Finite Group Databasebeta

← #49130866

Subgroups — #49130866

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
1C22×#17985375C211yesmaximal, characteristic, complemented
2#31826972C212yesmaximal, complemented
3#31826720C212yesmaximal, complemented
4#31826715C212yesmaximal, complemented
5#31826708C214yesmaximal, complemented
6#31826503C211yesmaximal, characteristic, complemented
7#31826461C212yesmaximal, complemented
8C2×#135×C283C211yesmaximal, characteristic, complemented
9C22×C4×D283C2211yescharacteristic
10C2×#17985375—24no—
11C2×#17985375C2212yes—
12C2×#17985375C2212yes—
13C22×C283⋊C8C2211yescharacteristic
14#22583591—22no—
15#22583586C2214yes—
16#22583581C2214yes—
17#22583578—22no—
18C4×C22⋊D283—24no—
19#22583569C2212yes—
20#22583544C2212yescomplemented
21#22583542C2212yescomplemented
22#22583534C2214yescomplemented
23#22583531C2214yescomplemented
24C2×#41×C283C2212yes—
25#135×C283—24no—
26C2×Q16×C283C2211yescharacteristic, complemented
27C2×SD16×C283C2212yescomplemented
28C2×D8×C283C2211yescharacteristic, complemented
29C22×C8×C283C2211yescharacteristic
30C23×D283D411yescharacteristic
31C2×C22⋊D283—24no—
32C22×Dic283D411yescharacteristic
33C2×C4×D283—22no—
34C2×C4×D283—22no—
35C2×C4×D283D412yes—
36C2×C4×D283C2312yes—
37#17985375—24no—
38#17985375—24no—
39C2×C283⋊C8—22no—
40C2×C283⋊C8C2312yes—
41C4⋊Dic283C2314yes—
42Dic283⋊C4—24no—
43C22⋊Dic283—24no—
44C22⋊Dic283—22no—
45(C2×D283)⋊C4—24no—
46C4×Dic283—22no—
47#41×C283—24no—
48#41×C283—24no—
49C2×Q8×C283C2312yes—
50C2×D4×C283—22no—
51C2×D4×C283C2312yes—
52C22×C4×C283—22no—
53C22×C4×C283C2311yescharacteristic
54Q16×C283—22no—
55SD16×C283—24no—
56D8×C283—22no—
57C2×C8×C283D414yescomplemented
58C2×C8×C283C2311yescharacteristic
59C2×C8×C283C2311yescharacteristic
60C22×D283—22no—
61C22×D283—42no—
62C22×D283C2×D412yes—
63C22⋊D283—48no—
64C2×Dic283—22no—
65C2×Dic283—24no—
66C2×Dic283C2×D412yes—
67C4×D283—24no—
68C4×D283—22no—
69C4×D283—22no—
70C283⋊C8—22no—
71C23×C283—22no—
72C23×C283C2×D411yescharacteristic
73Q8×C283—22no—
74Q8×C283—22no—
75D4×C283—22no—
76D4×C283—22no—
77D4×C283—44no—
78C2×C4×C283—22no—
79C2×C4×C283—44no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D412yes—
82C2×C4×C283#4112yes—
83C2×C4×C283C2411yescharacteristic
84C8×C283C2×D412yes—
85C8×C283C2×D412yes—
86C22×C283—22no—
87C22×C283—42no—
88C22×C283—44no—
89C22×C283#12112yes—
90C22×C283C22×D411yescharacteristic
91C2×D283—22no—
92C2×D283—24no—
93C2×D283—44no—
94C4×C283—42no—
95C4×C283#12112yes—
96C4×C283C22×D411yescharacteristic
97C4×C283C2×#4111yescharacteristic
98Dic283—22no—
99Dic283—44no—
100C2×C283—22no—
101C2×C283—82no—
102C2×C283C2×#12111yescharacteristic
103C2×C283#57512yes—
104D283—42no—
105C283#305411yescharacteristic, complemented, Sylow
106#3054—2831nomaximal, Sylow
107C2×#135D28311yescharacteristic, complemented
108C22×M16—2831no—
109#525—2832no—
110#470—2832no—
