Finite Group Databasebeta

← #28402244

Subgroups — #28402244

Order 14464.

620 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14268632C211yesmaximal, characteristic, complemented
2C2×D8×D113C211yesmaximal, characteristic, complemented
3#20299232C211yesmaximal, characteristic, complemented
4D4×C22⋊D113C211yesmaximal, characteristic, complemented
5#20298973C211yesmaximal, characteristic, complemented
6#20298833C211yesmaximal, characteristic, complemented
7#20298832C211yesmaximal, characteristic, complemented
8#20298792C211yesmaximal, characteristic, complemented
9#20298791C211yesmaximal, characteristic, complemented
10#20298734C211yesmaximal, characteristic, complemented
11#20298733C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298661C211yesmaximal, characteristic, complemented
15#447×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic, complemented
17C22×C22⋊D113—21no—
18C2×D4×D113—21no—
19C2×D4×D113C2211yescharacteristic, complemented
20C2×D4×D113C2211yescharacteristic, complemented
21C2×D904C2211yescharacteristic, complemented
22C2×D904C2211yescharacteristic, complemented
23C2×#14268632—24no—
24C2×#14268632C2211yescharacteristic
25C2×#14268632C2211yescharacteristic, complemented
26C2×#14268632C2211yescharacteristic, complemented
27C2×#14268632C2211yescharacteristic, complemented
28C2×#14268632C2211yescharacteristic, complemented
29D8×D113—24no—
30C22×#11744751C2211yescharacteristic, complemented
31C2×C8×D113C2211yescharacteristic, complemented
32#16813618C2211yescharacteristic, complemented
33#16813618C2211yescharacteristic, complemented
34#16813597C2211yescharacteristic, complemented
35#16813596C2211yescharacteristic, complemented
36#16813595—21no—
37#16813594—21no—
38#16813593C2211yescharacteristic, complemented
39#16813592—21no—
40#16813591—21no—
41#16813590—21no—
42#16813590—21no—
43D4×Dic113C2211yescharacteristic, complemented
44#16813584C2211yescharacteristic, complemented
45C4×C22⋊D113C2211yescharacteristic
46#16813555C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813543C2211yescharacteristic, complemented
51#16813542C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53C8×Dic113C2211yescharacteristic, complemented
54C22×D4×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic, complemented
56C2×D8×C113C2211yescharacteristic, complemented
57#121×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60C22⋊C8×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63C23×D113—21no—
64C2×D452—22no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452—41no—
68C2×D452C2311yescharacteristic
69C2×D452C2311yescharacteristic
70C2×D452C2311yescharacteristic
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77C2×C22⋊D113—21no—
78C2×C22⋊D113—21no—
79C2×C22⋊D113—44no—
80C2×C22⋊D113D411yescharacteristic
81D4×D113—22no—
82D4×D113—22no—
83D4×D113—41no—
84D4×D113—41no—
85D4×D113—44no—
86C22×Dic113—21no—
87C2×C4×D113—21no—
88C2×C4×D113C2311yescharacteristic
89D904—22no—
90D904—41no—
91#14268632—22no—
92#14268632—22no—
93#14268632—22no—
94#14268632—22no—
95#14268632D414yescomplemented
96C2×#11744751—22no—
