Finite Group Databasebeta

← #19145441

Subgroups — #19145441

Order 5504.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583463C211yesmaximal, characteristic, complemented
2#14583237C211yesmaximal, characteristic, complemented
3#14583220C211yesmaximal, characteristic, complemented
4#14583217C211yesmaximal, characteristic, complemented
5#14583212C211yesmaximal, characteristic, complemented
6#14583150C211yesmaximal, characteristic, complemented
7#14583147C211yesmaximal, characteristic, complemented
8#14583133C211yesmaximal, characteristic, complemented
9#14583130C211yesmaximal, characteristic, complemented
10#14583049C211yesmaximal, characteristic, complemented
11#14583044C211yesmaximal, characteristic, complemented
12#14583044C211yesmaximal, characteristic, complemented
13#14583032C211yesmaximal, characteristic, complemented
14#14582866C211yesmaximal, characteristic, complemented
15C43×#537C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×#10621877C2211yescharacteristic, complemented
22C22×C43⋊C8C2211yescharacteristic, complemented
23#13063321—21no—
24#13063314—21no—
25#13063299C2211yescharacteristic
26#13063299C2211yescharacteristic
27#13063299C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063293—21no—
30#13063293—21no—
31#13063284C2211yescharacteristic
32#13063258C2211yescharacteristic, complemented
33#13063258C2211yescharacteristic, complemented
34#13063256C2211yescharacteristic, complemented
35#13063256C2211yescharacteristic, complemented
36#13063249C2211yescharacteristic, complemented
37#13063249C2211yescharacteristic, complemented
38#13063246C2211yescharacteristic, complemented
39#13063246C2211yescharacteristic, complemented
40#13063245C2211yescharacteristic
41#13063245C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47C22⋊(C43⋊C8)C2211yescharacteristic, complemented
48C2×#41×C43C2211yescharacteristic
49C2×#41×C43C2211yescharacteristic, complemented
50C22⋊Q8×C43—21no—
51C22⋊Q8×C43C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic, complemented
53#121×C43—21no—
54#121×C43—21no—
55#121×C43—21no—
56#121×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic, complemented
58C2×C4⋊C4×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60#41×C43—41no—
61#41×C43—41no—
62#41×C43—41no—
63#41×C43—41no—
64C2×Q8×C43D411yescharacteristic
65C2×Q8×C43C2311yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43D411yescharacteristic
70C2×D4×C43D411yescharacteristic
71C2×D4×C43D411yescharacteristic
72C2×D4×C43C2311yescharacteristic
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43C2311yescharacteristic
76C22×C4×C43C2311yescharacteristic
77C22×C4×C43C2311yescharacteristic
78C2×C22⋊D43—21no—
79C2×C22⋊D43—21no—
80C2×C22⋊D43—21no—
81C2×C22⋊D43—21no—
82C2×D172—21no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172C2311yescharacteristic
86C2×D172C2311yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43C2311yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C22⋊Dic43—21no—
97#10621884—41no—
98#10621884—41no—
99#10621882—41no—
100#10621882—41no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105C4⋊Dic43C2311yescharacteristic
106C4⋊Dic43C2311yescharacteristic
107C4×Dic43—21no—
108#10621877—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112C2×C43⋊C8C2311yescharacteristic
113C2×C43⋊C8C2311yescharacteristic
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C23×C43C2×D411yescharacteristic
117C23×C43C2×D411yescharacteristic
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—42no—
121C22×D43—81no—
122C22×D43—81no—
123Q8×C43—21no—
124Q8×C43—21no—
125Q8×C43—41no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—41no—
129D4×C43—41no—
130D4×C43—41no—
131D4×C43—42no—
132D4×C43—81no—
133D4×C43—81no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—42no—
144C2×C4×C43—81no—
145C2×C4×C43C2×D411yescharacteristic
146C2×C4×C43C2×D411yescharacteristic
147C2×C4×C43C2×D411yescharacteristic
148C2×C4×C43C2411yescharacteristic
149C22⋊D43—81no—
150C22⋊D43—81no—
151C22⋊D43—81no—
152C22⋊D43—81no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155D172—21no—
156D172—21no—
157D172—21no—
158D172—21no—
159D172—42no—
160C43⋊C8—21no—
161C43⋊C8—21no—
162C43⋊C8—21no—
163C43⋊C8—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43C22×D411yescharacteristic
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—84no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—41no—
190C4×C43H(5,𝔽2)11yescharacteristic
191C4×C43H(5,𝔽2)11yescharacteristic
192Dic43—41no—
193Dic43—41no—
194#3198—431nomaximal, Sylow
195C2×C43—41no—
