Finite Group Databasebeta

← #49130560

Subgroups — #49130560

Order 36224.

764 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583655C211yesmaximal, characteristic, complemented
2C2×#22583634C211yesmaximal, characteristic, complemented
3C2×#22583629C211yesmaximal, characteristic, complemented
4#31827044C211yesmaximal, characteristic, complemented
5#31826629C211yesmaximal, characteristic, complemented
6#31826628C211yesmaximal, characteristic, complemented
7#31826617C211yesmaximal, characteristic, complemented
8#31826616C211yesmaximal, characteristic, complemented
9#31826608C211yesmaximal, characteristic, complemented
10#31826607C211yesmaximal, characteristic, complemented
11#31826597C211yesmaximal, characteristic, complemented
12#31826463C211yesmaximal, characteristic, complemented
13#102×D283C211yesmaximal, characteristic, complemented
14#31826430C211yesmaximal, characteristic, complemented
15#447×C283C211yesmaximal, characteristic, complemented
16#22583655—24no—
17#22583655—24no—
18C2×#17985392C2211yescharacteristic
19C2×#17985392C2211yescharacteristic
20C2×#17985391—21no—
21C2×#17985391C2211yescharacteristic
22C2×#17985391C2211yescharacteristic
23C2×#17985391C2211yescharacteristic, complemented
24C22×C22⋊D283—21no—
25C22×C22⋊D283—21no—
26C2×D4×D283—21no—
27C2×D4×D283C2211yescharacteristic
28C2×D4×D283C2211yescharacteristic
29#22583634—24no—
30#22583629—24no—
31C2×Dic1132C2211yescharacteristic, complemented
32C2×#17985381C2211yescharacteristic, complemented
33C2×#17985380C2211yescharacteristic, complemented
34C2×#17985380C2211yescharacteristic, complemented
35C2×#17985380C2211yescharacteristic, complemented
36C2×#17985377C2211yescharacteristic, complemented
37C2×#17985375C2211yescharacteristic, complemented
38C2×C8×D283C2211yescharacteristic, complemented
39#22583590C2211yescharacteristic, complemented
40#22583589C2211yescharacteristic, complemented
41#22583587—21no—
42#22583583—21no—
43#22583582—21no—
44#22583581—21no—
45#22583581C2211yescharacteristic, complemented
46C4⋊C4×D283C2211yescharacteristic, complemented
47#22583535C2211yescharacteristic, complemented
48#22583533C2211yescharacteristic, complemented
49#22583532C2211yescharacteristic, complemented
50#22583531C2211yescharacteristic, complemented
51#22583531C2211yescharacteristic, complemented
52#22583530C2211yescharacteristic, complemented
53C22⋊(C283⋊C8)C2211yescharacteristic, complemented
54(C2×D283)⋊C8C2211yescharacteristic, complemented
55(C2×D283)⋊C8C2211yescharacteristic, complemented
56C22×D4×C283C2211yescharacteristic
57C2×D8×C283C2211yescharacteristic, complemented
58C2×D8×C283C2211yescharacteristic, complemented
59#121×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61#102×C283C2211yescharacteristic, complemented
62C22⋊C8×C283C2211yescharacteristic, complemented
63C23×D283—21no—
64C23×D283—21no—
65#17985392—22no—
66#17985392—22no—
67#17985392—22no—
68#17985392—22no—
69#17985391—28no—
70#17985391—22no—
71#17985391—22no—
72#17985391—22no—
73#17985391—22no—
74#17985391—22no—
75#17985391D414yescomplemented
76C2×Dic566D411yescharacteristic
77C2×Dic566C2311yescharacteristic
78C2×Dic566C2311yescharacteristic
79C2×D1132D411yescharacteristic
80C2×D1132C2311yescharacteristic
81C2×C22⋊D283—28no—
