Finite Group Databasebeta

← #19145368

Subgroups — #19145368

Order 5504.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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×#13063301C211yesmaximal, characteristic
2C22⋊Q8×D43C211yesmaximal, characteristic
3#14583235C211yesmaximal, characteristic, complemented
4#14583233C212yesmaximal, complemented
5#14583232C211yesmaximal, characteristic, complemented
6#14583139C212yesmaximal, complemented
7#14583137C212yesmaximal, complemented
8#14583055C211yesmaximal, characteristic, complemented
9#14583053C212yesmaximal, complemented
10C22⋊C8×D43C211yesmaximal, characteristic
11C43×#451C211yesmaximal, characteristic, complemented
12C2×Q8×D43C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C2×#10621885C2212yescomplemented
15C2×C8×D43C2212yes—
16#13063305C2211yescharacteristic
17#13063304C2211yescharacteristic
18#13063303—21no—
19#13063302—21no—
20#13063301—21no—
21#13063301—21no—
22#13063301C2212yes—
23#13063301C2211yescharacteristic
24#13063301C2212yes—
25C2×C4⋊Dic43C2211yescharacteristic
26C2×Dic43⋊C4—21no—
27C4⋊C4×D43—21no—
28C4⋊C4×D43C2211yescharacteristic
29C2×(C2×D43)⋊C4—21no—
30C22⋊C4×D43—21no—
31#13063259C2212yescomplemented
32#13063258C2212yescomplemented
33#13063250C2212yescomplemented
34#13063249C2212yescomplemented
35#13063249C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic
37(C2×D43)⋊C8C2212yes—
38C22×Q8×C43C2211yescharacteristic
39C2×Q16×C43C2212yescomplemented
40C22⋊Q8×C43C2211yescharacteristic
41#103×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic
43C23×D43D411yescharacteristic
44C2×Q8×C43—21no—
45C2×Q8×C43—42no—
46C2×Q8×C43C2312yes—
47C2×Q8×C43C2311yescharacteristic
48C22×C4×C43—21no—
49C22×C4×C43C2311yescharacteristic
50C22×Dic43—21no—
51C22×Dic43D411yescharacteristic
52Q8×D43—42no—
53C2×C4×D43—21no—
54C2×C4×D43—21no—
55C2×C4×D43—42no—
56C2×C4×D43D411yescharacteristic
57C2×C4×D43D411yescharacteristic
58C2×C4×D43C2311yescharacteristic
59C2×C4×D43C2311yescharacteristic
60C2×Dic86—21no—
61C2×Dic86C2311yescharacteristic
62Q16×C43—42no—
63C2×C8×C43C2312yes—
64C4⋊C4×C43—21no—
65C4⋊C4×C43C2311yescharacteristic
66C22⋊C4×C43—21no—
67C22⋊Dic43—21no—
68#10621885—42no—
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—21no—
71(C2×D43)⋊C4—22no—
72(C2×D43)⋊C4—22no—
73C4⋊Dic43—21no—
74C4⋊Dic43—21no—
75C4⋊Dic43C2311yescharacteristic
76C4⋊Dic43C2312yes—
77Dic43⋊C4—21no—
78Dic43⋊C4—21no—
79Dic43⋊C4—21no—
80Dic43⋊C4—22no—
81Dic43⋊C4—22no—
82C2×C43⋊C8C2312yes—
83C8×D43—42no—
84C23×C43C2×D411yescharacteristic
85C22×D43—41no—
86C22×D43—41no—
87C22×D43Q1614yescomplemented
88C22×D43C2×D411yescharacteristic
89C22×D43C2×D411yescharacteristic
90Q8×C43—22no—
91Q8×C43—22no—
92Q8×C43—22no—
93Q8×C43—42no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—42no—
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2411yescharacteristic
101C2×Dic43—21no—
102C2×Dic43—22no—
103C2×Dic43—21no—
104C2×Dic43—41no—
105C2×Dic43—42no—
106C2×Dic43C2×D411yescharacteristic
107C2×Dic43C2×D411yescharacteristic
108C4×D43—22no—
109C4×D43—22no—
110C4×D43—41no—
111C4×D43—41no—
112C4×D43—42no—
113C4×D43—42no—
114Dic86—22no—
115Dic86—42no—
116C8×C43—22no—
117C43⋊C8—22no—
118C22×C43—21no—
119C22×C43—21no—
120C22×C43C2×Q1612yes—
121C22×C43C22×D411yescharacteristic
122C2×D43—21no—
123C2×D43—21no—
124C2×D43—21no—
125C2×D43—21no—
126C2×D43—44no—
127C2×D43C2×Q1612yes—
128C2×D43C2×Q1612yes—
129C4×C43—21no—
130C4×C43—41no—
131C4×C43—42no—
132C4×C43—41no—
133C4×C43H(5,𝔽2)12yes—
134Dic43—21no—
135Dic43—21no—
136Dic43—41no—
