Finite Group Databasebeta

← #28401035

Subgroups — #28401035

Order 14464.

572 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813654C211yesmaximal, characteristic, complemented
2C2×#16813651C211yesmaximal, characteristic, complemented
3C2×#16813649C211yesmaximal, characteristic, complemented
4C2×#16813646C211yesmaximal, characteristic, complemented
5#20299147C211yesmaximal, characteristic, complemented
6#124×D113C211yesmaximal, characteristic, complemented
7#20298991C211yesmaximal, characteristic, complemented
8#20298989C211yesmaximal, characteristic, complemented
9#20298986C211yesmaximal, characteristic, complemented
10#20298984C211yesmaximal, characteristic, complemented
11#20298982C211yesmaximal, characteristic, complemented
12#20298980C211yesmaximal, characteristic, complemented
13#20298980C211yesmaximal, characteristic, complemented
14C4×#14268630C211yesmaximal, characteristic, complemented
15#495×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic
20#16813654—24no—
21#16813651—24no—
22#16813649—24no—
23#16813646—24no—
24C2×Dic452C2211yescharacteristic, complemented
25C2×#14268637C2211yescharacteristic, complemented
26C2×#14268637C2211yescharacteristic, complemented
27C2×#14268636C2211yescharacteristic
28C2×#14268636C2211yescharacteristic, complemented
29C2×#14268635C2211yescharacteristic
30C2×#14268635C2211yescharacteristic, complemented
31C2×#14268634C2211yescharacteristic
32C2×#14268634C2211yescharacteristic, complemented
33C2×D904C2211yescharacteristic
34C2×#14268632C2211yescharacteristic
35C2×#14268632C2211yescharacteristic
36C2×#14268630C2211yescharacteristic
37C2×#14268630C2211yescharacteristic
38#16813620C2211yescharacteristic, complemented
39#16813618C2211yescharacteristic, complemented
40#16813611C2211yescharacteristic
41#16813610C2211yescharacteristic
42#16813610C2211yescharacteristic, complemented
43#16813609C2211yescharacteristic
44#16813608—22no—
45#16813595—22no—
46#16813582—22no—
47C22⋊C4×D113—22no—
48C42×D113C2211yescharacteristic
49#16813532C2211yescharacteristic, complemented
50#16813532C2211yescharacteristic, complemented
51C4×#11744751C2211yescharacteristic, complemented
52C2×Q16×C113C2211yescharacteristic, complemented
53C2×SD16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic
57#124×C113C2211yescharacteristic, complemented
58C4×C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268648—22no—
61#14268648—22no—
62#14268646—22no—
63#14268646—22no—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—22no—
69C2×D452—21no—
70C2×D452C2311yescharacteristic
71C2×D452C2311yescharacteristic
72C2×C22⋊D113—21no—
73C2×C22⋊D113—22no—
74C2×C22⋊D113—21no—
75D4×D113—22no—
76D4×D113—22no—
77C22×Dic113—21no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113D412yes—
81C2×C4×D113C2311yescharacteristic
82Dic452—22no—
83#14268637—22no—
84#14268637—22no—
85#14268636—22no—
86#14268636—22no—
87#14268635—22no—
88#14268635—22no—
89#14268634—22no—
90#14268634—22no—
91D904—22no—
92#14268632—22no—
93#14268632—22no—
94#14268630D414yescomplemented
95#14268630D414yescomplemented
96C2×#11744751C2311yescharacteristic
97C2×#11744751C2311yescharacteristic
98#14268626—22no—
99C22⋊Dic113—22no—
100#14268624—22no—
101#14268624—22no—
102#14268624—22no—
103C4×Dic113D412yes—
104C4×Dic113C2311yescharacteristic
105C2×Q8×C113C2311yescharacteristic
106C2×Q8×C113C2311yescharacteristic
