Finite Group Databasebeta

← #13126082

Subgroups — #13126082

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
1#11719434C211yesmaximal, characteristic, complemented
2#11719424C211yesmaximal, characteristic
3C13×#486C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718732C211yesmaximal, characteristic, complemented
6#11718445C211yesmaximal, characteristic, complemented
7#11718440C211yesmaximal, characteristic, complemented
8#11718438C211yesmaximal, characteristic, complemented
9#11718435C211yesmaximal, characteristic, complemented
10#11718427C211yesmaximal, characteristic, complemented
11#11718424C211yesmaximal, characteristic, complemented
12#11718422C211yesmaximal, characteristic, complemented
13#11718420C211yesmaximal, characteristic, complemented
14#11718351C211yesmaximal, characteristic, complemented
15#11718344C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#127C2211yescharacteristic
18#88200—21no—
19#88198—21no—
20#88193—21no—
21#88193—21no—
22#88192C2211yescharacteristic
23#88192C2211yescharacteristic
24#88189—21no—
25#88189—21no—
26D4×Dic13C2211yescharacteristic
27D4×Dic13C2211yescharacteristic
28#88150—21no—
29#88146C2211yescharacteristic
30C4⋊C4×D13C2211yescharacteristic
31#88144C2211yescharacteristic
32#88143—21no—
33#88142C2211yescharacteristic
34#88126C2211yescharacteristic
35#88124C2211yescharacteristic
36#88124C2211yescharacteristic
37C13×#102C2211yescharacteristic
38C13×#102C2211yescharacteristic
39C13×#102C2211yescharacteristic
40C13×#102C2211yescharacteristic
41C4×C8×C13C2211yescharacteristic
42#88072C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88060C2211yescharacteristic
47#88060C2211yescharacteristic
48#88058C2211yescharacteristic
49#88058C2211yescharacteristic
50#88057C2211yescharacteristic
51#88057C2211yescharacteristic
52#88054C2211yescharacteristic
53#88054C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C2×D4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C2×C4×D13—21no—
69C2×C4×D13C2311yescharacteristic
70C2×Dic26—21no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C42×C13C2311yescharacteristic
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81#6103—21no—
82#6103D411yescharacteristic
83#6103D411yescharacteristic
84C4⋊Dic13—21no—
85C4⋊Dic13C2311yescharacteristic
86C4⋊Dic13C2311yescharacteristic
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
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3241—131nomaximal, Sylow
103C23×C13—21no—
104C23×C13—21no—
105C22×D13C2×D411yescharacteristic
106Q8×C13—81no—
107D4×C13—21no—
108D4×C13—21no—
109D4×C13—21no—
110D4×C13—21no—
111D4×C13—81no—
112D4×C13—81no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2411yescharacteristic
118C22⋊D13—81no—
119C22⋊D13—81no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—81no—
125C2×Dic13—81no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C4×D13—21no—
130C4×D13—21no—
131C4×D13—81no—
132Dic26—81no—
133C8×C13—21no—
134C8×C13—21no—
135#1055—21no—
136#1055—21no—
137#544—131no—
138#540—131no—
139#501—131no—
140#499—131no—
141#490—131no—
142#486D1311yescharacteristic, complemented
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—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13C22×D411yescharacteristic
159C2×D13—21no—
160C2×D13—21no—
161C2×D13—21no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C132−1+411yescharacteristic
167C4×C132−1+411yescharacteristic
168Dic13—21no—
169Dic13—21no—
170Dic13—21no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175C4⋊Q8—131no—
176C4⋊Q8—261no—
177C4⋊Q8C2×D1311yescharacteristic
178#127C2×D1311yescharacteristic
179#125—131no—
180#125—131no—
181#125—131no—
182#125—261no—
183#123—261no—
184#123—261no—
185C22⋊Q8—261no—
186C22⋊Q8—261no—
187#121—131no—
188#121—131no—
189#121—261no—
190#121—261no—
191C4×D4—131no—
192C4×D4—131no—
193#117—131no—
194#117—131no—
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#102C2×D1311yescharacteristic
211#102C2×D1311yescharacteristic
212#102C2×D1311yescharacteristic
213#102C2×D1311yescharacteristic
214C22⋊C8—131no—
215C22⋊C8—131no—
216#97—131no—
217C4×C8C2×D1311yescharacteristic
218C2×C13—81no—
219C2×C13—81no—
220C2×C13#53611yescharacteristic
221C2×C13#57611yescharacteristic
222C2×C13#57711yescharacteristic
223D13—41no—
224C2×Q8—21no—
225C2×Q8—261no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—261no—
229C2×D4—261no—
230C2×D4C22×D1311yescharacteristic
231C2×D4C22×D1311yescharacteristic
232C22×C4—131no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—261no—
236C2×C8—131no—
237C2×C8—131no—
238C2×C8C22×D1311yescharacteristic
239C2×C8C22×D1311yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
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⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—131no—
258C22⋊C4—131no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—131no—
265C42—261no—
266C42C22×D1311yescharacteristic
267C13#324111yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—131no—
271Q8—81no—
272Q8—1041no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—1041no—
280D4—1041no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—1041no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4D4×D1311yescharacteristic
296C2×C4D4×D1311yescharacteristic
297C2×C4C23×D1311yescharacteristic
298C8—21no—
299C8—21no—
300C8—261no—
301C8—261no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—261no—
309C22—261no—
310C22—261no—
311C22C2×D4×D1311yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—261no—
317C4—261no—
318C4—261no—
319C4—521no—
320C4—521no—
321C4—521no—
322C4—521no—
323C4#8825711yescharacteristic
324C4#8825711yescharacteristic
325C2—81no—
326C2—81no—
327C2—521no—
328C2#1171938011yescharacteristic
329C2#1171946211yescharacteristic
330C2#1171946711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
prime radical#11719424C2
hypercenter#486D13
hypocenterC13#3241
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719434C2semidirect
3. C13×#486C2semidirect
4. #11718741C2semidirect
5. #11718732C2semidirect
6. #11718445C2semidirect
7. #11718440C2semidirect
8. #11718438C2semidirect
9. #11718435C2semidirect
10. #11718427C2semidirect
11. #11718424C2semidirect
12. #11718422C2semidirect
13. #11718420C2semidirect
14. #11718351C2semidirect
15. #11718344C2semidirect
142. #486D13semidirect
267. C13#3241semidirect

Maximal subgroups

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

subgroupindex
#117194342
#117194242
C13×#4862
#117187412
#117187322
#117184452
#117184402
#117184382
#117184352
#117184272
#117184242
#117184222
#117184202
#117183512
#117183442
#324113