Finite Group Databasebeta

← #19133550

Subgroups — #19133550

Order 5504.

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

normal subgroups only

This group has 256 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#14583524C211yesmaximal, characteristic
2#14583055C211yesmaximal, characteristic, complemented
3#14582810C211yesmaximal, characteristic
4#14582637C211yesmaximal, characteristic, complemented
5#14582636C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic
7C43×#451C211yesmaximal, characteristic, complemented
8C2×#10621885—21no—
9#13063305—21no—
10#13063304C2211yescharacteristic
11#13063303—21no—
12#13063303—21no—
13#13063302—21no—
14#13063301—21no—
15C2×(C2×D43)⋊C4—21no—
16C2×(C2×D43)⋊C4C2211yescharacteristic
17C22⋊C4×D43—21no—
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
27C23×D43D411yescharacteristic
28C2×Q8×C43—21no—
29C2×Q8×C43—21no—
30C2×Q8×C43—42no—
31C2×Q8×C43D411yescharacteristic
32C22×C4×C43—21no—
33C22×C4×C43C2311yescharacteristic
34C22×Dic43—21no—
35C22×Dic43D411yescharacteristic
36C2×C4×D43—21no—
37C2×C4×D43—21no—
38C2×Dic86—21no—
39C2×Dic86D411yescharacteristic
40Q16×C43—42no—
41C2×C8×C43—21no—
42C4⋊C4×C43—21no—
43C4⋊C4×C43D411yescharacteristic
44C22⋊C4×C43—21no—
45C22⋊Dic43—21no—
46#10621885—42no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51(C2×D43)⋊C4—42no—
52C4⋊Dic43—21no—
53C4⋊Dic43D411yescharacteristic
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—21no—
57C2×C43⋊C8—21no—
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60C22×D43—21no—
61C22×D43—41no—
62C22×D43—41no—
63C22×D43Q1612yescomplemented
64Q8×C43—22no—
65Q8×C43—22no—
66Q8×C43—41no—
67Q8×C43—41no—
68Q8×C43—41no—
69C2×C4×C43—22no—
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43—41no—
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—41no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83C2×Dic43—41no—
84C4×D43—81no—
85C4×D43—81no—
86Dic86—41no—
87Dic86—81no—
88C8×C43—41no—
89C43⋊C8—41no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43#12011yescharacteristic
93C22×C43C2×Q1611yescharacteristic
94C22×C43#13711yescharacteristic
95C2×D43—22no—
96C2×D43—41no—
97C2×D43—41no—
98C2×D43—42no—
99C2×D43—81no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—41no—
103C4×C43—41no—
104C4×C43—42no—
105Dic43—41no—
106Dic43—41no—
107Dic43—41no—
108Dic43—81no—
109#1602—431nomaximal, Sylow
110C2×C43—21no—
111C2×C43—21no—
112C2×C43#45111yescharacteristic
113C2×C43#45511yescharacteristic
114C2×C43B(4,𝔽2)11yescharacteristic
115D43—42no—
116#543—431no—
117#451—431no—
118#451D4311yescharacteristic, complemented
119#393—431no—
120#328—431no—
121#328—431no—
122#323—431no—
123C43#160211yescharacteristic, complemented, Sylow
124C22×Q8C2×D4311yescharacteristic
125C2×Q16—21no—
126C2×Q16—861no—
127C22⋊Q8—431no—
128C22⋊Q8—861no—
129C22⋊Q8—861no—
130C22⋊Q8—861no—
131C22⋊Q8—861no—
132C22⋊Q8—861no—
133C22⋊Q8C2×D4311yescharacteristic
134C2×C22⋊C4—431no—
135C2×C22⋊C4—861no—
136C2×C22⋊C4—861no—
137#103—21no—
138#103—861no—
139C22⋊C8—431no—
140C22⋊C8C2×D4311yescharacteristic
141#95—431no—
142#95—861no—
143C24—431no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—42no—
147C2×Q8—431no—
148C2×Q8—861no—
149C2×Q8C22⋊D4311yescharacteristic
150C22×C4—21no—
151C22×C4—431no—
152C22×C4—861no—
153C22×C4—861no—
154C22×C4—861no—
155C22×C4C22×D4311yescharacteristic
156Q16—42no—
157Q16—1722no—
158C2×C8—21no—
159C2×C8—861no—
160C4⋊C4—21no—
161C4⋊C4—431no—
162C4⋊C4—861no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4—861no—
166C4⋊C4C22⋊D4311yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—861no—
169C22⋊C4—861no—
170C22⋊C4—861no—
171C22⋊C4—861no—
172C22⋊C4—861no—
173C22⋊C4—1722no—
174C23—432no—
175C23—861no—
176C23—861no—
177C23—1721no—
178C23—1721no—
179C23D4×D4311yescharacteristic
180Q8—22no—
181Q8—22no—
182Q8—41no—
183Q8—41no—
184Q8—41no—
185Q8—3441no—
186Q8—1721no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—861no—
194C2×C4—861no—
195C2×C4—861no—
196C2×C4—3441no—
197C2×C4—3441no—
198C2×C4—1721no—
199C2×C4—1721no—
200C2×C4—1721no—
201C2×C4—1721no—
202C2×C4D4×D4311yescharacteristic
203C2×C4C2×C22⋊D4311yescharacteristic
204C8—41no—
205C8—1721no—
206C22—21no—
207C22—21no—
208C22—862no—
209C22—3441no—
210C22—1722no—
211C22—1721no—
212C22—1721no—
213C22#1306329311yescharacteristic
214C22Q16×D4311yescharacteristic
215C22#1306335711yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—42no—
220C4—41no—
221C4—3441no—
222C4—1721no—
223C4—1721no—
224C4—1721no—
225C2—21no—
226C2—21no—
227C2—1722no—
228C2#1458305311yescharacteristic
229C2#1458307511yescharacteristic
230C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#451C2
socleC22×C43#120
hypercenter#451D43
hypocenterC43#1602
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
2. #14583055C2semidirect
4. #14582637C2semidirect
5. #14582636C2semidirect
7. C43×#451C2semidirect
63. C22×D43Q16semidirect
118. #451D43semidirect
123. C43#1602semidirect