107C2×D4×C113C2311yescharacteristic
108C2×D4×C113C2311yescharacteristic
109Q16×C113—22no—
110SD16×C113—22no—
111SD16×C113—22no—
112D8×C113—22no—
113C2×C8×C113C2311yescharacteristic
114C2×C8×C113C2311yescharacteristic
115C22⋊C4×C113—22no—
116C22⋊C4×C113—22no—
117C42×C113C2311yescharacteristic
118C23×C113—21no—
119C23×C113—21no—
120C22×D113—21no—
121C22×D113—21no—
122C22×D113—44no—
123C22×D113—42no—
124C22×D113C2×D411yescharacteristic
125Q8×C113—21no—
126Q8×C113—21no—
127Q8×C113—21no—
128Q8×C113—21no—
129D4×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113C2×D412yes—
136C2×C4×C113C2411yescharacteristic
137C22⋊D113—44no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—42no—
143C2×Dic113C2×D412yes—
144C2×Dic113C2×D411yescharacteristic
145D452—21no—
146D452—21no—
147D452—21no—
148D452—21no—
149D452—42no—
150C4×D113—42no—
151C4×D113—42no—
152C4×D113—42no—
153C4×D113C2×D412yes—
154C4×D113C2×D412yes—
155Dic226—21no—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—42no—
160C8×C113C2×D412yes—
161C8×C113C2×D412yes—
162#11744751C2×D412yes—
163#11744751C2×D412yes—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—42no—
167C22×C113—42no—
168C22×C113C22×D411yescharacteristic
169C2×D113—22no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—42no—
173C2×D113—42no—
174C2×D113—84no—
175C2×D113#12712yes—
176C4×C113—22no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113C22×D411yescharacteristic
180C4×C113C22×D411yescharacteristic
181Dic113—22no—
182Dic113—41no—
183Dic113—41no—
184Dic113#12712yes—
185C2×C113—81no—
186C2×C113—81no—
187C2×C113C2×#12711yescharacteristic
188C2×C113#57512yes—
189D113—22no—
190D113—81no—
191D113—81no—
192#3153—1131nomaximal, Sylow
193C113#315311yescharacteristic, complemented, Sylow
194C2×#137—1131no—
195C2×#137—1131no—
196C2×AGL(1,ℤ/8)—1131no—
197C2×AGL(1,ℤ/8)—1131no—
198#532—1131no—
199C2×#124—1131no—
200#497—1131no—
201#497—1131no—
202#496—1131no—
203#496—1131no—
204#495—1131no—
205#495—1131no—
206#495—1131no—
207#495D11311yescharacteristic, complemented
208C4×M16—1131no—
209C2×#41—1131no—
210C2×#41—1131no—
211C22×Q8—1131no—
212C22×D4—1131no—
213#137—2264no—
214#137—2264no—
215AGL(1,ℤ/8)—2264no—
216AGL(1,ℤ/8)—2264no—
217C2×Q16—1131no—
218C2×Q16—1131no—
219C2×Q16—1131no—
220C2×Q16C2×D11311yescharacteristic, complemented
221C2×SD16—1131no—
222C2×SD16—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×SD16—1131no—
226C2×SD16—1131no—
227C2×SD16C2×D11311yescharacteristic
228C2×SD16C2×D11311yescharacteristic, complemented
229C2×D8—1131no—
230C2×D8—1131no—
231C2×D8—1131no—
232C2×D8C2×D11311yescharacteristic
233C2×M16—1131no—
234C2×M16—1131no—
235C4⋊Q8—1131no—
236#127—1131no—
237#124—1131no—
238#124—1131no—
239#124—1131no—
240#124—1131no—
241#124—2262no—
242#124C2×D11311yescharacteristic
243#124C2×D11311yescharacteristic, complemented
244#121—2262no—
245C4×D4—2262no—
246C2×C22⋊C4—2262no—
247C2×C42—1131no—
248#97—1131no—
249#97—1131no—
250C4×C8—1131no—
251C4×C8C2×D11311yescharacteristic, complemented
252C24—2261no—
253#41—2262no—
254#41—2262no—
255#41—2262no—
256#41—2262no—
257C2×Q8—1131no—
258C2×Q8—1131no—
259C2×Q8—2261no—
260C2×Q8—2262no—
261C2×Q8—2262no—
262C2×Q8C22×D11311yescharacteristic
263C2×Q8C22×D11311yescharacteristic
264C2×D4—1131no—
265C2×D4—1131no—
266C2×D4—2261no—
267C2×D4—2262no—
268C2×D4—2262no—
269C2×D4—2262no—
270C2×D4—2261no—
271C2×D4—2261no—
