Finite Group Databasebeta

← #19137220

Subgroups — #19137220

Order 5504.

600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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×#13063283C211yesmaximal, characteristic
2C2×#13063282C211yesmaximal, characteristic
3C2×C4⋊C4×D43C211yesmaximal, characteristic
4#14582796C214yesmaximal, complemented
5#14582773C214yesmaximal
6#14582769C211yesmaximal, characteristic, complemented
7#14582768C211yesmaximal, characteristic, complemented
8#14582764C211yesmaximal, characteristic, complemented
9C43×#382C211yesmaximal, characteristic, complemented
10C22×C4×D43C2212yes—
11C22×C4×D43C2211yescharacteristic
12#13063283—24no—
13#13063282C418yescomplemented
14C2×C4⋊Dic43C2211yescharacteristic
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2214yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2214yes—
19C2×Dic43⋊C4C2212yes—
20C4⋊C4×D43—24no—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×C4×Dic43C2212yes—
24C2×C4×Dic43C2211yescharacteristic
25C43⋊#95C2214yes—
26C2×C4⋊C4×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C42×C43C2211yescharacteristic
29#95×C43C2214yes—
30C23×D43C2311yescharacteristic
31C22×C4×C43C2312yes—
32C22×C4×C43C2312yes—
33C22×C4×C43C2312yes—
34C22×C4×C43C2311yescharacteristic
35C22×Dic43C2312yes—
36C22×Dic43C2312yes—
37C22×Dic43C2312yes—
38C22×Dic43C2311yescharacteristic
39C2×C4×D43—24no—
40C2×C4×D43—44no—
41C2×C4×D43C2×C414yes—
42C2×C4×D43D414yes—
43C2×C4×D43Q814yes—
44C4⋊C4×C43—22no—
45C4⋊C4×C43—22no—
46C42×C43C2×C414yescomplemented
47(C2×D43)⋊C4—24no—
48(C2×D43)⋊C4C2×C418yes—
49C4⋊Dic43—22no—
50C4⋊Dic43—22no—
51C4⋊Dic43—44no—
52Dic43⋊C4—24no—
53Dic43⋊C4—44no—
54Dic43⋊C4C2×C418yescomplemented
55C4×Dic43—24no—
56C4×Dic43C2×C414yescomplemented
57C23×C43C2411yescharacteristic
58C22×D43—22no—
59C22×D43—22no—
60C22×D43C22×C412yes—
61C22×D43C2×D412yes—
62C22×D43C2×Q812yes—
63C2×C4×C43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—24no—
68C2×C4×C43—24no—
69C2×C4×C43C22×C414yes—
70C2×C4×C43C22×C412yes—
71C2×C4×C43C2×D412yes—
72C2×C4×C43C2×Q812yes—
73C2×Dic43—22no—
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43—24no—
78C2×Dic43—24no—
79C2×Dic43C22×C414yes—
80C2×Dic43C22×C412yes—
81C2×Dic43C2×D412yes—
82C2×Dic43C2×Q812yes—
83C4×D43—48no—
84C4×D43C4⋊C4116yescomplemented
85C22×C43C23×C411yescharacteristic
86C22×C43C22×D411yescharacteristic
87C22×C43C22×Q811yescharacteristic
88C22×C43H(5,𝔽2)12yes—
89C22×C432−1+412yes—
90C2×D43—24no—
91C2×D43—22no—
92C2×D43—22no—
93C2×D43—24no—
94C2×D43C2×C4⋊C414yes—
95C4×C43—24no—
96C4×C43—42no—
97C4×C43—42no—
98C4×C43C2×C4⋊C414yes—
99Dic43—24no—
100Dic43—42no—
101Dic43—42no—
102Dic43C2×C4⋊C414yes—
103#2317—431nomaximal, Sylow
104C2×C43C22×C4⋊C411yescharacteristic
105C2×C43#52012yes—
106C2×C43#53511yescharacteristic
107C2×C43#53611yescharacteristic
108C2×C43#54412yes—
109D43—24no—
110C2×#117—431no—
111C2×#117—431no—
112C22×C4⋊C4—431no—
113#389—434no—
114#385—434no—
115#384—431no—
116#384—431no—
117#382—431no—
118#382D4311yescharacteristic, complemented
119C43#231711yescharacteristic, complemented, Sylow
120C23×C4—431no—
121C23×C4—432no—
122#117—438no—
123#117—864no—
124C2×C4⋊C4—432no—
125C2×C4⋊C4—432no—
126C2×C4⋊C4—431no—
127C2×C4⋊C4—431no—
128C2×C4⋊C4—434no—
129C2×C4⋊C4—434no—
130C2×C4⋊C4—864no—
131C2×C4⋊C4C2×D4311yescharacteristic
132C2×C4⋊C4C2×D4311yescharacteristic
133C2×C22⋊C4—432no—
134C2×C22⋊C4—432no—
135C2×C42—431no—
136C2×C42—432no—
137C2×C42C2×D4311yescharacteristic
138#95—434no—
139#95C2×D4314yes—
140C24—431no—
141C22×C4—431no—
142C22×C4—434no—
143C22×C4—434no—
144C22×C4—434no—
145C22×C4—432no—
146C22×C4—432no—
147C22×C4—432no—
148C22×C4—864no—
149C22×C4—1724no—
150C22×C4C22×D4312yes—
151C22×C4C22×D4312yes—
152C22×C4C22×D4312yes—
153C22×C4C22×D4311yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—438no—
157C4⋊C4—864no—
158C4⋊C4—862no—
159C4⋊C4—862no—
160C4⋊C4—1724no—
161C4⋊C4—1724no—
162C22⋊C4—438no—
163C22⋊C4—864no—
164C42—434no—
165C42—864no—
166C42C4×D4314yescomplemented
167C23—432no—
168C23—432no—
169C23—432no—
170C23—862no—
171C23—862no—
172C23C23×D4311yescharacteristic
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—432no—
180C2×C4—432no—
181C2×C4—432no—
182C2×C4—4316no—
183C2×C4—434no—
184C2×C4—862no—
185C2×C4—862no—
186C2×C4—862no—
187C2×C4—862no—
188C2×C4—864no—
189C2×C4—864no—
190C2×C4—1728no—
191C2×C4C2×C4×D4314yes—
192C2×C4C2×C4×D4312yes—
193C2×C4D4×D4312yes—
194C2×C4Q8×D4312yes—
195C22—434no—
196C22—864no—
197C22—862no—
198C22—862no—
199C22—864no—
200C22C22×C4×D4311yescharacteristic
201C22C2×D4×D4311yescharacteristic
202C22C2×Q8×D4311yescharacteristic
203C22#1306337112yes—
204C22#1306337212yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—434no—
209C4—864no—
210C4—1722no—
211C4—1722no—
212C4C4⋊C4×D4314yes—
213C2—864no—
214C2C2×C4⋊C4×D4311yescharacteristic
215C2#1458337912yes—
216C2#1458346711yescharacteristic
217C2#1458346911yescharacteristic
218C2#1458352912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#382C2
socleC23×C43C24
hypercenter#382D43
hypocenterC43#2317
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
4. #14582796C2semidirect
6. #14582769C2semidirect
7. #14582768C2semidirect
8. #14582764C2semidirect
9. C43×#382C2semidirect
13. #13063282C4semidirect
46. C42×C43C2×C4semidirect
54. Dic43⋊C4C2×C4semidirect
56. C4×Dic43C2×C4semidirect
84. C4×D43C4⋊C4semidirect
118. #382D43semidirect
119. C43#2317semidirect
166. C42C4×D43semidirect