Finite Group Databasebeta

← #13119588

Subgroups — #13119588

Order 1664.

398 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#397C211yesmaximal, characteristic
2#11718643C211yesmaximal, characteristic, complemented
3C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
4#11718612C211yesmaximal, characteristic
5#11718609C211yesmaximal, characteristic
6#11718606C211yesmaximal, characteristic
7#11718606C211yesmaximal, characteristic
8#11718605C211yesmaximal, characteristic
9#11718605C211yesmaximal, characteristic
10#11718318C211yesmaximal, characteristic, complemented
11#11718315C211yesmaximal, characteristic, complemented
12#11718313C211yesmaximal, characteristic, complemented
13#11718312C211yesmaximal, characteristic, complemented
14#11718310C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C22⋊Dic13C2211yescharacteristic
21C2×C22⋊Dic13C2211yescharacteristic
22C2×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×#6101C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×C4×Dic13C2211yescharacteristic
33C2×C4×Dic13C2211yescharacteristic
34C2×C4×Dic13C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C13×#95C2211yescharacteristic
38C13×#95C2211yescharacteristic
39C13×#95C2211yescharacteristic
40#88071C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C22×C4×C13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×Dic13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C13×C4⋊C4—22no—
67C13×C22⋊C4—22no—
68C13×C22⋊C4—41no—
69C13×C22⋊C4—41no—
70C22⋊Dic13—22no—
71C22⋊Dic13—22no—
72C22⋊Dic13—22no—
73C22⋊Dic13—22no—
74C4⋊Dic13—22no—
75C4⋊Dic13—22no—
76#6101—22no—
77#6101—22no—
78#6101—22no—
79#6101—22no—
80#6101—41no—
81#6101—41no—
82C4×Dic13—22no—
83C4×Dic13—22no—
84C4×Dic13—22no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87#2525—131nomaximal, Sylow
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13C2411yescharacteristic
96C2×C4×C13—21no—
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×Dic13—21no—
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#4112yes—
135C2×Dic13#4112yes—
136C2×Dic13#4112yes—
137C2×Dic13#4112yes—
138#400—131no—
139#398—131no—
140#397D1311yescharacteristic
141#396—131no—
142#389—131no—
143#388—131no—
144#388—131no—
145#388—131no—
146#388—131no—
147#388—131no—
148#387—131no—
149#387—131no—
150#383—131no—
151C4×C4⋊C4—131no—
152C4×C4⋊C4—131no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13C2×#4111yescharacteristic
161C22×C13C2×#4111yescharacteristic
162C22×C13C2×#4111yescharacteristic
163C22×C13C2×#4111yescharacteristic
164C22×C13C2×#4111yescharacteristic
165C22×C13H(5,𝔽2)11yescharacteristic
166C22×C132−1+411yescharacteristic
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173Dic13—22no—
174Dic13—22no—
175Dic13—22no—
176Dic13—22no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4C2×D1311yescharacteristic
190C2×C22⋊C4—131no—
191C2×C22⋊C4—131no—
192C2×C22⋊C4—131no—
193C2×C22⋊C4—131no—
194C2×C22⋊C4C2×D1311yescharacteristic
195C2×C22⋊C4C2×D1311yescharacteristic
196C2×C22⋊C4C2×D1311yescharacteristic
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—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#95C2×D1311yescharacteristic
214#95C2×D1311yescharacteristic
215#95C2×D1311yescharacteristic
216C2×C13—81no—
217C2×C13#52911yescharacteristic
218C2×C13#52911yescharacteristic
219C2×C13#54211yescharacteristic
220C2×C13#55211yescharacteristic
221C2×C13#55311yescharacteristic
222C2×C13#55311yescharacteristic
223C2×C13#55611yescharacteristic
224C24C22×D1311yescharacteristic
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4C22×D1311yescharacteristic
234C22×C4C22×D1311yescharacteristic
235C22×C4C22×D1311yescharacteristic
236C22×C4C22×D1311yescharacteristic
237C22×C4C22×D1311yescharacteristic
238C22×C4C22×D1311yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—262no—
241C4⋊C4—262no—
242C4⋊C4—262no—
243C4⋊C4—262no—
244C4⋊C4—262no—
245C4⋊C4—262no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C22⋊C4—22no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—262no—
252C22⋊C4—262no—
253C22⋊C4—262no—
254C22⋊C4—262no—
255C42—262no—
256C42—262no—
257C42—262no—
258C42—521no—
259C42—521no—
260C13#252511yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D1311yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
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—132no—
287C2×C4—132no—
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#612912yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C2×#612911yescharacteristic
319C22#8825111yescharacteristic
320C22#41×D1311yescharacteristic
321C22#41×D1311yescharacteristic
322C22#41×D1311yescharacteristic
323C22#41×D1311yescharacteristic
324C22#8825711yescharacteristic
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—262no—
332C4—262no—
333C4—262no—
334C4—262no—
335C4—521no—
336C4—521no—
337C4—521no—
338C4—521no—
339C2—81no—
340C2#1171930811yescharacteristic
341C2#1171935411yescharacteristic
342C2#1171936611yescharacteristic
343C2#1171936611yescharacteristic
344C2#1171938511yescharacteristic
345C2#1171940711yescharacteristic
346C2#1171941311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC24×C13C23
hypercenter#397D13
hypocenterC13#2525
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #11718643C2semidirect
3. C4⋊C4×Dic13C2semidirect
10. #11718318C2semidirect
11. #11718315C2semidirect
12. #11718313C2semidirect
13. #11718312C2semidirect
14. #11718310C2semidirect
15. #11718308C2semidirect
260. C13#2525semidirect

Maximal subgroups

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

subgroupindex
C13×#3972
#117186432
C4⋊C4×Dic132
#117186122
#117186092
#117186062
#117186052
#117183182
#117183152
#117183132
#117183122
#117183102
#117183082
#252513