Finite Group Databasebeta

← #19133117

Subgroups — #19133117

Order 5504.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#14583430C211yesmaximal, characteristic
2#14582953C211yesmaximal, characteristic, complemented
3#14582750C211yesmaximal, characteristic, complemented
4#14582637C211yesmaximal, characteristic, complemented
5#14582635C211yesmaximal, characteristic, complemented
6#14582633C211yesmaximal, characteristic
7C43×#327C211yesmaximal, characteristic
8#13063318—21no—
9#13063316C411yescharacteristic, complemented
10#13063312C411yescharacteristic, complemented
11#13063306—21no—
12#13063304C2211yescharacteristic
13#13063290C411yescharacteristic, complemented
14D4×Dic43—21no—
15D4×Dic43C411yescharacteristic, complemented
16#13063281—21no—
17C2×Dic43⋊C4—21no—
18C2×C4×Dic43—21no—
19C2×C4×Dic43C2211yescharacteristic
20Dic43⋊C8—21no—
21C22⋊(C43⋊C8)C2211yescharacteristic
22#13063235—21no—
23C43⋊#95C2211yescharacteristic
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C2×D4×C43—21no—
28C2×D4×C43C2×C411yescharacteristic
29C22×C4×C43—21no—
30C22×C4×C43C2311yescharacteristic
31C22×Dic43—21no—
32C22×Dic43—21no—
33C22×Dic43D411yescharacteristic
34C22×Dic43D411yescharacteristic
35C2×Dic86C2×C411yescharacteristic
36C2×C8×C43—21no—
37C4⋊C4×C43C2×C411yescharacteristic
38C22⋊C4×C43—21no—
39C22⋊Dic43—21no—
40C22⋊Dic43—21no—
41C22⋊Dic43—21no—
42C22⋊Dic43—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43C2×C411yescharacteristic
45Dic43⋊C4—24no—
46Dic43⋊C4—21no—
47Dic43⋊C4—21no—
48Dic43⋊C4—21no—
49C4×Dic43—21no—
50C4×Dic43—42no—
51C4×Dic43C2×C411yescharacteristic
52C4×Dic43C2×C411yescharacteristic
53C4×Dic43D411yescharacteristic
54C4×Dic43D411yescharacteristic
55C2×C43⋊C8—21no—
56C23×C43—21no—
57C23×C43C2×D411yescharacteristic
58D4×C43—41no—
59D4×C43—41no—
60D4×C43—41no—
61C2×C4×C43—22no—
62C2×C4×C43—21no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43C22×C411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×Dic43—21no—
69C2×Dic43—21no—
70C2×Dic43—22no—
71C2×Dic43—22no—
72C2×Dic43—21no—
73C2×Dic43—21no—
74C2×Dic43—41no—
75C2×Dic43—41no—
76C2×Dic43—42no—
77C2×Dic43C22⋊C411yescharacteristic
78C2×Dic43C22⋊C411yescharacteristic
79C2×Dic43C22⋊C411yescharacteristic
80C2×Dic43C22⋊C411yescharacteristic
81Dic86—41no—
82C8×C43—41no—
83C43⋊C8—41no—
84C22×C43—21no—
85C22×C43—21no—
86C22×C43—41no—
87C22×C43—41no—
88C22×C43—41no—
89C22×C43C2×C22⋊C411yescharacteristic
90C22×C43AGL(1,ℤ/8)11yescharacteristic
91C22×C43#13711yescharacteristic
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—42no—
95C4×C43—41no—
96Dic43—21no—
97Dic43—21no—
98Dic43—21no—
99Dic43—42no—
100Dic43—41no—
101Dic43—41no—
102Dic43#10412yes—
103#1509—431nomaximal, Sylow
104C2×C43—21no—
105C2×C43—21no—
106C2×C43—81no—
107C2×C43#41011yescharacteristic
108C2×C43#41711yescharacteristic
109C2×C43C2×#10411yescharacteristic
110#529—431no—
111#432—431no—
112C4×C4⋊C4—431no—
113#328—431no—
114#328—431no—
115#327—431no—
116#327D4311yescharacteristic
117C43#150911yescharacteristic, complemented, Sylow
118#126—861no—
119#125—431no—
120#124—431no—
121#123—861no—
122C22⋊Q8—431no—
123#121C2×D4311yescharacteristic
124C4×Q8—431no—
125C4×D4—431no—
126C4×D4—861no—
127#117—861no—
128C2×C4⋊C4—861no—
129C2×C42—431no—
130C2×C42—861no—
131C4⋊C8—861no—
132C22⋊C8—431no—
133C22⋊C8C2×D4311yescharacteristic
134#97—861no—
135#95—431no—
136#95C2×D4311yescharacteristic
137C2×Q8—431no—
138C2×D4—21no—
139C2×D4C4×D4311yescharacteristic
140C22×C4—21no—
141C22×C4—431no—
142C22×C4—431no—
143C22×C4—861no—
144C22×C4—861no—
145C22×C4C22×D4311yescharacteristic
146C2×C8—21no—
147C2×C8—861no—
148C4⋊C4—431no—
149C4⋊C4—861no—
150C4⋊C4—861no—
151C4⋊C4—861no—
152C4⋊C4—864no—
153C4⋊C4—861no—
154C4⋊C4C4×D4311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—861no—
157C22⋊C4—861no—
158C22⋊C4—861no—
159C22⋊C4—861no—
160C42—431no—
161C42—431no—
162C42—431no—
163C42—431no—
164C42—861no—
165C42—1722no—
166C23—21no—
167C23D4×D4311yescharacteristic
168Q8—1721no—
169D4—41no—
170D4—41no—
171D4—41no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—431no—
178C2×C4—431no—
179C2×C4—431no—
180C2×C4—431no—
181C2×C4—862no—
182C2×C4—861no—
183C2×C4—861no—
184C2×C4—862no—
185C2×C4—861no—
186C2×C4—861no—
187C2×C4—1722no—
188C2×C4—1721no—
189C2×C4—1721no—
190C2×C4C2×C4×D4311yescharacteristic
191C2×C4D4×D4311yescharacteristic
192C8—41no—
193C8—1721no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22C22⋊C4×D4311yescharacteristic
200C22#1306334911yescharacteristic
201C22#1306335411yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—432no—
207C4—861no—
208C4—861no—
209C4—861no—
210C4—1722no—
211C4—1721no—
212C4—1721no—
213C2—21no—
214C2—21no—
215C2—81no—
216C2#1458287111yescharacteristic
217C2#1458289711yescharacteristic
218C2#104×D4311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43C2×C22⋊C4
hypercenter#327D43
hypocenterC43#1509
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14582953C2semidirect
3. #14582750C2semidirect
4. #14582637C2semidirect
5. #14582635C2semidirect
9. #13063316C4semidirect
10. #13063312C4semidirect
13. #13063290C4semidirect
15. D4×Dic43C4semidirect
117. C43#1509semidirect