Finite Group Databasebeta

← #13131704

Subgroups — #13131704

Order 1664.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719361C211yesmaximal, characteristic
2#11719147C211yesmaximal, characteristic, complemented
3#11719146C211yesmaximal, characteristic, complemented
4#11719127C211yesmaximal, characteristic, complemented
5D13⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
6#11719076C211yesmaximal, characteristic, complemented
7#11719075C211yesmaximal, characteristic, complemented
8#11719075C211yesmaximal, characteristic, complemented
9#11719073C211yesmaximal, characteristic, complemented
10#11719068C211yesmaximal, characteristic, complemented
11#11719068C211yesmaximal, characteristic, complemented
12#11719066C211yesmaximal, characteristic, complemented
13#11719065C211yesmaximal, characteristic, complemented
14#11719064C211yesmaximal, characteristic, complemented
15#11719063C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C2×#6122C2211yescharacteristic, complemented
19C22×#1057C2211yescharacteristic, complemented
20C2×#6118C2211yescharacteristic
21C2×#6118C2211yescharacteristic
22C2×#6118C2211yescharacteristic, complemented
23C2×D13⋊C8C2211yescharacteristic
24C2×D13⋊C8C2211yescharacteristic
25C2×D13⋊C8C2211yescharacteristic, complemented
26C13×#123C411yescharacteristic
27#88191C411yescharacteristic
28#88183C411yescharacteristic
29#88150C411yescharacteristic
30#88150C411yescharacteristic
31#88147C2211yescharacteristic
32#88147C2211yescharacteristic
33#88138C411yescharacteristic
34#88138C411yescharacteristic
35#88136C411yescharacteristic
36#88135C2211yescharacteristic
37#88135C2211yescharacteristic
38#88131C2211yescharacteristic
39C22⋊#1057C2211yescharacteristic
40C22⋊#1057C2211yescharacteristic
41C22⋊#1057C2211yescharacteristic
42C22⋊#1057C2211yescharacteristic
43C22⋊#1057C2211yescharacteristic, complemented
44C22⋊#1057C2211yescharacteristic, complemented
45#88112C2211yescharacteristic, complemented
46#88112C2211yescharacteristic, complemented
47#88111C2211yescharacteristic
48#88111C2211yescharacteristic
49#88111C2211yescharacteristic
50#88111C2211yescharacteristic
51#88111C2211yescharacteristic, complemented
52#88111C2211yescharacteristic, complemented
53#88110C2211yescharacteristic, complemented
54#88110C2211yescharacteristic, complemented
55C4⋊#1057C2211yescharacteristic, complemented
56C4⋊#1057C2211yescharacteristic, complemented
57C4×#1057C2211yescharacteristic, complemented
58C4×#1057C2211yescharacteristic, complemented
59C23×D13C2×C411yescharacteristic
60C2×D4×C13C2×C411yescharacteristic
61C22×C4×C13C2×C411yescharacteristic
62C2×C22⋊D13C2×C411yescharacteristic
63C2×C22⋊D13C2×C411yescharacteristic
64C2×C22⋊D13C2×C411yescharacteristic
65C2×C22⋊D13C2×C411yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68#6129—41no—
69#6129—41no—
70C2×D52C2×C411yescharacteristic
71C2×D52C2×C411yescharacteristic
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13C2×C411yescharacteristic
75C2×C4×D13C2×C411yescharacteristic
76C2×C4×D13C2311yescharacteristic
77C2×C4×D13C2311yescharacteristic
78C2×C4×D13C2311yescharacteristic
79C2×Dic26C2×C411yescharacteristic
80#6122—41no—
81C2×#1057—41no—
82C2×#1057C2311yescharacteristic
83C2×#1057C2311yescharacteristic
84C2×#1057C2311yescharacteristic
85C2×#1057C2311yescharacteristic
86C2×#1057C2311yescharacteristic
87C2×#1057C2311yescharacteristic
88C2×#1057C2311yescharacteristic
