Finite Group Databasebeta

← #49130490

Subgroups — #49130490

Order 36224.

994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D283C211yesmaximal, characteristic, complemented
2C2×#22583638C211yesmaximal, characteristic, complemented
3C2×#22583636C211yesmaximal, characteristic, complemented
4#31826977C211yesmaximal, characteristic, complemented
5#31826617C214yesmaximal, complemented
6#31826600C214yesmaximal, complemented
7#31826469C211yesmaximal, characteristic, complemented
8#31826428C211yesmaximal, characteristic, complemented
9#418×C283C211yesmaximal, characteristic, complemented
10C24×D283—21no—
11C2×#17985392C2211yescharacteristic, complemented
12C22×D1132C2211yescharacteristic
13C22×C22⋊D283—21no—
14C2×D4×D283—24no—
15C2×D4×D283—22no—
16C2×D4×D283—24no—
17C2×D4×D283C2214yes—
18C22×C4×D283C2211yescharacteristic
19#22583638—24no—
20#22583636—24no—
21C2×#17985381C2212yescomplemented
22C2×#17985380C2212yescomplemented
23C2×D2264C2212yescomplemented
24C2×#17985377C2212yescomplemented
25C2×#17985376C2211yescharacteristic, complemented
26#22583594—21no—
27#22583590C2212yescomplemented
28#22583585C2212yescomplemented
29#22583580—21no—
30C4×D1132—22no—
31#22583530C2214yescomplemented
32(C2×D283)⋊C8C2214yescomplemented
33C22×D4×C283C2211yescharacteristic
34C2×M16×C283C2211yescharacteristic, complemented
35#117×C283C2211yescharacteristic, complemented
36#102×C283C2214yescomplemented
37C23×D283—28no—
38C23×D283—24no—
39C23×D283—21no—
40C23×D283—48no—
41C23×D283D411yescharacteristic
42#17985392—22no—
43#17985392—22no—
44C2×Dic566C2311yescharacteristic, complemented
45C2×D1132—22no—
46C2×D1132—21no—
47C2×D1132—22no—
48C2×D1132D414yescomplemented
49C2×D1132C2312yes—
50C2×D1132C2311yescharacteristic, complemented
51C2×C22⋊D283—28no—
52C2×C22⋊D283—24no—
53C2×C22⋊D283—21no—
54D4×D283—216no—
55D4×D283—28no—
56D4×D283—28no—
57C22×Dic283D411yescharacteristic
58C2×C4×D283—22no—
59C2×C4×D283—22no—
60C2×C4×D283—21no—
61C2×C4×D283D412yes—
62C2×C4×D283C2312yes—
63#17985381—24no—
64#17985380—24no—
65D2264—24no—
66#17985377—24no—
67#17985376—22no—
68C2×C283⋊C8C2312yescomplemented
69C4⋊Dic283—22no—
70(C2×D283)⋊C4—22no—
71(C2×D283)⋊C4—22no—
72C24×C283—21no—
73C2×D4×C283—21no—
74C2×D4×C283—22no—
75C2×D4×C283D414yescomplemented
76C2×D4×C283C2312yes—
77C22×C4×C283C2311yescharacteristic
78M16×C283—22no—
79C2×C8×C283C2312yescomplemented
80C4⋊C4×C283C2312yescomplemented
81C22⋊C4×C283—21no—
82C42×C283—21no—
83C22×D283—22no—
84C22×D283—24no—
85C22×D283—216no—
86C22×D283—24no—
87C22×D283—22no—
88C22×D283—21no—
89C22×D283—432no—
90C22×D283—48no—
91C22×D283—44no—
92C22×D283—48no—
93C22×D283C2×D412yes—
94Dic566—21no—
95Dic566—21no—
96D1132—24no—
97D1132—22no—
98D1132—21no—
99D1132—21no—
