Finite Group Databasebeta

← #13125707

Subgroups — #13125707

Order 1664.

410 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#11719333C211yesmaximal, characteristic, complemented
2#11719230C211yesmaximal, characteristic
3C13×#485C211yesmaximal, characteristic, complemented
4#11718707C211yesmaximal, characteristic, complemented
5#11718657C211yesmaximal, characteristic, complemented
6#11718547C211yesmaximal, characteristic, complemented
7#11718546C211yesmaximal, characteristic, complemented
8#11718527C211yesmaximal, characteristic, complemented
9#11718525C211yesmaximal, characteristic, complemented
10#11718473C211yesmaximal, characteristic, complemented
11#11718468C211yesmaximal, characteristic, complemented
12#11718467C211yesmaximal, characteristic, complemented
13#11718467C211yesmaximal, characteristic, complemented
14#11718392C211yesmaximal, characteristic, complemented
15#11718388C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic, complemented
17C2×#6127C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C13×C22⋊Q8C2211yescharacteristic
20C13×#117C2211yescharacteristic
21#88200C2211yescharacteristic, complemented
22C2×#6106C2211yescharacteristic
23C2×#6106C2211yescharacteristic
24#88178C2211yescharacteristic
25C2×#6095C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27C2×#6094C2211yescharacteristic, complemented
28C2×C8×D13C2211yescharacteristic, complemented
29#88151C2211yescharacteristic, complemented
30#88149C2211yescharacteristic
31#88149C2211yescharacteristic
32#88149C2211yescharacteristic
33#88149C2211yescharacteristic
34#88148—21no—
35#88146C2211yescharacteristic, complemented
36#88142—21no—
37#88139—21no—
38#88137—21no—
39#88136—21no—
40#88136—21no—
41#88129—21no—
42#88128—21no—
43C13×#107C2211yescharacteristic, complemented
44C13×#106C2211yescharacteristic, complemented
45C13×#103C2211yescharacteristic, complemented
46C13×#103C2211yescharacteristic, complemented
47C13×C22⋊C8C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88060C2211yescharacteristic, complemented
52#88060C2211yescharacteristic, complemented
53#88050C2211yescharacteristic, complemented
54#88050C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13D411yescharacteristic
63C2×C22⋊D13D411yescharacteristic
64Q8×D13—41no—
65Q8×D13—41no—
66#6127—41no—
67#6127—41no—
68C2×D52—21no—
69C2×D52—21no—
70C2×D52—21no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52—41no—
74C2×D52—41no—
75C2×D52D411yescharacteristic
76C2×D52C2311yescharacteristic
77C2×D52C2311yescharacteristic
78C2×C4×D13—21no—
79C2×C4×D13C2311yescharacteristic
80C2×C4×D13C2311yescharacteristic
81C2×Dic26—21no—
82C2×Dic26D411yescharacteristic
83C2×Dic26C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C2×C8×C13C2311yescharacteristic
86C13×C4⋊C4—21no—
87C13×C4⋊C4C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C4⋊C4C2311yescharacteristic
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C42×C13—21no—
93C22⋊Dic13—21no—
94#6106—41no—
95#6106—41no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103C4⋊Dic13—21no—
104C4⋊Dic13C2311yescharacteristic
105#6101—21no—
106#6101—21no—
107C4×Dic13—21no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6095—41no—
111#6095—41no—
112#6094—41no—
113C8×D13—41no—
114#3200—131nomaximal, Sylow
115C23×C13C2×D411yescharacteristic
116C22×D13—21no—
117C22×D13—21no—
118C22×D13—42no—
119C22×D13—81no—
120C22×D13—81no—
121C22×D13C2×D411yescharacteristic
122C22×D13C2×D411yescharacteristic
123Q8×C13—21no—
124Q8×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C22⋊D13—41no—
134C22⋊D13—41no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139D52—21no—
140D52—21no—
141D52—21no—
142D52—21no—
143D52—41no—
144D52—42no—
145D52—81no—
146D52—81no—
147D52—81no—
148D52—81no—
149C4×D13—21no—
150C4×D13—21no—
151C4×D13—21no—
152C4×D13—21no—
153C4×D13—42no—
154Dic26—21no—
155Dic26—21no—
156Dic26—41no—
157Dic26—42no—
158C8×C13—21no—
159C8×C13—21no—
160#1055—21no—
161#1055—21no—
162#536—131no—
163#535—131no—
164#485—131no—
165#485D1311yescharacteristic, complemented
166#482—131no—
167#482—131no—
168#468—131no—
169#468—131no—
170#465—131no—
171#465—131no—
172#450—131no—
173#450—131no—
174#448—131no—
175#448—131no—
176#408—131no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13C22×D411yescharacteristic
181C2×D13—21no—
182C2×D13—21no—
183C2×D13—21no—
184C2×D13—21no—
185C2×D13—21no—
186C2×D13—21no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—41no—
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—84no—
194C4×C13—21no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13H(5,𝔽2)11yescharacteristic
