Finite Group Databasebeta

← #49131399

Subgroups — #49131399

Order 36224.

450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#31826999C211yesmaximal, characteristic, complemented
2#31826795C211yesmaximal, characteristic, complemented
3#31826778C211yesmaximal, characteristic, complemented
4#31826765C212yesmaximal, complemented
5#31826680C212yesmaximal, complemented
6#31826616C211yesmaximal, characteristic, complemented
7#31826599C211yesmaximal, characteristic
8#31826575C212yesmaximal, complemented
9#31826565C212yesmaximal, complemented
10#31826522C211yesmaximal, characteristic, complemented
11C2×C4×D4×C283C211yesmaximal, characteristic, complemented
12C2×#17985380C2212yes—
13C2×#17985377C2212yes—
14#22583604—21no—
15#22583602C2211yescharacteristic, complemented
16#22583598C2211yescharacteristic, complemented
17#22583593—21no—
18#22583589C2211yescharacteristic
19#22583584C2211yescharacteristic
20C4×Dic566C2211yescharacteristic, complemented
21C4×D1132C2211yescharacteristic, complemented
22C4×C22⋊D283—21no—
23#22583567—21no—
24#22583543C2212yescomplemented
25#22583541C2212yescomplemented
26C4⋊(C283⋊C8)C2212yescomplemented
27#22583533C2212yescomplemented
28#22583531C2212yes—
29#22583531C2212yes—
30#22583530C2212yescomplemented
31C22⋊(C283⋊C8)C2211yescharacteristic
32C22⋊(C283⋊C8)C2211yescharacteristic
33#22583521C2212yescomplemented
34C22×D4×C283C2211yescharacteristic
35C23×C4×C283—21no—
36C4×D4×C283—21no—
37C4×D4×C283—21no—
38C4×D4×C283C2212yes—
39C4×D4×C283C2212yes—
40C2×C4⋊C4×C283C2211yescharacteristic
41C2×C22⋊C4×C283—21no—
42C2×C42×C283C2211yescharacteristic
43C2×Dic566C2311yescharacteristic
44C2×D1132C2311yescharacteristic
45C2×C22⋊D283—21no—
46C2×C4×D283—21no—
47#17985380—24no—
48#17985377—24no—
49C2×C283⋊C8C2312yes—
50C2×C283⋊C8C2312yes—
51C4⋊Dic283C2311yescharacteristic
52C4⋊Dic283C2311yescharacteristic
53Dic283⋊C4—21no—
54Dic283⋊C4—21no—
55Dic283⋊C4—21no—
56Dic283⋊C4—21no—
57C22⋊Dic283—21no—
58(C2×D283)⋊C4—21no—
59(C2×D283)⋊C4—21no—
60(C2×D283)⋊C4—21no—
61(C2×D283)⋊C4—21no—
62C4×Dic283—21no—
63C24×C283—21no—
64C2×D4×C283—24no—
65C2×D4×C283—21no—
66C2×D4×C283C2312yes—
67C22×C4×C283—21no—
68C22×C4×C283—22no—
69C22×C4×C283—22no—
70C22×C4×C283—44no—
71C22×C4×C283D411yescharacteristic
72C22×C4×C283D411yescharacteristic
73C22×C4×C283C2311yescharacteristic
74C4⋊C4×C283—21no—
75C4⋊C4×C283C2312yes—
76C22⋊C4×C283—22no—
77C22⋊C4×C283—22no—
78C42×C283D411yescharacteristic
79C42×C283D411yescharacteristic
80C42×C283C2311yescharacteristic
81C42×C283C2311yescharacteristic
82C22×D283—21no—
83Dic566—22no—
84D1132—22no—
85C22⋊D283—42no—
86C2×Dic283—21no—
87C2×Dic283—21no—
88C2×Dic283—21no—
89C4×D283—42no—
90C283⋊C8—22no—
91C283⋊C8—22no—
92C23×C283—24no—
93C23×C283—22no—
94C23×C283—42no—
95C23×C283—42no—
96C23×C283C2×D411yescharacteristic
97D4×C283—24no—
98D4×C283—22no—
99D4×C283#4114yes—
100C2×C4×C283—22no—
101C2×C4×C283—22no—
102C2×C4×C283—22no—
103C2×C4×C283—41no—
104C2×C4×C283—44no—
105C2×C4×C283—44no—
106C2×C4×C283—42no—
107C2×C4×C283C2×D411yescharacteristic
108C2×C4×C283C2×D411yescharacteristic
109C2×C4×C283C2×D411yescharacteristic
110C2×C4×C283C2×D411yescharacteristic
111C2×C4×C283C2×D411yescharacteristic
112C2×C4×C283C2411yescharacteristic
113C22×C283—21no—
114C22×C283—21no—
115C22×C283—24no—
116C22×C283—48no—
117C22×C283—42no—
118C22×C283—42no—
119C22×C283AGL(1,ℤ/8)12yes—
120C22×C283C22×D411yescharacteristic
121C2×D283—41no—
122C2×D283—41no—
123C2×D283—41no—
124C4×C283—21no—
125C4×C283—21no—
126C4×C283—21no—
127C4×C283—21no—
128C4×C283—21no—
129C4×C283—42no—
130C4×C283C2×#4112yes—
131Dic283—41no—
132Dic283—41no—
133Dic283—41no—
134C2×C283—22no—
135C2×C283—44no—
136C2×C283#52511yescharacteristic