97C2×#11744751C2311yescharacteristic
98C2×#11744751C2311yescharacteristic
99C8×D113—22no—
100C4⋊Dic113C2311yescharacteristic
101#14268626D411yescharacteristic
102C22⋊Dic113—21no—
103C22⋊Dic113—21no—
104C22⋊Dic113D411yescharacteristic
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624D411yescharacteristic
109C4×Dic113C2311yescharacteristic
110C24×C113—21no—
111C2×D4×C113—22no—
112C2×D4×C113—21no—
113C2×D4×C113—21no—
114C2×D4×C113—41no—
115C2×D4×C113C2311yescharacteristic
116C2×D4×C113C2311yescharacteristic
117C2×D4×C113C2311yescharacteristic
118C22×C4×C113C2311yescharacteristic
119D8×C113—22no—
120D8×C113—41no—
121C2×C8×C113C2311yescharacteristic
122C2×C8×C113C2311yescharacteristic
123C4⋊C4×C113C2311yescharacteristic
124C22⋊C4×C113—21no—
125C23×C113—21no—
126C23×C113—21no—
127C23×C113—21no—
128C23×C113—42no—
129C23×C113—42no—
130C23×C113—81no—
131C23×C113C2×D411yescharacteristic
132C22×D113—21no—
133C22×D113—21no—
134C22×D113—21no—
135C22×D113—42no—
136C22×D113—42no—
137C22×D113—42no—
138C22×D113—42no—
139C22×D113—42no—
140C22×D113—42no—
141C22×D113—81no—
142C22×D113—81no—
143C22×D113—81no—
144C22×D113C2×D411yescharacteristic
145D4×C113—21no—
146D4×C113—21no—
147D4×C113—21no—
148D4×C113—21no—
149D4×C113—21no—
150D4×C113—42no—
151D4×C113—42no—
152D4×C113C2×D412yescomplemented
153C2×C4×C113—21no—
154C2×C4×C113—21no—
155C2×C4×C113—21no—
156C2×C4×C113C2×D411yescharacteristic
157C2×C4×C113C2411yescharacteristic
158C22⋊D113—42no—
159C22⋊D113—42no—
160C22⋊D113—42no—
161C22⋊D113—42no—
162C22⋊D113—42no—
163C22⋊D113—42no—
164C22⋊D113—81no—
165C22⋊D113—81no—
166C22⋊D113D814yescomplemented
167C2×Dic113—21no—
168C2×Dic113—42no—
169C2×Dic113C2×D411yescharacteristic
170C2×Dic113C2×D411yescharacteristic
171C2×Dic113C2×D411yescharacteristic
172D452—21no—
173D452—21no—
174D452—21no—
175D452—21no—
176D452—21no—
177D452—42no—
178D452—42no—
179D452C2×D412yescomplemented
180C4×D113—21no—
181C4×D113—21no—
182C4×D113—42no—
183C8×C113—21no—
184C8×C113—21no—
185#11744751—21no—
186#11744751C2×D412yescomplemented
187C22×C113—21no—
188C22×C113—21no—
189C22×C113—22no—
190C22×C113—41no—
191C22×C113—41no—
192C22×C113—41no—
193C22×C113—41no—
194C22×C113—41no—
195C22×C113—41no—
196C22×C113—41no—
197C22×C113—41no—
198C22×C113—84no—
199C22×C113C2×D812yescomplemented
200C22×C113C22×D411yescharacteristic
201C2×D113—21no—
202C2×D113—21no—
203C2×D113—22no—
204C2×D113—41no—
205C2×D113—41no—
206C2×D113—41no—
207C2×D113—41no—
208C2×D113—41no—
209C2×D113—41no—
210C2×D113—41no—
211C2×D113—41no—
212C2×D113—84no—
213C2×D113—84no—
214C2×D113—84no—
215C2×D113C2×D812yescomplemented
216C4×C113—21no—
217C4×C113—41no—
218C4×C113C22×D411yescharacteristic
219C4×C113H(5,𝔽2)11yescharacteristic
220Dic113—21no—
221Dic113—21no—
222Dic113—41no—
223Dic113C2×D812yescomplemented
224C2×C113—22no—
225C2×C113—42no—
226C2×C113—81no—
227C2×C113—81no—
228C2×C113D4211yescharacteristic
229C2×C113C22×D811yescharacteristic
230C2×C113#57611yescharacteristic
231D113—22no—
232D113—42no—
233D113—81no—
234D113—81no—
235D4×D8—1131nomaximal, Sylow
236C113D4×D811yescharacteristic, complemented, Sylow
237C22×D8—1131no—
