Finite Group Databasebeta

← #13126680

Subgroups — #13126680

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#553C211yesmaximal, characteristic, complemented
2#11719255C211yesmaximal, characteristic, complemented
3#11718729C211yesmaximal, characteristic, complemented
4#11718727C211yesmaximal, characteristic, complemented
5#11718702C211yesmaximal, characteristic, complemented
6#11718699C211yesmaximal, characteristic, complemented
7#11718698C211yesmaximal, characteristic, complemented
8#11718697C211yesmaximal, characteristic, complemented
9#11718677C211yesmaximal, characteristic, complemented
10C4×#6104C211yesmaximal, characteristic, complemented
11D4×#1055C211yesmaximal, characteristic, complemented
12#11718664C211yesmaximal, characteristic, complemented
13#11718663C211yesmaximal, characteristic, complemented
14#11718631C211yesmaximal, characteristic, complemented
15C2×#88049C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C13×#126—21no—
19C13×#125C2211yescharacteristic, complemented
20C13×#123—21no—
21C13×#121—21no—
22C13×#121C2211yescharacteristic
23C13×#121C2211yescharacteristic, complemented
24C4×D4×C13—21no—
25C4×D4×C13C2211yescharacteristic
26C4×D4×C13C2211yescharacteristic, complemented
27C13×#117C2211yescharacteristic, complemented
28C2×C13×C4⋊C4C2211yescharacteristic
29#88191—21no—
30C2×#6105C2211yescharacteristic, complemented
31C2×#6104C2211yescharacteristic
32C2×#6104C2211yescharacteristic
33#88184C2211yescharacteristic
34#88178C2211yescharacteristic
35C22×#1055C2211yescharacteristic
36C22×#1055C2211yescharacteristic, complemented
37#88148—21no—
38#88138—21no—
39C22⋊C4×D13—21no—
40#88129C2211yescharacteristic
41C4×D52C2211yescharacteristic
42#88072C2211yescharacteristic, complemented
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic, complemented
45#88050C2211yescharacteristic, complemented
46#88050C2211yescharacteristic, complemented
47#88050C2211yescharacteristic, complemented
48#88049C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic, complemented
55#88047C2211yescharacteristic, complemented
56#88047C2211yescharacteristic, complemented
57C4⋊#1055C2211yescharacteristic, complemented
58C4×#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13D411yescharacteristic
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70#6127—22no—
71#6127—41no—
72C2×D52—22no—
73C2×D52—21no—
74C2×D52—41no—
75C2×D52C2311yescharacteristic
76C2×D52C2311yescharacteristic
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×Dic26C2311yescharacteristic
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4D411yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C22⋊C4—21no—
88C13×C22⋊C4—21no—
89C13×C22⋊C4—21no—
90C13×C22⋊C4—21no—
91C13×C22⋊C4D411yescharacteristic
92C13×C22⋊C4D411yescharacteristic
93C42×C13—21no—
94C42×C13C2311yescharacteristic
95C22⋊Dic13—21no—
96#6105—41no—
97#6104—22no—
98#6104—41no—
99#6103—21no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103C4⋊Dic13C2311yescharacteristic
104#6101—21no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3297—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C23×C13C2×D411yescharacteristic
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—42no—
118C22×D13—42no—
119C22×D13—81no—
120D4×C13—22no—
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—42no—
124D4×C13—81no—
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×C13—21no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2411yescharacteristic
139C22⋊D13—42no—
140C22⋊D13—81no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143D52—21no—
144D52—21no—
145D52—21no—
146D52—42no—
147D52#4112yes—
148C4×D13—42no—
149C4×D13—81no—
150Dic26—21no—
151Dic26—21no—
152#1055—21no—
153#1055—21no—
154#1055—21no—
155#1055—21no—
156#553D1311yescharacteristic, complemented
157#546—131no—
158#488—131no—
159#484—131no—
160#482—131no—
161#478—131no—
162#466—131no—
163#465—131no—
164#463—131no—
165#449—131no—
166#447—131no—
167C4×D8—131no—
168C8×D4—131no—
169#416—131no—
170C2×#102—131no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13#13512yes—
180C22×C13C22×D411yescharacteristic
181C2×D13—22no—
182C2×D13—41no—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—84no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13C2×#4111yescharacteristic
196C4×C13H(5,𝔽2)11yescharacteristic
197Dic13—41no—
198Dic13—41no—
199C2×#41—131no—
200C22×D4—131no—
201C2×SD16—131no—
