Finite Group Databasebeta

← #49131438

Subgroups — #49131438

Order 36224.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827082C211yesmaximal, characteristic, complemented
2#31826940C211yesmaximal, characteristic, complemented
3#31826807C211yesmaximal, characteristic, complemented
4#31826786C211yesmaximal, characteristic, complemented
5#31826753C211yesmaximal, characteristic, complemented
6#31826743C211yesmaximal, characteristic, complemented
7#31826678C211yesmaximal, characteristic, complemented
8#31826678C211yesmaximal, characteristic, complemented
9#31826616C211yesmaximal, characteristic, complemented
10#31826577C211yesmaximal, characteristic, complemented
11#31826562C211yesmaximal, characteristic, complemented
12#31826556C211yesmaximal, characteristic, complemented
13D8×Dic283C211yesmaximal, characteristic, complemented
14#31826523C211yesmaximal, characteristic, complemented
15#447×C283C211yesmaximal, characteristic
16C2×#17985380C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18#22583609C2211yescharacteristic, complemented
19#22583603—21no—
20#22583597—21no—
21#22583597C2211yescharacteristic, complemented
22#22583591—21no—
23#22583589C2211yescharacteristic
24#22583587—21no—
25#22583575C2211yescharacteristic, complemented
26D4×Dic283—21no—
27D4×Dic283—21no—
28D4×Dic283C2211yescharacteristic
29D4×Dic283C2211yescharacteristic
30D4×Dic283C2211yescharacteristic
31D4×Dic283C2211yescharacteristic
32D4×Dic283C2211yescharacteristic, complemented
33#22583569C2211yescharacteristic
34#22583569C2211yescharacteristic
35C2×C22⋊Dic283—21no—
36C2×C22⋊Dic283—21no—
37#22583544C2211yescharacteristic, complemented
38#22583543C2211yescharacteristic, complemented
39#22583542C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583531C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic, complemented
48#22583531C2211yescharacteristic, complemented
49C22⋊(C283⋊C8)C2211yescharacteristic
50#22583520C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52C22×D4×C283C2211yescharacteristic
53C2×D8×C283C2211yescharacteristic
54C2×D8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C22×Dic283—21no—
62C22×Dic283—21no—
63C22×Dic283—21no—
64C22×Dic283—21no—
65C22×Dic283—21no—
66#17985380—22no—
67#17985380—22no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C4⋊Dic283D411yescharacteristic
71C4⋊Dic283D411yescharacteristic
72C4⋊Dic283C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78C22⋊Dic283—21no—
79C22⋊Dic283—21no—
80C22⋊Dic283—21no—
81C22⋊Dic283—21no—
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283D411yescharacteristic
88C22⋊Dic283D411yescharacteristic
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283C2311yescharacteristic
92C4×Dic283C2311yescharacteristic
93C24×C283—21no—
94C2×D4×C283—22no—
95C2×D4×C283—22no—
96C2×D4×C283—21no—
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C2×D4×C283C2311yescharacteristic
100C2×D4×C283C2311yescharacteristic
101C22×C4×C283C2311yescharacteristic
102D8×C283—22no—
103D8×C283—22no—
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C22⋊C4×C283—21no—
108Dic566—21no—
109Dic566—21no—
110Dic566—81no—
111C2×Dic283—21no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—81no—
116C2×Dic283—81no—
117C2×Dic283—81no—
118C2×Dic283—81no—
119C2×Dic283—81no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C283⋊C8—21no—
125C283⋊C8—21no—
126C23×C283—24no—
127C23×C283—21no—
128C23×C283—21no—
129C23×C283—21no—
130C23×C283—81no—
131C23×C283—81no—
132C23×C283C2×D411yescharacteristic
133D4×C283—24no—
134D4×C283—21no—
135D4×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—81no—
139D4×C283#4112yes—
140D4×C283#4112yes—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—21no—
147C8×C283—21no—
148C22×C283—21no—
149C22×C283—22no—
150C22×C283—22no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—84no—
161C22×C283C22×D411yescharacteristic
162C4×C283—21no—
163C4×C283—41no—
164C4×C283C2×#4111yescharacteristic
165C4×C283C2×#4111yescharacteristic
166Dic283—21no—
167Dic283—21no—
168Dic283—21no—
169Dic283—21no—
170Dic283—41no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—41no—
175C2×C283—42no—
176C2×C283—42no—
177C2×C283—81no—
