Finite Group Databasebeta

← #49133300

Subgroups — #49133300

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#31827183C211yesmaximal, characteristic, complemented
2#31827106C211yesmaximal, characteristic
3#31826826C211yesmaximal, characteristic, complemented
4#31826792C211yesmaximal, characteristic, complemented
5#31826754C211yesmaximal, characteristic, complemented
6#31826721C211yesmaximal, characteristic, complemented
7#31826695C211yesmaximal, characteristic, complemented
8#31826690C211yesmaximal, characteristic, complemented
9#31826630C211yesmaximal, characteristic, complemented
10#31826618C211yesmaximal, characteristic, complemented
11#31826564C211yesmaximal, characteristic, complemented
12#31826539C211yesmaximal, characteristic, complemented
13#31826469C211yesmaximal, characteristic, complemented
14#31826460C211yesmaximal, characteristic, complemented
15#485×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C22×D1132C2211yescharacteristic
18C2×#17985382C2211yescharacteristic, complemented
19C2×#17985381C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21C2×#17985376C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic, complemented
23#22583609C2211yescharacteristic, complemented
24#22583604—21no—
25#22583603—21no—
26#22583599C2211yescharacteristic
27#22583596—21no—
28#22583595—21no—
29#22583590C2211yescharacteristic, complemented
30#22583589C2211yescharacteristic
31#22583585—21no—
32#22583585C2211yescharacteristic
33#22583580—21no—
34C4×Dic566—21no—
35#22583575C2211yescharacteristic, complemented
36#22583572C2211yescharacteristic
37C4×C22⋊D283C2211yescharacteristic
38#22583568C2211yescharacteristic, complemented
39C22⋊C4×D283—21no—
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42#22583534C2211yescharacteristic, complemented
43#22583533C2211yescharacteristic, complemented
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51#22583520C2211yescharacteristic, complemented
52C22⋊Q8×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic
59C23×D283—21no—
60#17985393—22no—
61#17985393—41no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×D1132—22no—
65C2×D1132—21no—
66C2×D1132—21no—
67C2×D1132—21no—
68C2×D1132—41no—
69C2×D1132C2311yescharacteristic
70C2×D1132C2311yescharacteristic
71C2×C22⋊D283D411yescharacteristic
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75#17985382—41no—
76#17985381—22no—
77#17985381—41no—
78#17985376—41no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C8×D283—41no—
82C4⋊Dic283—21no—
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4D411yescharacteristic
88C22⋊Dic283—21no—
89C22⋊Dic283D411yescharacteristic
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4D411yescharacteristic
97C4×Dic283—21no—
98C4×Dic283—21no—
99C4×Dic283C2311yescharacteristic
100C2×Q8×C283C2311yescharacteristic
101C22×C4×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C22⋊C4×C283—21no—
109C22⋊C4×C283—21no—
110C42×C283—21no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—42no—
114C22×D283—42no—
115C22×D283—81no—
116C22×D283C2×D411yescharacteristic
117Dic566—21no—
118Dic566—21no—
119Dic566—42no—
120D1132—21no—
121D1132—21no—
122D1132—21no—
123D1132—42no—
124D1132—42no—
125D1132—81no—
126D1132#4112yes—
127C22⋊D283—41no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283C2×D411yescharacteristic
131C2×Dic283C2×D411yescharacteristic
132C2×Dic283C2×D411yescharacteristic
133C4×D283—21no—
134C4×D283—21no—
135C4×D283—42no—
136C4×D283—81no—
137C283⋊C8—21no—
138C283⋊C8—21no—
139C23×C283C2×D411yescharacteristic
140Q8×C283—21no—
141Q8×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—22no—
158C2×D283—21no—
159C2×D283—21no—
160C2×D283—41no—
161C2×D283—41no—
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×C283—41no—
171C4×C283C2×#4111yescharacteristic
172C4×C283H(5,𝔽2)11yescharacteristic
173Dic283—21no—
174Dic283—21no—
175Dic283—21no—
176Dic283—41no—
177Dic283—41no—
178C2×C283—41no—
179C2×C283#54611yescharacteristic
180C2×C283#57511yescharacteristic
181C2×C283#57711yescharacteristic
182D283—41no—
183D283—42no—
184D283—81no—
185C283#331111yescharacteristic, complemented, Sylow
186#3311—2831nomaximal, Sylow
187#556—2831no—
188#546—2831no—
