Finite Group Databasebeta

← #49133301

Subgroups — #49133301

Order 36224.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827186C211yesmaximal, characteristic, complemented
2#31827103C211yesmaximal, characteristic
3#31826826C211yesmaximal, characteristic, complemented
4#31826805C211yesmaximal, characteristic, complemented
5#31826790C211yesmaximal, characteristic, complemented
6#31826753C211yesmaximal, characteristic, complemented
7#31826720C211yesmaximal, characteristic, complemented
8#31826696C211yesmaximal, characteristic, complemented
9#31826689C211yesmaximal, characteristic, complemented
10#31826614C211yesmaximal, characteristic, complemented
11#31826566C211yesmaximal, characteristic, complemented
12#31826533C211yesmaximal, characteristic, complemented
13#31826468C211yesmaximal, characteristic, complemented
14#31826461C211yesmaximal, characteristic, complemented
15#452×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C2211yescharacteristic
17C2×#17985379C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C22×C283⋊C8C2211yescharacteristic, complemented
20#22583609C2211yescharacteristic, complemented
21#22583605—21no—
22#22583603—21no—
23#22583599C2211yescharacteristic
24#22583596—21no—
25#22583593—21no—
26#22583586C2211yescharacteristic
27#22583586C2211yescharacteristic
28#22583584C2211yescharacteristic
29#22583582—21no—
30#22583578—21no—
31Q8×Dic283C2211yescharacteristic, complemented
32#22583575—21no—
33D4×Dic283C2211yescharacteristic
34C4×C22⋊D283C2211yescharacteristic
35#22583569C2211yescharacteristic, complemented
36#22583568C2211yescharacteristic
37C2×(C2×D283)⋊C4—21no—
38#22583544C2211yescharacteristic, complemented
39#22583542C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42#22583534C2211yescharacteristic, complemented
43#22583534C2211yescharacteristic, complemented
44#22583534C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic, complemented
52C2×#41×C283C2211yescharacteristic
53C2×Q16×C283C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic
55C22⋊Q8×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C2×Dic566—21no—
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64C2×C22⋊D283D411yescharacteristic
65D4×D283—22no—
66D4×D283—41no—
67C22×Dic283—21no—
68C2×C4×D283C2311yescharacteristic
69#17985379—41no—
70#17985375—41no—
71C2×C283⋊C8—41no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283D411yescharacteristic
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96#41×C283—22no—
97#41×C283—41no—
98C2×Q8×C283C2311yescharacteristic
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104Q16×C283—41no—
105SD16×C283—22no—
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283—21no—
112C22×D283—42no—
113C22×D283—42no—
114C22×D283—81no—
115C22×D283C2×D411yescharacteristic
116Dic566—42no—
117D1132—21no—
118D1132—21no—
119C22⋊D283—41no—
120C22⋊D283—42no—
121C22⋊D283—81no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—81no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—21no—
130C4×D283—21no—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C23×C283—21no—
134C23×C283C2×D411yescharacteristic
135Q8×C283—21no—
136Q8×C283—21no—
137Q8×C283—21no—
138Q8×C283—21no—
139D4×C283—21no—
140D4×C283—42no—
141D4×C283#4112yes—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—42no—
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—21no—
153C22×C283—22no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283C22×D411yescharacteristic
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—21no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—41no—
165C2×D283—84no—
166C4×C283—21no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283—41no—
170C4×C283C2×#4111yescharacteristic
171C4×C283H(5,𝔽2)11yescharacteristic
172Dic283—21no—
173Dic283—21no—
174Dic283—21no—
175Dic283—41no—
176Dic283—41no—
177Dic283—41no—
178C2×C283—42no—
179C2×C283—41no—
180C2×C283#54611yescharacteristic
181C2×C283#57511yescharacteristic
182C2×C283#57711yescharacteristic
183D283—41no—
184D283—81no—
185C283#331111yescharacteristic, complemented, Sylow
186#3311—2831nomaximal, Sylow
187#556—2831no—
188#546—2831no—
189#489—2831no—
190#485—2831no—
191#482—2831no—
192#476—2831no—
193#470—2831no—
194#465—2831no—
195#464—2831no—
196#452D28311yescharacteristic, complemented
