Finite Group Databasebeta

← #28402212

Subgroups — #28402212

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×#16813655C211yesmaximal, characteristic, complemented
2C2×#16813646C211yesmaximal, characteristic, complemented
3#20299254C211yesmaximal, characteristic, complemented
4#20299245C211yesmaximal, characteristic, complemented
5#20298981C211yesmaximal, characteristic, complemented
6#20298857C211yesmaximal, characteristic, complemented
7#20298819C211yesmaximal, characteristic, complemented
8#20298812C211yesmaximal, characteristic, complemented
9#20298761C211yesmaximal, characteristic, complemented
10#20298750C211yesmaximal, characteristic, complemented
11#20298741C211yesmaximal, characteristic, complemented
12#20298736C211yesmaximal, characteristic, complemented
13#20298685C211yesmaximal, characteristic, complemented
14#20298674C211yesmaximal, characteristic, complemented
15#469×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C22×Dic226C2211yescharacteristic, complemented
19C2×D4×D113C2211yescharacteristic
20#16813655—24no—
21#16813646—24no—
22C2×Dic452C2211yescharacteristic, complemented
23C2×Dic452C2211yescharacteristic, complemented
24C2×#14268636C2211yescharacteristic
25C2×#14268636C2211yescharacteristic
26C2×#14268635C2211yescharacteristic
27C2×#14268635C2211yescharacteristic
28C2×#14268635C2211yescharacteristic, complemented
29C2×#14268632C2211yescharacteristic
30C2×#14268630C2211yescharacteristic
31#16813609C2211yescharacteristic
32#16813609C2211yescharacteristic, complemented
33#16813608—21no—
34#16813604—21no—
35#16813602C2211yescharacteristic
36#16813602C2211yescharacteristic
37#16813599—21no—
38#16813594—21no—
39#16813593—21no—
40#16813590—21no—
41#16813587C2211yescharacteristic, complemented
42D4×Dic113—21no—
43#16813584C2211yescharacteristic
44C4×C22⋊D113C2211yescharacteristic
45C22⋊C4×D113—21no—
46#16813551C2211yescharacteristic, complemented
47#16813545C2211yescharacteristic, complemented
48#16813545C2211yescharacteristic, complemented
49#16813545C2211yescharacteristic, complemented
50#16813542C2211yescharacteristic
51C22⋊#11744751C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic
53C8×Dic113C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic
55C2×M16×C113C2211yescharacteristic, complemented
56#121×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic, complemented
58#106×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268647—22no—
63#14268647—41no—
64#14268646—22no—
65#14268646—41no—
66C2×Dic226—22no—
67C2×Dic226—21no—
68C2×Dic226—41no—
69C2×Dic226C2311yescharacteristic
70C2×Dic226C2311yescharacteristic
71C2×Dic226C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113D411yescharacteristic
77D4×D113—22no—
78D4×D113—41no—
79C22×Dic113—21no—
80C22×Dic113—21no—
81C2×C4×D113—21no—
82C2×C4×D113—21no—
83C2×C4×D113C2311yescharacteristic
84Dic452—22no—
85Dic452—22no—
86#14268636—22no—
87#14268636D414yescomplemented
88#14268635—22no—
89#14268635—41no—
90#14268635—41no—
91#14268632—22no—
92#14268630—22no—
93C2×#11744751C2311yescharacteristic
94C2×#11744751C2311yescharacteristic
95C4⋊Dic113—21no—
96C4⋊Dic113—21no—
97#14268626—21no—
98#14268626D411yescharacteristic
99C22⋊Dic113—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113—21no—
102C22⋊Dic113—21no—
103C22⋊Dic113D411yescharacteristic
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624D411yescharacteristic
108C4×Dic113—21no—
109C4×Dic113C2311yescharacteristic
110C2×D4×C113—21no—
111C2×D4×C113—21no—
112C2×D4×C113C2311yescharacteristic
113C2×D4×C113C2311yescharacteristic
114C22×C4×C113C2311yescharacteristic
115D8×C113—22no—
116M16×C113—22no—
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C4⋊C4×C113C2311yescharacteristic
120C4⋊C4×C113C2311yescharacteristic
121C22⋊C4×C113—21no—
122C22⋊C4×C113—21no—
123C23×C113—21no—
124C23×C113—21no—
125C23×C113C2×D411yescharacteristic
126C22×D113—21no—
127C22×D113—42no—
128C22×D113—42no—
129C22×D113—81no—
130C22×D113C2×D411yescharacteristic
131D4×C113—21no—
132D4×C113—21no—
133D4×C113—21no—
134D4×C113—21no—
135D4×C113—42no—
136D4×C113—81no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113C2×D411yescharacteristic
142C2×C4×C113C2411yescharacteristic
143C22⋊D113—41no—
144C22⋊D113—42no—
145C22⋊D113—42no—
146C22⋊D113—42no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—42no—
151C2×Dic113—42no—
152C2×Dic113C2×D411yescharacteristic
153C2×Dic113C2×D411yescharacteristic
154C2×Dic113C2×D411yescharacteristic
155D452—21no—
156D452C2×D412yes—
157C4×D113—21no—
158C4×D113—21no—
159C4×D113—42no—
160C4×D113—81no—
161Dic226—21no—
162Dic226—21no—
163Dic226—21no—
164Dic226—21no—
165Dic226—21no—
166Dic226—42no—
167Dic226C2×D412yes—
168C8×C113—21no—
