Finite Group Databasebeta

← #19145454

Subgroups — #19145454

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#14583480C211yesmaximal, characteristic, complemented
2#14583465C211yesmaximal, characteristic, complemented
3#14583242C211yesmaximal, characteristic, complemented
4#14583226C211yesmaximal, characteristic, complemented
5#14583217C211yesmaximal, characteristic, complemented
6#14583151C211yesmaximal, characteristic, complemented
7#14583146C211yesmaximal, characteristic, complemented
8#14583136C211yesmaximal, characteristic, complemented
9#14583127C211yesmaximal, characteristic, complemented
10#14583051C211yesmaximal, characteristic, complemented
11#14583046C211yesmaximal, characteristic, complemented
12#14583042C211yesmaximal, characteristic, complemented
13#14583034C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#480C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic, complemented
18C2×D4×D43C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×D344C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23C2×#10621872C2211yescharacteristic, complemented
24C2×C8×D43C2211yescharacteristic, complemented
25#13063321—21no—
26#13063311—21no—
27#13063305—21no—
28#13063305C2211yescharacteristic
29#13063305C2211yescharacteristic, complemented
30#13063300—21no—
31#13063300C2211yescharacteristic
32#13063300C2211yescharacteristic
33#13063300C2211yescharacteristic, complemented
34#13063299—21no—
35#13063299—21no—
36#13063299C2211yescharacteristic
37#13063296C2211yescharacteristic
38#13063295—21no—
39#13063293—21no—
40#13063283C2211yescharacteristic
41#13063256C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic, complemented
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic, complemented
54#107×C43C2211yescharacteristic, complemented
55#107×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
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
70D4×D43—41no—
71D4×D43—41no—
72#10621898—41no—
73#10621898—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×D43C2311yescharacteristic
84C2×C4×D43C2311yescharacteristic
85C2×Dic86D411yescharacteristic
86C2×Dic86C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C2×C8×C43C2311yescharacteristic
89C4⋊C4×C43—21no—
90C4⋊C4×C43C2311yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊Dic43—21no—
95#10621883—41no—
96#10621882—41no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
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—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43C2311yescharacteristic
107C4×Dic43—21no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110D344—41no—
111#10621873—41no—
112#10621872—41no—
113C8×D43—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
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—81no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—81no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—41no—
135C22⋊D43—41no—
136C22⋊D43—42no—
137C22⋊D43—42no—
138C22⋊D43—81no—
139C22⋊D43—81no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144D172—21no—
145D172—21no—
146D172—21no—
147D172—21no—
148D172—41no—
149D172—81no—
150D172—81no—
151D172—81no—
152C4×D43—21no—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—42no—
157Dic86—21no—
158Dic86—21no—
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#480D4311yescharacteristic, complemented
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×#41—431no—
221C2×#41—431no—
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—431no—
232C22⋊Q8—431no—
233C22⋊Q8—861no—
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⋊C4C2×D4311yescharacteristic, complemented
247#107C2×D4311yescharacteristic, complemented
248#107C2×D4311yescharacteristic, complemented
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#102C2×D4311yescharacteristic
258#102C2×D4311yescharacteristic
259C22⋊C8—431no—
260C22⋊C8—431no—
261C22⋊C8—431no—
262C22⋊C8C2×D4311yescharacteristic, complemented
263C24—861no—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267#41—1721no—
268C2×Q8—431no—
269C2×Q8—431no—
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—21no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—861no—
290C22×C4C22×D4311yescharacteristic
291SD16—1721no—
292SD16—1721no—
293D8—1721no—
294D8—1721no—
295M16—1721no—
296C2×C8—431no—
297C2×C8—431no—
298C2×C8—1721no—
299C2×C8C22×D4311yescharacteristic
300C2×C8C22×D4311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—431no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4C22×D4311yescharacteristic
306C4⋊C4C22×D4311yescharacteristic
307C4⋊C4C22×D4311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—861no—
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—861no—
328Q8—861no—
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—1721no—
344D4—1721no—
345D4—1722no—
346D4—1722no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—81no—
353C2×C4—431no—
354C2×C4—431no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
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#1306337111yescharacteristic
397C4#1306337111yescharacteristic
398C2—41no—
399C2—81no—
400C2—3441no—
401C2—3441no—
402C2—1721no—
403C2—1721no—
404C2#1458346011yescharacteristic
405C2#1458370011yescharacteristic
406C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#480C2
socleC22×C43C22×D4
hypercenter#480D43
hypocenterC43#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14583480C2semidirect
2. #14583465C2semidirect
3. #14583242C2semidirect
4. #14583226C2semidirect
5. #14583217C2semidirect
6. #14583151C2semidirect
7. #14583146C2semidirect
8. #14583136C2semidirect
9. #14583127C2semidirect
10. #14583051C2semidirect
11. #14583046C2semidirect
12. #14583042C2semidirect
13. #14583034C2semidirect
14. #14582864C2semidirect
15. C43×#480C2semidirect
17. C2×#10621898C22semidirect
23. C2×#10621872C22semidirect
24. C2×C8×D43C22semidirect
29. #13063305C22semidirect
33. #13063300C22semidirect
41. #13063256C22semidirect
42. #13063256C22semidirect
43. #13063250C22semidirect
44. #13063248C22semidirect
45. #13063247C22semidirect
48. #13063245C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
53. C2×C4⋊C4×C43C22semidirect
54. #107×C43C22semidirect
55. #107×C43C22semidirect
58. C22⋊C8×C43C22semidirect
209. #480D43semidirect
219. C43#3198semidirect
246. C2×C4⋊C4C2×D43semidirect
247. #107C2×D43semidirect
248. #107C2×D43semidirect
262. C22⋊C8C2×D43semidirect