Finite Group Databasebeta

← #19145448

Subgroups — #19145448

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#14583479C211yesmaximal, characteristic, complemented
2#14583465C211yesmaximal, characteristic, complemented
3#14583238C211yesmaximal, characteristic, complemented
4#14583226C211yesmaximal, characteristic, complemented
5#14583216C211yesmaximal, characteristic, complemented
6#14583214C211yesmaximal, characteristic, complemented
7#14583152C211yesmaximal, characteristic, complemented
8#14583133C211yesmaximal, characteristic, complemented
9#14583130C211yesmaximal, characteristic, complemented
10#14583048C211yesmaximal, characteristic, complemented
11#14583047C211yesmaximal, characteristic, complemented
12#14583043C211yesmaximal, characteristic, complemented
13#14583034C211yesmaximal, characteristic, complemented
14#14582867C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic, complemented
17C2×#10621898C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×D344C2211yescharacteristic
21C2×#10621882C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic, complemented
23#13063321—21no—
24#13063311—21no—
25#13063303—21no—
26#13063301C2211yescharacteristic
27#13063300—21no—
28#13063300C2211yescharacteristic
29#13063300C2211yescharacteristic
30#13063299C2211yescharacteristic
31#13063299C2211yescharacteristic, complemented
32#13063298—21no—
33#13063298—21no—
34#13063296C2211yescharacteristic
35#13063295—21no—
36#13063293—21no—
37#13063283C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic, complemented
39#13063258C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic, complemented
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, 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⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43D411yescharacteristic
69C2×C22⋊D43D411yescharacteristic
70#10621902—41no—
71#10621902—41no—
72D4×D43—41no—
73D4×D43—41no—
74#10621898—41no—
75#10621898—41no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172D411yescharacteristic
80C2×D172C2311yescharacteristic
81C2×D172C2311yescharacteristic
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43C2311yescharacteristic
85C2×C4×D43C2311yescharacteristic
86C2×Dic86D411yescharacteristic
87SD16×C43—41no—
88M16×C43—41no—
89C2×C8×C43C2311yescharacteristic
90C2×C8×C43C2311yescharacteristic
91C4⋊C4×C43—21no—
92C4⋊C4×C43C2311yescharacteristic
93C4⋊C4×C43C2311yescharacteristic
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C22⋊Dic43—21no—
97#10621884—41no—
98#10621882—41no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105C4⋊Dic43C2311yescharacteristic
106C4⋊Dic43C2311yescharacteristic
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109C4×Dic43—21no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8C2311yescharacteristic
112C2×C43⋊C8C2311yescharacteristic
113D344—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—42no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43C2×D411yescharacteristic
122C22×D43C2×D411yescharacteristic
123Q8×C43—21no—
124Q8×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—81no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—41no—
136C22⋊D43—41no—
137C22⋊D43—42no—
138C22⋊D43—81no—
139C22⋊D43—81no—
140C22⋊D43—81no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43C2×D411yescharacteristic
144C2×Dic43C2×D411yescharacteristic
145D172—21no—
146D172—21no—
147D172—21no—
148D172—21no—
149D172—41no—
150D172—42no—
151D172—81no—
152D172—81no—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—21no—
157C4×D43—42no—
158C4×D43—81no—
159Dic86—41no—
160C8×C43—21no—
161C8×C43—21no—
162C43⋊C8—21no—
163C43⋊C8—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43C22×D411yescharacteristic
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—21no—
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—41no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43H(5,𝔽2)11yescharacteristic
189C4×C43H(5,𝔽2)11yescharacteristic
190Dic43—21no—
191Dic43—21no—
192Dic43—41no—
193Dic43—41no—
194#3198—431nomaximal, Sylow
195C2×C43—41no—
196C2×C43—81no—
197C2×C43#53411yescharacteristic
198C2×C43#57611yescharacteristic
199C2×C43#57711yescharacteristic
200D43—41no—
201D43—41no—
202D43—81no—
203D43—81no—
204#537—431no—
205#535—431no—
206#485—431no—
207#482—431no—
208#481—431no—
209#480—431no—
