Finite Group Databasebeta

← #28402064

Subgroups — #28402064

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×#16813649C211yesmaximal, characteristic, complemented
2C2×SD16×D113C211yesmaximal, characteristic, complemented
3#20299260C211yesmaximal, characteristic, complemented
4#20299233C211yesmaximal, characteristic, complemented
5#20298985C211yesmaximal, characteristic, complemented
6#20298843C211yesmaximal, characteristic, complemented
7#20298833C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298750C211yesmaximal, characteristic, complemented
10#20298742C211yesmaximal, characteristic, complemented
11#20298735C211yesmaximal, characteristic, complemented
12#20298733C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#20298668C211yesmaximal, characteristic, complemented
15#460×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic, complemented
17C2×Q8×D113C2211yescharacteristic, complemented
18C2×D4×D113—21no—
19C2×D4×D113C2211yescharacteristic
20C2×D4×D113C2211yescharacteristic
21#16813649—24no—
22C2×#14268636C2211yescharacteristic
23C2×#14268635C2211yescharacteristic, complemented
24C2×#14268635C2211yescharacteristic, complemented
25C2×#14268634C2211yescharacteristic
26SD16×D113—24no—
27C2×D904C2211yescharacteristic
28C2×#14268632C2211yescharacteristic, complemented
29C2×#14268632C2211yescharacteristic, complemented
30C2×#14268630C2211yescharacteristic, complemented
31C2×C8×D113C2211yescharacteristic, complemented
32#16813610—21no—
33#16813610C2211yescharacteristic, complemented
34#16813602—21no—
35#16813602C2211yescharacteristic, complemented
36#16813597—21no—
37#16813597C2211yescharacteristic, complemented
38#16813593—21no—
39#16813593C2211yescharacteristic
40#16813593C2211yescharacteristic
41#16813590—21no—
42#16813590—21no—
43C4×D452—21no—
44C4×D452C2211yescharacteristic
45C4×D452C2211yescharacteristic
46#16813555C2211yescharacteristic, complemented
47#16813547C2211yescharacteristic, complemented
48#16813546C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813542C2211yescharacteristic
51#16813534C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53#16813533C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×SD16×C113C2211yescharacteristic, complemented
56#127×C113C2211yescharacteristic
57C4×Q8×C113C2211yescharacteristic, complemented
58C4⋊C8×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63#14268648—22no—
64#14268648—41no—
65C2×Dic226—21no—
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—41no—
69C2×D452—21no—
70C2×D452—21no—
71C2×D452D411yescharacteristic
72C2×D452C2311yescharacteristic
73C2×D452C2311yescharacteristic
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77C2×C22⋊D113—21no—
78D4×D113—22no—
79D4×D113—22no—
80D4×D113—41no—
81D4×D113—41no—
82D4×D113—44no—
83C2×C4×D113—21no—
84C2×C4×D113—21no—
85C2×C4×D113—21no—
86C2×C4×D113C2311yescharacteristic
87C2×C4×D113C2311yescharacteristic
88#14268636—22no—
89#14268635—22no—
90#14268635—41no—
91#14268634D414yescomplemented
92D904—22no—
93#14268632—22no—
94#14268632—41no—
95#14268630—22no—
96C2×#11744751C2311yescharacteristic
97C2×#11744751C2311yescharacteristic
98C8×D113—22no—
99C4⋊Dic113—21no—
100C4⋊Dic113D411yescharacteristic
101C4⋊Dic113C2311yescharacteristic
102C22⋊Dic113—21no—
103C22⋊Dic113—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109#14268624D411yescharacteristic
110#14268624D411yescharacteristic
111C2×Q8×C113C2311yescharacteristic
112C2×D4×C113—21no—
113C2×D4×C113—21no—
114C2×D4×C113C2311yescharacteristic
115C2×D4×C113C2311yescharacteristic
116SD16×C113—22no—
117SD16×C113—22no—
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C4⋊C4×C113—21no—
121C4⋊C4×C113C2311yescharacteristic
122C42×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×C113C2×D412yescomplemented
138D4×C113—21no—
139D4×C113—21no—
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—42no—
143D4×C113—81no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113C2×D411yescharacteristic
147C2×C4×C113C2×D411yescharacteristic
148C2×C4×C113C2411yescharacteristic
149C22⋊D113—42no—
150C22⋊D113—42no—
151C22⋊D113—42no—
152C22⋊D113—42no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113C2×D411yescharacteristic
156C2×Dic113C2×D411yescharacteristic
157D452—22no—
158D452—21no—
159D452—21no—
160D452—21no—
161D452—42no—
162D452—42no—
163D452C2×D412yes—
164C4×D113—21no—
165C4×D113—21no—
166C4×D113—21no—
167C4×D113—21no—
168C4×D113—42no—
169C4×D113—42no—
170C4×D113—42no—
171Dic226—21no—
172Dic226—21no—
173Dic226—42no—
174C8×C113—21no—
175C8×C113—21no—
176#11744751—21no—
177#11744751C2×D412yescomplemented
178C22×C113—41no—
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—22no—
