Finite Group Databasebeta

← #19133641

Subgroups — #19133641

Order 5504.

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

normal subgroups only

This group has 240 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#14583487C211yesmaximal, characteristic
2#14583234C211yesmaximal, characteristic, complemented
3#14583217C211yesmaximal, characteristic, complemented
4#14582635C211yesmaximal, characteristic, complemented
5#14582632C211yesmaximal, characteristic, complemented
6#14582623C211yesmaximal, characteristic, complemented
7C43×#399C211yesmaximal, characteristic, complemented
8#13063318—21no—
9#13063311—21no—
10#13063307—21no—
11#13063304C2211yescharacteristic
12#13063299C2211yescharacteristic
13#13063298—21no—
14#13063294—21no—
15C4×C22⋊D43—21no—
16#13063258—21no—
17#13063256—21no—
18#13063248—21no—
19#13063245—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21C22⋊(C43⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C43—21no—
23C2×C4⋊C4×C43C2211yescharacteristic
24C2×C22⋊C4×C43—21no—
25C2×C22⋊C4×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C24×C43D411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43D411yescharacteristic
31C22×C4×C43C2311yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C2×D172D411yescharacteristic
36C2×C4×D43—21no—
37C2×Dic86D411yescharacteristic
38C4⋊C4×C43—21no—
39C4⋊C4×C43—21no—
40C4⋊C4×C43—42no—
41C22⋊C4×C43—21no—
42C22⋊C4×C43—21no—
43C22⋊C4×C43—42no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49C4⋊Dic43D411yescharacteristic
50C4⋊Dic43D411yescharacteristic
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53C4×Dic43—21no—
54C2×C43⋊C8—21no—
55C2×C43⋊C8—21no—
56C23×C43—21no—
57C23×C43—21no—
58C23×C43—21no—
59C23×C43—41no—
60C23×C43—41no—
61C23×C43C2×D411yescharacteristic
62C22×D43—21no—
63C2×C4×C43—22no—
64C2×C4×C43—21no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43—41no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C22⋊D43—41no—
75C22⋊D43—41no—
76C22⋊D43—81no—
77C22⋊D43—81no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81D172—41no—
82C4×D43—81no—
83Dic86—41no—
84C43⋊C8—41no—
85C43⋊C8—41no—
86C22×C43—21no—
87C22×C43—21no—
88C22×C43—42no—
89C22×C43—41no—
90C22×C43—41no—
91C22×C43—41no—
92C22×C43—81no—
93C22×C43#12011yescharacteristic
94C22×C43#13511yescharacteristic
95C22×C43#13711yescharacteristic
96C2×D43—41no—
97C2×D43—41no—
98C2×D43—41no—
99C4×C43—21no—
100C4×C43—21no—
101C4×C43—42no—
102C4×C43—41no—
103C4×C43—81no—
104Dic43—41no—
105Dic43—41no—
106Dic43—41no—
107#1618—431nomaximal, Sylow
108C2×C43—21no—
109C2×C43—21no—
110C2×C43—81no—
111C2×C43#45211yescharacteristic
112C2×C43#45311yescharacteristic
113C2×C43#45811yescharacteristic
114D43—81no—
115#538—431no—
116#484—431no—
117#481—431no—
118#399D4311yescharacteristic, complemented
119#328—431no—
120#327—431no—
121#323—431no—
122C43#161811yescharacteristic, complemented, Sylow
123#126—861no—
124#124—861no—
125#123—861no—
126C22⋊Q8—431no—
127#121—431no—
128#121—861no—
129#120—861no—
130C4×D4—861no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4C2×D4311yescharacteristic
133C2×C22⋊C4—21no—
134C2×C22⋊C4C2×D4311yescharacteristic
135#107—861no—
136#106—861no—
137#103—861no—
138#102—861no—
139C22⋊C8—431no—
140C22⋊C8—431no—
141#95C2×D4311yescharacteristic
142C24C22⋊D4311yescharacteristic
143C2×Q8—431no—
144C2×D4—431no—
145C2×D4—861no—
146C2×D4—861no—
147C2×D4—861no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—861no—
151C22×C4C22⋊D4311yescharacteristic
152C22×C4C22×D4311yescharacteristic
153C2×C8—861no—
154C2×C8—861no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—42no—
158C4⋊C4—431no—
159C4⋊C4—431no—
160C4⋊C4—861no—
161C4⋊C4—861no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—42no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C22⋊C4—861no—
170C42—861no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—41no—
175C23—41no—
176C23—861no—
177C23C2×C22⋊D4311yescharacteristic
178Q8—1721no—
179D4—3441no—
180D4—3441no—
181D4—1721no—
182D4—1721no—
183D4—1721no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—861no—
194C2×C4—861no—
195C2×C4—861no—
196C2×C4—3441no—
197C2×C4D4×D4311yescharacteristic
198C2×C4D4×D4311yescharacteristic
199C8—1721no—
200C8—1721no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—1721no—
209C22—1721no—
210C22—1721no—
211C22#1306329311yescharacteristic
212C22#1306334511yescharacteristic
213C22#1306335611yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—81no—
219C4—1721no—
220C4—1721no—
221C4—1721no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—3441no—
226C2#1458305911yescharacteristic
227C2#1458306611yescharacteristic
228C2#1458308811yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#399C2
socleC22×C43#120
hypercenter#399D43
hypocenterC43#1618
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #14583234C2semidirect
3. #14583217C2semidirect
4. #14582635C2semidirect
5. #14582632C2semidirect
6. #14582623C2semidirect
7. C43×#399C2semidirect
118. #399D43semidirect
122. C43#1618semidirect