Finite Group Databasebeta

← #28402056

Subgroups — #28402056

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
2C2×D8×D113C211yesmaximal, characteristic, complemented
3#20299243C211yesmaximal, characteristic, complemented
4D4×D452C211yesmaximal, characteristic, complemented
5#20298987C211yesmaximal, characteristic, complemented
6#20298852C211yesmaximal, characteristic, complemented
7#20298828C211yesmaximal, characteristic, complemented
8#20298813C211yesmaximal, characteristic, complemented
9#20298793C211yesmaximal, characteristic, complemented
10#20298750C211yesmaximal, characteristic, complemented
11#20298744C211yesmaximal, characteristic, complemented
12#20298733C211yesmaximal, characteristic, complemented
13#20298733C211yesmaximal, characteristic, complemented
14#20298671C211yesmaximal, characteristic, complemented
15#442×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic, complemented
17C22×D452—21no—
18C2×D4×D113C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic, complemented
20C2×D4×D113C2211yescharacteristic, complemented
21#16813646—24no—
22C2×#14268636C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic, complemented
24C2×#14268635C2211yescharacteristic, complemented
25C2×D904C2211yescharacteristic, complemented
26C2×D904C2211yescharacteristic, complemented
27C2×#14268632C2211yescharacteristic
28C2×#14268632C2211yescharacteristic, complemented
29C2×#14268632C2211yescharacteristic, complemented
30D8×D113—24no—
31C2×#14268630C2211yescharacteristic, complemented
32C2×C8×D113C2211yescharacteristic, complemented
33#16813619C2211yescharacteristic, complemented
34#16813610C2211yescharacteristic, complemented
35#16813606—21no—
36#16813602C2211yescharacteristic, complemented
37#16813597C2211yescharacteristic
38#16813597C2211yescharacteristic, complemented
39#16813597C2211yescharacteristic, complemented
40#16813596—21no—
41#16813596—21no—
42#16813592—21no—
43#16813592—21no—
44#16813592—21no—
45C4×D452C2211yescharacteristic
46C2×#14268624—21no—
47C4⋊#11744751C2211yescharacteristic, complemented
48#16813545C2211yescharacteristic, complemented
49#16813542C2211yescharacteristic, complemented
50#16813542C2211yescharacteristic, complemented
51#16813542C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53#16813534C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic, complemented
56C4×D4×C113C2211yescharacteristic, complemented
57#106×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60#97×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63C23×D113—21no—
64#14268646—22no—
65#14268646—41no—
66C2×Dic226C2311yescharacteristic
67C2×D452—21no—
68C2×D452—21no—
69C2×D452—21no—
70C2×D452—21no—
71C2×D452—21no—
72C2×D452—44no—
73C2×D452D411yescharacteristic
74C2×D452C2311yescharacteristic
75C2×D452C2311yescharacteristic
76C2×D452C2311yescharacteristic
77C2×C22⋊D113—21no—
78C2×C22⋊D113—21no—
79C2×C22⋊D113—21no—
80C2×C22⋊D113—21no—
81D4×D113—22no—
82D4×D113—22no—
83D4×D113—22no—
84D4×D113—41no—
85D4×D113—41no—
86D4×D113—41no—
87C22×Dic113—21no—
88C2×C4×D113C2311yescharacteristic
89C2×C4×D113C2311yescharacteristic
90#14268636—22no—
91#14268636—41no—
92#14268635—22no—
93D904—22no—
94D904—41no—
95#14268632—22no—
96#14268632—22no—
97#14268632—22no—
98#14268630—22no—
99C2×#11744751C2311yescharacteristic
100C2×#11744751C2311yescharacteristic
101C8×D113—22no—
102C4⋊Dic113—21no—
103C4⋊Dic113D411yescharacteristic
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109#14268624—21no—
110#14268624D411yescharacteristic
111#14268624D411yescharacteristic
112C2×D4×C113C2311yescharacteristic
113C2×D4×C113C2311yescharacteristic
114C22×C4×C113—21no—
115C22×C4×C113—21no—
116D8×C113D414yescomplemented
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C4⋊C4×C113C2311yescharacteristic
120C4⋊C4×C113C2311yescharacteristic