238C22×D8—1131no—
239D42—1131no—
240D42—1131no—
241#493—1131no—
242#466—1131no—
243#466—1131no—
244#459—1131no—
245#459—1131no—
246#447—1131no—
247#447—1131no—
248#447—1131no—
249#447D11311yescharacteristic, complemented
250C4×D8—1131no—
251C8×D4—1131no—
252C22×D4—1131no—
253C22×D4—1131no—
254C22×D4—1131no—
255C22×D4—2261no—
256C22×D4—2261no—
257C22×D4C2×D11311yescharacteristic, complemented
258C2×D8—1131no—
259C2×D8—1131no—
260C2×D8—1131no—
261C2×D8—1131no—
262C2×D8—1131no—
263C2×D8—1131no—
264C2×D8—1131no—
265C2×D8—2264no—
266C2×D8—2264no—
267C2×D8C2×D11311yescharacteristic, complemented
268C2×D8C2×D11311yescharacteristic, complemented
269C22×C8—1131no—
270C22×C8—1131no—
271#127—1131no—
272#127—1131no—
273#121—1131no—
274#121—1131no—
275#121—1131no—
276#121—2261no—
277#121—2261no—
278#121C2×D11311yescharacteristic, complemented
279#120—2261no—
280#120—2261no—
281#120—2261no—
282#120—2261no—
283C4×D4—1131no—
284C4×D4—1131no—
285C4×D4—1131no—
286#107—1131no—
287C4⋊C8—1131no—
288#102—1131no—
289#102—1131no—
290#102—1131no—
291#102—1131no—
292#102C2×D11311yescharacteristic, complemented
293#102C2×D11311yescharacteristic, complemented
294C22⋊C8—1131no—
295C22⋊C8C2×D11311yescharacteristic, complemented
296C4×C8—1131no—
297C24—21no—
298C24—2261no—
299C24—2261no—
300C24—2261no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—1131no—
306C2×D4—1131no—
307C2×D4—1131no—
308C2×D4—1131no—
309C2×D4—4521no—
310C2×D4—4524no—
311C2×D4—4524no—
312C2×D4—4521no—
313C2×D4—4521no—
314C2×D4—2262no—
315C2×D4—2261no—
316C2×D4—2261no—
317C2×D4—2261no—
318C2×D4—2261no—
319C2×D4—2261no—
320C2×D4—2261no—
321C2×D4—2261no—
322C2×D4—2262no—
323C2×D4—2261no—
324C2×D4—2261no—
325C2×D4—2262no—
326C2×D4—2261no—
327C2×D4C22×D11311yescharacteristic
328C2×D4C22×D11311yescharacteristic
329C2×D4C22×D11311yescharacteristic
330C22×C4—1131no—
331C22×C4—2261no—
332C22×C4—2261no—
333C22×C4C22×D11311yescharacteristic
334D8—22no—
335D8—41no—
336D8—1134no—
337D8—4521no—
338D8—2262no—
339D8—2262no—
340D8—2262no—
341D8—2262no—
342D8—2262no—
343C2×C8—1131no—
344C2×C8—1131no—
345C2×C8—2262no—
346C2×C8—2262no—
347C2×C8C22×D11311yescharacteristic
348C2×C8C22×D11311yescharacteristic
349C4⋊C4—1131no—
350C4⋊C4—1131no—
351C4⋊C4C22×D11311yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—1131no—
354C22⋊C4—1131no—
355C22⋊C4—2261no—
356C22⋊C4—2261no—
357C22⋊C4—2261no—
358C22⋊C4—2261no—
359C22⋊C4—2261no—
360C42—1131no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—42no—
365C23—42no—
366C23—81no—
367C23—1131no—
368C23—9041no—
369C23—9041no—
370C23—9041no—
371C23—4522no—
372C23—4522no—
373C23—4522no—
374C23—4522no—
375C23—4522no—
376C23—4522no—
377C23—2261no—
378C23—2261no—
379C23—2261no—
380C23D4×D11311yescharacteristic
381D4—21no—
382D4—21no—
383D4—21no—
384D4—21no—
385D4—21no—
386D4—42no—
387D4—42no—
388D4—1134no—
389D4—1132no—
390D4—9041no—
391D4—9041no—
392D4—4522no—
393D4—4522no—
394D4—4522no—
395D4—4522no—
396D4—4522no—
397D4—4522no—
398D4—4522no—
399D4—4522no—
400D4—2261no—
401D4—2261no—
402D4—2261no—
403D4—2261no—
404D4—2261no—
405D4D4×D11312yescomplemented
