Finite Group Databasebeta

← #19145740

Subgroups — #19145740

Order 5504.

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

normal subgroups only

This group has 360 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#14583295C211yesmaximal, characteristic, complemented
4#14583251C211yesmaximal, characteristic, complemented
5#14583250C211yesmaximal, characteristic, complemented
6#14583231C214yesmaximal
7#14583183C214yesmaximal, complemented
8#14582950C211yesmaximal, characteristic
9C43×#498C211yesmaximal, characteristic, complemented
10C2×Q8×D43—21no—
11#13063325C2211yescharacteristic
12#13063325C2211yescharacteristic
13#13063324—21no—
14#13063324C2212yes—
15#13063323—21no—
16#13063316—21no—
17#13063305C2212yes—
18#13063301—21no—
19Q8×Dic43—21no—
20#13063290C2212yes—
21#13063283—21no—
22C4⋊C4×D43—21no—
23C4⋊C4×D43C2212yes—
24C42×D43C2211yescharacteristic
25#13063256C2214yes—
26Dic43⋊C8C2212yes—
27#13063250C2214yes—
28#13063248C2214yes—
29(C2×D43)⋊C8C2212yes—
30C4×C43⋊C8C2211yescharacteristic
31C4⋊Q8×C43C2211yescharacteristic
32C4⋊Q8×C43C2211yescharacteristic
33#106×C43C2214yes—
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43—21no—
36C2×Q8×C43—21no—
37Q8×D43—44no—
38C2×C4×D43—22no—
39C2×C4×D43D411yescharacteristic
40C2×C4×D43D411yescharacteristic
41C2×C4×D43C2311yescharacteristic
42C2×Dic86—21no—
43C2×Dic86—22no—
44C2×Dic86C2312yes—
45C2×C8×C43C2312yes—
46C4⋊C4×C43—21no—
47C4⋊C4×C43—21no—
48C4⋊C4×C43C2312yes—
49C4⋊C4×C43C2312yes—
50C42×C43C2311yescharacteristic
51(C2×D43)⋊C4—22no—
52C4⋊Dic43—21no—
53C4⋊Dic43—21no—
54C4⋊Dic43—21no—
55C4⋊Dic43—22no—
56C4⋊Dic43C2312yes—
57Dic43⋊C4—22no—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60C4×Dic43—22no—
61C4×Dic43D411yescharacteristic
62C4×Dic43D411yescharacteristic
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2312yes—
65C22×D43C2×D411yescharacteristic
66Q8×C43—42no—
67Q8×C43—42no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2411yescharacteristic
73C2×Dic43—22no—
74C2×Dic43—22no—
75C2×Dic43C2×D411yescharacteristic
76C2×Dic43C2×D411yescharacteristic
77C2×Dic43C2×D411yescharacteristic
78C4×D43—22no—
79C4×D43—22no—
80C4×D43—44no—
81C4×D43SD1614yes—
82Dic86—24no—
83Dic86—42no—
84Dic86—44no—
85C8×C43—22no—
86C43⋊C8—22no—
87C22×C43C22×D411yescharacteristic
88C2×D43—21no—
89C2×D43—21no—
90C2×D43C2×SD1612yes—
91C4×C43—42no—
92C4×C43—42no—
93C4×C43C2×SD1612yes—
94C4×C43#13712yes—
95C4×C432−1+412yes—
96Dic43—21no—
97Dic43—21no—
98Dic43—42no—
99Dic43—42no—
100Dic43C2×SD1612yes—
101#3229—431nomaximal, Sylow
102C2×C43#53611yescharacteristic
103C2×C43C22×SD1611yescharacteristic
104C2×C43C2×#13711yescharacteristic
105D43—22no—
106#533—431no—
107C2×C4⋊Q8—431no—
108#498—431no—
109#498D4311yescharacteristic, complemented
110#487—431no—
111#487—431no—
112#483—434no—
113#475—434no—
114#431—431no—
115C43#322911yescharacteristic, complemented, Sylow
116C22×Q8—861no—
117C4⋊Q8—432no—
118C4⋊Q8—431no—
119C4⋊Q8—431no—
120C4⋊Q8—861no—
121C4⋊Q8—861no—
122C4⋊Q8C2×D4311yescharacteristic
123C4⋊Q8C2×D4311yescharacteristic
124#125—861no—
125C22⋊Q8—432no—
126C22⋊Q8—861no—
127C4×Q8—432no—
128C4×Q8—861no—
129#117—861no—
130C2×C4⋊C4—432no—
131C2×C4⋊C4—861no—
132C2×C42—431no—
133#106—434no—
134#106C2×D4314yes—
135C4⋊C8—432no—
136#103—434no—
137#103—434no—
138C22⋊C8—432no—
139C4×C8—431no—
140C4×C8C2×D4311yescharacteristic
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—432no—
144C2×Q8—862no—
145C2×Q8—861no—
146C2×Q8—1724no—
147C22×C4—431no—
148C22×C4—431no—
149C22×C4—431no—
150C22×C4—862no—
151C2×C8—432no—
152C2×C8C22×D4312yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—432no—
156C4⋊C4—862no—
157C4⋊C4—862no—
158C4⋊C4—862no—
159C4⋊C4—862no—
160C4⋊C4—861no—
161C4⋊C4—861no—
162C4⋊C4—861no—
163C4⋊C4C22×D4312yes—
164C4⋊C4C22×D4312yes—
165C22⋊C4—862no—
166C42—431no—
167C42—431no—
168C42—431no—
169C42—862no—
170C42C22×D4311yescharacteristic
171C23—431no—
172Q8—42no—
173Q8—42no—
174Q8—864no—
175Q8—1724no—
176Q8—1722no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—431no—
180C2×C4—434no—
181C2×C4—431no—
182C2×C4—431no—
183C2×C4—862no—
184C2×C4—862no—
185C2×C4—862no—
186C2×C4—862no—
187C2×C4—1724no—
188C2×C4D4×D4311yescharacteristic
189C2×C4D4×D4311yescharacteristic
190C2×C4C23×D4311yescharacteristic
191C8—22no—
192C8—862no—
193C22—432no—
194C22—861no—
195C22—861no—
196C22C2×D4×D4311yescharacteristic
197C4—42no—
198C4—42no—
199C4—432no—
200C4—861no—
201C4—861no—
202C4—1722no—
203C4—1722no—
204C4SD16×D4312yes—
205C4#1306335412yes—
206C4#1306337312yes—
207C2—862no—
208C2#1458347411yescharacteristic
209C2C2×SD16×D4311yescharacteristic
210C2C2×#1306335411yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#498C2
socleC22×C43C22×D4
hypercenter#498D43
hypocenterC43#3229
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
3. #14583295C2semidirect
4. #14583251C2semidirect
5. #14583250C2semidirect
7. #14583183C2semidirect
9. C43×#498C2semidirect
109. #498D43semidirect
115. C43#3229semidirect