Finite Group Databasebeta

← #13126516

Subgroups — #13126516

Order 1664.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88170C211yesmaximal, characteristic, complemented
2C2×D8×D13C211yesmaximal, characteristic, complemented
3#11719381C211yesmaximal, characteristic, complemented
4#11719259C211yesmaximal, characteristic, complemented
5C13×#463C211yesmaximal, characteristic, complemented
6#11718830C211yesmaximal, characteristic, complemented
7#11718819C211yesmaximal, characteristic, complemented
8#11718720C211yesmaximal, characteristic, complemented
9C4×#6104C211yesmaximal, characteristic, complemented
10#11718505C211yesmaximal, characteristic, complemented
11#11718495C211yesmaximal, characteristic, complemented
12#11718474C211yesmaximal, characteristic, complemented
13#11718472C211yesmaximal, characteristic, complemented
14#11718437C211yesmaximal, characteristic, complemented
15#11718436C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic, complemented
17C2×#6129C2211yescharacteristic, complemented
18C2×D4×D13C2211yescharacteristic
19C2×D4×D13C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic, complemented
21C2×C13×D8C2211yescharacteristic
22C13×#124C2211yescharacteristic, complemented
23C4×D4×C13C2211yescharacteristic, complemented
24#88200C2211yescharacteristic
25C2×#6107C2211yescharacteristic, complemented
26C2×#6106C2211yescharacteristic, complemented
27#88192C2211yescharacteristic, complemented
28C2×#6105C2211yescharacteristic, complemented
29C2×#6104C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88184—21no—
32C2×#6103—21no—
33#88170—24no—
34D8×D13—24no—
35C2×D104C2211yescharacteristic
36C2×#6095C2211yescharacteristic, complemented
37C2×C8×D13C2211yescharacteristic
38C2×C8×D13C2211yescharacteristic, complemented
39#88151C2211yescharacteristic
40#88149C2211yescharacteristic, complemented
41#88140—21no—
42#88138—21no—
43#88137—21no—
44#88136—21no—
45#88136—21no—
46C22⋊C4×D13—21no—
47#88129C2211yescharacteristic, complemented
48C4×D52C2211yescharacteristic
49C4×D52C2211yescharacteristic, complemented
50C13×C4⋊C8C2211yescharacteristic, complemented
51C13×#103C2211yescharacteristic, complemented
52C13×#102C2211yescharacteristic, complemented
53#88072C2211yescharacteristic, complemented
54#88061C2211yescharacteristic, complemented
55#88060C2211yescharacteristic
56#88060C2211yescharacteristic, complemented
57#88056C2211yescharacteristic, complemented
58#88049C2211yescharacteristic, complemented
59#88047C2211yescharacteristic, complemented
60C4×#1055C2211yescharacteristic, complemented
61C23×D13—21no—
62C23×D13—21no—
63C2×Q8×C13C2311yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C22×Dic13—21no—
72#6131—22no—
73#6131—41no—
74#6129—22no—
75#6129—41no—
76D4×D13—22no—
77D4×D13—22no—
78D4×D13—41no—
79D4×D13—41no—
80C2×D52—21no—
81C2×D52—21no—
82C2×D52D411yescharacteristic
83C2×D52C2311yescharacteristic
84C2×D52C2311yescharacteristic
85C2×C4×D13—21no—
86C2×C4×D13—21no—
87C2×C4×D13C2311yescharacteristic
88C2×C4×D13C2311yescharacteristic
89C2×Dic26C2311yescharacteristic
90C13×SD16—22no—
91C13×D8—22no—
92C2×C8×C13C2311yescharacteristic
93C2×C8×C13C2311yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C42×C13C2311yescharacteristic
99C22⋊Dic13—21no—
100#6107—22no—
101#6106—41no—
102#6105—41no—
103#6104—22no—
104#6104D414yescomplemented
105#6103—21no—
106#6103—21no—
107#6103—21no—
108#6103—21no—
109#6103—21no—
110#6103—21no—
111#6103D411yescharacteristic
112#6103D411yescharacteristic
113C4⋊Dic13—21no—
114C4⋊Dic13D411yescharacteristic
115C4⋊Dic13C2311yescharacteristic
116#6101—21no—
117C2×#1055C2311yescharacteristic
