Finite Group Databasebeta

← #19143878

Subgroups — #19143878

Order 5504.

732 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063372C211yesmaximal, characteristic, complemented
2C2×#13063349C211yesmaximal, characteristic, complemented
3C2×SD16×D43C211yesmaximal, characteristic, complemented
4#14583465C211yesmaximal, characteristic, complemented
5#14583045C211yesmaximal, characteristic, complemented
6#14583044C211yesmaximal, characteristic, complemented
7#14583041C211yesmaximal, characteristic, complemented
8#14583040C211yesmaximal, characteristic, complemented
9#14583039C211yesmaximal, characteristic, complemented
10#14583037C211yesmaximal, characteristic, complemented
11#14583036C211yesmaximal, characteristic, complemented
12#14582906C211yesmaximal, characteristic, complemented
13#14582892C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#449C211yesmaximal, characteristic, complemented
16#13063372—24no—
17#13063372—24no—
18C2×#10621898—21no—
19C2×#10621898C2211yescharacteristic
20C2×#10621900—21no—
21C2×#10621900—21no—
22C2×#10621900C2211yescharacteristic
23C2×#10621900C2211yescharacteristic, complemented
24C22×Dic86—21no—
25C22×Dic86C2211yescharacteristic, complemented
26C2×Q8×D43C2211yescharacteristic
27C2×Q8×D43C2211yescharacteristic, complemented
28C2×D4×D43C2211yescharacteristic
29#13063349—24no—
30C2×#10621873C2211yescharacteristic
31C2×#10621873C2211yescharacteristic
32C2×#10621883C2211yescharacteristic
33C2×#10621883C2211yescharacteristic
34C2×#10621884C2211yescharacteristic
35SD16×D43—24no—
36C2×#10621882C2211yescharacteristic
37C2×#10621872C2211yescharacteristic
38C2×C8×D43C2211yescharacteristic
39#13063321—21no—
40#13063311—21no—
41#13063300C2211yescharacteristic
42#13063299C2211yescharacteristic
43#13063296C2211yescharacteristic
44#13063295—21no—
45#13063293—21no—
46#13063283C2211yescharacteristic
47#13063250C2211yescharacteristic, complemented
48#13063250C2211yescharacteristic, complemented
49#13063249C2211yescharacteristic, complemented
50#13063248C2211yescharacteristic, complemented
51#13063248C2211yescharacteristic, complemented
52#13063246C2211yescharacteristic, complemented
53C22⋊(C43⋊C8)C2211yescharacteristic, complemented
54(C2×D43)⋊C8C2211yescharacteristic, complemented
55(C2×D43)⋊C8C2211yescharacteristic, complemented
56C2×#41×C43C2211yescharacteristic, complemented
57C2×SD16×C43C2211yescharacteristic
58C2×D8×C43C2211yescharacteristic
59#121×C43C2211yescharacteristic
60#103×C43C2211yescharacteristic, complemented
61#102×C43C2211yescharacteristic, complemented
62C22⋊C8×C43C2211yescharacteristic, complemented
63C23×D43—21no—
64#41×C43—22no—
65#41×C43—22no—
66C2×Q8×C43C2311yescharacteristic
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43C2311yescharacteristic
70C2×D4×C43C2311yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43C2311yescharacteristic
73C2×C22⋊D43—21no—
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78C2×C22⋊D43D411yescharacteristic
79C2×C22⋊D43D411yescharacteristic
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83Q8×D43—22no—
84Q8×D43—22no—
85Q8×D43—22no—
86Q8×D43D414yescomplemented
87#10621900—28no—
88#10621900—28no—
89#10621900—22no—
90#10621900—22no—
91#10621900—22no—
92#10621900D414yescomplemented
93D4×D43—22no—
94D4×D43—22no—
95#10621898—28no—
96#10621898—22no—
97#10621898—22no—
98C2×D172—21no—
99C2×D172D411yescharacteristic
100C2×D172C2311yescharacteristic
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43C2311yescharacteristic
104C2×C4×D43C2311yescharacteristic
105C2×Dic86—28no—
106C2×Dic86—21no—
107C2×Dic86—21no—
108C2×Dic86—21no—
109C2×Dic86—22no—
110C2×Dic86—22no—
111C2×Dic86D411yescharacteristic
112C2×Dic86C2311yescharacteristic
113C2×Dic86C2311yescharacteristic
114SD16×C43—22no—
115D8×C43—22no—
