Finite Group Databasebeta

← #28402209

Subgroups — #28402209

Order 14464.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813651C211yesmaximal, characteristic, complemented
2C2×#16813648C211yesmaximal, characteristic, complemented
3#20299258C211yesmaximal, characteristic, complemented
4#20299242C211yesmaximal, characteristic, complemented
5#20298979C211yesmaximal, characteristic, complemented
6#20298854C211yesmaximal, characteristic, complemented
7#20298850C211yesmaximal, characteristic, complemented
8#20298819C211yesmaximal, characteristic, complemented
9#20298815C211yesmaximal, characteristic, complemented
10#20298762C211yesmaximal, characteristic, complemented
11#20298744C211yesmaximal, characteristic, complemented
12#20298735C211yesmaximal, characteristic, complemented
13#20298689C211yesmaximal, characteristic, complemented
14#20298673C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic, complemented
19#16813651—24no—
20#16813648—24no—
21C2×Dic452C2211yescharacteristic, complemented
22C2×#14268637C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic, complemented
24C2×#14268635C2211yescharacteristic
25C2×#14268635C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic
28C2×#14268631C2211yescharacteristic
29C2×#14268630C2211yescharacteristic, complemented
30#16813611C2211yescharacteristic, complemented
31#16813609C2211yescharacteristic
32#16813608—21no—
33#16813603—21no—
34#16813601C2211yescharacteristic
35#16813600—21no—
36#16813597C2211yescharacteristic, complemented
37#16813595—21no—
38#16813594—21no—
39#16813593C2211yescharacteristic
40#16813591—21no—
41#16813587C2211yescharacteristic, complemented
42D4×Dic113C2211yescharacteristic
43#16813584—21no—
44C4×C22⋊D113C2211yescharacteristic
45C2×C22⋊Dic113—21no—
46#16813553C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813546C2211yescharacteristic, complemented
50#16813545C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53C8×Dic113C2211yescharacteristic, complemented
54C22×D4×C113C2211yescharacteristic
55C2×SD16×C113C2211yescharacteristic
56C2×SD16×C113C2211yescharacteristic
57C22⋊Q8×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#102×C113C2211yescharacteristic
60C22⋊C8×C113C2211yescharacteristic
61#14268647—22no—
62#14268647—41no—
63#14268646—22no—
64#14268646—41no—
65C2×Dic226—21no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68Q8×D113—22no—
69Q8×D113—41no—
70C2×D452—21no—
71C2×D452C2311yescharacteristic
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113D411yescharacteristic
76C22×Dic113—21no—
77C22×Dic113—21no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113C2311yescharacteristic
81Dic452—22no—
82#14268637—22no—
83#14268636—41no—
84#14268635—22no—
85#14268635D414yescomplemented
86#14268632—22no—
87#14268632—22no—
88#14268631—22no—
89#14268630—22no—
90C2×#11744751C2311yescharacteristic
91C2×#11744751C2311yescharacteristic
92C4⋊Dic113C2311yescharacteristic
93#14268626—21no—
94#14268626—21no—
95#14268626D411yescharacteristic
96C22⋊Dic113—21no—
97C22⋊Dic113—21no—
98C22⋊Dic113—21no—
99C22⋊Dic113—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113D411yescharacteristic
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624D411yescharacteristic
106C4×Dic113—21no—
107C4×Dic113C2311yescharacteristic
108C24×C113—21no—
109C2×Q8×C113C2311yescharacteristic
110C2×D4×C113—22no—
111C2×D4×C113—21no—
112C2×D4×C113—41no—
