Finite Group Databasebeta

← #49130757

Subgroups — #49130757

Order 36224.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#22583635C211yesmaximal, characteristic
2C2×#22583599C211yesmaximal, characteristic, complemented
3#41×Dic283C211yesmaximal, characteristic, complemented
4#31826689C214yesmaximal, complemented
5#31826682C214yesmaximal, complemented
6#31826488C211yesmaximal, characteristic, complemented
7#31826474C211yesmaximal, characteristic, complemented
8#31826471C211yesmaximal, characteristic, complemented
9C2×#137×C283C211yesmaximal, characteristic, complemented
10C22×D1132C2211yescharacteristic
11#22583635—24no—
12C2×#17985379C2212yes—
13C2×#17985377C2212yes—
14C2×#17985376C2211yescharacteristic
15#22583599—21no—
16#22583599—21no—
17#22583599C2214yes—
18Q8×Dic283C2212yescomplemented
19D4×Dic283—22no—
20D4×Dic283C2212yescomplemented
21#22583569—21no—
22#22583569C2211yescharacteristic
23C2×(C2×D283)⋊C4—22no—
24C2×C4×Dic283—21no—
25C2×C4×Dic283C2211yescharacteristic
26Dic283⋊C8C2214yescomplemented
27#22583534C2214yescomplemented
28#22583532C2214yes—
29C2×#41×C283C2211yescharacteristic
30C22×Q8×C283C2211yescharacteristic
31#137×C283—24no—
32C2×Q16×C283C2212yescomplemented
33C2×SD16×C283C2212yescomplemented
34C2×M16×C283C2211yescharacteristic
35C23×D283—21no—
36C2×D1132—22no—
37C2×D1132—21no—
38C2×D1132—22no—
39C2×D1132C2312yes—
40C22×Dic283—22no—
41C22×Dic283D412yes—
42#17985379—24no—
43#17985377—24no—
44#17985376—22no—
45C2×C283⋊C8C2312yes—
46C4⋊Dic283—22no—
47C4⋊Dic283C2312yes—
48C22⋊Dic283—22no—
49C22⋊Dic283—21no—
50(C2×D283)⋊C4—24no—
51(C2×D283)⋊C4—24no—
52C4×Dic283—22no—
53C4×Dic283—21no—
54C4×Dic283D411yescharacteristic
55C4×Dic283D411yescharacteristic
56C4×Dic283C2312yes—
57#41×C283—22no—
58#41×C283D414yes—
59C2×Q8×C283—21no—
60C2×Q8×C283—22no—
61C2×Q8×C283—22no—
62C2×Q8×C283C2312yes—
63C2×Q8×C283C2311yescharacteristic
64C2×D4×C283—21no—
65C2×D4×C283C2311yescharacteristic
66C22×C4×C283—21no—
67C22×C4×C283—21no—
68C22×C4×C283C2311yescharacteristic
69Q16×C283—24no—
70SD16×C283—24no—
71M16×C283—22no—
72C2×C8×C283C2312yes—
73C22×D283—22no—
74C22×D283—44no—
75C22×D283—42no—
76D1132—22no—
77D1132—22no—
78D1132—42no—
79C2×Dic283—22no—
80C2×Dic283—42no—
81C2×Dic283—44no—
82C2×Dic283C2×D412yes—
83C2×Dic283C2×D412yes—
84C283⋊C8—22no—
85C23×C283—21no—
86C23×C283C2×D411yescharacteristic
87Q8×C283—21no—
88Q8×C283—22no—
89Q8×C283—22no—
90Q8×C283—42no—
91Q8×C283C2×D412yes—
92D4×C283—24no—
93D4×C283—21no—
94D4×C283C2×D412yes—
95C2×C4×C283—21no—
96C2×C4×C283—24no—
97C2×C4×C283—22no—
98C2×C4×C283—42no—
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2×D412yes—
101C2×C4×C283#4112yes—
102C2×C4×C283C2411yescharacteristic
103C8×C283—22no—
104C22×C283—22no—
105C22×C283—22no—
106C22×C283—42no—
107C22×C283#12112yes—
108C22×C283C22×D411yescharacteristic
109C2×D283—42no—
110C2×D283—44no—
111C2×D283—84no—
112C4×C283—22no—
113C4×C283—42no—
114C4×C283#12112yes—
115C4×C283C22×D411yescharacteristic
116C4×C283C2×#4111yescharacteristic
117Dic283—22no—
118Dic283—22no—
119Dic283—42no—
120C2×C283—22no—
121C2×C283—42no—
122C2×C283C2×#12111yescharacteristic
123C2×C283#57512yes—
124D283—82no—
125C283#304011yescharacteristic, complemented, Sylow
126#3040—2831nomaximal, Sylow
