Finite Group Databasebeta

← #49133278

Subgroups — #49133278

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#31827150C211yesmaximal, characteristic, complemented
2D4×C22⋊D283C211yesmaximal, characteristic
3#31826828C211yesmaximal, characteristic, complemented
4#31826788C211yesmaximal, characteristic, complemented
5#31826778C211yesmaximal, characteristic, complemented
6#31826767C211yesmaximal, characteristic, complemented
7#31826710C211yesmaximal, characteristic, complemented
8#31826694C211yesmaximal, characteristic, complemented
9#31826664C211yesmaximal, characteristic, complemented
10#31826617C211yesmaximal, characteristic, complemented
11#31826616C211yesmaximal, characteristic, complemented
12#31826562C211yesmaximal, characteristic, complemented
13#31826536C211yesmaximal, characteristic, complemented
14#31826468C211yesmaximal, characteristic, complemented
15C2×#102×C283C211yesmaximal, characteristic, complemented
16C22×C22⋊D283—21no—
17C2×D4×D283C2211yescharacteristic
18C2×#17985381C2211yescharacteristic, complemented
19C2×#17985380C2211yescharacteristic
20C2×#17985380C2211yescharacteristic, complemented
21C2×#17985375C2211yescharacteristic, complemented
22#22583606C2211yescharacteristic
23#22583605—21no—
24#22583601C2211yescharacteristic, complemented
25#22583600—21no—
26#22583593—21no—
27#22583590C2211yescharacteristic, complemented
28#22583589C2211yescharacteristic, complemented
29#22583584C2211yescharacteristic
30#22583582—21no—
31#22583581C2211yescharacteristic
32#22583579—21no—
33#22583578—21no—
34#22583575C2211yescharacteristic, complemented
35D4×Dic283C2211yescharacteristic
36C4×C22⋊D283C2211yescharacteristic
37#22583569—21no—
38#22583568C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40#22583543C2211yescharacteristic, complemented
41#22583542C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583532C2211yescharacteristic, complemented
45#22583531C2211yescharacteristic
46#22583531C2211yescharacteristic, complemented
47#22583530C2211yescharacteristic, complemented
48#22583530C2211yescharacteristic, complemented
49C22⋊(C283⋊C8)C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51#22583520C2211yescharacteristic, complemented
52C22×D4×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic, complemented
54C2×C4⋊C4×C283C2211yescharacteristic, complemented
55#102×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic, complemented
58#102×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—44no—
68C2×C22⋊D283D411yescharacteristic
69D4×D283—22no—
70D4×D283—41no—
71C22×Dic283—21no—
72C2×C4×D283C2311yescharacteristic
73#17985381—41no—
74#17985380—22no—
75#17985380—41no—
76#17985375—41no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C4⋊Dic283—21no—
80C4⋊Dic283—21no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4D411yescharacteristic
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283D411yescharacteristic
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4D411yescharacteristic
95C4×Dic283—21no—
96C4×Dic283—21no—
97C4×Dic283C2311yescharacteristic
98C24×C283—21no—
99C2×D4×C283—22no—
100C2×D4×C283—21no—
101C2×D4×C283—41no—
102C2×D4×C283C2311yescharacteristic
103C2×D4×C283C2311yescharacteristic
104C22×C4×C283—21no—
105C22×C4×C283C2311yescharacteristic
106C2×C8×C283—41no—
107C2×C8×C283C2311yescharacteristic
