Finite Group Databasebeta

← #19145449

Subgroups — #19145449

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#14583477C211yesmaximal, characteristic, complemented
2#14583463C211yesmaximal, characteristic, complemented
3#14583241C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic, complemented
5#14583218C211yesmaximal, characteristic, complemented
6#14583213C211yesmaximal, characteristic, complemented
7#14583152C211yesmaximal, characteristic, complemented
8#14583145C211yesmaximal, characteristic, complemented
9#14583135C211yesmaximal, characteristic, complemented
10#14583128C211yesmaximal, characteristic, complemented
11#14583052C211yesmaximal, characteristic, complemented
12#14583046C211yesmaximal, characteristic, complemented
13#14583046C211yesmaximal, characteristic, complemented
14#14583035C211yesmaximal, characteristic, complemented
15C43×#408C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic, complemented
17C22×D172C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×D344C2211yescharacteristic
21C2×D344C2211yescharacteristic
22#13063321—21no—
23#13063314—21no—
24#13063304C2211yescharacteristic
25#13063304C2211yescharacteristic, complemented
26#13063301—21no—
27#13063299C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063299C2211yescharacteristic
30#13063299C2211yescharacteristic
31#13063299C2211yescharacteristic
32#13063299C2211yescharacteristic, complemented
33#13063297—21no—
34#13063297—21no—
35#13063296—21no—
36#13063293—21no—
37#13063293—21no—
38#13063284C2211yescharacteristic
39C2×C4⋊Dic43C2211yescharacteristic, complemented
40#13063259C2211yescharacteristic, complemented
41#13063259C2211yescharacteristic, complemented
42#13063257C2211yescharacteristic, complemented
43#13063257C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063250C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic, complemented
51#13063247C2211yescharacteristic, complemented
52C2×#41×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic, complemented
54C22×C8×C43C2211yescharacteristic, complemented
55C22⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57C22⋊C8×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60#41×C43—41no—
61#41×C43—41no—
62C2×Q8×C43D411yescharacteristic
63C2×D4×C43D411yescharacteristic
64C2×D4×C43D411yescharacteristic
65C2×D4×C43D411yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C22×Dic43—21no—
77#10621898—41no—
78#10621898—41no—
79C2×D172—21no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172C2311yescharacteristic
83C2×D172C2311yescharacteristic
84C2×D172C2311yescharacteristic
85C2×C4×D43—21no—
86C2×Dic86C2311yescharacteristic
87M16×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43C2311yescharacteristic
90C2×C8×C43C2311yescharacteristic
91C2×C8×C43C2311yescharacteristic
92C2×C8×C43C2311yescharacteristic
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95C22⋊Dic43—21no—
96(C2×D43)⋊C4—21no—
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—
102C4⋊Dic43—21no—
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105C4⋊Dic43C2311yescharacteristic
106C4⋊Dic43C2311yescharacteristic
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109C4×Dic43—21no—
110D344—41no—
111D344—41no—
112#10621873—41no—
113#10621873—41no—
114C23×C43C2×D411yescharacteristic
115C23×C43C2×D411yescharacteristic
116C23×C43C2×D411yescharacteristic
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—42no—
121C22×D43—81no—
122C22×D43—81no—
123Q8×C43—41no—
124D4×C43—41no—
125D4×C43—41no—
126D4×C43—41no—
127C2×C4×C43—21no—
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×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2411yescharacteristic
137C22⋊D43—42no—
138C22⋊D43—81no—
139C22⋊D43—81no—
140C22⋊D43—81no—
141C22⋊D43—81no—
142C22⋊D43—81no—
143C22⋊D43—81no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—81no—
150D172—21no—
151D172—21no—
152D172—21no—
153D172—21no—
154D172—21no—
155D172—21no—
156D172—42no—
157C4×D43—42no—
158Dic86—21no—
159Dic86—21no—
160C8×C43—21no—
161C8×C43—21no—
162C8×C43—21no—
163C8×C43—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×C43C22×D411yescharacteristic
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
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×C43H(5,𝔽2)11yescharacteristic
188C4×C43H(5,𝔽2)11yescharacteristic
189Dic43—41no—
190Dic43—41no—
191Dic43—41no—