196C2×C43—41no—
197C2×C43—41no—
198C2×C43—81no—
199C2×C43#53411yescharacteristic
200C2×C43#57611yescharacteristic
201C2×C43#57711yescharacteristic
202D43—81no—
203D43—81no—
204#537D4311yescharacteristic, complemented
205#535—431no—
206#485—431no—
207#482—431no—
208#481—431no—
209#480—431no—
210#469—431no—
211#468—431no—
212#466—431no—
213#465—431no—
214#450—431no—
215#449—431no—
216#449—431no—
217#447—431no—
218#408—431no—
219C43#319811yescharacteristic, complemented, Sylow
220C2×#41C2×D4311yescharacteristic
221C2×#41C2×D4311yescharacteristic, complemented
222C22×D4—431no—
223C2×SD16—431no—
224C2×SD16—431no—
225C2×D8—431no—
226C2×D8—431no—
227C2×M16—431no—
228C22×C8—431no—
229#127—861no—
230#124—861no—
231C22⋊Q8—21no—
232C22⋊Q8C2×D4311yescharacteristic
233C22⋊Q8C2×D4311yescharacteristic, complemented
234#121—21no—
235#121—21no—
236#121—21no—
237#121—431no—
238#121—431no—
239#121—431no—
240#121—431no—
241#121C2×D4311yescharacteristic
242#121C2×D4311yescharacteristic, complemented
243#120—861no—
244#120—861no—
245#117—431no—
246C2×C4⋊C4C2×D4311yescharacteristic, complemented
247#107—431no—
248#107—431no—
249#106—431no—
250#106—431no—
251#103—431no—
252#103—431no—
253#102—431no—
254#102—431no—
255#102—431no—
256#102—431no—
257#102—431no—
258#102—431no—
259C22⋊C8—431no—
260C22⋊C8—431no—
261C22⋊C8—431no—
262C22⋊C8—431no—
263C24—861no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8C22⋊D4311yescharacteristic
269C2×Q8C22×D4311yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—431no—
274C2×D4—431no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—861no—
280C2×D4—1721no—
281C2×D4—1721no—
282C2×D4C22⋊D4311yescharacteristic
283C2×D4C22⋊D4311yescharacteristic
284C2×D4C22⋊D4311yescharacteristic
285C2×D4C22×D4311yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×D4311yescharacteristic
289C22×C4C22×D4311yescharacteristic
290C22×C4C22×D4311yescharacteristic
291SD16—1721no—
292SD16—1721no—
293D8—1721no—
294D8—1721no—
295M16—1721no—
296C2×C8—431no—
297C2×C8—431no—
298C2×C8—431no—
299C2×C8—431no—
300C2×C8—1721no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—431no—
305C4⋊C4—431no—
306C4⋊C4C22×D4311yescharacteristic
307C4⋊C4C22×D4311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C42—861no—
318C23—21no—
319C23—861no—
320C23—861no—
321C23—3441no—
322C23—3441no—
323C23—1722no—
324C23C2×C22⋊D4311yescharacteristic
325C23C2×C22⋊D4311yescharacteristic
326C23C2×C22⋊D4311yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—41no—
330D4—21no—
331D4—21no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—861no—
339D4—861no—
340D4—861no—
341D4—861no—
342D4—3441no—
343D4—3441no—
344D4—3441no—
345D4—3441no—
346D4—1722no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4C2×C22⋊D4311yescharacteristic
361C2×C4C2×C22⋊D4311yescharacteristic
362C2×C4C2×C22⋊D4311yescharacteristic
363C2×C4C23×D4311yescharacteristic
364C8—861no—
365C8—861no—
366C8—861no—
367C8—861no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—3444no—
381C22—1721no—
382C22—1721no—
383C22—1721no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22C22×C22⋊D4311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—1721no—
395C4—1721no—
396C4#1306337011yescharacteristic
397C4#1306337011yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—3441no—
403C2—3441no—
404C2#1458345811yescharacteristic
405C2#1458370211yescharacteristic
406C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#537C2
socleC22×C43C22×D4
hypercenter#537D43
hypocenterC43#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #14583463C2semidirect
2. #14583237C2semidirect
3. #14583220C2semidirect
4. #14583217C2semidirect
5. #14583212C2semidirect
6. #14583150C2semidirect
7. #14583147C2semidirect
8. #14583133C2semidirect
9. #14583130C2semidirect
10. #14583049C2semidirect
11. #14583044C2semidirect
12. #14583044C2semidirect
13. #14583032C2semidirect
14. #14582866C2semidirect
15. C43×#537C2semidirect
21. C2×#10621877C22semidirect
22. C22×C43⋊C8C22semidirect
32. #13063258C22semidirect
33. #13063258C22semidirect
34. #13063256C22semidirect
35. #13063256C22semidirect
36. #13063249C22semidirect
37. #13063249C22semidirect
38. #13063246C22semidirect
39. #13063246C22semidirect
46. C22⋊(C43⋊C8)C22semidirect
47. C22⋊(C43⋊C8)C22semidirect
49. C2×#41×C43C22semidirect
52. C22⋊Q8×C43C22semidirect
57. #121×C43C22semidirect
58. C2×C4⋊C4×C43C22semidirect
204. #537D43semidirect
219. C43#3198semidirect
221. C2×#41C2×D43semidirect
233. C22⋊Q8C2×D43semidirect
242. #121C2×D43semidirect
246. C2×C4⋊C4C2×D43semidirect