Finite Group Databasebeta

← #13126919

Subgroups — #13126919

Order 1664.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719255C211yesmaximal, characteristic
2#11719248C211yesmaximal, characteristic, complemented
3C13×#435C211yesmaximal, characteristic, complemented
4#11718795C211yesmaximal, characteristic, complemented
5#11718794C211yesmaximal, characteristic, complemented
6#11718777C211yesmaximal, characteristic, complemented
7C2×#88061C211yesmaximal, characteristic, complemented
8#11718507C211yesmaximal, characteristic, complemented
9#11718506C211yesmaximal, characteristic, complemented
10#11718397C211yesmaximal, characteristic, complemented
11#11718394C211yesmaximal, characteristic, complemented
12#11718392C211yesmaximal, characteristic, complemented
13#11718383C211yesmaximal, characteristic, complemented
14#11718375C211yesmaximal, characteristic, complemented
15#11718371C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic, complemented
19C22×C8×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88191—21no—
22D4×Dic13—21no—
23#88184C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic, complemented
26#88178C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic, complemented
29C2×Dic52C2211yescharacteristic, complemented
30C2×#6095C2211yescharacteristic
31C2×#6095C2211yescharacteristic
32#88148—21no—
33#88144—21no—
34#88138—21no—
35C22⋊C4×D13—21no—
36#88132—21no—
37#88132—21no—
38#88129C2211yescharacteristic
39C4×D52C2211yescharacteristic
40#88123C2211yescharacteristic, complemented
41C4×Dic26C2211yescharacteristic, complemented
42C13×C4⋊C8C2211yescharacteristic, complemented
43C13×C22⋊C8C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic, complemented
45C13×#97C2211yescharacteristic, complemented
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88058C2211yescharacteristic, complemented
53#88058C2211yescharacteristic, complemented
54#88058C2211yescharacteristic, complemented
55#88056C2211yescharacteristic, complemented
56#88056C2211yescharacteristic, complemented
57#88056C2211yescharacteristic, complemented
58#88056C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13D411yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67#6127—22no—
68#6127—41no—
69C2×D52—22no—
70C2×D52—21no—
71C2×D52—41no—
72C2×D52C2311yescharacteristic
73C2×D52C2311yescharacteristic
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×Dic26—21no—
77C2×Dic26C2311yescharacteristic
78C2×Dic26C2311yescharacteristic
79C13×M16—41no—
80C2×C8×C13—41no—
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C13×C4⋊C4D411yescharacteristic
86C13×C22⋊C4D411yescharacteristic
87C13×C22⋊C4D411yescharacteristic
88C42×C13C2311yescharacteristic
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101—21no—
107C4×Dic13—21no—
108Dic52—41no—
109#6095—22no—
110#6095—41no—
111#3314—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—42no—
117C22×D13—42no—
118C22×D13—81no—
119D4×C13—22no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2411yescharacteristic
129C22⋊D13—42no—
130C22⋊D13—81no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139D52—21no—
140D52—21no—
141D52—21no—
142D52—42no—
143D52#4112yes—
144C4×D13—42no—
145C4×D13—81no—
146Dic26—21no—
147Dic26—21no—
148Dic26—21no—
149Dic26—21no—
150Dic26—81no—
151C8×C13—21no—
152C8×C13—21no—
153C8×C13—21no—
154C8×C13—21no—
155#554—131no—
156#546—131no—
157#489—131no—
158#484—131no—
159#480—131no—
160#474—131no—
161#468—131no—
162#467—131no—
163#464—131no—
164#452—131no—
165#450—131no—
166#440—131no—
167#435D1311yescharacteristic, complemented
168#417—131no—
169C2×#102—131no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13#13712yes—
176C22×C13C22×D411yescharacteristic
177C2×D13—22no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—84no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13C2×#4111yescharacteristic
189C4×C13H(5,𝔽2)11yescharacteristic
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196C2×#41—131no—
197C22×D4—131no—
198C2×Q16—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×M16C2×D1311yescharacteristic, complemented
202C22×C8C2×D1311yescharacteristic
203C4⋊Q8—131no—
204#125—261no—
