Finite Group Databasebeta

← #49134670

Subgroups — #49134670

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#31827062C212yesmaximal, complemented
3#31827057C214yesmaximal, complemented
4#31827053C212yesmaximal, complemented
5#31827048C214yesmaximal, complemented
6#31827027C211yesmaximal, characteristic, complemented
7#31827024C212yesmaximal, complemented
8#31826999C212yesmaximal, complemented
9#31826995C214yesmaximal, complemented
10#31826976C212yesmaximal, complemented
11#31826974C214yesmaximal, complemented
12C2×C4×C22⋊D283C212yesmaximal, complemented
13C2×C4×D4×C283C211yesmaximal, characteristic, complemented
14C2×#17985392C2212yescomplemented
15C22×C22⋊D283C2212yes—
16C22×C4×D283C2212yescomplemented
17#22583605C2214yescomplemented
18#22583604C2214yescomplemented
19#22583603C2214yescomplemented
20#22583602C2212yescomplemented
21#22583600C2214yescomplemented
22#22583598C2212yescomplemented
23#22583596C2214yescomplemented
24#22583595C2214yescomplemented
25#22583594C2214yescomplemented
26#22583593C2214yescomplemented
27#22583593C2214yescomplemented
28#22583592C2214yescomplemented
29#22583591C2214yescomplemented
30#22583589C2212yescomplemented
31#22583589C2212yescomplemented
32#22583589C2212yescomplemented
33#22583588C2214yescomplemented
34#22583587C2214yescomplemented
35#22583587C2214yescomplemented
36#22583584C2212yes—
37#22583584C2212yes—
38#22583584C2212yescomplemented
39#22583583C2214yescomplemented
40#22583582C2214yes—
41#22583582C2214yes—
42#22583580C2214yescomplemented
43#22583579C2214yescomplemented
44#22583578C2214yescomplemented
45C4×Dic566C2212yescomplemented
46C4×D1132C2212yescomplemented
47C4×C22⋊D283C2214yescomplemented
48C4×C22⋊D283C2214yescomplemented
49C4×C22⋊D283C2214yescomplemented
50C4×C22⋊D283C2214yescomplemented
51C4×C22⋊D283C2214yescomplemented
52#22583569C2212yescomplemented
53#22583567C2214yescomplemented
54C2×Dic283⋊C4C2212yescomplemented
55C2×C22⋊Dic283C2212yes—
56C2×(C2×D283)⋊C4C2212yescomplemented
57C2×C4×Dic283C2212yescomplemented
58C22×D4×C283C2211yescharacteristic
59C23×C4×C283C2211yescharacteristic
60C23×C4×C283C2211yescharacteristic, complemented
61C4×D4×C283C2214yescomplemented
62C4×D4×C283C2214yescomplemented
63C2×C4⋊C4×C283C2211yescharacteristic, complemented
64C2×C22⋊C4×C283C2211yescharacteristic
65C2×C22⋊C4×C283C2211yescharacteristic, complemented
66C2×C42×C283C2211yescharacteristic, complemented
67C23×D283C2312yes—
68#17985392—44no—
69C2×Dic566C2312yes—
70C2×Dic566C2312yes—
71C2×D1132C2312yes—
72C2×D1132C2312yes—
73C2×C22⋊D283—28no—
74C2×C22⋊D283C2314yes—
75C2×C22⋊D283C2314yes—
76C2×C22⋊D283C2314yes—
77C2×C22⋊D283C2314yes—
78C22×Dic283C2312yes—
79C22×Dic283C2312yes—
80C22×Dic283C2312yes—
81C2×C4×D283—44no—
82C2×C4×D283C2314yes—
83C2×C4×D283C2314yes—
84C4⋊Dic283C2312yes—
85C4⋊Dic283C2312yes—
86C4⋊Dic283C2312yes—
87C4⋊Dic283C2312yes—
88Dic283⋊C4C2314yes—
89Dic283⋊C4C2314yes—