178C2×C283#52511yescharacteristic
179C2×C283#57611yescharacteristic
180C2×C283#57711yescharacteristic
181C283#311811yescharacteristic, complemented, Sylow
182#3118—2831nomaximal, Sylow
183#542—2831no—
184#518—2831no—
185#485—2831no—
186#482—2831no—
187#476—2831no—
188#474—2831no—
189#463—2831no—
190#463—2831no—
191#450—2831no—
192#447D28311yescharacteristic
193#442—2831no—
194#440—2831no—
195C4×SD16—2831no—
196C4×D8—2831no—
197#433—2831no—
198C22×D4C2×D28311yescharacteristic
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×D8C2×D28311yescharacteristic
202C2×D8C2×D28311yescharacteristic
203C4⋊Q8—2831no—
204#126—5661no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—5661no—
210#121C2×D28311yescharacteristic
211C4×Q8—2831no—
212C4×D4—2831no—
213C4×D4—2831no—
214C4×D4—2831no—
215C4×D4—2831no—
216C4×D4—2831no—
217C4×D4—5661no—
218C4×D4—5661no—
219#117—2831no—
220#117—2831no—
221C2×C22⋊C4—5661no—
222C2×C22⋊C4—5661no—
223#107—2831no—
224#107—2831no—
225#106—2831no—
226#106—2831no—
227C4⋊C8—2831no—
228C4⋊C8—2831no—
229#103—2831no—
230#103—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102C2×D28311yescharacteristic
236#102C2×D28311yescharacteristic
237C22⋊C8—2831no—
238C22⋊C8C2×D28311yescharacteristic
239#97—2831no—
240C4×C8—2831no—
241C24—21no—
242C2×Q8—2831no—
243C2×Q8—5661no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22×D28311yescharacteristic
249C2×D4C22×D28311yescharacteristic
250C2×D4C22×D28311yescharacteristic
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4C22×D28311yescharacteristic
257SD16—5662no—
258SD16—5662no—
259D8—22no—
260D8—22no—
261C2×C8—2831no—
262C2×C8—2831no—
263C2×C8C22×D28311yescharacteristic
264C2×C8C22×D28311yescharacteristic
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4C22×D28311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—2831no—
276C22⋊C4—2831no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—2831no—
287C42—2831no—
288C42—5661no—
289C42—5661no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23D4×D28311yescharacteristic
297Q8—5661no—
298Q8—5661no—
299Q8—22641no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#1798539112yes—
307D4#1798539112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2831no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—2831no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—22641no—
320C2×C4—22641no—
321C2×C4—22641no—
322C2×C4—22641no—
323C2×C4—22641no—
324C2×C4D4×D28311yescharacteristic
325C2×C4C23×D28311yescharacteristic
326C8—21no—
327C8—21no—
328C8—5661no—
329C8—5661no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C2×D4×D28311yescharacteristic
344C4—21no—
345C4—41no—
346C4—5661no—
347C4—5661no—
348C4—5661no—
349C4—5661no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4—11321no—
354C4C2×#1798539111yescharacteristic
355C4C2×#1798539111yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#3182697111yescharacteristic
361C2#3182726611yescharacteristic
362C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting, prime radical#447×C283C2
socleC22×C283C22×D4
hypercenter#447D283
hypocenterC283#3118
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #31827082C2semidirect
2. #31826940C2semidirect
3. #31826807C2semidirect
4. #31826786C2semidirect
5. #31826753C2semidirect
6. #31826743C2semidirect
7. #31826678C2semidirect
8. #31826678C2semidirect
9. #31826616C2semidirect
10. #31826577C2semidirect
11. #31826562C2semidirect
12. #31826556C2semidirect
13. D8×Dic283C2semidirect
14. #31826523C2semidirect
18. #22583609C22semidirect
21. #22583597C22semidirect
25. #22583575C22semidirect
32. D4×Dic283C22semidirect
37. #22583544C22semidirect
38. #22583543C22semidirect
39. #22583542C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583535C22semidirect
44. #22583535C22semidirect
47. #22583531C22semidirect
48. #22583531C22semidirect
50. #22583520C22semidirect
51. C8×Dic283C22semidirect
181. C283#3118semidirect

Maximal subgroups

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

subgroupindex
#318270822
#318269402
#318268072
#318267862
#318267532
#318267432
#318266782
#318266162
#318265772
#318265622
#318265562
D8×Dic2832
#318265232
#447×C2832
#3118283