Finite Group Databasebeta

← #19146140

Subgroups — #19146140

Order 5504.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063353C211yesmaximal, characteristic, complemented
2C2×#13063347C211yesmaximal, characteristic, complemented
3#14583570C211yesmaximal, characteristic, complemented
4#14583545C211yesmaximal, characteristic, complemented
5#14583288C211yesmaximal, characteristic, complemented
6#14583145C211yesmaximal, characteristic, complemented
7#14583135C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583095C211yesmaximal, characteristic, complemented
10#14583063C211yesmaximal, characteristic, complemented
11#14583046C211yesmaximal, characteristic, complemented
12#14583046C211yesmaximal, characteristic, complemented
13#14583035C211yesmaximal, characteristic, complemented
14#14583001C211yesmaximal, characteristic, complemented
15C43×#435C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×#10621898C2211yescharacteristic, complemented
19C22×D172C2211yescharacteristic
20#13063353—24no—
21#13063347—24no—
22C2×Dic172C2211yescharacteristic, complemented
23C2×#10621873C2211yescharacteristic
24C2×#10621873C2211yescharacteristic
25C2×#10621873C2211yescharacteristic, complemented
26C2×#10621873C2211yescharacteristic, complemented
27C2×D344C2211yescharacteristic
28C2×D344C2211yescharacteristic
29C2×D344C2211yescharacteristic
30C2×D344C2211yescharacteristic
31#13063322C2211yescharacteristic, complemented
32#13063321—21no—
33#13063313C2211yescharacteristic
34#13063310—21no—
35#13063304C2211yescharacteristic
36#13063299C2211yescharacteristic
37#13063299C2211yescharacteristic
38#13063299C2211yescharacteristic, complemented
39#13063298—21no—
40#13063298—21no—
41#13063298—21no—
42#13063293—21no—
43C4×Dic86C2211yescharacteristic, complemented
44C4×D172C2211yescharacteristic
45#13063287—21no—
46C22⋊C4×D43—21no—
47#13063259C2211yescharacteristic, complemented
48#13063250C2211yescharacteristic, complemented
49#13063250C2211yescharacteristic, complemented
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic
52#13063247C2211yescharacteristic, complemented
53#13063247C2211yescharacteristic, complemented
54C2×M16×C43C2211yescharacteristic
55C22×C8×C43C2211yescharacteristic, complemented
56C4×D4×C43C2211yescharacteristic
57C4⋊C8×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic
59C22⋊C8×C43C2211yescharacteristic, complemented
60#97×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62C2×D4×C43D411yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71#10621898—22no—
72#10621898—22no—
73#10621898—22no—
74#10621898—41no—
75#10621898—41no—
76#10621898—41no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—21no—
80C2×D172—22no—
81C2×D172—41no—
82C2×D172C2311yescharacteristic
83C2×D172C2311yescharacteristic
84C2×D172C2311yescharacteristic
85C2×D172C2311yescharacteristic
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×Dic86C2311yescharacteristic
91C2×Dic86C2311yescharacteristic
92M16×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43C2311yescharacteristic
95C2×C8×C43C2311yescharacteristic
96C2×C8×C43C2311yescharacteristic
97C2×C8×C43C2311yescharacteristic
98C4⋊C4×C43D411yescharacteristic
99C22⋊C4×C43D411yescharacteristic
100C22⋊C4×C43D411yescharacteristic
101C42×C43C2311yescharacteristic
102C22⋊Dic43—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109C4⋊Dic43C2311yescharacteristic
