Finite Group Databasebeta

← #49133282

Subgroups — #49133282

Order 36224.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827155C211yesmaximal, characteristic, complemented
2#31826829C211yesmaximal, characteristic, complemented
3#31826786C211yesmaximal, characteristic, complemented
4#31826776C211yesmaximal, characteristic, complemented
5#31826765C211yesmaximal, characteristic, complemented
6#31826709C211yesmaximal, characteristic, complemented
7#31826692C211yesmaximal, characteristic, complemented
8#31826662C211yesmaximal, characteristic, complemented
9#31826616C211yesmaximal, characteristic, complemented
10#31826616C211yesmaximal, characteristic, complemented
11#31826565C211yesmaximal, characteristic, complemented
12#31826537C211yesmaximal, characteristic, complemented
13#31826470C211yesmaximal, characteristic, complemented
14C2×#22583531C211yesmaximal, characteristic, complemented
15D42×C283C211yesmaximal, characteristic
16C2×#17985380C2211yescharacteristic
17C2×#17985380C2211yescharacteristic, complemented
18C2×#17985380C2211yescharacteristic, complemented
19C2×#17985376C2211yescharacteristic, complemented
20C22×C283⋊C8C2211yescharacteristic, complemented
21#22583603—21no—
22#22583602C2211yescharacteristic, complemented
23#22583600—21no—
24#22583591—21no—
25#22583589C2211yescharacteristic, complemented
26#22583589C2211yescharacteristic, complemented
27C4×Dic566C2211yescharacteristic, complemented
28#22583569C2211yescharacteristic, complemented
29#22583566—21no—
30C2×C4⋊Dic283C2211yescharacteristic, complemented
31#22583543C2211yescharacteristic, complemented
32#22583543C2211yescharacteristic, complemented
33#22583541C2211yescharacteristic, complemented
34C4⋊(C283⋊C8)C2211yescharacteristic, complemented
35#22583533C2211yescharacteristic, complemented
36#22583531C2211yescharacteristic
37#22583531C2211yescharacteristic
38#22583531C2211yescharacteristic
39#22583531C2211yescharacteristic, complemented
40#22583531C2211yescharacteristic, complemented
41#22583531C2211yescharacteristic, complemented
42#22583531C2211yescharacteristic, complemented
43#22583531C2211yescharacteristic, complemented
44#22583531C2211yescharacteristic, complemented
45C22⋊(C283⋊C8)C2211yescharacteristic, complemented
46C22⋊(C283⋊C8)C2211yescharacteristic, complemented
47#22583521C2211yescharacteristic, complemented
48C22×D4×C283—21no—
49C22×D4×C283C2211yescharacteristic
50C22×D4×C283C2211yescharacteristic
51#127×C283C2211yescharacteristic
52#121×C283—21no—
53#121×C283C2211yescharacteristic
54#121×C283C2211yescharacteristic
55#120×C283—21no—
56#120×C283—21no—
57C4×D4×C283C2211yescharacteristic
58C4×D4×C283C2211yescharacteristic
59C2×Dic566C2311yescharacteristic
60C22×Dic283—21no—
61#17985380—22no—
62#17985380—41no—
63#17985380—41no—
64#17985376—41no—
65C2×C283⋊C8—41no—
66C2×C283⋊C8C2311yescharacteristic
67C2×C283⋊C8C2311yescharacteristic
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C4⋊Dic283—21no—
71C4⋊Dic283C2311yescharacteristic
72C4⋊Dic283C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74Dic283⋊C4—21no—
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79C22⋊Dic283—21no—
80C22⋊Dic283—21no—
81C22⋊Dic283—21no—
82C4×Dic283—21no—
83C4×Dic283—21no—
84C24×C283—21no—
85C24×C283—21no—
86C2×D4×C283—22no—
87C2×D4×C283—22no—
88C2×D4×C283—21no—
89C2×D4×C283—21no—
90C2×D4×C283—21no—
91C2×D4×C283—21no—
