Finite Group Databasebeta

← #19133136

Subgroups — #19133136

Order 5504.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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#14583410C211yesmaximal, characteristic
2#14582863C211yesmaximal, characteristic, complemented
3#14582635C212yesmaximal, complemented
4#14582632C212yesmaximal, complemented
5C43×#380C211yesmaximal, characteristic, complemented
6C2×#10621898C411yescharacteristic, complemented
7C2×#10621877—21no—
8#13063308—21no—
9#13063304C411yescharacteristic, complemented
10#13063304C2211yescharacteristic
11#13063299C411yescharacteristic, complemented
12#13063299C2211yescharacteristic
13#13063294—21no—
14C4×C22⋊D43—21no—
15C4×C22⋊D43—21no—
16#13063284C411yescharacteristic, complemented
17C22⋊(C43⋊C8)—21no—
18C22⋊(C43⋊C8)C2212yes—
19C23×C4×C43C2211yescharacteristic
20C2×C4⋊C4×C43—21no—
21C2×C22⋊C4×C43—21no—
22#95×C43C2212yes—
23C24×C43D411yescharacteristic
24C22×C4×C43—22no—
25C22×C4×C43—42no—
26C22×C4×C43C2×C411yescharacteristic
27C22×C4×C43C2×C411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×C4×C43D411yescharacteristic
30C22×C4×C43D411yescharacteristic
31C22×C4×C43C2311yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35#10621898—42no—
36C2×D172C2×C411yescharacteristic
37C2×C4×D43—21no—
38C2×Dic86C2×C411yescharacteristic
39C4⋊C4×C43—42no—
40C22⋊C4×C43—42no—
41C22⋊Dic43—21no—
42C22⋊Dic43—21no—
43C22⋊Dic43—21no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46C4⋊Dic43C2×C411yescharacteristic
47C4⋊Dic43C2×C411yescharacteristic
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50C4×Dic43—21no—
51#10621877—42no—
52C2×C43⋊C8—22no—
53C23×C43—21no—
54C23×C43—21no—
55C23×C43—41no—
56C23×C43—41no—
57C23×C43C22⋊C411yescharacteristic
58C23×C43C22⋊C411yescharacteristic
59C23×C43C2×D411yescharacteristic
60C22×D43—21no—
61C2×C4×C43—22no—
62C2×C4×C43—22no—
63C2×C4×C43—22no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—42no—
68C2×C4×C43—42no—
69C2×C4×C43—42no—
70C2×C4×C43C22⋊C411yescharacteristic
71C2×C4×C43C22⋊C411yescharacteristic
72C2×C4×C43C22×C411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C22⋊D43—42no—
75C22⋊D43—42no—
76C22⋊D43—41no—
77C22⋊D43—41no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81D172—41no—
82C4×D43—42no—
83Dic86—41no—
84C43⋊C8—42no—
85C22×C43—21no—
86C22×C43—21no—
87C22×C43—21no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—42no—
94C22×C43—42no—
95C22×C43C2×C22⋊C411yescharacteristic
96C22×C43AGL(1,ℤ/8)11yescharacteristic
97C22×C43#13711yescharacteristic
98C2×D43—41no—
99C2×D43—41no—
100C2×D43—41no—
101C4×C43—21no—
102C4×C43—21no—
103C4×C43—21no—
104C4×C43—82no—
105C4×C43#9912yes—
106Dic43—41no—
107Dic43—41no—
108Dic43—41no—
109#1513—431nomaximal, Sylow
110C2×C43—21no—
111C2×C43—21no—
112C2×C43—41no—
113C2×C43—41no—
114C2×C43C2×#9911yescharacteristic
115C2×C43#41711yescharacteristic
116C2×C43#42111yescharacteristic
117D43—81no—
118#525—431no—
119#407—431no—
120#380D4311yescharacteristic, complemented
121#328—432no—
122#327—432no—
123C43#151311yescharacteristic, complemented, Sylow
124C2×#41—431no—
125C23×C4C2×D4311yescharacteristic
126C2×M16—861no—
127#123—861no—
128C22⋊Q8—431no—
129C22⋊Q8—431no—
130#121—431no—
131#121—431no—
132#120—861no—
133C4×D4—861no—
134C4×D4—861no—
135#117—431no—
136C2×C4⋊C4—21no—
137C2×C22⋊C4—21no—
138C22⋊C8—432no—
139C22⋊C8—861no—
140#95C2×D4312yes—
141C24C22⋊D4311yescharacteristic
142#41—1722no—
143C2×Q8—431no—
144C2×D4—431no—
145C2×D4—861no—
146C2×D4—861no—
147C2×D4—861no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—861no—
151C22×C4C4×D4311yescharacteristic
152C22×C4C4×D4311yescharacteristic
153C22×C4D17211yescharacteristic
154C22×C4D17211yescharacteristic
155C22×C4C22⋊D4311yescharacteristic
156C22×C4C22×D4311yescharacteristic
157M16—1722no—
158C2×C8—862no—
159C4⋊C4—42no—
160C4⋊C4—431no—
161C4⋊C4—431no—
162C4⋊C4—861no—
163C4⋊C4—861no—
164C22⋊C4—42no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C22⋊C4—861no—
170C42—861no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—861no—
176C23(C2×D43)⋊C411yescharacteristic
177C23(C2×D43)⋊C411yescharacteristic
178C23C2×C22⋊D4311yescharacteristic
179Q8—1721no—
180D4—1721no—
181D4—1722no—
182D4—1722no—
183D4—1721no—
184D4—1721no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—861no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—1722no—
198C2×C4(C2×D43)⋊C411yescharacteristic
199C2×C4(C2×D43)⋊C411yescharacteristic
200C2×C4C2×C4×D4311yescharacteristic
201C2×C4C2×D17211yescharacteristic
202C8—1722no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—1721no—
214C22—1721no—
215C22—1721no—
216C22C2×(C2×D43)⋊C411yescharacteristic
217C22#1306335111yescharacteristic
218C22#1306335611yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—82no—
223C4—1721no—
224C4—1721no—
225C4—1721no—
226C4#1306323912yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—3441no—
232C2C2×#1306323911yescharacteristic
233C2#1458289811yescharacteristic
234C2#1458291711yescharacteristic
subgroupG/H
centerC22C2×(C2×D43)⋊C4
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#380C2
socleC22×C43C2×C22⋊C4
hypercenter#380D43
hypocenterC43#1513
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #14582863C2semidirect
3. #14582635C2semidirect
4. #14582632C2semidirect
5. C43×#380C2semidirect
6. C2×#10621898C4semidirect
9. #13063304C4semidirect
11. #13063299C4semidirect
16. #13063284C4semidirect
120. #380D43semidirect
123. C43#1513semidirect