Finite Group Databasebeta

← #49134667

Subgroups — #49134667

Order 36224.

1160 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827091C211yesmaximal, characteristic, complemented
2#31827060C212yesmaximal, complemented
3#31827059C214yesmaximal, complemented
4#31827052C212yesmaximal, complemented
5#31827050C214yesmaximal, complemented
6#31827024C212yesmaximal, complemented
7#31826996C212yesmaximal, complemented
8#31826992C214yesmaximal, complemented
9#31826975C212yesmaximal, complemented
10#31826971C214yesmaximal, complemented
11C2×D4×Dic283C212yesmaximal, complemented
12C2×(C22⋊D283)⋊C4C211yesmaximal, characteristic, complemented
13#534×C283C211yesmaximal, characteristic, complemented
14C2×#17985391C2212yescomplemented
15C22×C22⋊D283C2211yescharacteristic
16C23×Dic283C2211yescharacteristic
17C23×Dic283C2212yescomplemented
18C22×C4×D283C2211yescharacteristic, complemented
19#22583605C2214yescomplemented
20#22583603C2214yescomplemented
21#22583603C2214yescomplemented
22#22583601C2212yescomplemented
23#22583600C2214yescomplemented
24#22583597C2212yescomplemented
25#22583596C2214yescomplemented
26#22583594C2214yescomplemented
27#22583593C2214yescomplemented
28#22583592C2214yescomplemented
29#22583591C2214yescomplemented
30#22583591C2214yescomplemented
31#22583590C2212yescomplemented
32#22583589C2212yescomplemented
33#22583589C2212yescomplemented
34#22583587C2214yescomplemented
35#22583587C2214yescomplemented
36#22583587C2214yescomplemented
37#22583582C2214yes—
38#22583582C2214yes—
39#22583582C2214yescomplemented
40#22583581C2212yescomplemented
41#22583579C2214yescomplemented
42#22583578C2214yescomplemented
43#22583575C2212yescomplemented
44D4×Dic283C2212yescomplemented
45D4×Dic283C2214yescomplemented
46D4×Dic283C2214yescomplemented
47D4×Dic283C2214yescomplemented
48D4×Dic283C2214yescomplemented
49(C22⋊D283)⋊C4C2214yescomplemented
50(C22⋊D283)⋊C4C2214yescomplemented
51(C22⋊D283)⋊C4C2214yescomplemented
52#22583568C2212yescomplemented
53#22583566C2214yescomplemented
54C2×C4⋊Dic283C2212yescomplemented
55C2×Dic283⋊C4C2211yescharacteristic, complemented
56C2×C22⋊Dic283C2212yes—
57C2×C22⋊Dic283C2212yescomplemented
58C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
59C2×C4×Dic283C2212yescomplemented
60C2×C4×Dic283C2211yescharacteristic, complemented
61C22×D4×C283C2212yes—
62#123×C283C2214yescomplemented
63#121×C283C2212yes—
64#121×C283C2212yes—
65#120×C283C2214yescomplemented
66C2×C22⋊C4×C283C2211yescharacteristic
67C23×D283C2311yescharacteristic
68#17985391—44no—
69C2×Dic566C2312yes—
70C2×Dic566C2312yes—
71C2×C22⋊D283—24no—
72C2×C22⋊D283C2314yes—
73C2×C22⋊D283C2314yes—
74C2×C22⋊D283C2314yes—
75C22×Dic283—42no—
76C22×Dic283—44no—
77C22×Dic283C2311yescharacteristic
78C22×Dic283C2312yes—
79C22×Dic283C2311yescharacteristic
80C22×Dic283C2314yes—
81C22×Dic283C2312yes—
82C22×Dic283C2311yescharacteristic