90Dic283⋊C4C2314yes—
91Dic283⋊C4C2314yes—
92Dic283⋊C4C2314yes—
93Dic283⋊C4C2314yes—
94C22⋊Dic283C2314yes—
95C22⋊Dic283C2314yes—
96C22⋊Dic283C2314yes—
97C22⋊Dic283C2314yes—
98(C2×D283)⋊C4C2314yes—
99(C2×D283)⋊C4C2314yes—
100(C2×D283)⋊C4C2314yes—
101(C2×D283)⋊C4C2314yes—
102(C2×D283)⋊C4C2314yes—
103(C2×D283)⋊C4C2314yes—
104C4×Dic283C2314yes—
105C4×Dic283C2314yes—
106C24×C283C2311yescharacteristic
107C24×C283C2311yescharacteristic
108C2×D4×C283—24no—
109C2×D4×C283C2314yes—
110C22×C4×C283—42no—
111C22×C4×C283—42no—
112C22×C4×C283C2312yes—
113C22×C4×C283C2312yes—
114C22×C4×C283C2311yescharacteristic
115C22×C4×C283C2311yescharacteristic
116C22×C4×C283C2312yes—
117C22×C4×C283C2311yescharacteristic
118C22×C4×C283C2311yescharacteristic
119C22×C4×C283C2311yescharacteristic
120C22×C4×C283C2312yes—
121C4⋊C4×C283C2314yes—
122C22⋊C4×C283C2314yes—
123C22⋊C4×C283C2314yes—
124C42×C283C2312yes—
125C42×C283C2312yes—
126C22×D283—24no—
127C22×D283—42no—
128C22×D283—42no—
129C22×D283C2414yes—
130Dic566—42no—
131Dic566—42no—
132D1132—42no—
133D1132—42no—
134C22⋊D283—28no—
135C22⋊D283—28no—
136C22⋊D283—44no—
137C22⋊D283—44no—
138C2×Dic283—24no—
139C2×Dic283—42no—
140C2×Dic283—42no—
141C2×Dic283C2414yes—
142C2×Dic283C2414yes—
143C2×Dic283C2414yes—
144C4×D283—28no—
145C4×D283—44no—
146C23×C283—22no—
147C23×C283—41no—
148C23×C283—41no—
149C23×C283—41no—
150C23×C283—41no—
151C23×C283#4114yescomplemented
152C23×C283C2412yes—
153C23×C283C2412yes—
154C23×C283C2411yescharacteristic
155D4×C283—28no—
156C2×C4×C283—22no—
157C2×C4×C283—22no—
158C2×C4×C283—24no—
159C2×C4×C283—24no—
160C2×C4×C283—42no—
161C2×C4×C283—42no—
162C2×C4×C283—41no—
163C2×C4×C283—41no—
164C2×C4×C283—41no—
165C2×C4×C283C2412yes—
166C2×C4×C283C2412yes—
167C2×C4×C283C2411yescharacteristic
168C2×C4×C283C2412yes—
169C2×C4×C283C2412yes—
170C2×C4×C283C2411yescharacteristic
171C22×C283—21no—
172C22×C283—22no—
173C22×C283—21no—
174C22×C283—22no—
175C22×C283—22no—
176C22×C283—22no—
177C22×C283—22no—
178C22×C283—44no—
179C22×C283—44no—
180C22×C283C2×#4112yes—
181C22×C283C2×#4114yes—
182C22×C283C2511yescharacteristic
183C2×D283—24no—
184C2×D283—24no—
185C2×D283—24no—
186C2×D283—48no—
187C4×C283—22no—
188C4×C283—21no—
189C4×C283—22no—
190C4×C283—22no—
191C4×C283—22no—
192C4×C283H(5,𝔽2)12yes—
193Dic283—24no—
194Dic283—24no—
195Dic283—24no—
196C2×C283—24no—
197C2×C283—22no—
198C2×C283—42no—
199C2×C283C22×#4111yescharacteristic
200C2×C283C2×H(5,𝔽2)11yescharacteristic
201C2×C283#58511yescharacteristic
202D283—44no—
203C283#345911yescharacteristic, complemented, Sylow
204#3459—2831nomaximal, Sylow
205#543—2831no—
206#539—2834no—
207#539—2832no—
208#538—2834no—
209#538—2832no—
210#534—2832no—
211#534—2831no—
212#529—2834no—
213#529—2832no—
214#525—2832no—
215#525—2834no—
216C2×C4×D4—2832no—
217C2×C4×D4D28311yescharacteristic, complemented
218C2×#41—2832no—
219C22×D4—2832no—
