Finite Group Databasebeta

← #13127896

Subgroups — #13127896

Order 1664.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#559C211yesmaximal, characteristic, complemented
2#11719289C211yesmaximal, characteristic, complemented
3#11718736C211yesmaximal, characteristic, complemented
4#11718735C211yesmaximal, characteristic
5#11718721C211yesmaximal, characteristic, complemented
6#11718720C211yesmaximal, characteristic, complemented
7#11718718C211yesmaximal, characteristic, complemented
8#11718715C211yesmaximal, characteristic, complemented
9#11718691C211yesmaximal, characteristic, complemented
10#11718689C211yesmaximal, characteristic, complemented
11#11718685C211yesmaximal, characteristic, complemented
12#11718680C211yesmaximal, characteristic, complemented
13C4×#6105C211yesmaximal, characteristic, complemented
14#11718677C211yesmaximal, characteristic, complemented
15#11718675C211yesmaximal, characteristic, complemented
16C13×#127C2211yescharacteristic
17C13×#124—21no—
18C13×#124C2211yescharacteristic
19C13×#124C2211yescharacteristic
20C13×#123—21no—
21C13×#123—21no—
22C4×Q8×C13C2211yescharacteristic
23C4×Q8×C13C2211yescharacteristic
24C4×D4×C13—21no—
25C4×D4×C13C2211yescharacteristic
26C4×D4×C13C2211yescharacteristic
27#88200—21no—
28C2×#6107C2211yescharacteristic
29C2×#6107C2211yescharacteristic
30C2×#6106C2211yescharacteristic
31C2×#6105C2211yescharacteristic
32C2×#6105C2211yescharacteristic
33C2×#6105C2211yescharacteristic
34C2×#6105C2211yescharacteristic
35C2×#6104C2211yescharacteristic
36C2×#6104C2211yescharacteristic
37#88152—21no—
38#88152—21no—
39#88146—21no—
40#88129C2211yescharacteristic
41#88129C2211yescharacteristic
42C4×D52C2211yescharacteristic
43#88123C2211yescharacteristic
44C4×Dic26C2211yescharacteristic
45C4×Dic26C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88050C2211yescharacteristic
50#88050C2211yescharacteristic
51#88049C2211yescharacteristic
52#88048C2211yescharacteristic
53C4⋊#1055C2211yescharacteristic
54C4⋊#1055C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56#88043C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13D411yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×Dic26C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4D411yescharacteristic
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C42×C13—21no—
83C42×C13C2311yescharacteristic
84C42×C13C2311yescharacteristic
85C42×C13C2311yescharacteristic
86#6107—22no—
87#6107—41no—
88#6106—41no—
89#6105—22no—
90#6105—41no—
91#6105—41no—
92#6105—41no—
93#6104—22no—
94#6104—41no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3401—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C22×D13—21no—
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—41no—
118D4×C13—21no—
119D4×C13—21no—
120D4×C13—21no—
121D4×C13—21no—
122D4×C13—42no—
123D4×C13—81no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2×D411yescharacteristic
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2411yescharacteristic
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138D52—21no—
139D52—21no—
140C4×D13—42no—
141Dic26—21no—
142Dic26—21no—
143Dic26—21no—
144Dic26—21no—
145#1055—21no—
146#1055—21no—
147#1055—21no—
148#1055#4112yes—
149#559D1311yescharacteristic, complemented
150#556—131no—
151#497—131no—
152#496—131no—
153#495—131no—
154#464—131no—
155#464—131no—
156#463—131no—
157#463—131no—
158#461—131no—
159#460—131no—
160#446—131no—
161#442—131no—
162#441—131no—
163C4×SD16—131no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13C22×D411yescharacteristic
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13C2×#4111yescharacteristic
183C4×C13H(5,𝔽2)11yescharacteristic
