825711yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2#1171953011yescharacteristic
329C2#1171954011yescharacteristic
330C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#540C2
socleC22×C13C22×D4
hypercenter#540D13
hypocenterC13#3241
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
2. #11719224C2semidirect
3. #11718732C2semidirect
4. #11718731C2semidirect
5. #11718726C2semidirect
6. #11718725C2semidirect
7. #11718696C2semidirect
8. #11718696C2semidirect
9. #11718695C2semidirect
10. #11718694C2semidirect
11. #11718670C2semidirect
12. #11718670C2semidirect
13. #11718669C2semidirect
14. #11718668C2semidirect
15. #11718661C2semidirect
267. C13#3241semidirect

Maximal subgroups

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

subgroupindex
C13×#5402
#117192242
#117187322
#117187312
#117187262
#117187252
#117186962
#117186952
#117186942
#117186702
#117186692
#117186682
#117186612
#324113