Finite Group Databasebeta

← #49130754

Subgroups — #49130754

Order 36224.

500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22583643C211yesmaximal, characteristic, complemented
2C2×#22583636C211yesmaximal, characteristic
3C2×#22583597C211yesmaximal, characteristic, complemented
4#31826933C211yesmaximal, characteristic, complemented
5#31826686C214yesmaximal, complemented
6#31826679C214yesmaximal, complemented
7#31826488C211yesmaximal, characteristic, complemented
8#31826473C211yesmaximal, characteristic, complemented
9#418×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×Dic566C2211yescharacteristic
12#22583643—24no—
13#22583636—24no—
14C2×Dic1132C2212yescomplemented
15C2×#17985381C2212yescomplemented
16C2×#17985380C2212yes—
17C2×#17985377C2212yes—
18C2×#17985376C2211yescharacteristic
19#22583597—21no—
20#22583597—21no—
21#22583597C2214yes—
22#22583575C2212yescomplemented
23#22583572C2212yescomplemented
24(C22⋊D283)⋊C4—22no—
25#22583567—21no—
26C2×C22⋊Dic283—22no—
27C2×C4×Dic283C2211yescharacteristic
28C42×D283—21no—
29Dic283⋊C8C2214yescomplemented
30#22583533C2214yescomplemented
31C22×D4×C283C2211yescharacteristic
32C2×M16×C283C2211yescharacteristic
33#117×C283C2211yescharacteristic
34#102×C283C2214yes—
35#17985392—22no—
36#17985392D414yes—
37C2×Dic566—21no—
38C2×Dic566—22no—
39C2×Dic566—22no—
40C2×Dic566C2312yes—
41C2×Dic566C2311yescharacteristic
42C2×D1132C2311yescharacteristic
43C2×C22⋊D283—21no—
44C22×Dic283—21no—
45C22×Dic283D412yes—
46C2×C4×D283—22no—
47C2×C4×D283—21no—
48Dic1132—24no—
49#17985381—24no—
50#17985380—24no—
51#17985377—24no—
52#17985376—22no—
53C2×C283⋊C8C2312yes—
54Dic283⋊C4—22no—
55C22⋊Dic283—24no—
56C22⋊Dic283—24no—
57(C2×D283)⋊C4—22no—
58C4×Dic283—22no—
59C4×Dic283D411yescharacteristic
60C4×Dic283D411yescharacteristic
61C4×Dic283C2312yes—
62C24×C283—21no—
63C2×D4×C283—22no—
64C2×D4×C283—21no—
65C2×D4×C283—22no—
66C2×D4×C283C2312yes—
67C22×C4×C283C2311yescharacteristic
68M16×C283—22no—
69C2×C8×C283C2312yes—
70C4⋊C4×C283C2312yes—
71C22⋊C4×C283—21no—
72C42×C283—21no—
73C22×D283—21no—
74Dic566—21no—
75Dic566—22no—
76Dic566—22no—
77Dic566—42no—
78Dic566C2×D412yes—
79D1132—21no—
80D1132C2×D412yes—
81C22⋊D283—24no—
82C2×Dic283—21no—
83C2×Dic283—22no—
84C2×Dic283—42no—
85C2×Dic283—42no—
86C2×Dic283C2×D412yes—
87C2×Dic283C2×D412yes—
88C4×D283—24no—
89C4×D283—44no—
90C283⋊C8—22no—
91C23×C283—22no—
92C23×C283—44no—
93C23×C283—42no—
94C23×C283C2×D411yescharacteristic
95D4×C283—22no—
96D4×C283—22no—
97D4×C283—42no—
98C2×C4×C283—22no—
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2×D412yes—
101C2×C4×C283#4112yes—
102C2×C4×C283C2411yescharacteristic
103C8×C283—22no—
104C22×C283—22no—
105C22×C283—42no—
106C22×C283—44no—
107C22×C283—84no—
108C22×C283#12112yes—
109C22×C283C22×D411yescharacteristic
110C2×D283—22no—
111C2×D283—42no—
112C4×C283—42no—
113C4×C283#12112yes—
114C4×C283C22×D411yescharacteristic
115C4×C283C2×#4111yescharacteristic
116Dic283—22no—
117Dic283—22no—
118Dic283—22no—
119Dic283—42no—
120C2×C283—22no—
121C2×C283—82no—