137C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C283#57511yescharacteristic
139D283—81no—
140C283#311411yescharacteristic, complemented, Sylow
141#3114—2831nomaximal, Sylow
142#529—2831no—
143C2×C4×D4D28311yescharacteristic, complemented
144#483—2831no—
145#480—2831no—
146#478—2832no—
147#463—2832no—
148#450—2831no—
149#447—2831no—
150#442—2832no—
151#440—2832no—
152#432—2831no—
153C22×D4C2×D28311yescharacteristic
154C23×C4—21no—
155C2×SD16—2832no—
156C2×D8—2832no—
157#126—5661no—
158#125—2831no—
159#124—2831no—
160#123—5661no—
161C22⋊Q8—2831no—
162#121—2831no—
163C4×Q8—2831no—
164C4×D4—21no—
165C4×D4—21no—
166C4×D4—2831no—
167C4×D4—5661no—
168C4×D4C2×D28312yes—
169C4×D4C2×D28312yes—
170#117—5661no—
171C2×C4⋊C4C2×D28311yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C2×D28311yescharacteristic
174#107—2832no—
175#106—2832no—
176C4⋊C8—2832no—
177#103—2832no—
178#102—2832no—
179#102—2832no—
180#102—2832no—
181C22⋊C8—2831no—
182C22⋊C8—2831no—
183#97—2832no—
184C24—21no—
185C2×Q8—2831no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—2831no—
189C2×D4—5661no—
190C2×D4C22×D28312yes—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—5661no—
196C22×C4C22⋊D28311yescharacteristic
197C22×C4C22⋊D28311yescharacteristic
198C22×C4C22×D28311yescharacteristic
199SD16—5664no—
200D8—5664no—
201C2×C8—2832no—
202C2×C8—2832no—
203C4⋊C4—21no—
204C4⋊C4—2831no—
205C4⋊C4—2831no—
206C4⋊C4—5661no—
207C4⋊C4—5661no—
208C4⋊C4—5661no—
209C4⋊C4—5661no—
210C4⋊C4C22×D28312yes—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—5661no—
214C22⋊C4—5661no—
215C22⋊C4—5661no—
216C22⋊C4—5661no—
217C22⋊C4—5661no—
218C42—5661no—
219C42C22⋊D28311yescharacteristic
220C42C22⋊D28311yescharacteristic
221C42C22×D28311yescharacteristic
222C42C22×D28311yescharacteristic
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—5661no—
228C23C2×C22⋊D28311yescharacteristic
229Q8—5662no—
230D4—24no—
231D4—22no—
232D4—5662no—
233D4—11322no—
234D4#1798539214yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—5661no—
243C2×C4—5661no—
244C2×C4—5661no—
245C2×C4—11322no—
246C2×C4C2×C22⋊D28311yescharacteristic
247C2×C4C2×C22⋊D28311yescharacteristic
248C2×C4C2×C22⋊D28311yescharacteristic
249C2×C4C2×C22⋊D28311yescharacteristic
250C2×C4C2×C22⋊D28311yescharacteristic
251C2×C4C23×D28311yescharacteristic
252C8—5662no—
253C8—5662no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—11321no—
261C22—11321no—
262C22—11321no—
263C22#2258363612yes—
264C22C22×C22⋊D28311yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—11321no—
272C4—11321no—
273C4—11321no—
274C4C2×#1798539212yes—
275C2—22no—
276C2—44no—
277C2—22641no—
278C2#3182697611yescharacteristic
279C2C2×#2258363611yescharacteristic
280C2#3182726311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×C4×D4×C283C2
socleC22×C283C22×D4
prime radical#31826599C2
hypercenterC2×C4×D4D283
hypocenterC283#3114
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #31826999C2semidirect
2. #31826795C2semidirect
3. #31826778C2semidirect
4. #31826765C2semidirect
5. #31826680C2semidirect
6. #31826616C2semidirect
8. #31826575C2semidirect
9. #31826565C2semidirect
10. #31826522C2semidirect
11. C2×C4×D4×C283C2semidirect
15. #22583602C22semidirect
16. #22583598C22semidirect
20. C4×Dic566C22semidirect
21. C4×D1132C22semidirect
24. #22583543C22semidirect
25. #22583541C22semidirect
26. C4⋊(C283⋊C8)C22semidirect
27. #22583533C22semidirect
30. #22583530C22semidirect
33. #22583521C22semidirect
140. C283#3114semidirect
143. C2×C4×D4D283semidirect

Maximal subgroups

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

subgroupindex
#318269992
#318267952
#318267782
#318267652
#318266802
#318266162
#318265992
#318265752
#318265652
#318265222
C2×C4×D4×C2832
#3114283