Finite Group Databasebeta

← #19133644

Subgroups — #19133644

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#14583486C211yesmaximal, characteristic
2#14583235C211yesmaximal, characteristic, complemented
3#14583215C211yesmaximal, characteristic, complemented
4#14582836C211yesmaximal, characteristic, complemented
5#14582635C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8#13063320—21no—
9#13063311—21no—
10#13063309—21no—
11#13063304C2211yescharacteristic
12#13063297—21no—
13#13063293—21no—
14D4×Dic43—21no—
15C2×C4⋊Dic43—21no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×(C2×D43)⋊C4—21no—
18C2×(C2×D43)⋊C4C2211yescharacteristic
19#13063259—21no—
20#13063256—21no—
21#13063250—21no—
22#13063246—21no—
23C22⋊(C43⋊C8)C2211yescharacteristic
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28C2×D4×C43—21no—
29C2×D4×C43D411yescharacteristic
30C22×C4×C43—21no—
31C22×C4×C43C2311yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C22×Dic43—21no—
35C22×Dic43—21no—
36C22×Dic43D411yescharacteristic
37C2×Dic86D411yescharacteristic
38C2×C8×C43—21no—
39C4⋊C4×C43D411yescharacteristic
40C22⋊C4×C43—21no—
41C22⋊Dic43—21no—
42C22⋊Dic43—21no—
43(C2×D43)⋊C4—21no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46(C2×D43)⋊C4—21no—
47(C2×D43)⋊C4—42no—
48C4⋊Dic43—21no—
49C4⋊Dic43—21no—
50C4⋊Dic43—21no—
51C4⋊Dic43—42no—
52C4⋊Dic43D411yescharacteristic
53Dic43⋊C4—21no—
54C4×Dic43—21no—
55C2×C43⋊C8—21no—
56C23×C43—21no—
57C23×C43C2×D411yescharacteristic
58C22×D43—21no—
59C22×D43—21no—
60C22×D43—21no—
61C22×D43—41no—
62C22×D43—41no—
63D4×C43—41no—
64D4×C43—41no—
65D4×C43—41no—
66C2×C4×C43—22no—
67C2×C4×C43—21no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C22⋊D43—81no—
74C22⋊D43—81no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C2×Dic43—41no—
81C2×Dic43—41no—
82C2×Dic43—81no—
83Dic86—41no—
84C8×C43—41no—
85C43⋊C8—41no—
86C22×C43—21no—
87C22×C43—21no—
88C22×C43—41no—
89C22×C43—41no—
90C22×C43—41no—
91C22×C43#12011yescharacteristic
92C22×C43#13511yescharacteristic
93C22×C43#13711yescharacteristic
94C2×D43—42no—
95C2×D43—41no—
96C2×D43—41no—
97C2×D43—41no—
98C2×D43—81no—
99C4×C43—21no—
100C4×C43—21no—
101C4×C43—42no—
102C4×C43—41no—
103Dic43—41no—
104Dic43—41no—
105Dic43—41no—
106Dic43—81no—
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#399—431no—
119#328—431no—
120#327D4311yescharacteristic, complemented
121#323—431no—
122C43#161811yescharacteristic, complemented, Sylow
123#126—861no—
124#124—861no—
125#123—861no—
126C22⋊Q8—431no—
127#121—861no—
128#121C2×D4311yescharacteristic
129#120—861no—
130C4×D4—861no—
131C2×C4⋊C4—431no—
132C2×C4⋊C4—861no—
133C2×C22⋊C4—431no—
134C2×C22⋊C4—861no—
135#107—861no—
136#106—861no—
137#103—861no—
138#102—861no—
139C22⋊C8—431no—
140C22⋊C8C2×D4311yescharacteristic
141#95C2×D4311yescharacteristic
142C24—431no—
143C2×Q8—431no—
144C2×D4—21no—
145C2×D4—861no—
146C2×D4—861no—
147C2×D4D17211yescharacteristic
148C22×C4—21no—
149C22×C4—431no—
150C22×C4—861no—
151C22×C4—861no—
152C22×C4C22×D4311yescharacteristic
153C2×C8—21no—
154C2×C8—861no—
155C4⋊C4—431no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—861no—
159C4⋊C4—861no—
160C4⋊C4—1722no—
161C4⋊C4D17211yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—861no—
164C22⋊C4—861no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C22⋊C4—1722no—
170C42—861no—
171C23—21no—
172C23—861no—
173C23—861no—
174C23—861no—
175C23—1721no—
176C23—1721no—
177C23D4×D4311yescharacteristic
178Q8—1721no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—3441no—
183D4—3441no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—861no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—3441no—
193C2×C4—1721no—
194C2×C4—1721no—
195C2×C4—1721no—
196C2×C4—1721no—
197C2×C4C2×D17211yescharacteristic
198C2×C4D4×D4311yescharacteristic
199C8—41no—
200C8—1721no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—3441no—
207C22—1722no—
208C22—1721no—
209C22—1721no—
210C22—1721no—
211C22#1306329511yescharacteristic
212C22#1306334411yescharacteristic
213C22#1306335411yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—3441no—
219C4—1721no—
220C4—1721no—
221C4—1721no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—3441no—
226C2#1458306211yescharacteristic
227C2#1458306811yescharacteristic
228C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1618
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14583235C2semidirect
3. #14583215C2semidirect
4. #14582836C2semidirect
5. #14582635C2semidirect
6. #14582622C2semidirect
7. C43×#327C2semidirect
120. #327D43semidirect
122. C43#1618semidirect