Finite Group Databasebeta

← #28402068

Subgroups — #28402068

Order 14464.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813646C211yesmaximal, characteristic, complemented
2C2×SD16×D113C211yesmaximal, characteristic, complemented
3#20299256C211yesmaximal, characteristic, complemented
4#20299233C211yesmaximal, characteristic, complemented
5#20298841C211yesmaximal, characteristic, complemented
6#20298831C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298795C211yesmaximal, characteristic, complemented
9#20298747C211yesmaximal, characteristic, complemented
10#20298740C211yesmaximal, characteristic, complemented
11#20298735C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298700C211yesmaximal, characteristic, complemented
14#20298671C211yesmaximal, characteristic, complemented
15#496×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic, complemented
17C2×Q8×D113C2211yescharacteristic, complemented
18C2×D4×D113—21no—
19C2×D4×D113C2211yescharacteristic
20C2×D4×D113C2211yescharacteristic
21#16813646—24no—
22C2×#14268636C2211yescharacteristic
23C2×#14268635C2211yescharacteristic, complemented
24C2×#14268635C2211yescharacteristic, complemented
25C2×#14268634C2211yescharacteristic
26SD16×D113—24no—
27C2×#14268632C2211yescharacteristic
28C2×#14268630C2211yescharacteristic, complemented
29C2×C8×D113C2211yescharacteristic, complemented
30#16813608—21no—
31#16813599—21no—
32#16813598C2211yescharacteristic, complemented
33#16813595—21no—
34#16813593—21no—
35#16813593C2211yescharacteristic
36#16813593C2211yescharacteristic
37#16813593C2211yescharacteristic, complemented
38#16813590—21no—
39#16813590—21no—
40C4×Dic226C2211yescharacteristic, complemented
41C4×D452C2211yescharacteristic
42C4×D452C2211yescharacteristic
43#16813582—21no—
44#16813556C2211yescharacteristic, complemented
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813547C2211yescharacteristic, complemented
47#16813546C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic
49#16813543C2211yescharacteristic, complemented
50#16813543C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53#16813534C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×SD16×C113C2211yescharacteristic, complemented
56C2×D8×C113C2211yescharacteristic, complemented
57C2×D8×C113C2211yescharacteristic, complemented
58#127×C113C2211yescharacteristic
59#124×C113C2211yescharacteristic, complemented
60#97×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63#14268646—22no—
64#14268646—41no—
65C2×Dic226—21no—
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—41no—
69C2×D452D411yescharacteristic
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—
77D4×D113—22no—
78D4×D113—22no—
79D4×D113—41no—
80D4×D113—41no—
81D4×D113—44no—
82C22×Dic113—21no—
83C2×C4×D113—21no—
84C2×C4×D113—21no—
85C2×C4×D113C2311yescharacteristic
86C2×C4×D113C2311yescharacteristic
87#14268636D414yescomplemented
88#14268635—22no—
89#14268635—22no—
90#14268634—22no—
91#14268632—22no—
92#14268630—22no—
93C2×#11744751C2311yescharacteristic
94C2×#11744751C2311yescharacteristic
95C8×D113—22no—
96C4⋊Dic113D411yescharacteristic
97C4⋊Dic113C2311yescharacteristic
98C4⋊Dic113C2311yescharacteristic
99#14268626—21no—
100#14268626—21no—
101C22⋊Dic113—21no—
102C22⋊Dic113—21no—
103C22⋊Dic113—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624D411yescharacteristic
107#14268624D411yescharacteristic
108C4×Dic113—21no—
109C2×Q8×C113C2311yescharacteristic
110C2×D4×C113—21no—
111C2×D4×C113—21no—
112C2×D4×C113C2311yescharacteristic
113C2×D4×C113C2311yescharacteristic
114C2×D4×C113C2311yescharacteristic
115SD16×C113—22no—
116SD16×C113—41no—
117D8×C113—22no—
118D8×C113—41no—
119C2×C8×C113C2311yescharacteristic
120C2×C8×C113C2311yescharacteristic
121C22⋊C4×C113—21no—
