Finite Group Databasebeta

← #28402047

Subgroups — #28402047

Order 14464.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813646C211yesmaximal, characteristic, complemented
2C22×#14268632C211yesmaximal, characteristic, complemented
3#20299242C211yesmaximal, characteristic, complemented
4#20299232C211yesmaximal, characteristic, complemented
5#20298986C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298825C211yesmaximal, characteristic, complemented
8#20298812C211yesmaximal, characteristic, complemented
9#20298791C211yesmaximal, characteristic, complemented
10#20298751C211yesmaximal, characteristic, complemented
11#20298744C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298707C211yesmaximal, characteristic, complemented
14#20298666C211yesmaximal, characteristic, complemented
15#447×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic, complemented
17C22×D452C2211yescharacteristic
18C2×D4×D113—21no—
19C2×D4×D113C2211yescharacteristic, complemented
20#16813646—24no—
21C2×#14268636C2211yescharacteristic, complemented
22C2×#14268636C2211yescharacteristic, complemented
23C2×#14268635C2211yescharacteristic, complemented
24C2×#14268632—24no—
25C2×#14268632C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic, complemented
28C2×#14268632C2211yescharacteristic, complemented
29C2×#14268630C2211yescharacteristic, complemented
30C22×#11744751C2211yescharacteristic, complemented
31#16813618C2211yescharacteristic, complemented
32#16813609C2211yescharacteristic, complemented
33#16813603—21no—
34#16813601C2211yescharacteristic, complemented
35#16813597C2211yescharacteristic, complemented
36#16813595—21no—
37#16813594—21no—
38#16813593C2211yescharacteristic, complemented
39#16813592—21no—
40#16813591—21no—
41#16813590—21no—
42D4×Dic113C2211yescharacteristic, complemented
43#16813584C2211yescharacteristic, complemented
44C4×C22⋊D113C2211yescharacteristic
45C2×C22⋊Dic113—21no—
46#16813553C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813545C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53#16813532C2211yescharacteristic, complemented
54C22×D4×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic, complemented
56C2×D8×C113C2211yescharacteristic, complemented
57#121×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60C22⋊C8×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63#14268646—22no—
64#14268646—41no—
65C2×Dic226C2311yescharacteristic
66C2×D452—22no—
67C2×D452—21no—
68C2×D452—21no—
69C2×D452—41no—
70C2×D452C2311yescharacteristic
71C2×D452C2311yescharacteristic
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77C2×C22⋊D113D411yescharacteristic
78D4×D113—22no—
79D4×D113—41no—
80D4×D113—44no—
81C22×Dic113—21no—
82C22×Dic113—21no—
83C2×C4×D113—21no—
84C2×C4×D113C2311yescharacteristic
85#14268636—22no—
86#14268636—41no—
87#14268635—22no—
88#14268632—22no—
89#14268632—22no—
90#14268632—22no—
91#14268632D414yescomplemented
92#14268630—22no—
93C2×#11744751—22no—
94C2×#11744751C2311yescharacteristic
95C2×#11744751C2311yescharacteristic
96C4⋊Dic113C2311yescharacteristic
97#14268626—21no—
98#14268626D411yescharacteristic
99C22⋊Dic113—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113—21no—
102C22⋊Dic113—21no—
103C22⋊Dic113—21no—
104C22⋊Dic113D411yescharacteristic
105#14268624—21no—
106#14268624—21no—
107#14268624D411yescharacteristic
108C4×Dic113C2311yescharacteristic
109C24×C113—21no—
110C2×D4×C113—22no—
111C2×D4×C113—21no—
112C2×D4×C113—21no—
113C2×D4×C113—41no—
114C2×D4×C113C2311yescharacteristic
115C2×D4×C113C2311yescharacteristic
116C2×D4×C113C2311yescharacteristic
117C22×C4×C113C2311yescharacteristic
118D8×C113—22no—
119D8×C113—41no—
120C2×C8×C113C2311yescharacteristic
121C2×C8×C113C2311yescharacteristic
122C4⋊C4×C113C2311yescharacteristic
123C22⋊C4×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
126C23×C113—21no—
127C23×C113—42no—
128C23×C113—42no—
129C23×C113—81no—
130C23×C113C2×D411yescharacteristic
