Finite Group Databasebeta

← #19144310

Subgroups — #19144310

Order 5504.

452 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583698C211yesmaximal, characteristic, complemented
2#14583695C211yesmaximal, characteristic, complemented
3C2×#13063346C211yesmaximal, characteristic, complemented
4#131×D43C211yesmaximal, characteristic, complemented
5#14583173C211yesmaximal, characteristic, complemented
6#14583172C211yesmaximal, characteristic, complemented
7#14583168C211yesmaximal, characteristic, complemented
8#14583167C211yesmaximal, characteristic, complemented
9#14583163C211yesmaximal, characteristic, complemented
10#14583162C211yesmaximal, characteristic, complemented
11#14583159C211yesmaximal, characteristic, complemented
12#108×D43C211yesmaximal, characteristic, complemented
13#14582882C211yesmaximal, characteristic, complemented
14#14582880C211yesmaximal, characteristic, complemented
15C43×#471C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18#41×D43C2211yescharacteristic
19#13063358C2211yescharacteristic
20#13063357—21no—
21#13063356C2211yescharacteristic
22#13063355C2211yescharacteristic
23#13063354—21no—
24#13063353C2211yescharacteristic
25#13063352—21no—
26#13063351C2211yescharacteristic
27#13063350C2211yescharacteristic
28#13063349—21no—
29#13063348—21no—
30#13063346—21no—
31#13063346—21no—
32#13063346—21no—
33#13063346—21no—
34#13063346—21no—
35#13063346—21no—
36#13063344—21no—
37C2×#10621885C2211yescharacteristic, complemented
38C2×#10621873C2211yescharacteristic, complemented
39C2×#10621882C2211yescharacteristic, complemented
40#13063333—21no—
41#13063333C2211yescharacteristic
42#13063332C2211yescharacteristic
43#13063331—21no—
44#13063331C2211yescharacteristic
45M16×D43—21no—
46M16×D43C2211yescharacteristic
47M16×D43C2211yescharacteristic
48M16×D43C2211yescharacteristic
49C2×C8×D43—21no—
50C2×C8×D43C2211yescharacteristic
51#13063261C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063260C2211yescharacteristic, complemented
54#13063244C2211yescharacteristic, complemented
55#13063243C2211yescharacteristic, complemented
56#13063243C2211yescharacteristic, complemented
57#13063242C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59#13063241C2211yescharacteristic, complemented
60#137×C43C2211yescharacteristic
61AGL(1,ℤ/8)×C43C2211yescharacteristic
62C2×SD16×C43C2211yescharacteristic, complemented
63#131×C43C2211yescharacteristic
64#108×C43C2211yescharacteristic, complemented
65#101×C43C2211yescharacteristic, complemented
66#100×C43C2211yescharacteristic, complemented
67#41×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C2×C22⋊D43—21no—
71C22×Dic43—21no—
72#10621902—21no—
73#10621902—21no—
74#10621902—21no—
75#10621902—21no—
76#10621902D411yescharacteristic
77Q8×D43D411yescharacteristic
78#10621900—21no—
79#10621900—21no—
80#10621900—21no—
81#10621900—21no—
82#10621900—21no—
83#10621900D411yescharacteristic
84D4×D43—21no—
85D4×D43D411yescharacteristic
86#10621898—21no—
87#10621898C2311yescharacteristic
88C2×D172—21no—
89C2×D172C2311yescharacteristic
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43C2311yescharacteristic
93C2×Dic86C2311yescharacteristic
94Q16×C43—21no—
95SD16×C43—21no—
96SD16×C43—21no—
97SD16×C43—21no—
98SD16×C43—21no—
99D8×C43—21no—
100M16×C43—21no—
101M16×C43C2311yescharacteristic
102M16×C43C2311yescharacteristic
103M16×C43C2311yescharacteristic
104C2×C8×C43—21no—
105C2×C8×C43C2311yescharacteristic
106#10621885—21no—
107#10621885—21no—
108#10621885—21no—
109#10621885—21no—
110#10621884—21no—
111#10621884—21no—
112#10621883—21no—
113#10621883—21no—
114#10621882—21no—
115#10621882—21no—
116#10621882—21no—
