Finite Group Databasebeta

← #19136234

Subgroups — #19136234

Order 5504.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#14583406C211yesmaximal, characteristic
2#14582883C211yesmaximal, characteristic, complemented
3#14582688C212yesmaximal, complemented
4#14582685C212yesmaximal, complemented
5C43×#410C211yesmaximal, characteristic, complemented
6C22×C4×D43C411yescharacteristic, complemented
7C2×#10621877—21no—
8#13063306C411yescharacteristic, complemented
9#13063306C2211yescharacteristic
10#13063301—21no—
11#13063296—21no—
12#13063293C411yescharacteristic, complemented
13#13063293C2211yescharacteristic
14C4×C22⋊D43—21no—
15C4×C22⋊D43—21no—
16#13063284C411yescharacteristic, complemented
17#13063244—21no—
18#13063242C2212yes—
19C2×#41×C43C2211yescharacteristic
20#117×C43—21no—
21#99×C43—21no—
22#99×C43C2212yes—
23C23×D43C2×C411yescharacteristic
24#41×C43—41no—
25#41×C43—41no—
26C2×Q8×C43D411yescharacteristic
27C2×D4×C43C2×C411yescharacteristic
28C2×D4×C43D411yescharacteristic
29C2×D4×C43C2311yescharacteristic
30C22×C4×C43C2×C411yescharacteristic
31C22×C4×C43D411yescharacteristic
32C22×C4×C43D411yescharacteristic
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C22×Dic43C2×C411yescharacteristic
36C2×C4×D43—21no—
37C2×C4×D43—21no—
38C2×C4×D43—41no—
39C2×C4×D43—41no—
40C4⋊C4×C43—41no—
41C22⋊C4×C43—22no—
42C42×C43—41no—
43C22⋊Dic43—21no—
44C22⋊Dic43—21no—
45C22⋊Dic43C2×C411yescharacteristic
46C22⋊Dic43C2×C411yescharacteristic
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49C4⋊Dic43—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52C4×Dic43—21no—
53#10621877—22no—
54#10621877—41no—
55C2×C43⋊C8—41no—
56C23×C43C22⋊C411yescharacteristic
57C23×C43C22×C411yescharacteristic
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60C22×D43—42no—
61C22×D43—41no—
62Q8×C43—41no—
63D4×C43—41no—
64D4×C43—41no—
65D4×C43—41no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—42no—
73C2×C4×C43C22⋊C411yescharacteristic
74C2×C4×C43C22⋊C411yescharacteristic
75C2×C4×C43C22⋊C411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C22⋊D43—42no—
78C22⋊D43—42no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—41no—
83C4×D43—42no—
84C4×D43—41no—
85C4×D43—41no—
86C43⋊C8—42no—
87C22×C43—21no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43—41no—
91C22×C43—41no—
92C22×C43—41no—
93C22×C43C2×C22⋊C411yescharacteristic
94C2×D43—22no—
95C2×D43—41no—
96C2×D43—42no—
97C2×D43—41no—
98C2×D43—42no—
99C4×C43—21no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—82no—
103C4×C43#9911yescharacteristic
104C4×C43#9911yescharacteristic
105Dic43—41no—
106Dic43—41no—
107Dic43—41no—
108#2120—431nomaximal, Sylow
109C2×C43—21no—
110C2×C43—41no—
111C2×C43—41no—
112C2×C43—41no—
113C2×C43C2×#9911yescharacteristic
114D43—42no—
115#525—431no—
116#413—431no—
117#410D4311yescharacteristic, complemented
118#352—432no—
119AΣL(1,𝔽16)—432no—
120C43#212011yescharacteristic, complemented, Sylow
121C2×#41C2×D4311yescharacteristic
122C23×C4—431no—
123C2×M16—861no—
124#123—431no—
125#123—431no—
126C22⋊Q8—861no—
127#121—861no—
128#120—431no—
129#120—431no—
130C4×D4—861no—
131C4×D4—861no—
132#117—21no—
133#117—431no—
134#101—861no—
135#100—432no—
136#99—21no—
137#99C2×D4312yes—
138C24—431no—
139#41—41no—
140#41—41no—
141C2×Q8D17211yescharacteristic
142C2×D4—861no—
143C2×D4—861no—
144C2×D4C4×D4311yescharacteristic
145C2×D4C22⋊D4311yescharacteristic
146C2×D4C22×D4311yescharacteristic
147C22×C4—431no—
148C22×C4—861no—
149C22×C4—861no—
150C22×C4—1721no—
151C22×C4—1721no—
152C22×C4C4×D4311yescharacteristic
153C22×C4D17211yescharacteristic
154C22×C4C22⋊D4311yescharacteristic
155M16—862no—
156M16—1721no—
157C2×C8—1721no—
158C4⋊C4—41no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C4⋊C4—861no—
162C22⋊C4—22no—
163C22⋊C4—431no—
164C22⋊C4—431no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C42—41no—
170C42—861no—
171C23—861no—
172C23—1721no—
173C23—1722no—
174C23(C2×D43)⋊C411yescharacteristic
175C23C2×C4×D4311yescharacteristic
176C23C2×C22⋊D4311yescharacteristic
177Q8—41no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—1722no—
182D4—1722no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—861no—
193C2×C4—1722no—
194C2×C4—1721no—
195C2×C4—1721no—
196C2×C4—1721no—
197C2×C4(C2×D43)⋊C411yescharacteristic
198C2×C4(C2×D43)⋊C411yescharacteristic
199C2×C4(C2×D43)⋊C411yescharacteristic
200C2×C4C2×D17211yescharacteristic
201C8—1722no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—862no—
209C22—1721no—
210C22—1722no—
211C22—1722no—
212C22—1721no—
213C22C2×(C2×D43)⋊C411yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—82no—
218C4—1721no—
219C4—1721no—
220C4—1721no—
221C4#1306323911yescharacteristic
222C4#1306323911yescharacteristic
223C2—21no—
224C2—41no—
225C2—41no—
226C2—41no—
227C2—1722no—
228C2C2×#1306323911yescharacteristic
subgroupG/H
centerC4#13063239
commutatorC23×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#410C2
socleC2×C43C2×#99
hypercenter#410D43
hypocenterC43#2120
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14582883C2semidirect
3. #14582688C2semidirect
4. #14582685C2semidirect
5. C43×#410C2semidirect
6. C22×C4×D43C4semidirect
8. #13063306C4semidirect
12. #13063293C4semidirect
16. #13063284C4semidirect
117. #410D43semidirect
120. C43#2120semidirect