Finite Group Databasebeta

← #49131513

Subgroups — #49131513

Order 36224.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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#31827077C211yesmaximal, characteristic, complemented
2#31826806C212yesmaximal, complemented
3#31826765C212yesmaximal, complemented
4#31826670C212yesmaximal, complemented
5#31826616C212yesmaximal
6#31826565C212yesmaximal, complemented
7C4×#17985380C212yesmaximal, complemented
8#31826526C211yesmaximal, characteristic, complemented
9#518×C283C211yesmaximal, characteristic
10C2×#17985380C2212yes—
11C2×#17985380C2212yes—
12#22583610C2211yescharacteristic, complemented
13#22583603—22no—
14#22583602C2211yescharacteristic, complemented
15#22583600—22no—
16#22583589C2212yes—
17C4×Dic566C2212yescomplemented
18#22583543C2212yescomplemented
19#22583541C2212yescomplemented
20C4⋊(C283⋊C8)C2212yescomplemented
21#22583533C2212yescomplemented
22#22583533C2212yescomplemented
23#22583531C2212yes—
24#22583531C2212yes—
25C22⋊(C283⋊C8)C2212yes—
26#22583521C2211yescharacteristic, complemented
27C4×C283⋊C8C2211yescharacteristic, complemented
28C22×D4×C283C2211yescharacteristic
29C4×D4×C283—22no—
30C4×D4×C283C2212yes—
31C4×D4×C283C2212yes—
32#117×C283C2211yescharacteristic
33#117×C283C2211yescharacteristic
34C2×C22⋊C4×C283—22no—
35C2×Dic566C2312yes—
36#17985380—24no—
37#17985380—24no—
38C2×C283⋊C8C2312yes—
39C2×C283⋊C8C2312yes—
40C4⋊Dic283—22no—
41C4⋊Dic283C2312yes—
42Dic283⋊C4—22no—
43Dic283⋊C4—22no—
44Dic283⋊C4—22no—
45C22⋊Dic283—22no—
46C4×Dic283—22no—
47C24×C283—21no—
48C2×D4×C283—24no—
49C2×D4×C283—21no—
50C2×D4×C283C2312yes—
51C22×C4×C283—22no—
52C22×C4×C283—22no—
53C22×C4×C283C2311yescharacteristic
54C4⋊C4×C283D412yes—
55C4⋊C4×C283C2312yes—
56C22⋊C4×C283—21no—
57C22⋊C4×C283—22no—
58C22⋊C4×C283—22no—
59C22⋊C4×C283D412yes—
60C42×C283—21no—
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63Dic566—22no—
64Dic566—22no—
65C2×Dic283—22no—
66C2×Dic283—22no—
67C283⋊C8—22no—
68C283⋊C8—22no—
69C23×C283—24no—
70C23×C283—22no—
71C23×C283—82no—
72C23×C283C2×D411yescharacteristic
73D4×C283—24no—
74D4×C283—22no—
75D4×C283#4114yes—
76C2×C4×C283—22no—
77C2×C4×C283—22no—
78C2×C4×C283—82no—
79C2×C4×C283—82no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D412yes—
82C2×C4×C283C2×D412yes—
83C2×C4×C283C2411yescharacteristic
84C22×C283—21no—
85C22×C283—24no—
86C22×C283—22no—
87C22×C283—42no—
88C22×C283—42no—
89C22×C283—84no—
90C22×C283C22×D411yescharacteristic
91C4×C283—21no—
92C4×C283—22no—
93C4×C283—22no—
94C4×C283—42no—
95C4×C283C2×#4112yes—
96Dic283—42no—
97Dic283—42no—
98C2×C283—41no—
99C2×C283—44no—
100C2×C283#52511yescharacteristic
101C2×C283#57712yes—
102C283#312311yescharacteristic, complemented, Sylow
103#3123—2831nomaximal, Sylow
104#541—2831no—
105#518D28311yescharacteristic
106#485—2832no—
107#478—2832no—
108#461—2832no—
109#450—2832no—
110#440—2832no—
111C4×SD16—2832no—
112#433—2831no—
113C22×D4C2×D28311yescharacteristic
114C2×SD16—2832no—
115C2×SD16—2832no—
116C4⋊Q8—2831no—
117#126—5662no—
118#125—2831no—
119#125—5662no—
120C22⋊Q8—2832no—
121C4×Q8—2832no—
122C4×D4—22no—
123C4×D4C2×D28312yes—
124C4×D4C2×D28312yes—
125#117C2×D28311yescharacteristic
126#117C2×D28311yescharacteristic
127C2×C22⋊C4—22no—
128#107—2832no—
129#106—2832no—
130C4⋊C8—2832no—
131#103—2832no—
132#103—2832no—
133#102—2832no—
134#102—2832no—
135C22⋊C8—2832no—
136#97—2831no—
137C4×C8—2831no—
138C24—21no—
139C2×Q8—2832no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D28312yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D28311yescharacteristic
146SD16—5664no—
147SD16—5664no—
148C2×C8—2832no—
149C2×C8—2832no—
150C4⋊C4—2832no—
151C4⋊C4—5662no—
152C4⋊C4—5662no—
153C4⋊C4—5662no—
154C4⋊C4—5662no—
155C4⋊C4C22⋊D28312yes—
156C4⋊C4C22×D28312yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—5662no—
161C22⋊C4C22⋊D28312yes—
162C42—21no—
163C42—5662no—
164C42C22×D28311yescharacteristic
165C42C22×D28311yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D28311yescharacteristic
170Q8—5662no—
171Q8—5662no—
172D4—24no—
173D4—22no—
174D4#1798539214yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—5662no—
180C2×C4—5662no—
181C2×C4C2×C22⋊D28311yescharacteristic
182C2×C4C2×C22⋊D28312yes—
183C2×C4C2×C22⋊D28312yes—
184C2×C4C23×D28311yescharacteristic
185C8—5662no—
186C8—5662no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D28311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—11322no—
199C4—11322no—
200C4C2×#1798539212yes—
201C2—41no—
202C2—44no—
203C2#3182697611yescharacteristic
204C2#3182727612yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#518×C283C2
socleC22×C283C22×D4
prime radicalC22×D4×C283C22
hypercenter#518D283
hypocenterC283#3123
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #31827077C2semidirect
2. #31826806C2semidirect
3. #31826765C2semidirect
4. #31826670C2semidirect
6. #31826565C2semidirect
7. C4×#17985380C2semidirect
8. #31826526C2semidirect
12. #22583610C22semidirect
14. #22583602C22semidirect
17. C4×Dic566C22semidirect
18. #22583543C22semidirect
19. #22583541C22semidirect
20. C4⋊(C283⋊C8)C22semidirect
21. #22583533C22semidirect
22. #22583533C22semidirect
26. #22583521C22semidirect
27. C4×C283⋊C8C22semidirect
102. C283#3123semidirect

Maximal subgroups

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

subgroupindex
#318270772
#318268062
#318267652
#318266702
#318266162
#318265652
C4×#179853802
#318265262
#518×C2832
#3123283