Finite Group Databasebeta

← #13125837

Subgroups — #13125837

Order 1664.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#124C211yesmaximal, characteristic
2#11719283C211yesmaximal, characteristic, complemented
3C13×#464C211yesmaximal, characteristic, complemented
4#11718851C211yesmaximal, characteristic, complemented
5#11718847C211yesmaximal, characteristic, complemented
6#11718830C211yesmaximal, characteristic
7#11718828C211yesmaximal, characteristic, complemented
8#11718715C211yesmaximal, characteristic, complemented
9#11718689C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718496C211yesmaximal, characteristic, complemented
12#11718469C211yesmaximal, characteristic, complemented
13#11718456C211yesmaximal, characteristic, complemented
14#11718437C211yesmaximal, characteristic
15#11718426C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic, complemented
19C2×C13×SD16C2211yescharacteristic
20C13×#124C2211yescharacteristic
21C4×Q8×C13C2211yescharacteristic, complemented
22#88201C2211yescharacteristic
23#88200C2211yescharacteristic
24#88198C2211yescharacteristic, complemented
25C2×#6107C2211yescharacteristic, complemented
26C2×#6107C2211yescharacteristic, complemented
27C2×#6106C2211yescharacteristic
28#88190C2211yescharacteristic
29C2×#6105C2211yescharacteristic
30C2×Dic52C2211yescharacteristic, complemented
31C2×#6095C2211yescharacteristic
32#88151C2211yescharacteristic
33#88150—21no—
34#88143—21no—
35#88142C2211yescharacteristic, complemented
36#88139—21no—
37#88139—21no—
38C22⋊C4×D13—21no—
39C22⋊C4×D13—21no—
40#88129C2211yescharacteristic
41#88126—21no—
42C42×D13C2211yescharacteristic
43C4×Dic26—21no—
44C4×Dic26C2211yescharacteristic, complemented
45C13×C4⋊C8C2211yescharacteristic, complemented
46C13×#103C2211yescharacteristic, complemented
47C13×#102C2211yescharacteristic
48#88075C2211yescharacteristic, complemented
49#88072C2211yescharacteristic
50#88061C2211yescharacteristic
51#88060C2211yescharacteristic
52#88060C2211yescharacteristic
53#88056C2211yescharacteristic, complemented
54#88055C2211yescharacteristic, complemented
55#88055C2211yescharacteristic, complemented
56#88050C2211yescharacteristic, complemented
57#88049C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64Q8×D13—41no—
65Q8×D13—41no—
66D4×D13—41no—
67D4×D13—41no—
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13D411yescharacteristic
71C2×C4×D13D411yescharacteristic
72C2×C4×D13C2311yescharacteristic
73C2×Dic26—21no—
74C2×Dic26—21no—
75C2×Dic26C2311yescharacteristic
76C2×Dic26C2311yescharacteristic
77C13×Q16—41no—
78C13×SD16—41no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4—21no—
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C42×C13—21no—
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89#6107—41no—
90#6107—41no—
91#6106—41no—
92#6105—41no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106C4×Dic13—21no—
107C4×Dic13D411yescharacteristic
108C4×Dic13D411yescharacteristic
109C4×Dic13C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112Dic52—41no—
113#6095—41no—
114#3215—131nomaximal, Sylow
115C23×C13—21no—
116C22×D13—21no—
117C22×D13—42no—
118C22×D13—42no—
119C22×D13—42no—
120C22×D13C2×D411yescharacteristic
121Q8×C13—21no—
122Q8×C13—21no—
123Q8×C13—21no—
124Q8×C13—21no—
125D4×C13—21no—
126D4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C22⋊D13—42no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140D52—21no—
141D52—21no—
142C4×D13—22no—
143C4×D13—21no—
144C4×D13—21no—
145C4×D13—41no—
146C4×D13—42no—
147Dic26—21no—
148Dic26—21no—
149Dic26—21no—
150Dic26—21no—
151Dic26—42no—
152Dic26—42no—
153C8×C13—21no—
154C8×C13—21no—
155#1055—21no—
156#1055—21no—
157#533—131no—
158C2×#124—131no—
159#497—131no—
160#497—131no—
161#489—131no—
162#489—131no—
163#464—131no—
164#464—131no—
165#464—131no—
166#464D1311yescharacteristic, complemented
167#451—131no—
168#451—131no—
169#450—131no—
170#450—131no—
171#432—131no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13C22×D411yescharacteristic
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—84no—
182C2×D13#13712yes—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13H(5,𝔽2)11yescharacteristic
189C4×C13H(5,𝔽2)11yescharacteristic
190Dic13—21no—
191Dic13—21no—
192Dic13—21no—
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196C22×Q8—131no—
