Finite Group Databasebeta

← #19145624

Subgroups — #19145624

Order 5504.

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

normal subgroups only

This group has 386 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
1C2×#13063325C211yesmaximal, characteristic, complemented
2#14583433C211yesmaximal, characteristic
3#14583293C212yesmaximal, complemented
4#14583268C212yesmaximal, complemented
5#14583110C212yesmaximal, complemented
6#14583105C212yesmaximal, complemented
7#14583057C212yesmaximal, complemented
8#14583040C212yesmaximal
9C43×#432C211yesmaximal, characteristic, complemented
10C22×Dic86C2212yes—
11C2×Dic172C2214yes—
12C2×#10621873C2214yes—
13#13063325—21no—
14#13063325—21no—
15#13063325C2212yes—
16#13063325C2212yes—
17#13063319—21no—
18#13063317C2211yescharacteristic
19#13063313C2211yescharacteristic
20#13063308—21no—
21#13063304C2211yescharacteristic
22#13063299C2211yescharacteristic
23C4×Dic86C2211yescharacteristic
24C4×D172C2211yescharacteristic
25C4×C22⋊D43—21no—
26#13063282—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29#13063250C2214yes—
30#13063250C2214yes—
31C2×C42×C43C2211yescharacteristic
32C4⋊C8×C43C2212yes—
33C22⋊C8×C43C2212yes—
34#97×C43C2212yes—
35C22×C4×C43D411yescharacteristic
36C22×C4×C43D411yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—21no—
39C22×Dic43—22no—
40C2×D172C2311yescharacteristic
41C2×C4×D43—21no—
42C2×Dic86—22no—
43C2×Dic86—44no—
44C2×Dic86C2314yes—
45C2×Dic86C2311yescharacteristic
46C2×C8×C43C2314yes—
47C42×C43D411yescharacteristic
48C42×C43D411yescharacteristic
49C42×C43C2311yescharacteristic
50C42×C43C2311yescharacteristic
51C22⋊Dic43—21no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—21no—
56C4⋊Dic43—22no—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43—22no—
60C4⋊Dic43C2311yescharacteristic
61C4⋊Dic43C2311yescharacteristic
62Dic43⋊C4—21no—
63Dic43⋊C4—21no—
64Dic43⋊C4—21no—
65Dic43⋊C4—21no—
66C4×Dic43—21no—
67Dic172—44no—
68#10621873—44no—
69C23×C43C2×D411yescharacteristic
70C22×D43—21no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2411yescharacteristic
80C22⋊D43—42no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—24no—
85C2×Dic43—44no—
86D172—22no—
87C4×D43—42no—
88Dic86—24no—
89Dic86—22no—
90Dic86—24no—
91Dic86—44no—
92C8×C43—24no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43#13712yes—
96C22×C43C22×D411yescharacteristic
97C2×D43—41no—
98C2×D43—41no—
99C2×D43—41no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—21no—
103C4×C43—21no—
104C4×C43#13712yes—
105C4×C43H(5,𝔽2)12yes—
106Dic43—44no—
107Dic43—41no—
108Dic43—41no—
109Dic43—41no—
110#3218—431nomaximal, Sylow
111C2×C43—22no—
112C2×C43#53511yescharacteristic
113C2×C43C2×#13711yescharacteristic
114C2×C43C2×#13711yescharacteristic
115D43—81no—
116C2×C4⋊Q8—431no—
117#529—431no—
118#497—432no—
119#491—432no—
120#462—432no—
121#461—432no—
122#451—432no—
123#448—432no—
124#432D4311yescharacteristic, complemented
125C43#321811yescharacteristic, complemented, Sylow
126C22×Q8—432no—
127C2×Q16—434no—
128C2×SD16—434no—
129C4⋊Q8—432no—
130C4⋊Q8—432no—
131C4⋊Q8—861no—
132C4⋊Q8—861no—
133#126—861no—
134#125—431no—
135#124—431no—
136#123—861no—
137C22⋊Q8—431no—
138#121—431no—
139C4×Q8—431no—
140C4×D4—431no—
141C4×D4—861no—
142#117—861no—
143C2×C4⋊C4—861no—
144C2×C4⋊C4—861no—
145C2×C42C2×D4311yescharacteristic
146C4⋊C8C2×D4312yes—
147#103—434no—
148#103—434no—
149C22⋊C8C2×D4312yes—
150#97C2×D4312yes—
151C2×Q8—434no—
152C2×Q8—431no—
153C2×Q8—862no—
154C2×Q8—1724no—
155C2×D4—431no—
156C2×D4—861no—
157C22×C4—862no—
158C22×C4—861no—
159C22×C4D17211yescharacteristic
160C22×C4D17211yescharacteristic
161C22×C4C22×D4311yescharacteristic
162Q16—1724no—
163SD16—1724no—
164C2×C8C22×D4314yes—
165C4⋊C4—431no—
166C4⋊C4—431no—
167C4⋊C4—862no—
168C4⋊C4—862no—
169C4⋊C4—862no—
170C4⋊C4—862no—
171C4⋊C4—861no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4—861no—
175C22⋊C4—861no—
176C22⋊C4—861no—
177C22⋊C4—861no—
178C22⋊C4—861no—
179C22⋊C4—861no—
180C42—861no—
181C42D17211yescharacteristic
182C42D17211yescharacteristic
183C42C22×D4311yescharacteristic
184C42C22×D4311yescharacteristic
185C23—861no—
186C23C2×D17211yescharacteristic
187Q8—864no—
188Q8—862no—
189Q8—864no—
190Q8—1724no—
191D4—862no—
192D4—1722no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—861no—
197C2×C4—861no—
198C2×C4—861no—
199C2×C4—864no—
200C2×C4—1724no—
201C2×C4—1722no—
202C2×C4C2×D17211yescharacteristic
203C2×C4C2×D17211yescharacteristic
204C2×C4C2×D17211yescharacteristic
205C2×C4C2×D17211yescharacteristic
206C2×C4C2×D17211yescharacteristic
207C2×C4C23×D4311yescharacteristic
208C8—24no—
209C22—21no—
210C22—21no—
211C22—1721no—
212C22—1721no—
213C22—1721no—
214C22#1306335812yes—
215C22C22×D17211yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—1721no—
221C4—1721no—
222C4—1724no—
223C4—1721no—
224C4#1306335812yes—
225C4#1306337112yes—
226C2—22no—
227C2—3441no—
228C2#1458346811yescharacteristic
229C2C2×#1306335811yescharacteristic
230C2C2×#1306335811yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#432C2
socleC22×C43C22×D4
hypercenter#432D43
hypocenterC43#3218
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. C2×#13063325C2semidirect
3. #14583293C2semidirect
4. #14583268C2semidirect
5. #14583110C2semidirect
6. #14583105C2semidirect
7. #14583057C2semidirect
9. C43×#432C2semidirect
124. #432D43semidirect
125. C43#3218semidirect