Finite Group Databasebeta

← #19133119

Subgroups — #19133119

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#14583435C211yesmaximal, characteristic
2#14582953C211yesmaximal, characteristic, complemented
3#14582750C211yesmaximal, characteristic, complemented
4#14582636C211yesmaximal, characteristic, complemented
5#14582634C211yesmaximal, characteristic
6#14582632C211yesmaximal, characteristic
7C43×#328C211yesmaximal, characteristic, complemented
8#13063320—21no—
9#13063316C411yescharacteristic, complemented
10#13063314C411yescharacteristic, complemented
11#13063309—21no—
12#13063299C2211yescharacteristic
13Q8×Dic43C411yescharacteristic, complemented
14#13063287C411yescharacteristic, complemented
15(C22⋊D43)⋊C4—21no—
16#13063283—21no—
17C2×Dic43⋊C4—21no—
18C2×C4×Dic43—21no—
19C2×C4×Dic43C2211yescharacteristic
20Dic43⋊C8—21no—
21C22⋊(C43⋊C8)C2211yescharacteristic
22#13063235—21no—
23C43⋊#95C2211yescharacteristic
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C2×Q8×C43C2×C411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31C22×Dic43—21no—
32C22×Dic43D411yescharacteristic
33C22×Dic43D411yescharacteristic
34C2×D172C2×C411yescharacteristic
35C2×C4×D43—21no—
36C2×C8×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43C2×C411yescharacteristic
39C22⋊C4×C43—21no—
40(C2×D43)⋊C4—21no—
41(C2×D43)⋊C4—21no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43—21no—
46C4⋊Dic43C2×C411yescharacteristic
47Dic43⋊C4—24no—
48Dic43⋊C4—21no—
49C4×Dic43—21no—
50C4×Dic43—42no—
51C4×Dic43C2×C411yescharacteristic
52C4×Dic43C2×C411yescharacteristic
53C4×Dic43D411yescharacteristic
54C4×Dic43D411yescharacteristic
55C2×C43⋊C8—21no—
56C23×C43C2×D411yescharacteristic
57C22×D43—21no—
58Q8×C43—41no—
59C2×C4×C43—22no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43C22×C411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C22⋊D43—41no—
68C22⋊D43—41no—
69C2×Dic43—21no—
70C2×Dic43—21no—
71C2×Dic43—22no—
72C2×Dic43—22no—
73C2×Dic43—21no—
74C2×Dic43—41no—
75C2×Dic43—41no—
76C2×Dic43C22⋊C411yescharacteristic
77C2×Dic43C22⋊C411yescharacteristic
78C2×Dic43C22⋊C411yescharacteristic
79C2×Dic43C22⋊C411yescharacteristic
80D172—41no—
81C4×D43—42no—
82C8×C43—41no—
83C43⋊C8—41no—
84C22×C43—21no—
85C22×C43—21no—
86C22×C43C2×C22⋊C411yescharacteristic
87C22×C43AGL(1,ℤ/8)11yescharacteristic
88C22×C43#13711yescharacteristic
89C2×D43—41no—
90C2×D43—41no—
91C2×D43—41no—
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—42no—
95C4×C43—41no—
96C4×C43—41no—
97Dic43—21no—
98Dic43—21no—
99Dic43—21no—
100Dic43—42no—
101Dic43—41no—
102Dic43#10412yes—
103#1509—431nomaximal, Sylow
104C2×C43—21no—
105C2×C43—21no—
106C2×C43#41011yescharacteristic
107C2×C43#41711yescharacteristic
108C2×C43C2×#10411yescharacteristic
109D43—81no—
110#529—431no—
111#432—431no—
112C4×C4⋊C4—431no—
113#328—431no—
114#328D4311yescharacteristic, complemented
115#327—431no—
116#327—431no—
117C43#150911yescharacteristic, complemented, Sylow
118#126—861no—
119#125—431no—
120#124—431no—
121#123—861no—
122C22⋊Q8C2×D4311yescharacteristic
123#121—431no—
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×Q8C4×D4311yescharacteristic
138C2×D4—431no—
139C2×D4—861no—
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—21no—
149C4⋊C4—431no—
150C4⋊C4—861no—
151C4⋊C4—861no—
152C4⋊C4—861no—
153C4⋊C4—864no—
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—861no—
167C23D4×D4311yescharacteristic
168Q8—41no—
169D4—1721no—
170D4—1721no—
171D4—1721no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—431no—
179C2×C4—431no—
180C2×C4—431no—
181C2×C4—431no—
182C2×C4—862no—
183C2×C4—861no—
184C2×C4—861no—
185C2×C4—862no—
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—1721no—
197C22—1721no—
198C22—1721no—
199C22C22⋊C4×D4311yescharacteristic
200C22#1306335211yescharacteristic
201C22#1306335711yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—432no—
208C4—861no—
209C4—861no—
210C4—861no—
211C4—1722no—
212C4—1721no—
213C2—21no—
214C2—21no—
215C2—3441no—
216C2#1458287111yescharacteristic
217C2#1458289911yescharacteristic
218C2#104×D4311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43C2×C22⋊C4
hypercenter#328D43
hypocenterC43#1509
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14582953C2semidirect
3. #14582750C2semidirect
4. #14582636C2semidirect
7. C43×#328C2semidirect
9. #13063316C4semidirect
10. #13063314C4semidirect
13. Q8×Dic43C4semidirect
14. #13063287C4semidirect
114. #328D43semidirect
117. C43#1509semidirect