Finite Group Databasebeta

← #13119616

Subgroups — #13119616

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#393C211yesmaximal, characteristic
2#11718891C211yesmaximal, characteristic, complemented
3#11718891C211yesmaximal, characteristic, complemented
4#11718614C211yesmaximal, characteristic
5#11718611C211yesmaximal, characteristic
6#11718606C211yesmaximal, characteristic
7#11718605C211yesmaximal, characteristic
8#11718604C211yesmaximal, characteristic
9C22⋊C4×Dic13C211yesmaximal, characteristic
10C13⋊#401C211yesmaximal, characteristic, complemented
11#11718321C211yesmaximal, characteristic, complemented
12#11718316C211yesmaximal, characteristic, complemented
13#11718315C211yesmaximal, characteristic, complemented
14#11718315C211yesmaximal, characteristic, complemented
15#11718309C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic13C2211yescharacteristic
22C2×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30C2×C4×Dic13C2211yescharacteristic
31C2×C4×Dic13C2211yescharacteristic
32C2×C4×Dic13C2211yescharacteristic
33C13×#95C2211yescharacteristic
34C13×#95C2211yescharacteristic
35C13×#95C2211yescharacteristic
36#88071C2211yescharacteristic
37#88071C2211yescharacteristic
38#88071C2211yescharacteristic
39#88071C2211yescharacteristic
40#88071C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C2×Q8×C13—22no—
53C2×Q8×C13—22no—
54C2×Q8×C13—41no—
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—41no—
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C13×C22⋊C4—22no—
73C13×C22⋊C4—22no—
74C13×C22⋊C4—41no—
75C22⋊Dic13—22no—
76C22⋊Dic13—22no—
77C22⋊Dic13—22no—
78C4⋊Dic13—22no—
79C4⋊Dic13—22no—
80C4⋊Dic13—41no—
81#6101—22no—
82#6101—41no—
83C4×Dic13—22no—
84C4×Dic13—22no—
85C4×Dic13—22no—
86C4×Dic13—41no—
87#2527—131nomaximal, Sylow
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13#4112yes—
95C23×C13C2411yescharacteristic
96Q8×C13—44no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13#4112yes—
114C2×C4×C13#4112yes—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—44no—
138C2×Dic13#4112yes—
139C2×Dic13#4112yes—
140#401—131no—
141#400—131no—
142#397—131no—
143#393D1311yescharacteristic
144#391—131no—
145#391—131no—
146#388—131no—
147#388—131no—
148#387—131no—
149#387—131no—
150#387—131no—
151#385—131no—
152#381—131no—
153C4×C22⋊C4—131no—
154#376—131no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13C2×#4111yescharacteristic
163C22×C13C2×#4111yescharacteristic
164C22×C13C2×#4111yescharacteristic
165C22×C13C2×#4111yescharacteristic
166C22×C13C2×#4111yescharacteristic
167C22×C13H(5,𝔽2)11yescharacteristic
168C22×C132−1+411yescharacteristic
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175Dic13—22no—
176Dic13—22no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182Dic13—41no—
183C22×Q8C2×D1311yescharacteristic
184C23×C4—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—131no—
190C2×C22⋊C4—131no—
191C2×C22⋊C4—131no—
192C2×C22⋊C4—131no—
193C2×C22⋊C4C2×D1311yescharacteristic
194C2×C22⋊C4C2×D1311yescharacteristic
195C2×C22⋊C4C2×D1311yescharacteristic
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200#95—131no—
201#95—131no—
202#95—131no—
203#95—131no—
204#95—131no—
205#95—131no—
206#95—131no—
207#95—131no—
208#95—131no—
209#95—131no—
210#95—131no—
211#95—131no—
212#95—131no—
213#95—131no—
214#95—131no—
215#95C2×D1311yescharacteristic
216#95C2×D1311yescharacteristic
217#95C2×D1311yescharacteristic
218C2×C13—42no—
219C2×C13#52911yescharacteristic
220C2×C13#52911yescharacteristic
221C2×C13#54211yescharacteristic
222C2×C13#55111yescharacteristic
223C2×C13#55111yescharacteristic
224C2×C13#55211yescharacteristic
225C2×C13#55611yescharacteristic
226C24C22×D1311yescharacteristic
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—41no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—262no—
239C22×C4—262no—
240C22×C4—521no—
241C22×C4C22×D1311yescharacteristic
242C22×C4C22×D1311yescharacteristic
243C22×C4C22×D1311yescharacteristic
244C22×C4C22×D1311yescharacteristic
245C22×C4C22×D1311yescharacteristic
246C22×C4C22×D1311yescharacteristic
247C4⋊C4—262no—
248C4⋊C4—262no—
249C4⋊C4—262no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—41no—
255C22⋊C4—262no—
256C22⋊C4—262no—
257C22⋊C4—262no—
258C42—262no—
259C42—262no—
260C42—262no—
261C42—521no—
262C13#252711yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23#613112yes—
270C23C23×D1311yescharacteristic
271Q8—44no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—132no—
289C2×C4—132no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—524no—
313C2×C4#612912yes—
314C2×C4#612912yes—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22C2×#612911yescharacteristic
323C22C2×#612911yescharacteristic
324C22#8825111yescharacteristic
325C22C2×#613111yescharacteristic
326C22#41×D1311yescharacteristic
327C22#41×D1311yescharacteristic
328C22#8825711yescharacteristic
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—262no—
336C4—262no—
337C4—521no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4—521no—
342C4—521no—
343C2—42no—
344C2#1171929211yescharacteristic
345C2#1171932911yescharacteristic
346C2#1171934211yescharacteristic
347C2#1171934711yescharacteristic
348C2#1171937411yescharacteristic
349C2#1171937611yescharacteristic
350C2#1171938511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC24×C13C23
hypercenter#393D13
hypocenterC13#2527
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #11718891C2semidirect
3. #11718891C2semidirect
10. C13⋊#401C2semidirect
11. #11718321C2semidirect
12. #11718316C2semidirect
13. #11718315C2semidirect
14. #11718315C2semidirect
15. #11718309C2semidirect
262. C13#2527semidirect

Maximal subgroups

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

subgroupindex
C13×#3932
#117188912
#117186142
#117186112
#117186062
#117186052
#117186042
C22⋊C4×Dic132
C13⋊#4012
#117183212
#117183162
#117183152
#117183092
#252713