205#124—131no—
206#123—261no—
207C22⋊Q8—131no—
208C22⋊Q8—131no—
209C22⋊Q8—131no—
210C22⋊Q8—261no—
211C22⋊Q8—261no—
212#121—131no—
213#121—261no—
214#120—261no—
215C4×Q8—131no—
216C4×D4—131no—
217C4×D4—261no—
218C4×D4C2×D1311yescharacteristic
219C2×C4⋊C4—131no—
220C2×C4⋊C4—131no—
221C2×C22⋊C4—261no—
222#107—131no—
223#107—131no—
224#107—131no—
225C4⋊C8C2×D1311yescharacteristic, complemented
226#103—131no—
227#103—131no—
228#103—131no—
229#103—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236C22⋊C8C2×D1311yescharacteristic
237C22⋊C8C2×D1311yescharacteristic, complemented
238#97C2×D1311yescharacteristic, complemented
239C2×C13—22no—
240C2×C13—41no—
241C2×C13#54611yescharacteristic
242C2×C13C2×#13711yescharacteristic
243C2×C13#57611yescharacteristic
244D13—42no—
245D13—81no—
246C24—261no—
247#41—262no—
248#41—521no—
249C2×Q8—131no—
250C2×Q8—131no—
251C2×Q8—261no—
252C2×D4—131no—
253C2×D4—131no—
254C2×D4—262no—
255C2×D4—261no—
256C2×D4—261no—
257C2×D4—261no—
258C2×D4—521no—
259C2×D4D5211yescharacteristic
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4C22×D1311yescharacteristic
265C22×C4C22×D1311yescharacteristic
266Q16—521no—
267SD16—262no—
268SD16—521no—
269M16—41no—
270C2×C8—41no—
271C2×C8C22×D1311yescharacteristic
272C2×C8C22×D1311yescharacteristic
273C2×C8C22×D1311yescharacteristic
274C2×C8C22×D1311yescharacteristic
275C4⋊C4—131no—
276C4⋊C4—131no—
277C4⋊C4—131no—
278C4⋊C4—131no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4D5211yescharacteristic
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4D5211yescharacteristic
295C22⋊C4D5211yescharacteristic
296C42—261no—
297C42C22×D1311yescharacteristic
298C13#331411yescharacteristic, complemented, Sylow
299C23—261no—
300C23—261no—
301C23—522no—
302C23—522no—
303C23—1041no—
304C23C2×D5211yescharacteristic
305C23C2×D5211yescharacteristic
306Q8—261no—
307Q8—261no—
308Q8—261no—
309Q8—261no—
310Q8—1041no—
311D4—22no—
312D4—132no—
313D4—261no—
314D4—261no—
315D4—261no—
316D4—522no—
317D4—522no—
318D4—1041no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—522no—
330C2×C4—1041no—
331C2×C4—1041no—
332C2×C4—1041no—
333C2×C4C2×D5211yescharacteristic
334C2×C4C2×D5211yescharacteristic
335C2×C4C2×D5211yescharacteristic
336C2×C4C2×D5211yescharacteristic
337C2×C4C23×D1311yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—262no—
348C22—521no—
349C22—521no—
350C22—521no—
351C22—521no—
352C22—521no—
353C22—1044no—
354C22#8816312yes—
355C22C22×D5211yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—521no—
361C4—521no—
362C4—521no—
363C4—521no—
364C4—521no—
365C4—521no—
366C4#8825111yescharacteristic
367C4#41×D1311yescharacteristic
368C2—22no—
369C2—41no—
370C2—522no—
371C2—1041no—
372C2#1171925911yescharacteristic
373C2C2×#8816311yescharacteristic
374C2#1171945711yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
prime radical#11719255C2
hypercenter#435D13
hypocenterC13#3314
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #11719248C2semidirect
3. C13×#435C2semidirect
4. #11718795C2semidirect
5. #11718794C2semidirect
6. #11718777C2semidirect
7. C2×#88061C2semidirect
8. #11718507C2semidirect
9. #11718506C2semidirect
10. #11718397C2semidirect
11. #11718394C2semidirect
12. #11718392C2semidirect
13. #11718383C2semidirect
14. #11718375C2semidirect
15. #11718371C2semidirect
18. C2×C13×M16C22semidirect
25. C2×C4⋊Dic13C22semidirect
28. #88178C22semidirect
29. C2×Dic52C22semidirect
40. #88123C22semidirect
41. C4×Dic26C22semidirect
42. C13×C4⋊C8C22semidirect
44. C13×C22⋊C8C22semidirect
45. C13×#97C22semidirect
52. #88058C22semidirect
53. #88058C22semidirect
54. #88058C22semidirect
55. #88056C22semidirect
56. #88056C22semidirect
57. #88056C22semidirect
58. #88056C22semidirect
167. #435D13semidirect
201. C2×M16C2×D13semidirect
225. C4⋊C8C2×D13semidirect
237. C22⋊C8C2×D13semidirect
238. #97C2×D13semidirect
298. C13#3314semidirect

Maximal subgroups

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

subgroupindex
#117192552
#117192482
C13×#4352
#117187952
#117187942
#117187772
C2×#880612
#117185072
#117185062
#117183972
#117183942
#117183922
#117183832
#117183752
#117183712
#331413