Finite Group Databasebeta

← #49131267

Subgroups — #49131267

Order 36224.

448 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827019C211yesmaximal, characteristic, complemented
2C4×D4×D283C211yesmaximal, characteristic
3#31826797C211yesmaximal, characteristic, complemented
4#31826794C211yesmaximal, characteristic, complemented
5#31826754C211yesmaximal, characteristic, complemented
6#31826753C211yesmaximal, characteristic, complemented
7#31826669C211yesmaximal, characteristic, complemented
8#31826668C211yesmaximal, characteristic, complemented
9#31826617C211yesmaximal, characteristic
10#31826614C211yesmaximal, characteristic
11C4×#17985381C211yesmaximal, characteristic, complemented
12C4×#17985379C211yesmaximal, characteristic, complemented
13C4×#17985380C211yesmaximal, characteristic, complemented
14#31826516C211yesmaximal, characteristic, complemented
15C4×SD16×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C2211yescharacteristic
17C22×C4×D283—21no—
18C2×#17985381C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985379C2211yescharacteristic
21#22583609C2211yescharacteristic, complemented
22#22583608C2211yescharacteristic, complemented
23#22583600—21no—
24#22583590C2211yescharacteristic
25#22583588—21no—
26#22583586C2211yescharacteristic
27C4×Dic566—21no—
28C4×Dic566C2211yescharacteristic, complemented
29C4×D1132C2211yescharacteristic
30D4×Dic283C2211yescharacteristic
31#22583572C2211yescharacteristic
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583567—21no—
35C4⋊C4×D283C2211yescharacteristic
36C22⋊C4×D283—21no—
37C42×D283C2211yescharacteristic
38#22583542C2211yescharacteristic, complemented
39#22583541C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583534C2211yescharacteristic, complemented
45#22583533C2211yescharacteristic, complemented
46#22583532C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic, complemented
52C2×SD16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic, complemented
54C4×D4×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64D4×D283—22no—
65D4×D283—22no—
66C22×Dic283—21no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—44no—
71C2×C4×D283D411yescharacteristic
72C2×C4×D283D411yescharacteristic
73C2×C4×D283C2311yescharacteristic
74#17985381—22no—
75#17985380—22no—
76#17985379—22no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C4⋊Dic283—21no—
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88C22⋊Dic283—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283—21no—
94C4×Dic283D411yescharacteristic
95C4×Dic283D411yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283C2311yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100SD16×C283—22no—
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283—21no—
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C42×C283C2311yescharacteristic
109C22×D283—24no—
110C22×D283—21no—
111C22×D283—42no—
112C22×D283—42no—
113C22×D283C2×D411yescharacteristic
114Dic566—21no—
115Dic566—21no—
116Dic566—42no—
117D1132—21no—
118D1132#4112yes—
119C22⋊D283—24no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—42no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—21no—
128C4×D283—21no—
129C4×D283—41no—
130C4×D283—42no—
131C4×D283—42no—
132C4×D283—42no—
133C4×D283SD1614yescomplemented
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137Q8×C283—21no—
138Q8×C283—21no—
139D4×C283—21no—
140D4×C283#4112yes—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—42no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C8×C283—21no—
149C8×C283—21no—
150C22×C283—22no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283C22×D411yescharacteristic
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—22no—
157C2×D283—48no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283C2×SD1612yes—
161C4×C283—21no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283C2×SD1612yes—
166C4×C283C2×#4111yescharacteristic
167C4×C283C2×#4111yescharacteristic
168Dic283—21no—
169Dic283—21no—
170Dic283—41no—
171Dic283—41no—
172Dic283—41no—
173Dic283C2×SD1612yes—
174C2×C283—42no—
175C2×C283#52511yescharacteristic
176C2×C283C22×SD1611yescharacteristic
177C2×C283#57511yescharacteristic
178D283—22no—
179D283—42no—
180C283#310111yescharacteristic, complemented, Sylow
181#3101—2831nomaximal, Sylow
182#533—2831no—
183C2×C4×D4—2831no—
184#483—2831no—
