Finite Group Databasebeta

← #19146806

Subgroups — #19146806

Order 5504.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583591C211yesmaximal, characteristic, complemented
2#14583546C211yesmaximal, characteristic
3#14583252C211yesmaximal, characteristic, complemented
4#14583242C211yesmaximal, characteristic, complemented
5#14583215C211yesmaximal, characteristic, complemented
6#14583202C211yesmaximal, characteristic, complemented
7#14583156C211yesmaximal, characteristic, complemented
8#14583119C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583048C211yesmaximal, characteristic, complemented
11#14582984C211yesmaximal, characteristic, complemented
12#14582975C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582901C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621885C2211yescharacteristic, complemented
19C2×#10621884C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21#13063320—21no—
22#13063316—21no—
23#13063316C2211yescharacteristic, complemented
24#13063312C2211yescharacteristic
25#13063309—21no—
26#13063307—21no—
27#13063305C2211yescharacteristic
28#13063301C2211yescharacteristic
29#13063296—21no—
30#13063293—21no—
31Q8×Dic43C2211yescharacteristic, complemented
32#13063287C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34#13063283C2211yescharacteristic
35#13063281—21no—
36C2×C4⋊Dic43C2211yescharacteristic, complemented
37C22⋊C4×D43—21no—
38#13063256C2211yescharacteristic, complemented
39#13063256C2211yescharacteristic, complemented
40Dic43⋊C8C2211yescharacteristic, complemented
41#13063250C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic, complemented
54C22⋊Q8×C43C2211yescharacteristic, complemented
55#121×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43D411yescharacteristic
67C22×Dic43—21no—
68D4×D43—22no—
69D4×D43—41no—
70#10621898—22no—
71#10621898—41no—
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43C2311yescharacteristic
76C2×Dic86C2311yescharacteristic
77SD16×C43—41no—
78M16×C43—41no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43D411yescharacteristic
89#10621885—41no—
90#10621884—22no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4D411yescharacteristic
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621872—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—81no—
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—81no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—41no—
131C22⋊D43—42no—
132C22⋊D43—42no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—42no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140D172—21no—
141D172#4112yes—
142C4×D43—21no—
143C4×D43—21no—
144C4×D43—42no—
145C4×D43—81no—
146Dic86—21no—
147Dic86—21no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43C22×D411yescharacteristic
159C2×D43—22no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—84no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43C2×#4111yescharacteristic
171C4×C43H(5,𝔽2)11yescharacteristic
172Dic43—21no—
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178#3323—431nomaximal, Sylow
179C2×C43—41no—
180C2×C43—81no—
181C2×C43#54611yescharacteristic
182C2×C43#57511yescharacteristic
183C2×C43#57711yescharacteristic
184D43—41no—
185D43—42no—
186#552—431no—
187#546—431no—
188#488—431no—
189#485—431no—
190#481—431no—
191#478—431no—
192#470—431no—
193#468D4311yescharacteristic, complemented
194#464—431no—
195#452—431no—
196#450—431no—
197C4×SD16—431no—
198#436—431no—
199#418—431no—
200#417—431no—
201C43#332311yescharacteristic, complemented, Sylow
202C2×#41—431no—
203C22×D4—431no—
204C2×Q16—431no—
205C2×SD16—431no—
206C2×SD16C2×D4311yescharacteristic
207C2×M16—431no—
208C2×M16C2×D4311yescharacteristic, complemented
209#126—861no—
210#125—431no—
211#125—861no—
212#124—431no—
213#123—861no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8C2×D4311yescharacteristic, complemented
218#121—861no—
219#121C2×D4311yescharacteristic
220#120—861no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4—431no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4—431no—
227C2×C22⋊C4—861no—
228#107C2×D4311yescharacteristic, complemented
229#106—431no—
230#106—431no—
231C4⋊C8—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103C2×D4311yescharacteristic, complemented
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102C2×D4311yescharacteristic
242C22⋊C8—431no—
243C22⋊C8—431no—
244C4×C8—431no—
245C24—861no—
246#41—862no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—21no—
251C2×D4—431no—
252C2×D4—431no—
253C2×D4—861no—
254C2×D4—862no—
255C2×D4—861no—
256C2×D4—1721no—
257C2×D4C22×D4311yescharacteristic
258C22×C4—431no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263Q16—1721no—
264SD16—41no—
265SD16—862no—
266M16—41no—
267M16—1721no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—431no—
287C22⋊C4—431no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—431no—
295C42—861no—
296C42—861no—
297C23—21no—
298C23—431no—
299C23—861no—
300C23—3441no—
301C23—1722no—
302C23—1722no—
303C23D4×D4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—861no—
307Q8—861no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—432no—
312D4—861no—
313D4—1721no—
314D4—1722no—
315D4—1722no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—431no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—3441no—
330C2×C4—1722no—
331C2×C4—1722no—
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—862no—
348C22—3444no—
349C22—1721no—
350C22—1721no—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—861no—
357C4—861no—
358C4—861no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C4#41×D4311yescharacteristic
363C4#1306337011yescharacteristic
364C2—41no—
365C2—81no—
366C2—1721no—
367C2—1722no—
368C2#1458353811yescharacteristic
369C2#1458369811yescharacteristic
370C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3323
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #14583591C2semidirect
3. #14583252C2semidirect
4. #14583242C2semidirect
5. #14583215C2semidirect
6. #14583202C2semidirect
7. #14583156C2semidirect
8. #14583119C2semidirect
9. #14583059C2semidirect
10. #14583048C2semidirect
11. #14582984C2semidirect
12. #14582975C2semidirect
13. #14582902C2semidirect
14. #14582901C2semidirect
15. C43×#468C2semidirect
18. C2×#10621885C22semidirect
23. #13063316C22semidirect
31. Q8×Dic43C22semidirect
36. C2×C4⋊Dic43C22semidirect
38. #13063256C22semidirect
39. #13063256C22semidirect
40. Dic43⋊C8C22semidirect
41. #13063250C22semidirect
42. #13063250C22semidirect
43. #13063248C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
51. C8×Dic43C22semidirect
53. C2×M16×C43C22semidirect
54. C22⋊Q8×C43C22semidirect
56. #107×C43C22semidirect
57. #103×C43C22semidirect
193. #468D43semidirect
201. C43#3323semidirect
208. C2×M16C2×D43semidirect
217. C22⋊Q8C2×D43semidirect
228. #107C2×D43semidirect
235. #103C2×D43semidirect