117#10621882—21no—
118#10621877—21no—
119#10621877C2311yescharacteristic
120#10621877C2311yescharacteristic
121#10621877C2311yescharacteristic
122C2×C43⋊C8—21no—
123C2×C43⋊C8C2311yescharacteristic
124Dic172—21no—
125D344—21no—
126#10621873—21no—
127#10621873—21no—
128#10621873—21no—
129#10621873—21no—
130#10621872—21no—
131#10621872—21no—
132#10621872—21no—
133#10621872—21no—
134#10621872—21no—
135C8×D43—21no—
136C8×D43—21no—
137C8×D43—21no—
138C8×D43—21no—
139C8×D43—21no—
140C8×D43D411yescharacteristic
141C8×D43D411yescharacteristic
142C8×D43D411yescharacteristic
143C8×D43D411yescharacteristic
144C23×C43—21no—
145C22×D43—21no—
146C22×D43—21no—
147C22×D43#4111yescharacteristic
148Q8×C43—21no—
149Q8×C43—21no—
150Q8×C43C2×D411yescharacteristic
151D4×C43—21no—
152D4×C43—21no—
153D4×C43—21no—
154D4×C43C2×D411yescharacteristic
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43C2411yescharacteristic
158C22⋊D43—21no—
159C22⋊D43—21no—
160C22⋊D43—21no—
161C22⋊D43—41no—
162C22⋊D43—41no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43#4111yescharacteristic
168D172—21no—
169D172—21no—
170D172—21no—
171D172—41no—
172D172—41no—
173D172C2×D411yescharacteristic
174C4×D43—21no—
175C4×D43—21no—
176C4×D43—21no—
177C4×D43—41no—
178C4×D43—41no—
179C4×D43C2×D411yescharacteristic
180C4×D43C2×D411yescharacteristic
181C4×D43C2×D411yescharacteristic
182C4×D43C2×D411yescharacteristic
183Dic86—21no—
184Dic86—21no—
185Dic86—21no—
186Dic86C2×D411yescharacteristic
187C8×C43—21no—
188C8×C43—21no—
189C8×C43—21no—
190C8×C43C2×D411yescharacteristic
191C8×C43C2×D411yescharacteristic
192C43⋊C8—21no—
193C43⋊C8—21no—
194C43⋊C8—21no—
195C43⋊C8C2×D411yescharacteristic
196C43⋊C8C2×D411yescharacteristic
197C22×C43—21no—
198C22×C43—41no—
199C22×C43—81no—
200C22×C43C2×#4111yescharacteristic
201C2×D43—21no—
202C2×D43—41no—
203C2×D43—42no—
204C2×D43—41no—
205C2×D43—81no—
206C2×D43#12111yescharacteristic
207C2×D43#12111yescharacteristic
208C4×C43—21no—
209C4×C43—41no—
210C4×C43C22×D411yescharacteristic
211C4×C43C22×D411yescharacteristic
212Dic43—21no—
213Dic43—41no—
214Dic43#12111yescharacteristic
215Dic43#12111yescharacteristic
216#3067—431nomaximal, Sylow
217C2×C43—21no—
218C2×C43—41no—
219C2×C43—81no—
220C2×C43C2×#12111yescharacteristic
221D43—21no—
222D43—21no—
223D43—41no—
224D43—81no—
225#575—431no—
226#575—431no—
227C2×#135—431no—
228C2×#131—431no—
229#473—431no—
230#473—431no—
231#472—431no—
232#472—431no—
233#471—431no—
234#471—431no—
235#471—431no—
236#471D4311yescharacteristic, complemented
237C2×#108—431no—
238#413—431no—
239#413—431no—
240C43#306711yescharacteristic, complemented, Sylow
241C2×#41—431no—
242C2×#41—431no—
243C2×#41—431no—
244#137—431no—
245#137—431no—
246#137—431no—
247#137—861no—
248#137—861no—
249#137C2×D4311yescharacteristic
250AGL(1,ℤ/8)—431no—
251AGL(1,ℤ/8)—431no—
252AGL(1,ℤ/8)—431no—
253AGL(1,ℤ/8)—861no—
254AGL(1,ℤ/8)—861no—
255AGL(1,ℤ/8)C2×D4311yescharacteristic
256#135—861no—
257#135—861no—
258#135—861no—
259#135—861no—
260#135—861no—
261#135—861no—
262#135—861no—
263#135—861no—
264C2×Q16—431no—
265C2×SD16—431no—
266C2×SD16C2×D4311yescharacteristic, complemented
267C2×D8—431no—
268#131—431no—
269#131—431no—
270#131—431no—
271#131—861no—
272#131—861no—
273#131C2×D4311yescharacteristic
274C2×M16—431no—
275C2×M16—431no—
276C2×M16—431no—
277C2×M16—861no—
278C22×C8—431no—
279C22×C8—861no—
280#108—431no—
281#108—431no—
282#108—431no—
283#108C2×D4311yescharacteristic, complemented
284#101—431no—
285#101—431no—
286#101—431no—
287#101C2×D4311yescharacteristic, complemented
288#100—431no—
289#100—431no—
290#100—431no—
291#100C2×D4311yescharacteristic, complemented
