Finite Group Databasebeta

← #13119480

Subgroups — #13119480

Order 1664.

412 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#397C211yesmaximal, characteristic
2#11718642C211yesmaximal, characteristic, complemented
3#11718638C211yesmaximal, characteristic, complemented
4#11718613C211yesmaximal, characteristic
5#11718613C211yesmaximal, characteristic
6#11718611C211yesmaximal, characteristic
7#11718610C211yesmaximal, characteristic
8C22⋊C4×Dic13C211yesmaximal, characteristic
9C22⋊C4×Dic13C211yesmaximal, characteristic
10#11718316C211yesmaximal, characteristic, complemented
11#11718315C211yesmaximal, characteristic, complemented
12#11718314C211yesmaximal, characteristic, complemented
13#11718314C211yesmaximal, characteristic, complemented
14#11718313C211yesmaximal, characteristic, complemented
15#11718311C211yesmaximal, characteristic, complemented
16C23×Dic13C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
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×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×C4×Dic13C2211yescharacteristic
32C2×C4×Dic13C2211yescharacteristic
33C2×C4×Dic13C2211yescharacteristic
34C2×C4×Dic13C2211yescharacteristic
35C13×#95C2211yescharacteristic
36C13×#95C2211yescharacteristic
37C13×#95C2211yescharacteristic
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
52C22×C4×C13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×Dic13—22no—
59C22×Dic13—22no—
60C22×Dic13—41no—
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C13×C4⋊C4—22no—
70C13×C22⋊C4—22no—
71C13×C22⋊C4—22no—
72C13×C22⋊C4—22no—
73C22⋊Dic13—22no—
74C22⋊Dic13—22no—
75C22⋊Dic13—41no—
76C4⋊Dic13—22no—
77C4⋊Dic13—22no—
78C4⋊Dic13—22no—
79#6101—22no—
80#6101—22no—
81#6101—41no—
82#6101—41no—
83C4×Dic13—22no—
84C4×Dic13—22no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87#2517—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
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—21no—
135C2×Dic13—44no—
136C2×Dic13#4112yes—
137C2×Dic13#4112yes—
138C2×Dic13#4112yes—
139#399—131no—
140#397—131no—
141#397—131no—
142#397D1311yescharacteristic
143#387—131no—
144#387—131no—
145#387—131no—
146#387—131no—
147#387—131no—
148#387—131no—
149#385—131no—
150#382—131no—
151#382—131no—
152C4×C22⋊C4—131no—
153C4×C22⋊C4—131no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C2×#4111yescharacteristic
162C22×C13C2×#4111yescharacteristic
163C22×C13C2×#4111yescharacteristic
164C22×C13C2×#4111yescharacteristic
165C22×C13C2×#4111yescharacteristic
166C22×C13H(5,𝔽2)11yescharacteristic
167C22×C132−1+411yescharacteristic
168C4×C13—22no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174Dic13—22no—
175Dic13—22no—
176Dic13—22no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C23×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⋊C4—131no—
190C2×C4⋊C4C2×D1311yescharacteristic
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—
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#95C2×D1311yescharacteristic
215#95C2×D1311yescharacteristic
216#95C2×D1311yescharacteristic
217C2×C13—42no—
218C2×C13#52911yescharacteristic
219C2×C13#52911yescharacteristic
220C2×C13#53911yescharacteristic
221C2×C13#55111yescharacteristic
222C2×C13#55211yescharacteristic
223C2×C13#55211yescharacteristic
224C2×C13#55911yescharacteristic
225C24C22×D1311yescharacteristic
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—262no—
235C22×C4—262no—
236C22×C4—521no—
237C22×C4C22×D1311yescharacteristic
238C22×C4C22×D1311yescharacteristic
239C22×C4C22×D1311yescharacteristic
240C22×C4C22×D1311yescharacteristic
241C22×C4C22×D1311yescharacteristic
242C22×C4C22×D1311yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—262no—
245C4⋊C4—262no—
246C4⋊C4—262no—
247C4⋊C4—262no—
248C4⋊C4—262no—
249C4⋊C4—521no—
250C4⋊C4—521no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—262no—
255C22⋊C4—262no—
256C22⋊C4—521no—
257C42—262no—
258C42—262no—
259C42—521no—
260C42—521no—
261C13#251711yescharacteristic, complemented, Sylow
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#612912yes—
269C23C23×D1311yescharacteristic
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—21no—
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—261no—
311C2×C4—524no—
312C2×C4#612912yes—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22C2×#612911yescharacteristic
321C22C2×#612911yescharacteristic
322C22#41×D1311yescharacteristic
323C22#41×D1311yescharacteristic
324C22#41×D1311yescharacteristic
325C22#8825611yescharacteristic
326C22#8825711yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—262no—
334C4—262no—
335C4—262no—
336C4—521no—
337C4—521no—
338C4—521no—
339C4—521no—
340C4—521no—
341C2—42no—
342C2#1171930511yescharacteristic
343C2#1171935411yescharacteristic
344C2#1171935511yescharacteristic
345C2#1171937011yescharacteristic
346C2#1171938611yescharacteristic
347C2#1171941011yescharacteristic
348C2#1171941311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC24×C13C23
hypercenter#397D13
hypocenterC13#2517
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #11718642C2semidirect
3. #11718638C2semidirect
10. #11718316C2semidirect
11. #11718315C2semidirect
12. #11718314C2semidirect
13. #11718314C2semidirect
14. #11718313C2semidirect
15. #11718311C2semidirect
261. C13#2517semidirect

Maximal subgroups

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

subgroupindex
C13×#3972
#117186422
#117186382
#117186132
#117186112
#117186102
C22⋊C4×Dic132
#117183162
#117183152
#117183142
#117183132
#117183112
#251713