169C8×C113C2×D412yes—
170#11744751—21no—
171#11744751—21no—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113C22×D411yescharacteristic
182C2×D113—21no—
183C2×D113—22no—
184C2×D113—21no—
185C2×D113—21no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—84no—
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—81no—
202C2×C113—81no—
203C2×C113D4211yescharacteristic
204C2×C113#57511yescharacteristic
205C2×C113#57711yescharacteristic
206D113—41no—
207D113—42no—
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#469D11311yescharacteristic, complemented
217#464—1131no—
218#463—1131no—
219#452—1131no—
220#450—1131no—
221#449—1131no—
222#448—1131no—
223C4×SD16—1131no—
224#436—1131no—
225C2×#41—1131no—
226C2×#41—1131no—
227C22×Q8—1131no—
228C22×D4—1131no—
229#137—2264no—
230AGL(1,ℤ/8)—2264no—
231C2×Q16—1131no—
232C2×Q16—1131no—
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16—1131no—
236C2×SD16—1131no—
237C2×SD16—1131no—
238C2×D8—1131no—
239C2×D8C2×D11311yescharacteristic
240C2×M16—1131no—
241C2×M16C2×D11311yescharacteristic, complemented
242#124—1131no—
243#124—1131no—
244#124—2261no—
245#123—2261no—
246C22⋊Q8—1131no—
247C22⋊Q8—1131no—
248C22⋊Q8—2261no—
249#121—2261no—
250#121—2261no—
251#121C2×D11311yescharacteristic
252#121C2×D11311yescharacteristic, complemented
253#120—2261no—
254C4×Q8—1131no—
255C4×D4—1131no—
256C4×D4—1131no—
257C4×D4—2261no—
258C2×C22⋊C4—2261no—
259#106C2×D11311yescharacteristic, complemented
260C4⋊C8—1131no—
261#103—1131no—
262#103—1131no—
263#103—1131no—
264#102—1131no—
265#102C2×D11311yescharacteristic
266#102C2×D11311yescharacteristic, complemented
267C22⋊C8—1131no—
268C22⋊C8—1131no—
269C4×C8—1131no—
270C24—2261no—
271#41—4521no—
272#41—4521no—
273#41—2262no—
274#41—2262no—
275C2×Q8—1131no—
276C2×Q8—1131no—
277C2×Q8—1131no—
278C2×Q8—4521no—
279C2×Q8—2262no—
280C2×Q8—2261no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—1131no—
284C2×D4—1131no—
285C2×D4—4521no—
286C2×D4—2261no—
287C2×D4—2262no—
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—1134no—
301SD16—4521no—
302SD16—4521no—
303SD16—2262no—
304SD16—2262no—
305D8—22no—
306D8—2262no—
307M16—22no—
308M16—2262no—
309C2×C8—1131no—
310C2×C8—1131no—
311C2×C8C22×D11311yescharacteristic
312C2×C8C22×D11311yescharacteristic
313C4⋊C4—1131no—
314C4⋊C4—2261no—
315C4⋊C4—2261no—
316C4⋊C4—2261no—
317C4⋊C4C22×D11311yescharacteristic
318C4⋊C4C22×D11311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—1131no—
322C22⋊C4—1131no—
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—1131no—
335C23—9041no—
336C23—4522no—
337C23—4522no—
338C23—2261no—
339C23D4×D11311yescharacteristic
340Q8—1132no—
341Q8—4522no—
342Q8—2261no—
343Q8—2261no—
344Q8—2261no—
345Q8—2261no—
346Q8—2261no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—1132no—
354D4—4522no—
355D4—4521no—
356D4—4522no—
357D4—4522no—
358D4—2261no—
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—2261no—
379C8—2261no—
380C8D4×D11312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—9044no—
391C22—4521no—
392C22—4521no—
393C22—2261no—
394C22—2261no—
395C22—2262no—
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#1681366811yescharacteristic
409C2—41no—
410C2—81no—
411C2—81no—
412C2—4521no—
413C2—4522no—
414C2#2029923211yescharacteristic
415C2#2029939411yescharacteristic
416C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#469×C113C2
socleC22×C113C22×D4
hypercenter#469D113
hypocenterC113#3275
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
2. C2×#16813646C2semidirect
3. #20299254C2semidirect
4. #20299245C2semidirect
5. #20298981C2semidirect
6. #20298857C2semidirect
7. #20298819C2semidirect
8. #20298812C2semidirect
9. #20298761C2semidirect
10. #20298750C2semidirect
11. #20298741C2semidirect
12. #20298736C2semidirect
13. #20298685C2semidirect
14. #20298674C2semidirect
15. #469×C113C2semidirect
18. C22×Dic226C22semidirect
22. C2×Dic452C22semidirect
23. C2×Dic452C22semidirect
28. C2×#14268635C22semidirect
32. #16813609C22semidirect
41. #16813587C22semidirect
46. #16813551C22semidirect
47. #16813545C22semidirect
48. #16813545C22semidirect
49. #16813545C22semidirect
51. C22⋊#11744751C22semidirect
53. C8×Dic113C22semidirect
55. C2×M16×C113C22semidirect
57. #121×C113C22semidirect
58. #106×C113C22semidirect
60. #102×C113C22semidirect
87. #14268636D4semidirect
209. C113#3275semidirect
216. #469D113semidirect
241. C2×M16C2×D113semidirect
252. #121C2×D113semidirect
259. #106C2×D113semidirect
266. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
C2×#168136462
#202992542
#202992452
#202989812
#202988572
#202988192
#202988122
#202987612
#202987502
#202987412
#202987362
#202986852
#202986742
#469×C1132
#3275113