Finite Group Databasebeta

← #28402058

Subgroups — #28402058

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×#16813649C211yesmaximal, characteristic, complemented
2C22×#14268632C211yesmaximal, characteristic, complemented
3#20299239C211yesmaximal, characteristic, complemented
4D4×C22⋊D113C211yesmaximal, characteristic, complemented
5#20298984C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298829C211yesmaximal, characteristic, complemented
8#20298815C211yesmaximal, characteristic, complemented
9#20298792C211yesmaximal, characteristic, complemented
10#20298742C211yesmaximal, characteristic, complemented
11#20298734C211yesmaximal, characteristic, complemented
12#20298733C211yesmaximal, characteristic, complemented
13#20298707C211yesmaximal, characteristic, complemented
14#20298666C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic, complemented
17C22×D452C2211yescharacteristic, complemented
18C22×C22⋊D113—21no—
19C2×D4×D113C2211yescharacteristic, complemented
20#16813649—24no—
21C2×#14268634C2211yescharacteristic, complemented
22C2×D904C2211yescharacteristic, complemented
23C2×D904C2211yescharacteristic, complemented
24C2×#14268632—24no—
25C2×#14268632C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic, complemented
28C2×#14268632C2211yescharacteristic, complemented
29C2×#14268630C2211yescharacteristic, complemented
30C22×#11744751C2211yescharacteristic, complemented
31#16813618C2211yescharacteristic, complemented
32#16813611C2211yescharacteristic, complemented
33#16813607—21no—
34#16813597—21no—
35#16813597C2211yescharacteristic, complemented
36#16813596C2211yescharacteristic
37#16813594—21no—
38#16813593C2211yescharacteristic, complemented
39#16813592—21no—
40#16813591—21no—
41#16813590—21no—
42D4×Dic113C2211yescharacteristic, complemented
43#16813584C2211yescharacteristic, complemented
44C4×C22⋊D113C2211yescharacteristic
45C22⋊C4×D113—21no—
46#16813553C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813546C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic, complemented
51#16813542C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53#16813532C2211yescharacteristic, complemented
54C22×D4×C113C2211yescharacteristic
55C2×SD16×C113C2211yescharacteristic, complemented
56C2×SD16×C113C2211yescharacteristic, complemented
57C22⋊Q8×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60C22⋊C8×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63#14268648—22no—
64#14268648—41no—
65C2×D452—22no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452—21no—
69C2×D452—41no—
70C2×D452C2311yescharacteristic
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77C2×C22⋊D113—21no—
78C2×C22⋊D113—44no—
79C2×C22⋊D113D411yescharacteristic
80D4×D113—22no—
81D4×D113—41no—
82C22×Dic113—21no—
83C2×C4×D113—21no—
84C2×C4×D113—21no—
85C2×C4×D113C2311yescharacteristic
86#14268634—22no—
87D904—22no—
88D904—41no—
89#14268632—22no—
90#14268632—22no—
91#14268632—22no—
92#14268632D414yescomplemented
93#14268630—22no—
94C2×#11744751—22no—
95C2×#11744751C2311yescharacteristic
96C2×#11744751C2311yescharacteristic
97C4⋊Dic113C2311yescharacteristic
98#14268626D411yescharacteristic
99C22⋊Dic113—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113D411yescharacteristic
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624D411yescharacteristic
108C4×Dic113C2311yescharacteristic
109C24×C113—21no—
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113—22no—
112C2×D4×C113—21no—
113C2×D4×C113—41no—
114C2×D4×C113C2311yescharacteristic
115C2×D4×C113C2311yescharacteristic
116C22×C4×C113C2311yescharacteristic
117SD16×C113—22no—
118SD16×C113—41no—
119C2×C8×C113C2311yescharacteristic
120C2×C8×C113C2311yescharacteristic
121C4⋊C4×C113—21no—
122C4⋊C4×C113C2311yescharacteristic
123C22⋊C4×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
126C23×C113—42no—
127C23×C113—42no—
128C23×C113—81no—
129C23×C113C2×D411yescharacteristic
130C22×D113—21no—
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
140Q8×C113—21no—
141Q8×C113—21no—
142D4×C113—21no—
143D4×C113—21no—
144D4×C113—21no—
145D4×C113—42no—
146D4×C113C2×D412yes—
147C2×C4×C113—21no—
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—42no—
158C22⋊D113—81no—
159C2×Dic113—21no—
160C2×Dic113—42no—
161C2×Dic113C2×D411yescharacteristic
162C2×Dic113C2×D411yescharacteristic
163C2×Dic113C2×D411yescharacteristic
164D452—21no—
165D452—21no—
166D452—21no—
167D452—21no—
168D452—21no—
169D452—42no—
170D452—42no—
171D452—81no—
172D452C2×D412yescomplemented
173C4×D113—21no—
174C4×D113—21no—
175C4×D113—42no—
176C4×D113—81no—
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—84no—
190C22×C113AGL(1,ℤ/8)12yescomplemented
191C22×C113C22×D411yescharacteristic
192C2×D113—21no—
193C2×D113—22no—
194C2×D113—21no—
195C2×D113—21no—
196C2×D113—41no—
197C2×D113—41no—
198C2×D113—41no—
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×C113—41no—
209C4×C113C22×D411yescharacteristic
