Finite Group Databasebeta

← #28402063

Subgroups — #28402063

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×SD16×D113C211yesmaximal, characteristic, complemented
2#20299255C211yesmaximal, characteristic, complemented
3D4×C22⋊D113C211yesmaximal, characteristic, complemented
4#20298986C211yesmaximal, characteristic, complemented
5#20298844C211yesmaximal, characteristic, complemented
6#20298831C211yesmaximal, characteristic, complemented
7#20298811C211yesmaximal, characteristic, complemented
8#20298796C211yesmaximal, characteristic, complemented
9#20298749C211yesmaximal, characteristic, complemented
10#20298743C211yesmaximal, characteristic, complemented
11#20298735C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298699C211yesmaximal, characteristic, complemented
14#20298667C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic, complemented
17C22×C22⋊D113—21no—
18C2×D4×D113C2211yescharacteristic
19C2×#14268636C2211yescharacteristic, complemented
20C2×#14268635C2211yescharacteristic
21C2×#14268635C2211yescharacteristic, complemented
22C2×#14268634C2211yescharacteristic, complemented
23SD16×D113—24no—
24C2×#14268632C2211yescharacteristic, complemented
25C2×C8×D113C2211yescharacteristic, complemented
26#16813618C2211yescharacteristic
27#16813609—21no—
28#16813609C2211yescharacteristic, complemented
29#16813601—21no—
30#16813601C2211yescharacteristic, complemented
31#16813596C2211yescharacteristic
32#16813594—21no—
33#16813593—21no—
34#16813593C2211yescharacteristic
35#16813593C2211yescharacteristic, complemented
36#16813591—21no—
37#16813590—21no—
38Q8×Dic113C2211yescharacteristic, complemented
39D4×Dic113C2211yescharacteristic
40C4×C22⋊D113—21no—
41C4×C22⋊D113C2211yescharacteristic
42#16813556C2211yescharacteristic, complemented
43#16813551C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic, complemented
49#16813543C2211yescharacteristic, complemented
50C22⋊#11744751C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52#16813532C2211yescharacteristic, complemented
53C2×#41×C113C2211yescharacteristic, complemented
54C22×D4×C113C2211yescharacteristic
55AGL(1,ℤ/8)×C113—24no—
56C2×SD16×C113C2211yescharacteristic
57C2×SD16×C113C2211yescharacteristic, complemented
58C2×D8×C113C2211yescharacteristic
59C2×D8×C113C2211yescharacteristic, complemented
60C2×M16×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64Q8×D113—22no—
65Q8×D113—41no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113—44no—
74C2×C22⋊D113D411yescharacteristic
75D4×D113—22no—
76D4×D113—41no—
77C22×Dic113—21no—
78C2×C4×D113—21no—
79C2×C4×D113C2311yescharacteristic
80#14268636—22no—
81#14268635—22no—
82#14268635—41no—
83#14268634—22no—
84#14268632—41no—
85C2×#11744751C2311yescharacteristic
86C2×#11744751C2311yescharacteristic
87C8×D113—22no—
88C4⋊Dic113—21no—
89C4⋊Dic113C2311yescharacteristic
90C4⋊Dic113C2311yescharacteristic
91#14268626—21no—
92#14268626D411yescharacteristic
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95C22⋊Dic113—21no—
96C22⋊Dic113—21no—
97C22⋊Dic113—21no—
98C22⋊Dic113—21no—
99C22⋊Dic113D411yescharacteristic
100#14268624—21no—
101#14268624D411yescharacteristic
102C4×Dic113—21no—
103C4×Dic113C2311yescharacteristic
104C24×C113—21no—
105#41×C113—22no—
106#41×C113—41no—
107C2×Q8×C113C2311yescharacteristic
108C2×D4×C113—22no—
109C2×D4×C113—21no—
110C2×D4×C113—21no—
111C2×D4×C113—41no—
112C2×D4×C113C2311yescharacteristic
113C2×D4×C113C2311yescharacteristic
114C2×D4×C113C2311yescharacteristic
115C22×C4×C113—21no—
116C22×C4×C113C2311yescharacteristic
117SD16×C113—22no—
118SD16×C113D414yescomplemented