113C2×D4×C113C2311yescharacteristic
114C2×D4×C113C2311yescharacteristic
115C22×C4×C113C2311yescharacteristic
116SD16×C113—22no—
117SD16×C113—41no—
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C4⋊C4×C113—21no—
121C4⋊C4×C113C2311yescharacteristic
122C22⋊C4×C113—21no—
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—42no—
126C23×C113—42no—
127C23×C113—81no—
128C23×C113C2×D411yescharacteristic
129C22×D113—21no—
130C22×D113C2×D411yescharacteristic
131Q8×C113—21no—
132Q8×C113—21no—
133D4×C113—21no—
134D4×C113—21no—
135D4×C113—21no—
136D4×C113—42no—
137D4×C113C2×D412yes—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2411yescharacteristic
144C22⋊D113—41no—
145C22⋊D113—42no—
146C22⋊D113—42no—
147C22⋊D113—81no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—21no—
151C2×Dic113—42no—
152C2×Dic113—81no—
153C2×Dic113C2×D411yescharacteristic
154C2×Dic113C2×D411yescharacteristic
155C2×Dic113C2×D411yescharacteristic
156D452—21no—
157D452—21no—
158D452—42no—
159C4×D113—21no—
160C4×D113—21no—
161C4×D113—42no—
162C4×D113—42no—
163Dic226—21no—
164Dic226—21no—
165Dic226—21no—
166Dic226—42no—
167Dic226C2×D412yes—
168C8×C113—21no—
169C8×C113—21no—
170#11744751—21no—
171#11744751C2×D412yes—
172C22×C113—22no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—21no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113—84no—
182C22×C113C22×D411yescharacteristic
183C2×D113—21no—
184C2×D113—21no—
185C2×D113—21no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—41no—
189C4×C113—21no—
190C4×C113—41no—
191C4×C113—41no—
192C4×C113C22×D411yescharacteristic
193C4×C113H(5,𝔽2)11yescharacteristic
194Dic113—22no—
195Dic113—21no—
196Dic113—21no—
197Dic113—21no—
198Dic113—41no—
199Dic113—41no—
200C2×C113—41no—
201C2×C113—42no—
202C2×C113—81no—
203C2×C113D4211yescharacteristic
204C2×C113#57511yescharacteristic
205C2×C113#57711yescharacteristic
206D113—41no—
207D113—81no—
208#3275—1131nomaximal, Sylow
209C113#327511yescharacteristic, complemented, Sylow
210C2×#137—1131no—
211C2×AGL(1,ℤ/8)—1131no—
212#548—1131no—
213#546—1131no—
214#495—1131no—
215#470—1131no—
216#469—1131no—
217#464—1131no—
218#463—1131no—
219#452—1131no—
220#450D11311yescharacteristic, complemented
221#449—1131no—
222#448—1131no—
223C4×SD16—1131no—
224#436—1131no—
225C2×#41—1131no—
226C2×#41—1131no—
227C22×Q8—1131no—
228C22×D4C2×D11311yescharacteristic
229#137—2264no—
230AGL(1,ℤ/8)—2264no—
231C2×Q16—1131no—
232C2×Q16—1131no—
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16—1131no—
236C2×SD16C2×D11311yescharacteristic
237C2×SD16C2×D11311yescharacteristic
238C2×D8—1131no—
239C2×D8—1131no—
240C2×M16—1131no—
241C2×M16—1131no—
242#124—1131no—
243#124—1131no—
244#124—2261no—
245#123—2261no—
246C22⋊Q8—1131no—
247C22⋊Q8—2261no—
248C22⋊Q8C2×D11311yescharacteristic
249#121—1131no—
250#121—1131no—
251#121—2261no—
252#121—2261no—
253#120—2261no—
254C4×Q8—1131no—
255C4×D4—1131no—
256C4×D4—1131no—
257C4×D4—2261no—
258C2×C22⋊C4—2261no—
259#106—1131no—
260C4⋊C8—1131no—
261#103—1131no—
262#103—1131no—
263#103—1131no—
264#102—1131no—
265#102C2×D11311yescharacteristic
266#102C2×D11311yescharacteristic
267C22⋊C8—1131no—
268C22⋊C8C2×D11311yescharacteristic
269C4×C8—1131no—
270C24—21no—
271#41—4521no—
272#41—4521no—
273#41—2262no—
274#41—2262no—
275C2×Q8—1131no—
276C2×Q8—1131no—
277C2×Q8—4521no—
278C2×Q8—2261no—
279C2×Q8—2262no—
280C2×Q8C22×D11311yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—1131no—