118C2×#1055C2311yescharacteristic
119D104—22no—
120#6095—22no—
121C8×D13—22no—
122C8×D13—22no—
123#3280—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13—21no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—42no—
129C22×D13—42no—
130C22×D13—42no—
131C22×D13—42no—
132C22×D13—81no—
133C22×D13—81no—
134C22×D13C2×D411yescharacteristic
135C22×D13C2×D411yescharacteristic
136Q8×C13—21no—
137Q8×C13—21no—
138D4×C13—21no—
139D4×C13—21no—
140D4×C13—21no—
141D4×C13C2×D412yes—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—81no—
145C2×C4×C13C2×D411yescharacteristic
146C2×C4×C13C2×D411yescharacteristic
147C2×C4×C13C2411yescharacteristic
148C22⋊D13—42no—
149C22⋊D13—42no—
150C22⋊D13—42no—
151C22⋊D13—81no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—42no—
155C2×Dic13C2×D411yescharacteristic
156C2×Dic13C2×D411yescharacteristic
157D52—22no—
158D52—21no—
159D52—21no—
160D52—21no—
161D52—42no—
162D52—81no—
163D52C2×D412yes—
164C4×D13—21no—
165C4×D13—21no—
166C4×D13—21no—
167C4×D13—21no—
168C4×D13—42no—
169C4×D13—81no—
170Dic26—21no—
171Dic26—21no—
172C8×C13—21no—
173C8×C13—21no—
174#1055—21no—
175#1055C2×D412yes—
176C2×#135—131no—
177C22×D8—131no—
178#546—131no—
179#546—131no—
180#495—131no—
181#467—131no—
182#466—131no—
183#463—131no—
184#463D1311yescharacteristic, complemented
185#450—131no—
186#450—131no—
187#449—131no—
188#449—131no—
189C4×D8—131no—
190C8×D4—131no—
191C22×C13—22no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13C22×D411yescharacteristic
198C2×D13—21no—
199C2×D13—21no—
200C2×D13—21no—
201C2×D13—22no—
202C2×D13—21no—
203C2×D13—21no—
204C2×D13—41no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C2×D13—84no—
210C2×D13—84no—
211C2×D13#13512yescomplemented
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—41no—
215C4×C13—41no—
216C4×C13C22×D411yescharacteristic
217C4×C13H(5,𝔽2)11yescharacteristic
218Dic13—21no—
219Dic13—21no—
220Dic13—41no—
221Dic13—41no—
222C2×#41—131no—
223C2×#41—131no—
224C22×D4—131no—
225C22×D4—131no—
226#135—264no—
227C2×Q16—131no—
228C2×SD16—131no—
229C2×SD16—131no—
230C2×SD16—131no—
231C2×SD16C2×D1311yescharacteristic, complemented
232C2×D8—131no—
233C2×D8—131no—
234C2×D8—131no—
235C2×D8—264no—
236C2×D8C2×D1311yescharacteristic
237C22×C8—131no—
238C22×C8—131no—
239#124—131no—
240#124C2×D1311yescharacteristic, complemented
241#123—261no—
242#123—261no—
243C22⋊Q8—131no—
244C22⋊Q8—131no—
245#121—131no—
246#121—131no—
247#121—261no—
248#121—261no—
249#120—261no—
250#120—261no—
251C4×D4—131no—
252C4×D4—131no—
253C4×D4C2×D1311yescharacteristic, complemented
254C2×C22⋊C4—261no—
255C2×C22⋊C4—261no—
256#107—131no—
257C4⋊C8C2×D1311yescharacteristic, complemented
258#103—131no—
259#103C2×D1311yescharacteristic, complemented
260#102—131no—
261#102—131no—
262#102—131no—
263#102C2×D1311yescharacteristic, complemented
264C22⋊C8—131no—
265C22⋊C8—131no—
266C4×C8—131no—
267C2×C13—42no—
268C2×C13—81no—
269C2×C13D4211yescharacteristic
270C2×C13C2×#13511yescharacteristic
271C2×C13#57611yescharacteristic
272D13—22no—
273D13—41no—
274D13—42no—
275D13—81no—
276C24—261no—
277C24—261no—
278#41—262no—
279#41—262no—
280#41—521no—
281#41—521no—
282C2×Q8—131no—
283C2×Q8C22×D1311yescharacteristic
284C2×D4—131no—
285C2×D4—131no—
286C2×D4—131no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—261no—
290C2×D4—261no—
291C2×D4—262no—
292C2×D4—262no—
293C2×D4—261no—
294C2×D4—261no—
295C2×D4—521no—
296C2×D4—521no—
297C2×D4C22×D1311yescharacteristic
298C2×D4C22×D1311yescharacteristic
299C22×C4—21no—
300C22×C4—131no—
301C22×C4—131no—
302C22×C4—261no—
303C22×C4—261no—
304C22×C4—261no—
305Q16—262no—
306SD16—22no—