210#469—431no—
211#468D4311yescharacteristic, complemented
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×#41—431no—
221C2×#41—431no—
222C22×D4—431no—
223C2×SD16—431no—
224C2×SD16C2×D4311yescharacteristic
225C2×D8—431no—
226C2×D8—431no—
227C2×M16C2×D4311yescharacteristic, complemented
228C22×C8—431no—
229#127—861no—
230#124—861no—
231C22⋊Q8—431no—
232C22⋊Q8—861no—
233C22⋊Q8C2×D4311yescharacteristic, complemented
234#121—431no—
235#121—431no—
236#121—431no—
237#121—431no—
238#121—431no—
239#121—861no—
240#121—861no—
241#121—861no—
242#121C2×D4311yescharacteristic
243#120—861no—
244#120—861no—
245#117—431no—
246C2×C4⋊C4—431no—
247#107—431no—
248#107C2×D4311yescharacteristic, complemented
249#106—431no—
250#106—431no—
251#103—431no—
252#103C2×D4311yescharacteristic, complemented
253#102—431no—
254#102—431no—
255#102—431no—
256#102—431no—
257#102—431no—
258#102C2×D4311yescharacteristic
259C22⋊C8—431no—
260C22⋊C8—431no—
261C22⋊C8—431no—
262C22⋊C8—431no—
263C24—861no—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267#41—1721no—
268C2×Q8—431no—
269C2×Q8C22×D4311yescharacteristic
270C2×D4—21no—
271C2×D4—431no—
272C2×D4—431no—
273C2×D4—431no—
274C2×D4—431no—
275C2×D4—431no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—861no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4—1721no—
284C2×D4—1721no—
285C2×D4C22×D4311yescharacteristic
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4C22×D4311yescharacteristic
291SD16—41no—
292SD16—1721no—
293D8—1721no—
294D8—1721no—
295M16—41no—
296C2×C8—431no—
297C2×C8—431no—
298C2×C8—1721no—
299C2×C8C22×D4311yescharacteristic
300C2×C8C22×D4311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—431no—
303C4⋊C4—431no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4C22×D4311yescharacteristic
307C4⋊C4C22×D4311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—861no—
311C22⋊C4—861no—
312C22⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C42—861no—
318C23—21no—
319C23—431no—
320C23—431no—
321C23—861no—
322C23—861no—
323C23—3441no—
324C23—3441no—
325C23—1722no—
326C23D4×D4311yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—1721no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—861no—
334D4—861no—
335D4—861no—
336D4—861no—
337D4—3441no—
338D4—3441no—
339D4—3441no—
340D4—3441no—
341D4—3441no—
342D4—1721no—
343D4—1722no—
344D4—1721no—
345D4—1721no—
346D4—1722no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—431no—
353C2×C4—431no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—3441no—
361C2×C4—1722no—
362C2×C4D4×D4311yescharacteristic
363C2×C4C23×D4311yescharacteristic
364C8—21no—
365C8—21no—
366C8—861no—
367C8—861no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—861no—
375C22—861no—
376C22—861no—
377C22—861no—
378C22—861no—
379C22—861no—
380C22—3444no—
381C22—1721no—
382C22—1721no—
383C22—1721no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22C2×D4×D4311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—861no—
393C4—861no—
394C4—1721no—
395C4—1721no—
396C4#1306337011yescharacteristic
397C4#1306337111yescharacteristic
398C2—41no—
399C2—81no—
400C2—3441no—
401C2—3441no—
402C2—1721no—
403C2—1721no—
404C2#1458345711yescharacteristic
405C2#1458370311yescharacteristic
406C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3198
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. #14583479C2semidirect
2. #14583465C2semidirect
3. #14583238C2semidirect
4. #14583226C2semidirect
5. #14583216C2semidirect
6. #14583214C2semidirect
7. #14583152C2semidirect
8. #14583133C2semidirect
9. #14583130C2semidirect
10. #14583048C2semidirect
11. #14583047C2semidirect
12. #14583043C2semidirect
13. #14583034C2semidirect
14. #14582867C2semidirect
15. C43×#468C2semidirect
16. C2×#10621902C22semidirect
22. C22×C43⋊C8C22semidirect
31. #13063299C22semidirect
38. C4⋊C4×D43C22semidirect
39. #13063258C22semidirect
40. #13063257C22semidirect
41. #13063256C22semidirect
42. #13063249C22semidirect
44. #13063247C22semidirect
47. #13063245C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
53. C2×M16×C43C22semidirect
54. C22⋊Q8×C43C22semidirect
56. #107×C43C22semidirect
57. #103×C43C22semidirect
211. #468D43semidirect
219. C43#3198semidirect
227. C2×M16C2×D43semidirect
233. C22⋊Q8C2×D43semidirect
248. #107C2×D43semidirect
252. #103C2×D43semidirect