Finite Group Databasebeta

← #13126915

Subgroups — #13126915

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#11719335C211yesmaximal, characteristic
2#11719216C211yesmaximal, characteristic, complemented
3C13×#484C211yesmaximal, characteristic, complemented
4#11718712C211yesmaximal, characteristic, complemented
5C2×#88049C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718550C211yesmaximal, characteristic, complemented
8#11718547C211yesmaximal, characteristic, complemented
9#11718543C211yesmaximal, characteristic, complemented
10#11718471C211yesmaximal, characteristic, complemented
11#11718464C211yesmaximal, characteristic, complemented
12#11718459C211yesmaximal, characteristic, complemented
13#11718456C211yesmaximal, characteristic, complemented
14#11718392C211yesmaximal, characteristic, complemented
15#11718391C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20#88201C2211yescharacteristic
21C2×#6107C2211yescharacteristic, complemented
22C4×C22⋊D13—21no—
23C4×C22⋊D13C2211yescharacteristic
24#88178—21no—
25#88178C2211yescharacteristic
26C22×#1055C2211yescharacteristic
27C2×#6095C2211yescharacteristic
28C2×#6095C2211yescharacteristic
29C2×#6094C2211yescharacteristic, complemented
30#88151C2211yescharacteristic, complemented
31#88150—21no—
32#88149—21no—
33#88149C2211yescharacteristic
34#88148—21no—
35#88147C2211yescharacteristic
36C4⋊C4×D13C2211yescharacteristic, complemented
37#88143—21no—
38#88142C2211yescharacteristic, complemented
39#88141C2211yescharacteristic, complemented
40#88136—21no—
41C22⋊C4×D13—21no—
42C13×#107C2211yescharacteristic, complemented
43C13×#107C2211yescharacteristic, complemented
44C13×#103C2211yescharacteristic, complemented
45C13×#103C2211yescharacteristic, complemented
46C13×C22⋊C8C2211yescharacteristic
47#88075C2211yescharacteristic, complemented
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic, complemented
51#88055C2211yescharacteristic, complemented
52#88054C2211yescharacteristic, complemented
53#88050C2211yescharacteristic, complemented
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88049C2211yescharacteristic
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13D411yescharacteristic
64#6131—22no—
65#6131—41no—
66C2×D52—22no—
67C2×D52—21no—
68C2×D52—21no—
69C2×D52—21no—
70C2×D52—41no—
71C2×D52C2311yescharacteristic
72C2×D52C2311yescharacteristic
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13C2311yescharacteristic
77C2×Dic26—21no—
78C2×Dic26C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C22⋊C4—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13D411yescharacteristic
89#6107—41no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103D411yescharacteristic
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101D411yescharacteristic
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105C2×#1055—41no—
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#6095—22no—
109#6095—41no—
110#6094—41no—
111#3314—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—42no—
116C22×D13—42no—
117C22×D13—81no—
118C22×D13C2×D411yescharacteristic
119Q8×C13—21no—
120Q8×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—81no—
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2411yescharacteristic
130C22⋊D13—22no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136D52—21no—
137D52—21no—
138D52—21no—
139D52—42no—
140D52—42no—
141D52—81no—
142D52#4112yes—
143C4×D13—21no—
144C4×D13—21no—
145C4×D13—42no—
146C4×D13—81no—
147C4×D13—81no—
148Dic26—21no—
149Dic26—21no—
150Dic26—81no—
151C8×C13—21no—
152C8×C13—21no—
153#1055—21no—
154#1055—21no—
155#554—131no—
156#546—131no—
157#489—131no—
158#484D1311yescharacteristic, complemented
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#435—131no—
168#417—131no—
169C2×#102—131no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13#13712yes—
173C22×C13C22×D411yescharacteristic
174C2×D13—21no—
175C2×D13—22no—
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—84no—
184C4×C13—21no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13C2×#4111yescharacteristic
190C4×C13H(5,𝔽2)11yescharacteristic
191Dic13—21no—
192Dic13—21no—
193Dic13—21no—
194Dic13—41no—
195Dic13—41no—
196C2×#41—131no—
197C22×D4—131no—
198C2×Q16—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×M16—131no—