127C2×#137D28311yescharacteristic, complemented
128C2×AGL(1,ℤ/8)—2831no—
129C2×#124—2831no—
130C4×#41—2831no—
131#464—2834no—
132#463—2834no—
133#423—2831no—
134#419—2831no—
135#418—2831no—
136C2×#41C2×D28311yescharacteristic
137C22×Q8C2×D28311yescharacteristic
138C22×D4—2831no—
139#137—24no—
140AGL(1,ℤ/8)—5664no—
141C2×Q16C2×D28312yescomplemented
142C2×SD16—2832no—
143C2×SD16C2×D28312yescomplemented
144C2×D8—2832no—
145C2×M16—2831no—
146C2×M16C2×D28311yescharacteristic
147#124—2834no—
148#124—5661no—
149#124—5661no—
150C4×Q8—2832no—
151C4×D4—2832no—
152C4×D4—5662no—
153#117—2831no—
154#117—5661no—
155C2×C22⋊C4—5662no—
156C2×C42—2831no—
157C2×C42—5661no—
158C4⋊C8—2834no—
159#103—2834no—
160#102—2834no—
161C24—5661no—
162#41—22no—
163#41C22⋊D28314yes—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8C22×D28312yes—
168C2×Q8C22×D28311yescharacteristic
169C2×D4—21no—
170C2×D4—2832no—
171C2×D4—5661no—
172C2×D4—5662no—
173C2×D4—5662no—
174C2×D4C22×D28311yescharacteristic
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—2832no—
178C22×C4—5662no—
179C22×C4C22×D28311yescharacteristic
180Q16—24no—
181SD16—24no—
182SD16—5664no—
183D8—5664no—
184M16—22no—
185M16—5662no—
186C2×C8—2832no—
187C2×C8C22×D28312yes—
188C4⋊C4—2832no—
189C4⋊C4—5662no—
190C22⋊C4—5664no—
191C22⋊C4—5664no—
192C22⋊C4—5662no—
193C22⋊C4—5661no—
194C42—2831no—
195C42—2831no—
196C42—2832no—
197C42—5662no—
198C42—5661no—
199C23—21no—
200C23—5662no—
201C23—11324no—
202C23—11322no—
203C23D4×D28311yescharacteristic
204Q8—21no—
205Q8—22no—
206Q8—22no—
207Q8—42no—
208Q8C2×C22⋊D28312yes—
209D4—24no—
210D4—21no—
211D4—5662no—
212D4—5662no—
213D4—11322no—
214D4C2×C22⋊D28312yes—
215C2×C4—21no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—2832no—
220C2×C4—2832no—
221C2×C4—5662no—
222C2×C4—11322no—
223C2×C4—11324no—
224C2×C4D4×D28311yescharacteristic
225C2×C4C2×C22⋊D28312yes—
226C2×C4#1798539112yes—
227C2×C4C23×D28311yescharacteristic
228C8—22no—
229C8—5662no—
230C22—22no—
231C22—22no—
232C22—42no—
233C22—11322no—
234C22—11324no—
235C22—22644no—
236C22#2258358212yes—
237C22C2×D4×D28311yescharacteristic
238C4—22no—
239C4—42no—
240C4—5662no—
241C4—5662no—
242C4—11322no—
243C4#2258358212yes—
244C4C22×C22⋊D28311yescharacteristic
245C4C2×#1798539111yescharacteristic
246C2—22no—
247C2—42no—
248C2—22642no—
249C2C2×#2258358211yescharacteristic
250C2#3182726412yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#137×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583635C2
hypercenterC2×#137D283
hypocenterC283#3040
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#22583599C2semidirect
3. #41×Dic283C2semidirect
4. #31826689C2semidirect
5. #31826682C2semidirect
6. #31826488C2semidirect
7. #31826474C2semidirect
8. #31826471C2semidirect
9. C2×#137×C283C2semidirect
18. Q8×Dic283C22semidirect
20. D4×Dic283C22semidirect
26. Dic283⋊C8C22semidirect
27. #22583534C22semidirect
32. C2×Q16×C283C22semidirect
33. C2×SD16×C283C22semidirect
125. C283#3040semidirect
127. C2×#137D283semidirect
141. C2×Q16C2×D283semidirect
143. C2×SD16C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836352
C2×#225835992
#41×Dic2832
#318266892
#318266822
#318264882
#318264742
#318264712
C2×#137×C2832
#3040283