Finite Group Databasebeta

← #13126280

Subgroups — #13126280

Order 1664.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719424C211yesmaximal, characteristic
2#11719288C211yesmaximal, characteristic, complemented
3C13×#460C211yesmaximal, characteristic, complemented
4#11718835C211yesmaximal, characteristic, complemented
5#11718832C211yesmaximal, characteristic, complemented
6#11718823C211yesmaximal, characteristic, complemented
7#11718823C211yesmaximal, characteristic, complemented
8#11718736C211yesmaximal, characteristic, complemented
9#11718683C211yesmaximal, characteristic, complemented
10#11718500C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718441C211yesmaximal, characteristic, complemented
13#11718439C211yesmaximal, characteristic, complemented
14#11718427C211yesmaximal, characteristic, complemented
15#11718424C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C13×#127C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20#88200C2211yescharacteristic
21#88198C2211yescharacteristic
22#88193—21no—
23#88193—21no—
24#88192C2211yescharacteristic
25#88192C2211yescharacteristic
26#88189—21no—
27#88189—21no—
28D4×Dic13C2211yescharacteristic
29D4×Dic13C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31C2×#6105C2211yescharacteristic
32C2×#6094C2211yescharacteristic
33C2×C8×D13C2211yescharacteristic
34#88152—21no—
35#88151C2211yescharacteristic
36#88144C2211yescharacteristic
37#88143—21no—
38#88130—21no—
39#88126C2211yescharacteristic
40#88124—21no—
41#88124C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43C13×C4⋊C8C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
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×D13C2311yescharacteristic
69C2×Dic26C2311yescharacteristic
70C13×SD16—41no—
71C13×SD16—41no—
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C42×C13—21no—
77C42×C13C2311yescharacteristic
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82#6105—41no—
83#6105—41no—
84#6103—21no—
85#6103—21no—
86#6103D411yescharacteristic
87#6103D411yescharacteristic
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
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#6101D411yescharacteristic
101#6101D411yescharacteristic
102C4×Dic13—21no—
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—41no—
107C8×D13—41no—
108#3260—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13—21no—
111C22×D13C2×D411yescharacteristic
112Q8×C13—21no—
113Q8×C13—21no—
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—21no—
118D4×C13—81no—
119D4×C13—81no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C22⋊D13—81no—
126C22⋊D13—81no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—81no—
132C2×Dic13—81no—
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C4×D13—21no—
137C4×D13—21no—
138Dic26—21no—
139Dic26—21no—
140C8×C13—21no—
141C8×C13—21no—
142#1055—21no—
143#1055—21no—
144#541—131no—
145#540—131no—
146#479—131no—
147#479—131no—
148#478—131no—
149#478—131no—
150#468—131no—
151#468—131no—
152#465—131no—
153#465—131no—
154#461—131no—
155#461—131no—
156#460—131no—
157#460D1311yescharacteristic, complemented
158#424—131no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13C22×D411yescharacteristic
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13H(5,𝔽2)11yescharacteristic
174C4×C132−1+411yescharacteristic
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×SD16—131no—
183C2×SD16—131no—
184C2×SD16C2×D1311yescharacteristic
185C2×SD16C2×D1311yescharacteristic
186C2×M16—131no—
187C22×C8—131no—
188C4⋊Q8—131no—
189#127C2×D1311yescharacteristic
190#126—261no—
191#126—261no—
192#125—131no—
193#125—131no—
194#125—261no—
195#125—261no—
196#123—261no—
197#123—261no—
198C22⋊Q8—131no—
199C22⋊Q8—131no—
200#121—131no—
201#121—131no—
202#121—261no—
203#121—261no—
204C4×Q8—131no—
205C4×Q8C2×D1311yescharacteristic
206C4×D4—131no—
207C4×D4—131no—
208#117—131no—
209#107—131no—
210#107—131no—
211#106—131no—
212#106—131no—
213C4⋊C8—131no—
214C4⋊C8—131no—
215C4⋊C8—131no—
216C4⋊C8C2×D1311yescharacteristic
217#103—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#102—131no—
222#102—131no—
223#102C2×D1311yescharacteristic
224#102C2×D1311yescharacteristic
225C2×C13—81no—
226C2×C13—81no—
227C2×C13#53711yescharacteristic
228C2×C13#57711yescharacteristic
229C2×C13#57711yescharacteristic
230D13—41no—
231C2×Q8—131no—
232C2×Q8C22×D1311yescharacteristic
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—261no—
236C2×D4—261no—
237C2×D4C22×D1311yescharacteristic
238C2×D4C22×D1311yescharacteristic
239C22×C4—131no—
240C22×C4—261no—
241C22×C4—261no—
242SD16—41no—
243SD16—41no—
244SD16—521no—
245SD16—521no—
246M16—521no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—521no—
250C2×C8C22×D1311yescharacteristic
251C2×C8C22×D1311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4C22×D1311yescharacteristic
268C22⋊C4—131no—
269C22⋊C4—131no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C42—21no—
277C42—131no—
278C42—261no—
279C42C22×D1311yescharacteristic
280C13#326011yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—131no—
284Q8—21no—
285Q8—21no—
286Q8—261no—
287Q8—261no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—81no—
294D4—1041no—
295D4—1041no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—131no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—1041no—
308C2×C4—1041no—
309C2×C4D4×D1311yescharacteristic
310C2×C4D4×D1311yescharacteristic
311C2×C4C23×D1311yescharacteristic
312C8—21no—
313C8—21no—
314C8—261no—
315C8—261no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—261no—
323C22—261no—
324C22—261no—
325C22C2×D4×D1311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—261no—
331C4—261no—
332C4—261no—
333C4—521no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4#8825111yescharacteristic
338C4#8825711yescharacteristic
339C2—81no—
340C2—81no—
341C2—521no—
342C2#1171931311yescharacteristic
343C2#1171946711yescharacteristic
344C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#460C2
socleC22×C13C22×D4
prime radical#11719424C2
hypercenter#460D13
hypocenterC13#3260
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #11719288C2semidirect
3. C13×#460C2semidirect
4. #11718835C2semidirect
5. #11718832C2semidirect
6. #11718823C2semidirect
7. #11718823C2semidirect
8. #11718736C2semidirect
9. #11718683C2semidirect
10. #11718500C2semidirect
11. #11718490C2semidirect
12. #11718441C2semidirect
13. #11718439C2semidirect
14. #11718427C2semidirect
15. #11718424C2semidirect
157. #460D13semidirect
280. C13#3260semidirect

Maximal subgroups

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

subgroupindex
#117194242
#117192882
C13×#4602
#117188352
#117188322
#117188232
#117187362
#117186832
#117185002
#117184902
#117184412
#117184392
#117184272
#117184242
#326013