Finite Group Databasebeta

← #19144778

Subgroups — #19144778

Order 5504.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583518C211yesmaximal, characteristic, complemented
2#14583371C211yesmaximal, characteristic, complemented
3#14583238C211yesmaximal, characteristic, complemented
4#14583222C211yesmaximal, characteristic, complemented
5#14583190C211yesmaximal, characteristic, complemented
6#14583179C211yesmaximal, characteristic, complemented
7#14583111C211yesmaximal, characteristic, complemented
8#14583048C211yesmaximal, characteristic, complemented
9#14583031C211yesmaximal, characteristic
10#14583011C211yesmaximal, characteristic, complemented
11#14583002C211yesmaximal, characteristic, complemented
12SD16×Dic43C211yesmaximal, characteristic, complemented
13#14582979C211yesmaximal, characteristic, complemented
14#14582959C211yesmaximal, characteristic, complemented
15C43×#463C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19#13063325C2211yescharacteristic, complemented
20#13063318—21no—
21#13063311—21no—
22#13063309—21no—
23#13063302—21no—
24#13063301C2211yescharacteristic
25#13063296C2211yescharacteristic
26Q8×Dic43C2211yescharacteristic, complemented
27C4×D172C2211yescharacteristic
28D4×Dic43C2211yescharacteristic
29D4×Dic43C2211yescharacteristic, complemented
30#13063287C2211yescharacteristic
31C4×C22⋊D43—21no—
32(C22⋊D43)⋊C4—21no—
33#13063283C2211yescharacteristic
34#13063282C2211yescharacteristic
35C2×(C2×D43)⋊C4—21no—
36C22⋊C4×D43—21no—
37#13063258C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic, complemented
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic
53C2×D8×C43C2211yescharacteristic
54#124×C43C2211yescharacteristic, complemented
55C4×D4×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67C22×Dic43—21no—
68D4×D43—22no—
69D4×D43—22no—
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43C2311yescharacteristic
74C2×Dic86—21no—
75SD16×C43—22no—
76D8×C43—22no—
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C42×C43C2311yescharacteristic
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87#10621884—22no—
88#10621882—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43—21no—
110C22×D43—21no—
111C22×D43—24no—
112C22×D43—81no—
113C22×D43—81no—
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43#4112yes—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—81no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—24no—
128C22⋊D43—81no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137D172—21no—
138D172#4112yes—
139C4×D43—21no—
140C4×D43—21no—
141C4×D43—81no—
142C4×D43—81no—
143Dic86—81no—
144C8×C43—21no—
145C8×C43—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—22no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C2×D43—21no—
156C2×D43—22no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—84no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43C2×#4111yescharacteristic
167C4×C43C2×#4111yescharacteristic
168Dic43—21no—
169Dic43—21no—
170Dic43—21no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3118—431nomaximal, Sylow
175C2×C43—42no—
176C2×C43—81no—
177C2×C43#52511yescharacteristic
178C2×C43#57611yescharacteristic
179C2×C43#57711yescharacteristic
180D43—41no—
181D43—42no—
182#542—431no—
183#518—431no—
184#485—431no—
185#482—431no—
186#476—431no—
187#474—431no—
188#463—431no—
189#463D4311yescharacteristic, complemented
190#450—431no—
191#447—431no—
192#442—431no—
193#440—431no—
194C4×SD16—431no—
195C4×D8—431no—
196#433—431no—
197C43#311811yescharacteristic, complemented, Sylow
198C22×D4—431no—
199C2×SD16—431no—
200C2×SD16C2×D4311yescharacteristic
201C2×D8—431no—
202C2×D8C2×D4311yescharacteristic
203C4⋊Q8—431no—
204#126—861no—
205#124—861no—
206#124C2×D4311yescharacteristic, complemented
207#123—861no—
208C22⋊Q8—431no—
209C22⋊Q8—861no—
210#121—431no—
211C4×Q8—431no—
212C4×D4—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—861no—
217C4×D4—861no—
218C4×D4C2×D4311yescharacteristic
219#117—431no—
220#117—431no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223#107—431no—
224#107—431no—
225#106—431no—
226#106—431no—
227C4⋊C8—431no—
228C4⋊C8C2×D4311yescharacteristic, complemented
229#103—431no—
230#103C2×D4311yescharacteristic, complemented
231#102—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102—431no—
236#102C2×D4311yescharacteristic, complemented
237C22⋊C8—431no—
238C22⋊C8—431no—
239#97—431no—
240C4×C8—431no—
241C24—861no—
242C2×Q8—861no—
243C2×Q8C22×D4311yescharacteristic
244C2×D4—431no—
245C2×D4—861no—
246C2×D4—862no—
247C2×D4—862no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C2×D4C22×D4311yescharacteristic
251C22×C4—21no—
252C22×C4—431no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257SD16—22no—
258SD16—862no—
259D8—22no—
260D8—862no—
261C2×C8—431no—
262C2×C8—431no—
263C2×C8C22×D4311yescharacteristic
264C2×C8C22×D4311yescharacteristic
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4C22×D4311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—431no—
278C22⋊C4—431no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—431no—
287C42—861no—
288C42—861no—
289C42C22×D4311yescharacteristic
290C23—21no—
291C23—21no—
292C23—431no—
293C23—864no—
294C23—861no—
295C23—3441no—
296C23—3441no—
297Q8—21no—
298Q8—21no—
299Q8—3441no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—432no—
304D4—864no—
305D4—861no—
306D4—3441no—
307D4#1062190012yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4D4×D4311yescharacteristic
324C2×C4D4×D4311yescharacteristic
325C2×C4C23×D4311yescharacteristic
326C8—21no—
327C8—21no—
328C8—861no—
329C8—861no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—861no—
337C22—862no—
338C22—861no—
339C22—861no—
340C22—3444no—
341C22—1721no—
342C22—1721no—
343C22C2×D4×D4311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—861no—
349C4—861no—
350C4—861no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4#41×D4311yescharacteristic
355C4C2×#1062190011yescharacteristic
356C2—42no—
357C2—81no—
358C2—1721no—
359C2—1722no—
360C2#1458340911yescharacteristic
361C2#1458370311yescharacteristic
362C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#463C2
socleC22×C43C22×D4
hypercenter#463D43
hypocenterC43#3118
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #14583518C2semidirect
2. #14583371C2semidirect
3. #14583238C2semidirect
4. #14583222C2semidirect
5. #14583190C2semidirect
6. #14583179C2semidirect
7. #14583111C2semidirect
8. #14583048C2semidirect
10. #14583011C2semidirect
11. #14583002C2semidirect
12. SD16×Dic43C2semidirect
13. #14582979C2semidirect
14. #14582959C2semidirect
15. C43×#463C2semidirect
19. #13063325C22semidirect
26. Q8×Dic43C22semidirect
29. D4×Dic43C22semidirect
37. #13063258C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063257C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063249C22semidirect
47. #13063246C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
54. #124×C43C22semidirect
56. C4⋊C8×C43C22semidirect
57. #103×C43C22semidirect
58. #102×C43C22semidirect
189. #463D43semidirect
197. C43#3118semidirect
206. #124C2×D43semidirect
228. C4⋊C8C2×D43semidirect
230. #103C2×D43semidirect
236. #102C2×D43semidirect