Finite Group Databasebeta

← #19133555

Subgroups — #19133555

Order 5504.

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

normal subgroups only

This group has 244 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#14583494C211yesmaximal, characteristic
2#14583055C211yesmaximal, characteristic, complemented
3#14582818C211yesmaximal, characteristic, complemented
4#14582637C211yesmaximal, characteristic, complemented
5#14582633C211yesmaximal, characteristic
6#14582624C211yesmaximal, characteristic, complemented
7C43×#448C211yesmaximal, characteristic
8C2×#10621885—21no—
9#13063318—21no—
10#13063315—21no—
11#13063306—21no—
12#13063306—21no—
13#13063304C2211yescharacteristic
14#13063302—21no—
15D4×Dic43—21no—
16C2×Dic43⋊C4—21no—
17C2×Dic43⋊C4C2211yescharacteristic
18#13063249—21no—
19C22⋊(C43⋊C8)C2211yescharacteristic
20C43⋊#95—21no—
21C43⋊#95C2211yescharacteristic
22C22×Q8×C43C2211yescharacteristic
23C2×SD16×C43—21no—
24#121×C43C2211yescharacteristic
25#103×C43—21no—
26C22⋊C8×C43C2211yescharacteristic
27C2×Q8×C43—21no—
28C2×Q8×C43—21no—
29C2×Q8×C43—42no—
30C2×D4×C43—21no—
31C2×D4×C43D411yescharacteristic
32C22×C4×C43—21no—
33C22×C4×C43C2311yescharacteristic
34C22×Dic43—21no—
35C22×Dic43—21no—
36C22×Dic43D411yescharacteristic
37C22×Dic43D411yescharacteristic
38C2×Dic86D411yescharacteristic
39SD16×C43—42no—
40C2×C8×C43—21no—
41C4⋊C4×C43D411yescharacteristic
42C22⋊C4×C43—21no—
43C22⋊Dic43—21no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47#10621885—42no—
48C4⋊Dic43—21no—
49C4⋊Dic43D411yescharacteristic
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—42no—
56C4×Dic43—21no—
57C2×C43⋊C8—21no—
58C23×C43—21no—
59C23×C43C2×D411yescharacteristic
60Q8×C43—22no—
61Q8×C43—22no—
62Q8×C43—41no—
63Q8×C43—41no—
64D4×C43—41no—
65D4×C43—41no—
66D4×C43—41no—
67C2×C4×C43—22no—
68C2×C4×C43—21no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43—41no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×Dic43—22no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83C2×Dic43—41no—
84C2×Dic43—81no—
85Dic86—41no—
86C8×C43—41no—
87C43⋊C8—41no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43—41no—
91C22×C43—41no—
92C22×C43—41no—
93C22×C43#12011yescharacteristic
94C22×C43#13511yescharacteristic
95C22×C43#13711yescharacteristic
96C4×C43—21no—
97C4×C43—21no—
98C4×C43—41no—
99C4×C43—42no—
100Dic43—42no—
101Dic43—41no—
102Dic43—41no—
103Dic43—41no—
104Dic43—41no—
105#1603—431nomaximal, Sylow
106C2×C43—21no—
107C2×C43—21no—
108C2×C43—81no—
109C2×C43#45211yescharacteristic
110C2×C43#45611yescharacteristic
111C2×C43B(4,𝔽2)11yescharacteristic
112#539—431no—
113#451—431no—
114#448D4311yescharacteristic
115#395—431no—
116#328—431no—
117#327—431no—
118#324—431no—
119C43#160311yescharacteristic, complemented, Sylow
120C22×Q8C2×D4311yescharacteristic
121C2×Q16—861no—
122C2×SD16—21no—
123#126—861no—
124#125—861no—
125#123—861no—
126#123—861no—
127C22⋊Q8—431no—
128C22⋊Q8—861no—
129#121C2×D4311yescharacteristic
130C4×D4—861no—
131C2×C4⋊C4—431no—
132C2×C4⋊C4—861no—
133#103—21no—
134#103—861no—
135C22⋊C8—431no—
136C22⋊C8C2×D4311yescharacteristic
137#95—431no—
138#95—861no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8—431no—
143C2×D4—21no—
144C2×D4C22⋊D4311yescharacteristic
145C22×C4—21no—
146C22×C4—431no—
147C22×C4—431no—
148C22×C4—861no—
149C22×C4—861no—
150C22×C4C22×D4311yescharacteristic
151Q16—1722no—
152SD16—42no—
153C2×C8—21no—
154C2×C8—861no—
155C4⋊C4—431no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—861no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C4⋊C4—861no—
162C4⋊C4—1722no—
163C4⋊C4C22⋊D4311yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C42—861no—
170C23—21no—
171C23D4×D4311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—1721no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—862no—
186C2×C4—861no—
187C2×C4—861no—
188C2×C4—861no—
189C2×C4—861no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—3441no—
193C2×C4—1721no—
194C2×C4—1721no—
195C2×C4—1721no—
196C2×C4D4×D4311yescharacteristic
197C2×C4C2×C22⋊D4311yescharacteristic
198C8—41no—
199C8—1721no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#1306329311yescharacteristic
206C22#1306334611yescharacteristic
207C22#1306335411yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—42no—
212C4—1722no—
213C4—1721no—
214C4—1721no—
215C4—1721no—
216C4—1721no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#1458305811yescharacteristic
221C2#1458308011yescharacteristic
222C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#448C2
socleC22×C43#120
hypercenter#448D43
hypocenterC43#1603
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #14583055C2semidirect
3. #14582818C2semidirect
4. #14582637C2semidirect
6. #14582624C2semidirect
119. C43#1603semidirect