Finite Group Databasebeta

← #13125936

Subgroups — #13125936

Order 1664.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719535C211yesmaximal, characteristic, complemented
2#11719348C211yesmaximal, characteristic, complemented
3C13×#452C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718852C211yesmaximal, characteristic, complemented
6#11718846C211yesmaximal, characteristic, complemented
7#11718837C211yesmaximal, characteristic, complemented
8#11718824C211yesmaximal, characteristic, complemented
9#11718707C211yesmaximal, characteristic, complemented
10#11718480C211yesmaximal, characteristic, complemented
11#11718456C211yesmaximal, characteristic, complemented
12#11718447C211yesmaximal, characteristic, complemented
13#11718421C211yesmaximal, characteristic, complemented
14#11718393C211yesmaximal, characteristic, complemented
15#11718381C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic, complemented
19C2×C13×SD16C2211yescharacteristic, complemented
20C13×C22⋊Q8C2211yescharacteristic
21#88201C2211yescharacteristic
22#88201C2211yescharacteristic
23#88201C2211yescharacteristic, complemented
24Q8×Dic13C2211yescharacteristic, complemented
25C2×#6106C2211yescharacteristic
26C2×#6106C2211yescharacteristic
27C2×#6106C2211yescharacteristic, complemented
28#88194C2211yescharacteristic
29#88194C2211yescharacteristic
30#88191—21no—
31#88191—21no—
32C2×#6104C2211yescharacteristic, complemented
33#88184—21no—
34#88184—21no—
35#88184C2211yescharacteristic
36#88180C2211yescharacteristic
37C2×D104C2211yescharacteristic
38C2×D104C2211yescharacteristic
39#88152—21no—
40#88151—21no—
41#88147C2211yescharacteristic, complemented
42#88142C2211yescharacteristic, complemented
43#88139—21no—
44#88137—21no—
45C13×#103C2211yescharacteristic, complemented
46C13×#102C2211yescharacteristic, complemented
47C13×C22⋊C8C2211yescharacteristic
48#88075C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50C22⋊#1055C2211yescharacteristic
51#88061C2211yescharacteristic
52#88061C2211yescharacteristic
53#88055C2211yescharacteristic, complemented
54#88054C2211yescharacteristic, complemented
55#88054C2211yescharacteristic, complemented
56C8×Dic13C2211yescharacteristic, complemented
57#88049C2211yescharacteristic
58#88049C2211yescharacteristic
59C23×D13—21no—
60C13×#41—41no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×Q8×C13C2311yescharacteristic
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73C2×D52—21no—
74C2×D52—41no—
75C2×D52—41no—
76C2×D52C2311yescharacteristic
77C2×D52C2311yescharacteristic
78C2×D52C2311yescharacteristic
79C2×C4×D13—21no—
80C2×Dic26—21no—
81C13×Q16—41no—
82C13×SD16—41no—
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C13×C4⋊C4—21no—
86C13×C4⋊C4C2311yescharacteristic
87C13×C22⋊C4—21no—
88C22⋊Dic13D411yescharacteristic
89C22⋊Dic13D411yescharacteristic
90#6106—41no—
91#6106—41no—
92#6106—41no—
93#6104—41no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100#6103—21no—
101#6103—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13D411yescharacteristic
104C4⋊Dic13D411yescharacteristic
105C4⋊Dic13C2311yescharacteristic
106#6101—21no—
107C4×Dic13—21no—
108C4×Dic13C2311yescharacteristic
109C4×Dic13C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112D104—41no—
113D104—41no—
114#3224—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13C2×D411yescharacteristic
117C22×D13—21no—
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—42no—
121C22×D13—81no—
122C22×D13—81no—
123Q8×C13—21no—
124Q8×C13—21no—
125Q8×C13—21no—
126Q8×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—42no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—42no—
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2411yescharacteristic
138C22⋊D13—81no—
139C22⋊D13—81no—
140C22⋊D13—81no—
141C22⋊D13—81no—
142C22⋊D13—81no—
143C2×Dic13—21no—
144C2×Dic13C2×D411yescharacteristic
145C2×Dic13C2×D411yescharacteristic
146C2×Dic13C2×D411yescharacteristic
147C2×Dic13C2×D411yescharacteristic
148D52—21no—
149D52—21no—
150D52—21no—
151D52—21no—
152D52—21no—
153D52—21no—
154D52—42no—
155C4×D13—81no—
156Dic26—81no—
157C8×C13—21no—
158C8×C13—21no—
159#1055—21no—
160#1055—21no—
161#542—131no—
162#535—131no—
163#496—131no—
164#495—131no—
165#489—131no—
166#486—131no—
167#464—131no—
168#463—131no—
169#460—131no—
170#459—131no—
171#452D1311yescharacteristic, complemented
172#450—131no—
173#449—131no—
174#447—131no—
175#433—131no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13C22×D411yescharacteristic
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—41no—
191C2×D13—41no—
192C2×D13—84no—
193C4×C13—21no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13H(5,𝔽2)11yescharacteristic