292#41—431no—
293#41—431no—
294#41—431no—
295#41—861no—
296#41—861no—
297#41—861no—
298#41—861no—
299#41—861no—
300#41—861no—
301#41—861no—
302#41—861no—
303#41—861no—
304#41—861no—
305#41C22×D4311yescharacteristic
306C2×Q8—431no—
307C2×Q8—431no—
308C2×Q8C22×D4311yescharacteristic
309C2×D4—431no—
310C2×D4—431no—
311C2×D4—861no—
312C2×D4—861no—
313C2×D4—861no—
314C2×D4C22×D4311yescharacteristic
315C22×C4—431no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319Q16—21no—
320Q16—861no—
321Q16—861no—
322Q16—861no—
323Q16—861no—
324Q16—861no—
325SD16—21no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—861no—
330SD16—861no—
331SD16—861no—
332SD16—861no—
333SD16—861no—
334SD16—861no—
335SD16—861no—
336SD16—861no—
337D8—21no—
338D8—861no—
339D8—861no—
340D8—861no—
341D8—861no—
342D8—861no—
343M16—21no—
344M16—431no—
345M16—431no—
346M16—431no—
347M16—861no—
348M16—861no—
349M16—861no—
350M16—861no—
351M16—861no—
352M16—861no—
353M16C22×D4311yescharacteristic
354M16C22×D4311yescharacteristic
355M16C22×D4311yescharacteristic
356C2×C8—21no—
357C2×C8—431no—
358C2×C8—431no—
359C2×C8—431no—
360C2×C8—431no—
361C2×C8—431no—
362C2×C8—861no—
363C2×C8—861no—
364C2×C8—861no—
365C2×C8—861no—
366C2×C8—861no—
367C2×C8—861no—
368C2×C8C22×D4311yescharacteristic
369C23—21no—
370C23—431no—
371C23—861no—
372C23—861no—
373Q8—21no—
374Q8—21no—
375Q8—431no—
376Q8—861no—
377Q8—861no—
378Q8—861no—
379Q8D4×D4311yescharacteristic
380D4—21no—
381D4—21no—
382D4—21no—
383D4—431no—
384D4—861no—
385D4—861no—
386D4—861no—
387D4—861no—
388D4—861no—
389D4—861no—
390D4—1721no—
391D4—1721no—
392D4—1721no—
393D4—1721no—
394D4D4×D4311yescharacteristic
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—431no—
398C2×C4—431no—
399C2×C4—431no—
400C2×C4—431no—
401C2×C4—431no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4C23×D4311yescharacteristic
412C8—21no—
413C8—21no—
414C8—21no—
415C8—431no—
416C8—431no—
417C8—861no—
418C8—861no—
419C8—861no—
420C8D4×D4311yescharacteristic
421C8D4×D4311yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—431no—
426C22—431no—
427C22—861no—
428C22—3441no—
429C22—1721no—
430C22—1722no—
431C22—1721no—
432C22#41×D4311yescharacteristic
433C4—21no—
434C4—41no—
435C4—431no—
436C4—431no—
437C4—861no—
438C4—1721no—
439C4C2×D4×D4311yescharacteristic
440C4C2×D4×D4311yescharacteristic
441C2—21no—
442C2—41no—
443C2—81no—
444C2—861no—
445C2—861no—
446C2—3441no—
447C2—1721no—
448C2#121×D4311yescharacteristic
subgroupG/H
centerC2#121×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#471C2
socleC2×C43C2×#121
hypercenter#471D43
hypocenterC43#3067
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #14583698C2semidirect
2. #14583695C2semidirect
3. C2×#13063346C2semidirect
4. #131×D43C2semidirect
5. #14583173C2semidirect
6. #14583172C2semidirect
7. #14583168C2semidirect
8. #14583167C2semidirect
9. #14583163C2semidirect
10. #14583162C2semidirect
11. #14583159C2semidirect
12. #108×D43C2semidirect
13. #14582882C2semidirect
14. #14582880C2semidirect
15. C43×#471C2semidirect
37. C2×#10621885C22semidirect
38. C2×#10621873C22semidirect
39. C2×#10621882C22semidirect
51. #13063261C22semidirect
52. #13063260C22semidirect
53. #13063260C22semidirect
54. #13063244C22semidirect
55. #13063243C22semidirect
56. #13063243C22semidirect
57. #13063242C22semidirect
58. #13063241C22semidirect
59. #13063241C22semidirect
62. C2×SD16×C43C22semidirect
64. #108×C43C22semidirect
65. #101×C43C22semidirect
66. #100×C43C22semidirect
236. #471D43semidirect
240. C43#3067semidirect
266. C2×SD16C2×D43semidirect
283. #108C2×D43semidirect
287. #101C2×D43semidirect
291. #100C2×D43semidirect