307SD16—262no—
308SD16—521no—
309SD16—521no—
310D8—22no—
311D8—134no—
312D8—262no—
313D8—262no—
314C2×C8—131no—
315C2×C8—131no—
316C2×C8—262no—
317C2×C8—262no—
318C2×C8C22×D1311yescharacteristic
319C2×C8C22×D1311yescharacteristic
320C4⋊C4—131no—
321C4⋊C4—131no—
322C4⋊C4—261no—
323C4⋊C4—261no—
324C4⋊C4C22×D1311yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—131no—
329C22⋊C4—131no—
330C22⋊C4—261no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C22⋊C4—261no—
334C22⋊C4—261no—
335C22⋊C4—261no—
336C22⋊C4—261no—
337C42C22×D1311yescharacteristic
338C13#328011yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—131no—
342C23—131no—
343C23—261no—
344C23—261no—
345C23—522no—
346C23—522no—
347C23—522no—
348C23—522no—
349C23—1041no—
350C23—1041no—
351Q8—21no—
352Q8—21no—
353Q8—261no—
354Q8—261no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—132no—
359D4—262no—
360D4—261no—
361D4—261no—
362D4—261no—
363D4—522no—
364D4—522no—
365D4—522no—
366D4—522no—
367D4—1041no—
368D4—1041no—
369D4D4×D1312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—131no—
374C2×C4—131no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—261no—
380C2×C4—261no—
381C2×C4—522no—
382C2×C4—522no—
383C2×C4—1041no—
384C2×C4D4×D1311yescharacteristic
385C2×C4D4×D1311yescharacteristic
386C2×C4C23×D1311yescharacteristic
387C8—21no—
388C8—21no—
389C8—132no—
390C8—261no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—132no—
398C22—261no—
399C22—261no—
400C22—261no—
401C22—261no—
402C22—261no—
403C22—262no—
404C22—521no—
405C22—521no—
406C22—521no—
407C22—521no—
408C22—521no—
409C22—1044no—
410C22—1044no—
411C22C2×D4×D1311yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—261no—
417C4—261no—
418C4—521no—
419C4—521no—
420C4C2×D4×D1311yescharacteristic
421C4#8825611yescharacteristic
422C2—42no—
423C2—81no—
424C2—262no—
425C2—521no—
426C2—522no—
427C2—1041no—
428C2#1171931411yescharacteristic
429C2D13×#13511yescharacteristic
430C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#463C2
socleC22×C13C22×D4
hypercenter#463D13
hypocenterC13#3280
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#88170C2semidirect
2. C2×D8×D13C2semidirect
3. #11719381C2semidirect
4. #11719259C2semidirect
5. C13×#463C2semidirect
6. #11718830C2semidirect
7. #11718819C2semidirect
8. #11718720C2semidirect
9. C4×#6104C2semidirect
10. #11718505C2semidirect
11. #11718495C2semidirect
12. #11718474C2semidirect
13. #11718472C2semidirect
14. #11718437C2semidirect
15. #11718436C2semidirect
16. C2×#6131C22semidirect
17. C2×#6129C22semidirect
20. C2×C13×SD16C22semidirect
22. C13×#124C22semidirect
23. C4×D4×C13C22semidirect
25. C2×#6107C22semidirect
26. C2×#6106C22semidirect
27. #88192C22semidirect
28. C2×#6105C22semidirect
36. C2×#6095C22semidirect
38. C2×C8×D13C22semidirect
40. #88149C22semidirect
47. #88129C22semidirect
49. C4×D52C22semidirect
50. C13×C4⋊C8C22semidirect
51. C13×#103C22semidirect
52. C13×#102C22semidirect
53. #88072C22semidirect
54. #88061C22semidirect
56. #88060C22semidirect
57. #88056C22semidirect
58. #88049C22semidirect
59. #88047C22semidirect
60. C4×#1055C22semidirect
104. #6104D4semidirect
184. #463D13semidirect
211. C2×D13#135semidirect
231. C2×SD16C2×D13semidirect
240. #124C2×D13semidirect
253. C4×D4C2×D13semidirect
257. C4⋊C8C2×D13semidirect
259. #103C2×D13semidirect
263. #102C2×D13semidirect
338. C13#3280semidirect

Maximal subgroups

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

subgroupindex
C2×#881702
C2×D8×D132
#117193812
#117192592
C13×#4632
#117188302
#117188192
#117187202
C4×#61042
#117185052
#117184952
#117184742
#117184722
#117184372
#117184362
#328013