Finite Group Databasebeta

← #19145544

Subgroups — #19145544

Order 5504.

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

normal subgroups only

This group has 384 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
1#14583454C211yesmaximal, characteristic
2C4⋊Q8×D43C211yesmaximal, characteristic
3#14583279C211yesmaximal, characteristic, complemented
4#14583278C211yesmaximal, characteristic, complemented
5#14583251C211yesmaximal, characteristic, complemented
6#14583108C214yesmaximal, complemented
7#14583056C214yesmaximal
8#14582950C211yesmaximal, characteristic
9C43×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D43C2212yes—
11C2×Dic172C2214yes—
12C2×#10621885C2214yes—
13#13063325C2211yescharacteristic
14#13063325C2211yescharacteristic
15#13063324—21no—
16#13063324—21no—
17#13063323C2212yes—
18#13063316—21no—
19#13063305C2212yes—
20#13063301—21no—
21Q8×Dic43—21no—
22#13063290C2212yes—
23#13063283—21no—
24C4⋊C4×D43—21no—
25C4⋊C4×D43—21no—
26C42×D43C2211yescharacteristic
27Dic43⋊C8C2212yes—
28#13063248C2214yes—
29(C2×D43)⋊C8C2212yes—
30C4×C43⋊C8C2211yescharacteristic
31C4⋊Q8×C43C2211yescharacteristic
32C4⋊Q8×C43C2211yescharacteristic
33#103×C43C2214yes—
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43—21no—
36C2×Q8×C43C2312yes—
37Q8×D43—44no—
38C2×C4×D43—22no—
39C2×C4×D43D411yescharacteristic
40C2×C4×D43D411yescharacteristic
41C2×C4×D43C2311yescharacteristic
42C2×Dic86—22no—
43C2×Dic86C2312yes—
44C2×Dic86C2312yes—
45C2×C8×C43C2312yes—
46C4⋊C4×C43—21no—
47C4⋊C4×C43—21no—
48C4⋊C4×C43—21no—
49C4⋊C4×C43C2312yes—
50C42×C43C2311yescharacteristic
51#10621885—44no—
52(C2×D43)⋊C4—22no—
53C4⋊Dic43—21no—
54C4⋊Dic43—21no—
55C4⋊Dic43—21no—
56C4⋊Dic43—21no—
57C4⋊Dic43—22no—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61C4×Dic43—22no—
62C4×Dic43D411yescharacteristic
63C4×Dic43D411yescharacteristic
64C4×Dic43C2311yescharacteristic
65C2×C43⋊C8C2312yes—
66Dic172—44no—
67C22×D43C2×D411yescharacteristic
68Q8×C43—24no—
69Q8×C43—42no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2411yescharacteristic
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43C2×D411yescharacteristic
78C2×Dic43C2×D411yescharacteristic
79C2×Dic43C2×D411yescharacteristic
80C4×D43—22no—
81C4×D43—22no—
82C4×D43—44no—
83C4×D43Q1614yescomplemented
84Dic86—24no—
85Dic86—24no—
86Dic86—44no—
87C8×C43—22no—
88C43⋊C8—22no—
89C22×C43C22×D411yescharacteristic
90C2×D43—21no—
91C2×D43—21no—
92C2×D43C2×Q1612yes—
93C4×C43—42no—
94C4×C43—42no—
95C4×C43C2×Q1612yes—
96C4×C43#13712yes—
97C4×C43H(5,𝔽2)12yes—
98Dic43—21no—
99Dic43—21no—
100Dic43—42no—
101Dic43—42no—
102Dic43C2×Q1612yes—
103#3209—431nomaximal, Sylow
104C2×C43#53511yescharacteristic
105C2×C43C22×Q1611yescharacteristic
106C2×C43C2×#13711yescharacteristic
107D43—22no—
108#533—431no—
109C2×C4⋊Q8—431no—
110#494—431no—
111#494—431no—
112#487—431no—
113#487D4311yescharacteristic, complemented
114#462—434no—
115#451—434no—
116#431—431no—
117C43#320911yescharacteristic, complemented, Sylow
118C22×Q8—432no—
119C2×Q16—434no—
120C2×Q16—434no—
121C4⋊Q8—432no—
122C4⋊Q8—431no—
123C4⋊Q8—431no—
124C4⋊Q8—861no—
125C4⋊Q8—861no—
126C4⋊Q8C2×D4311yescharacteristic
127C4⋊Q8C2×D4311yescharacteristic
128#125—861no—
129C22⋊Q8—432no—
130C22⋊Q8—861no—
131C4×Q8—432no—
132C4×Q8—861no—
133#117—861no—
134C2×C4⋊C4—861no—
135C2×C4⋊C4—861no—
136C2×C42—431no—
137C4⋊C8—432no—
138#103—434no—
139#103C2×D4314yes—
140C22⋊C8—432no—
141C4×C8—431no—
142C4×C8C2×D4311yescharacteristic
143C2×Q8—21no—
144C2×Q8—432no—
145C2×Q8—432no—
146C2×Q8—862no—
147C2×Q8—1724no—
148C2×Q8C22×D4312yes—
149C22×C4—431no—
150C22×C4—431no—
151C22×C4—431no—
152C22×C4—862no—
153Q16—1724no—
154Q16—1724no—
155C2×C8—432no—
156C2×C8C22×D4312yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—862no—
161C4⋊C4—862no—
162C4⋊C4—862no—
163C4⋊C4—862no—
164C4⋊C4—861no—
165C4⋊C4—861no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C4⋊C4C22×D4312yes—
169C22⋊C4—862no—
170C42—431no—
171C42—431no—
172C42—431no—
173C42—862no—
174C42C22×D4311yescharacteristic
175C23—431no—
176Q8—24no—
177Q8—42no—
178Q8—864no—
179Q8—864no—
180Q8—1724no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—431no—
184C2×C4—434no—
185C2×C4—431no—
186C2×C4—431no—
187C2×C4—862no—
188C2×C4—862no—
189C2×C4—862no—
190C2×C4—862no—
191C2×C4—1724no—
192C2×C4D4×D4311yescharacteristic
193C2×C4D4×D4311yescharacteristic
194C2×C4C23×D4311yescharacteristic
195C8—22no—
196C8—862no—
197C22—432no—
198C22—861no—
199C22—861no—
200C22C2×D4×D4311yescharacteristic
201C4—42no—
202C4—42no—
203C4—432no—
204C4—861no—
205C4—861no—
206C4—1722no—
207C4—1722no—
208C4Q16×D4312yes—
209C4#1306335412yes—
210C4#1306337112yes—
211C2—862no—
212C2#1458346711yescharacteristic
213C2C2×Q16×D4311yescharacteristic
214C2C2×#1306335411yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43#3209
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #14583279C2semidirect
4. #14583278C2semidirect
5. #14583251C2semidirect
6. #14583108C2semidirect
9. C43×#487C2semidirect
83. C4×D43Q16semidirect
113. #487D43semidirect
117. C43#3209semidirect