Finite Group Databasebeta

← #19133149

Subgroups — #19133149

Order 5504.

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

normal subgroups only

This group has 284 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
2C2×C22⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
3#14582635C212yesmaximal, complemented
4#14582632C212yesmaximal, complemented
5C43×#381C211yesmaximal, characteristic, complemented
6C2×#10621898C411yescharacteristic, complemented
7C22×C43⋊C8—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×C22⋊C4×C43—21no—
21#95×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
39C22⋊C4×C43—42no—
40C22⋊Dic43—21no—
41C22⋊Dic43—21no—
42C22⋊Dic43—21no—
43(C2×D43)⋊C4—21no—
44(C2×D43)⋊C4—21no—
45C4⋊Dic43C2×C411yescharacteristic
46C4⋊Dic43C2×C411yescharacteristic
47Dic43⋊C4—21no—
48Dic43⋊C4—21no—
49C4×Dic43—21no—
50C2×C43⋊C8—22no—
51C2×C43⋊C8—42no—
52C23×C43—22no—
53C23×C43—22no—
54C23×C43—41no—
55C23×C43C22⋊C411yescharacteristic
56C23×C43C22⋊C411yescharacteristic
57C23×C43C2×D411yescharacteristic
58C22×D43—21no—
59C2×C4×C43—22no—
60C2×C4×C43—22no—
61C2×C4×C43—41no—
62C2×C4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43—42no—
66C2×C4×C43—42no—
67C2×C4×C43—42no—
68C2×C4×C43C22⋊C411yescharacteristic
69C2×C4×C43C22⋊C411yescharacteristic
70C2×C4×C43C22×C411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C22⋊D43—42no—
73C22⋊D43—42no—
74C22⋊D43—42no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78D172—41no—
79C4×D43—42no—
80Dic86—41no—
81C43⋊C8—42no—
82C22×C43—21no—
83C22×C43—21no—
84C22×C43—21no—
85C22×C43—21no—
86C22×C43—21no—
87C22×C43—21no—
88C22×C43—21no—
89C22×C43—44no—
90C22×C43#9912yes—
91C22×C43C2×C22⋊C411yescharacteristic
92C22×C43#13512yes—
93C2×D43—41no—
94C2×D43—41no—
95C2×D43—41no—
96C4×C43—21no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—82no—
101Dic43—41no—
102Dic43—41no—
103Dic43—41no—
104#1516—431nomaximal, Sylow
105C2×C43—22no—
106C2×C43—22no—
107C2×C43—41no—
108C2×C43C2×#9911yescharacteristic
109C2×C43#41611yescharacteristic
110C2×C43#42111yescharacteristic
111D43—81no—
112#525—431no—
113C2×C22⋊C8—431no—
114#381D4311yescharacteristic, complemented
115#328—432no—
116#327—432no—
117C43#151611yescharacteristic, complemented, Sylow
118C2×#41—431no—
119C23×C4C2×D4311yescharacteristic
120C22×C8—861no—
121#123—861no—
122C22⋊Q8—431no—
123C22⋊Q8—431no—
124#121—431no—
125#121—431no—
126#120—861no—
127C4×D4—861no—
128C4×D4—861no—
129#117—431no—
130C2×C22⋊C4—21no—
131C22⋊C8—432no—
132C22⋊C8—861no—
133#95—21no—
134#95C2×D4312yes—
135C24C22⋊D4311yescharacteristic
136#41—1722no—
137C2×Q8—431no—
138C2×D4—431no—
139C2×D4—861no—
140C2×D4—861no—
141C2×D4—861no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4—861no—
145C22×C4C4×D4311yescharacteristic
146C22×C4C4×D4311yescharacteristic
147C22×C4D17211yescharacteristic
148C22×C4D17211yescharacteristic
149C22×C4C22⋊D4311yescharacteristic
150C22×C4C22×D4311yescharacteristic
151C2×C8—862no—
152C2×C8—1722no—
153C4⋊C4—431no—
154C4⋊C4—431no—
155C4⋊C4—861no—
156C4⋊C4—861no—
157C22⋊C4—42no—
158C22⋊C4—861no—
159C22⋊C4—861no—
160C22⋊C4—861no—
161C22⋊C4—861no—
162C22⋊C4—861no—
163C42—861no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—861no—
168C23(C2×D43)⋊C411yescharacteristic
169C23(C2×D43)⋊C411yescharacteristic
170C23C2×C22⋊D4311yescharacteristic
171Q8—1721no—
172D4—1721no—
173D4—1722no—
174D4—1722no—
175D4—1722no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—861no—
186C2×C4—861no—
187C2×C4—861no—
188C2×C4—1722no—
189C2×C4(C2×D43)⋊C411yescharacteristic
190C2×C4(C2×D43)⋊C411yescharacteristic
191C2×C4C2×C4×D4311yescharacteristic
192C2×C4C2×D17211yescharacteristic
193C8—1722no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—1721no—
203C22—1721no—
204C22—1721no—
205C22#1306323912yes—
206C22C2×(C2×D43)⋊C411yescharacteristic
207C22#1306334512yes—
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—82no—
213C4—1721no—
214C4—1721no—
215C4—1721no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—3441no—
220C2C2×#1306323911yescharacteristic
221C2#1458289311yescharacteristic
222C2#1458291711yescharacteristic
subgroupG/H
centerC22C2×(C2×D43)⋊C4
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#381C2
socleC22×C43C2×C22⋊C4
hypercenter#381D43
hypocenterC43#1516
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C43⋊C8)C2semidirect
3. #14582635C2semidirect
4. #14582632C2semidirect
5. C43×#381C2semidirect
6. C2×#10621898C4semidirect
9. #13063304C4semidirect
11. #13063299C4semidirect
16. #13063284C4semidirect
114. #381D43semidirect
117. C43#1516semidirect