185#483—2831no—
186#476—2831no—
187#476—2831no—
188#461—2831no—
189#461—2831no—
190#450—2831no—
191#450—2831no—
192C4×SD16—2831no—
193C4×SD16—2831no—
194C4×SD16—2831no—
195C4×SD16D28311yescharacteristic, complemented
196#431—2831no—
197C22×D4—2831no—
198C23×C4—5661no—
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×SD16—2831no—
202C2×SD16C2×D28311yescharacteristic
203C4⋊Q8—2831no—
204C4⋊Q8—2831no—
205#125—5661no—
206C22⋊Q8—2831no—
207C22⋊Q8—2831no—
208C22⋊Q8—5661no—
209C4×Q8—2831no—
210C4×Q8—5661no—
211C4×Q8C2×D28311yescharacteristic, complemented
212C4×D4—2831no—
213C4×D4—2831no—
214C4×D4—2831no—
215C4×D4—5661no—
216C4×D4—5661no—
217C4×D4C2×D28311yescharacteristic
218#117—5661no—
219C2×C4⋊C4—2831no—
220C2×C22⋊C4—5661no—
221C2×C42—2831no—
222#106—2831no—
223#106—2831no—
224#106—2831no—
225#106C2×D28311yescharacteristic, complemented
226C4⋊C8—2831no—
227C4⋊C8—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103C2×D28311yescharacteristic, complemented
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102C2×D28311yescharacteristic
236C22⋊C8—2831no—
237C22⋊C8—2831no—
238C4×C8—2831no—
239C4×C8C2×D28311yescharacteristic, complemented
240C24—5661no—
241C2×Q8—2831no—
242C2×Q8—5661no—
243C2×Q8C22×D28311yescharacteristic
244C2×D4—2831no—
245C2×D4—5661no—
246C2×D4—5662no—
247C2×D4—5662no—
248C2×D4C22×D28311yescharacteristic
249C22×C4—21no—
250C22×C4—2831no—
251C22×C4—2831no—
252C22×C4—2831no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4—11324no—
258SD16—22no—
259SD16—5662no—
260SD16—5662no—
261SD16—5662no—
262C2×C8—2831no—
263C2×C8—2831no—
264C2×C8C22×D28311yescharacteristic
265C2×C8C22×D28311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4C22×D28311yescharacteristic
277C4⋊C4C22×D28311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C42—21no—
285C42—2831no—
286C42—2831no—
287C42—2831no—
288C42—5661no—
289C42C22×D28311yescharacteristic
290C23—21no—
291C23—2831no—
292C23—5664no—
293C23—5661no—
294C23—11322no—
295C23—11322no—
296Q8—21no—
297Q8—21no—
298Q8—5661no—
299Q8—5661no—
300Q8—11322no—
301D4—21no—
302D4—2832no—
303D4—5664no—
304D4—5661no—
305D4#1798539212yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—2831no—
311C2×C4—2834no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—11321no—
320C2×C4—11322no—
321C2×C4—11322no—
322C2×C4—11322no—
323C2×C4—11322no—
324C2×C4D4×D28311yescharacteristic
325C2×C4D4×D28311yescharacteristic
326C2×C4C23×D28311yescharacteristic
327C8—21no—
328C8—21no—
329C8—5661no—
330C8—5661no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—2832no—
335C22—5661no—
336C22—5661no—
337C22—5662no—
338C22—11328no—
339C22—11321no—
340C22—11321no—
341C22C2×D4×D28311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—2832no—
347C4—5661no—
348C4—5661no—
349C4—11321no—
350C4—11321no—
351C4—11321no—
352C4SD16×D28312yes—
353C4#41×D28311yescharacteristic
354C4C2×#1798539211yescharacteristic
355C2—42no—
356C2—5662no—
357C2—11322no—
358C2#3182697411yescharacteristic
359C2C2×SD16×D28311yescharacteristic
360C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×SD16×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×D283C22
hypercenterC4×SD16D283
hypocenterC283#3101
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #31827019C2semidirect
3. #31826797C2semidirect
4. #31826794C2semidirect
5. #31826754C2semidirect
6. #31826753C2semidirect
7. #31826669C2semidirect
8. #31826668C2semidirect
11. C4×#17985381C2semidirect
12. C4×#17985379C2semidirect
13. C4×#17985380C2semidirect
14. #31826516C2semidirect
15. C4×SD16×C283C2semidirect
21. #22583609C22semidirect
22. #22583608C22semidirect
28. C4×Dic566C22semidirect
38. #22583542C22semidirect
39. #22583541C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583535C22semidirect
44. #22583534C22semidirect
45. #22583533C22semidirect
51. C4×C283⋊C8C22semidirect
53. C4×Q8×C283C22semidirect
55. #106×C283C22semidirect
56. #103×C283C22semidirect
58. C4×C8×C283C22semidirect
133. C4×D283SD16semidirect
180. C283#3101semidirect
195. C4×SD16D283semidirect
211. C4×Q8C2×D283semidirect
225. #106C2×D283semidirect
231. #103C2×D283semidirect
239. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270192
C4×D4×D2832
#318267972
#318267942
#318267542
#318267532
#318266692
#318266682
#318266172
#318266142
C4×#179853812
C4×#179853792
C4×#179853802
#318265162
C4×SD16×C2832
#3101283