119D8×C113—22no—
120D8×C113—22no—
121M16×C113—22no—
122C2×C8×C113C2311yescharacteristic
123C2×C8×C113C2311yescharacteristic
124C23×C113—21no—
125C23×C113—21no—
126C23×C113—21no—
127C23×C113—42no—
128C23×C113—42no—
129C23×C113—81no—
130C23×C113C2×D411yescharacteristic
131C22×D113—21no—
132C22×D113—42no—
133C22×D113—42no—
134C22×D113—81no—
135C22×D113C2×D411yescharacteristic
136Q8×C113—21no—
137Q8×C113C2×D412yescomplemented
138D4×C113—21no—
139D4×C113—21no—
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—21no—
143D4×C113—42no—
144D4×C113—42no—
145D4×C113C2×D412yes—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—21no—
149C2×C4×C113—42no—
150C2×C4×C113C2×D411yescharacteristic
151C2×C4×C113C2411yescharacteristic
152C22⋊D113—22no—
153C22⋊D113—42no—
154C22⋊D113—42no—
155C22⋊D113—42no—
156C22⋊D113—42no—
157C22⋊D113—42no—
158C22⋊D113—81no—
159C2×Dic113—21no—
160C2×Dic113—21no—
161C2×Dic113—21no—
162C2×Dic113—42no—
163C2×Dic113C2×D411yescharacteristic
164C2×Dic113C2×D411yescharacteristic
165C2×Dic113C2×D411yescharacteristic
166D452—21no—
167D452—21no—
168C4×D113—21no—
169C4×D113—21no—
170C4×D113—42no—
171Dic226—21no—
172Dic226—21no—
173Dic226—42no—
174C8×C113—21no—
175C8×C113C2×D412yescomplemented
176#11744751—21no—
177#11744751—21no—
178C22×C113—22no—
179C22×C113—21no—
180C22×C113—21no—
181C22×C113—21no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113—41no—
188C22×C113—41no—
189C22×C113—41no—
190C22×C113—84no—
191C22×C113C22×D411yescharacteristic
192C2×D113—21no—
193C2×D113—21no—
194C2×D113—41no—
195C2×D113—41no—
196C2×D113—41no—
197C2×D113—84no—
198C2×D113AGL(1,ℤ/8)12yescomplemented
199C4×C113—22no—
200C4×C113—21no—
201C4×C113C22×D411yescharacteristic
202C4×C113H(5,𝔽2)11yescharacteristic
203Dic113—21no—
204Dic113—21no—
205Dic113—21no—
206Dic113—41no—
207Dic113—41no—
208Dic113—41no—
209C2×C113—42no—
210C2×C113—41no—
211C2×C113—81no—
212C2×C113—81no—
213C2×C113D4211yescharacteristic
214C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C113#57711yescharacteristic
216D113—22no—
217D113—81no—
218#3265—1131nomaximal, Sylow
219C113#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)D11311yescharacteristic, complemented
221C22×SD16—1131no—
222#548—1131no—
223D42—1131no—
224#496—1131no—
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×#41C2×D11311yescharacteristic, complemented
236C22×Q8—1131no—
237C22×D4—1131no—
238C22×D4—2261no—
239C22×D4C2×D11311yescharacteristic
240AGL(1,ℤ/8)—24no—
241C2×SD16—1131no—
242C2×SD16—1131no—
243C2×SD16—1131no—
244C2×SD16—1131no—
245C2×SD16—2264no—
246C2×SD16C2×D11311yescharacteristic
247C2×SD16C2×D11311yescharacteristic, complemented
248C2×D8—1131no—
249C2×D8C2×D11311yescharacteristic
250C2×D8C2×D11311yescharacteristic, complemented
251C2×M16C2×D11311yescharacteristic, complemented
252C22×C8—1131no—
253#127—1131no—
254#124—1131no—
255#124—2261no—
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#97—1131no—
280C24—21no—
281C24—2261no—
282#41—22no—
283#41—41no—
284C2×Q8—1131no—
285C2×Q8—4521no—
286C2×Q8—2261no—
287C2×Q8—2262no—
288C2×Q8C22×D11311yescharacteristic
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—1131no—
294C2×D4—1131no—
295C2×D4—4524no—
296C2×D4—4521no—
297C2×D4—2261no—
298C2×D4—2261no—
299C2×D4—2261no—
300C2×D4—2261no—
301C2×D4—2261no—
302C2×D4—2261no—
303C2×D4—2262no—
304C2×D4C22×D11311yescharacteristic
305C2×D4C22×D11311yescharacteristic
306C2×D4C22×D11311yescharacteristic
307C22×C4—21no—
308C22×C4—1131no—
309C22×C4—2261no—
310C22×C4—2261no—
311C22×C4C22×D11311yescharacteristic
312SD16—22no—
313SD16—4521no—
