Finite Group Databasebeta

← #13126327

Subgroups — #13126327

Order 1664.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D42×C13C211yesmaximal, characteristic, complemented
2C22×#6105C211yesmaximal, characteristic, complemented
3C2×#88186C211yesmaximal, characteristic, complemented
4#11719257C211yesmaximal, characteristic, complemented
5#11718879C211yesmaximal, characteristic, complemented
6#11718878C211yesmaximal, characteristic, complemented
7#11718736C211yesmaximal, characteristic, complemented
8#11718735C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic, complemented
10#11718701C211yesmaximal, characteristic, complemented
11#11718699C211yesmaximal, characteristic, complemented
12#11718698C211yesmaximal, characteristic, complemented
13#11718679C211yesmaximal, characteristic, complemented
14#11718677C211yesmaximal, characteristic, complemented
15#11718672C211yesmaximal, characteristic, complemented
16C22×D4×C13—21no—
17C22×D4×C13C2211yescharacteristic
18C22×D4×C13C2211yescharacteristic
19C2×#6127C2211yescharacteristic, complemented
20C22×Dic26C2211yescharacteristic, complemented
21C13×#127C2211yescharacteristic
22C13×#121—21no—
23C13×#121C2211yescharacteristic
24C13×#121C2211yescharacteristic
25C13×#120—21no—
26C13×#120—21no—
27C4×D4×C13C2211yescharacteristic
28C4×D4×C13C2211yescharacteristic
29#88193—21no—
30C2×#6105—24no—
31C2×#6105C2211yescharacteristic
32C2×#6105C2211yescharacteristic
33C2×#6105C2211yescharacteristic, complemented
34C2×#6105C2211yescharacteristic, complemented
35C2×#6105C2211yescharacteristic, complemented
36C2×#6105C2211yescharacteristic, complemented
37#88186—24no—
38C2×#6104C2211yescharacteristic
39C2×#6104C2211yescharacteristic, complemented
40C2×#6104C2211yescharacteristic, complemented
41#88184C2211yescharacteristic, complemented
42#88178C2211yescharacteristic, complemented
43C2×#6099C2211yescharacteristic, complemented
44C22×#1055C2211yescharacteristic, complemented
45#88150—21no—
46#88139—21no—
47#88135—21no—
48#88129C2211yescharacteristic, complemented
49C4×Dic26C2211yescharacteristic, complemented
50#88072C2211yescharacteristic
51#88072C2211yescharacteristic, complemented
52#88072C2211yescharacteristic, complemented
53C22⋊#1055C2211yescharacteristic, complemented
54C22⋊#1055C2211yescharacteristic, complemented
55#88050C2211yescharacteristic, complemented
56#88050C2211yescharacteristic, complemented
57#88049C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C4⋊#1055C2211yescharacteristic, complemented
60#88043C2211yescharacteristic, complemented
61C24×C13—21no—
62C24×C13—21no—
63C2×D4×C13—22no—
64C2×D4×C13—22no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—44no—
74C2×D4×C13D411yescharacteristic
75C2×D4×C13C2311yescharacteristic
76C2×D4×C13C2311yescharacteristic
77C2×D4×C13C2311yescharacteristic
78C22×C4×C13—21no—
79C22×C4×C13C2311yescharacteristic
80C22×C4×C13C2311yescharacteristic
81C2×C22⋊D13—21no—
82C2×C22⋊D13—21no—
83C22×Dic13—21no—
84#6127—22no—
85#6127—41no—
86C2×D52C2311yescharacteristic
87C2×C4×D13—21no—
88C2×Dic26—22no—
89C2×Dic26—21no—
90C2×Dic26—41no—
91C2×Dic26C2311yescharacteristic
92C2×Dic26C2311yescharacteristic
93C13×C4⋊C4D411yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C13×C22⋊C4D411yescharacteristic
99C13×C22⋊C4D411yescharacteristic
100C42×C13C2311yescharacteristic
101C22⋊Dic13—21no—
102#6105—22no—
103#6105—22no—
104#6105—22no—
105#6105—22no—
106#6105—41no—
107#6105D414yescomplemented
108#6104—22no—