110C4⋊Dic43C2311yescharacteristic
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113C4×Dic43—21no—
114Dic172—22no—
115D344—22no—
116D344—22no—
117D344—22no—
118D344—41no—
119#10621873—22no—
120#10621873—22no—
121#10621873—41no—
122#10621873D414yescomplemented
123C23×C43C2×D411yescharacteristic
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—42no—
130C22×D43—42no—
131C22×D43—81no—
132D4×C43—41no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2411yescharacteristic
142C22⋊D43—42no—
143C22⋊D43—42no—
144C22⋊D43—42no—
145C22⋊D43—81no—
146C22⋊D43—81no—
147C22⋊D43—81no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152D172—21no—
153D172—21no—
154D172—21no—
155D172—21no—
156D172—21no—
157D172—21no—
158D172—21no—
159D172—42no—
160D172—42no—
161D172—81no—
162D172C2×D412yes—
163C4×D43—42no—
164C4×D43—42no—
165C4×D43—42no—
166C4×D43—81no—
167Dic86—21no—
168Dic86—21no—
169Dic86—21no—
170Dic86C2×D412yes—
171C8×C43—21no—
172C8×C43—21no—
173C8×C43—21no—
174C8×C43C2×D412yes—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43C22×D411yescharacteristic
182C2×D43—22no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—41no—
190C2×D43—41no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—84no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43C22×D411yescharacteristic
200C4×C43H(5,𝔽2)11yescharacteristic
201Dic43—22no—
202Dic43—41no—
203Dic43—41no—
204Dic43—41no—
205#3268—431nomaximal, Sylow
206C2×C43—41no—
207C2×C43—41no—
208C2×C43D4211yescharacteristic
209C2×C43#57511yescharacteristic
210C2×C43#57611yescharacteristic
211D43—42no—
212D43—81no—
213D43—81no—
214D43—81no—
215C2×AGL(1,ℤ/8)—431no—
216C2×#135—431no—
217#550—431no—
218#546—431no—
219#496—431no—
220#468—431no—
221#466—431no—
222#464—431no—
223#459—431no—
224#452—431no—
225#449—431no—
226#449—431no—
227#447—431no—
228#440—431no—
229#435D4311yescharacteristic, complemented
230C43#326811yescharacteristic, complemented, Sylow
231C2×#41—431no—
232C2×#41—431no—
233C2×#41—431no—
234C22×D4—431no—
235AGL(1,ℤ/8)—864no—
236#135—864no—
237C2×Q16—431no—
238C2×SD16—431no—
239C2×SD16—431no—
240C2×SD16—431no—
241C2×SD16—431no—
242C2×D8—431no—
243C2×D8—431no—
244C2×D8—431no—
245C2×D8—431no—
246C2×M16C2×D4311yescharacteristic
247C22×C8C2×D4311yescharacteristic, complemented
248#127—431no—
249#127—861no—
250#124—431no—
251#123—861no—
252C22⋊Q8—431no—
253#121—431no—
254#121—431no—
255#121—431no—
256#121—861no—
257#121—861no—
258#121—861no—
259#120—861no—
260C4×Q8—431no—
261C4×D4—431no—
262C4×D4—861no—
263C4×D4C2×D4311yescharacteristic
264C2×C22⋊C4—861no—
265#107—431no—
266C4⋊C8C2×D4311yescharacteristic, complemented
267#103—431no—
268#103—431no—
269#102—431no—
270#102—431no—
271#102—431no—
272#102—431no—
273C22⋊C8C2×D4311yescharacteristic
274C22⋊C8C2×D4311yescharacteristic, complemented
275#97C2×D4311yescharacteristic, complemented
276C24—861no—
277#41—862no—
278#41—862no—
279#41—862no—
280#41—1721no—
281#41—1721no—
282#41—1721no—
283C2×Q8—431no—
284C2×Q8—431no—
285C2×D4—431no—
286C2×D4—431no—
287C2×D4—431no—
288C2×D4—431no—
289C2×D4—862no—
290C2×D4—861no—
291C2×D4—861no—
292C2×D4—861no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—861no—
298C2×D4—861no—
299C2×D4—1721no—
300C2×D4D17211yescharacteristic
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4C22×D4311yescharacteristic