116C2×C8×C43C2311yescharacteristic
117C2×C8×C43C2311yescharacteristic
118C4⋊C4×C43C2311yescharacteristic
119C22⋊C4×C43—21no—
120C22⋊Dic43—21no—
121#10621884—22no—
122#10621883—22no—
123#10621883—22no—
124#10621882—22no—
125(C2×D43)⋊C4—21no—
126(C2×D43)⋊C4—21no—
127(C2×D43)⋊C4—21no—
128C4⋊Dic43C2311yescharacteristic
129C4×Dic43—21no—
130C2×C43⋊C8C2311yescharacteristic
131C2×C43⋊C8C2311yescharacteristic
132#10621873—22no—
133#10621873—22no—
134#10621872—22no—
135C8×D43—22no—
136C23×C43—21no—
137C23×C43—21no—
138C23×C43C2×D411yescharacteristic
139C22×D43—21no—
140C22×D43—42no—
141C22×D43—81no—
142C22×D43—81no—
143C22×D43C2×D411yescharacteristic
144C22×D43C2×D411yescharacteristic
145Q8×C43—21no—
146Q8×C43C2×D412yes—
147D4×C43—24no—
148D4×C43—21no—
149D4×C43—21no—
150D4×C43—21no—
151D4×C43—81no—
152D4×C43C2×D412yes—
153C2×C4×C43—24no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43C2×D411yescharacteristic
159C2×C4×C43C2411yescharacteristic
160C22⋊D43—24no—
161C22⋊D43—22no—
162C22⋊D43—24no—
163C22⋊D43—22no—
164C22⋊D43—42no—
165C22⋊D43—81no—
166C22⋊D43—81no—
167C2×Dic43—24no—
168C2×Dic43—24no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—24no—
172C2×Dic43—21no—
173C2×Dic43C2×D411yescharacteristic
174C2×Dic43C2×D411yescharacteristic
175D172—22no—
176D172—21no—
177D172—21no—
178D172—81no—
179C4×D43—24no—
180C4×D43—24no—
181C4×D43—21no—
182C4×D43—21no—
183C4×D43C2×D412yes—
184C4×D43C2×D412yes—
185Dic86—24no—
186Dic86—24no—
187Dic86—21no—
188Dic86—21no—
189Dic86—22no—
190Dic86—24no—
191Dic86C2×D412yes—
192Dic86C2×D412yes—
193C8×C43—21no—
194C8×C43—21no—
195C43⋊C8—21no—
196C43⋊C8—21no—
197C22×C43—22no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43C22×D411yescharacteristic
207C2×D43—21no—
208C2×D43—21no—
209C2×D43—21no—
210C2×D43—21no—
211C2×D43—21no—
212C2×D43—41no—
213C2×D43—41no—
214C2×D43—41no—
215C2×D43—84no—
216C2×D43#12012yes—
217C4×C43—21no—
218C4×C43—22no—
219C4×C43—41no—
220C4×C43C22×D411yescharacteristic
221C4×C43C22×D411yescharacteristic
222Dic43—21no—
223Dic43—22no—
224Dic43—22no—
225Dic43—41no—
226Dic43#12012yes—
227#3010—431nomaximal, Sylow
228C2×C43—41no—
229C2×C43—42no—
230C2×C43—81no—
231C2×C43C2×#12011yescharacteristic
232C2×C43#57711yescharacteristic
233C2×C43#57711yescharacteristic
234D43—22no—
235D43—41no—
236D43—81no—
237C2×2−1+4—431no—
238C2×AGL(1,ℤ/8)—431no—
239C22×SD16—431no—
240#535—431no—
241#449—431no—
242#449—431no—
243#449—431no—
244#449D4311yescharacteristic, complemented
245#448—431no—
246#448—431no—
247#448—431no—
248#448—431no—
249#419—431no—
250#416—431no—
251#408—431no—
252C43#301011yescharacteristic, complemented, Sylow
2532−1+4—864no—
2542−1+4—864no—
255C2×#41—431no—
256C2×#41—431no—
257C2×#41—431no—
258C2×#41—861no—
259C2×#41—861no—
260C2×#41—861no—
261C2×#41C2×D4311yescharacteristic, complemented
262C22×Q8—431no—
263C22×Q8—431no—
264C22×Q8—431no—
265C22×Q8—861no—
266C22×D4—431no—
267AGL(1,ℤ/8)—864no—
268C2×SD16—431no—
269C2×SD16—431no—
270C2×SD16—431no—
271C2×SD16—431no—
272C2×SD16—431no—
273C2×SD16—864no—
274C2×SD16C2×D4311yescharacteristic
275C2×D8—431no—
276C2×D8C2×D4311yescharacteristic
277C2×M16—431no—
278C22×C8—431no—
279#127—861no—
280#124—861no—
281#121—431no—
282#121—431no—
283#121—431no—
284#121C2×D4311yescharacteristic
285#120—861no—
286#120—861no—
287#117—431no—
288#103—431no—
289#103—431no—
290#103—431no—
291#103—431no—
292#103—431no—
293#103C2×D4311yescharacteristic, complemented
294#102—431no—
295#102C2×D4311yescharacteristic, complemented
296C22⋊C8—431no—
297C22⋊C8—431no—
298C22⋊C8—431no—
299C22⋊C8C2×D4311yescharacteristic, complemented
300C24—861no—
301#41—22no—
302#41—22no—
303#41—434no—
304#41—862no—
305#41—862no—
306#41—868no—
307#41—862no—
308#41—862no—
309#41—868no—
310#41—868no—
311#41—862no—
312C2×Q8—431no—
313C2×Q8—434no—