82C2×C22⋊D283—28no—
83C2×C22⋊D283—21no—
84C2×C22⋊D283—21no—
85C2×C22⋊D283—21no—
86C2×C22⋊D283—21no—
87C2×C22⋊D283—21no—
88C2×C22⋊D283—21no—
89C2×C22⋊D283—21no—
90C2×C22⋊D283D411yescharacteristic
91C2×C22⋊D283D411yescharacteristic
92D4×D283—28no—
93D4×D283—22no—
94D4×D283—22no—
95D4×D283—22no—
96D4×D283D414yescomplemented
97C22×Dic283—21no—
98C22×Dic283—21no—
99C22×Dic283—21no—
100C2×C4×D283—21no—
101C2×C4×D283—21no—
102C2×C4×D283C2311yescharacteristic
103C2×C4×D283C2311yescharacteristic
104Dic1132—22no—
105#17985381—22no—
106#17985380—22no—
107#17985380—22no—
108#17985380—22no—
109#17985377—22no—
110#17985375—22no—
111C2×C283⋊C8C2311yescharacteristic
112C2×C283⋊C8C2311yescharacteristic
113C8×D283—22no—
114C4⋊Dic283—21no—
115C4⋊Dic283C2311yescharacteristic
116Dic283⋊C4—21no—
117Dic283⋊C4—21no—
118C22⋊Dic283—21no—
119C22⋊Dic283—21no—
120(C2×D283)⋊C4—21no—
121C24×C283—21no—
122C2×D4×C283—22no—
123C2×D4×C283—22no—
124C2×D4×C283—21no—
125C2×D4×C283—21no—
126C2×D4×C283C2311yescharacteristic
127C2×D4×C283C2311yescharacteristic
128C2×D4×C283C2311yescharacteristic
129C22×C4×C283C2311yescharacteristic
130D8×C283—22no—
131D8×C283—22no—
132C2×C8×C283C2311yescharacteristic
133C2×C8×C283C2311yescharacteristic
134C4⋊C4×C283C2311yescharacteristic
135C22⋊C4×C283—21no—
136C22×D283—21no—
137C22×D283—24no—
138C22×D283—24no—
139C22×D283—81no—
140C22×D283—81no—
141C22×D283—81no—
142C22×D283—81no—
143C22×D283C2×D411yescharacteristic
144C22×D283C2×D411yescharacteristic
145Dic566—21no—
146Dic566—22no—
147Dic566—21no—
148Dic566—21no—
149Dic566C2×D412yes—
150D1132—22no—
151D1132—21no—
152D1132C2×D412yes—
153C22⋊D283—24no—
154C22⋊D283—24no—
155C22⋊D283—24no—
156C22⋊D283—24no—
157C22⋊D283—22no—
158C22⋊D283—24no—
159C22⋊D283—22no—
160C22⋊D283—42no—
161C22⋊D283—81no—
162C2×Dic283—24no—
163C2×Dic283—21no—
164C2×Dic283—24no—
165C2×Dic283—21no—
166C2×Dic283—21no—
167C2×Dic283—42no—
168C2×Dic283C2×D411yescharacteristic
169C2×Dic283C2×D411yescharacteristic
170C4×D283—24no—
171C4×D283—21no—
172C4×D283—21no—
173C4×D283—81no—
174C4×D283C2×D412yes—
175C4×D283C2×D412yes—
176C283⋊C8—21no—
177C283⋊C8—21no—
178C23×C283—24no—
179C23×C283—21no—
180C23×C283—21no—
181C23×C283—21no—
182C23×C283—81no—
183C23×C283—81no—
184C23×C283C2×D411yescharacteristic
185D4×C283—24no—
186D4×C283—21no—
187D4×C283—21no—
188D4×C283—21no—
189D4×C283—21no—
190D4×C283—81no—
191D4×C283C2×D412yes—
192D4×C283C2×D412yes—
193C2×C4×C283—21no—
194C2×C4×C283—21no—
195C2×C4×C283—21no—
196C2×C4×C283C2×D411yescharacteristic
197C2×C4×C283C2411yescharacteristic
198C8×C283—21no—
199C8×C283—21no—
200C22×C283—21no—
201C22×C283—22no—
202C22×C283—22no—
203C22×C283—21no—
204C22×C283—21no—
205C22×C283—41no—
206C22×C283—41no—
207C22×C283—41no—
208C22×C283—41no—
209C22×C283—41no—
210C22×C283—41no—
211C22×C283—41no—
212C22×C283—84no—
213C22×C283C22×D411yescharacteristic
214C2×D283—21no—
215C2×D283—21no—
216C2×D283—21no—
217C2×D283—22no—
218C2×D283—21no—
219C2×D283—21no—
220C2×D283—41no—
221C2×D283—41no—
222C2×D283—84no—
223C2×D283—84no—
224C2×D283#12012yes—
225C4×C283—21no—
226C4×C283—41no—
227C4×C283C22×D411yescharacteristic
228C4×C283C22×D411yescharacteristic
229Dic283—22no—
230Dic283—21no—
231Dic283—41no—
232Dic283—41no—
233Dic283#12012yes—