189C2×D113—21no—
190C2×D113—21no—
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—22no—
200C4×C113—21no—
201C4×C113—21no—
202C4×C113—41no—
203C4×C113C22×D411yescharacteristic
204C4×C113H(5,𝔽2)11yescharacteristic
205Dic113—21no—
206Dic113—21no—
207Dic113—41no—
208Dic113—41no—
209C2×C113—81no—
210C2×C113—81no—
211C2×C113D4211yescharacteristic
212C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C113#57711yescharacteristic
214D113—22no—
215D113—41no—
216D113—42no—
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#463—1131no—
228#460D11311yescharacteristic, complemented
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×D8—1131no—
250C2×D8—1131no—
251C2×M16—1131no—
252C22×C8—1131no—
253#127C2×D11311yescharacteristic
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×Q8C2×D11311yescharacteristic, complemented
266C4×D4—1131no—
267C4×D4—1131no—
268C4×D4—2261no—
269#107—1131no—
270C4⋊C8C2×D11311yescharacteristic, complemented
271#103—1131no—
272#103—1131no—
273#102—1131no—
274#102—1131no—
275#102C2×D11311yescharacteristic, complemented
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—21no—
290C2×D4—21no—
291C2×D4—1131no—
292C2×D4—1131no—
293C2×D4—1131no—
294C2×D4—4524no—
295C2×D4—4521no—
296C2×D4—4521no—
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—1131no—
308C22×C4—1131no—
309C22×C4—2261no—
310C22×C4—2261no—
311C22×C4—2261no—
312SD16—22no—
313SD16—22no—
314SD16—1134no—
315SD16—4521no—
316SD16—2262no—
317SD16—2262no—
318D8—4521no—
319D8—2262no—
320D8—2262no—
321M16—2262no—
322C2×C8—1131no—
323C2×C8—1131no—
324C2×C8—2262no—
325C2×C8C22×D11311yescharacteristic
326C2×C8C22×D11311yescharacteristic
327C4⋊C4—21no—
328C4⋊C4—1131no—
329C4⋊C4—1131no—
330C4⋊C4—2261no—
331C4⋊C4C22×D11311yescharacteristic
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—21no—
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—4522no—
357Q8—2261no—
358Q8—2261no—
359Q8D4×D11312yescomplemented
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—42no—
365D4—81no—
366D4—1132no—
367D4—4522no—
368D4—4522no—
369D4—4522no—
370D4—4522no—
371D4—4522no—
372D4—4522no—
373D4—2262no—
374D4—2261no—
375D4—2261no—
376D4—2261no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—1131no—
380C2×C4—1131no—
381C2×C4—4522no—
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—41no—
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—2261no—
412C22—2261no—
413C22—2261no—
414C22—2262no—
415C22—2261no—
416C22—2261no—
417C22C2×D4×D11311yescharacteristic
418C4—21no—
419C4—21no—
420C4—22no—
421C4—41no—
422C4—4521no—
423C4—4521no—
424C4—2261no—
425C4—2261no—
426C4C2×D4×D11311yescharacteristic
427C4#1681366811yescharacteristic
428C2—81no—
429C2—81no—
430C2—9041no—
431C2—4522no—
432C2—4521no—
433C2—2262no—
434C2#2029923211yescharacteristic
435C2AGL(1,ℤ/8)×D11311yescharacteristic
436C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#460×C113C2
socleC22×C113C22×D4
hypercenter#460D113
hypocenterC113#3265
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. C2×SD16×D113C2semidirect
3. #20299260C2semidirect
4. #20299233C2semidirect
5. #20298985C2semidirect
6. #20298843C2semidirect
7. #20298833C2semidirect
8. #20298814C2semidirect
9. #20298750C2semidirect
10. #20298742C2semidirect
11. #20298735C2semidirect
12. #20298733C2semidirect
13. #20298696C2semidirect
14. #20298668C2semidirect
15. #460×C113C2semidirect
16. C2×#14268648C22semidirect
17. C2×Q8×D113C22semidirect
23. C2×#14268635C22semidirect
24. C2×#14268635C22semidirect
28. C2×#14268632C22semidirect
29. C2×#14268632C22semidirect
30. C2×#14268630C22semidirect
31. C2×C8×D113C22semidirect
33. #16813610C22semidirect
35. #16813602C22semidirect
37. #16813597C22semidirect
46. #16813555C22semidirect
47. #16813547C22semidirect
48. #16813546C22semidirect
49. #16813544C22semidirect
51. #16813534C22semidirect
52. #16813534C22semidirect
53. #16813533C22semidirect
54. C2×SD16×C113C22semidirect
55. C2×SD16×C113C22semidirect
57. C4×Q8×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #102×C113C22semidirect
60. #102×C113C22semidirect
91. #14268634D4semidirect
137. Q8×C113C2×D4semidirect
177. #11744751C2×D4semidirect
198. C2×D113AGL(1,ℤ/8)semidirect
219. C113#3265semidirect
228. #460D113semidirect
246. C2×SD16C2×D113semidirect
247. C2×SD16C2×D113semidirect
265. C4×Q8C2×D113semidirect
270. C4⋊C8C2×D113semidirect
275. #102C2×D113semidirect
276. #102C2×D113semidirect
359. Q8D4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C2×SD16×D1132
#202992602
#202992332
#202989852
#202988432
#202988332
#202988142
#202987502
#202987422
#202987352
#202987332
#202986962
#202986682
#460×C1132
#3265113