92C2×D4×C283—21no—
93C2×D4×C283—21no—
94C2×D4×C283—41no—
95C2×D4×C283—41no—
96C2×D4×C283—44no—
97C2×D4×C283D411yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C2×D4×C283C2311yescharacteristic
100C2×D4×C283C2311yescharacteristic
101C22×C4×C283—21no—
102C22×C4×C283C2311yescharacteristic
103C22×C4×C283C2311yescharacteristic
104C4⋊C4×C283D411yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C22⋊C4×C283—21no—
108C22⋊C4×C283—21no—
109C22⋊C4×C283D411yescharacteristic
110C22⋊C4×C283D411yescharacteristic
111C42×C283C2311yescharacteristic
112Dic566—21no—
113Dic566—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—42no—
119C283⋊C8—21no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C23×C283—21no—
124C23×C283—21no—
125C23×C283—21no—
126C23×C283—42no—
127C23×C283—42no—
128C23×C283—42no—
129C23×C283—42no—
130C23×C283—81no—
131C23×C283—81no—
132C23×C283C2×D411yescharacteristic
133C23×C283C2×D411yescharacteristic
134D4×C283—22no—
135D4×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—21no—
139D4×C283—21no—
140D4×C283—42no—
141D4×C283—42no—
142D4×C283—42no—
143D4×C283—42no—
144D4×C283—42no—
145D4×C283—81no—
146D4×C283#4112yes—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—42no—
153C2×C4×C283C2×D411yescharacteristic
154C2×C4×C283C2×D411yescharacteristic
155C2×C4×C283C2×D411yescharacteristic
156C2×C4×C283C2×D411yescharacteristic
157C2×C4×C283C2411yescharacteristic
158C22×C283—21no—
159C22×C283—21no—
160C22×C283—21no—
161C22×C283—22no—
162C22×C283—21no—
163C22×C283—21no—
164C22×C283—41no—
165C22×C283—41no—
166C22×C283—41no—
167C22×C283—41no—
168C22×C283—41no—
169C22×C283—41no—
170C22×C283—41no—
171C22×C283—41no—
172C22×C283—84no—
173C22×C283—84no—
174C22×C283AGL(1,ℤ/8)12yes—
175C22×C283C22×D411yescharacteristic
176C4×C283—21no—
177C4×C283—21no—
178C4×C283—21no—
179C4×C283—21no—
180C4×C283—41no—
181C4×C283C2×#4111yescharacteristic
182C4×C283H(5,𝔽2)11yescharacteristic
183Dic283—41no—
184Dic283—41no—
185Dic283—41no—
186Dic283—41no—
187C2×C283—22no—
188C2×C283—41no—
189C2×C283—42no—
190C2×C283—81no—
191C2×C283—81no—
192C2×C283#54611yescharacteristic
193C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C283#57711yescharacteristic
195C283#331011yescharacteristic, complemented, Sylow
196#3310—2831nomaximal, Sylow
197#552—2831no—
198D42D28311yescharacteristic
199#490—2831no—
200#482—2831no—
201#480—2831no—
202#478—2831no—
203#468—2831no—
204#465—2831no—
205#460—2831no—
206#450—2831no—
207#450—2831no—
208#440—2831no—
209#435—2831no—
210#418—2831no—
211C2×#102—2831no—
212C22×D4—21no—
213C22×D4C2×D28311yescharacteristic
214C22×D4C2×D28311yescharacteristic
215C2×SD16—2831no—
216C2×SD16—2831no—
217C2×SD16—2831no—
218C2×M16—2831no—
219C22×C8—2831no—
220#127C2×D28311yescharacteristic
221#126—5661no—
222#125—2831no—
223#125—5661no—
224#123—5661no—
225C22⋊Q8—2831no—
226C22⋊Q8—2831no—
227#121—21no—
228#121C2×D28311yescharacteristic
229#121C2×D28311yescharacteristic
230#120—21no—
231#120—21no—
232C4×Q8—2831no—
233C4×D4C2×D28311yescharacteristic
234C4×D4C2×D28311yescharacteristic
235#117—2831no—
236#117—5661no—
237C2×C4⋊C4—2831no—
238#107—2831no—
239#107—2831no—
240#106—2831no—
241C4⋊C8—2831no—
242#103—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102—2831no—
247#102—2831no—
248#102—2831no—
249#102—2831no—
250#102—2831no—
251#102—2831no—
252C22⋊C8—2831no—
253C22⋊C8—2831no—
254#97—2831no—