234C2×C283—42no—
235C2×C283—42no—
236C2×C283—41no—
237C2×C283—81no—
238C2×C283C2×#12011yescharacteristic
239C2×C283#57611yescharacteristic
240C2×C283#57711yescharacteristic
241D283—22no—
242D283—41no—
243D283—42no—
244C283#301211yescharacteristic, complemented, Sylow
245#3012—2831nomaximal, Sylow
246C2×H(5,𝔽2)—2831no—
247C2×AGL(1,ℤ/8)—2831no—
248C2×#135—2831no—
249#537—2831no—
250#452—2831no—
251#452—2831no—
252#450—2831no—
253#450—2831no—
254#449—2831no—
255#449—2831no—
256#447—2831no—
257#447D28311yescharacteristic, complemented
258#417—2831no—
259C2×#102—2831no—
260#408—2831no—
261H(5,𝔽2)—5664no—
262H(5,𝔽2)—5664no—
263C2×#41—2831no—
264C2×#41—2831no—
265C2×#41—2831no—
266C2×#41—2831no—
267C2×#41—2831no—
268C2×#41—5661no—
269C22×D4—2831no—
270C22×D4—2831no—
271C22×D4—5661no—
272C22×D4—5661no—
273C22×D4—5661no—
274C22×D4C2×D28311yescharacteristic
275AGL(1,ℤ/8)—5664no—
276#135—5664no—
277C2×Q16—2831no—
278C2×SD16—2831no—
279C2×SD16—2831no—
280C2×SD16—2831no—
281C2×SD16—2831no—
282C2×D8—2831no—
283C2×D8C2×D28311yescharacteristic, complemented
284C2×D8C2×D28311yescharacteristic, complemented
285C2×M16—2831no—
286C22×C8—2831no—
287C22⋊Q8—2831no—
288C22⋊Q8—2831no—
289C22⋊Q8—5661no—
290#121—2831no—
291#121—5661no—
292#121—5661no—
293#121—5661no—
294#121C2×D28311yescharacteristic, complemented
295C2×C4⋊C4—2831no—
296#103—2831no—
297#103—2831no—
298#102—2831no—
299#102—2831no—
300#102—2831no—
301#102—2831no—
302#102C2×D28311yescharacteristic, complemented
303#102C2×D28311yescharacteristic, complemented
304C22⋊C8—2831no—
305C22⋊C8—2831no—
306C22⋊C8—2831no—
307C22⋊C8C2×D28311yescharacteristic, complemented
308C24—21no—
309C24—5661no—
310C24—5661no—
311#41—2834no—
312#41—5662no—
313#41—5662no—
314#41—5662no—
315#41—5662no—
316#41—5662no—
317#41—5662no—
318#41—5662no—
319#41—5662no—
320#41—5668no—
321#41—5662no—
322C2×Q8—2831no—
323C2×Q8—2831no—
324C2×Q8—2831no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—2834no—
330C2×D4—2831no—
331C2×D4—2831no—
332C2×D4—2831no—
333C2×D4—2831no—
334C2×D4—5662no—
335C2×D4—5661no—
336C2×D4—5661no—
337C2×D4—5662no—
338C2×D4—5668no—
339C2×D4—5661no—
340C2×D4—5661no—
341C2×D4—5668no—
342C2×D4—5668no—
343C2×D4—5661no—
344C2×D4—5662no—
345C2×D4—5661no—
346C2×D4—5661no—
347C2×D4C22×D28311yescharacteristic
348C2×D4C22×D28311yescharacteristic
349C2×D4C22×D28311yescharacteristic
350C22×C4—2831no—
351C22×C4—2831no—
352C22×C4—5661no—
353C22×C4—5661no—
354C22×C4—5661no—
355C22×C4—5661no—
356C22×C4—5661no—
357C22×C4C22×D28311yescharacteristic
358Q16—5662no—
359SD16—5662no—
360SD16—5662no—
361SD16—5662no—
362SD16—5662no—
363D8—22no—
364D8—22no—
365D8—5662no—
366M16—5662no—
367C2×C8—2831no—
368C2×C8—2831no—
369C2×C8—5662no—
370C2×C8C22×D28311yescharacteristic
371C2×C8C22×D28311yescharacteristic
372C4⋊C4—2831no—
373C4⋊C4—5661no—
374C4⋊C4—5661no—
375C4⋊C4—5661no—
376C4⋊C4C22×D28311yescharacteristic
377C22⋊C4—21no—
378C22⋊C4—5661no—
379C22⋊C4—5661no—
380C22⋊C4—5661no—
381C23—24no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—81no—
386C23—81no—
387C23—2831no—
388C23—2831no—
389C23—5664no—
390C23—5664no—
391C23—5661no—
392C23—22641no—
393C23—22641no—
394C23—22641no—
395C23—22641no—
396C23D4×D28311yescharacteristic
397Q8—2832no—
398Q8—5662no—
