Finite Group Databasebeta

← #49123641

Subgroups — #49123641

Order 36224.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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
1C23×C4×D283C211yesmaximal, characteristic
2C2×#22583566C212yesmaximal, complemented
3#31826328C211yesmaximal, characteristic, complemented
4#31826324C214yesmaximal, complemented
5#31826320C212yesmaximal
6#31826312C214yesmaximal, complemented
7#381×C283C211yesmaximal, characteristic, complemented
8C24×D283C2211yescharacteristic
9C23×Dic283C2211yescharacteristic
10C22×C4×D283—28no—
11C22×C4×D283C418yescomplemented
12C22×C4×D283C2212yes—
13C22×C4×D283C2212yes—
14#22583566—28no—
15C2×Dic283⋊C4C2214yescomplemented
16C2×C22⋊Dic283C2212yes—
17C2×(C2×D283)⋊C4C2218yes—
18C2×C4×Dic283C2214yescomplemented
19C283⋊#95C2214yescomplemented
20C23×C4×C283C2211yescharacteristic
21C2×C22⋊C4×C283C2212yes—
22#95×C283C2214yescomplemented
23C23×D283—28no—
24C23×D283—24no—
25C23×D283C2×C414yes—
26C23×D283C2312yes—
27C22×Dic283C2×C414yes—
28C22×Dic283D418yes—
29C22×Dic283C2314yes—
30C22×Dic283C2311yescharacteristic
31C22×Dic283C2311yescharacteristic
32C2×C4×D283—232no—
33C2×C4×D283—28no—
34C2×C4×D283—28no—
35C2×C4×D283C2×C418yes—
36C2×C4×D283C2×C418yes—
37Dic283⋊C4—28no—
38C22⋊Dic283—24no—
39(C2×D283)⋊C4—216no—
40C4×Dic283—28no—
41C24×C283C2311yescharacteristic
42C22×C4×C283—24no—
43C22×C4×C283C2×C414yes—
44C22×C4×C283C2314yes—
45C22×C4×C283C2312yes—
46C22⋊C4×C283—24no—
47C22×D283—232no—
48C22×D283—28no—
49C22×D283—24no—
50C22×D283—24no—
51C22×D283—216no—
52C22×D283C22×C414yes—
53C22×D283#4118yes—
54C2×Dic283—24no—
55C2×Dic283—28no—
56C2×Dic283C22⋊C4116yescomplemented
57C2×Dic283C22×C412yes—
58C2×Dic283C22×C412yes—
59C2×Dic283C2×D414yes—
60C2×Dic283C2×D414yes—
61C4×D283—216no—
62C4×D283—216no—
63C23×C283—24no—
64C23×C283C22×C412yes—
65C23×C283C2×D414yes—
66C23×C283C2411yescharacteristic
67C2×C4×C283—28no—
68C2×C4×C283—24no—
69C2×C4×C283—24no—
70C2×C4×C283—28no—
71C2×C4×C283C22×C414yes—
72C22×C283—24no—
73C22×C283—28no—
74C22×C283C2×C22⋊C414yes—
75C22×C283C23×C411yescharacteristic
76C22×C283C22×D412yes—
77C22×C283C2×#4114yes—
78C2×D283—232no—
79C2×D283—24no—
80C2×D283—24no—
81C2×D283—216no—
82C2×D283#11718yescomplemented
83C4×C283—24no—
84C4×C283—44no—
85Dic283—44no—
86Dic283C2×C22⋊C414yes—
87Dic283C2×C22⋊C414yes—
88C2×C283—24no—
89C2×C283C22×C22⋊C411yescharacteristic
90C2×C283C2×#11712yes—
91C2×C283#52514yes—
92D283—28no—
93C283#228011yescharacteristic, complemented, Sylow
94#2280—2831nomaximal, Sylow
95C24×C4—2831no—
96C2×#117—2832no—
97#381—2831no—
98#381D28311yescharacteristic, complemented
99#380—2834no—
100#379—2832no—
101C4×C22⋊C4—2834no—
102C25—2831no—
103C23×C4—2831no—
104C23×C4—2838no—
105C23×C4—2832no—
106C23×C4—2832no—
107C23×C4—5668no—
108C23×C4C2×D28311yescharacteristic
109#117—5668no—
110C2×C4⋊C4—2834no—
111C2×C22⋊C4—2832no—
112C2×C22⋊C4—2838no—
113C2×C22⋊C4C2×D28312yes—
114C2×C42—2834no—
115#95—2834no—
116#95C2×D28314yescomplemented
117C24—2832no—
118C24—2834no—
119C24—5668no—
120C24—5664no—
121C24C22×D28311yescharacteristic
122C22×C4—24no—
123C22×C4—2834no—
124C22×C4—2838no—
125C22×C4—2831no—
126C22×C4—2831no—
127C22×C4—2838no—
128C22×C4—2838no—
129C22×C4—2834no—
130C22×C4—56632no—
131C22×C4—5668no—
132C22×C4—5668no—
133C22×C4C4×D28314yes—
134C22×C4C22×D28314yes—
135C22×C4C22×D28312yes—
136C4⋊C4—5668no—
137C22⋊C4—24no—
138C22⋊C4—56616no—
139C22⋊C4—5664no—
140C42—5668no—
141C23—24no—
142C23—2834no—
143C23—2838no—
144C23—56616no—
145C23—56632no—
146C23—5668no—
147C23—5664no—
148C23—5664no—
149C23C2×C4×D28312yes—
150C23D4×D28314yes—
151C23C23×D28311yescharacteristic
152C2×C4—28no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—28316no—
157C2×C4—2832no—
158C2×C4—2832no—
159C2×C4—2834no—
160C2×C4—2834no—
161C2×C4—56616no—
162C2×C4—56616no—
163C2×C4—5664no—
164C2×C4—5668no—
165C2×C4C2×C4×D28314yes—
166C22—28no—
167C22—24no—
168C22—2838no—
169C22—56632no—
170C22—56616no—
171C22—5664no—
172C22—5664no—
173C22C22⋊C4×D28314yes—
174C22C22×C4×D28311yescharacteristic
175C22C2×D4×D28312yes—
176C22#41×D28314yes—
177C4—24no—
178C4—44no—
179C4—2834no—
180C4—2834no—
181C4—11324no—
182C2—24no—
183C2—5668no—
184C2C2×C22⋊C4×D28311yescharacteristic
185C2#117×D28312yes—
186C2#3182697314yes—
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#381×C283C2
socle, cosocleC23×C283C24
prime radicalC24×D283C22
hypercenter#381D283
hypocenterC283#2280
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#22583566C2semidirect
3. #31826328C2semidirect
4. #31826324C2semidirect
6. #31826312C2semidirect
7. #381×C283C2semidirect
11. C22×C4×D283C4semidirect
15. C2×Dic283⋊C4C22semidirect
18. C2×C4×Dic283C22semidirect
19. C283⋊#95C22semidirect
22. #95×C283C22semidirect
56. C2×Dic283C22⋊C4semidirect
82. C2×D283#117semidirect
93. C283#2280semidirect
98. #381D283semidirect
116. #95C2×D283semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D2832
C2×#225835662
#318263282
#318263242
#318263202
#318263122
#381×C2832
#2280283