Finite Group Databasebeta

← #19137405

Subgroups — #19137405

Order 5504.

540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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×#13063313C211yesmaximal, characteristic
2#14582803C212yesmaximal, complemented
3#14582791C212yesmaximal, complemented
4#14582788C212yesmaximal, complemented
5#14582777C212yesmaximal
6#14582773C212yesmaximal, complemented
7C4×C4⋊Dic43C211yesmaximal, characteristic, complemented
8#14582746C212yesmaximal, complemented
9C43×#383C211yesmaximal, characteristic, complemented
10C22×Dic86C2211yescharacteristic
11C22×D172C2211yescharacteristic
12C22×C4×D43C2212yes—
13#13063313C418yescomplemented
14C2×C4⋊Dic43C2212yes—
15C2×Dic43⋊C4C2212yes—
16C2×(C2×D43)⋊C4C2212yes—
17C2×(C2×D43)⋊C4C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×C4×Dic43C2211yescharacteristic
22C2×C4×Dic43C2212yes—
23C2×C4×Dic43C2211yescharacteristic
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C2×C42×C43C2211yescharacteristic
28#95×C43C2212yes—
29#95×C43C2211yescharacteristic
30#95×C43C2212yes—
31#95×C43C2211yescharacteristic
32C23×D43C2312yes—
33C22×C4×C43C2312yes—
34C22×C4×C43C2312yes—
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C22×Dic43C2312yes—
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C2×D172—42no—
42C2×D172C2×C414yes—
43C2×C4×D43—24no—
44C2×C4×D43—42no—
45C2×C4×D43—42no—
46C2×Dic86—42no—
47C2×Dic86C2×C414yescomplemented
48C42×C43C2×C414yescomplemented
49(C2×D43)⋊C4—24no—
50(C2×D43)⋊C4—42no—
51(C2×D43)⋊C4—42no—
52(C2×D43)⋊C4C2×C418yescomplemented
53(C2×D43)⋊C4C2×C418yescomplemented
54C4⋊Dic43—24no—
55Dic43⋊C4—42no—
56C4×Dic43—42no—
57C4×Dic43—41no—
58C4×Dic43—41no—
59C23×C43C2411yescharacteristic
60C22×D43—22no—
61C22×D43—22no—
62C22×D43—22no—
63C22×D43—22no—
64C22×D43—22no—
65C22×D43—22no—
66C22×D43C22×C414yes—
67C2×C4×C43—22no—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—21no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43C22×C412yes—
78C2×C4×C43C22×C412yes—
79C2×C4×C43C22×C412yes—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43C22×C414yes—
88C2×Dic43#4114yes—
89D172—44no—
90C4×D43—48no—
91Dic86—44no—
92C22×C43C23×C411yescharacteristic
93C22×C43C2×#4112yes—
94C22×C43H(5,𝔽2)12yes—
95C22×C43H(5,𝔽2)11yescharacteristic
96C22×C432−1+411yescharacteristic
97C2×D43—24no—
98C2×D43—24no—
99C2×D43—24no—
100C2×D43—42no—
101C2×D43—42no—
102C2×D43—42no—
103C2×D43—42no—
104C4×C43—22no—
105C4×C43—22no—
106C4×C43—22no—
107C4×C43—42no—
108C4×C43—42no—
109Dic43—24no—
110Dic43—24no—
111Dic43—42no—
112#2337—431nomaximal, Sylow
113C2×C43C4×#4111yescharacteristic
114C2×C43#51811yescharacteristic
115C2×C43#52011yescharacteristic
116C2×C43#53812yes—
117C2×C43#54212yes—
118D43—44no—
119C2×#124—431no—
120#391—432no—
121#388—432no—
122#388—432no—
123#386—432no—
124#385—432no—
125#383D4311yescharacteristic, complemented
126C4×C4⋊C4—431no—
127C4×C22⋊C4—432no—
128C43#233711yescharacteristic, complemented, Sylow
129C22×Q8—431no—
130C22×D4—431no—
131C23×C4—432no—
132#124—438no—
133C2×C4⋊C4—432no—
134C2×C4⋊C4—432no—
135C2×C22⋊C4—432no—
136C2×C22⋊C4—432no—
137C2×C22⋊C4—432no—
138C2×C22⋊C4—432no—
139C2×C22⋊C4—432no—
140C2×C42—431no—
141C2×C42—432no—
142C2×C42—431no—
143C2×C42C2×D4311yescharacteristic
144#95—432no—
145#95—432no—
146#95—432no—
147#95C2×D4312yes—
148#95C2×D4311yescharacteristic
149#95C2×D4312yes—
150#95C2×D4311yescharacteristic
151C24—432no—
152C2×Q8—434no—
153C2×Q8—1722no—
154C2×D4—434no—
155C2×D4—1722no—
156C22×C4—432no—
157C22×C4—432no—
158C22×C4—432no—
159C22×C4—864no—
160C22×C4—1722no—
161C22×C4—1722no—
162C22×C4C22×D4312yes—
163C22×C4C22×D4312yes—
164C22×C4C22×D4311yescharacteristic
165C22×C4C22×D4311yescharacteristic
166C22×C4C22×D4311yescharacteristic
167C4⋊C4—864no—
168C4⋊C4—1722no—
169C22⋊C4—438no—
170C22⋊C4—438no—
171C22⋊C4—864no—
172C22⋊C4—1722no—
173C22⋊C4—1722no—
174C42—1721no—
175C42—1721no—
176C42—1722no—
177C42C4×D4314yescomplemented
178C23—434no—
179C23—862no—
180C23—862no—
181C23—862no—
182C23—862no—
183C23—862no—
184C23—862no—
185C23C23×D4311yescharacteristic
186Q8—1724no—
187D4—1724no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—434no—
199C2×C4—434no—
200C2×C4—862no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—1728no—
208C2×C4C2×C4×D4312yes—
209C2×C4C2×C4×D4312yes—
210C2×C4C2×C4×D4312yes—
211C22—864no—
212C22—864no—
213C22—864no—
214C22—1722no—
215C22—1722no—
216C22—1722no—
217C22—1722no—
218C22C22×C4×D4311yescharacteristic
219C22#41×D4312yes—
220C22#1306337112yes—
221C22#1306337111yescharacteristic
222C22#1306337211yescharacteristic
223C4—22no—
224C4—22no—
225C4—22no—
226C4—42no—
227C4—42no—
228C4—864no—
229C4—864no—
230C4—1722no—
231C2—1724no—
232C2#1458336711yescharacteristic
233C2#1458337311yescharacteristic
234C2#1458337911yescharacteristic
235C2#1458348812yes—
236C2#1458351512yes—
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#383C2
socleC23×C43C24
hypercenter#383D43
hypocenterC43#2337
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #14582803C2semidirect
3. #14582791C2semidirect
4. #14582788C2semidirect
6. #14582773C2semidirect
7. C4×C4⋊Dic43C2semidirect
8. #14582746C2semidirect
9. C43×#383C2semidirect
13. #13063313C4semidirect
47. C2×Dic86C2×C4semidirect
48. C42×C43C2×C4semidirect
52. (C2×D43)⋊C4C2×C4semidirect
53. (C2×D43)⋊C4C2×C4semidirect
125. #383D43semidirect
128. C43#2337semidirect
177. C42C4×D43semidirect