200C4×C13H(5,𝔽2)11yescharacteristic
201Dic13—21no—
202Dic13—21no—
203Dic13—41no—
204Dic13—41no—
205C2×#41—131no—
206C22×Q8—131no—
207C22×D4—131no—
208C2×SD16—131no—
209C2×SD16—131no—
210C2×SD16—131no—
211C2×SD16—131no—
212C2×M16—131no—
213C22×C8—131no—
214C4⋊Q8—261no—
215#127—261no—
216#124—261no—
217#124—261no—
218#123—261no—
219#123—261no—
220C22⋊Q8—131no—
221C22⋊Q8—131no—
222C22⋊Q8—131no—
223C22⋊Q8C2×D1311yescharacteristic
224#121—131no—
225#121—131no—
226#121—131no—
227#121—131no—
228#120—261no—
229#120—261no—
230#117—131no—
231#117C2×D1311yescharacteristic
232#107—131no—
233#107C2×D1311yescharacteristic, complemented
234#106—131no—
235#106C2×D1311yescharacteristic, complemented
236#103—131no—
237#103—131no—
238#103C2×D1311yescharacteristic, complemented
239#103C2×D1311yescharacteristic, complemented
240#102—131no—
241#102—131no—
242#102—131no—
243#102—131no—
244C22⋊C8—131no—
245C22⋊C8—131no—
246C22⋊C8—131no—
247C22⋊C8C2×D1311yescharacteristic
248C2×C13—41no—
249C2×C13#53411yescharacteristic
250C2×C13#57711yescharacteristic
251C2×C13#57711yescharacteristic
252D13—41no—
253D13—41no—
254D13—81no—
255D13—81no—
256C24—261no—
257#41—521no—
258#41—521no—
259C2×Q8—131no—
260C2×Q8—131no—
261C2×Q8—261no—
262C2×Q8—521no—
263C2×Q8—521no—
264C2×Q8C22×D1311yescharacteristic
265C2×D4—131no—
266C2×D4—131no—
267C2×D4—131no—
268C2×D4—131no—
269C2×D4—131no—
270C2×D4—261no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—521no—
276C2×D4—521no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—261no—
280C22×C4C22×D1311yescharacteristic
281SD16—521no—
282SD16—521no—
283SD16—521no—
284SD16—521no—
285M16—521no—
286C2×C8—131no—
287C2×C8—131no—
288C2×C8—521no—
289C2×C8C22×D1311yescharacteristic
290C2×C8C22×D1311yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—131no—
293C4⋊C4—261no—
294C4⋊C4—261no—
295C4⋊C4—261no—
296C4⋊C4C22×D1311yescharacteristic
297C4⋊C4C22×D1311yescharacteristic
298C4⋊C4C22×D1311yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4—261no—
304C22⋊C4—261no—
305C22⋊C4—261no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C42—21no—
310C42—261no—
311C13#320011yescharacteristic, complemented, Sylow
312C23—131no—
313C23—131no—
314C23—261no—
315C23—261no—
316C23—522no—
317C23—1041no—
318C23—1041no—
319C23D4×D1311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—261no—
323Q8—261no—
324Q8—521no—
325Q8—522no—
326D4—261no—
327D4—261no—
328D4—261no—
329D4—261no—
330D4—521no—
331D4—522no—
332D4—521no—
333D4—521no—
334D4—1041no—
335D4—1041no—
336D4—1041no—
337D4—1041no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—522no—
353C2×C4D4×D1311yescharacteristic
354C2×C4C23×D1311yescharacteristic
355C8—21no—
356C8—21no—
357C8—261no—
358C8—261no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—261no—
363C22—261no—
364C22—261no—
365C22—261no—
366C22—261no—
367C22—261no—
368C22—521no—
369C22—521no—
370C22—521no—
371C22—521no—
372C22—521no—
373C22—521no—
374C22—1044no—
375C22C2×D4×D1311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—261no—
382C4—261no—
383C4—521no—
384C4—521no—
385C4#8825611yescharacteristic
386C4#8825611yescharacteristic
387C2—41no—
388C2—521no—
389C2—521no—
390C2—1041no—
391C2—1041no—
392C2#1171935811yescharacteristic
393C2#1171947511yescharacteristic
394C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
prime radical#11719230C2
hypercenter#485D13
hypocenterC13#3200
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #11719333C2semidirect
3. C13×#485C2semidirect
4. #11718707C2semidirect
5. #11718657C2semidirect
6. #11718547C2semidirect
7. #11718546C2semidirect
8. #11718527C2semidirect
9. #11718525C2semidirect
10. #11718473C2semidirect
11. #11718468C2semidirect
12. #11718467C2semidirect
13. #11718467C2semidirect
14. #11718392C2semidirect
15. #11718388C2semidirect
16. C2×Q8×D13C22semidirect
21. #88200C22semidirect
27. C2×#6094C22semidirect
28. C2×C8×D13C22semidirect
29. #88151C22semidirect
35. #88146C22semidirect
43. C13×#107C22semidirect
44. C13×#106C22semidirect
45. C13×#103C22semidirect
46. C13×#103C22semidirect
51. #88060C22semidirect
52. #88060C22semidirect
53. #88050C22semidirect
54. #88050C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
165. #485D13semidirect
233. #107C2×D13semidirect
235. #106C2×D13semidirect
238. #103C2×D13semidirect
239. #103C2×D13semidirect
311. C13#3200semidirect

Maximal subgroups

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

subgroupindex
#117193332
#117192302
C13×#4852
#117187072
#117186572
#117185472
#117185462
#117185272
#117185252
#117184732
#117184682
#117184672
#117183922
#117183882
#320013