131C22×D113—21no—
132C22×D113—21no—
133C22×D113—42no—
134C22×D113—42no—
135C22×D113—42no—
136C22×D113—42no—
137C22×D113—81no—
138C22×D113—81no—
139C22×D113C2×D411yescharacteristic
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—21no—
143D4×C113—21no—
144D4×C113—21no—
145D4×C113—42no—
146D4×C113—42no—
147D4×C113C2×D412yescomplemented
148C2×C4×C113—21no—
149C2×C4×C113—21no—
150C2×C4×C113—21no—
151C2×C4×C113C2×D411yescharacteristic
152C2×C4×C113C2411yescharacteristic
153C22⋊D113—22no—
154C22⋊D113—42no—
155C22⋊D113—42no—
156C22⋊D113—42no—
157C22⋊D113—81no—
158C22⋊D113—81no—
159C2×Dic113—21no—
160C2×Dic113—21no—
161C2×Dic113—42no—
162C2×Dic113—81no—
163C2×Dic113C2×D411yescharacteristic
164C2×Dic113C2×D411yescharacteristic
165C2×Dic113C2×D411yescharacteristic
166D452—21no—
167D452—21no—
168D452—21no—
169D452—42no—
170D452—42no—
171D452C2×D412yes—
172C4×D113—21no—
173C4×D113—21no—
174C4×D113—42no—
175Dic226—21no—
176Dic226—21no—
177C8×C113—21no—
178C8×C113—21no—
179#11744751—21no—
180#11744751C2×D412yescomplemented
181C22×C113—21no—
182C22×C113—21no—
183C22×C113—22no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113—41no—
188C22×C113—41no—
189C22×C113—41no—
190C22×C113—41no—
191C22×C113—41no—
192C22×C113—84no—
193C22×C113AGL(1,ℤ/8)12yescomplemented
194C22×C113C22×D411yescharacteristic
195C2×D113—21no—
196C2×D113—22no—
197C2×D113—21no—
198C2×D113—21no—
199C2×D113—41no—
200C2×D113—41no—
201C2×D113—41no—
202C2×D113—41no—
203C2×D113—41no—
204C2×D113—84no—
205C2×D113—84no—
206C4×C113—21no—
207C4×C113—41no—
208C4×C113C22×D411yescharacteristic
209C4×C113H(5,𝔽2)11yescharacteristic
210Dic113—21no—
211Dic113—21no—
212Dic113—21no—
213Dic113—41no—
214Dic113—41no—
215C2×C113—22no—
216C2×C113—42no—
217C2×C113—81no—
218C2×C113—81no—
219C2×C113D4211yescharacteristic
220C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
221C2×C113#57611yescharacteristic
222D113—41no—
223D113—42no—
224D113—81no—
225#3264—1131nomaximal, Sylow
226C113#326411yescharacteristic, complemented, Sylow
227C2×AGL(1,ℤ/8)—1131no—
228C22×D8—1131no—
229#546—1131no—
230D42—1131no—
231#496—1131no—
232#469—1131no—
233#465—1131no—
234#463—1131no—
235#459—1131no—
236#450—1131no—
237#449—1131no—
238#447—1131no—
239#447D11311yescharacteristic, complemented
240#442—1131no—
241#435—1131no—
242C2×#41—1131no—
243C22×D4—1131no—
244C22×D4—1131no—
245C22×D4—2261no—
246C22×D4C2×D11311yescharacteristic, complemented
247AGL(1,ℤ/8)—2264no—
248C2×SD16—1131no—
249C2×SD16—1131no—
250C2×SD16—1131no—
251C2×D8—1131no—
252C2×D8—1131no—
253C2×D8—1131no—
254C2×D8—1131no—
255C2×D8—2264no—
256C2×D8C2×D11311yescharacteristic, complemented
257C2×D8C2×D11311yescharacteristic, complemented
258C2×M16—1131no—
259C22×C8—1131no—
260#127—1131no—
261#124—1131no—
262#123—2261no—
263C22⋊Q8—1131no—
264#121—1131no—
265#121—1131no—
266#121—2261no—
267#121—2261no—
268#121C2×D11311yescharacteristic
269#120—2261no—
270#120—2261no—
271#120—2261no—
272C4×D4—1131no—
273C4×D4—1131no—
274C4×D4—1131no—
275C2×C22⋊C4—2261no—
276#106—1131no—
277C4⋊C8—1131no—
278#103—1131no—
279#102—1131no—
280#102—1131no—
281#102—1131no—
282#102C2×D11311yescharacteristic, complemented
283#102C2×D11311yescharacteristic, complemented
284C22⋊C8—1131no—
285C22⋊C8C2×D11311yescharacteristic, complemented
286#97—1131no—
287C24—21no—
288C24—2261no—
289C24—2261no—
290#41—4521no—
291#41—2262no—
292C2×Q8—1131no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—1131no—
298C2×D4—1131no—
299C2×D4—1131no—
300C2×D4—4521no—
301C2×D4—4524no—
302C2×D4—4521no—
303C2×D4—2262no—
304C2×D4—2261no—
305C2×D4—2261no—
306C2×D4—2261no—
307C2×D4—2261no—
308C2×D4—2262no—
309C2×D4—2261no—
310C2×D4—2261no—
311C2×D4—2261no—
312C2×D4C22×D11311yescharacteristic
313C2×D4C22×D11311yescharacteristic
314C2×D4C22×D11311yescharacteristic
315C22×C4—1131no—
316C22×C4—2261no—
317C22×C4—2261no—
318C22×C4—2261no—
319C22×C4C22×D11311yescharacteristic
320SD16—4521no—
321SD16—2262no—
322SD16—2262no—
