Finite Group Databasebeta

← #19133536

Subgroups — #19133536

Order 5504.

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

normal subgroups only

This group has 266 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, complemented
2#14583052C211yesmaximal, characteristic
3#14583049C211yesmaximal, characteristic
4#14582817C211yesmaximal, characteristic
5#14582635C211yesmaximal, characteristic, complemented
6#14582624C211yesmaximal, characteristic, complemented
7C43×#328C211yesmaximal, characteristic, complemented
8C22×D172C2211yescharacteristic
9C2×#10621873—21no—
10C2×#10621884—21no—
11#13063324—21no—
12#13063323—21no—
13#13063315—21no—
14#13063315—21no—
15#13063304C2211yescharacteristic
16#13063302—21no—
17#13063281—21no—
18C2×Dic43⋊C4C2211yescharacteristic
19C2×(C2×D43)⋊C4—21no—
20C2×(C2×D43)⋊C4—21no—
21#13063247—21no—
22#13063245—21no—
23C22⋊(C43⋊C8)C2211yescharacteristic
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43—21no—
28C2×Q8×C43D411yescharacteristic
29C22×C4×C43—21no—
30C22×C4×C43C2311yescharacteristic
31C22×Dic43D411yescharacteristic
32C22×Dic43D411yescharacteristic
33C2×D172—21no—
34C2×D172—21no—
35C2×D172—42no—
36C2×Dic86—21no—
37C2×Dic86D411yescharacteristic
38C2×C8×C43—21no—
39C4⋊C4×C43—21no—
40C4⋊C4×C43D411yescharacteristic
41C22⋊C4×C43—21no—
42C22⋊Dic43—21no—
43#10621884—42no—
44(C2×D43)⋊C4—42no—
45(C2×D43)⋊C4—42no—
46C4⋊Dic43—21no—
47C4⋊Dic43D411yescharacteristic
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55C4×Dic43—21no—
56C4×Dic43—21no—
57C2×C43⋊C8—21no—
58#10621873—42no—
59C23×C43C2×D411yescharacteristic
60C22×D43—22no—
61C22×D43—41no—
62C22×D43—41no—
63C22×D43—41no—
64C22×D43—41no—
65C22×D43—41no—
66C22×D43—41no—
67Q8×C43—41no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—41no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—41no—
82C2×Dic43SD1612yescomplemented
83D172—22no—
84D172—22no—
85D172—41no—
86D172—41no—
87Dic86—41no—
88Dic86—81no—
89C8×C43—41no—
90C43⋊C8—41no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43#12011yescharacteristic
94C22×C43C2×SD1611yescharacteristic
95C22×C43#13711yescharacteristic
96C2×D43—42no—
97C2×D43—42no—
98C2×D43—42no—
99C2×D43—81no—
100C2×D43—81no—
101C2×D43—81no—
102C2×D43—81no—
103C4×C43—21no—
104C4×C43—21no—
105C4×C43—41no—
106C4×C43—41no—
107C4×C43—81no—
108Dic43—22no—
109Dic43—41no—
110Dic43—41no—
111Dic43—41no—
112#1599—431nomaximal, Sylow
113C2×C43—21no—
114C2×C43—21no—
115C2×C43#44811yescharacteristic
116C2×C43#45411yescharacteristic
117C2×C43B(4,𝔽2)11yescharacteristic
118D43—82no—
119#544—431no—
120#450—431no—
121#450—431no—
122#394—431no—
123#328—431no—
124#328D4311yescharacteristic, complemented
125#324—431no—
126C43#159911yescharacteristic, complemented, Sylow
127C22×D4—431no—
128C2×SD16—861no—
129C2×SD16—861no—
130C4⋊Q8—861no—
131C4⋊Q8—861no—
132#125—861no—
133#125—861no—
134C22⋊Q8—431no—
135C22⋊Q8—861no—
136C22⋊Q8C2×D4311yescharacteristic
137#117—861no—
138C2×C4⋊C4—431no—
139C2×C22⋊C4—861no—
140C2×C22⋊C4—861no—
141#102—861no—
142#102—861no—
143C22⋊C8—431no—
144C22⋊C8C2×D4311yescharacteristic
145#95C2×D4311yescharacteristic
146C24—861no—
147C2×Q8—431no—
148C2×Q8—861no—
149C2×Q8D17211yescharacteristic
150C2×D4—861no—
151C2×D4—861no—
152C2×D4—1722no—
153C22×C4—21no—
154C22×C4—431no—
155C22×C4—431no—
156C22×C4C22×D4311yescharacteristic
157SD16—1722no—
158SD16—1722no—
159C2×C8—21no—
160C2×C8—861no—
161C4⋊C4—21no—
162C4⋊C4—431no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4—861no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C4⋊C4—861no—
169C4⋊C4—861no—
170C4⋊C4—861no—
171C4⋊C4D17211yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—861no—
174C22⋊C4—1722no—
175C22⋊C4—1722no—
176C42—861no—
177C42—861no—
178C23—862no—
179C23—1721no—
180C23—1721no—
181C23—1721no—
182C23—1721no—
183C23—1721no—
184C23—1721no—
185C23D4×D4311yescharacteristic
186Q8—41no—
187Q8—3441no—
188Q8—1721no—
189D4—862no—
190D4—862no—
191D4—1721no—
192D4—1721no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—432no—
200C2×C4—861no—
201C2×C4—861no—
202C2×C4—861no—
203C2×C4—861no—
204C2×C4—861no—
205C2×C4—1721no—
206C2×C4C2×D17211yescharacteristic
207C2×C4D4×D4311yescharacteristic
208C8—41no—
209C8—1721no—
210C22—21no—
211C22—21no—
212C22—3441no—
213C22—3441no—
214C22—3441no—
215C22—3441no—
216C22—1722no—
217C22—1722no—
218C22—1722no—
219C22#1306329511yescharacteristic
220C22SD16×D4311yescharacteristic
221C22#1306335711yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—862no—
228C4—1721no—
229C4—1721no—
230C4—1721no—
231C2—21no—
232C2—21no—
233C2—3442no—
234C2#1458303911yescharacteristic
235C2#1458307311yescharacteristic
236C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43#120
hypercenter#328D43
hypocenterC43#1599
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
1. #14583528C2semidirect
5. #14582635C2semidirect
6. #14582624C2semidirect
7. C43×#328C2semidirect
82. C2×Dic43SD16semidirect
124. #328D43semidirect
126. C43#1599semidirect