Finite Group Databasebeta

← #19133567

Subgroups — #19133567

Order 5504.

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

normal subgroups only

This group has 238 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
2#14583055C211yesmaximal, characteristic
3#14582818C211yesmaximal, characteristic
4#14582637C211yesmaximal, characteristic
5#14582636C211yesmaximal, characteristic
6#14582624C211yesmaximal, characteristic
7C43×#451C211yesmaximal, characteristic
8C2×#10621885—21no—
9#13063324—21no—
10#13063323—21no—
11#13063315—21no—
12#13063315—21no—
13#13063304C2211yescharacteristic
14#13063302—21no—
15#13063281—21no—
16C2×Dic43⋊C4—21no—
17C2×Dic43⋊C4C2211yescharacteristic
18#13063249—21no—
19C22⋊(C43⋊C8)C2211yescharacteristic
20C43⋊#95—21no—
21C43⋊#95C2211yescharacteristic
22C22×Q8×C43C2211yescharacteristic
23C2×Q16×C43—21no—
24C22⋊Q8×C43C2211yescharacteristic
25#103×C43—21no—
26C22⋊C8×C43C2211yescharacteristic
27C2×Q8×C43—21no—
28C2×Q8×C43—21no—
29C2×Q8×C43—42no—
30C2×Q8×C43D411yescharacteristic
31C22×C4×C43—21no—
32C22×C4×C43C2311yescharacteristic
33C22×Dic43—21no—
34C22×Dic43D411yescharacteristic
35C22×Dic43D411yescharacteristic
36C2×Dic86—21no—
37C2×Dic86D411yescharacteristic
38Q16×C43—42no—
39C2×C8×C43—21no—
40C4⋊C4×C43—21no—
41C4⋊C4×C43D411yescharacteristic
42C22⋊C4×C43—21no—
43C22⋊Dic43—21no—
44#10621885—42no—
45C4⋊Dic43—21no—
46C4⋊Dic43D411yescharacteristic
47Dic43⋊C4—21no—
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—42no—
55C4×Dic43—21no—
56C4×Dic43—21no—
57C2×C43⋊C8—21no—
58C23×C43C2×D411yescharacteristic
59Q8×C43—22no—
60Q8×C43—22no—
61Q8×C43—41no—
62Q8×C43—41no—
63Q8×C43—41no—
64C2×C4×C43—22no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×Dic43—21no—
73C2×Dic43—21no—
74C2×Dic43—22no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C2×Dic43—41no—
81C2×Dic43Q1612yescomplemented
82Dic86—41no—
83Dic86—81no—
84C8×C43—41no—
85C43⋊C8—41no—
86C22×C43—21no—
87C22×C43—21no—
88C22×C43#12011yescharacteristic
89C22×C43C2×Q1611yescharacteristic
90C22×C43#13711yescharacteristic
91C4×C43—21no—
92C4×C43—21no—
93C4×C43—41no—
94C4×C43—41no—
95C4×C43—42no—
96Dic43—22no—
97Dic43—42no—
98Dic43—41no—
99Dic43—41no—
100Dic43—41no—
101#1605—431nomaximal, Sylow
102C2×C43—21no—
103C2×C43—21no—
104C2×C43#45111yescharacteristic
105C2×C43#45611yescharacteristic
106C2×C43B(4,𝔽2)11yescharacteristic
107#544—431no—
108#451—431no—
109#451D4311yescharacteristic
110#395—431no—
111#328—431no—
112#328—431no—
113#324—431no—
114C43#160511yescharacteristic, complemented, Sylow
115C22×Q8C2×D4311yescharacteristic
116C2×Q16—21no—
117C2×Q16—861no—
118C4⋊Q8—861no—
119C4⋊Q8—861no—
120#125—861no—
121#125—861no—
122C22⋊Q8—431no—
123C22⋊Q8—861no—
124C22⋊Q8C2×D4311yescharacteristic
125#117—861no—
126C2×C4⋊C4—431no—
127C2×C4⋊C4—861no—
128#103—21no—
129#103—861no—
130C22⋊C8—431no—
131C22⋊C8C2×D4311yescharacteristic
132#95—431no—
133#95—861no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—42no—
137C2×Q8—431no—
138C2×Q8—861no—
139C2×Q8C22⋊D4311yescharacteristic
140C22×C4—21no—
141C22×C4—431no—
142C22×C4—431no—
143C22×C4—861no—
144C22×C4C22×D4311yescharacteristic
145Q16—42no—
146Q16—1722no—
147C2×C8—21no—
148C2×C8—861no—
149C4⋊C4—21no—
150C4⋊C4—431no—
151C4⋊C4—861no—
152C4⋊C4—861no—
153C4⋊C4—861no—
154C4⋊C4—861no—
155C4⋊C4—861no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—861no—
159C4⋊C4—1722no—
160C4⋊C4C22⋊D4311yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—861no—
163C42—861no—
164C42—861no—
165C23D4×D4311yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—41no—
171Q8—3441no—
172Q8—1721no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—432no—
180C2×C4—861no—
181C2×C4—861no—
182C2×C4—862no—
183C2×C4—861no—
184C2×C4—861no—
185C2×C4—861no—
186C2×C4—1721no—
187C2×C4—1721no—
188C2×C4—1721no—
189C2×C4D4×D4311yescharacteristic
190C2×C4C2×C22⋊D4311yescharacteristic
191C8—41no—
192C8—1721no—
193C22—21no—
194C22—21no—
195C22#1306329311yescharacteristic
196C22Q16×D4311yescharacteristic
197C22#1306335711yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4—862no—
204C4—1722no—
205C4—1721no—
206C4—1721no—
207C4—1721no—
208C2—21no—
209C2—21no—
210C2#1458305311yescharacteristic
211C2#1458308011yescharacteristic
212C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#451C2
socleC22×C43#120
hypercenter#451D43
hypocenterC43#1605
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
81. C2×Dic43Q16semidirect
114. C43#1605semidirect