220C22×D4C2×D28311yescharacteristic
221C23×C4—2832no—
222C23×C4C2×D28311yescharacteristic
223C23×C4C2×D28311yescharacteristic, complemented
224#126—2834no—
225#126—2834no—
226#126—2834no—
227#125—2834no—
228#125—2832no—
229#124—2834no—
230#124—2832no—
231#123—2834no—
232#123—2834no—
233#123—2834no—
234#123—2834no—
235#123—2834no—
236#123—2834no—
237C22⋊Q8—2832no—
238C22⋊Q8—2832no—
239C22⋊Q8—2832no—
240C22⋊Q8—2834no—
241C22⋊Q8—2834no—
242C22⋊Q8—2834no—
243#121—2834no—
244#121—2834no—
245#121—2832no—
246#121—2832no—
247#121—2832no—
248#121—2834no—
249#120—2834no—
250#120—2834no—
251#120—2834no—
252C4×Q8—2832no—
253C4×D4—2834no—
254C4×D4—2834no—
255C4×D4—2834no—
256C4×D4—2834no—
257C4×D4—2834no—
258C4×D4—2832no—
259C4×D4C2×D28314yescomplemented
260C4×D4C2×D28314yescomplemented
261#117—2832no—
262#117—2834no—
263C2×C4⋊C4—2832no—
264C2×C4⋊C4C2×D28311yescharacteristic, complemented
265C2×C22⋊C4—2832no—
266C2×C22⋊C4—2832no—
267C2×C22⋊C4C2×D28311yescharacteristic
268C2×C22⋊C4C2×D28311yescharacteristic, complemented
269C2×C42—2832no—
270C2×C42C2×D28311yescharacteristic, complemented
271C24—2832no—
272C24C22×D28311yescharacteristic
273C24C22×D28311yescharacteristic
274#41—11324no—
275C2×Q8—2832no—
276C2×Q8—2832no—
277C2×D4—24no—
278C2×D4—2834no—
279C2×D4—2834no—
280C2×D4—2834no—
281C2×D4—2834no—
282C2×D4—2832no—
283C2×D4—2832no—
284C2×D4—5668no—
285C2×D4C22×D28314yes—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—2832no—
289C22×C4—2832no—
290C22×C4—2832no—
291C22×C4—2834no—
292C22×C4—2834no—
293C22×C4—11324no—
294C22×C4C22×D28311yescharacteristic
295C22×C4C22×D28312yes—
296C22×C4C22×D28311yescharacteristic
297C22×C4C22×D28312yes—
298C22×C4C22×D28311yescharacteristic
299C22×C4C22×D28312yes—
300C22×C4C22×D28311yescharacteristic
301C22×C4C22×D28311yescharacteristic
302C22×C4C22×D28312yes—
303C4⋊C4—2834no—
304C4⋊C4—2834no—
305C4⋊C4—2834no—
306C4⋊C4—2834no—
307C4⋊C4—2834no—
308C4⋊C4—2834no—
309C4⋊C4—2832no—
310C4⋊C4—2832no—
311C4⋊C4—2832no—
312C4⋊C4—2832no—
313C4⋊C4C22×D28314yes—
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⋊C4—2834no—
324C22⋊C4C22×D28314yes—
325C22⋊C4C22×D28314yes—
326C42—2834no—
327C42—2834no—
328C42C22×D28312yes—
329C42C22×D28312yes—
330C23—22no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—2834no—
336C23—5664no—
337C23—11322no—
338C23—11322no—
339C23#1798539214yescomplemented
340C23C23×D28312yes—
341C23C23×D28311yescharacteristic
342C23C23×D28312yes—
343Q8—11322no—
344Q8—11322no—
345D4—28no—
346D4—5668no—
347D4—5668no—
348D4—11322no—
349D4—11322no—
350D4—11324no—
351D4—11324no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—2834no—
362C2×C4—2834no—
363C2×C4—2834no—
364C2×C4—5664no—
365C2×C4—5668no—
366C2×C4—11324no—
367C2×C4—11322no—
368C2×C4—11322no—
369C2×C4C23×D28312yes—
370C2×C4C23×D28312yes—
371C2×C4C23×D28311yescharacteristic
372C2×C4C23×D28312yes—
373C2×C4C23×D28312yes—
374C2×C4C23×D28311yescharacteristic