122C2×C283C2×#12111yescharacteristic
123C2×C283#57512yes—
124D283—42no—
125C283#304011yescharacteristic, complemented, Sylow
126#3040—2831nomaximal, Sylow
127C2×#137—2831no—
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#418D28311yescharacteristic, complemented
136C2×#41—2831no—
137C22×Q8—2831no—
138C22×D4C2×D28311yescharacteristic
139#137—5664no—
140AGL(1,ℤ/8)—5664no—
141C2×Q16—2832no—
142C2×SD16—2832no—
143C2×SD16—2832no—
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—5661no—
154#117C2×D28311yescharacteristic
155C2×C22⋊C4—5662no—
156C2×C42—2831no—
157C2×C42—5661no—
158C4⋊C8—2834no—
159#103—2834no—
160#102C2×D28314yes—
161C24—21no—
162#41—2834no—
163#41—5662no—
164C2×Q8—2831no—
165C2×Q8—2832no—
166C2×Q8—5661no—
167C2×Q8—5662no—
168C2×Q8—5662no—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—22no—
172C2×D4—2831no—
173C2×D4—5661no—
174C2×D4C22×D28312yes—
175C22×C4—2832no—
176C22×C4—5662no—
177C22×C4—5661no—
178C22×C4—5661no—
179C22×C4C22×D28311yescharacteristic
180Q16—5664no—
181SD16—5664no—
182SD16—5664no—
183D8—5664no—
184M16—22no—
185M16—5662no—
186C2×C8—2832no—
187C2×C8C22×D28312yes—
188C4⋊C4—5662no—
189C4⋊C4C22×D28312yes—
190C22⋊C4—21no—
191C22⋊C4—5662no—
192C22⋊C4—5664no—
193C22⋊C4—5664no—
194C42—21no—
195C42—2831no—
196C42—2831no—
197C42—2832no—
198C42—5662no—
199C23—22no—
200C23—44no—
201C23—42no—
202C23—5661no—
203C23D4×D28311yescharacteristic
204Q8—2832no—
205Q8—5661no—
206Q8—5662no—
207Q8—5662no—
208Q8—11322no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—2832no—
213D4—5664no—
214D4—5661no—
215C2×C4—22no—
216C2×C4—2832no—
217C2×C4—2832no—
218C2×C4—5661no—
219C2×C4—5664no—
220C2×C4—5662no—
221C2×C4—11324no—
222C2×C4—11322no—
223C2×C4—11322no—
224C2×C4D4×D28311yescharacteristic
225C2×C4D4×D28312yes—
226C2×C4#1798539212yes—
227C2×C4C23×D28311yescharacteristic
228C8—22no—
229C8—5662no—
230C22—22no—
231C22—42no—
232C22—44no—
233C22—84no—
234C22—5662no—
235C22—11322no—
236C22#2258358312yes—
237C22C2×D4×D28311yescharacteristic
238C4—42no—
239C4—5662no—
240C4—5662no—
241C4—5662no—
242C4—11322no—
243C4#2258358312yes—
244C4C2×D4×D28311yescharacteristic
245C4C2×#1798539211yescharacteristic
246C2—22no—
247C2—82no—
248C2—11322no—
249C2C2×#2258358311yescharacteristic
250C2#3182726112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#418×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583636C2
hypercenter#418D283
hypocenterC283#3040
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. C2×#22583643C2semidirect
3. C2×#22583597C2semidirect
4. #31826933C2semidirect
5. #31826686C2semidirect
6. #31826679C2semidirect
7. #31826488C2semidirect
8. #31826473C2semidirect
9. #418×C283C2semidirect
14. C2×Dic1132C22semidirect
15. C2×#17985381C22semidirect
22. #22583575C22semidirect
23. #22583572C22semidirect
29. Dic283⋊C8C22semidirect
30. #22583533C22semidirect
125. C283#3040semidirect
135. #418D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
C2×#225836362
C2×#225835972
#318269332
#318266862
#318266792
#318264882
#318264732
#418×C2832
#3040283