122C22⋊C4×C113—21no—
123C42×C113C2311yescharacteristic
124C23×C113—21no—
125C23×C113—21no—
126C23×C113—21no—
127C22×D113—21no—
128C22×D113—42no—
129C22×D113—42no—
130C22×D113—42no—
131C22×D113—42no—
132C22×D113—81no—
133C22×D113—81no—
134C22×D113C2×D411yescharacteristic
135C22×D113C2×D411yescharacteristic
136Q8×C113—21no—
137Q8×C113—21no—
138D4×C113—21no—
139D4×C113—21no—
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—21no—
143D4×C113—21no—
144D4×C113—42no—
145D4×C113—81no—
146C2×C4×C113—21no—
147C2×C4×C113C2×D411yescharacteristic
148C2×C4×C113C2×D411yescharacteristic
149C2×C4×C113C2411yescharacteristic
150C22⋊D113—42no—
151C22⋊D113—42no—
152C22⋊D113—42no—
153C22⋊D113—42no—
154C22⋊D113—42no—
155C22⋊D113—42no—
156C2×Dic113—21no—
157C2×Dic113—21no—
158C2×Dic113—21no—
159C2×Dic113—42no—
160C2×Dic113C2×D411yescharacteristic
161C2×Dic113C2×D411yescharacteristic
162D452—22no—
163D452—21no—
164D452C2×D412yes—
165C4×D113—21no—
166C4×D113—21no—
167C4×D113—21no—
168C4×D113—21no—
169C4×D113—42no—
170C4×D113—42no—
171Dic226—21no—
172Dic226—42no—
173Dic226C2×D412yescomplemented
174C8×C113—21no—
175C8×C113C2×D412yescomplemented
176#11744751—21no—
177#11744751—21no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113—41no—
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—22no—
192C2×D113—21no—
193C2×D113—21no—
194C2×D113—41no—
195C2×D113—41no—
196C2×D113—84no—
197C2×D113—84no—
198C2×D113AGL(1,ℤ/8)12yescomplemented
199C4×C113—21no—
200C4×C113—21no—
201C4×C113—41no—
202C4×C113C22×D411yescharacteristic
203C4×C113H(5,𝔽2)11yescharacteristic
204Dic113—22no—
205Dic113—21no—
206Dic113—21no—
207Dic113—41no—
208Dic113—41no—
209C2×C113—81no—
210C2×C113—81no—
211C2×C113—81no—
212C2×C113D4211yescharacteristic
213C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C113#57711yescharacteristic
215D113—22no—
216D113—41no—
217D113—42no—
218#3265—1131nomaximal, Sylow
219C113#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—1131no—
221C22×SD16—1131no—
222#548—1131no—
223D42—1131no—
224#496D11311yescharacteristic, complemented
225#468—1131no—
226#466—1131no—
227#463—1131no—
228#460—1131no—
229#450—1131no—
230#449—1131no—
231#448—1131no—
232#447—1131no—
233#440—1131no—
234#435—1131no—
235C2×#41—1131no—
236C22×Q8—1131no—
237C22×D4—1131no—
238C22×D4—1131no—
239C22×D4—2261no—
240AGL(1,ℤ/8)—2264no—
241C2×SD16—1131no—
242C2×SD16—1131no—
243C2×SD16—1131no—
244C2×SD16—1131no—
245C2×SD16—2264no—
246C2×SD16C2×D11311yescharacteristic, complemented
247C2×SD16C2×D11311yescharacteristic, complemented
248C2×D8—1131no—
249C2×D8C2×D11311yescharacteristic, complemented
250C2×D8C2×D11311yescharacteristic, complemented
251C2×M16—1131no—
252C22×C8—1131no—
253#127C2×D11311yescharacteristic
254#124—2261no—
255#124C2×D11311yescharacteristic, complemented
256C22⋊Q8—1131no—
257C22⋊Q8—2261no—
258#121—1131no—
259#121—1131no—
260#121—1131no—
261#121—2261no—
262#121—2261no—
263#120—2261no—
264#120—2261no—
265C4×Q8—1131no—
266C4×D4—1131no—
267C4×D4—1131no—
268C4×D4—2261no—
269#107—1131no—
270C4⋊C8—1131no—
271#103—1131no—
272#103—1131no—
273#102—1131no—
274#102—1131no—
275#102—1131no—
276#102—1131no—
277C22⋊C8—1131no—
278C22⋊C8—1131no—
279#97C2×D11311yescharacteristic, complemented
280C24—2261no—
281C24—2261no—
282#41—4521no—
283#41—2262no—
284C2×Q8—1131no—
285C2×Q8—4521no—
286C2×Q8—2261no—
287C2×Q8—2262no—
288C2×Q8C22×D11311yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—1131no—
292C2×D4—1131no—
293C2×D4—4524no—
294C2×D4—4521no—
295C2×D4—4521no—
296C2×D4—2261no—
297C2×D4—2261no—
298C2×D4—2262no—
299C2×D4—2262no—
300C2×D4—2261no—
301C2×D4—2261no—
302C2×D4—2261no—
303C2×D4—2261no—
304C2×D4C22×D11311yescharacteristic
305C2×D4C22×D11311yescharacteristic
306C2×D4C22×D11311yescharacteristic
307C22×C4—1131no—
308C22×C4—1131no—