89C2×#1057C2311yescharacteristic
90#6118—41no—
91#6118—41no—
92#6118—41no—
93D13⋊C8—41no—
94D13⋊C8—41no—
95D13⋊C8—41no—
96C13×C4⋊C4C2×C411yescharacteristic
97C13×C4⋊C4C2×C411yescharacteristic
98C13×C22⋊C4C2×C411yescharacteristic
99C13×C22⋊C4C2×C411yescharacteristic
100C13×C22⋊C4C2×C411yescharacteristic
101C22⋊Dic13C2×C411yescharacteristic
102#6103C2×C411yescharacteristic
103#6103C2×C411yescharacteristic
104#6103C2×C411yescharacteristic
105#6103C2×C411yescharacteristic
106#6103C2×C411yescharacteristic
107#6103C2×C411yescharacteristic
108#6101C2×C411yescharacteristic
109#6101C2×C411yescharacteristic
110#6101C2×C411yescharacteristic
111#6101C2×C411yescharacteristic
112C4×Dic13C2311yescharacteristic
113C4×Dic13C2311yescharacteristic
114#2976—131nomaximal, Sylow
115C23×C13C22×C411yescharacteristic
116C23×C13C22×C411yescharacteristic
117C22×D13—22no—
118C22×D13—41no—
119C22×D13—41no—
120C22×D13C22×C411yescharacteristic
121C22×D13C22×C411yescharacteristic
122C22×D13C22×C411yescharacteristic
123D4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13C22×C411yescharacteristic
126C2×C4×C13C22×C411yescharacteristic
127C2×C4×C13C22×C411yescharacteristic
128C2×C4×C13C22×C411yescharacteristic
129C2×C4×C13C22×C411yescharacteristic
130C22⋊D13—22no—
131C22⋊D13—41no—
132C22⋊D13—41no—
133C22⋊D13—41no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13C22×C411yescharacteristic
139C2×Dic13C22×C411yescharacteristic
140C2×Dic13C22×C411yescharacteristic
141C2×Dic13C22×C411yescharacteristic
142C2×Dic13C2411yescharacteristic
143D52—22no—
144D52—41no—
145C4×D13—21no—
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—21no—
149C4×D13—21no—
150C4×D13—21no—
151C4×D13—41no—
152C4×D13—41no—
153Dic26—41no—
154#1057—21no—
155#1057—21no—
156#1057—21no—
157#1057—21no—
158#1057—21no—
159#1057—21no—
160#1057—21no—
161#1057—21no—
162#525—131no—
163#436—131no—
164#436—131no—
165#435—131no—
166#435—131no—
167#435—131no—
168#435—131no—
169C8×D4—131no—
170C8×D4—131no—
171#433—131no—
172#433—131no—
173#408—131no—
174#408—131no—
175#407—131no—
176C2×C22⋊C8—131no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13C23×C411yescharacteristic
184C2×D13—21no—
185C2×D13—21no—
186C2×D13—21no—
187C2×D13—21no—
188C2×D13—21no—
189C2×D13—21no—
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—44no—
193C2×D13#13112yes—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199Dic13—21no—
200Dic13—21no—
201Dic13—21no—
202Dic13—21no—
203Dic13H(5,𝔽2)11yescharacteristic
204Dic13H(5,𝔽2)11yescharacteristic
205C2×#41—131no—
206C23×C4—131no—
207C2×M16—131no—
208C2×M16—131no—
209C2×M16—131no—
210C2×M16—131no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—131no—
214C22×C8—131no—
215#123—131no—
216#123#26111yescharacteristic
217C22⋊Q8—131no—
218C22⋊Q8—131no—
219#121—131no—
220#121—131no—
221#120—131no—
222#120—131no—
223C4×D4—131no—
224C4×D4—131no—
225C4×D4—131no—
226C4×D4—131no—
227#117—131no—
228C4⋊C8—131no—
229C4⋊C8—131no—
230C4⋊C8—131no—
231C4⋊C8—131no—
232C22⋊C8—131no—
233C22⋊C8—131no—
234C22⋊C8—131no—
235C22⋊C8—131no—
236C22⋊C8—131no—
237C22⋊C8—131no—
238C22⋊C8—131no—
239C22⋊C8—131no—
240C22⋊C8—131no—
241C22⋊C8—131no—
242C22⋊C8—131no—
243C22⋊C8—131no—
244#97—131no—
245#97—131no—
246C4×C8—131no—
247C4×C8—131no—
248C2×C13—41no—
249C2×C13—41no—
250C2×C13#51811yescharacteristic
251C2×C13C2×#13111yescharacteristic
252C2×C13#56811yescharacteristic
253D13—22no—
254D13—41no—
255D13—41no—
256C24—131no—
