Finite Group Databasebeta

← #19136239

Subgroups — #19136239

Order 5504.

280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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#14583458C211yesmaximal, characteristic
2C2×#13063242C211yesmaximal, characteristic, complemented
3#14582688C212yesmaximal, complemented
4#14582685C212yesmaximal, complemented
5C2×#99×C43C211yesmaximal, characteristic, complemented
6C22×C22⋊D43C411yescharacteristic, complemented
7C2×#10621877—21no—
8#13063308—21no—
9#13063306C411yescharacteristic, complemented
10#13063306C2211yescharacteristic
11#13063297—21no—
12#13063297—21no—
13#13063294—21no—
14#13063293C411yescharacteristic, complemented
15#13063293C2211yescharacteristic
16C2×C22⋊Dic43C411yescharacteristic, complemented
17#13063242—21no—
18#13063242C2212yes—
19C22×D4×C43C2211yescharacteristic
20C2×C22⋊C4×C43—21no—
21#99×C43—21no—
22#99×C43C2212yes—
23C24×C43C2×C411yescharacteristic
24C24×C43D411yescharacteristic
25C23×D43C2×C411yescharacteristic, complemented
26C2×D4×C43—41no—
27C2×D4×C43—41no—
28C2×D4×C43C2×C411yescharacteristic
29C2×D4×C43D411yescharacteristic
30C2×D4×C43D411yescharacteristic
31C2×D4×C43C2311yescharacteristic
32C22×C4×C43—41no—
33C22×C4×C43D411yescharacteristic
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C2×C22⋊D43—21no—
37C2×C22⋊D43—21no—
38C2×C22⋊D43—41no—
39C2×C22⋊D43—41no—
40C22×Dic43—21no—
41C22×Dic43C2×C411yescharacteristic, complemented
42C22⋊C4×C43—22no—
43C22⋊C4×C43—41no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47C22⋊Dic43C2×C411yescharacteristic, complemented
48C22⋊Dic43C2×C411yescharacteristic, complemented
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53#10621877—22no—
54#10621877—41no—
55C2×C43⋊C8—41no—
56C23×C43—21no—
57C23×C43—21no—
58C23×C43—21no—
59C23×C43—21no—
60C23×C43—81no—
61C23×C43—81no—
62C23×C43C22⋊C411yescharacteristic
63C23×C43C22⋊C411yescharacteristic
64C23×C43C22⋊C411yescharacteristic
65C23×C43C22×C411yescharacteristic
66C23×C43C2×D411yescharacteristic
67C22×D43—21no—
68C22×D43—41no—
69C22×D43—81no—
70D4×C43—41no—
71D4×C43—41no—
72D4×C43—41no—
73D4×C43—41no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—42no—
77C2×C4×C43—82no—
78C2×C4×C43C22⋊C411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C22⋊D43—42no—
81C22⋊D43—41no—
82C22⋊D43—41no—
83C22⋊D43—81no—
84C22⋊D43—81no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—41no—
89C2×Dic43—81no—
90C43⋊C8—42no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43—42no—
101C22×C43—81no—
102C22×C43—81no—
103C22×C43—81no—
104C22×C43#9911yescharacteristic
105C22×C43#9911yescharacteristic
106C22×C43C2×C22⋊C411yescharacteristic
107C2×D43—41no—
108C2×D43—41no—
109C2×D43—41no—
110C2×D43—82no—
111C4×C43—21no—
112C4×C43—21no—
113C4×C43—82no—
114Dic43—41no—
115Dic43—41no—
116Dic43—41no—
117#2121—431nomaximal, Sylow
118C2×C43—21no—
119C2×C43—21no—
120C2×C43—21no—
121C2×C43—41no—
122C2×C43—41no—
123C2×C43—41no—
124C2×C43—41no—
125C2×C43C2×#9911yescharacteristic
126D43—81no—
127#534—431no—
128C2×#100—431no—
129C2×#99D4311yescharacteristic, complemented
130#352—432no—
131AΣL(1,𝔽16)—432no—
132C43#212111yescharacteristic, complemented, Sylow
133C22×D4—431no—
134C22×D4C2×D4311yescharacteristic
135C2×M16—861no—
136#123—431no—
137#123—431no—
138#123—861no—
139#121—861no—
140#121—861no—
141#120—431no—
142#120—431no—
143#120—861no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—431no—
146#100—432no—
147#100—861no—
148#99—21no—
149#99C2×D4312yes—
150C24—431no—
151C24C4×D4311yescharacteristic
152C24C22⋊D4311yescharacteristic
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—861no—
156C2×D4—861no—
157C2×D4—861no—
158C2×D4—861no—
159C2×D4—1721no—
160C2×D4—1721no—
161C2×D4C4×D4311yescharacteristic
162C2×D4D17211yescharacteristic
163C2×D4C22⋊D4311yescharacteristic
164C2×D4C22×D4311yescharacteristic
165C22×C4—41no—
166C22×C4—431no—
167C22×C4—861no—
168C22×C4D17211yescharacteristic
169M16—862no—
170M16—1721no—
171C2×C8—1721no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C22⋊C4—22no—
175C22⋊C4—41no—
176C22⋊C4—431no—
177C22⋊C4—431no—
178C22⋊C4—861no—
179C22⋊C4—861no—
180C22⋊C4—861no—
181C22⋊C4—861no—
182C22⋊C4—861no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—81no—
188C23—81no—
189C23—861no—
190C23—3441no—
191C23—1721no—
192C23(C2×D43)⋊C411yescharacteristic
193C23(C2×D43)⋊C411yescharacteristic
194C23(C2×D43)⋊C411yescharacteristic
195C23C2×C4×D4311yescharacteristic
196C23C2×C22⋊D4311yescharacteristic
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—3441no—
202D4—3441no—
203D4—1722no—
204D4—1721no—
205D4—1721no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—42no—
209C2×C4—82no—
210C2×C4—861no—
211C2×C4—861no—
212C2×C4—861no—
213C2×C4—3441no—
214C2×C4—1721no—
215C2×C4(C2×D43)⋊C411yescharacteristic
216C2×C4C2×D17211yescharacteristic
217C8—1722no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—81no—
229C22—81no—
230C22—81no—
231C22—3442no—
232C22—1721no—
233C22—1721no—
234C22—1721no—
235C22#1306323911yescharacteristic
236C22#1306323911yescharacteristic
237C22C2×(C2×D43)⋊C411yescharacteristic
238C4—21no—
239C4—21no—
240C4—82no—
241C4—1721no—
242C4—1721no—
243C4—1721no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—41no—
250C2—41no—
251C2—3441no—
252C2C2×#1306323911yescharacteristic
subgroupG/H
centerC2C2×#13063239
commutatorC23×C43C22×C4
FrattiniC2×D4C22×D43
FittingC2×#99×C43C2
socleC2×C43C2×#99
hypercenterC2×#99D43
hypocenterC43#2121
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#13063242C2semidirect
3. #14582688C2semidirect
4. #14582685C2semidirect
5. C2×#99×C43C2semidirect
6. C22×C22⋊D43C4semidirect
9. #13063306C4semidirect
14. #13063293C4semidirect
16. C2×C22⋊Dic43C4semidirect
25. C23×D43C2×C4semidirect
41. C22×Dic43C2×C4semidirect
47. C22⋊Dic43C2×C4semidirect
48. C22⋊Dic43C2×C4semidirect
129. C2×#99D43semidirect
132. C43#2121semidirect