285C2×D4—1131no—
286C2×D4—2261no—
287C2×D4—2261no—
288C2×D4—2261no—
289C2×D4—2261no—
290C2×D4C22×D11311yescharacteristic
291C2×D4C22×D11311yescharacteristic
292C22×C4—1131no—
293C22×C4—2261no—
294C22×C4—2261no—
295C22×C4—2261no—
296C22×C4—2261no—
297C22×C4C22×D11311yescharacteristic
298Q16—2262no—
299Q16—2262no—
300SD16—22no—
301SD16—41no—
302SD16—1134no—
303SD16—4521no—
304SD16—2262no—
305D8—2262no—
306D8—2262no—
307M16—2262no—
308M16—2262no—
309C2×C8—1131no—
310C2×C8—1131no—
311C2×C8C22×D11311yescharacteristic
312C2×C8C22×D11311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—1131no—
315C4⋊C4—1131no—
316C4⋊C4—2261no—
317C4⋊C4—2261no—
318C4⋊C4C22×D11311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—1131no—
321C22⋊C4—1131no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C22⋊C4—2261no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C22⋊C4—2261no—
330C42—1131no—
331C42—2261no—
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—1131no—
338C23—2261no—
339C23D4×D11311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—1132no—
343Q8—4522no—
344Q8—2261no—
345Q8—2261no—
346Q8—2261no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—9041no—
352D4—4522no—
353D4—4522no—
354D4—4522no—
355D4—4521no—
356D4—2261no—
357D4—2261no—
358D4D4×D11312yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—1131no—
364C2×C4—1131no—
365C2×C4—1131no—
366C2×C4—9041no—
367C2×C4—4522no—
368C2×C4—4522no—
369C2×C4—4522no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4—2261no—
373C2×C4—2261no—
374C2×C4—2261no—
375C2×C4D4×D11311yescharacteristic
376C2×C4C23×D11311yescharacteristic
377C8—21no—
378C8—21no—
379C8—1132no—
380C8—2261no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—4521no—
392C22—4521no—
393C22—4521no—
394C22—2261no—
395C22—2261no—
396C22—2261no—
397C22C2×D4×D11311yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—4521no—
402C4—4521no—
403C4—2261no—
404C4—2261no—
405C4—2261no—
406C4—2262no—
407C4C2×D4×D11311yescharacteristic
408C4#1681366711yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—9041no—
413C2—4521no—
414C2#2029923011yescharacteristic
415C2#2029939411yescharacteristic
416C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
hypercenter#450D113
hypocenterC113#3275
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#16813651C2semidirect
2. C2×#16813648C2semidirect
3. #20299258C2semidirect
4. #20299242C2semidirect
5. #20298979C2semidirect
6. #20298854C2semidirect
7. #20298850C2semidirect
8. #20298819C2semidirect
9. #20298815C2semidirect
10. #20298762C2semidirect
11. #20298744C2semidirect
12. #20298735C2semidirect
13. #20298689C2semidirect
14. #20298673C2semidirect
15. #450×C113C2semidirect
18. C2×Q8×D113C22semidirect
21. C2×Dic452C22semidirect
22. C2×#14268637C22semidirect
23. C2×#14268636C22semidirect
29. C2×#14268630C22semidirect
30. #16813611C22semidirect
36. #16813597C22semidirect
41. #16813587C22semidirect
46. #16813553C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
49. #16813546C22semidirect
50. #16813545C22semidirect
51. #16813544C22semidirect
52. #16813534C22semidirect
53. C8×Dic113C22semidirect
85. #14268635D4semidirect
209. C113#3275semidirect
220. #450D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
C2×#168136482
#202992582
#202992422
#202989792
#202988542
#202988502
#202988192
#202988152
#202987622
#202987442
#202987352
#202986892
#202986732
#450×C1132
#3275113