197C22×D4—131no—
198C2×Q16—131no—
199C2×Q16—131no—
200C2×Q16—131no—
201C2×Q16C2×D1311yescharacteristic, complemented
202C2×SD16—131no—
203C2×SD16—131no—
204C2×SD16—131no—
205C2×SD16C2×D1311yescharacteristic
206C4⋊Q8—131no—
207C4⋊Q8—131no—
208#125—261no—
209#124—131no—
210#124—131no—
211#124—131no—
212#124—261no—
213#124—261no—
214#124C2×D1311yescharacteristic
215C22⋊Q8—131no—
216C22⋊Q8—131no—
217C22⋊Q8—261no—
218C4×Q8—131no—
219C4×Q8—261no—
220C4×Q8C2×D1311yescharacteristic, complemented
221#117—261no—
222C2×C22⋊C4—261no—
223C2×C22⋊C4—261no—
224C2×C42—131no—
225C4⋊C8—131no—
226C4⋊C8C2×D1311yescharacteristic, complemented
227#103—131no—
228#103—131no—
229#103—131no—
230#103C2×D1311yescharacteristic, complemented
231#102—131no—
232#102—131no—
233#102—131no—
234#102C2×D1311yescharacteristic
235C22⋊C8—131no—
236C22⋊C8—131no—
237#97—131no—
238#97—131no—
239C2×C13—81no—
240C2×C13#53511yescharacteristic
241C2×C13C2×#13711yescharacteristic
242C2×C13#57511yescharacteristic
243D13—22no—
244D13—81no—
245C24—261no—
246C2×Q8—131no—
247C2×Q8—131no—
248C2×Q8—261no—
249C2×Q8—261no—
250C2×Q8—521no—
251C2×Q8—521no—
252C2×Q8C22×D1311yescharacteristic
253C2×Q8C22×D1311yescharacteristic
254C2×D4—131no—
255C2×D4—261no—
256C2×D4—521no—
257C2×D4—521no—
258C2×D4C22×D1311yescharacteristic
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—131no—
262C22×C4—261no—
263Q16—41no—
264Q16—521no—
265Q16—521no—
266Q16—521no—
267SD16—41no—
268SD16—521no—
269SD16—521no—
270SD16—521no—
271C2×C8—131no—
272C2×C8—131no—
273C2×C8C22×D1311yescharacteristic
274C2×C8C22×D1311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—131no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4C22×D1311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C42—21no—
295C42—131no—
296C42—131no—
297C42—131no—
298C42—261no—
299C42C22×D1311yescharacteristic
300C13#321511yescharacteristic, complemented, Sylow
301C23—21no—
302C23—131no—
303C23—261no—
304C23—522no—
305C23—522no—
306C23—522no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—261no—
312Q8—261no—
313Q8—261no—
314Q8—261no—
315Q8—522no—
316Q8—522no—
317D4—21no—
318D4—21no—
319D4—261no—
320D4—261no—
321D4—522no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—131no—
326C2×C4—131no—
327C2×C4—131no—
328C2×C4—262no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—521no—
335C2×C4—522no—
336C2×C4D4×D1311yescharacteristic
337C2×C4D4×D1311yescharacteristic
338C2×C4C23×D1311yescharacteristic
339C8—21no—
340C8—21no—
341C8—261no—
342C8—261no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—132no—
347C22—261no—
348C22—261no—
349C22—521no—
350C22—521no—
351C22—521no—
352C22—1044no—
353C22C2×D4×D1311yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—261no—
360C4—261no—
361C4—261no—
362C4—521no—
363C4—521no—
364C4—521no—
365C4#8825111yescharacteristic
366C4#8825611yescharacteristic
367C2—81no—
368C2—262no—
369C2—1041no—
370C2#1171931211yescharacteristic
371C2#1171947311yescharacteristic
372C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#464C2
socleC22×C13C22×D4
prime radicalC2×D4×D13C22
hypercenter#464D13
hypocenterC13#3215
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #11719283C2semidirect
3. C13×#464C2semidirect
4. #11718851C2semidirect
5. #11718847C2semidirect
7. #11718828C2semidirect
8. #11718715C2semidirect
9. #11718689C2semidirect
10. #11718506C2semidirect
11. #11718496C2semidirect
12. #11718469C2semidirect
13. #11718456C2semidirect
15. #11718426C2semidirect
18. C2×C13×Q16C22semidirect
21. C4×Q8×C13C22semidirect
24. #88198C22semidirect
25. C2×#6107C22semidirect
26. C2×#6107C22semidirect
30. C2×Dic52C22semidirect
35. #88142C22semidirect
44. C4×Dic26C22semidirect
45. C13×C4⋊C8C22semidirect
46. C13×#103C22semidirect
48. #88075C22semidirect
53. #88056C22semidirect
54. #88055C22semidirect
55. #88055C22semidirect
56. #88050C22semidirect
58. C4⋊#1055C22semidirect
166. #464D13semidirect
201. C2×Q16C2×D13semidirect
220. C4×Q8C2×D13semidirect
226. C4⋊C8C2×D13semidirect
230. #103C2×D13semidirect
300. C13#3215semidirect

Maximal subgroups

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

subgroupindex
D13×#1242
#117192832
C13×#4642
#117188512
#117188472
#117188302
#117188282
#117187152
#117186892
#117185062
#117184962
#117184692
#117184562
#117184372
#117184262
#321513