Finite Group Databasebeta

← #19133533

Subgroups — #19133533

Order 5504.

266 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 51 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#14583528C211yesmaximal, characteristic, complemented
2#14583050C211yesmaximal, characteristic
3#14582813C211yesmaximal, characteristic
4#14582637C211yesmaximal, characteristic, complemented
5#14582636C211yesmaximal, characteristic, complemented
6#14582624C211yesmaximal, characteristic, complemented
7C43×#450C211yesmaximal, characteristic
8C2×#10621883—21no—
9#13063324—21no—
10#13063323—21no—
11#13063315—21no—
12#13063315—21no—
13#13063304C2211yescharacteristic
14#13063302—21no—
15#13063281—21no—
16C2×Dic43⋊C4C2211yescharacteristic
17C2×C22⋊Dic43—21no—
18C2×C22⋊Dic43—21no—
19#13063246—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21C43⋊#95C2211yescharacteristic
22C22×D4×C43C2211yescharacteristic
23C2×SD16×C43—21no—
24C22⋊Q8×C43C2211yescharacteristic
25#102×C43—21no—
26C22⋊C8×C43C2211yescharacteristic
27C24×C43—21no—
28C2×Q8×C43D411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43—21no—
31C2×D4×C43—42no—
32C22×C4×C43C2311yescharacteristic
33C22×Dic43—21no—
34C22×Dic43D411yescharacteristic
35C22×Dic43D411yescharacteristic
36C2×Dic86—21no—
37C2×Dic86D411yescharacteristic
38SD16×C43—42no—
39C2×C8×C43—21no—
40C4⋊C4×C43—21no—
41C4⋊C4×C43D411yescharacteristic
42C22⋊C4×C43—21no—
43C22⋊Dic43—21no—
44C22⋊Dic43—42no—
45C22⋊Dic43—42no—
46#10621883—42no—
47C4⋊Dic43—21no—
48C4⋊Dic43D411yescharacteristic
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56C4×Dic43—21no—
57C4×Dic43—21no—
58C2×C43⋊C8—21no—
59C23×C43—22no—
60C23×C43—41no—
61C23×C43—41no—
62C23×C43—41no—
63C23×C43—41no—
64C23×C43—41no—
65C23×C43—41no—
66C23×C43C2×D411yescharacteristic
67Q8×C43—41no—
68D4×C43—22no—
69D4×C43—22no—
70D4×C43—41no—
71D4×C43—41no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—41no—
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—41no—
83C2×Dic43—41no—
84C2×Dic43—41no—
85C2×Dic43—41no—
86C2×Dic43SD1612yescomplemented
87Dic86—41no—
88Dic86—81no—
89C8×C43—41no—
90C43⋊C8—41no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—42no—
94C22×C43—42no—
95C22×C43—42no—
96C22×C43—81no—
97C22×C43—81no—
98C22×C43—81no—
99C22×C43—81no—
100C22×C43#12011yescharacteristic
101C22×C43C2×SD1611yescharacteristic
102C22×C43#13711yescharacteristic
103C4×C43—21no—
104C4×C43—21no—
105C4×C43—41no—
106C4×C43—41no—
107Dic43—22no—
108Dic43—41no—
109Dic43—41no—
110Dic43—41no—
111Dic43—81no—
112#1599—431nomaximal, Sylow
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—82no—
116C2×C43#44811yescharacteristic
117C2×C43#45411yescharacteristic
118C2×C43B(4,𝔽2)11yescharacteristic
119#544—431no—
120#450—431no—
121#450D4311yescharacteristic
122#394—431no—
123#328—431no—
124#328—431no—
125#324—431no—
126C43#159911yescharacteristic, complemented, Sylow
127C22×D4C2×D4311yescharacteristic
128C2×SD16—21no—
129C2×SD16—861no—
130C4⋊Q8—861no—
131C4⋊Q8—861no—
132#125—861no—
133#125—861no—
134C22⋊Q8—431no—
135C22⋊Q8—861no—
136C22⋊Q8C2×D4311yescharacteristic
137#117—861no—
138C2×C4⋊C4—431no—
139C2×C22⋊C4—861no—
140C2×C22⋊C4—861no—
141#102—21no—
142#102—861no—
143C22⋊C8—431no—
144C22⋊C8C2×D4311yescharacteristic
145#95—431no—
146C24—21no—
147C2×Q8—431no—
148C2×Q8—861no—
149C2×Q8C22⋊D4311yescharacteristic
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—42no—
153C22×C4—431no—
154C22×C4—431no—
155C22×C4—861no—
156C22×C4C22×D4311yescharacteristic
157SD16—42no—
158SD16—1722no—
159C2×C8—21no—
160C2×C8—861no—
161C4⋊C4—21no—
162C4⋊C4—431no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4—861no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C4⋊C4—861no—
169C4⋊C4—861no—
170C4⋊C4—861no—
171C4⋊C4C22⋊D4311yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—861no—
174C22⋊C4—1722no—
175C22⋊C4—1722no—
176C42—861no—
177C42—861no—
178C23—22no—
179C23—41no—
180C23—41no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23D4×D4311yescharacteristic
186Q8—41no—
187Q8—3441no—
188Q8—1721no—
189D4—22no—
190D4—22no—
191D4—41no—
192D4—41no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—432no—
197C2×C4—861no—
198C2×C4—861no—
199C2×C4—861no—
200C2×C4—861no—
201C2×C4—861no—
202C2×C4—1721no—
203C2×C4—1721no—
204C2×C4—1721no—
205C2×C4—1721no—
206C2×C4D4×D4311yescharacteristic
207C2×C4C2×C22⋊D4311yescharacteristic
208C8—41no—
209C8—1721no—
210C22—21no—
211C22—21no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—81no—
216C22—81no—
217C22—81no—
218C22—81no—
219C22#1306329311yescharacteristic
220C22SD16×D4311yescharacteristic
221C22#1306335411yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—862no—
227C4—3441no—
228C4—1721no—
229C4—1721no—
230C4—1721no—
231C2—21no—
232C2—21no—
233C2—82no—
234C2#1458303611yescharacteristic
235C2#1458307011yescharacteristic
236C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#450C2
socleC22×C43#120
hypercenter#450D43
hypocenterC43#1599
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14583528C2semidirect
4. #14582637C2semidirect
5. #14582636C2semidirect
6. #14582624C2semidirect
86. C2×Dic43SD16semidirect
126. C43#1599semidirect