109#6104—22no—
110#6104—41no—
111#6103—21no—
112#6103—21no—
113#6103—21no—
114C4⋊Dic13C2311yescharacteristic
115#6101—21no—
116#6101—21no—
117C4×Dic13—21no—
118#6099—22no—
119C2×#1055—22no—
120C2×#1055C2311yescharacteristic
121C2×#1055C2311yescharacteristic
122C2×#1055C2311yescharacteristic
123C2×#1055C2311yescharacteristic
124#3265—131nomaximal, Sylow
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—81no—
133C23×C13—81no—
134C23×C13C2×D411yescharacteristic
135C23×C13C2×D411yescharacteristic
136C22×D13—21no—
137D4×C13—22no—
138D4×C13—21no—
139D4×C13—21no—
140D4×C13—21no—
141D4×C13—21no—
142D4×C13—21no—
143D4×C13—42no—
144D4×C13—42no—
145D4×C13—42no—
146D4×C13—42no—
147D4×C13—42no—
148D4×C13—81no—
149D4×C13C2×D412yes—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—42no—
156C2×C4×C13C2×D411yescharacteristic
157C2×C4×C13C2×D411yescharacteristic
158C2×C4×C13C2×D411yescharacteristic
159C2×C4×C13C2×D411yescharacteristic
160C2×C4×C13C2411yescharacteristic
161C22⋊D13—42no—
162C22⋊D13—42no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—42no—
167D52—21no—
168D52—21no—
169C4×D13—42no—
170Dic26—21no—
171Dic26—21no—
172Dic26—21no—
173Dic26—42no—
174Dic26C2×D412yescomplemented
175#1055—21no—
176#1055—21no—
177#1055—21no—
178#1055C2×D412yescomplemented
179C2×AGL(1,ℤ/8)—131no—
180C22×SD16—131no—
181#548—131no—
182D42D1311yescharacteristic, complemented
183#496—131no—
184#468—131no—
185#466—131no—
186#463—131no—
187#460—131no—
188#450—131no—
189#449—131no—
190#448—131no—
191#447—131no—
192#440—131no—
193#435—131no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—22no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—84no—
209C22×C13—84no—
210C22×C13AGL(1,ℤ/8)12yescomplemented
211C22×C13C22×D411yescharacteristic
212C2×D13—41no—
213C2×D13—41no—
214C2×D13—41no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—41no—
220C4×C13C22×D411yescharacteristic
221C4×C13H(5,𝔽2)11yescharacteristic
222Dic13—22no—
223Dic13—41no—
224Dic13—41no—
225C2×#41—131no—
226C22×Q8—131no—
227C22×D4—21no—
228C22×D4C2×D1311yescharacteristic
229C22×D4C2×D1311yescharacteristic
230AGL(1,ℤ/8)—264no—
231C2×SD16—131no—
232C2×SD16—131no—
233C2×SD16—131no—
234C2×SD16—131no—
235C2×SD16—131no—
236C2×SD16—131no—
237C2×SD16—264no—
238C2×D8—131no—
239C2×D8—131no—
240C2×D8—131no—
241C2×M16—131no—
242C22×C8—131no—
243#127C2×D1311yescharacteristic
244#124—131no—
245#124—261no—
246C22⋊Q8—131no—
247C22⋊Q8—261no—
248#121—21no—
249#121—131no—
250#121—261no—
251#121C2×D1311yescharacteristic
252#121C2×D1311yescharacteristic
253#120—21no—
254#120—21no—
255C4×Q8—131no—
256C4×D4—261no—
257C4×D4C2×D1311yescharacteristic
258C4×D4C2×D1311yescharacteristic
259#107—131no—
260C4⋊C8—131no—
261#103—131no—
262#103—131no—
263#102—131no—
264#102—131no—
265#102—131no—
266#102—131no—
267C22⋊C8—131no—
268C22⋊C8—131no—
269#97—131no—
270C2×C13—22no—
271C2×C13—41no—
272C2×C13—42no—
273C2×C13—81no—
274C2×C13—81no—
275C2×C13D4211yescharacteristic
276C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
277C2×C13#57711yescharacteristic
278D13—81no—
279C24—21no—
280C24—21no—
281#41—262no—
282#41—521no—
283C2×Q8—131no—
284C2×Q8—131no—
285C2×Q8—262no—
286C2×Q8—261no—
287C2×Q8—521no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—44no—
299C2×D4—131no—
300C2×D4—261no—
301C2×D4—261no—
302C2×D4C22⋊D1311yescharacteristic
303C2×D4C22×D1311yescharacteristic
304C2×D4C22×D1311yescharacteristic
305C2×D4C22×D1311yescharacteristic
306C22×C4—21no—