210C4×C113H(5,𝔽2)11yescharacteristic
211Dic113—21no—
212Dic113—21no—
213Dic113—21no—
214Dic113—41no—
215C2×C113—22no—
216C2×C113—42no—
217C2×C113—81no—
218C2×C113D4211yescharacteristic
219C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C113#57611yescharacteristic
221D113—41no—
222D113—42no—
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#450D11311yescharacteristic, complemented
237#449—1131no—
238#447—1131no—
239#447—1131no—
240#442—1131no—
241#435—1131no—
242C2×#41—1131no—
243C22×D4—1131no—
244C22×D4—1131no—
245C22×D4—2261no—
246C22×D4C2×D11311yescharacteristic
247AGL(1,ℤ/8)—2264no—
248C2×SD16—1131no—
249C2×SD16C2×D11311yescharacteristic, complemented
250C2×SD16C2×D11311yescharacteristic, complemented
251C2×D8—1131no—
252C2×D8—1131no—
253C2×D8—1131no—
254C2×D8—1131no—
255C2×D8—1131no—
256C2×D8—1131no—
257C2×D8—2264no—
258C2×M16—1131no—
259C22×C8—1131no—
260#127—1131no—
261#124—1131no—
262#123—2261no—
263C22⋊Q8C2×D11311yescharacteristic, complemented
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×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×Q8C22×D11311yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—1131no—
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—2261no—
309C2×D4—2261no—
310C2×D4—2261no—
311C2×D4—2262no—
312C2×D4—2261no—
313C2×D4C22×D11311yescharacteristic
314C2×D4C22×D11311yescharacteristic
315C22×C4—1131no—
316C22×C4—2261no—
317C22×C4—2261no—
318C22×C4—2261no—
319C22×C4C22×D11311yescharacteristic
320SD16—22no—
321SD16—41no—
322SD16—2262no—
323D8—1134no—
324D8—4521no—
325D8—2262no—
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—21no—
336C4⋊C4—1131no—
337C4⋊C4—1131no—
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—42no—
353C23—42no—
354C23—81no—
355C23—1131no—
356C23—9041no—
357C23—9041no—
358C23—4522no—
359C23—4522no—
360C23—4522no—
361C23—4522no—
362C23—2261no—
363C23—2261no—
364C23—2261no—
365C23D4×D11311yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—42no—
372D4—1132no—
373D4—9041no—
374D4—9041no—
375D4—4522no—
376D4—4522no—
377D4—4522no—
378D4—4522no—
379D4—4522no—
380D4—4522no—
381D4—2262no—
382D4—2261no—
383D4—2261no—
384D4—2261no—
385D4—2261no—
386D4—2261no—
387D4D4×D11312yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—1131no—
393C2×C4—1131no—
394C2×C4—1131no—
395C2×C4—9041no—
396C2×C4—4522no—
397C2×C4—4522no—
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—84no—
416C22—9044no—
417C22—9044no—
418C22—4521no—
419C22—4521no—
420C22—4521no—
421C22—4521no—
422C22—4521no—
423C22—4521no—
424C22—4521no—
425C22—4521no—
426C22—2261no—
427C22—2261no—
428C22—2262no—
429C22—2261no—
430C22#1681364912yescomplemented
431C22C2×D4×D11311yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—4521no—
436C4—2261no—
437C4—2261no—
438C4—2261no—
439C4C2×D4×D11311yescharacteristic
440C4#1681366711yescharacteristic
441C2—22no—
442C2—42no—
443C2—81no—
444C2—9041no—
445C2—9041no—
446C2—4521no—
447C2—4522no—
448C2#2029923011yescharacteristic
449C2C2×#1681364911yescharacteristic
450C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
hypercenter#450D113
hypocenterC113#3264
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. C22×#14268632C2semidirect
3. #20299239C2semidirect
4. D4×C22⋊D113C2semidirect
5. #20298984C2semidirect
6. #20298850C2semidirect
7. #20298829C2semidirect
8. #20298815C2semidirect
9. #20298792C2semidirect
10. #20298742C2semidirect
11. #20298734C2semidirect
12. #20298733C2semidirect
13. #20298707C2semidirect
14. #20298666C2semidirect
15. #450×C113C2semidirect
16. C2×#14268648C22semidirect
17. C22×D452C22semidirect
19. C2×D4×D113C22semidirect
21. C2×#14268634C22semidirect
22. C2×D904C22semidirect
23. C2×D904C22semidirect
27. C2×#14268632C22semidirect
28. C2×#14268632C22semidirect
29. C2×#14268630C22semidirect
30. C22×#11744751C22semidirect
31. #16813618C22semidirect
32. #16813611C22semidirect
35. #16813597C22semidirect
38. #16813593C22semidirect
42. D4×Dic113C22semidirect
43. #16813584C22semidirect
46. #16813553C22semidirect
47. #16813551C22semidirect
48. #16813546C22semidirect
49. #16813544C22semidirect
50. #16813544C22semidirect
51. #16813542C22semidirect
52. #16813534C22semidirect
53. #16813532C22semidirect
55. C2×SD16×C113C22semidirect
56. C2×SD16×C113C22semidirect
57. C22⋊Q8×C113C22semidirect
58. #102×C113C22semidirect
59. #102×C113C22semidirect
60. C22⋊C8×C113C22semidirect
92. #14268632D4semidirect
172. D452C2×D4semidirect
180. #11744751C2×D4semidirect
190. C22×C113AGL(1,ℤ/8)semidirect
226. C113#3264semidirect
236. #450D113semidirect
249. C2×SD16C2×D113semidirect
250. C2×SD16C2×D113semidirect
263. C22⋊Q8C2×D113semidirect
282. #102C2×D113semidirect
283. #102C2×D113semidirect
285. C22⋊C8C2×D113semidirect
430. C22#16813649semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C22×#142686322
#202992392
D4×C22⋊D1132
#202989842
#202988502
#202988292
#202988152
#202987922
#202987422
#202987342
#202987332
#202987072
#202986662
#450×C1132
#3264113