306C22×C4C22×D4311yescharacteristic
307Q16—862no—
308SD16—434no—
309SD16—862no—
310SD16—862no—
311SD16—1721no—
312D8—862no—
313D8—862no—
314D8—862no—
315D8—1721no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D4311yescharacteristic
319C2×C8C22×D4311yescharacteristic
320C2×C8C22×D4311yescharacteristic
321C2×C8C22×D4311yescharacteristic
322C4⋊C4—431no—
323C4⋊C4—431no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4D17211yescharacteristic
327C22⋊C4—861no—
328C22⋊C4—861no—
329C22⋊C4—861no—
330C22⋊C4—861no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4D17211yescharacteristic
335C22⋊C4D17211yescharacteristic
336C42—861no—
337C42C22×D4311yescharacteristic
338C23—861no—
339C23—861no—
340C23—861no—
341C23—861no—
342C23—3441no—
343C23—1722no—
344C23—1722no—
345C23C2×D17211yescharacteristic
346C23C2×D17211yescharacteristic
347Q8—432no—
348Q8—861no—
349Q8—861no—
350Q8—861no—
351D4—41no—
352D4—432no—
353D4—861no—
354D4—861no—
355D4—861no—
356D4—861no—
357D4—861no—
358D4—861no—
359D4—861no—
360D4—3441no—
361D4—3441no—
362D4—3441no—
363D4—3441no—
364D4—1722no—
365D4—1722no—
366D4—1722no—
367D4—1722no—
368D4—1722no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—861no—
374C2×C4—861no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—3441no—
378C2×C4—1722no—
379C2×C4—1722no—
380C2×C4—1722no—
381C2×C4C2×D17211yescharacteristic
382C2×C4C2×D17211yescharacteristic
383C2×C4C2×D17211yescharacteristic
384C2×C4C2×D17211yescharacteristic
385C2×C4C23×D4311yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D4312yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—862no—
397C22—3444no—
398C22—1721no—
399C22—1721no—
400C22—1721no—
401C22—1721no—
402C22—1721no—
403C22—1721no—
404C22—1721no—
405C22—1721no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22C22×D17211yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—862no—
415C4—1721no—
416C4—1721no—
417C4—1721no—
418C4C2×D4×D4311yescharacteristic
419C4#1306337111yescharacteristic
420C2—41no—
421C2—41no—
422C2—3441no—
423C2—3441no—
424C2—3441no—
425C2—1722no—
426C2D4×D17211yescharacteristic
427C2#1458369911yescharacteristic
428C2#1458370411yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#435C2
socleC22×C43C22×D4
hypercenter#435D43
hypocenterC43#3268
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#13063353C2semidirect
2. C2×#13063347C2semidirect
3. #14583570C2semidirect
4. #14583545C2semidirect
5. #14583288C2semidirect
6. #14583145C2semidirect
7. #14583135C2semidirect
8. #14583122C2semidirect
9. #14583095C2semidirect
10. #14583063C2semidirect
11. #14583046C2semidirect
12. #14583046C2semidirect
13. #14583035C2semidirect
14. #14583001C2semidirect
15. C43×#435C2semidirect
18. C2×#10621898C22semidirect
22. C2×Dic172C22semidirect
25. C2×#10621873C22semidirect
26. C2×#10621873C22semidirect
31. #13063322C22semidirect
38. #13063299C22semidirect
43. C4×Dic86C22semidirect
47. #13063259C22semidirect
48. #13063250C22semidirect
49. #13063250C22semidirect
52. #13063247C22semidirect
53. #13063247C22semidirect
55. C22×C8×C43C22semidirect
57. C4⋊C8×C43C22semidirect
59. C22⋊C8×C43C22semidirect
60. #97×C43C22semidirect
122. #10621873D4semidirect
229. #435D43semidirect
230. C43#3268semidirect
247. C22×C8C2×D43semidirect
266. C4⋊C8C2×D43semidirect
274. C22⋊C8C2×D43semidirect
275. #97C2×D43semidirect