100D1132—44no—
101D1132C2×D414yes—
102C22⋊D283—216no—
103C22⋊D283—42no—
104C2×Dic283—22no—
105C2×Dic283—21no—
106C2×Dic283C2×D412yes—
107C4×D283—24no—
108C4×D283—22no—
109C4×D283—22no—
110C4×D283—42no—
111C283⋊C8—22no—
112C23×C283—24no—
113C23×C283—22no—
114C23×C283—44no—
115C23×C283C2×D411yescharacteristic
116D4×C283—24no—
117D4×C283—22no—
118D4×C283C2×D414yes—
119C2×C4×C283—22no—
120C2×C4×C283C2×D411yescharacteristic
121C2×C4×C283C2×D412yes—
122C2×C4×C283C2×D412yes—
123C2×C4×C283C2411yescharacteristic
124C8×C283—22no—
125C22×C283—22no—
126C22×C283—24no—
127C22×C283—48no—
128C22×C283—44no—
129C22×C283#12012yes—
130C22×C283C22×D411yescharacteristic
131C2×D283—28no—
132C2×D283—22no—
133C2×D283—22no—
134C2×D283—24no—
135C2×D283—432no—
136C2×D283—48no—
137C2×D283—44no—
138C2×D283—41no—
139C2×D283—42no—
140C2×D283AGL(1,ℤ/8)14yescomplemented
141C4×C283—42no—
142C4×C283#12012yes—
143C4×C283C22×D411yescharacteristic
144C4×C283C22×D411yescharacteristic
145Dic283—22no—
146Dic283—41no—
147C2×C283—22no—
148C2×C283—44no—
149C2×C283C2×#12011yescharacteristic
150C2×C283C2×AGL(1,ℤ/8)12yes—
151D283—24no—
152D283—44no—
153D283—81no—
154C283#300311yescharacteristic, complemented, Sylow
155#3003—2831nomaximal, Sylow
156C23×D4—2831no—
157C2×AGL(1,ℤ/8)—2831no—
158C2×AGL(1,ℤ/8)—2831no—
159#525—2831no—
160#450—2834no—
161#447—2834no—
162#418—2831no—
163#418D28311yescharacteristic, complemented
164#407—2831no—
165C25—5661no—
166C2×#41—2831no—
167C22×D4—2834no—
168C22×D4—2831no—
169C22×D4—5662no—
170C22×D4—5661no—
171C22×D4—5664no—
172C22×D4—5664no—
173C22×D4C2×D28311yescharacteristic
174C23×C4—2831no—
175AGL(1,ℤ/8)—5664no—
176AGL(1,ℤ/8)—5664no—
177C2×SD16—2832no—
178C2×SD16—2832no—
179C2×D8—2832no—
180C2×D8—2832no—
181C2×M16—2831no—
182C2×M16C2×D28311yescharacteristic, complemented
183#123—5661no—
184C22⋊Q8—2832no—
185#121—2832no—
186#120—5661no—
187C4×D4—5662no—
188#117C2×D28311yescharacteristic, complemented
189#102—2834no—
190#102C2×D28314yescomplemented
191C22⋊C8—2834no—
192C24—21no—
193C24—2831no—
194C24—5664no—
195C24—5668no—
196C24—5661no—
197C24—11328no—
198#41—5662no—
199#41—5662no—
200C2×Q8—2831no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—2834no—
204C2×D4—2832no—
205C2×D4—2831no—
206C2×D4—5662no—
207C2×D4—5664no—
208C2×D4—5668no—
209C2×D4—56616no—
210C2×D4—5668no—
211C2×D4—5668no—
212C2×D4—5661no—
213C2×D4—5661no—
214C2×D4—5662no—
215C2×D4D113214yescomplemented
216C2×D4C22×D28312yes—
217C22×C4—2831no—
218C22×C4—2832no—
219C22×C4—2832no—
220C22×C4—5662no—
221C22×C4—5662no—
222C22×C4—5661no—
223C22×C4C22×D28311yescharacteristic
224SD16—5664no—
225SD16—5664no—
226D8—5664no—
227D8—5664no—
228M16—22no—
229M16—5662no—
230C2×C8—2832no—
231C2×C8C22×D28312yescomplemented