202C22×C8—131no—
203C4⋊Q8—131no—
204#125—261no—
205#124—131no—
206#123—261no—
207C22⋊Q8—131no—
208C22⋊Q8—131no—
209C22⋊Q8—261no—
210C22⋊Q8—261no—
211C22⋊Q8C2×D1311yescharacteristic
212#121—131no—
213#121—261no—
214#120—261no—
215C4×Q8—131no—
216C4×D4—131no—
217C4×D4—131no—
218C4×D4—261no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4C2×D1311yescharacteristic
221C2×C22⋊C4—261no—
222#107—131no—
223#107C2×D1311yescharacteristic, complemented
224#107C2×D1311yescharacteristic, complemented
225C4⋊C8—131no—
226#103—131no—
227#103—131no—
228#103C2×D1311yescharacteristic, complemented
229#103C2×D1311yescharacteristic, complemented
230#102—131no—
231#102—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236C22⋊C8—131no—
237C22⋊C8C2×D1311yescharacteristic
238#97—131no—
239C2×C13—22no—
240C2×C13#54611yescharacteristic
241C2×C13C2×#13711yescharacteristic
242C2×C13#57611yescharacteristic
243D13—41no—
244D13—42no—
245D13—81no—
246C24—261no—
247#41—262no—
248#41—521no—
249C2×Q8—131no—
250C2×Q8—261no—
251C2×Q8C22×D1311yescharacteristic
252C2×D4—131no—
253C2×D4—131no—
254C2×D4—131no—
255C2×D4—262no—
256C2×D4—261no—
257C2×D4—261no—
258C2×D4—261no—
259C2×D4—521no—
260C22×C4—21no—
261C22×C4—131no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4C22×D1311yescharacteristic
266Q16—521no—
267SD16—262no—
268SD16—521no—
269M16—521no—
270C2×C8—131no—
271C2×C8—131no—
272C2×C8—521no—
273C2×C8C22×D1311yescharacteristic
274C2×C8C22×D1311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—131no—
278C4⋊C4—131no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4C22×D1311yescharacteristic
285C4⋊C4C22×D1311yescharacteristic
286C4⋊C4C22×D1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—131no—
289C22⋊C4—131no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C42—131no—
297C42—261no—
298C13#331411yescharacteristic, complemented, Sylow
299C23—131no—
300C23—261no—
301C23—261no—
302C23—522no—
303C23—522no—
304C23—1041no—
305C23D4×D1311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—261no—
309Q8—261no—
310Q8—1041no—
311D4—132no—
312D4—262no—
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—21no—
324C2×C4—21no—
325C2×C4—81no—
326C2×C4—131no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—522no—
334C2×C4—1041no—
335C2×C4—1041no—
336C2×C4D4×D1311yescharacteristic
337C2×C4C23×D1311yescharacteristic
338C8—21no—
339C8—21no—
340C8—261no—
341C8—261no—
342C22—21no—
343C22—21no—
344C22—261no—
345C22—261no—
346C22—261no—
347C22—262no—
348C22—521no—
349C22—521no—
350C22—521no—
351C22—521no—
352C22—521no—
353C22—1044no—
354C22#8817212yes—
355C22C2×D4×D1311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—261no—
362C4—261no—
363C4—261no—
364C4—521no—
365C4—521no—
366C4#41×D1311yescharacteristic
367C4#8825611yescharacteristic
368C2—22no—
369C2—521no—
370C2—522no—
371C2—1041no—
372C2#1171935911yescharacteristic
373C2C2×#8817211yescharacteristic
374C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#484C2
socleC22×C13C22×D4
prime radical#11719335C2
hypercenter#484D13
hypocenterC13#3314
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #11719216C2semidirect
3. C13×#484C2semidirect
4. #11718712C2semidirect
5. C2×#88049C2semidirect
6. #11718551C2semidirect
7. #11718550C2semidirect
8. #11718547C2semidirect
9. #11718543C2semidirect
10. #11718471C2semidirect
11. #11718464C2semidirect
12. #11718459C2semidirect
13. #11718456C2semidirect
14. #11718392C2semidirect
15. #11718391C2semidirect
21. C2×#6107C22semidirect
29. C2×#6094C22semidirect
30. #88151C22semidirect
36. C4⋊C4×D13C22semidirect
38. #88142C22semidirect
39. #88141C22semidirect
42. C13×#107C22semidirect
43. C13×#107C22semidirect
44. C13×#103C22semidirect
45. C13×#103C22semidirect
47. #88075C22semidirect
50. #88060C22semidirect
51. #88055C22semidirect
52. #88054C22semidirect
53. #88050C22semidirect
58. #88047C22semidirect
158. #484D13semidirect
223. #107C2×D13semidirect
224. #107C2×D13semidirect
228. #103C2×D13semidirect
229. #103C2×D13semidirect
298. C13#3314semidirect

Maximal subgroups

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

subgroupindex
#117193352
#117192162
C13×#4842
#117187122
C2×#880492
#117185512
#117185502
#117185472
#117185432
#117184712
#117184642
#117184592
#117184562
#117183922
#117183912
#331413