Finite Group Databasebeta

← #19133519

Subgroups — #19133519

Order 5504.

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

normal subgroups only

This group has 316 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, complemented
2#14583052C211yesmaximal, characteristic, complemented
3#14583049C211yesmaximal, characteristic, complemented
4#14582809C211yesmaximal, characteristic
5#14582635C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic, complemented
7C43×#328C211yesmaximal, characteristic, complemented
8C22×D172—21no—
9C22×D172C2211yescharacteristic
10C2×#10621873—21no—
11C2×#10621884—21no—
12#13063305—21no—
13#13063304C2211yescharacteristic
14#13063303—21no—
15#13063303—21no—
16#13063302—21no—
17#13063301—21no—
18C2×(C2×D43)⋊C4—21no—
19C2×(C2×D43)⋊C4C2211yescharacteristic
20C22⋊C4×D43—21no—
21#13063247—21no—
22#13063245—21no—
23C22⋊(C43⋊C8)C2211yescharacteristic
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43—21no—
28C23×D43D411yescharacteristic
29C2×Q8×C43D411yescharacteristic, complemented
30C22×C4×C43—21no—
31C22×C4×C43C2311yescharacteristic
32C22×Dic43D411yescharacteristic
33C2×D172—21no—
34C2×D172—21no—
35C2×D172—42no—
36C2×D172—42no—
37C2×D172—42no—
38C2×D172—42no—
39C2×C4×D43—21no—
40C2×C4×D43—21no—
41C2×Dic86—21no—
42C2×Dic86D411yescharacteristic, complemented
43C2×C8×C43—21no—
44C4⋊C4×C43—21no—
45C4⋊C4×C43D411yescharacteristic, complemented
46C22⋊C4×C43—21no—
47C22⋊Dic43—21no—
48#10621884—42no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51(C2×D43)⋊C4—21no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—42no—
54C4⋊Dic43—21no—
55C4⋊Dic43D411yescharacteristic, complemented
56Dic43⋊C4—21no—
57Dic43⋊C4—21no—
58Dic43⋊C4—21no—
59C2×C43⋊C8—21no—
60#10621873—42no—
61C23×C43C2×D411yescharacteristic
62C22×D43—21no—
63C22×D43—21no—
64C22×D43—22no—
65C22×D43—41no—
66C22×D43—41no—
67C22×D43—41no—
68C22×D43—41no—
69C22×D43—41no—
70C22×D43—41no—
71C22×D43—41no—
72C22×D43—41no—
73C22×D43SD1612yescomplemented
74Q8×C43—41no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—41no—
87D172—22no—
88D172—22no—
89D172—41no—
90D172—41no—
91D172—48no—
92C4×D43—81no—
93C4×D43—81no—
94Dic86—41no—
95Dic86—81no—
96C8×C43—41no—
97C43⋊C8—41no—
98C22×C43—21no—
99C22×C43—21no—
100C22×C43#12011yescharacteristic
101C22×C43C2×SD1611yescharacteristic
102C22×C43#13711yescharacteristic
103C2×D43—22no—
104C2×D43—41no—
105C2×D43—41no—
106C2×D43—42no—
107C2×D43—42no—
108C2×D43—42no—
109C2×D43—42no—
110C2×D43—81no—
111C2×D43—81no—
112C2×D43—81no—
113C2×D43—81no—
114C2×D43—81no—
115C4×C43—21no—
116C4×C43—21no—
117C4×C43—42no—
118C4×C43—41no—
119C4×C43—41no—
120Dic43—41no—
121Dic43—41no—
122Dic43—41no—
123#1596—431nomaximal, Sylow
124C2×C43—21no—
125C2×C43—21no—
126C2×C43#44811yescharacteristic
127C2×C43#45311yescharacteristic
128C2×C43B(4,𝔽2)11yescharacteristic
129D43—42no—
