Finite Group Databasebeta

← #13125664

Subgroups — #13125664

Order 1664.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719533C211yesmaximal, characteristic
2D13×C22⋊Q8C211yesmaximal, characteristic, complemented
3C13×#452C211yesmaximal, characteristic, complemented
4#11718900C211yesmaximal, characteristic, complemented
5#11718850C211yesmaximal, characteristic, complemented
6#11718847C211yesmaximal, characteristic, complemented
7#11718835C211yesmaximal, characteristic, complemented
8#11718831C211yesmaximal, characteristic, complemented
9#11718706C211yesmaximal, characteristic, complemented
10#11718477C211yesmaximal, characteristic, complemented
11#11718470C211yesmaximal, characteristic, complemented
12#11718441C211yesmaximal, characteristic, complemented
13#11718438C211yesmaximal, characteristic, complemented
14#11718387C211yesmaximal, characteristic, complemented
15#11718384C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C2×C13×Q16C2211yescharacteristic, complemented
20C2×C13×SD16C2211yescharacteristic, complemented
21C13×C22⋊Q8C2211yescharacteristic
22#88200C2211yescharacteristic
23#88200C2211yescharacteristic
24#88200C2211yescharacteristic
25C2×#6107C2211yescharacteristic, complemented
26#88192C2211yescharacteristic
27#88192C2211yescharacteristic
28#88191—21no—
29#88189—21no—
30C2×#6105C2211yescharacteristic, complemented
31C4×C22⋊D13—21no—
32C4×C22⋊D13—21no—
33#88180C2211yescharacteristic
34#88178C2211yescharacteristic
35C2×#6094C2211yescharacteristic
36C2×#6094C2211yescharacteristic
37#88151C2211yescharacteristic
38#88150—21no—
39C4⋊C4×D13—21no—
40C4⋊C4×D13C2211yescharacteristic
41C22⋊C4×D13—21no—
42#88132—21no—
43C13×#103C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic, complemented
45C13×C22⋊C8C2211yescharacteristic
46#88075C2211yescharacteristic, complemented
47#88075C2211yescharacteristic, complemented
48#88075C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50C22⋊#1055C2211yescharacteristic
51#88060C2211yescharacteristic
52#88060C2211yescharacteristic
53#88058C2211yescharacteristic, complemented
54#88057C2211yescharacteristic, complemented
55#88056C2211yescharacteristic, complemented
56#88056C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13D411yescharacteristic
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—
70C22×Dic13D411yescharacteristic
71Q8×D13—41no—
72Q8×D13—41no—
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C4×D13D411yescharacteristic
78C2×C4×D13D411yescharacteristic
79C2×C4×D13C2311yescharacteristic
80C2×C4×D13C2311yescharacteristic
81C2×Dic26—21no—
82C2×Dic26C2311yescharacteristic
83C13×Q16—41no—
84C13×SD16—41no—
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C13×C4⋊C4—21no—
88C13×C4⋊C4C2311yescharacteristic
89C13×C22⋊C4—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94#6107—41no—
95#6105—41no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13C2311yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103C4⋊Dic13C2311yescharacteristic
104#6101—21no—
105#6101—21no—
106#6101—21no—
107#6101—21no—
108#6101—21no—
109C4×Dic13—21no—
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112#6094—41no—
113#6094—41no—
114#3196—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13C2×D411yescharacteristic
117C22×D13—22no—
118C22×D13—41no—
119C22×D13—41no—
120C22×D13C2×D411yescharacteristic
121C22×D13C2×D411yescharacteristic
122Q8×C13—21no—
123Q8×C13—21no—
124Q8×C13—21no—
125Q8×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—42no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—42no—
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2411yescharacteristic
137C22⋊D13—42no—
138C22⋊D13—42no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—41no—
144C2×Dic13C2×D411yescharacteristic
145C2×Dic13C2×D411yescharacteristic
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—21no—
149C4×D13—21no—
150C4×D13—41no—
151C4×D13—41no—
152C4×D13—42no—
153C4×D13—42no—
154Dic26—21no—
155Dic26—21no—
156Dic26—42no—
157C8×C13—21no—
158C8×C13—21no—
159#1055—21no—
160#1055—21no—
161#525—131no—
162C2×C22⋊Q8—131no—
163#485—131no—
164#485—131no—
165#484—131no—
166#481—131no—
167#470—131no—
168#470—131no—
169#468—131no—
170#468—131no—
171#452—131no—
172#452D1311yescharacteristic, complemented
173#451—131no—
174#448—131no—
175#407—131no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13C22×D411yescharacteristic
183C2×D13—21no—
184C2×D13—21no—
185C2×D13—21no—
186C2×D13—21no—
187C2×D13—21no—
188C2×D13—44no—
189C2×D13#13712yes—
190C4×C13—21no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13H(5,𝔽2)11yescharacteristic
