Finite Group Databasebeta

← #28403901

Subgroups — #28403901

Order 14464.

1556 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D113C212yesmaximal, complemented
2#20299175C214yesmaximal, complemented
3#20299173C212yesmaximal, complemented
4#20299168C212yesmaximal, complemented
5#20299166C212yesmaximal, complemented
6#20299161C212yesmaximal, complemented
7#20299156C214yesmaximal, complemented
8#20299148C211yesmaximal, characteristic, complemented
9#20299144C212yesmaximal, complemented
10#20299107C218yesmaximal, complemented
11C2×#16813579C211yesmaximal, characteristic, complemented
12#532×C113C211yesmaximal, characteristic, complemented
13C2×#14268648C2212yes—
14C2×#14268647C2214yes—
15C2×#14268647C2212yescomplemented
16C2×#14268646C2212yes—
17C2×#14268646C2214yescomplemented
18#41×D113—216no—
19C2×Q8×D113C2212yescomplemented
20C2×D4×D113C2214yes—
21C2×D4×D113C2212yescomplemented
22C22×C4×D113C2211yescharacteristic
23C22×C4×D113C2214yescomplemented
24#16813622C2211yescharacteristic, complemented
25#16813620C2212yescomplemented
26#16813619C2211yescharacteristic, complemented
27#16813618C2212yescomplemented
28#16813611C2212yescomplemented
29#16813610C2212yescomplemented
30#16813609C2212yescomplemented
31#16813607C2218yescomplemented
32#16813604C2218yescomplemented
33#16813600C2218yescomplemented
34#16813599C2218yescomplemented
35#16813596C2214yescomplemented
36#16813595C2218yescomplemented
37#16813594C2218yescomplemented
38#16813594C2218yescomplemented
39#16813592C2218yescomplemented
40#16813590C2218yescomplemented
41C4×D452C2214yescomplemented
42C4×C22⋊D113C2218yescomplemented
43#16813579C2214yescomplemented
44#16813579C2212yescomplemented
45#16813579C2212yescomplemented
46C2×#14268626C2212yescomplemented
47C2×#14268624C2212yes—
48C2×C4×Dic113C2211yescharacteristic, complemented
49C2×#41×C113C2212yescomplemented
50C4⋊Q8×C113C2211yescharacteristic, complemented
51#127×C113C2211yescharacteristic, complemented
52#124×C113C2212yescomplemented
53#121×C113C2214yescomplemented
54C4×D4×C113C2214yescomplemented
55C2×C42×C113C2211yescharacteristic, complemented
56C23×D113C2314yes—
57C23×D113C2311yescharacteristic
58#14268648—28no—
59#14268647—28no—
60#14268647—216no—
61#14268646—216no—
62#14268646—28no—
63C2×Dic226C2314yes—
64C2×Dic226C2312yes—
65Q8×D113—28no—
66C2×D452C2314yes—
67C2×D452C2312yes—
68C2×D452C2314yes—
69C2×C22⋊D113C2314yes—
70C2×C22⋊D113C2314yes—
71C2×C22⋊D113C2314yes—
72C2×C22⋊D113C2318yes—
73D4×D113—216no—
74D4×D113—28no—
75C22×Dic113C2314yes—
76C22×Dic113C2312yes—
77C22×Dic113C2311yescharacteristic
78C2×C4×D113—216no—
79C2×C4×D113D418yescomplemented
80C2×C4×D113C2314yes—
81C2×C4×D113C2314yes—
82C2×C4×D113C2314yes—
83C2×C4×D113C2312yes—
84C2×C4×D113C2312yes—
85C4⋊Dic113C2314yes—
86#14268626C2314yes—
87#14268626C2314yes—
88#14268626C2318yes—
89C22⋊Dic113C2318yes—
90#14268624C2314yes—
91#14268624C2314yes—
92#14268624C2318yes—
93#14268624C2318yes—
94C4×Dic113C2312yes—
95C4×Dic113C2312yes—
96#41×C113—28no—
97C2×Q8×C113C2312yes—
98C2×D4×C113C2314yes—
99C2×D4×C113C2312yes—
100C2×D4×C113C2314yes—
101C22×C4×C113C2314yes—
102C22×C4×C113C2312yes—
103C22×C4×C113C2311yescharacteristic
104C4⋊C4×C113C2314yes—
105C22⋊C4×C113C2318yes—
106C42×C113C2312yes—
107C42×C113C2311yescharacteristic
108C42×C113C2311yescharacteristic
