Finite Group Databasebeta

← #19144093

Subgroups — #19144093

Order 5504.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063349C211yesmaximal, characteristic, complemented
2C2×D8×D43C211yesmaximal, characteristic, complemented
3#14583462C211yesmaximal, characteristic, complemented
4#14583371C211yesmaximal, characteristic, complemented
5#14583115C211yesmaximal, characteristic, complemented
6#14583114C211yesmaximal, characteristic, complemented
7#14583113C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583093C211yesmaximal, characteristic, complemented
10#14583092C211yesmaximal, characteristic, complemented
11#14583091C211yesmaximal, characteristic, complemented
12#14582924C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582892C211yesmaximal, characteristic, complemented
15C43×#459C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19#13063349—24no—
20C2×#10621873C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic, complemented
22C2×D344C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25C2×#10621882C2211yescharacteristic, complemented
26D8×D43—24no—
27C2×#10621872C2211yescharacteristic
28C2×C8×D43C2211yescharacteristic
29#13063321C2211yescharacteristic, complemented
30#13063313C2211yescharacteristic, complemented
31#13063312C2211yescharacteristic, complemented
32#13063297—21no—
33#13063297—21no—
34#13063293—21no—
35#13063293—21no—
36C4×D172C2211yescharacteristic, complemented
37D4×Dic43C2211yescharacteristic, complemented
38#13063287C2211yescharacteristic, complemented
39C4×C22⋊D43—21no—
40(C22⋊D43)⋊C4—21no—
41#13063283C2211yescharacteristic
42#13063282C2211yescharacteristic
43C2×(C2×D43)⋊C4—21no—
44C22⋊C4×D43—21no—
45C4⋊(C43⋊C8)C2211yescharacteristic, complemented
46Dic43⋊C8C2211yescharacteristic, complemented
47Dic43⋊C8C2211yescharacteristic, complemented
48#13063250C2211yescharacteristic, complemented
49#13063248C2211yescharacteristic, complemented
50#13063247C2211yescharacteristic, complemented
51#13063246C2211yescharacteristic, complemented
52#13063246C2211yescharacteristic, complemented
53#13063245C2211yescharacteristic, complemented
54C2×D8×C43C2211yescharacteristic
55C2×D8×C43C2211yescharacteristic, complemented
56#127×C43C2211yescharacteristic, complemented
57C4×D4×C43C2211yescharacteristic, complemented
58C4⋊C8×C43C2211yescharacteristic, complemented
59#102×C43C2211yescharacteristic, complemented
60#102×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62C23×D43—21no—
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C2×D4×C43C2311yescharacteristic
68C22×C4×C43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76#10621900—22no—
77#10621900—22no—
78D4×D43—22no—
79D4×D43—22no—
80D4×D43—22no—
81D4×D43D414yescomplemented
82C2×D172C2311yescharacteristic
83C2×D172C2311yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43C2311yescharacteristic
87C2×Dic86C2311yescharacteristic
88D8×C43—22no—
89D8×C43—22no—
90C2×C8×C43C2311yescharacteristic
91C2×C8×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C42×C43C2311yescharacteristic
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43—21no—
98#10621883—22no—
99#10621882—22no—
100#10621882—22no—
101#10621882—22no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4D411yescharacteristic
108(C2×D43)⋊C4D411yescharacteristic
109C4⋊Dic43C2311yescharacteristic
110Dic43⋊C4D411yescharacteristic
111Dic43⋊C4D411yescharacteristic
112C4×Dic43—21no—
