Finite Group Databasebeta

← #19133599

Subgroups — #19133599

Order 5504.

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

normal subgroups only

This group has 254 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#14583476C211yesmaximal, characteristic
2#14583213C211yesmaximal, characteristic, complemented
3#14583210C211yesmaximal, characteristic, complemented
4#14582831C211yesmaximal, characteristic, complemented
5#14582632C211yesmaximal, characteristic, complemented
6#14582624C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C2×#10621900—21no—
9#13063303—21no—
10#13063302—21no—
11#13063299C2211yescharacteristic
12#13063298—21no—
13#13063297—21no—
14#13063297—21no—
15C2×C4⋊Dic43—21no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18#13063259—21no—
19#13063258—21no—
20#13063247—21no—
21#13063246—21no—
22C22⋊(C43⋊C8)C2211yescharacteristic
23C43⋊#95—21no—
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C2×D4×C43—21no—
28C2×D4×C43D411yescharacteristic
29C22×C4×C43—21no—
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C22×Dic43—21no—
35C22×Dic43—21no—
36C22×Dic43D411yescharacteristic
37C22×Dic43D411yescharacteristic
38#10621900—42no—
39#10621900—42no—
40C2×D172D411yescharacteristic
41C2×C4×D43—21no—
42C2×Dic86—21no—
43C2×C8×C43—21no—
44C4⋊C4×C43D411yescharacteristic
45C22⋊C4×C43—21no—
46C22⋊Dic43—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49C4⋊Dic43—21no—
50C4⋊Dic43—21no—
51C4⋊Dic43—42no—
52C4⋊Dic43D411yescharacteristic
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56C2×C43⋊C8—21no—
57C23×C43—21no—
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60D4×C43—41no—
61D4×C43—41no—
62D4×C43—41no—
63C2×C4×C43—22no—
64C2×C4×C43—21no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C22⋊D43—42no—
71C22⋊D43—41no—
72C22⋊D43—41no—
73C22⋊D43—81no—
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—42no—
79C2×Dic43—41no—
80C2×Dic43—41no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83C2×Dic43D812yes—
84D172—41no—
85C4×D43—42no—
86Dic86—42no—
87C8×C43—41no—
88C43⋊C8—41no—
89C22×C43—21no—
90C22×C43—21no—
91C22×C43—41no—
92C22×C43—41no—
93C22×C43—41no—
94C22×C43#12011yescharacteristic
95C22×C43C2×D811yescharacteristic
96C22×C43AGL(1,ℤ/8)11yescharacteristic
97C2×D43—41no—
98C2×D43—41no—
99C2×D43—41no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—42no—
103C4×C43—41no—
104Dic43—22no—
105Dic43—41no—
106Dic43—41no—
107Dic43—81no—
108#1610—431nomaximal, Sylow
109C2×C43—21no—
110C2×C43—21no—
111C2×C43—81no—
112C2×C43#44711yescharacteristic
113C2×C43#45611yescharacteristic
114C2×C43#45811yescharacteristic
115D43—81no—
116#537—431no—
117#480—431no—
118#480—431no—
119#398—431no—
120#327—431no—
121#327D4311yescharacteristic, complemented
122#324—431no—
123C43#161011yescharacteristic, complemented, Sylow
124C2×#41—861no—
125C22⋊Q8—861no—
126C22⋊Q8—861no—
127#121—431no—
128#121—861no—
129#121—861no—
130#121—861no—
131#121C2×D4311yescharacteristic
132C2×C4⋊C4—431no—
133C2×C4⋊C4—431no—
134C2×C4⋊C4—861no—
135#107—861no—
136#107—861no—
137#102—861no—
138#102—861no—
139C22⋊C8—431no—
140C22⋊C8C2×D4311yescharacteristic
141#95—861no—
142#95C2×D4311yescharacteristic
143#41—1722no—
144#41—1722no—
145C2×Q8—861no—
146C2×D4—21no—
147C2×D4—431no—
148C2×D4—861no—
149C2×D4—861no—
150C2×D4—861no—
151C2×D4D17211yescharacteristic
152C22×C4—21no—
153C22×C4—431no—
154C22×C4—431no—
155C22×C4—861no—
156C22×C4—861no—
157C22×C4—861no—
158C22×C4C22×D4311yescharacteristic
159C2×C8—21no—
160C2×C8—861no—
161C4⋊C4—431no—
162C4⋊C4—861no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4—861no—
166C4⋊C4—861no—
167C4⋊C4—1722no—
168C4⋊C4D17211yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—861no—
171C22⋊C4—861no—
172C22⋊C4—861no—
173C23—21no—
174C23—861no—
175C23D4×D4311yescharacteristic
176Q8—1722no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—3441no—
181D4—1721no—
182D4—1722no—
183D4—1721no—
184D4—1721no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—432no—
191C2×C4—861no—
192C2×C4—861no—
193C2×C4—861no—
194C2×C4—861no—
195C2×C4—1722no—
196C2×C4—1722no—
197C2×C4—1721no—
198C2×C4—1721no—
199C2×C4—1721no—
200C2×C4—1721no—
201C2×C4C2×D17211yescharacteristic
202C2×C4D4×D4311yescharacteristic
203C8—41no—
204C8—1721no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—1721no—
211C22—1721no—
212C22—1721no—
213C22#1306329511yescharacteristic
214C22D8×D4311yescharacteristic
215C22#1306335211yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—862no—
221C4—3441no—
222C4—1721no—
223C4—1721no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—3441no—
228C2#1458303411yescharacteristic
229C2#1458308311yescharacteristic
230C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1610
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. #14583213C2semidirect
3. #14583210C2semidirect
4. #14582831C2semidirect
5. #14582632C2semidirect
6. #14582624C2semidirect
7. C43×#327C2semidirect
121. #327D43semidirect
123. C43#1610semidirect