83C22×Dic283C2312yes—
84C22×Dic283C2312yes—
85C22×Dic283C2314yes—
86C2×C4×D283—42no—
87C2×C4×D283C2312yes—
88C2×C4×D283C2312yes—
89C4⋊Dic283C2314yes—
90C4⋊Dic283C2314yes—
91C4⋊Dic283C2312yes—
92C4⋊Dic283C2312yes—
93Dic283⋊C4C2314yes—
94Dic283⋊C4C2314yes—
95Dic283⋊C4C2314yes—
96Dic283⋊C4C2314yes—
97Dic283⋊C4C2314yes—
98C22⋊Dic283C2314yes—
99C22⋊Dic283C2314yes—
100C22⋊Dic283C2314yes—
101C22⋊Dic283C2314yes—
102C22⋊Dic283C2314yes—
103C22⋊Dic283C2314yes—
104(C2×D283)⋊C4C2314yes—
105(C2×D283)⋊C4C2314yes—
106(C2×D283)⋊C4C2314yes—
107C4×Dic283C2312yes—
108C4×Dic283C2314yes—
109C4×Dic283C2312yes—
110C4×Dic283C2314yes—
111C24×C283C2312yes—
112C24×C283C2311yescharacteristic
113C2×D4×C283—28no—
114C2×D4×C283C2314yes—
115C2×D4×C283C2314yes—
116C2×D4×C283C2312yes—
117C2×D4×C283C2312yes—
118C22×C4×C283C2312yes—
119C22×C4×C283C2311yescharacteristic
120C22×C4×C283C2311yescharacteristic
121C4⋊C4×C283C2312yes—
122C4⋊C4×C283C2312yes—
123C22⋊C4×C283C2314yes—
124C22⋊C4×C283C2314yes—
125C22⋊C4×C283C2314yes—
126C22×D283—22no—
127C22×D283—41no—
128C22×D283—41no—
129C22×D283C2412yes—
130Dic566—42no—
131Dic566—42no—
132C22⋊D283—28no—
133C22⋊D283—44no—
134C22⋊D283—44no—
135C2×Dic283—22no—
136C2×Dic283—22no—
137C2×Dic283—24no—
138C2×Dic283—28no—
139C2×Dic283—42no—
140C2×Dic283—41no—
141C2×Dic283—44no—
142C2×Dic283—42no—
143C2×Dic283—42no—
144C2×Dic283C2412yes—
145C2×Dic283C2414yes—
146C2×Dic283C2412yes—
147C2×Dic283C2411yescharacteristic
148C2×Dic283C2414yes—
149C2×Dic283C2411yescharacteristic
150C4×D283—24no—
151C4×D283—42no—
152C23×C283—24no—
153C23×C283—41no—
154C23×C283—42no—
155C23×C283—41no—
156C23×C283—42no—
157C23×C283#4114yescomplemented
158C23×C283C2414yes—
159C23×C283C2412yes—
160C23×C283C2411yescharacteristic
161D4×C283—28no—
162D4×C283—28no—
163D4×C283—42no—
164D4×C283—42no—
165C2×C4×C283—24no—
166C2×C4×C283—41no—
167C2×C4×C283—41no—
168C2×C4×C283C2412yes—
169C2×C4×C283C2412yes—
170C2×C4×C283C2414yes—
171C22×C283—21no—
172C22×C283—22no—
173C22×C283—21no—
174C22×C283—22no—
175C22×C283—24no—
176C22×C283—24no—
177C22×C283—24no—
178C22×C283—44no—
179C22×C283—48no—
180C22×C283C2×#4114yes—
181C22×C283C2×#4112yes—
182C22×C283C2511yescharacteristic
183C2×D283—22no—
184C2×D283—22no—
185C2×D283—22no—
186C2×D283—44no—
187C4×C283—24no—
188C4×C283—22no—
189C4×C283—22no—
190Dic283—22no—
191Dic283—21no—
192Dic283—22no—
193Dic283—24no—
194Dic283—24no—
195Dic283H(5,𝔽2)12yes—
196C2×C283—22no—
197C2×C283—24no—
198C2×C283—44no—
199C2×C283C22×#4111yescharacteristic
200C2×C283C2×H(5,𝔽2)11yescharacteristic
201C2×C283#58511yescharacteristic
202D283—42no—
203C283#345911yescharacteristic, complemented, Sylow
204#3459—2831nomaximal, Sylow
205#543—2831no—
206#539—2834no—
207#539—2832no—
208#538—2832no—
209#538—2834no—
210#534—2832no—
211#534D28311yescharacteristic, complemented
212#529—2834no—
213#529—2832no—
