Finite Group Databasebeta

← #19144330

Subgroups — #19144330

Order 5504.

446 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583698C211yesmaximal, characteristic
2C2×#13063357C211yesmaximal, characteristic, complemented
3#137×D43C211yesmaximal, characteristic, complemented
4#14583664C211yesmaximal, characteristic, complemented
5#14583173C211yesmaximal, characteristic, complemented
6#14583172C211yesmaximal, characteristic, complemented
7#14583171C211yesmaximal, characteristic, complemented
8#14583165C211yesmaximal, characteristic, complemented
9#14583164C211yesmaximal, characteristic, complemented
10#14583163C211yesmaximal, characteristic, complemented
11#14583162C211yesmaximal, characteristic, complemented
12#14582946C211yesmaximal, characteristic, complemented
13#14582882C211yesmaximal, characteristic, complemented
14#101×D43C211yesmaximal, characteristic, complemented
15C43×#473C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17#41×D43C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19#13063358C2211yescharacteristic
20#13063357—21no—
21#13063357—21no—
22#13063357—21no—
23#13063357—21no—
24#13063357—21no—
25#13063357—21no—
26#13063356C2211yescharacteristic
27#13063356C2211yescharacteristic
28#13063355C2211yescharacteristic
29#13063354—21no—
30#13063353C2211yescharacteristic
31#13063352—21no—
32#13063350C2211yescharacteristic
33#13063348—21no—
34#13063346—21no—
35C2×#10621885C2211yescharacteristic, complemented
36Q16×D43—21no—
37C2×#10621873C2211yescharacteristic, complemented
38C2×#10621884C2211yescharacteristic, complemented
39SD16×D43—21no—
40#13063333—21no—
41#13063333C2211yescharacteristic
42#13063332C2211yescharacteristic
43#13063331—21no—
44#13063331C2211yescharacteristic
45C2×#10621872—21no—
46C2×#10621872C2211yescharacteristic
47M16×D43—21no—
48M16×D43C2211yescharacteristic
49M16×D43C2211yescharacteristic
50M16×D43C2211yescharacteristic
51#13063261C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063260C2211yescharacteristic, complemented
54#13063244C2211yescharacteristic, complemented
55#13063244C2211yescharacteristic, complemented
56#13063243C2211yescharacteristic, complemented
57#13063243C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59#13063241C2211yescharacteristic, complemented
60#137×C43C2211yescharacteristic
61#137×C43C2211yescharacteristic
62C2×Q16×C43C2211yescharacteristic, complemented
63#131×C43C2211yescharacteristic
64#108×C43C2211yescharacteristic, complemented
65#101×C43C2211yescharacteristic, complemented
66#101×C43C2211yescharacteristic, complemented
67#41×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C2×Q8×C43C2311yescharacteristic
70#10621902—21no—
71#10621902—21no—
72#10621902—21no—
73#10621902—21no—
74#10621902D411yescharacteristic
75Q8×D43—21no—
76Q8×D43—21no—
77Q8×D43—21no—
78Q8×D43—21no—
79Q8×D43D411yescharacteristic
80#10621900—21no—
81#10621900D411yescharacteristic
82D4×D43—21no—
83D4×D43D411yescharacteristic
84#10621898—21no—
85#10621898C2311yescharacteristic
86C2×D172—21no—
87C2×D172C2311yescharacteristic
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43C2311yescharacteristic
92C2×Dic86—21no—
93C2×Dic86C2311yescharacteristic
94Q16×C43—21no—
95Q16×C43—21no—
96Q16×C43—21no—
97Q16×C43—21no—
98SD16×C43—21no—
99SD16×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#10621885—21no—
111#10621884—21no—
112#10621884—21no—
113#10621884—21no—
114#10621884—21no—
115#10621884—21no—
116#10621883—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—
135#10621872D411yescharacteristic
136#10621872D411yescharacteristic
137#10621872D411yescharacteristic
138#10621872D411yescharacteristic
139C8×D43—21no—
140C8×D43—21no—
141C8×D43—21no—
142C8×D43—21no—
143C8×D43—21no—
144C22×D43—21no—
145C22×D43—21no—
146C22×D43#4111yescharacteristic
147Q8×C43—21no—
148Q8×C43—21no—
149Q8×C43—21no—
150Q8×C43—21no—
151Q8×C43C2×D411yescharacteristic
152D4×C43—21no—
153D4×C43C2×D411yescharacteristic
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43C2411yescharacteristic
158C22⋊D43—21no—
159C22⋊D43—21no—
160C22⋊D43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43#4111yescharacteristic
164D172—21no—
165D172—21no—
166D172—21no—
167D172—41no—
168D172—41no—
169D172C2×D411yescharacteristic
170C4×D43—21no—
171C4×D43—21no—
172C4×D43—21no—
173C4×D43—41no—
174C4×D43—41no—
175C4×D43—41no—
176C4×D43—41no—
177C4×D43C2×D411yescharacteristic
178C4×D43C2×D411yescharacteristic
179C4×D43C2×D411yescharacteristic