113C4×Dic43C2311yescharacteristic
114C2×C43⋊C8C2311yescharacteristic
115C2×C43⋊C8C2311yescharacteristic
116D344—22no—
117#10621873—22no—
118#10621872—22no—
119C8×D43—22no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C22×D43—21no—
124C22×D43—24no—
125C22×D43—21no—
126C22×D43—42no—
127C22×D43—81no—
128C22×D43—81no—
129C22×D43—81no—
130C22×D43—81no—
131C22×D43C2×D411yescharacteristic
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—21no—
135D4×C43—21no—
136D4×C43—21no—
137D4×C43—81no—
138D4×C43—81no—
139D4×C43C2×D412yes—
140C2×C4×C43—21no—
141C2×C4×C43—81no—
142C2×C4×C43C2×D411yescharacteristic
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2411yescharacteristic
145C22⋊D43—24no—
146C22⋊D43—42no—
147C22⋊D43—42no—
148C22⋊D43—81no—
149C22⋊D43—81no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—42no—
153C2×Dic43—81no—
154C2×Dic43C2×D411yescharacteristic
155C2×Dic43C2×D411yescharacteristic
156C2×Dic43C2×D411yescharacteristic
157D172—21no—
158D172—21no—
159D172—21no—
160D172C2×D412yes—
161C4×D43—81no—
162C4×D43—81no—
163C4×D43C2×D412yes—
164C4×D43#4112yes—
165Dic86—21no—
166Dic86—21no—
167C8×C43—21no—
168C8×C43—21no—
169C43⋊C8—21no—
170C43⋊C8—21no—
171C22×C43—22no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43C22×D411yescharacteristic
181C2×D43—21no—
182C2×D43—21no—
183C2×D43—22no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—84no—
190C2×D43—84no—
191C2×D43#12112yes—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—41no—
195C4×C43C22×D411yescharacteristic
196C4×C43C2×#4111yescharacteristic
197Dic43—21no—
198Dic43—21no—
199Dic43—41no—
200Dic43—41no—
201Dic43#12112yes—
202#3041—431nomaximal, Sylow
203C2×C43—42no—
204C2×C43—81no—
205C2×C43—81no—
206C2×C43C2×#12111yescharacteristic
207C2×C43#57611yescharacteristic
208C2×C43#57611yescharacteristic
209D43—22no—
210D43—42no—
211D43—81no—
212C2×AGL(1,ℤ/8)—431no—
213C22×D8—431no—
214#535—431no—
215#518—431no—
216#463—431no—
217#463—431no—
218#463—431no—
219#463—431no—
220#459—431no—
221#459—431no—
222#459—431no—
223#459D4311yescharacteristic, complemented
224#424—431no—
225#418—431no—
226#416—431no—
227C43#304111yescharacteristic, complemented, Sylow
228C2×#41—431no—
229C22×D4—431no—
230C22×D4—431no—
231AGL(1,ℤ/8)—864no—
232C2×SD16—431no—
233C2×SD16—431no—
234C2×D8—431no—
235C2×D8—431no—
236C2×D8—431no—
237C2×D8—431no—
238C2×D8—864no—
239C2×D8C2×D4311yescharacteristic
240C2×D8C2×D4311yescharacteristic, complemented
241C2×M16—431no—
242C22×C8—431no—
243#127—431no—
244#127C2×D4311yescharacteristic, complemented
245#124—431no—
246#124—431no—
247#121—861no—
248#121—861no—
249#120—861no—
250#120—861no—
251C4×D4—431no—
252C4×D4—431no—
253C4×D4—431no—
254C4×D4—861no—
255C4×D4—861no—
256C4×D4C2×D4311yescharacteristic, complemented
257#117—431no—
258#117—431no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C4⋊C8—431no—
262C4⋊C8—431no—
263C4⋊C8—431no—
264C4⋊C8C2×D4311yescharacteristic, complemented
265#103—431no—
266#103—431no—
267#102—431no—
268#102—431no—
269#102—431no—
270#102—431no—
271#102C2×D4311yescharacteristic, complemented
272#102C2×D4311yescharacteristic, complemented
273C24—861no—
274C24—861no—
275#41—862no—
276#41—862no—
277C2×Q8—431no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—434no—
281C2×D4—431no—
282C2×D4—431no—
283C2×D4—862no—
284C2×D4—862no—
285C2×D4—862no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4C22×D4311yescharacteristic