307C22×C4—261no—
308C22×C4—261no—
309C22×C4C22×D1311yescharacteristic
310C22×C4C22×D1311yescharacteristic
311SD16—134no—
312SD16—262no—
313SD16—262no—
314SD16—262no—
315SD16—262no—
316SD16—521no—
317D8—262no—
318D8—262no—
319D8—521no—
320M16—262no—
321C2×C8—131no—
322C2×C8—131no—
323C2×C8—131no—
324C2×C8—131no—
325C2×C8—262no—
326C4⋊C4—131no—
327C4⋊C4—261no—
328C4⋊C4—261no—
329C4⋊C4C22⋊D1311yescharacteristic
330C4⋊C4C22×D1311yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—261no—
335C22⋊C4—261no—
336C22⋊C4—261no—
337C22⋊C4—261no—
338C22⋊C4C22⋊D1311yescharacteristic
339C22⋊C4C22⋊D1311yescharacteristic
340C42—261no—
341C42C22×D1311yescharacteristic
342C13#326511yescharacteristic, complemented, Sylow
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—261no—
353C23C2×C22⋊D1311yescharacteristic
354C23C2×C22⋊D1311yescharacteristic
355Q8—132no—
356Q8—261no—
357Q8—261no—
358Q8—261no—
359Q8—522no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—261no—
373D4—261no—
374D4—522no—
375D4—522no—
376D4D4×D1312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—261no—
384C2×C4—261no—
385C2×C4—261no—
386C2×C4—522no—
387C2×C4—522no—
388C2×C4C2×C22⋊D1311yescharacteristic
389C2×C4C2×C22⋊D1311yescharacteristic
390C2×C4C2×C22⋊D1311yescharacteristic
391C2×C4C2×C22⋊D1311yescharacteristic
392C2×C4C23×D1311yescharacteristic
393C8—132no—
394C8—261no—
395C8—261no—
396C8—261no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—22no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—521no—
414C22—521no—
415C22—521no—
416C22#8818612yescomplemented
417C22C22×C22⋊D1311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—262no—
424C4—521no—
425C4—521no—
426C4C2×D4×D1311yescharacteristic
427C4#8825111yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—1041no—
434C2C2×#8818611yescharacteristic
435C2D4×C22⋊D1311yescharacteristic
436C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD42×C13C2
socleC22×C13C22×D4
hypercenterD42D13
hypocenterC13#3265
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. D42×C13C2semidirect
2. C22×#6105C2semidirect
3. C2×#88186C2semidirect
4. #11719257C2semidirect
5. #11718879C2semidirect
6. #11718878C2semidirect
7. #11718736C2semidirect
8. #11718735C2semidirect
9. #11718703C2semidirect
10. #11718701C2semidirect
11. #11718699C2semidirect
12. #11718698C2semidirect
13. #11718679C2semidirect
14. #11718677C2semidirect
15. #11718672C2semidirect
19. C2×#6127C22semidirect
20. C22×Dic26C22semidirect
33. C2×#6105C22semidirect
34. C2×#6105C22semidirect
35. C2×#6105C22semidirect
36. C2×#6105C22semidirect
39. C2×#6104C22semidirect
40. C2×#6104C22semidirect
41. #88184C22semidirect
42. #88178C22semidirect
43. C2×#6099C22semidirect
44. C22×#1055C22semidirect
48. #88129C22semidirect
49. C4×Dic26C22semidirect
51. #88072C22semidirect
52. #88072C22semidirect
53. C22⋊#1055C22semidirect
54. C22⋊#1055C22semidirect
55. #88050C22semidirect
56. #88050C22semidirect
57. #88049C22semidirect
58. #88047C22semidirect
59. C4⋊#1055C22semidirect
60. #88043C22semidirect
107. #6105D4semidirect
174. Dic26C2×D4semidirect
178. #1055C2×D4semidirect
182. D42D13semidirect
210. C22×C13AGL(1,ℤ/8)semidirect
342. C13#3265semidirect
416. C22#88186semidirect

Maximal subgroups

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

subgroupindex
D42×C132
C22×#61052
C2×#881862
#117192572
#117188792
#117188782
#117187362
#117187352
#117187032
#117187012
#117186992
#117186982
#117186792
#117186772
#117186722
#326513