189#489—2831no—
190#485D28311yescharacteristic, complemented
191#482—2831no—
192#476—2831no—
193#470—2831no—
194#465—2831no—
195#464—2831no—
196#452—2831no—
197#450—2831no—
198#440—2831no—
199#435—2831no—
200#418—2831no—
201#416—2831no—
202C2×#41—2831no—
203C22×D4—2831no—
204C2×Q16—2831no—
205C2×SD16—2831no—
206C2×SD16—2831no—
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
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#117C2×D28311yescharacteristic
227C2×C22⋊C4—5661no—
228#107C2×D28311yescharacteristic, complemented
229#106—2831no—
230#106C2×D28311yescharacteristic, complemented
231C4⋊C8—2831no—
232#103—2831no—
233#103—2831no—
234#103C2×D28311yescharacteristic, complemented
235#103C2×D28311yescharacteristic, complemented
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102—2831no—
242C22⋊C8—2831no—
243C22⋊C8C2×D28311yescharacteristic
244#97—2831no—
245C24—5661no—
246#41—5662no—
247#41—11321no—
248C2×Q8—2831no—
249C2×Q8—5661no—
250C2×Q8C22×D28311yescharacteristic
251C2×D4—2831no—
252C2×D4—2831no—
253C2×D4—2831no—
254C2×D4—5662no—
255C2×D4—5661no—
256C2×D4—5661no—
257C2×D4—5661no—
258C2×D4—11321no—
259C22×C4—2831no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4C22×D28311yescharacteristic
263Q16—11321no—
264SD16—5662no—
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—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4C22×D28311yescharacteristic
280C4⋊C4C22×D28311yescharacteristic
281C4⋊C4C22×D28311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2831no—
285C22⋊C4—2831no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C42—21no—
294C42—2831no—
295C42—5661no—
296C42—5661no—
297C23—2831no—
298C23—5661no—
299C23—5661no—
300C23—11322no—
301C23—11322no—
302C23—22641no—
303C23D4×D28311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—5661no—
307Q8—5661no—
308Q8—11322no—
309D4—2832no—
310D4—5661no—
311D4—5661no—
312D4—5661no—
313D4—11322no—
314D4—11322no—
315D4—11321no—
316D4—22641no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—2831no—
324C2×C4—2831no—
325C2×C4—2831no—
326C2×C4—5661no—
327C2×C4—5661no—
328C2×C4—5661no—
329C2×C4—5661no—
330C2×C4—11322no—
331C2×C4—22641no—
332C2×C4D4×D28311yescharacteristic
333C2×C4C23×D28311yescharacteristic
334C8—21no—
335C8—21no—
336C8—5661no—
337C8—5661no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—5661no—
342C22—5661no—
343C22—5661no—
344C22—5662no—
345C22—11321no—
346C22—11321no—
347C22—11321no—
348C22—11321no—
349C22—11321no—
350C22—22644no—
351C22C2×D4×D28311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—5661no—
358C4—5661no—
359C4—5661no—
360C4—11321no—
361C4—11321no—
362C4#41×D28311yescharacteristic
363C4#2258365611yescharacteristic
364C2—41no—
365C2—11321no—
366C2—11322no—
367C2—22641no—
368C2#3182710711yescharacteristic
369C2#3182726411yescharacteristic
370C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#485×C283C2
socleC22×C283C22×D4
prime radical#31827106C2
hypercenter#485D283
hypocenterC283#3311
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #31827183C2semidirect
3. #31826826C2semidirect
4. #31826792C2semidirect
5. #31826754C2semidirect
6. #31826721C2semidirect
7. #31826695C2semidirect
8. #31826690C2semidirect
9. #31826630C2semidirect
10. #31826618C2semidirect
11. #31826564C2semidirect
12. #31826539C2semidirect
13. #31826469C2semidirect
14. #31826460C2semidirect
15. #485×C283C2semidirect
18. C2×#17985382C22semidirect
22. C2×C8×D283C22semidirect
23. #22583609C22semidirect
29. #22583590C22semidirect
35. #22583575C22semidirect
38. #22583568C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. #22583534C22semidirect
43. #22583533C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. #22583520C22semidirect
54. #107×C283C22semidirect
55. #106×C283C22semidirect
56. #103×C283C22semidirect
57. #103×C283C22semidirect
185. C283#3311semidirect
190. #485D283semidirect
228. #107C2×D283semidirect
230. #106C2×D283semidirect
234. #103C2×D283semidirect
235. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271832
#318271062
#318268262
#318267922
#318267542
#318267212
#318266952
#318266902
#318266302
#318266182
#318265642
#318265392
#318264692
#318264602
#485×C2832
#3311283