Finite Group Databasebeta

← #28402075

Subgroups — #28402075

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
4D4×D452C211yesmaximal, characteristic, complemented
5#20298988C211yesmaximal, characteristic, complemented
6#20298847C211yesmaximal, characteristic, complemented
7#20298833C211yesmaximal, characteristic, complemented
8#20298799C211yesmaximal, characteristic, complemented
9#20298747C211yesmaximal, characteristic, complemented
10#20298744C211yesmaximal, characteristic, complemented
11#20298738C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298698C211yesmaximal, characteristic, complemented
14#20298668C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic, complemented
17C2×Q8×D113C2211yescharacteristic, complemented
18C22×D452—21no—
19C2×D4×D113C2211yescharacteristic
20C2×D4×D113C2211yescharacteristic
21#16813646—24no—
22C2×#14268636C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic, complemented
24C2×#14268635C2211yescharacteristic
25C2×#14268634C2211yescharacteristic, complemented
26C2×#14268634C2211yescharacteristic, complemented
27SD16×D113—24no—
28C2×#14268632C2211yescharacteristic, complemented
29C2×#14268632C2211yescharacteristic, complemented
30C2×#14268630C2211yescharacteristic, complemented
31C2×C8×D113C2211yescharacteristic, complemented
32#16813619C2211yescharacteristic
33#16813608—21no—
34#16813599—21no—
35#16813598C2211yescharacteristic, complemented
36#16813597C2211yescharacteristic
37#16813597C2211yescharacteristic
38#16813596—21no—
39#16813595—21no—
40#16813593C2211yescharacteristic, complemented
41#16813592—21no—
42#16813592—21no—
43C4×Dic226C2211yescharacteristic, complemented
44C4×D452C2211yescharacteristic
45#16813582—21no—
46#16813555C2211yescharacteristic, complemented
47#16813545C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813543C2211yescharacteristic
51#16813534C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53#16813533C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic
55C2×D8×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic
58C4⋊C8×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×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×D452—21no—
70C2×D452—21no—
71C2×D452—21no—
72C2×D452—21no—
73C2×D452—44no—
74C2×D452D411yescharacteristic
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—41no—
84D4×D113—41no—
85C22×Dic113—21no—
86C2×C4×D113—21no—
87C2×C4×D113C2311yescharacteristic
88C2×C4×D113C2311yescharacteristic
89#14268636—22no—
90#14268636—22no—
91#14268635D414yescomplemented
92#14268634—22no—
93#14268634—41no—
94#14268632—22no—
95#14268632—41no—
96#14268630—22no—
97C2×#11744751C2311yescharacteristic
98C2×#11744751C2311yescharacteristic
99C8×D113—22no—
100C4⋊Dic113D411yescharacteristic
101C4⋊Dic113C2311yescharacteristic
102#14268626—21no—
103#14268626—21no—
104C22⋊Dic113—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624D411yescharacteristic
109#14268624D411yescharacteristic
110C4×Dic113—21no—
111C2×Q8×C113C2311yescharacteristic
112C2×D4×C113C2311yescharacteristic
113C2×D4×C113C2311yescharacteristic
114C22×C4×C113—21no—
115SD16×C113—22no—
116D8×C113—22no—
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C4⋊C4×C113C2311yescharacteristic
120C22⋊C4×C113—21no—
121C22⋊C4×C113—21no—
122C22⋊C4×C113—21no—
123C42×C113C2311yescharacteristic
124C23×C113—21no—
125C23×C113—21no—
126C22×D113—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×C113C2×D412yes—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—42no—
145C2×C4×C113C2×D411yescharacteristic
146C2×C4×C113C2×D411yescharacteristic
147C2×C4×C113C2411yescharacteristic
148C22⋊D113—42no—
149C22⋊D113—42no—
150C22⋊D113—42no—
151C22⋊D113—42no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—42no—
155C2×Dic113C2×D411yescharacteristic
156C2×Dic113C2×D411yescharacteristic
157D452—22no—
158D452—21no—
159D452—21no—
160D452—21no—
161D452—21no—
162D452—42no—
163D452—42no—
164D452—42no—
165D452—81no—
166C4×D113—21no—
167C4×D113—21no—
168C4×D113—21no—
169C4×D113—21no—
170C4×D113—42no—
171Dic226—21no—
172Dic226—42no—
173Dic226C2×D412yescomplemented
174C8×C113—21no—
175C8×C113—21no—
176#11744751—21no—
177#11744751C2×D412yescomplemented
178C22×C113—22no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113C22×D411yescharacteristic
185C2×D113—21no—
186C2×D113—21no—
187C2×D113—21no—
188C2×D113—21no—
189C2×D113—21no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—41no—
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×C113—41no—
203C4×C113C22×D411yescharacteristic
204C4×C113H(5,𝔽2)11yescharacteristic
205Dic113—22no—
206Dic113—21no—
207Dic113—21no—
208Dic113—41no—
209C2×C113—42no—
210C2×C113—81no—
211C2×C113D4211yescharacteristic
212C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C113#57711yescharacteristic
214D113—22no—