314C2×Q8—431no—
315C2×Q8—431no—
316C2×Q8—861no—
317C2×Q8—861no—
318C2×Q8—862no—
319C2×Q8—862no—
320C2×Q8—868no—
321C2×Q8—862no—
322C2×Q8—862no—
323C2×Q8—862no—
324C2×Q8—861no—
325C2×Q8C22×D4311yescharacteristic
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—431no—
329C2×D4—431no—
330C2×D4—431no—
331C2×D4—431no—
332C2×D4—861no—
333C2×D4—862no—
334C2×D4—862no—
335C2×D4—861no—
336C2×D4—861no—
337C2×D4—861no—
338C2×D4—861no—
339C2×D4—861no—
340C2×D4C22×D4311yescharacteristic
341C2×D4C22×D4311yescharacteristic
342C22×C4—21no—
343C22×C4—431no—
344C22×C4—431no—
345C22×C4—861no—
346C22×C4—861no—
347C22×C4—861no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4C22×D4311yescharacteristic
351SD16—22no—
352SD16—862no—
353SD16—862no—
354SD16—862no—
355SD16—862no—
356SD16—862no—
357D8—22no—
358D8—862no—
359M16—862no—
360C2×C8—431no—
361C2×C8—431no—
362C2×C8—862no—
363C2×C8C22×D4311yescharacteristic
364C2×C8C22×D4311yescharacteristic
365C4⋊C4—431no—
366C4⋊C4C22×D4311yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—861no—
369C22⋊C4—861no—
370C22⋊C4—861no—
371C22⋊C4—861no—
372C42—861no—
373C23—21no—
374C23—21no—
375C23—431no—
376C23—431no—
377C23—861no—
378C23—3441no—
379C23—3441no—
380C23—1722no—
381C23D4×D4311yescharacteristic
382Q8—21no—
383Q8—432no—
384Q8—432no—
385Q8—862no—
386Q8—864no—
387Q8—864no—
388Q8—864no—
389Q8—861no—
390Q8—861no—
391Q8D4×D4312yes—
392D4—24no—
393D4—21no—
394D4—21no—
395D4—21no—
396D4—81no—
397D4—862no—
398D4—862no—
399D4—862no—
400D4—864no—
401D4—864no—
402D4—861no—
403D4—861no—
404D4—3441no—
405D4—3441no—
406D4—3441no—
407D4—1722no—
408D4D4×D4312yes—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—431no—
415C2×C4—432no—
416C2×C4—432no—
417C2×C4—431no—
418C2×C4—864no—
419C2×C4—864no—
420C2×C4—864no—
421C2×C4—864no—
422C2×C4—864no—
423C2×C4—861no—
424C2×C4—861no—
425C2×C4—861no—
426C2×C4—861no—
427C2×C4—861no—
428C2×C4D4×D4311yescharacteristic
429C2×C4C23×D4311yescharacteristic
430C8—21no—
431C8—21no—
432C8—861no—
433C8—861no—
434C22—21no—
435C22—22no—
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—432no—
444C22—861no—
445C22—861no—
446C22—861no—
447C22—861no—
448C22—861no—
449C22—3444no—
450C22—1721no—
451C22—1721no—
452C22—1721no—
453C22C2×D4×D4311yescharacteristic
454C4—21no—
455C4—22no—
456C4—41no—
457C4—432no—
458C4—861no—
459C4—862no—
460C4—862no—
461C4—1721no—
462C4C2×D4×D4311yescharacteristic
463C4C2×D4×D4311yescharacteristic
464C2—41no—
465C2—42no—
466C2—81no—
467C2—862no—
468C2—3441no—
469C2—1721no—
470C2#120×D4311yescharacteristic
471C2#1458370611yescharacteristic
472C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#449C2
socleC22×C43C22×D4
hypercenter#449D43
hypocenterC43#3010
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×#13063372C2semidirect
2. C2×#13063349C2semidirect
3. C2×SD16×D43C2semidirect
4. #14583465C2semidirect
5. #14583045C2semidirect
6. #14583044C2semidirect
7. #14583041C2semidirect
8. #14583040C2semidirect
9. #14583039C2semidirect
10. #14583037C2semidirect
11. #14583036C2semidirect
12. #14582906C2semidirect
13. #14582892C2semidirect
14. #14582864C2semidirect
15. C43×#449C2semidirect
23. C2×#10621900C22semidirect
25. C22×Dic86C22semidirect
27. C2×Q8×D43C22semidirect
47. #13063250C22semidirect
48. #13063250C22semidirect
49. #13063249C22semidirect
50. #13063248C22semidirect
51. #13063248C22semidirect
52. #13063246C22semidirect
53. C22⋊(C43⋊C8)C22semidirect
54. (C2×D43)⋊C8C22semidirect
55. (C2×D43)⋊C8C22semidirect
56. C2×#41×C43C22semidirect
60. #103×C43C22semidirect
61. #102×C43C22semidirect
62. C22⋊C8×C43C22semidirect
86. Q8×D43D4semidirect
92. #10621900D4semidirect
244. #449D43semidirect
252. C43#3010semidirect
261. C2×#41C2×D43semidirect
293. #103C2×D43semidirect
295. #102C2×D43semidirect
299. C22⋊C8C2×D43semidirect