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—1131no—
410C2×C4—1131no—
411C2×C4—1131no—
412C2×C4—4522no—
413C2×C4—4522no—
414C2×C4—2261no—
415C2×C4—2261no—
416C2×C4—2261no—
417C2×C4D4×D11311yescharacteristic
418C2×C4C23×D11311yescharacteristic
419C8—21no—
420C8—21no—
421C8—1132no—
422C8—2261no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—84no—
435C22—1132no—
436C22—9044no—
437C22—9044no—
438C22—9044no—
439C22—4521no—
440C22—4521no—
441C22—4521no—
442C22—4521no—
443C22—4521no—
444C22—4521no—
445C22—4521no—
446C22—4521no—
447C22—2262no—
448C22—2261no—
449C22—2261no—
450C22D8×D11312yescomplemented
451C22C2×D4×D11311yescharacteristic
452C4—21no—
453C4—41no—
454C4—1132no—
455C4—4521no—
456C4—2261no—
457C4—2261no—
458C4C2×D4×D11311yescharacteristic
459C4#1681366711yescharacteristic
460C2—22no—
461C2—42no—
462C2—81no—
463C2—81no—
464C2—9041no—
465C2—9041no—
466C2—4522no—
467C2—2262no—
468C2#2029923011yescharacteristic
469C2C2×D8×D11311yescharacteristic
470C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113D4×D8
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. C22×#14268632C2semidirect
2. C2×D8×D113C2semidirect
3. #20299232C2semidirect
4. D4×C22⋊D113C2semidirect
5. #20298973C2semidirect
6. #20298833C2semidirect
7. #20298832C2semidirect
8. #20298792C2semidirect
9. #20298791C2semidirect
10. #20298734C2semidirect
11. #20298733C2semidirect
12. #20298730C2semidirect
13. #20298678C2semidirect
14. #20298661C2semidirect
15. #447×C113C2semidirect
16. C22×D452C22semidirect
19. C2×D4×D113C22semidirect
20. C2×D4×D113C22semidirect
21. C2×D904C22semidirect
22. C2×D904C22semidirect
25. C2×#14268632C22semidirect
26. C2×#14268632C22semidirect
27. C2×#14268632C22semidirect
28. C2×#14268632C22semidirect
30. C22×#11744751C22semidirect
31. C2×C8×D113C22semidirect
32. #16813618C22semidirect
33. #16813618C22semidirect
34. #16813597C22semidirect
35. #16813596C22semidirect
38. #16813593C22semidirect
43. D4×Dic113C22semidirect
44. #16813584C22semidirect
46. #16813555C22semidirect
47. #16813551C22semidirect
48. #16813544C22semidirect
49. #16813544C22semidirect
50. #16813543C22semidirect
51. #16813542C22semidirect
52. #16813534C22semidirect
53. C8×Dic113C22semidirect
54. C22×D4×C113C22semidirect
55. C2×D8×C113C22semidirect
56. C2×D8×C113C22semidirect
57. #121×C113C22semidirect
58. #102×C113C22semidirect
59. #102×C113C22semidirect
60. C22⋊C8×C113C22semidirect
95. #14268632D4semidirect
152. D4×C113C2×D4semidirect
166. C22⋊D113D8semidirect
179. D452C2×D4semidirect
186. #11744751C2×D4semidirect
199. C22×C113C2×D8semidirect
215. C2×D113C2×D8semidirect
223. Dic113C2×D8semidirect
236. C113D4×D8semidirect
249. #447D113semidirect
257. C22×D4C2×D113semidirect
267. C2×D8C2×D113semidirect
268. C2×D8C2×D113semidirect
278. #121C2×D113semidirect
292. #102C2×D113semidirect
293. #102C2×D113semidirect
295. C22⋊C8C2×D113semidirect
405. D4D4×D113semidirect
450. C22D8×D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686322
C2×D8×D1132
#202992322
D4×C22⋊D1132
#202989732
#202988332
#202988322
#202987922
#202987912
#202987342
#202987332
#202987302
#202986782
#202986612
#447×C1132
D4×D8113