Finite Group Databasebeta

← #19146113

Subgroups — #19146113

Order 5504.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063349C211yesmaximal, characteristic, complemented
2C2×#13063345C211yesmaximal, characteristic, complemented
3#14583548C211yesmaximal, characteristic, complemented
4#14583546C211yesmaximal, characteristic, complemented
5#14583290C211yesmaximal, characteristic, complemented
6#14583156C211yesmaximal, characteristic, complemented
7#14583126C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583103C211yesmaximal, characteristic, complemented
10#14583063C211yesmaximal, characteristic, complemented
11#14583062C211yesmaximal, characteristic, complemented
12#14583048C211yesmaximal, characteristic, complemented
13#14583008C211yesmaximal, characteristic, complemented
14#14582967C211yesmaximal, characteristic, complemented
15C43×#449C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19#13063349—24no—
20#13063345—24no—
21C2×Dic172C2211yescharacteristic, complemented
22C2×#10621885C2211yescharacteristic, complemented
23C2×#10621873C2211yescharacteristic
24C2×#10621883C2211yescharacteristic
25C2×#10621883C2211yescharacteristic, complemented
26C2×#10621884C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621872C2211yescharacteristic
29C22×C43⋊C8C2211yescharacteristic, complemented
30#13063323C2211yescharacteristic, complemented
31#13063312C2211yescharacteristic
32#13063308—21no—
33#13063307—21no—
34#13063306—21no—
35#13063305C2211yescharacteristic
36#13063304C2211yescharacteristic, complemented
37#13063301C2211yescharacteristic
38#13063297—21no—
39#13063296—21no—
40#13063293—21no—
41D4×Dic43C2211yescharacteristic, complemented
42#13063287C2211yescharacteristic
43C4×C22⋊D43C2211yescharacteristic
44C2×Dic43⋊C4—21no—
45C22⋊C4×D43—21no—
46#13063256C2211yescharacteristic, complemented
47Dic43⋊C8C2211yescharacteristic, complemented
48#13063250C2211yescharacteristic, complemented
49#13063248C2211yescharacteristic, complemented
50#13063247C2211yescharacteristic
51#13063246C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53#13063235C2211yescharacteristic, complemented
54C2×#41×C43C2211yescharacteristic, complemented
55C2×SD16×C43C2211yescharacteristic
56C2×D8×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic, complemented
59#102×C43C2211yescharacteristic, complemented
60C22⋊C8×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62#41×C43—22no—
63#41×C43—41no—
64C2×Q8×C43C2311yescharacteristic
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43C2311yescharacteristic
68C2×D4×C43C2311yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43C2311yescharacteristic
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43D411yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77#10621900—22no—
78#10621900—41no—
79D4×D43—22no—
80D4×D43—41no—
81#10621898—22no—
82#10621898—41no—
83C2×D172C2311yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43C2311yescharacteristic
87C2×Dic86C2311yescharacteristic
88C2×Dic86C2311yescharacteristic
89SD16×C43—41no—
90D8×C43—22no—
91C2×C8×C43C2311yescharacteristic
92C2×C8×C43C2311yescharacteristic
93C4⋊C4×C43C2311yescharacteristic
94C22⋊C4×C43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43—21no—
98C22⋊Dic43—21no—
99C22⋊Dic43D411yescharacteristic
100#10621885—22no—
101#10621884—22no—
102#10621883—22no—
103#10621883—22no—
104#10621882D414yescomplemented
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4D411yescharacteristic
109C4⋊Dic43—21no—
110C4⋊Dic43C2311yescharacteristic
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113Dic43⋊C4—21no—
114Dic43⋊C4—21no—
115Dic43⋊C4D411yescharacteristic
116C4×Dic43C2311yescharacteristic
117C2×C43⋊C8—22no—
118C2×C43⋊C8C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120Dic172—41no—
121#10621873—22no—
122#10621872—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43C2×D411yescharacteristic
126C22×D43—21no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—81no—
130C22×D43C2×D411yescharacteristic
131Q8×C43—21no—
132Q8×C43—21no—
133D4×C43—21no—
134D4×C43—21no—
135D4×C43—21no—
136D4×C43—42no—
137D4×C43—81no—
138D4×C43C2×D412yes—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—42no—
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2411yescharacteristic
146C22⋊D43—41no—
147C22⋊D43—42no—
148C22⋊D43—42no—
149C22⋊D43—42no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43C2×D411yescharacteristic
156C2×Dic43C2×D411yescharacteristic
157C2×Dic43C2×D411yescharacteristic
158D172—21no—
159D172C2×D412yes—
160C4×D43—21no—
161C4×D43—21no—
162C4×D43—42no—
163C4×D43—81no—
164Dic86—21no—
165Dic86—21no—
166Dic86—21no—
167Dic86—21no—
168C8×C43—21no—
169C8×C43—21no—
170C43⋊C8—21no—
171C43⋊C8C2×D412yes—
172C22×C43—22no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43C22×D411yescharacteristic
182C2×D43—22no—
183C2×D43—21no—
184C2×D43—21no—
185C2×D43—21no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—84no—
189C4×C43—21no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43C22×D411yescharacteristic
