Finite Group Databasebeta

← #13122167

Subgroups — #13122167

Order 1664.

434 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#386C211yesmaximal, characteristic
2#11718883C211yesmaximal, characteristic
3#11718882C211yesmaximal, characteristic
4#11718871C211yesmaximal, characteristic, complemented
5#11718871C211yesmaximal, characteristic, complemented
6#11718613C211yesmaximal, characteristic, complemented
7#11718613C211yesmaximal, characteristic, complemented
8#11718613C211yesmaximal, characteristic, complemented
9#11718612C211yesmaximal, characteristic, complemented
10#11718609C211yesmaximal, characteristic, complemented
11#11718605C211yesmaximal, characteristic, complemented
12#11718318C211yesmaximal, characteristic, complemented
13#11718314C211yesmaximal, characteristic, complemented
14#11718312C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic13C2211yescharacteristic
22C2×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C13×#95C2211yescharacteristic
40C13×#95C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C24×C13C2311yescharacteristic
53C2×D4×C13—22no—
54C2×D4×C13—22no—
55C2×D4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C13×C22⋊C4—22no—
73C13×C22⋊C4—41no—
74C13×C22⋊C4—41no—
75C22⋊Dic13—22no—
76C22⋊Dic13—22no—
77C22⋊Dic13—22no—
78C22⋊Dic13—41no—
79C22⋊Dic13—41no—
80C22⋊Dic13—41no—
81C22⋊Dic13—41no—
82C22⋊Dic13—41no—
83C4⋊Dic13—22no—
84C4⋊Dic13—41no—
85#6101—22no—
86#6101—41no—
87#6101—41no—
88#6101—41no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—22no—
92C4×Dic13—41no—
93#2757—131nomaximal, Sylow
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13#4112yes—
108C23×C13C2411yescharacteristic
109D4×C13—44no—
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—44no—
125C2×C4×C13#4112yes—
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—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—21no—
148C2×Dic13—21no—
149C2×Dic13#4112yes—
150#398—131no—
151#397—131no—
152#397—131no—
153#397—131no—
154#396—131no—
155#394—131no—
156#390—131no—
157#389—131no—
158#388—131no—
159#388—131no—
160#387—131no—
161#386D1311yescharacteristic
162#385—131no—
163#385—131no—
164#383—131no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13C2×#4111yescharacteristic
180C22×C13C2×#4111yescharacteristic
181C22×C13C2×#4111yescharacteristic
182C22×C13H(5,𝔽2)11yescharacteristic
183C22×C13H(5,𝔽2)11yescharacteristic
184C22×C13H(5,𝔽2)11yescharacteristic
185C22×C132−1+411yescharacteristic
186C4×C13—22no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191Dic13—22no—
192Dic13—41no—
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199C22×D4C2×D1311yescharacteristic
200C23×C4C2×D1311yescharacteristic
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊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⋊C4C2×D1311yescharacteristic
218C2×C22⋊C4C2×D1311yescharacteristic
219C2×C22⋊C4C2×D1311yescharacteristic
220C2×C42—131no—
221C2×C42—131no—
222#95—131no—
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#95—131no—
232#95C2×D1311yescharacteristic
233#95C2×D1311yescharacteristic
234C2×C13—42no—
235C2×C13—81no—
236C2×C13#53911yescharacteristic
237C2×C13#54211yescharacteristic
238C2×C13#54211yescharacteristic
239C2×C13#55111yescharacteristic
240C2×C13#55311yescharacteristic
241C2×C13#55311yescharacteristic
242C2×C13#56011yescharacteristic
243C24C22×D1311yescharacteristic
244C24C22×D1311yescharacteristic
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4C22×D1311yescharacteristic
260C22×C4C22×D1311yescharacteristic
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263C22×C4C22×D1311yescharacteristic
264C4⋊C4—262no—
265C4⋊C4—262no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C22⋊C4—22no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—262no—
276C22⋊C4—262no—
277C22⋊C4—262no—
278C22⋊C4—521no—
279C22⋊C4—521no—
280C22⋊C4—521no—
281C22⋊C4—521no—
282C22⋊C4—521no—
283C42—262no—
284C42—521no—
285C13#275711yescharacteristic, complemented, Sylow
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23#612912yes—
300C23C23×D1311yescharacteristic
301D4—44no—
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—44no—
317C2×C4—132no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
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—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4#612712yes—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22C2×#612711yescharacteristic
357C22C2×#612911yescharacteristic
358C22#8825111yescharacteristic
359C22#8825111yescharacteristic
360C22#8825111yescharacteristic
361C22#41×D1311yescharacteristic
362C22#8825711yescharacteristic
363C4—22no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—262no—
369C4—521no—
370C4—521no—
371C4—521no—
372C4—521no—
373C4—521no—
374C4—521no—
375C4—521no—
376C2—42no—
377C2—81no—
378C2#1171920011yescharacteristic
379C2#1171926311yescharacteristic
380C2#1171926611yescharacteristic
381C2#1171930011yescharacteristic
382C2#1171930611yescharacteristic
383C2#1171930711yescharacteristic
384C2#1171936711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC22×D4×C13C22
hypercenter#386D13
hypocenterC13#2757
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
4. #11718871C2semidirect
5. #11718871C2semidirect
6. #11718613C2semidirect
7. #11718613C2semidirect
8. #11718613C2semidirect
9. #11718612C2semidirect
10. #11718609C2semidirect
11. #11718605C2semidirect
12. #11718318C2semidirect
13. #11718314C2semidirect
14. #11718312C2semidirect
15. #11718308C2semidirect
285. C13#2757semidirect

Maximal subgroups

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

subgroupindex
C13×#3862
#117188832
#117188822
#117188712
#117186132
#117186122
#117186092
#117186052
#117183182
#117183142
#117183122
#117183082
#275713