255C24—21no—
256C24—21no—
257C2×Q8—2831no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D28311yescharacteristic
270C2×D4C22×D28311yescharacteristic
271C2×D4C22×D28311yescharacteristic
272C2×D4C22×D28311yescharacteristic
273C22×C4—21no—
274C22×C4—5661no—
275C22×C4C22×D28311yescharacteristic
276C22×C4C22×D28311yescharacteristic
277SD16—5662no—
278SD16—11321no—
279SD16—11321no—
280M16—11321no—
281C2×C8—2831no—
282C2×C8—2831no—
283C2×C8—2831no—
284C2×C8—2831no—
285C2×C8—11321no—
286C4⋊C4—2831no—
287C4⋊C4—2831no—
288C4⋊C4—2831no—
289C4⋊C4—5661no—
290C4⋊C4—5661no—
291C4⋊C4—5661no—
292C4⋊C4—5661no—
293C4⋊C4—5661no—
294C4⋊C4—5661no—
295C4⋊C4C22⋊D28311yescharacteristic
296C4⋊C4C22×D28311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—5661no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4C22⋊D28311yescharacteristic
304C22⋊C4C22⋊D28311yescharacteristic
305C42—5661no—
306C42—5661no—
307C42C22×D28311yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D28311yescharacteristic
318C23C2×C22⋊D28311yescharacteristic
319Q8—5661no—
320Q8—5661no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#1798539112yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—5661no—
344C2×C4—11322no—
345C2×C4C2×C22⋊D28311yescharacteristic
346C2×C4C2×C22⋊D28311yescharacteristic
347C2×C4C2×C22⋊D28311yescharacteristic
348C2×C4C2×C22⋊D28311yescharacteristic
349C2×C4C23×D28311yescharacteristic
350C8—5661no—
351C8—5661no—
352C8—5661no—
353C8—5661no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#2258363612yes—
371C22C22×C22⋊D28311yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—11321no—
378C4—11321no—
379C4—11321no—
380C4—11321no—
381C4C2×#1798539111yescharacteristic
382C4#2258365511yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#3182710911yescharacteristic
389C2C2×#2258363611yescharacteristic
390C2#3182727611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting, prime radicalD42×C283C2
socleC22×C283C22×D4
hypercenterD42D283
hypocenterC283#3310
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #31827155C2semidirect
2. #31826829C2semidirect
3. #31826786C2semidirect
4. #31826776C2semidirect
5. #31826765C2semidirect
6. #31826709C2semidirect
7. #31826692C2semidirect
8. #31826662C2semidirect
9. #31826616C2semidirect
10. #31826616C2semidirect
11. #31826565C2semidirect
12. #31826537C2semidirect
13. #31826470C2semidirect
14. C2×#22583531C2semidirect
17. C2×#17985380C22semidirect
18. C2×#17985380C22semidirect
19. C2×#17985376C22semidirect
20. C22×C283⋊C8C22semidirect
22. #22583602C22semidirect
25. #22583589C22semidirect
26. #22583589C22semidirect
27. C4×Dic566C22semidirect
28. #22583569C22semidirect
30. C2×C4⋊Dic283C22semidirect
31. #22583543C22semidirect
32. #22583543C22semidirect
33. #22583541C22semidirect
34. C4⋊(C283⋊C8)C22semidirect
35. #22583533C22semidirect
39. #22583531C22semidirect
40. #22583531C22semidirect
41. #22583531C22semidirect
42. #22583531C22semidirect
43. #22583531C22semidirect
44. #22583531C22semidirect
45. C22⋊(C283⋊C8)C22semidirect
46. C22⋊(C283⋊C8)C22semidirect
47. #22583521C22semidirect
195. C283#3310semidirect

Maximal subgroups

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

subgroupindex
#318271552
#318268292
#318267862
#318267762
#318267652
#318267092
#318266922
#318266622
#318266162
#318265652
#318265372
#318264702
C2×#225835312
D42×C2832
#3310283