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187C2×Q16—131no—
188C2×Q16—131no—
189C2×SD16—131no—
190C2×SD16—131no—
191C2×SD16—131no—
192C2×SD16—131no—
193C2×SD16—131no—
194C2×D8—131no—
195C2×D8—131no—
196C4⋊Q8—131no—
197#127C2×D1311yescharacteristic
198#126—261no—
199#126—261no—
200#124—21no—
201#124—131no—
202#124—131no—
203#124C2×D1311yescharacteristic
204#124C2×D1311yescharacteristic
205#123—21no—
206#123—21no—
207C22⋊Q8—261no—
208C4×Q8—131no—
209C4×Q8—131no—
210C4×Q8C2×D1311yescharacteristic
211C4×Q8C2×D1311yescharacteristic
212C4×D4—21no—
213C4×D4—131no—
214C4×D4C2×D1311yescharacteristic
215C4×D4C2×D1311yescharacteristic
216#117—261no—
217#106—131no—
218C4⋊C8—131no—
219C4⋊C8—131no—
220C4⋊C8—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#102—131no—
225#102—131no—
226#102—131no—
227#97—131no—
228#97—131no—
229C4×C8—131no—
230C2×C13—81no—
231C2×C13—81no—
232C2×C13#55011yescharacteristic
233C2×C13#57511yescharacteristic
234C2×C13#57711yescharacteristic
235D13—81no—
236C2×Q8—131no—
237C2×Q8—131no—
238C2×Q8C22⋊D1311yescharacteristic
239C2×Q8C22×D1311yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—131no—
243C2×D4C22×D1311yescharacteristic
244C2×D4C22×D1311yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—261no—
248Q16—262no—
249Q16—521no—
250SD16—262no—
251SD16—521no—
252SD16—521no—
253SD16—521no—
254SD16—521no—
255D8—262no—
256D8—521no—
257C2×C8—131no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—131no—
261C4⋊C4—21no—
262C4⋊C4—131no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4C22⋊D1311yescharacteristic
268C4⋊C4C22⋊D1311yescharacteristic
269C4⋊C4C22⋊D1311yescharacteristic
270C4⋊C4C22×D1311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C42—21no—
283C42—261no—
284C42—261no—
285C42C22×D1311yescharacteristic
286C42C22×D1311yescharacteristic
287C42C22×D1311yescharacteristic
288C13#340111yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—261no—
292Q8—21no—
293Q8—21no—
294Q8—41no—
295Q8—261no—
296Q8—261no—
297Q8—261no—
298Q8—261no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—81no—
305D4—261no—
306D4—261no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—522no—
315C2×C4C2×C22⋊D1311yescharacteristic
316C2×C4C2×C22⋊D1311yescharacteristic
317C2×C4C2×C22⋊D1311yescharacteristic
318C2×C4C2×C22⋊D1311yescharacteristic
319C2×C4C2×C22⋊D1311yescharacteristic
320C2×C4C2×C22⋊D1311yescharacteristic
321C2×C4C23×D1311yescharacteristic
322C8—132no—
323C8—261no—
324C8—261no—
325C8—261no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—521no—
333C22—521no—
334C22—521no—
335C22C22×C22⋊D1311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—521no—
345C4—521no—
346C4—521no—
347C4#41×D1311yescharacteristic
348C4#8825611yescharacteristic
349C2—81no—
350C2—81no—
351C2—1041no—
352C2#1171952711yescharacteristic
353C2#1171953911yescharacteristic
354C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#559C2
socleC22×C13C22×D4
prime radical#11718735C2
hypercenter#559D13
hypocenterC13#3401
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. C13×#559C2semidirect
2. #11719289C2semidirect
3. #11718736C2semidirect
5. #11718721C2semidirect
6. #11718720C2semidirect
7. #11718718C2semidirect
8. #11718715C2semidirect
9. #11718691C2semidirect
10. #11718689C2semidirect
11. #11718685C2semidirect
12. #11718680C2semidirect
13. C4×#6105C2semidirect
14. #11718677C2semidirect
15. #11718675C2semidirect
149. #559D13semidirect
288. C13#3401semidirect

Maximal subgroups

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

subgroupindex
C13×#5592
#117192892
#117187362
#117187352
#117187212
#117187202
#117187182
#117187152
#117186912
#117186892
#117186852
#117186802
C4×#61052
#117186772
#117186752
#340113