198C4×C13H(5,𝔽2)11yescharacteristic
199Dic13—21no—
200Dic13—21no—
201Dic13—21no—
202Dic13—21no—
203Dic13—41no—
204C2×#41C2×D1311yescharacteristic
205C22×D4—131no—
206C2×Q16C2×D1311yescharacteristic, complemented
207C2×SD16—131no—
208C2×SD16—131no—
209C2×SD16—131no—
210C2×SD16C2×D1311yescharacteristic, complemented
211C2×D8—131no—
212C2×D8—131no—
213C2×D8—131no—
214C4⋊Q8—131no—
215#127—131no—
216#127—131no—
217#126—261no—
218#124—131no—
219#124—131no—
220#124—131no—
221#124—261no—
222#123—261no—
223C22⋊Q8—261no—
224C22⋊Q8C2×D1311yescharacteristic
225#121—131no—
226#121—261no—
227#121—261no—
228#120—261no—
229#120—261no—
230C4×Q8—131no—
231C4×D4—131no—
232#117—131no—
233C4⋊C8—131no—
234C4⋊C8—131no—
235#103—131no—
236#103C2×D1311yescharacteristic, complemented
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242#102C2×D1311yescharacteristic, complemented
243C22⋊C8—131no—
244C22⋊C8C2×D1311yescharacteristic
245#97—131no—
246C4×C8—131no—
247C2×C13—41no—
248C2×C13—81no—
249C2×C13#53511yescharacteristic
250C2×C13#57611yescharacteristic
251C2×C13#57711yescharacteristic
252D13—81no—
253D13—81no—
254D13—81no—
255C24—261no—
256#41—41no—
257#41—41no—
258C2×Q8—261no—
259C2×Q8C22×D1311yescharacteristic
260C2×Q8C22×D1311yescharacteristic
261C2×D4—21no—
262C2×D4—131no—
263C2×D4—131no—
264C2×D4—131no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—261no—
269C2×D4—261no—
270C2×D4—261no—
271C2×D4—521no—
272C2×D4—521no—
273C2×D4C22×D1311yescharacteristic
274C22×C4—21no—
275C22×C4—261no—
276C22×C4C22×D1311yescharacteristic
277Q16—41no—
278SD16—41no—
279SD16—521no—
280SD16—521no—
281SD16—521no—
282D8—521no—
283D8—521no—
284D8—521no—
285C2×C8—131no—
286C2×C8—131no—
287C2×C8C22×D1311yescharacteristic
288C2×C8C22×D1311yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—131no—
291C4⋊C4—131no—
292C4⋊C4—131no—
293C4⋊C4—261no—
294C4⋊C4—261no—
295C4⋊C4C22×D1311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—131no—
298C22⋊C4—131no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4—261no—
304C22⋊C4—261no—
305C22⋊C4—261no—
306C22⋊C4—261no—
307C42—131no—
308C42—131no—
309C42—261no—
310C13#322411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—261no—
313C23—261no—
314C23—261no—
315C23—522no—
316C23—1041no—
317C23—1041no—
318C23D4×D1311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—1041no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—261no—
328D4—261no—
329D4—261no—
330D4—261no—
331D4—261no—
332D4—261no—
333D4—522no—
334D4—1041no—
335D4—1041no—
336D4—1041no—
337D4—1041no—
338D4—1041no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—131no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—261no—
350C2×C4—1041no—
351C2×C4D4×D1311yescharacteristic
352C2×C4C23×D1311yescharacteristic
353C8—21no—
354C8—21no—
355C8—261no—
356C8—261no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—521no—
364C22—521no—
365C22—521no—
366C22—521no—
367C22—521no—
368C22—521no—
369C22—521no—
370C22—521no—
371C22—521no—
372C22—1044no—
373C22C2×D4×D1311yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—261no—
379C4—261no—
380C4—261no—
381C4—261no—
382C4—521no—
383C4#8825111yescharacteristic
384C4#8825111yescharacteristic
385C2—41no—
386C2—81no—
387C2—1041no—
388C2—1041no—
389C2—1041no—
390C2#1171929711yescharacteristic
391C2#1171947411yescharacteristic
392C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#452C2
socleC22×C13C22×D4
hypercenter#452D13
hypocenterC13#3224
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #11719535C2semidirect
2. #11719348C2semidirect
3. C13×#452C2semidirect
4. #11718899C2semidirect
5. #11718852C2semidirect
6. #11718846C2semidirect
7. #11718837C2semidirect
8. #11718824C2semidirect
9. #11718707C2semidirect
10. #11718480C2semidirect
11. #11718456C2semidirect
12. #11718447C2semidirect
13. #11718421C2semidirect
14. #11718393C2semidirect
15. #11718381C2semidirect
18. C2×C13×Q16C22semidirect
19. C2×C13×SD16C22semidirect
23. #88201C22semidirect
24. Q8×Dic13C22semidirect
27. C2×#6106C22semidirect
32. C2×#6104C22semidirect
41. #88147C22semidirect
42. #88142C22semidirect
45. C13×#103C22semidirect
46. C13×#102C22semidirect
48. #88075C22semidirect
49. #88072C22semidirect
53. #88055C22semidirect
54. #88054C22semidirect
55. #88054C22semidirect
56. C8×Dic13C22semidirect
171. #452D13semidirect
206. C2×Q16C2×D13semidirect
210. C2×SD16C2×D13semidirect
236. #103C2×D13semidirect
242. #102C2×D13semidirect
310. C13#3224semidirect

Maximal subgroups

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

subgroupindex
#117195352
#117193482
C13×#4522
#117188992
#117188522
#117188462
#117188372
#117188242
#117187072
#117184802
#117184562
#117184472
#117184212
#117183932
#117183812
#322413