Finite Group Databasebeta

← #13126995

Subgroups — #13126995

Order 1664.

414 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
1#11719335C211yesmaximal, characteristic, complemented
2#11719237C211yesmaximal, characteristic, complemented
3C13×#485C211yesmaximal, characteristic, complemented
4#11718710C211yesmaximal, characteristic, complemented
5#11718662C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718544C211yesmaximal, characteristic, complemented
8#11718530C211yesmaximal, characteristic, complemented
9#11718527C211yesmaximal, characteristic, complemented
10#11718480C211yesmaximal, characteristic, complemented
11#11718472C211yesmaximal, characteristic, complemented
12#11718465C211yesmaximal, characteristic, complemented
13#11718456C211yesmaximal, characteristic, complemented
14#11718393C211yesmaximal, characteristic, complemented
15#11718389C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#117C2211yescharacteristic
20#88201C2211yescharacteristic
21C2×#6106C2211yescharacteristic, complemented
22#88184C2211yescharacteristic
23C4×C22⋊D13C2211yescharacteristic
24C2×#6099C2211yescharacteristic
25C2×D104C2211yescharacteristic
26C2×D104C2211yescharacteristic
27C2×C8×D13C2211yescharacteristic, complemented
28#88149—21no—
29#88149C2211yescharacteristic
30#88149C2211yescharacteristic, complemented
31#88148—21no—
32#88147C2211yescharacteristic
33#88147C2211yescharacteristic, complemented
34#88146C2211yescharacteristic, complemented
35#88142C2211yescharacteristic, complemented
36#88139—21no—
37#88138—21no—
38#88136—21no—
39C22⋊C4×D13—21no—
40#88129—21no—
41#88126—21no—
42C13×#107C2211yescharacteristic, complemented
43C13×#106C2211yescharacteristic, 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#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88049C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13D411yescharacteristic
64#6131—22no—
65#6131—41no—
66C2×D52—22no—
67C2×D52—21no—
68C2×D52—21no—
69C2×D52—21no—
70C2×D52—21no—
71C2×D52—41no—
72C2×D52C2311yescharacteristic
73C2×D52C2311yescharacteristic
74C2×D52C2311yescharacteristic
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13C2311yescharacteristic
79C2×Dic26—21no—
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C22⋊C4—21no—
87C13×C22⋊C4—21no—
88C42×C13—21no—
89C22⋊Dic13D411yescharacteristic
90#6106—41no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103D411yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101D411yescharacteristic
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105#6099—41no—
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108D104—22no—
109D104—41no—
110C8×D13—41no—
111#3319—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—42no—
117C22×D13—42no—
118C22×D13—81no—
119C22×D13C2×D411yescharacteristic
120Q8×C13—21no—
121Q8×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—21no—
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2411yescharacteristic
130C22⋊D13—41no—
131C22⋊D13—81no—
132C2×Dic13—21no—
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136D52—21no—
137D52—21no—
138D52—21no—
139D52—21no—
140D52—21no—
141D52—42no—
142D52—42no—
143D52—81no—
144D52—81no—
145D52#4112yes—
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—42no—
149C4×D13—42no—
150C4×D13—81no—
151Dic26—81no—
152C8×C13—21no—
153C8×C13—21no—
154#1055—21no—
155#1055—21no—
156#555—131no—
157#546—131no—
158#489—131no—
159#485D1311yescharacteristic, complemented
160#482—131no—
161#474—131no—
162#468—131no—
163#466—131no—
164#463—131no—
165#449—131no—
166#447—131no—
167#442—131no—
168#435—131no—
169#418—131no—
170#416—131no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13C22×D411yescharacteristic
175C2×D13—21no—
176C2×D13—22no—
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—41no—
186C2×D13—41no—
187C2×D13—84no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13C2×#4111yescharacteristic
194C4×C13H(5,𝔽2)11yescharacteristic
195Dic13—21no—
196Dic13—21no—
197Dic13—21no—
198Dic13—41no—
199C2×#41—131no—
200C22×D4—131no—
201C2×SD16—131no—
202C2×D8—131no—
203C2×D8—131no—
204C2×M16—131no—
205C22×C8—131no—
206C4⋊Q8—131no—
207#124—131no—
208#124—261no—
209#124—261no—
210#123—261no—
