Finite Group Databasebeta

← #19146751

Subgroups — #19146751

Order 5504.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583614C211yesmaximal, characteristic, complemented
2#14583258C211yesmaximal, characteristic, complemented
3#14583237C211yesmaximal, characteristic, complemented
4#14583220C211yesmaximal, characteristic, complemented
5#14583179C211yesmaximal, characteristic, complemented
6#14583147C211yesmaximal, characteristic, complemented
7#14583133C211yesmaximal, characteristic, complemented
8#14583111C211yesmaximal, characteristic, complemented
9#14583044C211yesmaximal, characteristic, complemented
10#14583033C211yesmaximal, characteristic, complemented
11#14583009C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582904C211yesmaximal, characteristic, complemented
14#14582895C211yesmaximal, characteristic, complemented
15C43×#546C211yesmaximal, characteristic, complemented
16C2×#10621884C2211yescharacteristic, complemented
17C2×#10621882C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20C22×C43⋊C8C2211yescharacteristic, complemented
21#13063325C2211yescharacteristic, complemented
22#13063311—21no—
23#13063311—21no—
24#13063299C2211yescharacteristic
25#13063299C2211yescharacteristic, complemented
26#13063296—21no—
27C4×D172C2211yescharacteristic, complemented
28#13063284C2211yescharacteristic
29#13063284C2211yescharacteristic, complemented
30#13063283—21no—
31#13063258C2211yescharacteristic, complemented
32#13063258C2211yescharacteristic, complemented
33#13063256C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35#13063249C2211yescharacteristic, complemented
36#13063249C2211yescharacteristic, complemented
37#13063249C2211yescharacteristic, complemented
38#13063246C2211yescharacteristic
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063245C2211yescharacteristic, complemented
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47#13063236C2211yescharacteristic, complemented
48C2×#41×C43C2211yescharacteristic
49C22×D4×C43C2211yescharacteristic
50#124×C43C2211yescharacteristic
51#123×C43—21no—
52C22⋊Q8×C43C2211yescharacteristic
53#121×C43—21no—
54#121×C43C2211yescharacteristic
55#120×C43—21no—
56C4×D4×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic
58C2×C22⋊C4×C43—21no—
59C24×C43—21no—
60#41×C43—22no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—22no—
67C2×D4×C43—41no—
68C2×D4×C43D411yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C2×D4×C43C2311yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2311yescharacteristic
74C22×C4×C43C2311yescharacteristic
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77C2×D172C2311yescharacteristic
78C2×C4×D43—21no—
79C2×Dic86—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43D411yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C22⋊C4×C43—21no—
88C22⋊C4×C43D411yescharacteristic
89C22⋊C4×C43D411yescharacteristic
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93#10621884—41no—
94#10621882—22no—
95#10621882—41no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103C4×Dic43—21no—
104C4×Dic43—21no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—81no—
116C23×C43C2×D411yescharacteristic
117C23×C43C2×D411yescharacteristic
118C22×D43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—41no—
125D4×C43—42no—
126D4×C43—42no—
127D4×C43—81no—
128D4×C43#4112yes—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—42no—
136C2×C4×C43—81no—
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2411yescharacteristic
142C22⋊D43—81no—
143C22⋊D43—81no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147D172—21no—
148D172—21no—
149C4×D43—42no—
150Dic86—81no—
151C43⋊C8—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—22no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—84no—
168C22×C43C22×D411yescharacteristic
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43C2×#4111yescharacteristic
179C4×C43H(5,𝔽2)11yescharacteristic
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183#3319—431nomaximal, Sylow
184C2×C43—41no—
185C2×C43—41no—
186C2×C43—42no—
187C2×C43—81no—
188C2×C43#54611yescharacteristic