399Q8—5661no—
400Q8—5661no—
401Q8—5661no—
402D4—24no—
403D4—21no—
404D4—21no—
405D4—21no—
406D4—21no—
407D4—81no—
408D4—2832no—
409D4—5662no—
410D4—5662no—
411D4—5664no—
412D4—5662no—
413D4—5664no—
414D4—5664no—
415D4—5664no—
416D4—5664no—
417D4—5661no—
418D4—11322no—
419D4—22641no—
420D4D4×D28312yes—
421D4D4×D28312yes—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—2831no—
426C2×C4—2832no—
427C2×C4—2832no—
428C2×C4—2831no—
429C2×C4—5664no—
430C2×C4—5664no—
431C2×C4—5664no—
432C2×C4—5661no—
433C2×C4—5661no—
434C2×C4—5661no—
435C2×C4—5661no—
436C2×C4—5661no—
437C2×C4—11322no—
438C2×C4—22641no—
439C2×C4D4×D28311yescharacteristic
440C2×C4C23×D28311yescharacteristic
441C8—21no—
442C8—21no—
443C8—5661no—
444C8—5661no—
445C22—21no—
446C22—22no—
447C22—22no—
448C22—21no—
449C22—21no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—84no—
458C22—2832no—
459C22—5661no—
460C22—5661no—
461C22—5662no—
462C22—5661no—
463C22—5661no—
464C22—5661no—
465C22—11321no—
466C22—11321no—
467C22—22644no—
468C22—22644no—
469C22C2×D4×D28311yescharacteristic
470C4—21no—
471C4—41no—
472C4—2832no—
473C4—5661no—
474C4—5662no—
475C4—11321no—
476C4—11321no—
477C4C2×D4×D28311yescharacteristic
478C4C2×D4×D28311yescharacteristic
479C2—41no—
480C2—42no—
481C2—42no—
482C2—81no—
483C2—5662no—
484C2—11321no—
485C2—11322no—
486C2#120×D28311yescharacteristic
487C2#3182726611yescharacteristic
488C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#447×C283C2
socleC22×C283C22×D4
hypercenter#447D283
hypocenterC283#3012
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#22583655C2semidirect
2. C2×#22583634C2semidirect
3. C2×#22583629C2semidirect
4. #31827044C2semidirect
5. #31826629C2semidirect
6. #31826628C2semidirect
7. #31826617C2semidirect
8. #31826616C2semidirect
9. #31826608C2semidirect
10. #31826607C2semidirect
11. #31826597C2semidirect
12. #31826463C2semidirect
13. #102×D283C2semidirect
14. #31826430C2semidirect
15. #447×C283C2semidirect
23. C2×#17985391C22semidirect
31. C2×Dic1132C22semidirect
32. C2×#17985381C22semidirect
33. C2×#17985380C22semidirect
34. C2×#17985380C22semidirect
35. C2×#17985380C22semidirect
36. C2×#17985377C22semidirect
37. C2×#17985375C22semidirect
38. C2×C8×D283C22semidirect
39. #22583590C22semidirect
40. #22583589C22semidirect
45. #22583581C22semidirect
46. C4⋊C4×D283C22semidirect
47. #22583535C22semidirect
48. #22583533C22semidirect
49. #22583532C22semidirect
50. #22583531C22semidirect
51. #22583531C22semidirect
52. #22583530C22semidirect
53. C22⋊(C283⋊C8)C22semidirect
54. (C2×D283)⋊C8C22semidirect
55. (C2×D283)⋊C8C22semidirect
57. C2×D8×C283C22semidirect
58. C2×D8×C283C22semidirect
59. #121×C283C22semidirect
60. #102×C283C22semidirect
61. #102×C283C22semidirect
62. C22⋊C8×C283C22semidirect
75. #17985391D4semidirect
96. D4×D283D4semidirect
244. C283#3012semidirect
257. #447D283semidirect
283. C2×D8C2×D283semidirect
284. C2×D8C2×D283semidirect
294. #121C2×D283semidirect
302. #102C2×D283semidirect
303. #102C2×D283semidirect
307. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836552
C2×#225836342
C2×#225836292
#318270442
#318266292
#318266282
#318266172
#318266162
#318266082
#318266072
#318265972
#318264632
#102×D2832
#318264302
#447×C2832
#3012283