Finite Group Databasebeta

← #13122736

Subgroups — #13122736

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#389C211yesmaximal, characteristic, complemented
2#11718655C211yesmaximal, characteristic, complemented
3#11718655C211yesmaximal, characteristic, complemented
4#11718654C211yesmaximal, characteristic, complemented
5#11718652C211yesmaximal, characteristic
6#11718651C211yesmaximal, characteristic, complemented
7#11718649C211yesmaximal, characteristic
8#11718639C211yesmaximal, characteristic, complemented
9#11718633C211yesmaximal, characteristic, complemented
10#11718601C211yesmaximal, characteristic, complemented
11#11718601C211yesmaximal, characteristic, complemented
12#11718336C211yesmaximal, characteristic, complemented
13#11718333C211yesmaximal, characteristic
14#11718330C211yesmaximal, characteristic, complemented
15#11718315C211yesmaximal, characteristic, complemented
16C22×D52C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C42×C13C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41C13×#95C2211yescharacteristic
42C13×#95C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C23×D13C2311yescharacteristic
52C23×D13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C2×D52—22no—
67C2×D52—41no—
68C2×D52—41no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C42×C13—41no—
74#6103—22no—
75#6103—22no—
76#6103—22no—
77#6103—22no—
78#6103—41no—
79#6103—41no—
80#6103—41no—
81#6103—41no—
82#6103—41no—
83#6103—41no—
84#6103—41no—
85#6103—41no—
86C4⋊Dic13—22no—
87#6101—22no—
88#6101—22no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93#2800—131nomaximal, Sylow
94C23×C13C2411yescharacteristic
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—21no—
98C22×D13—21no—
99C22×D13—21no—
100C22×D13—21no—
101C22×D13—21no—
102C22×D13—21no—
103C22×D13—21no—
104C22×D13—21no—
105C22×D13—21no—
106C22×D13—21no—
107C22×D13—21no—
108C22×D13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13#4112yes—
129C2×C4×C13#4112yes—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13#4112yes—
148D52—44no—
149#397—131no—
150#397—131no—
151#396—131no—
152#396—131no—
153#394—131no—
154#394—131no—
155#390—131no—
156#389—131no—
157#389D1311yescharacteristic, complemented
158#388—131no—
159#388—131no—
160#388—131no—
161#388—131no—
162#387—131no—
163#387—131no—
164C22×C13C2×#4111yescharacteristic
165C22×C13C2×#4111yescharacteristic
166C22×C13C2×#4111yescharacteristic
167C22×C13H(5,𝔽2)11yescharacteristic
168C22×C13H(5,𝔽2)11yescharacteristic
169C22×C13H(5,𝔽2)11yescharacteristic
170C22×C132−1+411yescharacteristic
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—41no—
184C2×D13—41no—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192Dic13—22no—
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196Dic13—41no—
197Dic13—41no—
198C22×D4—131no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4C2×D1311yescharacteristic
205C2×C4⋊C4C2×D1311yescharacteristic
206C2×C4⋊C4C2×D1311yescharacteristic
207C2×C4⋊C4C2×D1311yescharacteristic
208C2×C22⋊C4—131no—
209C2×C22⋊C4—131no—
210C2×C22⋊C4—131no—
211C2×C22⋊C4—131no—
212C2×C22⋊C4—131no—
213C2×C22⋊C4—131no—
214C2×C22⋊C4—131no—
215C2×C22⋊C4—131no—
216C2×C22⋊C4—131no—
217C2×C22⋊C4—131no—
218C2×C22⋊C4—131no—
219C2×C22⋊C4—131no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42C2×D1311yescharacteristic
223#95—131no—
224#95—131no—
225#95—131no—
226#95—131no—
227#95—131no—
228#95—131no—
229#95—131no—
230#95—131no—
231#95C2×D1311yescharacteristic
232#95C2×D1311yescharacteristic
233C2×C13#53811yescharacteristic
234C2×C13#54011yescharacteristic
235C2×C13#54211yescharacteristic
236C2×C13#55311yescharacteristic
237C2×C13#55311yescharacteristic
238C2×C13#55611yescharacteristic
239C2×C13#56211yescharacteristic
240D13—81no—
241D13—81no—
242C24—131no—
243C24—131no—
244C2×D4—262no—
245C2×D4—521no—
246C2×D4—521no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4C22×D1311yescharacteristic
254C22×C4C22×D1311yescharacteristic
255C22×C4C22×D1311yescharacteristic
256C22×C4C22×D1311yescharacteristic
257C22×C4C22×D1311yescharacteristic
258C22×C4C22×D1311yescharacteristic
259C22×C4C22×D1311yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—262no—
265C4⋊C4—262no—
266C4⋊C4—262no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C22⋊C4—262no—
270C22⋊C4—262no—
271C22⋊C4—262no—
272C22⋊C4—262no—
273C22⋊C4—521no—
274C22⋊C4—521no—
275C22⋊C4—521no—
276C22⋊C4—521no—
277C22⋊C4—521no—
278C22⋊C4—521no—
279C22⋊C4—521no—
280C22⋊C4—521no—
281C42—41no—
282C42—521no—
283C42—521no—
284C13#280011yescharacteristic, complemented, Sylow
285C23—261no—
286C23—261no—
287C23—261no—
288C23—261no—
289C23—261no—
290C23—261no—
291C23—261no—
292C23—261no—
293C23—261no—
294C23—261no—
295C23—261no—
296C23—261no—
297C23—261no—
298C23—261no—
299C23C23×D1311yescharacteristic
300D4—524no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—132no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4#612712yes—
339C2×C4#613112yes—
340C22—521no—
341C22—521no—
342C22—521no—
343C22—521no—
344C22—521no—
345C22—521no—
346C22—521no—
347C22—521no—
348C22—521no—
349C22—521no—
350C22—521no—
351C22—521no—
352C22—521no—
353C22—521no—
354C22C2×#612711yescharacteristic
355C22#8825111yescharacteristic
356C22#8825111yescharacteristic
357C22C2×#613111yescharacteristic
358C22#8825411yescharacteristic
359C22#41×D1311yescharacteristic
360C22#8825611yescharacteristic
361C4—22no—
362C4—22no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—262no—
369C4—521no—
370C4—521no—
371C4—521no—
372C4—521no—
373C4—521no—
374C2—1041no—
375C2—1041no—
376C2#1171921911yescharacteristic
377C2#1171926511yescharacteristic
378C2#1171927311yescharacteristic
379C2#1171932011yescharacteristic
380C2#1171935211yescharacteristic
381C2#1171940011yescharacteristic
382C2#1171943811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
prime radicalC22×D52C22
hypercenter#389D13
hypocenterC13#2800
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C13×#389C2semidirect
2. #11718655C2semidirect
3. #11718655C2semidirect
4. #11718654C2semidirect
6. #11718651C2semidirect
8. #11718639C2semidirect
9. #11718633C2semidirect
10. #11718601C2semidirect
11. #11718601C2semidirect
12. #11718336C2semidirect
14. #11718330C2semidirect
15. #11718315C2semidirect
157. #389D13semidirect
284. C13#2800semidirect

Maximal subgroups

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

subgroupindex
C13×#3892
#117186552
#117186542
#117186522
#117186512
#117186492
#117186392
#117186332
#117186012
#117183362
#117183332
#117183302
#117183152
#280013