189C2×C43#57511yescharacteristic
190C2×C43#57611yescharacteristic
191D43—81no—
192#555—431no—
193#546D4311yescharacteristic, complemented
194#489—431no—
195#485—431no—
196#482—431no—
197#474—431no—
198#468—431no—
199#466—431no—
200#463—431no—
201#449—431no—
202#447—431no—
203#442—431no—
204#435—431no—
205#418—431no—
206#416—431no—
207C43#331911yescharacteristic, complemented, Sylow
208C2×#41C2×D4311yescharacteristic
209C22×D4C2×D4311yescharacteristic
210C2×SD16—431no—
211C2×D8—431no—
212C2×D8—431no—
213C2×M16—431no—
214C22×C8—431no—
215C4⋊Q8—431no—
216#124—861no—
217#124—861no—
218#124C2×D4311yescharacteristic
219#123—21no—
220C22⋊Q8C2×D4311yescharacteristic
221#121—21no—
222#121—431no—
223#121—431no—
224#121—861no—
225#121C2×D4311yescharacteristic
226#120—21no—
227C4×D4—431no—
228C4×D4C2×D4311yescharacteristic
229C4×D4C2×D4311yescharacteristic
230#117—431no—
231#117—431no—
232#117—861no—
233C2×C22⋊C4—21no—
234#107—431no—
235#107—431no—
236#106—431no—
237C4⋊C8—431no—
238#103—431no—
239#103—431no—
240#103—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248C22⋊C8—431no—
249C22⋊C8—431no—
250#97—431no—
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8—861no—
255C2×Q8C22×D4311yescharacteristic
256C2×D4—22no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—431no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4C22⋊D4311yescharacteristic
265C2×D4C22×D4311yescharacteristic
266C2×D4C22×D4311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—861no—
270C22×C4C22×D4311yescharacteristic
271C22×C4C22×D4311yescharacteristic
272SD16—1721no—
273D8—862no—
274D8—1721no—
275M16—1721no—
276C2×C8—431no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8—431no—
280C2×C8—1721no—
281C4⋊C4—21no—
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—431no—
285C4⋊C4—861no—
286C4⋊C4C22⋊D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4C22⋊D4311yescharacteristic
299C22⋊C4C22⋊D4311yescharacteristic
300C42—861no—
301C42—861no—
302C42C22×D4311yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—861no—
309C23C2×C22⋊D4311yescharacteristic
310C23C2×C22⋊D4311yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—3441no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—41no—
318D4—42no—
319D4—42no—
320D4—81no—
321D4—861no—
322D4—861no—
323D4—3441no—
324D4—3441no—
325D4#1062190012yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—1722no—
338C2×C4C2×C22⋊D4311yescharacteristic
339C2×C4C2×C22⋊D4311yescharacteristic
340C2×C4C2×C22⋊D4311yescharacteristic
341C2×C4C2×C22⋊D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—861no—
344C8—861no—
345C8—861no—
346C8—861no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—84no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22C22×C22⋊D4311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—1721no—
371C4—1721no—
372C4—1721no—
373C4C2×#1062190011yescharacteristic
374C4#1306337011yescharacteristic
375C2—41no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—3441no—
380C2#1458354311yescharacteristic
381C2#1458369711yescharacteristic
382C2#1458370211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#546C2
socleC22×C43C22×D4
hypercenter#546D43
hypocenterC43#3319
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #14583614C2semidirect
2. #14583258C2semidirect
3. #14583237C2semidirect
4. #14583220C2semidirect
5. #14583179C2semidirect
6. #14583147C2semidirect
7. #14583133C2semidirect
8. #14583111C2semidirect
9. #14583044C2semidirect
10. #14583033C2semidirect
11. #14583009C2semidirect
12. #14582971C2semidirect
13. #14582904C2semidirect
14. #14582895C2semidirect
15. C43×#546C2semidirect
16. C2×#10621884C22semidirect
20. C22×C43⋊C8C22semidirect
21. #13063325C22semidirect
25. #13063299C22semidirect
27. C4×D172C22semidirect
29. #13063284C22semidirect
31. #13063258C22semidirect
32. #13063258C22semidirect
33. #13063256C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. #13063249C22semidirect
36. #13063249C22semidirect
37. #13063249C22semidirect
44. #13063245C22semidirect
46. C22⋊(C43⋊C8)C22semidirect
47. #13063236C22semidirect
193. #546D43semidirect
207. C43#3319semidirect