375C22—21no—
376C22—22no—
377C22—21no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—44no—
383C22—44no—
384C22—5664no—
385C22—5664no—
386C22—5664no—
387C22—11328no—
388C22C2×#1798539212yes—
389C22C2×#1798539214yes—
390C22C24×D28311yescharacteristic
391C4—22no—
392C4—21no—
393C4—22no—
394C4—22no—
395C4—22no—
396C4—5664no—
397C4—5664no—
398C4—5664no—
399C4#2258365512yes—
400C2—22no—
401C2—24no—
402C2—42no—
403C2—11324no—
404C2C22×#1798539211yescharacteristic
405C2C2×#2258365511yescharacteristic
406C2#3182730111yescharacteristic
subgroupG/H
centerC2×C4C23×D283
commutator, socle, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×C4×D4×C283C2
hypercenterC2×C4×D4D283
hypocenterC283#3459
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #31827091C2semidirect
2. #31827062C2semidirect
3. #31827057C2semidirect
4. #31827053C2semidirect
5. #31827048C2semidirect
6. #31827027C2semidirect
7. #31827024C2semidirect
8. #31826999C2semidirect
9. #31826995C2semidirect
10. #31826976C2semidirect
11. #31826974C2semidirect
12. C2×C4×C22⋊D283C2semidirect
13. C2×C4×D4×C283C2semidirect
14. C2×#17985392C22semidirect
16. C22×C4×D283C22semidirect
17. #22583605C22semidirect
18. #22583604C22semidirect
19. #22583603C22semidirect
20. #22583602C22semidirect
21. #22583600C22semidirect
22. #22583598C22semidirect
23. #22583596C22semidirect
24. #22583595C22semidirect
25. #22583594C22semidirect
26. #22583593C22semidirect
27. #22583593C22semidirect
28. #22583592C22semidirect
29. #22583591C22semidirect
30. #22583589C22semidirect
31. #22583589C22semidirect
32. #22583589C22semidirect
33. #22583588C22semidirect
34. #22583587C22semidirect
35. #22583587C22semidirect
38. #22583584C22semidirect
39. #22583583C22semidirect
42. #22583580C22semidirect
43. #22583579C22semidirect
44. #22583578C22semidirect
45. C4×Dic566C22semidirect
46. C4×D1132C22semidirect
47. C4×C22⋊D283C22semidirect
48. C4×C22⋊D283C22semidirect
49. C4×C22⋊D283C22semidirect
50. C4×C22⋊D283C22semidirect
51. C4×C22⋊D283C22semidirect
52. #22583569C22semidirect
53. #22583567C22semidirect
54. C2×Dic283⋊C4C22semidirect
56. C2×(C2×D283)⋊C4C22semidirect
57. C2×C4×Dic283C22semidirect
60. C23×C4×C283C22semidirect
61. C4×D4×C283C22semidirect
62. C4×D4×C283C22semidirect
63. C2×C4⋊C4×C283C22semidirect
65. C2×C22⋊C4×C283C22semidirect
66. C2×C42×C283C22semidirect
151. C23×C283#41semidirect
203. C283#3459semidirect
217. C2×C4×D4D283semidirect
223. C23×C4C2×D283semidirect
259. C4×D4C2×D283semidirect
260. C4×D4C2×D283semidirect
264. C2×C4⋊C4C2×D283semidirect
268. C2×C22⋊C4C2×D283semidirect
270. C2×C42C2×D283semidirect
339. C23#17985392semidirect

Maximal subgroups

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

subgroupindex
#318270912
#318270622
#318270572
#318270532
#318270482
#318270272
#318270242
#318269992
#318269952
#318269762
#318269742
C2×C4×C22⋊D2832
C2×C4×D4×C2832
#3459283