193C4×C43H(5,𝔽2)11yescharacteristic
194Dic43—21no—
195Dic43—21no—
196Dic43—21no—
197Dic43—41no—
198Dic43—41no—
199Dic43—41no—
200#3267—431nomaximal, Sylow
201C2×C43—41no—
202C2×C43—42no—
203C2×C43—81no—
204C2×C43D4211yescharacteristic
205C2×C43#57511yescharacteristic
206C2×C43#57711yescharacteristic
207D43—41no—
208D43—42no—
209C2×AGL(1,ℤ/8)—431no—
210C2×#135—431no—
211#547—431no—
212#546—431no—
213#497—431no—
214#470—431no—
215#465—431no—
216#463—431no—
217#461—431no—
218#452—431no—
219#452—431no—
220#450—431no—
221#449D4311yescharacteristic, complemented
222#442—431no—
223#435—431no—
224C43#326711yescharacteristic, complemented, Sylow
225C2×#41—431no—
226C2×#41—431no—
227C2×#41C2×D4311yescharacteristic, complemented
228C22×D4—431no—
229AGL(1,ℤ/8)—864no—
230#135—864no—
231C2×Q16—431no—
232C2×Q16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—431no—
236C2×SD16—431no—
237C2×SD16C2×D4311yescharacteristic
238C2×D8—431no—
239C2×D8C2×D4311yescharacteristic
240C2×M16—431no—
241C22×C8—431no—
242C4⋊Q8—431no—
243#124—431no—
244#123—861no—
245#123—861no—
246#123—861no—
247C22⋊Q8—431no—
248C22⋊Q8—431no—
249C22⋊Q8—431no—
250#121—861no—
251#121—861no—
252#121C2×D4311yescharacteristic
253#120—861no—
254C4×D4—431no—
255C4×D4—431no—
256C4×D4—431no—
257C2×C4⋊C4—861no—
258C2×C22⋊C4—861no—
259#106—431no—
260C4⋊C8—431no—
261#103—431no—
262#103—431no—
263#103C2×D4311yescharacteristic, complemented
264#102—431no—
265#102—431no—
266#102C2×D4311yescharacteristic, complemented
267C22⋊C8—431no—
268C22⋊C8C2×D4311yescharacteristic, complemented
269#97—431no—
270C24—861no—
271#41—22no—
272#41—41no—
273#41—862no—
274#41—862no—
275#41—1721no—
276#41—1721no—
277C2×Q8—431no—
278C2×Q8—431no—
279C2×Q8C22×D4311yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—431no—
283C2×D4—431no—
284C2×D4—861no—
285C2×D4—862no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—1721no—
289C2×D4C22×D4311yescharacteristic
290C2×D4C22×D4311yescharacteristic
291C22×C4—21no—
292C22×C4—431no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4C22×D4311yescharacteristic
298Q16—862no—
299Q16—1721no—
300SD16—41no—
301SD16—862no—
302SD16—862no—
303SD16—862no—
304SD16—862no—
305D8—22no—
306D8—434no—
307M16—862no—
308C2×C8—431no—
309C2×C8—431no—
310C2×C8—862no—
311C2×C8C22×D4311yescharacteristic
312C2×C8C22×D4311yescharacteristic
313C4⋊C4—431no—
314C4⋊C4—431no—
315C4⋊C4—861no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—861no—
320C4⋊C4C22×D4311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—431no—
323C22⋊C4—431no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4—861no—
329C22⋊C4—861no—
330C22⋊C4—861no—
331C42—431no—
332C23—21no—
333C23—21no—
334C23—431no—
335C23—861no—
336C23—3441no—
337C23—1722no—
338C23—1722no—
339C23D4×D4311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—861no—
343Q8—861no—
344Q8—861no—
345Q8—861no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—81no—
351D4—432no—
352D4—861no—
353D4—1721no—
354D4—1722no—
355D4—1722no—
356D4—1722no—
357D4D4×D4312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—431no—
364C2×C4—431no—
365C2×C4—431no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—3441no—
372C2×C4—1722no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4D4×D4311yescharacteristic
376C2×C4C23×D4311yescharacteristic
377C8—21no—
378C8—21no—
379C8—432no—
380C8—861no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—861no—
391C22—861no—
392C22—861no—
393C22—862no—
394C22—3444no—
395C22—1721no—
396C22—1721no—
397C22C2×D4×D4311yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—861no—
402C4—861no—
403C4—861no—
404C4—1721no—
405C4—1721no—
406C4—1721no—
407C4C2×D4×D4311yescharacteristic
408C4#1306337011yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—1721no—
413C2—1722no—
414C2#1458353111yescharacteristic
415C2#1458369611yescharacteristic
416C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#449C2
socleC22×C43C22×D4
hypercenter#449D43
hypocenterC43#3267
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#13063349C2semidirect
2. C2×#13063345C2semidirect
3. #14583548C2semidirect
4. #14583546C2semidirect
5. #14583290C2semidirect
6. #14583156C2semidirect
7. #14583126C2semidirect
8. #14583112C2semidirect
9. #14583103C2semidirect
10. #14583063C2semidirect
11. #14583062C2semidirect
12. #14583048C2semidirect
13. #14583008C2semidirect
14. #14582967C2semidirect
15. C43×#449C2semidirect
21. C2×Dic172C22semidirect
22. C2×#10621885C22semidirect
25. C2×#10621883C22semidirect
29. C22×C43⋊C8C22semidirect
30. #13063323C22semidirect
36. #13063304C22semidirect
41. D4×Dic43C22semidirect
46. #13063256C22semidirect
47. Dic43⋊C8C22semidirect
48. #13063250C22semidirect
49. #13063248C22semidirect
53. #13063235C22semidirect
54. C2×#41×C43C22semidirect
58. #103×C43C22semidirect
59. #102×C43C22semidirect
60. C22⋊C8×C43C22semidirect
104. #10621882D4semidirect
221. #449D43semidirect
224. C43#3267semidirect
227. C2×#41C2×D43semidirect
263. #103C2×D43semidirect
266. #102C2×D43semidirect
268. C22⋊C8C2×D43semidirect