121C22⋊C4×C113—21no—
122C22⋊C4×C113—21no—
123C42×C113C2311yescharacteristic
124C23×C113—21no—
125C23×C113—21no—
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—42no—
130C22×D113—42no—
131C22×D113—42no—
132C22×D113—42no—
133C22×D113—42no—
134C22×D113—42no—
135C22×D113—81no—
136C22×D113—81no—
137C22×D113—81no—
138C22×D113C2×D411yescharacteristic
139C22×D113C2×D411yescharacteristic
140D4×C113—21no—
141D4×C113—21no—
142D4×C113C2×D412yes—
143D4×C113C2×D412yescomplemented
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113—42no—
147C2×C4×C113—81no—
148C2×C4×C113C2×D411yescharacteristic
149C2×C4×C113C2×D411yescharacteristic
150C2×C4×C113C2411yescharacteristic
151C22⋊D113—42no—
152C22⋊D113—42no—
153C22⋊D113—42no—
154C22⋊D113—42no—
155C2×Dic113—21no—
156C2×Dic113—42no—
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159D452—22no—
160D452—21no—
161D452—21no—
162D452—21no—
163D452—21no—
164D452—21no—
165D452—21no—
166D452—42no—
167D452—42no—
168D452—42no—
169D452—81no—
170D452—81no—
171C4×D113—21no—
172C4×D113—21no—
173C4×D113—21no—
174C4×D113—21no—
175Dic226—21no—
176Dic226—21no—
177C8×C113—21no—
178C8×C113C2×D412yescomplemented
179#11744751—21no—
180#11744751—21no—
181C22×C113—22no—
182C22×C113—22no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113C22×D411yescharacteristic
188C2×D113—21no—
189C2×D113—21no—
190C2×D113—21no—
191C2×D113—21no—
192C2×D113—21no—
193C2×D113—41no—
194C2×D113—41no—
195C2×D113—41no—
196C2×D113—41no—
197C2×D113—41no—
198C2×D113—41no—
199C2×D113—41no—
200C2×D113—41no—
201C2×D113—41no—
202C2×D113—84no—
203C2×D113—84no—
204C2×D113—84no—
205C2×D113AGL(1,ℤ/8)12yescomplemented
206C4×C113—21no—
207C4×C113—21no—
208C4×C113—41no—
209C4×C113—41no—
210C4×C113C22×D411yescharacteristic
211C4×C113H(5,𝔽2)11yescharacteristic
212Dic113—21no—
213Dic113—21no—
214Dic113—41no—
215C2×C113—42no—
216C2×C113—42no—
217C2×C113D4211yescharacteristic
218C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C113#57611yescharacteristic
220D113—22no—
221D113—41no—
222D113—81no—
223D113—81no—
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#447—1131no—
240#442D11311yescharacteristic, complemented
241#435—1131no—
242C2×#41—1131no—
243C22×D4—1131no—
244C22×D4—1131no—
245C22×D4—1131no—
246C22×D4—2261no—
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—1131no—
256C2×D8—2264no—
257C2×D8C2×D11311yescharacteristic
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—1131no—
267#121—2261no—
268#121—2261no—
269#120—2261no—
270#120—2261no—
271#120—2261no—
272C4×D4—1131no—
273C4×D4C2×D11311yescharacteristic, complemented
274C4×D4C2×D11311yescharacteristic, complemented
275C2×C22⋊C4—2261no—
276#106C2×D11311yescharacteristic, complemented
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⋊C8—1131no—
286#97C2×D11311yescharacteristic, complemented
287C24—2261no—
288C24—2261no—
289C24—2261no—
290#41—4521no—
291#41—2262no—
292C2×Q8—1131no—
293C2×D4—1131no—
294C2×D4—1131no—
295C2×D4—1131no—
296C2×D4—1131no—
297C2×D4—4524no—
298C2×D4—4521no—
299C2×D4—4521no—
300C2×D4—4521no—
301C2×D4—2261no—
302C2×D4—2261no—
303C2×D4—2261no—
304C2×D4—2261no—
305C2×D4—2261no—
306C2×D4—2261no—
307C2×D4—2261no—
308C2×D4—2262no—
309C2×D4—2262no—
310C2×D4—2262no—
311C2×D4—2261no—
312C2×D4—2261no—
313C2×D4C22×D11311yescharacteristic
314C2×D4C22×D11311yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—1131no—
318C22×C4—1131no—
319C22×C4—2261no—
320SD16—4521no—
321SD16—2262no—
322SD16—2262no—
323D8—4521no—
324D8—2262no—
325D8—2262no—
326D8—2262no—
327D8—2262no—
328D8D45214yescomplemented
329M16—2262no—
330C2×C8—1131no—
331C2×C8—1131no—
332C2×C8—2262no—
333C2×C8C22×D11311yescharacteristic
334C2×C8C22×D11311yescharacteristic
335C4⋊C4—1131no—
336C4⋊C4—2261no—
337C4⋊C4C22×D11311yescharacteristic