211C22⋊Q8C2×D1311yescharacteristic
212#121—131no—
213#121—131no—
214#121—131no—
215#121—261no—
216#121—261no—
217#120—261no—
218C4×D4—131no—
219C4×D4—131no—
220C4×D4—131no—
221#117—131no—
222#117—261no—
223#117C2×D1311yescharacteristic
224C2×C22⋊C4—261no—
225#107—131no—
226#107C2×D1311yescharacteristic, complemented
227#106C2×D1311yescharacteristic, complemented
228C4⋊C8—131no—
229#103—131no—
230#103C2×D1311yescharacteristic, complemented
231#103C2×D1311yescharacteristic, complemented
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⋊C8C2×D1311yescharacteristic
241#97—131no—
242C2×C13—41no—
243C2×C13#54611yescharacteristic
244C2×C13#57511yescharacteristic
245C2×C13#57611yescharacteristic
246D13—41no—
247D13—42no—
248D13—81no—
249D13—81no—
250C24—261no—
251#41—262no—
252#41—521no—
253C2×Q8—261no—
254C2×Q8C22×D1311yescharacteristic
255C2×D4—131no—
256C2×D4—131no—
257C2×D4—131no—
258C2×D4—131no—
259C2×D4—262no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—261no—
264C2×D4—261no—
265C2×D4—521no—
266C22×C4—131no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4C22×D1311yescharacteristic
271SD16—521no—
272D8—262no—
273D8—521no—
274M16—521no—
275C2×C8—131no—
276C2×C8—131no—
277C2×C8—521no—
278C2×C8C22×D1311yescharacteristic
279C2×C8C22×D1311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C4⋊C4—261no—
284C4⋊C4C22×D1311yescharacteristic
285C4⋊C4C22×D1311yescharacteristic
286C4⋊C4C22×D1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—131no—
290C22⋊C4—131no—
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—21no—
300C42—131no—
301C42—261no—
302C13#331911yescharacteristic, complemented, Sylow
303C23—131no—
304C23—261no—
305C23—261no—
306C23—261no—
307C23—522no—
308C23—522no—
309C23—1041no—
310C23D4×D1311yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—1041no—
314D4—132no—
315D4—261no—
316D4—261no—
317D4—261no—
318D4—261no—
319D4—261no—
320D4—522no—
321D4—522no—
322D4—521no—
323D4—1041no—
324D4—1041no—
325D4—1041no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—131no—
333C2×C4—131no—
334C2×C4—131no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—522no—
339C2×C4—522no—
340C2×C4—1041no—
341C2×C4D4×D1311yescharacteristic
342C2×C4C23×D1311yescharacteristic
343C8—21no—
344C8—21no—
345C8—261no—
346C8—261no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—261no—
351C22—261no—
352C22—261no—
353C22—262no—
354C22—521no—
355C22—521no—
356C22—521no—
357C22—521no—
358C22—521no—
359C22—521no—
360C22—521no—
361C22—521no—
362C22—1044no—
363C22C2×D4×D1311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—261no—
370C4—261no—
371C4—261no—
372C4—521no—
373C4#41×D1311yescharacteristic
374C4#8825611yescharacteristic
375C2—41no—
376C2—521no—
377C2—522no—
378C2—1041no—
379C2—1041no—
380C2#1171935911yescharacteristic
381C2#1171947411yescharacteristic
382C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
hypercenter#485D13
hypocenterC13#3319
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #11719335C2semidirect
2. #11719237C2semidirect
3. C13×#485C2semidirect
4. #11718710C2semidirect
5. #11718662C2semidirect
6. #11718551C2semidirect
7. #11718544C2semidirect
8. #11718530C2semidirect
9. #11718527C2semidirect
10. #11718480C2semidirect
11. #11718472C2semidirect
12. #11718465C2semidirect
13. #11718456C2semidirect
14. #11718393C2semidirect
15. #11718389C2semidirect
21. C2×#6106C22semidirect
27. C2×C8×D13C22semidirect
30. #88149C22semidirect
33. #88147C22semidirect
34. #88146C22semidirect
35. #88142C22semidirect
42. C13×#107C22semidirect
43. C13×#106C22semidirect
44. C13×#103C22semidirect
45. C13×#103C22semidirect
47. #88075C22semidirect
50. #88060C22semidirect
51. #88055C22semidirect
52. #88054C22semidirect
57. #88049C22semidirect
58. #88047C22semidirect
159. #485D13semidirect
226. #107C2×D13semidirect
227. #106C2×D13semidirect
230. #103C2×D13semidirect
231. #103C2×D13semidirect
302. C13#3319semidirect

Maximal subgroups

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

subgroupindex
#117193352
#117192372
C13×#4852
#117187102
#117186622
#117185512
#117185442
#117185302
#117185272
#117184802
#117184722
#117184652
#117184562
#117183932
#117183892
#331913