Finite Group Databasebeta

← #13125802

Subgroups — #13125802

Order 1664.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719396C211yesmaximal, characteristic, complemented
2D13×#124C211yesmaximal, characteristic, complemented
3C13×#488C211yesmaximal, characteristic, complemented
4#11718729C211yesmaximal, characteristic, complemented
5#11718720C211yesmaximal, characteristic, complemented
6#11718480C211yesmaximal, characteristic, complemented
7#11718469C211yesmaximal, characteristic, complemented
8#11718467C211yesmaximal, characteristic, complemented
9#11718459C211yesmaximal, characteristic, complemented
10#11718448C211yesmaximal, characteristic, complemented
11#11718437C211yesmaximal, characteristic, complemented
12#11718434C211yesmaximal, characteristic
13#11718428C211yesmaximal, characteristic, complemented
14#11718357C211yesmaximal, characteristic, complemented
15#11718346C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C13×#125C2211yescharacteristic, complemented
19C13×#124C2211yescharacteristic
20#88201C2211yescharacteristic
21C2×#6107C2211yescharacteristic, complemented
22C2×#6106C2211yescharacteristic, complemented
23#88190C2211yescharacteristic
24C2×#6105C2211yescharacteristic
25C2×#6104C2211yescharacteristic
26C2×Dic52C2211yescharacteristic, complemented
27C2×D104C2211yescharacteristic
28C2×#6095C2211yescharacteristic
29C2×#6095C2211yescharacteristic, complemented
30#88152—21no—
31#88151C2211yescharacteristic
32#88149C2211yescharacteristic
33#88148—21no—
34#88147—21no—
35#88147C2211yescharacteristic, complemented
36#88146—21no—
37#88141C2211yescharacteristic, complemented
38#88139—21no—
39#88139—21no—
40C22⋊C4×D13—21no—
41C22⋊C4×D13—21no—
42#88129C2211yescharacteristic
43#88129C2211yescharacteristic, complemented
44C42×D13C2211yescharacteristic
45C13×#103C2211yescharacteristic, complemented
46C13×#103C2211yescharacteristic, complemented
47C13×#102C2211yescharacteristic
48C13×#102C2211yescharacteristic
49C4×C8×C13C2211yescharacteristic, complemented
50#88060C2211yescharacteristic
51#88060C2211yescharacteristic
52#88054C2211yescharacteristic, complemented
53#88054C2211yescharacteristic, complemented
54#88050C2211yescharacteristic, complemented
55#88050C2211yescharacteristic, complemented
56#88049C2211yescharacteristic
57#88049C2211yescharacteristic
58C4×#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63Q8×D13—41no—
64Q8×D13—41no—
65D4×D13—41no—
66D4×D13—41no—
67C2×D52—21no—
68C2×D52C2311yescharacteristic
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13D411yescharacteristic
73C2×C4×D13D411yescharacteristic
74C2×C4×D13C2311yescharacteristic
75C2×Dic26—21no—
76C2×Dic26C2311yescharacteristic
77C2×Dic26C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89#6107—41no—
90#6106—41no—
91#6105—41no—
92#6104—41no—
93#6103—21no—
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—
103#6101—21no—
104C4×Dic13—21no—
105C4×Dic13D411yescharacteristic
106C4×Dic13D411yescharacteristic
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110Dic52—41no—
111D104—41no—
112#6095—41no—
113#6095—41no—
114#3211—131nomaximal, Sylow
115C23×C13—21no—
116C22×D13—21no—
117C22×D13—21no—
118C22×D13—42no—
119C22×D13—42no—
120C22×D13—42no—
121C22×D13C2×D411yescharacteristic
122Q8×C13—21no—
123Q8×C13—21no—
124D4×C13—21no—
125D4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2411yescharacteristic
132C22⋊D13—42no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138D52—21no—
139D52—21no—
140D52—21no—
141D52—21no—
142D52—42no—
143C4×D13—22no—
144C4×D13—21no—
145C4×D13—21no—
146C4×D13—41no—
147C4×D13—42no—
148C4×D13—42no—
149Dic26—21no—
150Dic26—21no—
151Dic26—21no—
152Dic26—21no—
153Dic26—42no—
154C8×C13—21no—
155C8×C13—21no—
156#1055—21no—
157#1055—21no—
158#529—131no—
159C2×#124—131no—
160#495—131no—
161#495—131no—
162#488—131no—
163#488D1311yescharacteristic, complemented
164#464—131no—
165#464—131no—
166#463—131no—
167#463—131no—
168#451—131no—
169#450—131no—
170#448—131no—
171#447—131no—
172#431—131no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13C22×D411yescharacteristic
177C2×D13—21no—
178C2×D13—21no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—84no—
186C2×D13#13512yes—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13H(5,𝔽2)11yescharacteristic
193C4×C13H(5,𝔽2)11yescharacteristic
194Dic13—21no—
195Dic13—21no—
196Dic13—21no—
197Dic13—41no—
198Dic13—41no—
199C22×Q8—131no—
200C22×D4—131no—