215D113—41no—
216D113—81no—
217D113—81no—
218#3265—1131nomaximal, Sylow
219C113#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—1131no—
221C22×SD16—1131no—
222#548—1131no—
223D42—1131no—
224#496—1131no—
225#468—1131no—
226#466—1131no—
227#463D11311yescharacteristic, complemented
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—1131no—
246C2×SD16—2264no—
247C2×SD16C2×D11311yescharacteristic
248C2×D8—1131no—
249C2×D8—1131no—
250C2×D8C2×D11311yescharacteristic
251C2×M16—1131no—
252C22×C8—1131no—
253#127—1131no—
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—2261no—
268C4×D4C2×D11311yescharacteristic
269#107—1131no—
270C4⋊C8C2×D11311yescharacteristic, complemented
271#103—1131no—
272#103C2×D11311yescharacteristic, complemented
273#102—1131no—
274#102—1131no—
275#102—1131no—
276#102C2×D11311yescharacteristic, complemented
277C22⋊C8—1131no—
278C22⋊C8—1131no—
279#97—1131no—
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—1131no—
290C2×D4—1131no—
291C2×D4—1131no—
292C2×D4—4524no—
293C2×D4—4521no—
294C2×D4—4521no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4—2261no—
298C2×D4—2261no—
299C2×D4—2261no—
300C2×D4—2261no—
301C2×D4—2262no—
302C2×D4—2262no—
303C2×D4—2261no—
304C2×D4—2261no—
305C2×D4C22×D11311yescharacteristic
306C2×D4C22×D11311yescharacteristic
307C22×C4—21no—
308C22×C4—1131no—
309C22×C4—1131no—
310C22×C4—2261no—
311C22×C4—2261no—
312SD16—22no—
313SD16—1134no—
314SD16—4521no—
315SD16—2262no—
316SD16—2262no—
317SD16—2262no—
318D8—22no—
319D8—4521no—
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—2261no—
330C4⋊C4—2261no—
331C4⋊C4C22×D11311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—1131no—
336C22⋊C4—1131no—
337C22⋊C4—2261no—
338C22⋊C4—2261no—
339C22⋊C4—2261no—
340C22⋊C4—2261no—
341C42—2261no—
342C42C22×D11311yescharacteristic
343C23—21no—
344C23—21no—
345C23—1131no—
346C23—1131no—
347C23—9041no—
348C23—9041no—
349C23—4522no—
350C23—4522no—
351C23—4522no—
352C23—4522no—
353C23—2261no—
354C23—2261no—
355Q8—21no—
356Q8—21no—
357Q8—1132no—
358Q8—4522no—
359Q8—2261no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—9041no—
364D4—4522no—
365D4—4522no—
366D4—4522no—
367D4—4522no—
368D4—4522no—
369D4—4522no—
370D4—4522no—
371D4—2262no—
372D4—2261no—
373D4—2261no—
374D4—2261no—
375D4—2261no—
376D4D4×D11312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—1131no—
381C2×C4—1131no—
382C2×C4—4522no—
383C2×C4—4522no—
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—21no—
395C8—1132no—
396C8—2261no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—1132no—
404C22—9044no—
405C22—9044no—
406C22—4521no—
407C22—4521no—
408C22—4521no—
409C22—4521no—
410C22—4521no—
411C22—4521no—
412C22—2261no—
413C22—2261no—
414C22—2261no—
415C22—2261no—
416C22—2261no—
417C22C2×D4×D11311yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—4521no—
423C4—2261no—
424C4—2261no—
425C4—2262no—
426C4C2×D4×D11311yescharacteristic
427C4#1681366811yescharacteristic
428C2—42no—
429C2—81no—
430C2—9041no—
431C2—9041no—
432C2—4521no—
433C2—2262no—
434C2#2029923211yescharacteristic
435C2AGL(1,ℤ/8)×D11311yescharacteristic
436C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
hypercenter#463D113
hypocenterC113#3265
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#16813646C2semidirect
2. C2×SD16×D113C2semidirect
3. #20299256C2semidirect
4. D4×D452C2semidirect
5. #20298988C2semidirect
6. #20298847C2semidirect
7. #20298833C2semidirect
8. #20298799C2semidirect
9. #20298747C2semidirect
10. #20298744C2semidirect
11. #20298738C2semidirect
12. #20298730C2semidirect
13. #20298698C2semidirect
14. #20298668C2semidirect
15. #463×C113C2semidirect
16. C2×#14268646C22semidirect
17. C2×Q8×D113C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268636C22semidirect
25. C2×#14268634C22semidirect
26. C2×#14268634C22semidirect
28. C2×#14268632C22semidirect
29. C2×#14268632C22semidirect
30. C2×#14268630C22semidirect
31. C2×C8×D113C22semidirect
35. #16813598C22semidirect
40. #16813593C22semidirect
43. C4×Dic226C22semidirect
46. #16813555C22semidirect
47. #16813545C22semidirect
48. #16813544C22semidirect
49. #16813544C22semidirect
51. #16813534C22semidirect
52. #16813534C22semidirect
53. #16813533C22semidirect
56. #124×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #103×C113C22semidirect
60. #102×C113C22semidirect
91. #14268635D4semidirect
173. Dic226C2×D4semidirect
177. #11744751C2×D4semidirect
198. C2×D113AGL(1,ℤ/8)semidirect
219. C113#3265semidirect
227. #463D113semidirect
255. #124C2×D113semidirect
270. C4⋊C8C2×D113semidirect
272. #103C2×D113semidirect
276. #102C2×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
D4×D4522
#202989882
#202988472
#202988332
#202987992
#202987472
#202987442
#202987382
#202987302
#202986982
#202986682
#463×C1132
#3265113