109C23×C113C2414yes—
110C23×C113C2411yescharacteristic
111C22×D113—28no—
112C22×D113—42no—
113C22×D113—48no—
114C22×D113C2×D414yes—
115C22×D113C2414yes—
116C22×D113C2412yes—
117Q8×C113—24no—
118D4×C113—28no—
119D4×C113—24no—
120D4×C113—44no—
121C2×C4×C113—28no—
122C2×C4×C113—42no—
123C2×C4×C113C2×D414yes—
124C2×C4×C113C2412yes—
125C2×C4×C113C2412yes—
126C2×C4×C113C2414yes—
127C2×C4×C113C2411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—28no—
130C22⋊D113—28no—
131C22⋊D113—28no—
132C22⋊D113—48no—
133C2×Dic113—28no—
134C2×Dic113—42no—
135C2×Dic113C2×D414yes—
136C2×Dic113C2414yes—
137C2×Dic113C2414yes—
138C2×Dic113C2412yes—
139D452—28no—
140D452—24no—
141D452—44no—
142C4×D113—28no—
143C4×D113—28no—
144C4×D113—28no—
145C4×D113C2×D418yes—
146C4×D113C2×D418yes—
147Dic226—24no—
148Dic226—28no—
149C22×C113—22no—
150C22×C113—24no—
151C22×C113—28no—
152C22×C113C22×D412yes—
153C22×C113C2511yescharacteristic
154C2×D113—24no—
155C2×D113—24no—
156C2×D113—28no—
157C2×D113—44no—
158C2×D113—416no—
159C2×D113C22×D414yes—
160C4×C113—24no—
161C4×C113—22no—
162C4×C113—22no—
163C4×C113C22×D412yes—
164C4×C113C22×D412yes—
165Dic113—24no—
166Dic113—24no—
167Dic113C22×D414yes—
168C2×C113—22no—
169C2×C113—44no—
170C2×C113C23×D411yescharacteristic
171C2×C113#58512yes—
172D113—24no—
173D113—44no—
174#3449—1131nomaximal, Sylow
175C113#344911yescharacteristic, complemented, Sylow
176C22×#41—1132no—
177#537—1134no—
178#536—1132no—
179#536—1132no—
180#535—1132no—
181#535—1132no—
182#534—1134no—
183#532—1132no—
184#532—1131no—
185#532D11311yescharacteristic, complemented
186#525—1138no—
187C2×#117—1131no—
188C2×#41—1132no—
189C2×#41—1132no—
190C2×#41—1134no—
191C2×#41—1134no—
192C2×#41—1132no—
193C2×#41—22616no—
194C2×#41C2×D11312yescomplemented
195C22×Q8—1132no—
196C22×D4—1134no—
197C22×D4—1132no—
198C23×C4—1131no—
199C23×C4—1134no—
200C4⋊Q8—1132no—
201C4⋊Q8—1131no—
202C4⋊Q8C2×D11311yescharacteristic, complemented
203#127—1132no—
204#127—1131no—
205#127C2×D11311yescharacteristic, complemented
206#124—1132no—
207#124—1132no—
208#124—1132no—
209#124C2×D11312yescomplemented
210#123—1138no—
211#123—1138no—
212C22⋊Q8—1138no—
213C22⋊Q8—1138no—
214#121—1138no—
215#121—1138no—
216#121—1134no—
217#121—1138no—
218#121C2×D11314yescomplemented
219#120—1138no—
220#120—1138no—
221C4×D4—1138no—
222C4×D4—1134no—
223C4×D4C2×D11314yescomplemented
224#117—1134no—
225#117—1132no—
226#117—1132no—
227C2×C4⋊C4—1132no—
228C2×C22⋊C4—1132no—
229C2×C42—1131no—
230C2×C42C2×D11311yescharacteristic, complemented
231C24—1131no—
232C24—1134no—
233#41—28no—
234#41—22616no—
235#41—22616no—
236#41—2268no—
237#41—2268no—
238#41—2268no—
239C2×Q8—1134no—
240C2×Q8—1132no—
241C2×Q8—2268no—
242C2×Q8C22×D11312yes—
243C2×D4—1138no—
244C2×D4—1134no—
245C2×D4—1134no—
246C2×D4—1134no—
247C2×D4—1134no—
248C2×D4—1134no—
249C2×D4—1132no—
250C2×D4—2268no—
251C2×D4—22616no—
252C2×D4C22×D11314yes—
253C2×D4C22×D11312yes—
254C2×D4C22×D11314yes—
255C22×C4—1131no—
256C22×C4—1138no—
257C22×C4—1132no—
258C22×C4—1132no—
259C22×C4—1132no—
260C22×C4—1134no—
261C22×C4—1134no—
262C22×C4—1134no—
263C22×C4—1134no—
264C22×C4—22616no—
265C22×C4C22×D11314yes—
266C22×C4C22×D11312yes—
267C22×C4C22×D11311yescharacteristic
268C4⋊C4—1134no—
269C4⋊C4—1134no—
270C4⋊C4—1138no—
271C4⋊C4—1134no—
272C4⋊C4C22×D11314yes—
273C22⋊C4—1138no—