314SD16—2262no—
315SD16—2262no—
316SD16—2262no—
317SD16C22⋊D11314yescomplemented
318D8—22no—
319D8—22no—
320D8—4521no—
321M16—22no—
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—1131no—
333C22⋊C4—1131no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C22⋊C4—2261no—
337C22⋊C4—2261no—
338C22⋊C4—2261no—
339C22⋊C4—2261no—
340C22⋊C4—2261no—
341C42—1131no—
342C42—2261no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—1131no—
350C23—9041no—
351C23—4522no—
352C23—4522no—
353C23—2261no—
354C23D4×D11311yescharacteristic
355Q8—21no—
356Q8—4522no—
357Q8—2261no—
358Q8—2261no—
359Q8C2×C22⋊D11312yescomplemented
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—42no—
366D4—42no—
367D4—9041no—
368D4—4522no—
369D4—4522no—
370D4—4522no—
371D4—4522no—
372D4—4522no—
373D4—2262no—
374D4—2261no—
375D4—2261no—
376D4C2×C22⋊D11312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—1131no—
382C2×C4—1131no—
383C2×C4—1131no—
384C2×C4—4522no—
385C2×C4—4522no—
386C2×C4—2261no—
387C2×C4—2261no—
388C2×C4—2261no—
389C2×C4—2261no—
390C2×C4—2261no—
391C2×C4D4×D11311yescharacteristic
392C2×C4C23×D11311yescharacteristic
393C8—21no—
394C8—2261no—
395C8—2261no—
396C8C2×C22⋊D11312yescomplemented
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—84no—
410C22—1132no—
411C22—9044no—
412C22—4521no—
413C22—4521no—
414C22—4521no—
415C22—2261no—
416C22—2261no—
417C22C2×D4×D11311yescharacteristic
418C4—21no—
419C4—22no—
420C4—4521no—
421C4—4521no—
422C4—4521no—
423C4—2261no—
424C4—2261no—
425C4—2261no—
426C4C22×C22⋊D11311yescharacteristic
427C4#1681366711yescharacteristic
428C2—41no—
429C2—42no—
430C2—81no—
431C2—81no—
432C2—9041no—
433C2—2262no—
434C2D4×C22⋊D11311yescharacteristic
435C2AGL(1,ℤ/8)×D11311yescharacteristic
436C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×AGL(1,ℤ/8)×C113C2
socleC22×C113C22×D4
hypercenterC2×AGL(1,ℤ/8)D113
hypocenterC113#3265
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D113C2semidirect
2. #20299255C2semidirect
3. D4×C22⋊D113C2semidirect
4. #20298986C2semidirect
5. #20298844C2semidirect
6. #20298831C2semidirect
7. #20298811C2semidirect
8. #20298796C2semidirect
9. #20298749C2semidirect
10. #20298743C2semidirect
11. #20298735C2semidirect
12. #20298730C2semidirect
13. #20298699C2semidirect
14. #20298667C2semidirect
15. C2×AGL(1,ℤ/8)×C113C2semidirect
16. C2×Q8×D113C22semidirect
19. C2×#14268636C22semidirect
21. C2×#14268635C22semidirect
22. C2×#14268634C22semidirect
24. C2×#14268632C22semidirect
25. C2×C8×D113C22semidirect
28. #16813609C22semidirect
30. #16813601C22semidirect
35. #16813593C22semidirect
38. Q8×Dic113C22semidirect
42. #16813556C22semidirect
43. #16813551C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813544C22semidirect
48. #16813543C22semidirect
49. #16813543C22semidirect
50. C22⋊#11744751C22semidirect
51. #16813534C22semidirect
52. #16813532C22semidirect
53. C2×#41×C113C22semidirect
57. C2×SD16×C113C22semidirect
59. C2×D8×C113C22semidirect
60. C2×M16×C113C22semidirect
118. SD16×C113D4semidirect
137. Q8×C113C2×D4semidirect
175. C8×C113C2×D4semidirect
198. C2×D113AGL(1,ℤ/8)semidirect
219. C113#3265semidirect
220. C2×AGL(1,ℤ/8)D113semidirect
235. C2×#41C2×D113semidirect
247. C2×SD16C2×D113semidirect
250. C2×D8C2×D113semidirect
251. C2×M16C2×D113semidirect
317. SD16C22⋊D113semidirect
359. Q8C2×C22⋊D113semidirect
396. C8C2×C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1132
#202992552
D4×C22⋊D1132
#202989862
#202988442
#202988312
#202988112
#202987962
#202987492
#202987432
#202987352
#202987302
#202986992
#202986672
C2×AGL(1,ℤ/8)×C1132
#3265113