214#525—2832no—
215#525—2834no—
216C2×C4×D4—2832no—
217C2×C4×D4—2831no—
218C2×#41—2832no—
219C22×D4—2831no—
220C22×D4C2×D28312yes—
221C23×C4—2831no—
222C23×C4—2832no—
223C23×C4—2831no—
224#126—2834no—
225#126—2834no—
226#126—2834no—
227#125—2834no—
228#125—2832no—
229#124—2832no—
230#124—2834no—
231#123—2834no—
232#123—2834no—
233#123—2834no—
234#123—2834no—
235#123—2834no—
236#123C2×D28314yescomplemented
237C22⋊Q8—2832no—
238C22⋊Q8—2832no—
239C22⋊Q8—2832no—
240C22⋊Q8—2834no—
241C22⋊Q8—2834no—
242C22⋊Q8—2834no—
243#121—2834no—
244#121—2832no—
245#121—2834no—
246#121—2834no—
247#121C2×D28312yes—
248#121C2×D28312yes—
249#120—2834no—
250#120—2834no—
251#120C2×D28314yescomplemented
252C4×Q8—2832no—
253C4×D4—2834no—
254C4×D4—2834no—
255C4×D4—2834no—
256C4×D4—2834no—
257C4×D4—2832no—
258C4×D4—2834no—
259C4×D4—2834no—
260C4×D4—2834no—
261#117—2832no—
262#117—2834no—
263C2×C4⋊C4—2831no—
264C2×C4⋊C4—2832no—
265C2×C22⋊C4—2832no—
266C2×C22⋊C4—2832no—
267C2×C22⋊C4—2831no—
268C2×C22⋊C4C2×D28311yescharacteristic
269C2×C42—2831no—
270C2×C42—2832no—
271C24—2831no—
272C24C22×D28312yes—
273C24C22×D28311yescharacteristic
274#41—11324no—
275C2×Q8—2832no—
276C2×Q8—2832no—
277C2×D4—28no—
278C2×D4—2834no—
279C2×D4—2834no—
280C2×D4—2834no—
281C2×D4—5664no—
282C2×D4C22×D28314yes—
283C2×D4C22×D28314yes—
284C2×D4C22×D28312yes—
285C2×D4C22×D28312yes—
286C22×C4—2831no—
287C22×C4—2831no—
288C22×C4—2832no—
289C22×C4—2834no—
290C22×C4—2832no—
291C22×C4—2831no—
292C22×C4—2832no—
293C22×C4—2832no—
294C22×C4—2834no—
295C22×C4—2832no—
296C22×C4—2832no—
297C22×C4—11322no—
298C22×C4—11322no—
299C22×C4—11324no—
300C22×C4C22×D28312yes—
301C22×C4C22×D28311yescharacteristic
302C22×C4C22×D28311yescharacteristic
303C4⋊C4—2834no—
304C4⋊C4—2834no—
305C4⋊C4—2834no—
306C4⋊C4—2834no—
307C4⋊C4—2834no—
308C4⋊C4—2834no—
309C4⋊C4—2834no—
310C4⋊C4—2832no—
311C4⋊C4—2832no—
312C4⋊C4C22×D28312yes—
313C4⋊C4C22×D28312yes—
314C22⋊C4—2834no—
315C22⋊C4—2834no—
316C22⋊C4—2834no—
317C22⋊C4—2834no—
318C22⋊C4—2834no—
319C22⋊C4—2834no—
320C22⋊C4—2834no—
321C22⋊C4—2834no—
322C22⋊C4—2834no—
323C22⋊C4C22×D28314yes—
324C22⋊C4C22×D28314yes—
325C22⋊C4C22×D28314yes—
326C42—2834no—
327C42—2832no—
328C42—2834no—
329C42—2832no—
330C23—24no—
331C23—41no—
332C23—42no—
333C23—41no—
334C23—42no—
335C23—2832no—
336C23—5662no—
337C23—11321no—
338C23—11321no—
339C23#1798539114yescomplemented
340C23C23×D28314yes—
341C23C23×D28311yescharacteristic
342C23C23×D28312yes—
343Q8—11322no—
344Q8—11322no—
345D4—28no—
346D4—28no—
347D4—42no—
348D4—42no—
349D4—5668no—
350D4—11324no—
351D4—11324no—
352C2×C4—24no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—2831no—
356C2×C4—2834no—
357C2×C4—2832no—
358C2×C4—2831no—
359C2×C4—2832no—
360C2×C4—2834no—
361C2×C4—5664no—
362C2×C4—5662no—
363C2×C4—5664no—
364C2×C4—5668no—
365C2×C4—5662no—
366C2×C4—11322no—
367C2×C4—11321no—
368C2×C4—11322no—