201C2×Q16—131no—
202C2×Q16—131no—
203C2×SD16—131no—
204C2×SD16—131no—
205C2×SD16—131no—
206C2×SD16—131no—
207C2×D8—131no—
208C2×D8—131no—
209#126—261no—
210#125C2×D1311yescharacteristic, complemented
211#124—131no—
212#124—131no—
213#124—131no—
214#124—131no—
215#124—261no—
216#124—261no—
217#124C2×D1311yescharacteristic
218#123—261no—
219C22⋊Q8—131no—
220#121—131no—
221C4×Q8—131no—
222C4×D4—131no—
223C4×D4—261no—
224#117—261no—
225C2×C22⋊C4—261no—
226C2×C22⋊C4—261no—
227C2×C42—131no—
228C4⋊C8—131no—
229C4⋊C8—131no—
230#103—131no—
231#103—131no—
232#103C2×D1311yescharacteristic, complemented
233#103C2×D1311yescharacteristic, complemented
234#102—131no—
235#102—131no—
236#102C2×D1311yescharacteristic
237#102C2×D1311yescharacteristic
238C22⋊C8—131no—
239C22⋊C8—131no—
240C4×C8—131no—
241C4×C8C2×D1311yescharacteristic, complemented
242C2×C13—81no—
243C2×C13#53511yescharacteristic
244C2×C13C2×#13511yescharacteristic
245C2×C13#57511yescharacteristic
246D13—22no—
247D13—81no—
248D13—81no—
249C24—261no—
250C2×Q8—131no—
251C2×Q8—131no—
252C2×Q8—261no—
253C2×Q8—521no—
254C2×Q8—521no—
255C2×Q8C22×D1311yescharacteristic
256C2×D4—131no—
257C2×D4—131no—
258C2×D4—261no—
259C2×D4—261no—
260C2×D4—521no—
261C2×D4—521no—
262C2×D4C22×D1311yescharacteristic
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—261no—
267C22×C4—261no—
268Q16—521no—
269Q16—521no—
270SD16—521no—
271SD16—521no—
272SD16—521no—
273SD16—521no—
274D8—521no—
275D8—521no—
276C2×C8—131no—
277C2×C8—131no—
278C2×C8C22×D1311yescharacteristic
279C2×C8C22×D1311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4C22×D1311yescharacteristic
285C4⋊C4C22×D1311yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C22⋊C4—261no—
298C22⋊C4—261no—
299C42—131no—
300C42—131no—
301C42—131no—
302C42—261no—
303C42C22×D1311yescharacteristic
304C13#321111yescharacteristic, complemented, Sylow
305C23—21no—
306C23—131no—
307C23—261no—
308C23—261no—
309C23—522no—
310C23—522no—
311C23—522no—
312Q8—21no—
313Q8—21no—
314Q8—261no—
315Q8—261no—
316Q8—261no—
317Q8—261no—
318Q8—522no—
319D4—21no—
320D4—21no—
321D4—261no—
322D4—261no—
323D4—261no—
324D4—261no—
325D4—522no—
326D4—522no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—131no—
331C2×C4—131no—
332C2×C4—131no—
333C2×C4—262no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—521no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4D4×D1311yescharacteristic
342C2×C4D4×D1311yescharacteristic
343C2×C4C23×D1311yescharacteristic
344C8—21no—
345C8—21no—
346C8—261no—
347C8—261no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—132no—
352C22—261no—
353C22—261no—
354C22—521no—
355C22—521no—
356C22—521no—
357C22—521no—
358C22—521no—
359C22—521no—
360C22—1044no—
361C22C2×D4×D1311yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—261no—
368C4—261no—
369C4—261no—
370C4—521no—
371C4—521no—
372C4#8825611yescharacteristic
373C4#8825611yescharacteristic
374C2—81no—
375C2—262no—
376C2—1041no—
377C2—1041no—
378C2#1171937911yescharacteristic
379C2D13×#13511yescharacteristic
380C2#1171947311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#488C2
socleC22×C13C22×D4
prime radical#11718434C2
hypercenter#488D13
hypocenterC13#3211
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #11719396C2semidirect
2. D13×#124C2semidirect
3. C13×#488C2semidirect
4. #11718729C2semidirect
5. #11718720C2semidirect
6. #11718480C2semidirect
7. #11718469C2semidirect
8. #11718467C2semidirect
9. #11718459C2semidirect
10. #11718448C2semidirect
11. #11718437C2semidirect
13. #11718428C2semidirect
14. #11718357C2semidirect
15. #11718346C2semidirect
18. C13×#125C22semidirect
21. C2×#6107C22semidirect
22. C2×#6106C22semidirect
26. C2×Dic52C22semidirect
29. C2×#6095C22semidirect
35. #88147C22semidirect
37. #88141C22semidirect
43. #88129C22semidirect
45. C13×#103C22semidirect
46. C13×#103C22semidirect
49. C4×C8×C13C22semidirect
52. #88054C22semidirect
53. #88054C22semidirect
54. #88050C22semidirect
55. #88050C22semidirect
58. C4×#1055C22semidirect
163. #488D13semidirect
210. #125C2×D13semidirect
232. #103C2×D13semidirect
233. #103C2×D13semidirect
241. C4×C8C2×D13semidirect
304. C13#3211semidirect

Maximal subgroups

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

subgroupindex
#117193962
D13×#1242
C13×#4882
#117187292
#117187202
#117184802
#117184692
#117184672
#117184592
#117184482
#117184372
#117184342
#117184282
#117183572
#117183462
#321113