272C2×D4C22×D11311yescharacteristic
273C2×D4C22×D11311yescharacteristic
274C22×C4—1131no—
275C22×C4—1132no—
276C22×C4—2261no—
277C22×C4—2261no—
278C22×C4—2261no—
279Q16—22no—
280Q16—2262no—
281Q16—2262no—
282Q16—2262no—
283SD16—22no—
284SD16—22no—
285SD16—2262no—
286SD16—2262no—
287SD16—2262no—
288SD16—2262no—
289SD16—2262no—
290SD16—2262no—
291D8—22no—
292D8—2262no—
293D8—2262no—
294D8—2262no—
295M16—1134no—
296M16—1134no—
297C2×C8—1131no—
298C2×C8—1131no—
299C2×C8C22×D11311yescharacteristic
300C2×C8C22×D11311yescharacteristic
301C4⋊C4—2262no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—2262no—
305C22⋊C4—2262no—
306C22⋊C4—2262no—
307C22⋊C4—2262no—
308C42—1132no—
309C42—1131no—
310C42C22×D11311yescharacteristic
311C23—21no—
312C23—21no—
313C23—1131no—
314C23—4522no—
315C23—4524no—
316C23—2261no—
317C23—2261no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—4522no—
323Q8—2261no—
324Q8—2261no—
325Q8—2261no—
326Q8—2261no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—4522no—
332D4—4522no—
333D4—4522no—
334D4—4524no—
335D4—2261no—
336D4—2261no—
337D4—2261no—
338D4—2261no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—1131no—
342C2×C4—1132no—
343C2×C4—1132no—
344C2×C4—1132no—
345C2×C4—4522no—
346C2×C4—4522no—
347C2×C4—4522no—
348C2×C4—4522no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4D4×D11312yes—
352C2×C4C23×D11311yescharacteristic
353C8—1132no—
354C8—1132no—
355C8D4×D11312yes—
356C8D4×D11312yes—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—42no—
361C22—1132no—
362C22—9044no—
363C22—4521no—
364C22—4521no—
365C22—4522no—
366C22—4522no—
367C22—2262no—
368C22C2×D4×D11311yescharacteristic
369C4—22no—
370C4—41no—
371C4—41no—
372C4—1132no—
373C4—4521no—
374C4—4521no—
375C4—2262no—
376C4C2×D4×D11311yescharacteristic
377C4C2×D4×D11311yescharacteristic
378C2—81no—
379C2—81no—
380C2—9041no—
381C2—9041no—
382C2—2262no—
383C2#127×D11311yescharacteristic
384C2#2029939512yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#495×C113C2
socleC22×C113C22×D4
hypercenter#495D113
hypocenterC113#3153
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#16813654C2semidirect
2. C2×#16813651C2semidirect
3. C2×#16813649C2semidirect
4. C2×#16813646C2semidirect
5. #20299147C2semidirect
6. #124×D113C2semidirect
7. #20298991C2semidirect
8. #20298989C2semidirect
9. #20298986C2semidirect
10. #20298984C2semidirect
11. #20298982C2semidirect
12. #20298980C2semidirect
13. #20298980C2semidirect
14. C4×#14268630C2semidirect
15. #495×C113C2semidirect
24. C2×Dic452C22semidirect
25. C2×#14268637C22semidirect
26. C2×#14268637C22semidirect
28. C2×#14268636C22semidirect
30. C2×#14268635C22semidirect
32. C2×#14268634C22semidirect
38. #16813620C22semidirect
39. #16813618C22semidirect
42. #16813610C22semidirect
49. #16813532C22semidirect
50. #16813532C22semidirect
51. C4×#11744751C22semidirect
52. C2×Q16×C113C22semidirect
54. C2×SD16×C113C22semidirect
57. #124×C113C22semidirect
58. C4×C8×C113C22semidirect
94. #14268630D4semidirect
95. #14268630D4semidirect
193. C113#3153semidirect
207. #495D113semidirect
220. C2×Q16C2×D113semidirect
228. C2×SD16C2×D113semidirect
243. #124C2×D113semidirect
251. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C2×#168136512
C2×#168136492
C2×#168136462
#202991472
#124×D1132
#202989912
#202989892
#202989862
#202989842
#202989822
#202989802
C4×#142686302
#495×C1132
#3153113