108C2×C8×C283C2311yescharacteristic
109C4⋊C4×C283—21no—
110C4⋊C4×C283C2311yescharacteristic
111C4⋊C4×C283C2311yescharacteristic
112C22×D283—21no—
113C22×D283—42no—
114C22×D283—42no—
115C22×D283—81no—
116C22×D283C2×D411yescharacteristic
117Dic566—21no—
118Dic566—21no—
119D1132—21no—
120D1132—21no—
121C22⋊D283—22no—
122C22⋊D283—42no—
123C22⋊D283—42no—
124C22⋊D283—42no—
125C22⋊D283—42no—
126C22⋊D283—81no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—42no—
131C2×Dic283C2×D411yescharacteristic
132C2×Dic283C2×D411yescharacteristic
133C2×Dic283C2×D411yescharacteristic
134C4×D283—21no—
135C4×D283—21no—
136C283⋊C8—21no—
137C283⋊C8—21no—
138C23×C283—21no—
139C23×C283—21no—
140C23×C283—42no—
141C23×C283—42no—
142C23×C283—81no—
143C23×C283C2×D411yescharacteristic
144D4×C283—21no—
145D4×C283—21no—
146D4×C283—21no—
147D4×C283—42no—
148D4×C283#4112yes—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283—42no—
154C2×C4×C283C2×D411yescharacteristic
155C2×C4×C283C2411yescharacteristic
156C8×C283—21no—
157C8×C283—21no—
158C22×C283—21no—
159C22×C283—21no—
160C22×C283—22no—
161C22×C283—41no—
162C22×C283—41no—
163C22×C283—41no—
164C22×C283—41no—
165C22×C283—41no—
166C22×C283—84no—
167C22×C283AGL(1,ℤ/8)12yes—
168C22×C283C22×D411yescharacteristic
169C2×D283—21no—
170C2×D283—21no—
171C2×D283—21no—
172C2×D283—41no—
173C2×D283—41no—
174C2×D283—41no—
175C2×D283—84no—
176C4×C283—21no—
177C4×C283—41no—
178C4×C283—41no—
179C4×C283C2×#4111yescharacteristic
180C4×C283H(5,𝔽2)11yescharacteristic
181Dic283—21no—
182Dic283—21no—
183Dic283—21no—
184Dic283—41no—
185Dic283—41no—
186Dic283—41no—
187C2×C283—22no—
188C2×C283—42no—
189C2×C283—81no—
190C2×C283#54611yescharacteristic
191C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C283#57711yescharacteristic
193D283—41no—
194D283—81no—
195C283#331011yescharacteristic, complemented, Sylow
196#3310—2831nomaximal, Sylow
197#552—2831no—
198D42—2831no—
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×#102D28311yescharacteristic, complemented
212C22×D4—2831no—
213C22×D4—5661no—
214C22×D4C2×D28311yescharacteristic
215C2×SD16—2831no—
216C2×SD16—2831no—
217C2×SD16—2831no—
218C2×M16—2831no—
219C22×C8C2×D28311yescharacteristic, complemented
220#127—2831no—
221#126—5661no—
222#125—2831no—
223#125—5661no—
224#123—5661no—
225C22⋊Q8—2831no—
226C22⋊Q8—2831no—
227#121—2831no—
228#121—2831no—
229#121—5661no—
230#120—5661no—
231#120—5661no—
232C4×Q8—2831no—
233C4×D4—2831no—
234C4×D4—2831no—
235#117—2831no—
236#117—5661no—
237C2×C4⋊C4C2×D28311yescharacteristic, complemented
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#102C2×D28311yescharacteristic
249#102C2×D28311yescharacteristic
250#102C2×D28311yescharacteristic, complemented
251#102C2×D28311yescharacteristic, complemented
252C22⋊C8—2831no—
253C22⋊C8—2831no—
254#97—2831no—
255C24—21no—
256C24—5661no—
257C2×Q8—2831no—
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—2831no—
262C2×D4—2831no—
263C2×D4—5661no—
264C2×D4—5661no—
265C2×D4—5661no—
266C2×D4—5662no—
267C2×D4—5661no—
268C2×D4—5661no—
269C2×D4—11321no—
270C2×D4—11324no—
271C2×D4C22×D28311yescharacteristic
272C2×D4C22×D28311yescharacteristic
273C22×C4—21no—
274C22×C4—2831no—
275C22×C4—5661no—
276C22×C4C22×D28311yescharacteristic
277SD16—5662no—
278SD16—11321no—
279SD16—11321no—
280M16—11321no—
281C2×C8—41no—
282C2×C8—2831no—
283C2×C8—2831no—