232C4⋊C4—5662no—
233C4⋊C4C22×D28312yescomplemented
234C22⋊C4—21no—
235C22⋊C4—5662no—
236C22⋊C4—5662no—
237C42—21no—
238C23—24no—
239C23—22no—
240C23—44no—
241C23—2832no—
242C23—5664no—
243C23—56616no—
244C23—5662no—
245C23—5664no—
246C23—5662no—
247C23—5661no—
248C23—11324no—
249C23—11328no—
250C23—113232no—
251C23—11328no—
252C23D4×D28311yescharacteristic
253Q8—5661no—
254Q8—5661no—
255D4—24no—
256D4—22no—
257D4—2834no—
258D4—56616no—
259D4—5664no—
260D4—5661no—
261D4—5662no—
262D4—5661no—
263D4—11324no—
264D4—11322no—
265D4C2×D113214yes—
266C2×C4—22no—
267C2×C4—2832no—
268C2×C4—5662no—
269C2×C4—5664no—
270C2×C4—5662no—
271C2×C4—5662no—
272C2×C4—5661no—
273C2×C4—11322no—
274C2×C4D4×D28311yescharacteristic
275C2×C4D4×D28312yes—
276C2×C4C2×D113212yes—
277C2×C4C23×D28311yescharacteristic
278C8—22no—
279C8—5662no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—2834no—
285C22—5668no—
286C22—5662no—
287C22—5662no—
288C22—5664no—
289C22—11328no—
290C22—113232no—
291C22—11324no—
292C22—11321no—
293C22—11322no—
294C22#2258358012yes—
295C22C2×D4×D28311yescharacteristic
296C4—42no—
297C4—5662no—
298C4—11321no—
299C4#2258358012yes—
300C4C2×D4×D28311yescharacteristic
301C4C22×D113211yescharacteristic
302C2—22no—
303C2—44no—
304C2—5664no—
305C2—11324no—
306C2—22641no—
307C2C2×#2258358011yescharacteristic
308C2AGL(1,ℤ/8)×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#418×C283C2
socleC22×C283C22×D4
hypercenter#418D283
hypocenterC283#3003
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C22×D4×D283C2semidirect
2. C2×#22583638C2semidirect
3. C2×#22583636C2semidirect
4. #31826977C2semidirect
5. #31826617C2semidirect
6. #31826600C2semidirect
7. #31826469C2semidirect
8. #31826428C2semidirect
9. #418×C283C2semidirect
11. C2×#17985392C22semidirect
21. C2×#17985381C22semidirect
22. C2×#17985380C22semidirect
23. C2×D2264C22semidirect
24. C2×#17985377C22semidirect
25. C2×#17985376C22semidirect
27. #22583590C22semidirect
28. #22583585C22semidirect
31. #22583530C22semidirect
32. (C2×D283)⋊C8C22semidirect
34. C2×M16×C283C22semidirect
35. #117×C283C22semidirect
36. #102×C283C22semidirect
44. C2×Dic566C23semidirect
48. C2×D1132D4semidirect
50. C2×D1132C23semidirect
68. C2×C283⋊C8C23semidirect
75. C2×D4×C283D4semidirect
79. C2×C8×C283C23semidirect
80. C4⋊C4×C283C23semidirect
140. C2×D283AGL(1,ℤ/8)semidirect
154. C283#3003semidirect
163. #418D283semidirect
182. C2×M16C2×D283semidirect
188. #117C2×D283semidirect
190. #102C2×D283semidirect
215. C2×D4D1132semidirect
231. C2×C8C22×D283semidirect
233. C4⋊C4C22×D283semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D2832
C2×#225836382
C2×#225836362
#318269772
#318266172
#318266002
#318264692
#318264282
#418×C2832
#3003283