130D43—82no—
131#543—431no—
132#450—431no—
133#450—431no—
134#392—431no—
135#328—431no—
136#328D4311yescharacteristic, complemented
137#323—431no—
138C43#159611yescharacteristic, complemented, Sylow
139C22×D4—431no—
140C22×D4—861no—
141C2×SD16—861no—
142C2×SD16—861no—
143C22⋊Q8—431no—
144C22⋊Q8—861no—
145C22⋊Q8—861no—
146C22⋊Q8—861no—
147C22⋊Q8—861no—
148C22⋊Q8—861no—
149C22⋊Q8C2×D4311yescharacteristic
150C2×C22⋊C4—431no—
151C2×C22⋊C4—861no—
152C2×C22⋊C4—861no—
153#102—861no—
154#102—861no—
155C22⋊C8—431no—
156C22⋊C8C2×D4311yescharacteristic
157#95C2×D4311yescharacteristic
158C24—431no—
159C24—861no—
160C2×Q8—431no—
161C2×Q8—861no—
162C2×Q8D17211yescharacteristic, complemented
163C2×D4—861no—
164C2×D4—861no—
165C2×D4—1722no—
166C2×D4—1722no—
167C2×D4—1722no—
168C2×D4—1722no—
169C22×C4—21no—
170C22×C4—431no—
171C22×C4—861no—
172C22×C4—861no—
173C22×C4C22×D4311yescharacteristic
174SD16—1722no—
175SD16—1722no—
176C2×C8—21no—
177C2×C8—861no—
178C4⋊C4—21no—
179C4⋊C4—431no—
180C4⋊C4—861no—
181C4⋊C4—861no—
182C4⋊C4—861no—
183C4⋊C4—861no—
184C4⋊C4D17211yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—861no—
187C22⋊C4—861no—
188C22⋊C4—861no—
189C22⋊C4—861no—
190C22⋊C4—861no—
191C22⋊C4—1722no—
192C23—432no—
193C23—862no—
194C23—861no—
195C23—861no—
196C23—1721no—
197C23—1721no—
198C23—1721no—
199C23—1721no—
200C23—1721no—
201C23—1721no—
202C23—1721no—
203C23—1721no—
204C23D4×D4311yescharacteristic
205Q8—41no—
206Q8—3441no—
207Q8—1721no—
208D4—862no—
209D4—862no—
210D4—1721no—
211D4—1721no—
212D4—1728no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—861no—
220C2×C4—861no—
221C2×C4—861no—
222C2×C4—3441no—
223C2×C4—3441no—
224C2×C4—1721no—
225C2×C4C2×D17211yescharacteristic
226C2×C4D4×D4311yescharacteristic
227C8—41no—
228C8—1721no—
229C22—21no—
230C22—21no—
231C22—862no—
232C22—3441no—
233C22—3441no—
234C22—3441no—
235C22—3441no—
236C22—3441no—
237C22—1722no—
238C22—1722no—
239C22—1722no—
240C22—1722no—
241C22—1721no—
242C22—1721no—
243C22#1306329511yescharacteristic
244C22SD16×D4311yescharacteristic
245C22#1306335711yescharacteristic
246C4—21no—
247C4—21no—
248C4—42no—
249C4—41no—
250C4—41no—
251C4—1721no—
252C4—1721no—
253C4—1721no—
254C2—21no—
255C2—21no—
256C2—3442no—
257C2—1722no—
258C2#1458303911yescharacteristic
259C2#1458306811yescharacteristic
260C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43#120
hypercenter#328D43
hypocenterC43#1596
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. #14583524C2semidirect
2. #14583052C2semidirect
3. #14583049C2semidirect
5. #14582635C2semidirect
6. #14582622C2semidirect
7. C43×#328C2semidirect
29. C2×Q8×C43D4semidirect
42. C2×Dic86D4semidirect
45. C4⋊C4×C43D4semidirect
55. C4⋊Dic43D4semidirect
73. C22×D43SD16semidirect
136. #328D43semidirect
138. C43#1596semidirect
162. C2×Q8D172semidirect
184. C4⋊C4D172semidirect