274C22⋊C4—1134no—
275C22⋊C4—1134no—
276C22⋊C4—1138no—
277C22⋊C4—1138no—
278C22⋊C4C22×D11318yes—
279C42—1132no—
280C42—1132no—
281C42C22×D11311yescharacteristic
282C42C22×D11311yescharacteristic
283C42C22×D11312yes—
284C23—1134no—
285C23—1132no—
286C23—1134no—
287C23—4522no—
288C23—4528no—
289C23—2268no—
290C23C23×D11314yes—
291C23C23×D11311yescharacteristic
292Q8—24no—
293Q8—2268no—
294Q8—2264no—
295D4—28no—
296D4—24no—
297D4—44no—
298D4—4524no—
299D4—4528no—
300D4—2268no—
301D4—2268no—
302D4—2268no—
303D4—2268no—
304D4—2264no—
305C2×C4—28no—
306C2×C4—42no—
307C2×C4—1134no—
308C2×C4—1132no—
309C2×C4—1138no—
310C2×C4—1138no—
311C2×C4—1134no—
312C2×C4—1134no—
313C2×C4—4522no—
314C2×C4—2268no—
315C2×C4—2268no—
316C2×C4—2268no—
317C2×C4—2268no—
318C2×C4D4×D11314yes—
319C2×C4C23×D11312yes—
320C2×C4C23×D11312yes—
321C2×C4C23×D11314yes—
322C2×C4C23×D11311yescharacteristic
323C2×C4C23×D11311yescharacteristic
324C22—22no—
325C22—24no—
326C22—28no—
327C22—1134no—
328C22—4524no—
329C22—45216no—
330C22—2264no—
331C22—2268no—
332C22—2264no—
333C22C2×D4×D11312yes—
334C22C24×D11311yescharacteristic
335C4—24no—
336C4—22no—
337C4—22no—
338C4—1134no—
339C4—2264no—
340C4—2264no—
341C4C2×D4×D11312yes—
342C4C2×D4×D11312yes—
343C2—22no—
344C2—44no—
345C2—4524no—
346C2—2264no—
347C2C22×D4×D11311yescharacteristic
348C2#2029943412yes—
subgroupG/H
centerC2×C4C23×D113
commutator, socle, cosocleC22×C113C25
FrattiniC22C24×D113
Fitting#532×C113C2
hypercenter#532D113
hypocenterC113#3449
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#41×D113C2semidirect
2. #20299175C2semidirect
3. #20299173C2semidirect
4. #20299168C2semidirect
5. #20299166C2semidirect
6. #20299161C2semidirect
7. #20299156C2semidirect
8. #20299148C2semidirect
9. #20299144C2semidirect
10. #20299107C2semidirect
11. C2×#16813579C2semidirect
12. #532×C113C2semidirect
15. C2×#14268647C22semidirect
17. C2×#14268646C22semidirect
19. C2×Q8×D113C22semidirect
21. C2×D4×D113C22semidirect
23. C22×C4×D113C22semidirect
24. #16813622C22semidirect
25. #16813620C22semidirect
26. #16813619C22semidirect
27. #16813618C22semidirect
28. #16813611C22semidirect
29. #16813610C22semidirect
30. #16813609C22semidirect
31. #16813607C22semidirect
32. #16813604C22semidirect
33. #16813600C22semidirect
34. #16813599C22semidirect
35. #16813596C22semidirect
36. #16813595C22semidirect
37. #16813594C22semidirect
38. #16813594C22semidirect
39. #16813592C22semidirect
40. #16813590C22semidirect
41. C4×D452C22semidirect
42. C4×C22⋊D113C22semidirect
43. #16813579C22semidirect
44. #16813579C22semidirect
45. #16813579C22semidirect
46. C2×#14268626C22semidirect
48. C2×C4×Dic113C22semidirect
49. C2×#41×C113C22semidirect
50. C4⋊Q8×C113C22semidirect
51. #127×C113C22semidirect
52. #124×C113C22semidirect
53. #121×C113C22semidirect
54. C4×D4×C113C22semidirect
55. C2×C42×C113C22semidirect
79. C2×C4×D113D4semidirect
175. C113#3449semidirect
185. #532D113semidirect
194. C2×#41C2×D113semidirect
202. C4⋊Q8C2×D113semidirect
205. #127C2×D113semidirect
209. #124C2×D113semidirect
218. #121C2×D113semidirect
223. C4×D4C2×D113semidirect
230. C2×C42C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1132
#202991752
#202991732
#202991682
#202991662
#202991612
#202991562
#202991482
#202991442
#202991072
C2×#168135792
#532×C1132
#3449113