Finite Group Databasebeta

← #13125509

Subgroups — #13125509

Order 1664.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719438C211yesmaximal, characteristic
2#11719402C211yesmaximal, characteristic, complemented
3C13×#501C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718550C211yesmaximal, characteristic, complemented
7#11718548C211yesmaximal, characteristic, complemented
8#11718547C211yesmaximal, characteristic
9#11718534C211yesmaximal, characteristic, complemented
10#11718529C211yesmaximal, characteristic, complemented
11#11718525C211yesmaximal, characteristic
12#11718514C211yesmaximal, characteristic, complemented
13#11718513C211yesmaximal, characteristic, complemented
14#11718376C211yesmaximal, characteristic, complemented
15#11718369C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#125C2211yescharacteristic
18#88201—21no—
19#88200—21no—
20C2×Dic52C2211yescharacteristic
21C2×Dic52C2211yescharacteristic
22C2×#6095C2211yescharacteristic
23C2×#6095C2211yescharacteristic
24C2×#6094C2211yescharacteristic
25C2×C8×D13C2211yescharacteristic
26#88152—21no—
27#88152—21no—
28#88152—21no—
29#88151C2211yescharacteristic
30#88151C2211yescharacteristic
31#88151C2211yescharacteristic
32#88149C2211yescharacteristic
33#88148—21no—
34#88147C2211yescharacteristic
35#88144—21no—
36#88144—21no—
37#88141C2211yescharacteristic
38#88141C2211yescharacteristic
39#88141C2211yescharacteristic
40#88129C2211yescharacteristic
41#88126C2211yescharacteristic
42#88123C2211yescharacteristic
43C13×#107C2211yescharacteristic
44C13×#107C2211yescharacteristic
45C13×#106C2211yescharacteristic
46C13×#106C2211yescharacteristic
47C13×#97C2211yescharacteristic
48#88055C2211yescharacteristic
49C8×Dic13C2211yescharacteristic
50#88050C2211yescharacteristic
51#88050C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88049C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D52—21no—
61C2×D52C2311yescharacteristic
62C2×C4×D13—21no—
63C2×C4×D13C2311yescharacteristic
64C2×Dic26C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C2×Dic26C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C42×C13C2311yescharacteristic
77#6103—21no—
78#6103—21no—
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103D411yescharacteristic
85#6103D411yescharacteristic
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101D411yescharacteristic
95#6101D411yescharacteristic
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102Dic52—22no—
103Dic52—22no—
104#6095—22no—
105#6095—22no—
106#6094—22no—
107C8×D13—22no—
108#3178—131nomaximal, Sylow
109C22×D13—21no—
110C22×D13C2×D411yescharacteristic
111Q8×C13—81no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125D52—21no—
126D52—21no—
127D52—81no—
128C4×D13—21no—
129C4×D13—21no—
130C4×D13—81no—
131Dic26—21no—
132Dic26—21no—
133Dic26—21no—
134Dic26—21no—
135Dic26—21no—
136Dic26—21no—
137C8×C13#4112yes—
138C8×C13#4112yes—
139#1055—21no—
140#1055—21no—
141#542—131no—
142#541—131no—
143#501D1311yescharacteristic, complemented
144#497—131no—
145#488—131no—
146#487—131no—
147#470—131no—
148#468—131no—
149#467—131no—
150#465—131no—
151#441—131no—
152#440—131no—
153C4×Q16—131no—
154C4×SD16—131no—
155#405—131no—
156C22×C13C22×D411yescharacteristic
157C2×D13—21no—
158C2×D13—21no—
159C2×D13—21no—
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13C2×#4111yescharacteristic
170C4×C13C2×#4111yescharacteristic
171Dic13—21no—
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×Q16—131no—
178C2×Q16—131no—
179C2×SD16—131no—
180C2×SD16—131no—
181C2×M16—131no—
182C22×C8—131no—
183C4⋊Q8—131no—
184C4⋊Q8C2×D1311yescharacteristic
185#126—261no—
186#126—261no—
187#126—261no—
188#125—261no—
189#125—261no—
190#125C2×D1311yescharacteristic
191#124—131no—
192#124—261no—
193#123—261no—
194C22⋊Q8—131no—
195C22⋊Q8—131no—
196C22⋊Q8—131no—
197C22⋊Q8—261no—
198#121—131no—
199C4×Q8—131no—
200C4×Q8—131no—
201C4×Q8—131no—
202C4×D4—131no—
203#117—131no—
204#107C2×D1311yescharacteristic
205#107C2×D1311yescharacteristic
206#106C2×D1311yescharacteristic
207#106C2×D1311yescharacteristic
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#102—131no—
215#102—131no—
216#97—131no—
217#97C2×D1311yescharacteristic
218C4×C8—131no—
219C4×C8—131no—
220C2×C13#53211yescharacteristic
221C2×C13#57711yescharacteristic
222C2×C13#57811yescharacteristic
223D13—41no—
224D13—81no—
225C2×Q8—21no—
226C2×Q8—131no—
227C2×Q8—131no—
228C2×Q8—131no—
229C2×D4—131no—
230C2×D4—261no—
231C22×C4—131no—
232C22×C4—261no—
233Q16—262no—
234Q16—262no—
235SD16—262no—
236SD16—262no—
237M16—262no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—262no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4C22×D1311yescharacteristic
257C4⋊C4C22×D1311yescharacteristic
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—131no—
261C22⋊C4—131no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—131no—
270C42—261no—
271C42—261no—
272C42—261no—
273C42C22×D1311yescharacteristic
274C13#317811yescharacteristic, complemented, Sylow
275C23—131no—
276C23—261no—
277Q8—81no—
278Q8—261no—
279Q8—261no—
280Q8—261no—
281Q8—261no—
282Q8—261no—
283Q8—261no—
284D4—261no—
285D4—261no—
286D4—1041no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—1041no—
300C2×C4D4×D1311yescharacteristic
301C2×C4D4×D1311yescharacteristic
302C2×C4C23×D1311yescharacteristic
303C8—261no—
304C8—261no—
305C8#613112yes—
306C8#613112yes—
307C22—261no—
308C22—261no—
309C22—261no—
310C22—521no—
311C22—521no—
312C22—521no—
313C22C2×D4×D1311yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—261no—
321C4—261no—
322C4—261no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4C2×#613111yescharacteristic
327C4C2×#613111yescharacteristic
328C2—521no—
329C2—1041no—
330C2#1171943011yescharacteristic
331C2#1171948011yescharacteristic
332C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radical#88149C22
hypercenter#501D13
hypocenterC13#3178
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #11719402C2semidirect
3. C13×#501C2semidirect
4. #11718754C2semidirect
5. #11718729C2semidirect
6. #11718550C2semidirect
7. #11718548C2semidirect
9. #11718534C2semidirect
10. #11718529C2semidirect
12. #11718514C2semidirect
13. #11718513C2semidirect
14. #11718376C2semidirect
15. #11718369C2semidirect
143. #501D13semidirect
274. C13#3178semidirect

Maximal subgroups

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

subgroupindex
#117194382
#117194022
C13×#5012
#117187542
#117187292
#117185502
#117185482
#117185472
#117185342
#117185292
#117185252
#117185142
#117185132
#117183762
#117183692
#317813