137Dic43—41no—
138Dic43—42no—
139#3189—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43#53411yescharacteristic
142C2×C43C22×Q1611yescharacteristic
143C2×C43#57511yescharacteristic
144D43—22no—
145D43—22no—
146C2×C22⋊Q8—431no—
147C2×C22⋊Q8—431no—
148#484—431no—
149#484—432no—
150#484—431no—
151#467—432no—
152#467—432no—
153#451—431no—
154#451—432no—
155#451D4311yescharacteristic, complemented
156C2×C22⋊C8—431no—
157C43#318911yescharacteristic, complemented, Sylow
158C22×Q8—431no—
159C22×Q8C2×D4311yescharacteristic
160C23×C4—431no—
161C2×Q16—432no—
162C2×Q16C2×D4312yescomplemented
163C22×C8—432no—
164C22⋊Q8—432no—
165C22⋊Q8—431no—
166C22⋊Q8—432no—
167C22⋊Q8—431no—
168C22⋊Q8—431no—
169C22⋊Q8—861no—
170C22⋊Q8—861no—
171C22⋊Q8—861no—
172C22⋊Q8—861no—
173C22⋊Q8C2×D4311yescharacteristic
174C2×C4⋊C4—431no—
175C2×C4⋊C4—431no—
176C2×C4⋊C4—861no—
177C2×C4⋊C4—861no—
178C2×C22⋊C4—861no—
179C2×C22⋊C4—861no—
180#107—432no—
181#107—432no—
182#103—432no—
183#103—432no—
184#103—432no—
185#103C2×D4312yescomplemented
186C22⋊C8—431no—
187C22⋊C8—432no—
188C22⋊C8C2×D4311yescharacteristic
189C24—431no—
190C2×Q8—21no—
191C2×Q8—42no—
192C2×Q8—431no—
193C2×Q8—861no—
194C2×Q8—1722no—
195C2×Q8C22×D4311yescharacteristic
196C2×Q8C22×D4312yes—
197C22×C4—21no—
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—431no—
201C22×C4—431no—
202C22×C4—431no—
203C22×C4—861no—
204C22×C4—861no—
205C22×C4—861no—
206C22×C4—1722no—
207C22×C4C22×D4311yescharacteristic
208Q16—42no—
209Q16—1722no—
210C2×C8—432no—
211C2×C8—1722no—
212C2×C8C22×D4312yes—
213C4⋊C4—21no—
214C4⋊C4—431no—
215C4⋊C4—432no—
216C4⋊C4—861no—
217C4⋊C4—861no—
218C4⋊C4—862no—
219C4⋊C4—862no—
220C4⋊C4—861no—
221C4⋊C4—861no—
222C4⋊C4—861no—
223C4⋊C4C22×D4311yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—861no—
226C22⋊C4—861no—
227C22⋊C4—862no—
228C22⋊C4—862no—
229C22⋊C4—861no—
230C23—431no—
231C23—431no—
232C23—434no—
233C23—1721no—
234C23—1721no—
235C23D4×D4311yescharacteristic
236Q8—22no—
237Q8—22no—
238Q8—22no—
239Q8—42no—
240Q8—862no—
241Q8—1722no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—431no—
248C2×C4—431no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—861no—
253C2×C4—861no—
254C2×C4—1721no—
255C2×C4—1721no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1721no—
259C2×C4—1722no—
260C2×C4D4×D4311yescharacteristic
261C2×C4C23×D4311yescharacteristic
262C8—22no—
263C8—862no—
264C22—21no—
265C22—21no—
266C22—432no—
267C22—432no—
268C22—861no—
269C22—861no—
270C22—861no—
271C22—861no—
272C22—1724no—
273C22Q16×D4312yes—
274C22C2×D4×D4311yescharacteristic
275C4—21no—
276C4—41no—
277C4—42no—
278C4—41no—
279C4—861no—
280C4—861no—
281C4—1721no—
282C4—1722no—
283C4—1721no—
284C4#1306337012yes—
285C2—22no—
286C2—862no—
287C2—862no—
288C2#1458345911yescharacteristic
289C2C2×Q16×D4311yescharacteristic
290C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#451C2
socleC22×C43C22×D4
hypercenter#451D43
hypocenterC43#3189
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #14583235C2semidirect
4. #14583233C2semidirect
5. #14583232C2semidirect
6. #14583139C2semidirect
7. #14583137C2semidirect
8. #14583055C2semidirect
9. #14583053C2semidirect
11. C43×#451C2semidirect
14. C2×#10621885C22semidirect
31. #13063259C22semidirect
32. #13063258C22semidirect
33. #13063250C22semidirect
34. #13063249C22semidirect
35. #13063249C22semidirect
39. C2×Q16×C43C22semidirect
41. #103×C43C22semidirect
87. C22×D43Q16semidirect
155. #451D43semidirect
157. C43#3189semidirect
162. C2×Q16C2×D43semidirect
185. #103C2×D43semidirect