202C2×D8—131no—
203C2×D8—131no—
204C22×C8—131no—
205C22×C8—131no—
206#126—21no—
207#125C2×D1311yescharacteristic, complemented
208#124—131no—
209#123—21no—
210#123—261no—
211C22⋊Q8—131no—
212#121—21no—
213#121—131no—
214#121—261no—
215#121C2×D1311yescharacteristic
216#121C2×D1311yescharacteristic, complemented
217#120—261no—
218C4×D4—21no—
219C4×D4—131no—
220C4×D4C2×D1311yescharacteristic
221C4×D4C2×D1311yescharacteristic, complemented
222#117C2×D1311yescharacteristic, complemented
223C2×C4⋊C4C2×D1311yescharacteristic
224C2×C22⋊C4—261no—
225#107—131no—
226#107—131no—
227#106—131no—
228C4⋊C8—131no—
229#103—131no—
230#103—131no—
231#103—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236#102—131no—
237#102—131no—
238#102—131no—
239C22⋊C8—131no—
240C22⋊C8—131no—
241C4×C8—131no—
242C2×C13—22no—
243C2×C13—41no—
244C2×C13—81no—
245C2×C13#54611yescharacteristic
246C2×C13C2×#13511yescharacteristic
247C2×C13#57611yescharacteristic
248D13—42no—
249D13—81no—
250C24—261no—
251#41—262no—
252#41—521no—
253C2×Q8—131no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—131no—
257C2×D4—131no—
258C2×D4—262no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—521no—
263C2×D4C22⋊D1311yescharacteristic
264C2×D4C22×D1311yescharacteristic
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4C22×D1311yescharacteristic
270C22×C4C22×D1311yescharacteristic
271SD16—521no—
272D8—262no—
273D8—521no—
274C2×C8—131no—
275C2×C8—131no—
276C2×C8—131no—
277C2×C8—131no—
278C2×C8—521no—
279C2×C8—521no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—131no—
284C4⋊C4—261no—
285C4⋊C4C22⋊D1311yescharacteristic
286C4⋊C4C22×D1311yescharacteristic
287C4⋊C4C22×D1311yescharacteristic
288C4⋊C4C22×D1311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C22⋊C4—261no—
298C22⋊C4C22⋊D1311yescharacteristic
299C22⋊C4C22⋊D1311yescharacteristic
300C42—21no—
301C42C22×D1311yescharacteristic
302C13#329711yescharacteristic, complemented, Sylow
303C23—21no—
304C23—261no—
305C23—261no—
306C23—522no—
307C23—522no—
308C23—1041no—
309C23C2×C22⋊D1311yescharacteristic
310C23C2×C22⋊D1311yescharacteristic
311Q8—261no—
312Q8—261no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—132no—
319D4—261no—
320D4—261no—
321D4—261no—
322D4—522no—
323D4—522no—
324D4—1041no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—522no—
337C2×C4—1041no—
338C2×C4C2×C22⋊D1311yescharacteristic
339C2×C4C2×C22⋊D1311yescharacteristic
340C2×C4C2×C22⋊D1311yescharacteristic
341C2×C4C2×C22⋊D1311yescharacteristic
342C2×C4C23×D1311yescharacteristic
343C8—261no—
344C8—261no—
345C8—261no—
346C8—261no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—262no—
356C22—521no—
357C22—521no—
358C22—521no—
359C22—521no—
360C22—521no—
361C22—1044no—
362C22#8820412yes—
363C22C22×C22⋊D1311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—521no—
372C4—521no—
373C4#41×D1311yescharacteristic
374C4#8825611yescharacteristic
375C2—22no—
376C2—41no—
377C2—81no—
378C2—522no—
379C2—1041no—
380C2C2×#8820411yescharacteristic
381C2#1171953411yescharacteristic
382C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#553C2
socleC22×C13C22×D4
hypercenter#553D13
hypocenterC13#3297
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C13×#553C2semidirect
2. #11719255C2semidirect
3. #11718729C2semidirect
4. #11718727C2semidirect
5. #11718702C2semidirect
6. #11718699C2semidirect
7. #11718698C2semidirect
8. #11718697C2semidirect
9. #11718677C2semidirect
10. C4×#6104C2semidirect
11. D4×#1055C2semidirect
12. #11718664C2semidirect
13. #11718663C2semidirect
14. #11718631C2semidirect
15. C2×#88049C2semidirect
19. C13×#125C22semidirect
23. C13×#121C22semidirect
26. C4×D4×C13C22semidirect
27. C13×#117C22semidirect
30. C2×#6105C22semidirect
36. C22×#1055C22semidirect
42. #88072C22semidirect
44. C22⋊#1055C22semidirect
45. #88050C22semidirect
46. #88050C22semidirect
47. #88050C22semidirect
54. #88048C22semidirect
55. #88047C22semidirect
56. #88047C22semidirect
57. C4⋊#1055C22semidirect
58. C4×#1055C22semidirect
156. #553D13semidirect
207. #125C2×D13semidirect
216. #121C2×D13semidirect
221. C4×D4C2×D13semidirect
222. #117C2×D13semidirect
302. C13#3297semidirect

Maximal subgroups

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

subgroupindex
C13×#5532
#117192552
#117187292
#117187272
#117187022
#117186992
#117186982
#117186972
#117186772
C4×#61042
D4×#10552
#117186642
#117186632
#117186312
C2×#880492
#329713