111#469—2832no—
112#468—2834no—
113#427—2831no—
114#416—2832no—
115C2×#41C2×D28312yes—
116C23×C4—2831no—
117#135—24no—
118C2×Q16C2×D28311yescharacteristic, complemented
119C2×SD16C2×D28312yescomplemented
120C2×D8C2×D28311yescharacteristic, complemented
121C2×M16—2832no—
122C2×M16—2832no—
123C2×M16—5664no—
124C22×C8—2831no—
125C22×C8C2×D28311yescharacteristic
126#123—5662no—
127C22⋊Q8—2834no—
128#121—2834no—
129#120—5662no—
130C4×D4—5664no—
131#117—2832no—
132#107—2832no—
133#106—2832no—
134#103—2834no—
135#102—2834no—
136C24—2831no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D28312yes—
140C2×D4—22no—
141C2×D4—5664no—
142C2×D4C22×D28312yes—
143C22×C4—22no—
144C22×C4—2831no—
145C22×C4—2832no—
146C22×C4—2832no—
147C22×C4—5662no—
148C22×C4—5662no—
149C22×C4C22×D28311yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—5664no—
154M16—5664no—
155C2×C8—2832no—
156C2×C8—5662no—
157C2×C8C22⋊D28314yescomplemented
158C2×C8C22×D28311yescharacteristic
159C2×C8C22×D28311yescharacteristic
160C4⋊C4—2834no—
161C4⋊C4—5664no—
162C22⋊C4—5664no—
163C22⋊C4—5664no—
164C22⋊C4—5662no—
165C42—5662no—
166C23—22no—
167C23—2832no—
168C23—5662no—
169C23—11322no—
170C23D4×D28311yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—11328no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—2832no—
180C2×C4—5662no—
181C2×C4—5664no—
182C2×C4—5662no—
183C2×C4—5662no—
184C2×C4—5664no—
185C2×C4D4×D28311yescharacteristic
186C2×C4C2×C22⋊D28312yes—
187C2×C4#1798539112yes—
188C2×C4C23×D28311yescharacteristic
189C8—5662no—
190C8C2×C22⋊D28312yes—
191C8C2×C22⋊D28312yes—
192C22—22no—
193C22—42no—
194C22—44no—
195C22—5662no—
196C22—5664no—
197C22—11324no—
198C22#2258358112yes—
199C22C2×D4×D28311yescharacteristic
200C4—42no—
201C4—5662no—
202C4—11324no—
203C4#2258358112yes—
204C4C22×C22⋊D28311yescharacteristic
205C4C2×#1798539111yescharacteristic
206C2—22no—
207C2—82no—
208C2—11322no—
209C2C2×#2258358111yescharacteristic
210C2#3182726212yes—
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#135×C283C2
socleC22×C283C22×D4
hypercenterC2×#135D283
hypocenterC283#3054
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#17985375C2semidirect
2. #31826972C2semidirect
3. #31826720C2semidirect
4. #31826715C2semidirect
5. #31826708C2semidirect
6. #31826503C2semidirect
7. #31826461C2semidirect
8. C2×#135×C283C2semidirect
20. #22583544C22semidirect
21. #22583542C22semidirect
22. #22583534C22semidirect
23. #22583531C22semidirect
26. C2×Q16×C283C22semidirect
27. C2×SD16×C283C22semidirect
28. C2×D8×C283C22semidirect
57. C2×C8×C283D4semidirect
105. C283#3054semidirect
107. C2×#135D283semidirect
118. C2×Q16C2×D283semidirect
119. C2×SD16C2×D283semidirect
120. C2×D8C2×D283semidirect
157. C2×C8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853752
#318269722
#318267202
#318267152
#318267082
#318265032
#318264612
C2×#135×C2832
#3054283