Finite Group Databasebeta

← #19133612

Subgroups — #19133612

Order 5504.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#14583489C211yesmaximal, characteristic
2#14583227C211yesmaximal, characteristic, complemented
3#14583213C211yesmaximal, characteristic, complemented
4#14582826C211yesmaximal, characteristic, complemented
5#14582632C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic, complemented
7C43×#328C211yesmaximal, characteristic, complemented
8#13063320—21no—
9#13063314—21no—
10#13063310—21no—
11#13063300—21no—
12#13063299C2211yescharacteristic
13#13063295—21no—
14(C22⋊D43)⋊C4—21no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×(C2×D43)⋊C4—21no—
17C2×(C2×D43)⋊C4C2211yescharacteristic
18#13063259—21no—
19#13063256—21no—
20#13063249—21no—
21#13063247—21no—
22C22⋊(C43⋊C8)C2211yescharacteristic
23C43⋊#95—21no—
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28C2×Q8×C43D411yescharacteristic
29C22×C4×C43—21no—
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—21no—
32C22×Dic43—21no—
33C22×Dic43D411yescharacteristic
34C2×D172—21no—
35C2×D172—21no—
36C2×D172D411yescharacteristic
37C2×C4×D43—21no—
38C2×C8×C43—21no—
39C4⋊C4×C43—21no—
40C4⋊C4×C43D411yescharacteristic
41C22⋊C4×C43—21no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46(C2×D43)⋊C4—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—42no—
49C4⋊Dic43—21no—
50C4⋊Dic43—21no—
51C4⋊Dic43D411yescharacteristic
52Dic43⋊C4—21no—
53C4×Dic43—21no—
54C2×C43⋊C8—21no—
55C23×C43C2×D411yescharacteristic
56C22×D43—21no—
57C22×D43—21no—
58C22×D43—21no—
59C22×D43—21no—
60C22×D43—41no—
61C22×D43—41no—
62Q8×C43—41no—
63C2×C4×C43—21no—
64C2×C4×C43—21no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C22⋊D43—41no—
72C22⋊D43—41no—
73C2×Dic43—21no—
74C2×Dic43—21no—
75C2×Dic43—41no—
76C2×Dic43—41no—
77C2×Dic43—41no—
78C2×Dic43—41no—
79D172—41no—
80D172—81no—
81D172—81no—
82C4×D43—81no—
83C8×C43—41no—
84C43⋊C8—41no—
85C22×C43—21no—
86C22×C43—21no—
87C22×C43#12011yescharacteristic
88C22×C43#13511yescharacteristic
89C22×C43AGL(1,ℤ/8)11yescharacteristic
90C2×D43—42no—
91C2×D43—41no—
92C2×D43—41no—
93C2×D43—41no—
94C2×D43—41no—
95C2×D43—41no—
96C2×D43—41no—
97C2×D43—81no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—41no—
101C4×C43—41no—
102C4×C43—81no—
103Dic43—41no—
104Dic43—41no—
105Dic43—81no—
106#1612—431nomaximal, Sylow
107C2×C43—21no—
108C2×C43—21no—
109C2×C43#44911yescharacteristic
110C2×C43#45511yescharacteristic
111C2×C43#45811yescharacteristic
112D43—81no—
113D43—81no—
114#538—431no—
115#483—431no—
116#480—431no—
117#397—431no—
118#328D4311yescharacteristic, complemented
119#327—431no—
120#323—431no—
121C43#161211yescharacteristic, complemented, Sylow
122#126—861no—
123#124—861no—
124#123—861no—
125C22⋊Q8C2×D4311yescharacteristic
126#121—431no—
127#121—861no—
128#120—861no—
129C4×D4—861no—
130C2×C4⋊C4—431no—
131C2×C22⋊C4—431no—
132C2×C22⋊C4—861no—
133#107—861no—
134#106—861no—
135#103—861no—
136#102—861no—
137C22⋊C8—431no—
138C22⋊C8C2×D4311yescharacteristic
139#95—861no—
140#95C2×D4311yescharacteristic
141C24—431no—
142C2×Q8D17211yescharacteristic
143C2×D4—431no—
144C2×D4—861no—
145C2×D4—861no—
146C2×D4—861no—
147C22×C4—21no—
148C22×C4—431no—
149C22×C4—861no—
150C22×C4—861no—
151C22×C4C22×D4311yescharacteristic
152C2×C8—21no—
153C2×C8—861no—
154C4⋊C4—21no—
155C4⋊C4—431no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—861no—
159C4⋊C4D17211yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—861no—
162C22⋊C4—861no—
163C22⋊C4—861no—
164C22⋊C4—861no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C22⋊C4—1722no—
168C42—861no—
169C23—861no—
170C23—861no—
171C23—861no—
172C23—861no—
173C23—1721no—
174C23—1721no—
175C23D4×D4311yescharacteristic
176Q8—41no—
177D4—3441no—
178D4—3441no—
179D4—1721no—
180D4—1721no—
181D4—1721no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—861no—
189C2×C4—861no—
190C2×C4—3441no—
191C2×C4—1721no—
192C2×C4—1721no—
193C2×C4—1721no—
194C2×C4—1721no—
195C2×C4C2×D17211yescharacteristic
196C2×C4D4×D4311yescharacteristic
197C8—41no—
198C8—1721no—
199C22—21no—
200C22—21no—
201C22—3441no—
202C22—1722no—
203C22—1721no—
204C22—1721no—
205C22—1721no—
206C22—1721no—
207C22—1721no—
208C22—1721no—
209C22#1306329511yescharacteristic
210C22#1306334811yescharacteristic
211C22#1306335211yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—3441no—
218C4—1721no—
219C4—1721no—
220C2—21no—
221C2—21no—
222C2—3441no—
223C2—3441no—
224C2#1458304711yescharacteristic
225C2#1458307811yescharacteristic
226C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43#120
hypercenter#328D43
hypocenterC43#1612
LCSG ▷ C22×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. #14583227C2semidirect
3. #14583213C2semidirect
4. #14582826C2semidirect
5. #14582632C2semidirect
6. #14582622C2semidirect
7. C43×#328C2semidirect
118. #328D43semidirect
121. C43#1612semidirect