338C4⋊C4C22×D11311yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—1131no—
342C22⋊C4—1131no—
343C22⋊C4—2261no—
344C22⋊C4—2261no—
345C22⋊C4—2261no—
346C22⋊C4—2261no—
347C22⋊C4—2261no—
348C22⋊C4—2261no—
349C42C22×D11311yescharacteristic
350C23—21no—
351C23—21no—
352C23—1131no—
353C23—1131no—
354C23—9041no—
355C23—9041no—
356C23—9041no—
357C23—4522no—
358C23—4522no—
359C23—4522no—
360C23—4522no—
361C23—4522no—
362C23—4522no—
363C23—2261no—
364C23—2261no—
365C23—2261no—
366Q8—2261no—
367Q8—2261no—
368D4—21no—
369D4—21no—
370D4—9041no—
371D4—9041no—
372D4—4522no—
373D4—4522no—
374D4—4522no—
375D4—4522no—
376D4—4522no—
377D4—4522no—
378D4—4522no—
379D4—2262no—
380D4—2261no—
381D4—2261no—
382D4—2261no—
383D4—2261no—
384D4—2261no—
385D4—2261no—
386D4C2×D45212yes—
387D4C2×D45212yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—1131no—
393C2×C4—1131no—
394C2×C4—4522no—
395C2×C4—2261no—
396C2×C4—2261no—
397C2×C4—2261no—
398C2×C4—2261no—
399C2×C4—2261no—
400C2×C4D4×D11311yescharacteristic
401C2×C4D4×D11311yescharacteristic
402C2×C4C23×D11311yescharacteristic
403C8—21no—
404C8—2261no—
405C8—2261no—
406C8C2×D45212yescomplemented
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—1132no—
414C22—9044no—
415C22—9044no—
416C22—9044no—
417C22—4521no—
418C22—4521no—
419C22—4521no—
420C22—4521no—
421C22—4521no—
422C22—4521no—
423C22—4521no—
424C22—4521no—
425C22—4521no—
426C22—2261no—
427C22—2261no—
428C22—2261no—
429C22—2261no—
430C22—2261no—
431C22C2×D4×D11311yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—4521no—
437C4—2261no—
438C4—2261no—
439C4C22×D45211yescharacteristic
440C4#1681366811yescharacteristic
441C2—42no—
442C2—42no—
443C2—9041no—
444C2—9041no—
445C2—9041no—
446C2—4521no—
447C2—2262no—
448C2D4×D45211yescharacteristic
449C2AGL(1,ℤ/8)×D11311yescharacteristic
450C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#442×C113C2
socleC22×C113C22×D4
hypercenter#442D113
hypocenterC113#3264
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#16813646C2semidirect
2. C2×D8×D113C2semidirect
3. #20299243C2semidirect
4. D4×D452C2semidirect
5. #20298987C2semidirect
6. #20298852C2semidirect
7. #20298828C2semidirect
8. #20298813C2semidirect
9. #20298793C2semidirect
10. #20298750C2semidirect
11. #20298744C2semidirect
12. #20298733C2semidirect
13. #20298733C2semidirect
14. #20298671C2semidirect
15. #442×C113C2semidirect
16. C2×#14268646C22semidirect
19. C2×D4×D113C22semidirect
20. C2×D4×D113C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268636C22semidirect
24. C2×#14268635C22semidirect
25. C2×D904C22semidirect
26. C2×D904C22semidirect
28. C2×#14268632C22semidirect
29. C2×#14268632C22semidirect
31. C2×#14268630C22semidirect
32. C2×C8×D113C22semidirect
33. #16813619C22semidirect
34. #16813610C22semidirect
36. #16813602C22semidirect
38. #16813597C22semidirect
39. #16813597C22semidirect
47. C4⋊#11744751C22semidirect
48. #16813545C22semidirect
49. #16813542C22semidirect
50. #16813542C22semidirect
51. #16813542C22semidirect
52. #16813534C22semidirect
53. #16813534C22semidirect
55. C4×D4×C113C22semidirect
56. C4×D4×C113C22semidirect
57. #106×C113C22semidirect
58. #102×C113C22semidirect
59. #102×C113C22semidirect
60. #97×C113C22semidirect
116. D8×C113D4semidirect
143. D4×C113C2×D4semidirect
178. C8×C113C2×D4semidirect
205. C2×D113AGL(1,ℤ/8)semidirect
226. C113#3264semidirect
240. #442D113semidirect
273. C4×D4C2×D113semidirect
274. C4×D4C2×D113semidirect
276. #106C2×D113semidirect
282. #102C2×D113semidirect
283. #102C2×D113semidirect
286. #97C2×D113semidirect
328. D8D452semidirect
387. D4C2×D452semidirect
406. C8C2×D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C2×D8×D1132
#202992432
D4×D4522
#202989872
#202988522
#202988282
#202988132
#202987932
#202987502
#202987442
#202987332
#202986712
#442×C1132
#3264113