309C22×C4—2261no—
310C22×C4—2261no—
311C22×C4—2261no—
312SD16—22no—
313SD16—41no—
314SD16—1134no—
315SD16—2262no—
316SD16—2262no—
317SD16—2262no—
318D8—22no—
319D8—41no—
320D8—2262no—
321M16—2262no—
322C2×C8—1131no—
323C2×C8—1131no—
324C2×C8—2262no—
325C2×C8C22×D11311yescharacteristic
326C2×C8C22×D11311yescharacteristic
327C4⋊C4—1131no—
328C4⋊C4—1131no—
329C4⋊C4—1131no—
330C4⋊C4—2261no—
331C4⋊C4—2261no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—1131no—
335C22⋊C4—1131no—
336C22⋊C4—2261no—
337C22⋊C4—2261no—
338C22⋊C4—2261no—
339C22⋊C4—2261no—
340C22⋊C4—2261no—
341C42—2261no—
342C42C22×D11311yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—1131no—
347C23—1131no—
348C23—9041no—
349C23—9041no—
350C23—4522no—
351C23—4522no—
352C23—4522no—
353C23—4522no—
354C23—2261no—
355Q8—21no—
356Q8—21no—
357Q8—1132no—
358Q8—4522no—
359Q8—2261no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—81no—
368D4—1132no—
369D4—4522no—
370D4—4522no—
371D4—4522no—
372D4—4522no—
373D4—4522no—
374D4—4522no—
375D4—2262no—
376D4—2261no—
377C2×C4—21no—
378C2×C4—1131no—
379C2×C4—1131no—
380C2×C4—4522no—
381C2×C4—4522no—
382C2×C4—4522no—
383C2×C4—2261no—
384C2×C4—2261no—
385C2×C4—2261no—
386C2×C4—2261no—
387C2×C4—2261no—
388C2×C4—2261no—
389C2×C4—2261no—
390C2×C4D4×D11311yescharacteristic
391C2×C4D4×D11311yescharacteristic
392C2×C4C23×D11311yescharacteristic
393C8—21no—
394C8—2261no—
395C8—2261no—
396C8D4×D11312yescomplemented
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—1132no—
407C22—9044no—
408C22—9044no—
409C22—4521no—
410C22—4521no—
411C22—2261no—
412C22—2261no—
413C22—2261no—
414C22—2262no—
415C22—2261no—
416C22—2261no—
417C22C2×D4×D11311yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—4521no—
422C4—4521no—
423C4—2261no—
424C4—2261no—
425C4—2262no—
426C4C2×D4×D11311yescharacteristic
427C4#1681366711yescharacteristic
428C2—81no—
429C2—81no—
430C2—81no—
431C2—4522no—
432C2—4521no—
433C2—2262no—
434C2#2029923311yescharacteristic
435C2AGL(1,ℤ/8)×D11311yescharacteristic
436C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3265
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#16813646C2semidirect
2. C2×SD16×D113C2semidirect
3. #20299256C2semidirect
4. #20299233C2semidirect
5. #20298841C2semidirect
6. #20298831C2semidirect
7. #20298810C2semidirect
8. #20298795C2semidirect
9. #20298747C2semidirect
10. #20298740C2semidirect
11. #20298735C2semidirect
12. #20298730C2semidirect
13. #20298700C2semidirect
14. #20298671C2semidirect
15. #496×C113C2semidirect
16. C2×#14268646C22semidirect
17. C2×Q8×D113C22semidirect
23. C2×#14268635C22semidirect
24. C2×#14268635C22semidirect
28. C2×#14268630C22semidirect
29. C2×C8×D113C22semidirect
32. #16813598C22semidirect
37. #16813593C22semidirect
40. C4×Dic226C22semidirect
44. #16813556C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813547C22semidirect
47. #16813546C22semidirect
49. #16813543C22semidirect
50. #16813543C22semidirect
51. #16813543C22semidirect
52. #16813534C22semidirect
53. #16813534C22semidirect
54. C2×SD16×C113C22semidirect
55. C2×SD16×C113C22semidirect
56. C2×D8×C113C22semidirect
57. C2×D8×C113C22semidirect
59. #124×C113C22semidirect
60. #97×C113C22semidirect
87. #14268636D4semidirect
173. Dic226C2×D4semidirect
175. C8×C113C2×D4semidirect
198. C2×D113AGL(1,ℤ/8)semidirect
219. C113#3265semidirect
224. #496D113semidirect
246. C2×SD16C2×D113semidirect
247. C2×SD16C2×D113semidirect
249. C2×D8C2×D113semidirect
250. C2×D8C2×D113semidirect
255. #124C2×D113semidirect
279. #97C2×D113semidirect
396. C8D4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C2×SD16×D1132
#202992562
#202992332
#202988412
#202988312
#202988102
#202987952
#202987472
#202987402
#202987352
#202987302
#202987002
#202986712
#496×C1132
#3265113