195C4×C13H(5,𝔽2)11yescharacteristic
196Dic13—21no—
197Dic13—21no—
198Dic13—41no—
199Dic13—41no—
200Dic13—41no—
201Dic13—41no—
202C2×#41C2×D1311yescharacteristic
203C22×Q8—131no—
204C23×C4—131no—
205C2×Q16—131no—
206C2×Q16C2×D1311yescharacteristic, complemented
207C2×SD16—131no—
208C2×SD16C2×D1311yescharacteristic, complemented
209C2×M16—131no—
210C2×M16—131no—
211#123—261no—
212C22⋊Q8—131no—
213C22⋊Q8—131no—
214C22⋊Q8—131no—
215C22⋊Q8—131no—
216C22⋊Q8—131no—
217C22⋊Q8—261no—
218C22⋊Q8—261no—
219C22⋊Q8C2×D1311yescharacteristic
220#121—131no—
221#121—131no—
222#120—261no—
223C4×D4—261no—
224C4×D4—261no—
225#117—131no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—261no—
228C2×C22⋊C4—261no—
229#107—131no—
230#107—131no—
231#106—131no—
232#106—131no—
233#103—131no—
234#103—131no—
235#103—131no—
236#103—131no—
237#103—131no—
238#103C2×D1311yescharacteristic, complemented
239#102—131no—
240#102C2×D1311yescharacteristic, complemented
241C22⋊C8—131no—
242C22⋊C8—131no—
243C22⋊C8—131no—
244C22⋊C8C2×D1311yescharacteristic
245C2×C13—41no—
246C2×C13—81no—
247C2×C13#53411yescharacteristic
248C2×C13C2×#13711yescharacteristic
249C2×C13#57511yescharacteristic
250D13—22no—
251D13—41no—
252C24—131no—
253#41—41no—
254#41—41no—
255C2×Q8—131no—
256C2×Q8—261no—
257C2×Q8—521no—
258C2×Q8—521no—
259C2×Q8C22×D1311yescharacteristic
260C2×Q8C22×D1311yescharacteristic
261C2×D4—21no—
262C2×D4—261no—
263C2×D4—261no—
264C2×D4C22×D1311yescharacteristic
265C22×C4—21no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—521no—
274C22×C4—521no—
275C22×C4C22×D1311yescharacteristic
276Q16—41no—
277Q16—521no—
278SD16—41no—
279SD16—521no—
280M16—521no—
281M16—521no—
282C2×C8—131no—
283C2×C8—131no—
284C2×C8C22×D1311yescharacteristic
285C2×C8C22×D1311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—131no—
288C4⋊C4—131no—
289C4⋊C4—131no—
290C4⋊C4—261no—
291C4⋊C4—261no—
292C4⋊C4—261no—
293C4⋊C4—261no—
294C4⋊C4—261no—
295C4⋊C4—261no—
296C4⋊C4C22×D1311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—261no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4—261no—
304C22⋊C4—261no—
305C22⋊C4—261no—
306C42—261no—
307C13#319611yescharacteristic, complemented, Sylow
308C23—21no—
309C23—131no—
310C23—131no—
311C23—262no—
312C23—521no—
313C23—521no—
314C23D4×D1311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—261no—
320Q8—261no—
321Q8—522no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—522no—
326D4—522no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—131no—
334C2×C4—131no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4—521no—
348C2×C4D4×D1311yescharacteristic
349C2×C4C23×D1311yescharacteristic
350C8—21no—
351C8—21no—
352C8—261no—
353C8—261no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—132no—
361C22—261no—
362C22—261no—
363C22—261no—
364C22—261no—
365C22—261no—
366C22—524no—
367C22C2×D4×D1311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—261no—
373C4—261no—
374C4—521no—
375C4—521no—
376C4—521no—
377C4—521no—
378C4#8825111yescharacteristic
379C4#8825111yescharacteristic
380C2—41no—
381C2—81no—
382C2—262no—
383C2—521no—
384C2#1171929411yescharacteristic
385C2#1171947311yescharacteristic
386C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#452C2
socleC22×C13C22×D4
prime radical#11719533C2
hypercenter#452D13
hypocenterC13#3196
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
2. D13×C22⋊Q8C2semidirect
3. C13×#452C2semidirect
4. #11718900C2semidirect
5. #11718850C2semidirect
6. #11718847C2semidirect
7. #11718835C2semidirect
8. #11718831C2semidirect
9. #11718706C2semidirect
10. #11718477C2semidirect
11. #11718470C2semidirect
12. #11718441C2semidirect
13. #11718438C2semidirect
14. #11718387C2semidirect
15. #11718384C2semidirect
19. C2×C13×Q16C22semidirect
20. C2×C13×SD16C22semidirect
25. C2×#6107C22semidirect
30. C2×#6105C22semidirect
43. C13×#103C22semidirect
44. C13×#102C22semidirect
46. #88075C22semidirect
47. #88075C22semidirect
48. #88075C22semidirect
49. #88072C22semidirect
53. #88058C22semidirect
54. #88057C22semidirect
55. #88056C22semidirect
56. #88056C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
172. #452D13semidirect
206. C2×Q16C2×D13semidirect
208. C2×SD16C2×D13semidirect
238. #103C2×D13semidirect
240. #102C2×D13semidirect
307. C13#3196semidirect

Maximal subgroups

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

subgroupindex
#117195332
D13×C22⋊Q82
C13×#4522
#117189002
#117188502
#117188472
#117188352
#117188312
#117187062
#117184772
#117184702
#117184412
#117184382
#117183872
#117183842
#319613