192Dic43—41no—
193Dic43—41no—
194#3198—431nomaximal, Sylow
195C2×C43—41no—
196C2×C43—41no—
197C2×C43—41no—
198C2×C43#53411yescharacteristic
199C2×C43#57611yescharacteristic
200C2×C43#57711yescharacteristic
201D43—81no—
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#468—431no—
212#466—431no—
213#465—431no—
214#450—431no—
215#449—431no—
216#449—431no—
217#447—431no—
218#408D4311yescharacteristic, complemented
219C43#319811yescharacteristic, complemented, Sylow
220C2×#41—431no—
221C2×#41C2×D4311yescharacteristic
222C22×D4—431no—
223C2×SD16—431no—
224C2×SD16—431no—
225C2×D8—431no—
226C2×D8—431no—
227C2×M16C2×D4311yescharacteristic, complemented
228C22×C8C2×D4311yescharacteristic, complemented
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—431no—
240#121—861no—
241#121—861no—
242#121—861no—
243#120—861no—
244#120—861no—
245#117—431no—
246C2×C4⋊C4—431no—
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⋊C8C2×D4311yescharacteristic
260C22⋊C8C2×D4311yescharacteristic
261C22⋊C8C2×D4311yescharacteristic, complemented
262C22⋊C8C2×D4311yescharacteristic, complemented
263C24—861no—
264#41—41no—
265#41—41no—
266#41—1721no—
267#41—1721no—
268C2×Q8—431no—
269C2×Q8D17211yescharacteristic
270C2×D4—431no—
271C2×D4—431no—
272C2×D4—431no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—861no—
280C2×D4—861no—
281C2×D4—1721no—
282C2×D4—1721no—
283C2×D4D17211yescharacteristic
284C2×D4D17211yescharacteristic
285C2×D4D17211yescharacteristic
286C22×C4—861no—
287C22×C4—861no—
288C22×C4C22×D4311yescharacteristic
289C22×C4C22×D4311yescharacteristic
290C22×C4C22×D4311yescharacteristic
291SD16—1721no—
292SD16—1721no—
293D8—1721no—
294D8—1721no—
295M16—41no—
296C2×C8—41no—
297C2×C8C22×D4311yescharacteristic
298C2×C8C22×D4311yescharacteristic
299C2×C8C22×D4311yescharacteristic
300C2×C8C22×D4311yescharacteristic
301C4⋊C4—431no—
302C4⋊C4—431no—
303C4⋊C4—431no—
304C4⋊C4—431no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C22⋊C4—861no—
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—861no—
319C23—861no—
320C23—861no—
321C23—3441no—
322C23—3441no—
323C23—1722no—
324C23C2×D17211yescharacteristic
325C23C2×D17211yescharacteristic
326C23C2×D17211yescharacteristic
327Q8—41no—
328Q8—861no—
329Q8—861no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—861no—
334D4—861no—
335D4—861no—
336D4—861no—
337D4—861no—
338D4—861no—
339D4—3441no—
340D4—3441no—
341D4—3441no—
342D4—3441no—
343D4—3441no—
344D4—3441no—
345D4—1722no—
346D4—1722no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—3441no—
359C2×C4—1722no—
360C2×C4C2×D17211yescharacteristic
361C2×C4C2×D17211yescharacteristic
362C2×C4C2×D17211yescharacteristic
363C2×C4C23×D4311yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—3444no—
378C22—1721no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22—1721no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22C22×D17211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—1721no—
392C4—1721no—
393C4—1721no—
394C4—1721no—
395C4—1721no—
396C4#1306337011yescharacteristic
397C4#1306337011yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—3441no—
402C2—3441no—
403C2—3441no—
404C2#1458346111yescharacteristic
405C2#1458370411yescharacteristic
406C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#408C2
socleC22×C43C22×D4
hypercenter#408D43
hypocenterC43#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #14583477C2semidirect
2. #14583463C2semidirect
3. #14583241C2semidirect
4. #14583224C2semidirect
5. #14583218C2semidirect
6. #14583213C2semidirect
7. #14583152C2semidirect
8. #14583145C2semidirect
9. #14583135C2semidirect
10. #14583128C2semidirect
11. #14583052C2semidirect
12. #14583046C2semidirect
13. #14583046C2semidirect
14. #14583035C2semidirect
15. C43×#408C2semidirect
16. C2×#10621898C22semidirect
25. #13063304C22semidirect
32. #13063299C22semidirect
39. C2×C4⋊Dic43C22semidirect
40. #13063259C22semidirect
41. #13063259C22semidirect
42. #13063257C22semidirect
43. #13063257C22semidirect
44. #13063250C22semidirect
45. #13063250C22semidirect
50. #13063247C22semidirect
51. #13063247C22semidirect
53. C2×M16×C43C22semidirect
54. C22×C8×C43C22semidirect
57. C22⋊C8×C43C22semidirect
58. C22⋊C8×C43C22semidirect
218. #408D43semidirect
219. C43#3198semidirect
227. C2×M16C2×D43semidirect
228. C22×C8C2×D43semidirect
261. C22⋊C8C2×D43semidirect
262. C22⋊C8C2×D43semidirect