Finite Group Databasebeta

← #13125504

Subgroups — #13125504

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#11719239C211yesmaximal, characteristic
2#11719223C211yesmaximal, characteristic, complemented
3C13×#405C211yesmaximal, characteristic, complemented
4#11718798C211yesmaximal, characteristic, complemented
5#11718795C211yesmaximal, characteristic
6#11718777C211yesmaximal, characteristic, complemented
7#11718775C211yesmaximal, characteristic
8#11718377C211yesmaximal, characteristic, complemented
9#11718376C211yesmaximal, characteristic, complemented
10#11718371C211yesmaximal, characteristic, complemented
11#11718363C211yesmaximal, characteristic, complemented
12C4×Dic52C211yesmaximal, characteristic, complemented
13#11718358C211yesmaximal, characteristic, complemented
14C4×#6095C211yesmaximal, characteristic, complemented
15#11718342C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C22×C8×C13C2211yescharacteristic
18C13×#117C2211yescharacteristic
19#88184C2211yescharacteristic
20#88178C2211yescharacteristic
21#88178C2211yescharacteristic
22#88178C2211yescharacteristic
23C2×Dic52C2211yescharacteristic
24C2×Dic52C2211yescharacteristic
25C2×#6095C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27#88152—21no—
28#88150—21no—
29#88143—21no—
30#88143—21no—
31#88139—21no—
32#88137—21no—
33#88133—21no—
34#88133—21no—
35#88129C2211yescharacteristic
36C4×D52C2211yescharacteristic
37#88124C2211yescharacteristic
38#88123C2211yescharacteristic
39#88123C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43C13×#97C2211yescharacteristic
44C13×#97C2211yescharacteristic
45C4×C8×C13C2211yescharacteristic
46C4×C8×C13C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C2×C22⋊D13—21no—
61C2×D52C2311yescharacteristic
62C2×C4×D13—21no—
63C2×Dic26—21no—
64C2×Dic26C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C2×Dic26C2311yescharacteristic
67C13×M16—22no—
68C2×C8×C13—22no—
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4D411yescharacteristic
75C13×C22⋊C4D411yescharacteristic
76C13×C22⋊C4D411yescharacteristic
77C42×C13C2311yescharacteristic
78C42×C13C2311yescharacteristic
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—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—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104Dic52—22no—
105Dic52—22no—
106#6095—22no—
107#6095—22no—
108#3178—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—81no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127D52—21no—
128D52—21no—
129C4×D13—81no—
130Dic26—21no—
131Dic26—21no—
132Dic26—21no—
133Dic26—21no—
134Dic26—21no—
135Dic26—21no—
136Dic26—81no—
137C8×C13—21no—
138C8×C13—21no—
139C8×C13#4112yes—
140C8×C13#4112yes—
141#542—131no—
142#541—131no—
143#501—131no—
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#405D1311yescharacteristic, complemented
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13C22×D411yescharacteristic
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13C2×#4111yescharacteristic
169C4×C13C2×#4111yescharacteristic
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×Q16—131no—
178C2×Q16—131no—
179C2×SD16—131no—
180C2×SD16—131no—
181C2×M16C2×D1311yescharacteristic
182C22×C8C2×D1311yescharacteristic
183C4⋊Q8—131no—
184C4⋊Q8—131no—
185#126—261no—
186#126—261no—
187#126—261no—
188#125—131no—
189#125—261no—
190#125—261no—
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#117C2×D1311yescharacteristic
204#107—131no—
205#107—131no—
206#106—131no—
207#106—131no—
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#97C2×D1311yescharacteristic
217#97C2×D1311yescharacteristic
218C4×C8C2×D1311yescharacteristic
219C4×C8C2×D1311yescharacteristic
220C2×C13—41no—
221C2×C13#53211yescharacteristic
222C2×C13#57711yescharacteristic
223C2×C13#57811yescharacteristic
224D13—81no—
225C2×Q8—131no—
226C2×Q8—131no—
227C2×Q8—131no—
228C2×Q8—261no—
229C2×D4—131no—
230C2×D4—261no—
231C22×C4—261no—
232C22×C4C22×D1311yescharacteristic
233Q16—262no—
234Q16—262no—
235SD16—262no—
236SD16—262no—
237M16—22no—
238C2×C8—22no—
239C2×C8C22×D1311yescharacteristic
240C2×C8C22×D1311yescharacteristic
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
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⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4D5211yescharacteristic
259C4⋊C4D5211yescharacteristic
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4D5211yescharacteristic
268C22⋊C4D5211yescharacteristic
269C42—261no—
270C42—261no—
271C42—261no—
272C42C22×D1311yescharacteristic
273C42C22×D1311yescharacteristic
274C13#317811yescharacteristic, complemented, Sylow
275C23—261no—
276C23C2×D5211yescharacteristic
277Q8—261no—
278Q8—261no—
279Q8—261no—
280Q8—261no—
281Q8—261no—
282Q8—261no—
283Q8—1041no—
284D4—261no—
285D4—261no—
286D4—1041no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—1041no—
297C2×C4C2×D5211yescharacteristic
298C2×C4C2×D5211yescharacteristic
299C2×C4C2×D5211yescharacteristic
300C2×C4C2×D5211yescharacteristic
301C2×C4C2×D5211yescharacteristic
302C2×C4C23×D1311yescharacteristic
303C8—21no—
304C8—21no—
305C8#612712yes—
306C8#612712yes—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—521no—
311C22—521no—
312C22—521no—
313C22C22×D5211yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—521no—
320C4—521no—
321C4—521no—
322C4—521no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4C2×#612711yescharacteristic
327C4C2×#612711yescharacteristic
328C2—41no—
329C2—1041no—
330C2#1171918211yescharacteristic
331C2#1171945611yescharacteristic
332C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#405C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#405D13
hypocenterC13#3178
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
2. #11719223C2semidirect
3. C13×#405C2semidirect
4. #11718798C2semidirect
6. #11718777C2semidirect
8. #11718377C2semidirect
9. #11718376C2semidirect
10. #11718371C2semidirect
11. #11718363C2semidirect
12. C4×Dic52C2semidirect
13. #11718358C2semidirect
14. C4×#6095C2semidirect
15. #11718342C2semidirect
155. #405D13semidirect
274. C13#3178semidirect

Maximal subgroups

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

subgroupindex
#117192392
#117192232
C13×#4052
#117187982
#117187952
#117187772
#117187752
#117183772
#117183762
#117183712
#117183632
C4×Dic522
#117183582
C4×#60952
#117183422
#317813