Finite Group Databasebeta

← #13126266

Subgroups — #13126266

Order 1664.

334 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#11719402C211yesmaximal, characteristic, complemented
2#11719266C211yesmaximal, characteristic
3C13×#478C211yesmaximal, characteristic, complemented
4#11718724C211yesmaximal, characteristic, complemented
5#11718680C211yesmaximal, characteristic, complemented
6#11718548C211yesmaximal, characteristic, complemented
7#11718536C211yesmaximal, characteristic, complemented
8#11718529C211yesmaximal, characteristic, complemented
9#11718515C211yesmaximal, characteristic, complemented
10#11718510C211yesmaximal, characteristic, complemented
11#11718500C211yesmaximal, characteristic, complemented
12#11718441C211yesmaximal, characteristic
13#11718439C211yesmaximal, characteristic
14#11718428C211yesmaximal, characteristic, complemented
15#11718428C211yesmaximal, characteristic, complemented
16C13×#125C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic
18#88192C2211yescharacteristic
19#88190C2211yescharacteristic
20C2×#6105C2211yescharacteristic
21C2×#6105C2211yescharacteristic
22#88183—21no—
23#88178—21no—
24C2×Dic52C2211yescharacteristic
25C2×Dic52C2211yescharacteristic
26C2×#6094C2211yescharacteristic
27C2×C8×D13C2211yescharacteristic
28#88152—21no—
29#88152—21no—
30#88151C2211yescharacteristic
31#88151C2211yescharacteristic
32#88151C2211yescharacteristic
33#88144—21no—
34#88144—21no—
35#88142C2211yescharacteristic
36#88141C2211yescharacteristic
37#88141C2211yescharacteristic
38#88139—21no—
39#88133—21no—
40#88126C2211yescharacteristic
41#88123C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43C13×#107C2211yescharacteristic
44C13×#106C2211yescharacteristic
45C13×C4⋊C8C2211yescharacteristic
46C13×#102C2211yescharacteristic
47C13×#102C2211yescharacteristic
48#88056C2211yescharacteristic
49#88056C2211yescharacteristic
50#88054C2211yescharacteristic
51#88054C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×D4×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C2×C22⋊D13—21no—
62C2×C4×D13C2311yescharacteristic
63C2×Dic26—21no—
64C2×Dic26C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C2×Dic26C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4C2311yescharacteristic
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C42×C13C2311yescharacteristic
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79#6105—41no—
80#6105—41no—
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—
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101D411yescharacteristic
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104Dic52—41no—
105Dic52—41no—
106#6094—41no—
107C8×D13—41no—
108#3258—131nomaximal, Sylow
109C23×C13—21no—
110C22×D13C2×D411yescharacteristic
111D4×C13—21no—
112D4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—81no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—81no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C4×D13—21no—
129C4×D13—21no—
130Dic26—21no—
131Dic26—21no—
132Dic26—21no—
133Dic26—21no—
134Dic26—21no—
135Dic26—21no—
136Dic26—81no—
137C8×C13—21no—
138C8×C13—21no—
139#1055—21no—
140#1055—21no—
141#542—131no—
142#541—131no—
143#479—131no—
144#478D1311yescharacteristic, complemented
145#477—131no—
146#475—131no—
147#470—131no—
148#468—131no—
149#467—131no—
150#465—131no—
151#464—131no—
152#464—131no—
153#462—131no—
154#461—131no—
155#424—131no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13C22×D411yescharacteristic
160C2×D13—21no—
161C2×D13—21no—
162C2×D13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13H(5,𝔽2)11yescharacteristic
169C4×C132−1+411yescharacteristic
170Dic13—21no—
171Dic13—21no—
172Dic13—21no—
173Dic13—41no—
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⋊Q8—131no—
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×D4C2×D1311yescharacteristic
203#117—131no—
204#107—131no—
205#107C2×D1311yescharacteristic
206#106—131no—
207#106C2×D1311yescharacteristic
208C4⋊C8—131no—
209C4⋊C8—131no—
210C4⋊C8—131no—
211C4⋊C8C2×D1311yescharacteristic
212#103—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#102C2×D1311yescharacteristic
219#102C2×D1311yescharacteristic
220C2×C13—81no—
221C2×C13#53711yescharacteristic
222C2×C13#57711yescharacteristic
223C2×C13#57811yescharacteristic
224D13—41no—
225C2×Q8—131no—
226C2×Q8—131no—
227C2×Q8—131no—
228C2×Q8—261no—
229C2×D4—261no—
230C2×D4C22×D1311yescharacteristic
231C22×C4—21no—
232C22×C4—131no—
233Q16—521no—
234Q16—521no—
235SD16—521no—
236SD16—521no—
237M16—521no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—521no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—131no—
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⋊C4—261no—
257C4⋊C4C22×D1311yescharacteristic
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—131no—
262C22⋊C4—131no—
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#325811yescharacteristic, complemented, Sylow
275C23—21no—
276C23—131no—
277Q8—261no—
278Q8—261no—
279Q8—261no—
280Q8—261no—
281Q8—261no—
282Q8—261no—
283Q8—1041no—
284D4—21no—
285D4—21no—
286D4—1041no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—81no—
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—261no—
300C2×C4D4×D1311yescharacteristic
301C2×C4D4×D1311yescharacteristic
302C2×C4C23×D1311yescharacteristic
303C8—21no—
304C8—21no—
305C8—261no—
306C8—261no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—261no—
311C22—261no—
312C22—261no—
313C22C2×D4×D1311yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—261no—
320C4—261no—
321C4—261no—
322C4—521no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4#8825411yescharacteristic
327C4#8825611yescharacteristic
328C2—81no—
329C2—521no—
330C2#1171933411yescharacteristic
331C2#1171947611yescharacteristic
332C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#478C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#478D13
hypocenterC13#3258
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #11719402C2semidirect
3. C13×#478C2semidirect
4. #11718724C2semidirect
5. #11718680C2semidirect
6. #11718548C2semidirect
7. #11718536C2semidirect
8. #11718529C2semidirect
9. #11718515C2semidirect
10. #11718510C2semidirect
11. #11718500C2semidirect
14. #11718428C2semidirect
15. #11718428C2semidirect
144. #478D13semidirect
274. C13#3258semidirect

Maximal subgroups

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

subgroupindex
#117194022
#117192662
C13×#4782
#117187242
#117186802
#117185482
#117185362
#117185292
#117185152
#117185102
#117185002
#117184412
#117184392
#117184282
#325813