292C2×D4C22×D4311yescharacteristic
293C2×D4C22×D4311yescharacteristic
294C22×C4—21no—
295C22×C4—431no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—861no—
299C22×C4—861no—
300SD16—862no—
301SD16—862no—
302D8—22no—
303D8—22no—
304D8—862no—
305D8—862no—
306D8—862no—
307D8—862no—
308M16—862no—
309C2×C8—431no—
310C2×C8—431no—
311C2×C8—862no—
312C2×C8C22×D4311yescharacteristic
313C2×C8C22×D4311yescharacteristic
314C4⋊C4—431no—
315C4⋊C4—431no—
316C4⋊C4—431no—
317C4⋊C4C22×D4311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—431no—
320C22⋊C4—431no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4—861no—
329C42—431no—
330C42—861no—
331C42C22×D4311yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—431no—
336C23—864no—
337C23—861no—
338C23—861no—
339C23—3441no—
340C23—3441no—
341C23—3441no—
342C23—3441no—
343C23—1722no—
344Q8—861no—
345Q8—861no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—432no—
354D4—864no—
355D4—861no—
356D4—861no—
357D4—861no—
358D4—3441no—
359D4—3441no—
360D4—1722no—
361D4—1722no—
362D4D4×D4312yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—431no—
366C2×C4—432no—
367C2×C4—432no—
368C2×C4—431no—
369C2×C4—431no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—3441no—
373C2×C4—3441no—
374C2×C4—3441no—
375C2×C4—1722no—
376C2×C4D4×D4311yescharacteristic
377C2×C4D4×D4311yescharacteristic
378C2×C4C23×D4311yescharacteristic
379C8—21no—
380C8—21no—
381C8—861no—
382C8—861no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—432no—
393C22—861no—
394C22—861no—
395C22—862no—
396C22—3444no—
397C22—3444no—
398C22—1721no—
399C22—1721no—
400C22—1721no—
401C22—1721no—
402C22—1721no—
403C22C2×D4×D4311yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—432no—
408C4—861no—
409C4—861no—
410C4—1721no—
411C4—1721no—
412C4C2×D4×D4311yescharacteristic
413C4#41×D4311yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—862no—
418C2—3441no—
419C2—1722no—
420C2#121×D4311yescharacteristic
421C2#1458370011yescharacteristic
422C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3041
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#13063349C2semidirect
2. C2×D8×D43C2semidirect
3. #14583462C2semidirect
4. #14583371C2semidirect
5. #14583115C2semidirect
6. #14583114C2semidirect
7. #14583113C2semidirect
8. #14583112C2semidirect
9. #14583093C2semidirect
10. #14583092C2semidirect
11. #14583091C2semidirect
12. #14582924C2semidirect
13. #14582902C2semidirect
14. #14582892C2semidirect
15. C43×#459C2semidirect
20. C2×#10621873C22semidirect
21. C2×#10621883C22semidirect
25. C2×#10621882C22semidirect
29. #13063321C22semidirect
30. #13063313C22semidirect
31. #13063312C22semidirect
36. C4×D172C22semidirect
37. D4×Dic43C22semidirect
38. #13063287C22semidirect
45. C4⋊(C43⋊C8)C22semidirect
46. Dic43⋊C8C22semidirect
47. Dic43⋊C8C22semidirect
48. #13063250C22semidirect
49. #13063248C22semidirect
50. #13063247C22semidirect
51. #13063246C22semidirect
52. #13063246C22semidirect
53. #13063245C22semidirect
55. C2×D8×C43C22semidirect
56. #127×C43C22semidirect
57. C4×D4×C43C22semidirect
58. C4⋊C8×C43C22semidirect
59. #102×C43C22semidirect
60. #102×C43C22semidirect
81. D4×D43D4semidirect
223. #459D43semidirect
227. C43#3041semidirect
240. C2×D8C2×D43semidirect
244. #127C2×D43semidirect
256. C4×D4C2×D43semidirect
264. C4⋊C8C2×D43semidirect
271. #102C2×D43semidirect
272. #102C2×D43semidirect