Finite Group Databasebeta

← #19133513

Subgroups — #19133513

Order 5504.

368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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#14583032C212yesmaximal, complemented
2#14582808C211yesmaximal, characteristic, complemented
3#14582633C212yesmaximal, complemented
4#14582623C211yesmaximal, characteristic, complemented
5C43×#534C211yesmaximal, characteristic, complemented
6C22×D172C2211yescharacteristic, complemented
7C22×C22⋊D43—21no—
8C2×#10621882—22no—
9C2×(C2×D43)⋊C4—21no—
10#13063245—22no—
11C22⋊(C43⋊C8)C2212yescomplemented
12C43⋊#95C2211yescharacteristic, complemented
13C22×D4×C43—21no—
14#123×C43—22no—
15#121×C43—21no—
16#121×C43C2212yes—
17#120×C43—22no—
18C2×C22⋊C4×C43C2211yescharacteristic
19C24×C43—21no—
20C24×C43D411yescharacteristic
21C23×D43—21no—
22C2×D4×C43—22no—
23C2×D4×C43—21no—
24C2×D4×C43—22no—
25C2×D4×C43—42no—
26C2×D4×C43—42no—
27C2×D4×C43D412yescomplemented
28C22×C4×C43—21no—
29C22×C4×C43D411yescharacteristic
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—42no—
32C2×C22⋊D43—42no—
33C2×C22⋊D43—42no—
34C22×Dic43—21no—
35C2×D172—22no—
36C2×D172—42no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43D412yescomplemented
39C22⋊C4×C43—22no—
40C22⋊C4×C43—22no—
41C22⋊C4×C43—22no—
42#10621882—44no—
43(C2×D43)⋊C4—42no—
44C2×C43⋊C8—22no—
45C23×C43—21no—
46C23×C43—21no—
47C23×C43—22no—
48C23×C43—41no—
49C23×C43—41no—
50C23×C43—42no—
51C23×C43—81no—
52C23×C43—81no—
53C23×C43D812yescomplemented
54C23×C43C2×D411yescharacteristic
55C22×D43—22no—
56C22×D43—41no—
57C22×D43—41no—
58C22×D43—41no—
59C22×D43—41no—
60C22×D43—41no—
61C22×D43—41no—
62D4×C43—42no—
63D4×C43—44no—
64D4×C43—42no—
65D4×C43—42no—
66D4×C43—81no—
67C2×C4×C43—21no—
68C2×C4×C43—22no—
69C2×C4×C43—41no—
70C2×C4×C43—42no—
71C2×C4×C43—41no—
72C2×C4×C43C2×D412yes—
73C22⋊D43—48no—
74C2×Dic43—22no—
75C2×Dic43—41no—
76C2×Dic43—41no—
77D172—24no—
78D172—42no—
79C43⋊C8—42no—
80C22×C43—21no—
81C22×C43—21no—
82C22×C43—22no—
83C22×C43—42no—
84C22×C43—41no—
85C22×C43—41no—
86C22×C43—42no—
87C22×C43—42no—
88C22×C43—42no—
89C22×C43—81no—
90C22×C43—84no—
91C22×C43#12011yescharacteristic
92C22×C43C2×D811yescharacteristic
93C22×C43AGL(1,ℤ/8)11yescharacteristic
94C2×D43—42no—
95C2×D43—42no—
96C2×D43—42no—
97C2×D43—81no—
98C2×D43—81no—
99C2×D43—81no—
100C2×D43—81no—
101C4×C43—22no—
102C4×C43—42no—
103C4×C43—41no—
104Dic43—42no—
105#1595—431nomaximal, Sylow
106C2×C43—21no—
107C2×C43—21no—
108C2×C43—42no—
109C2×C43—82no—
110C2×C43#44711yescharacteristic
111C2×C43#45311yescharacteristic
112C2×C43B(4,𝔽2)11yescharacteristic
113D43—82no—
114#534D4311yescharacteristic, complemented
115#447—432no—
116#392—431no—
117#327—432no—
118#323—431no—
119C43#159511yescharacteristic, complemented, Sylow
120C22×D4—21no—
121C22×D4—431no—
122C22×D4—861no—
123C2×D8—862no—
124#123—22no—
125#121—21no—
126#121C2×D4312yes—
127#120—22no—
128C2×C22⋊C4—861no—
129C2×C22⋊C4C2×D4311yescharacteristic
130#102—862no—
131C22⋊C8—432no—
132#95—431no—
133C24—21no—
134C24—861no—
135C24C22⋊D4311yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—21no—
139C2×D4—42no—
140C2×D4—42no—
141C2×D4—862no—
142C2×D4—1722no—
143C2×D4—1722no—
144C2×D4—1722no—
145C2×D4—1722no—
146C2×D4C22⋊D4312yescomplemented
147C22×C4—21no—
148C22×C4—861no—
149C22×C4C22⋊D4311yescharacteristic
150C22×C4C22×D4311yescharacteristic
151D8—1724no—
152C2×C8—862no—
153C4⋊C4—21no—
154C4⋊C4C22⋊D4312yescomplemented
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—1722no—
159C23—21no—
160C23—21no—
161C23—22no—
162C23—41no—
163C23—41no—
164C23—42no—
165C23—81no—
166C23—81no—
167C23—862no—
168C23—1721no—
169C23—1721no—
170C23—1721no—
171C23—1721no—
172C23—1721no—
173C23—1721no—
174C23#1062188212yescomplemented
175C23C2×C22⋊D4311yescharacteristic
176D4—42no—
177D4—44no—
178D4—42no—
179D4—42no—
180D4—81no—
181D4—864no—
182D4—1722no—
183D4—1728no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—41no—
189C2×C4—862no—
190C2×C4—1721no—
191C2×C4—1721no—
192C2×C4C2×C22⋊D4312yes—
193C8—1722no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—84no—
205C22—3441no—
206C22—3441no—
207C22—3441no—
208C22—3441no—
209C22—1722no—
210C22—1722no—
211C22—1722no—
212C22#1306329411yescharacteristic
213C22C2×#1062188211yescharacteristic
214C22#1306335111yescharacteristic
215C4—22no—
216C4—41no—
217C4—42no—
218C4—1722no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—82no—
223C2—3442no—
224C2#1458303311yescharacteristic
225C2#1458306711yescharacteristic
226C2#1458308611yescharacteristic
subgroupG/H
centerC22#13063294
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#534C2
socleC22×C43#120
hypercenter#534D43
hypocenterC43#1595
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14583032C2semidirect
2. #14582808C2semidirect
3. #14582633C2semidirect
4. #14582623C2semidirect
5. C43×#534C2semidirect
6. C22×D172C22semidirect
11. C22⋊(C43⋊C8)C22semidirect
12. C43⋊#95C22semidirect
27. C2×D4×C43D4semidirect
38. C4⋊C4×C43D4semidirect
53. C23×C43D8semidirect
114. #534D43semidirect
119. C43#1595semidirect
146. C2×D4C22⋊D43semidirect
154. C4⋊C4C22⋊D43semidirect
174. C23#10621882semidirect