323D8—22no—
324D8—41no—
325D8—1134no—
326D8—2262no—
327D8—2262no—
328D8—2262no—
329M16—2262no—
330C2×C8—1131no—
331C2×C8—1131no—
332C2×C8—2262no—
333C2×C8C22×D11311yescharacteristic
334C2×C8C22×D11311yescharacteristic
335C4⋊C4—1131no—
336C4⋊C4—1131no—
337C4⋊C4—2261no—
338C4⋊C4C22×D11311yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—1131no—
341C22⋊C4—1131no—
342C22⋊C4—2261no—
343C22⋊C4—2261no—
344C22⋊C4—2261no—
345C22⋊C4—2261no—
346C22⋊C4—2261no—
347C22⋊C4—2261no—
348C22⋊C4—2261no—
349C42—1131no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—81no—
356C23—1131no—
357C23—9041no—
358C23—9041no—
359C23—4522no—
360C23—4522no—
361C23—4522no—
362C23—4522no—
363C23—2261no—
364C23—2261no—
365C23D4×D11311yescharacteristic
366Q8—2261no—
367Q8—2261no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—42no—
374D4—42no—
375D4—1132no—
376D4—9041no—
377D4—9041no—
378D4—4522no—
379D4—4522no—
380D4—4522no—
381D4—4522no—
382D4—4522no—
383D4—2262no—
384D4—2261no—
385D4—2261no—
386D4—2261no—
387D4D4×D11312yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—1131no—
392C2×C4—1131no—
393C2×C4—1131no—
394C2×C4—9041no—
395C2×C4—4522no—
396C2×C4—4522no—
397C2×C4—2261no—
398C2×C4—2261no—
399C2×C4—2261no—
400C2×C4—2261no—
401C2×C4D4×D11311yescharacteristic
402C2×C4C23×D11311yescharacteristic
403C8—21no—
404C8—21no—
405C8—1132no—
406C8—2261no—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—84no—
419C22—9044no—
420C22—9044no—
421C22—4521no—
422C22—4521no—
423C22—4521no—
424C22—4521no—
425C22—4521no—
426C22—2261no—
427C22—2261no—
428C22—2261no—
429C22—2262no—
430C22#1681364612yescomplemented
431C22C2×D4×D11311yescharacteristic
432C4—21no—
433C4—41no—
434C4—4521no—
435C4—4521no—
436C4—2261no—
437C4—2261no—
438C4—2261no—
439C4C2×D4×D11311yescharacteristic
440C4#1681366711yescharacteristic
441C2—22no—
442C2—42no—
443C2—81no—
444C2—81no—
445C2—9041no—
446C2—4522no—
447C2—4521no—
448C2#2029923011yescharacteristic
449C2C2×#1681364611yescharacteristic
450C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3264
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#16813646C2semidirect
2. C22×#14268632C2semidirect
3. #20299242C2semidirect
4. #20299232C2semidirect
5. #20298986C2semidirect
6. #20298850C2semidirect
7. #20298825C2semidirect
8. #20298812C2semidirect
9. #20298791C2semidirect
10. #20298751C2semidirect
11. #20298744C2semidirect
12. #20298730C2semidirect
13. #20298707C2semidirect
14. #20298666C2semidirect
15. #447×C113C2semidirect
16. C2×#14268646C22semidirect
19. C2×D4×D113C22semidirect
21. C2×#14268636C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268635C22semidirect
27. C2×#14268632C22semidirect
28. C2×#14268632C22semidirect
29. C2×#14268630C22semidirect
30. C22×#11744751C22semidirect
31. #16813618C22semidirect
32. #16813609C22semidirect
34. #16813601C22semidirect
35. #16813597C22semidirect
38. #16813593C22semidirect
42. D4×Dic113C22semidirect
43. #16813584C22semidirect
46. #16813553C22semidirect
47. #16813551C22semidirect
48. #16813545C22semidirect
49. #16813544C22semidirect
50. #16813544C22semidirect
51. #16813543C22semidirect
52. #16813534C22semidirect
53. #16813532C22semidirect
54. C22×D4×C113C22semidirect
55. C2×D8×C113C22semidirect
56. C2×D8×C113C22semidirect
58. #102×C113C22semidirect
59. #102×C113C22semidirect
60. C22⋊C8×C113C22semidirect
91. #14268632D4semidirect
147. D4×C113C2×D4semidirect
180. #11744751C2×D4semidirect
193. C22×C113AGL(1,ℤ/8)semidirect
226. C113#3264semidirect
239. #447D113semidirect
246. C22×D4C2×D113semidirect
256. C2×D8C2×D113semidirect
257. C2×D8C2×D113semidirect
282. #102C2×D113semidirect
283. #102C2×D113semidirect
285. C22⋊C8C2×D113semidirect
387. D4D4×D113semidirect
430. C22#16813646semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C22×#142686322
#202992422
#202992322
#202989862
#202988502
#202988252
#202988122
#202987912
#202987512
#202987442
#202987302
#202987072
#202986662
#447×C1132
#3264113