284C2×C8C22×D28311yescharacteristic
285C2×C8C22×D28311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—2831no—
288C4⋊C4—2831no—
289C4⋊C4—2831no—
290C4⋊C4—5661no—
291C4⋊C4—5661no—
292C4⋊C4—5661no—
293C4⋊C4—5661no—
294C4⋊C4—5661no—
295C4⋊C4C22×D28311yescharacteristic
296C4⋊C4C22×D28311yescharacteristic
297C22⋊C4—2831no—
298C22⋊C4—2831no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4—5661no—
304C22⋊C4—5661no—
305C42—2831no—
306C42—5661no—
307C42—5661no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—2831no—
314C23—5661no—
315C23—11322no—
316C23—11322no—
317C23—22641no—
318C23D4×D28311yescharacteristic
319Q8—5661no—
320Q8—5661no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—5662no—
326D4—5661no—
327D4—5661no—
328D4—11322no—
329D4—11322no—
330D4—11322no—
331D4—11322no—
332D4—22641no—
333D4#1798539212yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—2831no—
340C2×C4—2831no—
341C2×C4—2831no—
342C2×C4—5661no—
343C2×C4—5661no—
344C2×C4—5661no—
345C2×C4—5661no—
346C2×C4—5661no—
347C2×C4—11322no—
348C2×C4D4×D28311yescharacteristic
349C2×C4C23×D28311yescharacteristic
350C8—21no—
351C8—21no—
352C8—5661no—
353C8—5661no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—84no—
363C22—5661no—
364C22—5661no—
365C22—5661no—
366C22—11321no—
367C22—11321no—
368C22—11321no—
369C22—22644no—
370C22#2258363412yes—
371C22C2×D4×D28311yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—5661no—
376C4—5661no—
377C4—5661no—
378C4—11321no—
379C4—11321no—
380C4—11321no—
381C4C2×#1798539211yescharacteristic
382C4#2258365511yescharacteristic
383C2—22no—
384C2—42no—
385C2—81no—
386C2—11321no—
387C2—22641no—
388C2#3182710511yescharacteristic
389C2C2×#2258363411yescharacteristic
390C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#102×C283C2
socleC22×C283C22×D4
prime radicalD4×C22⋊D283C2
hypercenterC2×#102D283
hypocenterC283#3310
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #31827150C2semidirect
3. #31826828C2semidirect
4. #31826788C2semidirect
5. #31826778C2semidirect
6. #31826767C2semidirect
7. #31826710C2semidirect
8. #31826694C2semidirect
9. #31826664C2semidirect
10. #31826617C2semidirect
11. #31826616C2semidirect
12. #31826562C2semidirect
13. #31826536C2semidirect
14. #31826468C2semidirect
15. C2×#102×C283C2semidirect
18. C2×#17985381C22semidirect
20. C2×#17985380C22semidirect
21. C2×#17985375C22semidirect
24. #22583601C22semidirect
27. #22583590C22semidirect
28. #22583589C22semidirect
34. #22583575C22semidirect
38. #22583568C22semidirect
39. #22583543C22semidirect
40. #22583543C22semidirect
41. #22583542C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583535C22semidirect
44. #22583532C22semidirect
46. #22583531C22semidirect
47. #22583530C22semidirect
48. #22583530C22semidirect
49. C22⋊(C283⋊C8)C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. #22583520C22semidirect
53. C22×C8×C283C22semidirect
54. C2×C4⋊C4×C283C22semidirect
57. #102×C283C22semidirect
58. #102×C283C22semidirect
195. C283#3310semidirect
211. C2×#102D283semidirect
219. C22×C8C2×D283semidirect
237. C2×C4⋊C4C2×D283semidirect
250. #102C2×D283semidirect
251. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271502
D4×C22⋊D2832
#318268282
#318267882
#318267782
#318267672
#318267102
#318266942
#318266642
#318266172
#318266162
#318265622
#318265362
#318264682
C2×#102×C2832
#3310283