257#41—521no—
258#41—521no—
259C2×Q8—131no—
260C2×D4—131no—
261C2×D4—131no—
262C2×D4—131no—
263C2×D4—131no—
264C2×D4—131no—
265C2×D4—131no—
266C2×D4C2×#26111yescharacteristic
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—521no—
275C22×C4—521no—
276C22×C4C2×#26111yescharacteristic
277M16—521no—
278M16—521no—
279M16—521no—
280M16—521no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8—131no—
284C2×C8—131no—
285C2×C8—131no—
286C2×C8—131no—
287C2×C8—131no—
288C2×C8—131no—
289C2×C8—521no—
290C2×C8—521no—
291C2×C8—521no—
292C2×C8—521no—
293C4⋊C4—131no—
294C4⋊C4—131no—
295C4⋊C4—131no—
296C4⋊C4—131no—
297C4⋊C4C2×#26111yescharacteristic
298C4⋊C4C2×#26111yescharacteristic
299C22⋊C4—131no—
300C22⋊C4—131no—
301C22⋊C4—131no—
302C22⋊C4—131no—
303C22⋊C4—131no—
304C22⋊C4—131no—
305C22⋊C4—131no—
306C22⋊C4C2×#26111yescharacteristic
307C22⋊C4C2×#26111yescharacteristic
308C22⋊C4C2×#26111yescharacteristic
309C42—131no—
310C42—131no—
311C13#297611yescharacteristic, complemented, Sylow
312C23—131no—
313C23—131no—
314C23—131no—
315C23—262no—
316C23—521no—
317C23—521no—
318C23C22×#26111yescharacteristic
319C23C22×#26111yescharacteristic
320Q8—521no—
321D4—41no—
322D4—262no—
323D4—262no—
324D4—521no—
325D4—521no—
326D4—521no—
327D4—521no—
328C2×C4—41no—
329C2×C4—131no—
330C2×C4—131no—
331C2×C4—131no—
332C2×C4—131no—
333C2×C4—131no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4C22×#26111yescharacteristic
347C2×C4C22×#26111yescharacteristic
348C2×C4C22×#26111yescharacteristic
349C2×C4C22×#26111yescharacteristic
350C2×C4C22×#26111yescharacteristic
351C8—261no—
352C8—261no—
353C8—261no—
354C8—261no—
355C8—261no—
356C8—261no—
357C8—261no—
358C8—261no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—132no—
366C22—261no—
367C22—261no—
368C22—261no—
369C22—261no—
370C22—261no—
371C22—261no—
372C22—261no—
373C22—261no—
374C22—524no—
375C22C23×#26111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—131no—
382C4—131no—
383C4—261no—
384C4—261no—
385C4—261no—
386C4—261no—
387C2—41no—
388C2—41no—
389C2—262no—
390C2—521no—
391C2—521no—
392C2#1171962311yescharacteristic
393C2D13⋊#13111yescharacteristic
394C2#1171962911yescharacteristic
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC13×#123C4
prime radical#11719361C2
cosocleC2×Dic13C24
hypercenter#123#261
hypocenterC13#2976
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #11719147C2semidirect
3. #11719146C2semidirect
4. #11719127C2semidirect
5. D13⋊(C22⋊C8)C2semidirect
6. #11719076C2semidirect
7. #11719075C2semidirect
8. #11719075C2semidirect
9. #11719073C2semidirect
10. #11719068C2semidirect
11. #11719068C2semidirect
12. #11719066C2semidirect
13. #11719065C2semidirect
14. #11719064C2semidirect
15. #11719063C2semidirect
18. C2×#6122C22semidirect
19. C22×#1057C22semidirect
22. C2×#6118C22semidirect
25. C2×D13⋊C8C22semidirect
43. C22⋊#1057C22semidirect
44. C22⋊#1057C22semidirect
45. #88112C22semidirect
46. #88112C22semidirect
51. #88111C22semidirect
52. #88111C22semidirect
53. #88110C22semidirect
54. #88110C22semidirect
55. C4⋊#1057C22semidirect
56. C4⋊#1057C22semidirect
57. C4×#1057C22semidirect
58. C4×#1057C22semidirect
311. C13#2976semidirect

Maximal subgroups

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

subgroupindex
#117193612
#117191472
#117191462
#117191272
D13⋊(C22⋊C8)2
#117190762
#117190752
#117190732
#117190682
#117190662
#117190652
#117190642
#117190632
#297613