369C2×C4—11324no—
370C2×C4—11322no—
371C2×C4—11322no—
372C2×C4C23×D28312yes—
373C2×C4C23×D28314yes—
374C2×C4C23×D28312yes—
375C22—21no—
376C22—22no—
377C22—21no—
378C22—22no—
379C22—24no—
380C22—24no—
381C22—24no—
382C22—44no—
383C22—48no—
384C22—5662no—
385C22—5662no—
386C22—5662no—
387C22—11324no—
388C22C2×#1798539114yes—
389C22C2×#1798539112yes—
390C22C24×D28311yescharacteristic
391C4—24no—
392C4—22no—
393C4—22no—
394C4—2832no—
395C4—5662no—
396C4—5661no—
397C4—5662no—
398C4—5664no—
399C4—5664no—
400C2—24no—
401C2—22no—
402C2—44no—
403C2—11322no—
404C2C22×#1798539111yescharacteristic
405C2H(5,𝔽2)×D28311yescharacteristic
406C2#3182730011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D283
commutator, socle, cosocleC22×C283C25
Fitting#534×C283C2
hypercenter#534D283
hypocenterC283#3459
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #31827091C2semidirect
2. #31827060C2semidirect
3. #31827059C2semidirect
4. #31827052C2semidirect
5. #31827050C2semidirect
6. #31827024C2semidirect
7. #31826996C2semidirect
8. #31826992C2semidirect
9. #31826975C2semidirect
10. #31826971C2semidirect
11. C2×D4×Dic283C2semidirect
12. C2×(C22⋊D283)⋊C4C2semidirect
13. #534×C283C2semidirect
14. C2×#17985391C22semidirect
17. C23×Dic283C22semidirect
18. C22×C4×D283C22semidirect
19. #22583605C22semidirect
20. #22583603C22semidirect
21. #22583603C22semidirect
22. #22583601C22semidirect
23. #22583600C22semidirect
24. #22583597C22semidirect
25. #22583596C22semidirect
26. #22583594C22semidirect
27. #22583593C22semidirect
28. #22583592C22semidirect
29. #22583591C22semidirect
30. #22583591C22semidirect
31. #22583590C22semidirect
32. #22583589C22semidirect
33. #22583589C22semidirect
34. #22583587C22semidirect
35. #22583587C22semidirect
36. #22583587C22semidirect
39. #22583582C22semidirect
40. #22583581C22semidirect
41. #22583579C22semidirect
42. #22583578C22semidirect
43. #22583575C22semidirect
44. D4×Dic283C22semidirect
45. D4×Dic283C22semidirect
46. D4×Dic283C22semidirect
47. D4×Dic283C22semidirect
48. D4×Dic283C22semidirect
49. (C22⋊D283)⋊C4C22semidirect
50. (C22⋊D283)⋊C4C22semidirect
51. (C22⋊D283)⋊C4C22semidirect
52. #22583568C22semidirect
53. #22583566C22semidirect
54. C2×C4⋊Dic283C22semidirect
55. C2×Dic283⋊C4C22semidirect
57. C2×C22⋊Dic283C22semidirect
58. C2×(C2×D283)⋊C4C22semidirect
59. C2×C4×Dic283C22semidirect
60. C2×C4×Dic283C22semidirect
62. #123×C283C22semidirect
65. #120×C283C22semidirect
157. C23×C283#41semidirect
203. C283#3459semidirect
211. #534D283semidirect
236. #123C2×D283semidirect
251. #120C2×D283semidirect
339. C23#17985391semidirect

Maximal subgroups

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

subgroupindex
#318270912
#318270602
#318270592
#318270522
#318270502
#318270242
#318269962
#318269922
#318269752
#318269712
C2×D4×Dic2832
C2×(C22⋊D283)⋊C42
#534×C2832
#3459283