Finite Group Databasebeta

← #19140746

Subgroups — #19140746

Order 5504.

498 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#13063308C211yesmaximal, characteristic
2#14582837C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic, complemented
4#14582827C212yesmaximal, complemented
5#14582818C211yesmaximal, characteristic, complemented
6#14582814C212yesmaximal
7#14582810C211yesmaximal, characteristic, complemented
8#14582794C212yesmaximal, complemented
9#14582789C212yesmaximal, complemented
10C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
11C2×C22⋊Q8×C43C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13#13063308—24no—
14C2×Dic43⋊C4C2211yescharacteristic
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2211yescharacteristic
17C2×Dic43⋊C4C2212yes—
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2211yescharacteristic
20C2×(C2×D43)⋊C4C2211yescharacteristic
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2212yes—
24C2×C4×Dic43C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2211yescharacteristic
31C22×Q8×C43C2211yescharacteristic
32C23×C4×C43C2211yescharacteristic
33C22⋊Q8×C43—24no—
34C2×C4⋊C4×C43C2212yes—
35C2×C4⋊C4×C43C2211yescharacteristic
36C2×C22⋊C4×C43C2212yes—
37C24×C43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C2×Q8×C43—22no—
40C2×Q8×C43—42no—
41C22×C4×C43—42no—
42C22×C4×C43D414yes—
43C22×C4×C43C2312yes—
44C22×C4×C43C2312yes—
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—22no—
48C2×C22⋊D43—42no—
49C22×Dic43C2312yes—
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C22×Dic43C2312yes—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—24no—
56C22⋊C4×C43—24no—
57C22⋊Dic43—24no—
58C22⋊Dic43—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—24no—
62(C2×D43)⋊C4—42no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65Dic43⋊C4—24no—
66Dic43⋊C4—42no—
67C4×Dic43—42no—
68C23×C43—22no—
69C23×C43—22no—
70C23×C43—21no—
71C23×C43—21no—
72C23×C43C2×D412yes—
73C23×C43C2411yescharacteristic
74C22×D43—21no—
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—21no—
78C22×D43—21no—
79Q8×C43—44no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—44no—
89C2×C4×C43C2×D412yes—
90C2×C4×C43C2×D412yes—
91C22⋊D43—44no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—21no—
96C2×Dic43—21no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—21no—
102C2×Dic43—21no—
103C2×Dic43—22no—
104C2×Dic43#4114yes—
105C22×C43—22no—
106C22×C43—22no—
107C22×C43—22no—
108C22×C43—42no—
109C22×C43—42no—
110C22×C43C22×D411yescharacteristic
111C22×C43C2×#4112yes—
112C22×C43H(5,𝔽2)12yes—
113C22×C432−1+411yescharacteristic
114C22×C432−1+411yescharacteristic
115C2×D43—41no—
116C2×D43—41no—
117C2×D43—41no—
118C2×D43—42no—
119C2×D43—42no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—42no—
123C4×C43—42no—
124Dic43—24no—
125Dic43—41no—
126Dic43—41no—
127Dic43—41no—
128Dic43—42no—
129#2663—431nomaximal, Sylow
130C2×C43—42no—
131C2×C43#53211yescharacteristic
132C2×C43#53411yescharacteristic
133C2×C43#53611yescharacteristic
134C2×C43#53912yes—
135C2×C43#54212yes—
136D43—81no—
137C2×#123—431no—
138C2×C22⋊Q8D4311yescharacteristic, complemented
139#400—431no—
140#399—431no—
141#397—432no—
142#395—431no—
143#394—432no—
144#393—431no—
145#389—432no—
146#388—432no—
147C4×C22⋊C4—431no—
148C43#266311yescharacteristic, complemented, Sylow
149C22×Q8C2×D4311yescharacteristic
150C22×D4—431no—
151C23×C4C2×D4311yescharacteristic
152#123—864no—
153C22⋊Q8—24no—
154C2×C4⋊C4—431no—
155C2×C4⋊C4—431no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4C2×D4312yes—
159C2×C4⋊C4C2×D4311yescharacteristic
160C2×C22⋊C4—431no—
161C2×C22⋊C4—432no—
162C2×C22⋊C4—431no—
163C2×C22⋊C4—431no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4—432no—
166C2×C22⋊C4C2×D4312yes—
167C2×C42—432no—
168#95—431no—
169#95—431no—
170#95—432no—
171#95—432no—
172#95—432no—
173#95—432no—
174C24—431no—
175C24C22×D4311yescharacteristic
176C2×Q8—22no—
177C2×Q8—42no—
178C2×D4—862no—
179C2×D4—1722no—
180C22×C4—42no—
181C22×C4—432no—
182C22×C4—432no—
183C22×C4—431no—
184C22×C4—431no—
185C22×C4—431no—
186C22×C4C22⋊D4314yes—
187C22×C4C22×D4312yes—
188C22×C4C22×D4312yes—
189C22×C4C22×D4311yescharacteristic
190C22×C4C22×D4311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—24no—
193C4⋊C4—864no—
194C4⋊C4—862no—
195C4⋊C4—862no—
196C4⋊C4—1722no—
197C22⋊C4—24no—
198C22⋊C4—864no—
199C22⋊C4—864no—
200C22⋊C4—862no—
201C22⋊C4—862no—
202C22⋊C4—862no—
203C22⋊C4—1722no—
204C42—1722no—
205C23—22no—
206C23—22no—
207C23—21no—
208C23—21no—
209C23—861no—
210C23—862no—
211C23—862no—
212C23—861no—
213C23—861no—
214C23C2×C22⋊D4312yes—
215C23C23×D4311yescharacteristic
216Q8—44no—
217D4—1724no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—44no—
227C2×C4—434no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—861no—
231C2×C4—861no—
232C2×C4—861no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—861no—
238C2×C4—861no—
239C2×C4—862no—
240C2×C4C2×C22⋊D4312yes—
241C2×C4C2×C22⋊D4312yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—1721no—
248C22—1721no—
249C22—1721no—
250C22—1722no—
251C22—1722no—
252C22C22×C22⋊D4311yescharacteristic
253C22#41×D4312yes—
254C22#1306337012yes—
255C22#1306337311yescharacteristic
256C22#1306337311yescharacteristic
257C4—22no—
258C4—22no—
259C4—42no—
260C4—42no—
261C4—864no—
262C4—1721no—
263C4—1721no—
264C4—1721no—
265C4—1722no—
266C2—42no—
267C2—3441no—
268C2#1458344511yescharacteristic
269C2#1458345811yescharacteristic
270C2#1458347311yescharacteristic
271C2#1458349512yes—
272C2#1458351912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×C22⋊Q8×C43C2
hypercenterC2×C22⋊Q8D43
hypocenterC43#2663
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #14582837C2semidirect
3. #14582834C2semidirect
4. #14582827C2semidirect
5. #14582818C2semidirect
7. #14582810C2semidirect
8. #14582794C2semidirect
9. #14582789C2semidirect
10. C4×C22⋊Dic43C2semidirect
11. C2×C22⋊Q8×C43C2semidirect
138. C2×C22⋊Q8D43semidirect
148. C43#2663semidirect