197#450—2831no—
198#440—2831no—
199#435—2831no—
200#418—2831no—
201#416—2831no—
202C2×#41C2×D28311yescharacteristic
203C22×D4—2831no—
204C2×Q16C2×D28311yescharacteristic, complemented
205C2×SD16—2831no—
206C2×SD16C2×D28311yescharacteristic
207C2×M16—2831no—
208C22×C8—2831no—
209C4⋊Q8—2831no—
210#126—5661no—
211#126—5661no—
212#124—2831no—
213#124—5661no—
214#123—5661no—
215C22⋊Q8—2831no—
216C22⋊Q8—2831no—
217C22⋊Q8C2×D28311yescharacteristic, complemented
218#121—2831no—
219#121—5661no—
220#120—5661no—
221C4×Q8—2831no—
222C4×Q8—5661no—
223C4×D4—2831no—
224C4×D4—2831no—
225#117—2831no—
226#117—2831no—
227C2×C22⋊C4—5661no—
228#107—2831no—
229#106—2831no—
230#106—2831no—
231C4⋊C8—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103C2×D28311yescharacteristic, complemented
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102C2×D28311yescharacteristic
242C22⋊C8—2831no—
243C22⋊C8C2×D28311yescharacteristic, complemented
244#97—2831no—
245C24—5661no—
246#41—22no—
247#41—41no—
248C2×Q8—5661no—
249C2×Q8C22×D28311yescharacteristic
250C2×Q8C22×D28311yescharacteristic
251C2×D4—21no—
252C2×D4—2831no—
253C2×D4—2831no—
254C2×D4—5661no—
255C2×D4—5662no—
256C2×D4—5661no—
257C2×D4—11321no—
258C2×D4C22×D28311yescharacteristic
259C22×C4—21no—
260C22×C4—2831no—
261C22×C4—5661no—
262C22×C4C22×D28311yescharacteristic
263Q16—41no—
264SD16—22no—
265SD16—11321no—
266M16—11321no—
267C2×C8—2831no—
268C2×C8—2831no—
269C2×C8—11321no—
270C2×C8C22×D28311yescharacteristic
271C2×C8C22×D28311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—2831no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4C22×D28311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—2831no—
284C22⋊C4—2831no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C42—2831no—
294C42—5661no—
295C42—5661no—
296C42—5661no—
297C23—21no—
298C23—2831no—
299C23—5661no—
300C23—11322no—
301C23—11322no—
302C23—22641no—
303C23D4×D28311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—11322no—
309D4—21no—
310D4—42no—
311D4—5661no—
312D4—5661no—
313D4—11321no—
314D4—11322no—
315D4—22641no—
316D4#1798539112yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—2831no—
324C2×C4—2831no—
325C2×C4—2831no—
326C2×C4—5661no—
327C2×C4—5661no—
328C2×C4—5661no—
329C2×C4—5661no—
330C2×C4—5661no—
331C2×C4—22641no—
332C2×C4D4×D28311yescharacteristic
333C2×C4C23×D28311yescharacteristic
334C8—21no—
335C8—21no—
336C8—5661no—
337C8—5661no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—5661no—
345C22—5661no—
346C22—5661no—
347C22—11321no—
348C22—11321no—
349C22—11321no—
350C22—22644no—
351C22C2×D4×D28311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—5661no—
357C4—5661no—
358C4—5661no—
359C4—11321no—
360C4—11321no—
361C4—11321no—
362C4C2×#1798539111yescharacteristic
363C4#2258365511yescharacteristic
364C2—41no—
365C2—42no—
366C2—11321no—
367C2—22641no—
368C2#3182710211yescharacteristic
369C2#3182726211yescharacteristic
370C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#452×C283C2
socleC22×C283C22×D4
prime radical#31827103C2
hypercenter#452D283
hypocenterC283#3311
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #31827186C2semidirect
3. #31826826C2semidirect
4. #31826805C2semidirect
5. #31826790C2semidirect
6. #31826753C2semidirect
7. #31826720C2semidirect
8. #31826696C2semidirect
9. #31826689C2semidirect
10. #31826614C2semidirect
11. #31826566C2semidirect
12. #31826533C2semidirect
13. #31826468C2semidirect
14. #31826461C2semidirect
15. #452×C283C2semidirect
19. C22×C283⋊C8C22semidirect
20. #22583609C22semidirect
31. Q8×Dic283C22semidirect
35. #22583569C22semidirect
38. #22583544C22semidirect
39. #22583542C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. #22583534C22semidirect
43. #22583534C22semidirect
44. #22583534C22semidirect
51. #22583520C22semidirect
53. C2×Q16×C283C22semidirect
55. C22⋊Q8×C283C22semidirect
56. #103×C283C22semidirect
58. C22⋊C8×C283C22semidirect
185. C283#3311semidirect
196. #452D283semidirect
204. C2×Q16C2×D283semidirect
217. C22⋊Q8C2×D283semidirect
235. #103C2×D283semidirect
243. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271862
#318271032
#318268262
#318268052
#318267902
#318267532
#318267202
#318266962
#318266892
#318266142
#318265662
#318265332
#318264682
#318264612
#452×C2832
#3311283