180C4×D43C2×D411yescharacteristic
181Dic86—21no—
182Dic86—21no—
183Dic86—21no—
184Dic86—41no—
185Dic86—41no—
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×C43C2×#4111yescharacteristic
199C2×D43—21no—
200C2×D43—41no—
201C2×D43—41no—
202C2×D43—81no—
203C2×D43—81no—
204C2×D43#12111yescharacteristic
205C2×D43#12111yescharacteristic
206C4×C43—21no—
207C4×C43—41no—
208C4×C43—41no—
209C4×C43C22×D411yescharacteristic
210C4×C43C22×D411yescharacteristic
211Dic43—21no—
212Dic43—41no—
213Dic43#12111yescharacteristic
214Dic43#12111yescharacteristic
215#3069—431nomaximal, Sylow
216C2×C43—21no—
217C2×C43—41no—
218C2×C43C2×#12111yescharacteristic
219D43—21no—
220D43—21no—
221D43—41no—
222D43—81no—
223#575—431no—
224C2×#137—431no—
225C2×#137—431no—
226#568—431no—
227#473—431no—
228#473—431no—
229#473—431no—
230#473D4311yescharacteristic, complemented
231#471—431no—
232#471—431no—
233#471—431no—
234#471—431no—
235#430—431no—
236#413—431no—
237C2×#101—431no—
238C43#306911yescharacteristic, complemented, Sylow
239C2×#41—431no—
240C2×#41—431no—
241C22×Q8—431no—
242#137—431no—
243#137—431no—
244#137—431no—
245#137—431no—
246#137—861no—
247#137—861no—
248#137—861no—
249#137—861no—
250#137—861no—
251#137—861no—
252#137—861no—
253#137C2×D4311yescharacteristic
254#137C2×D4311yescharacteristic
255AGL(1,ℤ/8)—431no—
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—861no—
258#135—861no—
259#135—861no—
260C2×Q16—431no—
261C2×Q16—861no—
262C2×Q16C2×D4311yescharacteristic, complemented
263C2×SD16—431no—
264C2×SD16—431no—
265C2×SD16—861no—
266#131—431no—
267#131—431no—
268#131—431no—
269#131—861no—
270#131—861no—
271#131C2×D4311yescharacteristic
272C2×M16—431no—
273C2×M16—431no—
274C2×M16—431no—
275C2×M16—431no—
276C2×M16—861no—
277C2×M16—861no—
278#108—431no—
279#108—431no—
280#108—431no—
281#108C2×D4311yescharacteristic, complemented
282#101—431no—
283#101—431no—
284#101—431no—
285#101—431no—
286#101C2×D4311yescharacteristic, complemented
287#101C2×D4311yescharacteristic, complemented
288#100—431no—
289#100—431no—
290#41—431no—
291#41—431no—
292#41—431no—
293#41—861no—
294#41—861no—
295#41—861no—
296#41—861no—
297#41—861no—
298#41—861no—
299#41C22×D4311yescharacteristic
300C2×Q8—431no—
301C2×Q8—431no—
302C2×Q8—861no—
303C2×Q8—861no—
304C2×Q8—861no—
305C2×Q8—861no—
306C2×Q8—861no—
307C2×Q8C22×D4311yescharacteristic
308C2×Q8C22×D4311yescharacteristic
309C2×D4—431no—
310C2×D4—431no—
311C2×D4—861no—
312C2×D4—861no—
313C22×C4—431no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317Q16—21no—
318Q16—21no—
319Q16—21no—
320Q16—21no—
321Q16—861no—
322Q16—861no—
323Q16—861no—
324Q16—861no—
325Q16—861no—
326Q16—861no—
327SD16—21no—
328SD16—21no—
329SD16—861no—
330SD16—861no—
331SD16—861no—
332SD16—861no—
333SD16—861no—
334SD16—861no—
335SD16—861no—
336SD16—861no—
337SD16—861no—
338SD16—861no—
339D8—861no—
340D8—861no—
341M16—21no—
342M16—431no—
343M16—431no—
344M16—431no—
345M16—431no—
346M16—431no—
347M16—431no—
348M16—431no—
349M16—861no—
350M16—861no—
351M16—861no—
352M16—861no—
353M16—861no—
354M16—861no—
355M16C22×D4311yescharacteristic
356M16C22×D4311yescharacteristic
357M16C22×D4311yescharacteristic
358C2×C8—21no—
359C2×C8—431no—
360C2×C8—861no—
361C2×C8—861no—
362C2×C8—861no—
363C2×C8—861no—
364C2×C8—861no—
365C2×C8—861no—
366C2×C8C22×D4311yescharacteristic
367C23—431no—
368C23—861no—
369C23—861no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—431no—
375Q8—861no—
376Q8—861no—
377Q8—861no—
378Q8—1721no—
379Q8—1721no—
380Q8D4×D4311yescharacteristic
381D4—21no—
382D4—431no—
383D4—861no—
384D4—861no—
385D4—861no—
386D4—861no—
387D4—861no—
388D4—861no—
389D4—1721no—
390D4—1721no—
391D4D4×D4311yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—431no—
396C2×C4—431no—
397C2×C4—431no—
398C2×C4—431no—
399C2×C4—431no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4C23×D4311yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8—431no—
414C8—431no—
415C8—861no—
416C8—861no—
417C8—861no—
418C8D4×D4311yescharacteristic
419C8D4×D4311yescharacteristic
420C22—21no—
421C22—431no—
422C22—431no—
423C22—861no—
424C22—3441no—
425C22—3441no—
426C22—1721no—
427C22—1721no—
428C22#41×D4311yescharacteristic
429C4—21no—
430C4—41no—
431C4—41no—
432C4—431no—
433C4—431no—
434C4—861no—
435C4—1721no—
436C4C2×D4×D4311yescharacteristic
437C4C2×D4×D4311yescharacteristic
438C2—21no—
439C2—41no—
440C2—861no—
441C2—861no—
442C2—3441no—
443C2—1721no—
444C2#121×D4311yescharacteristic
subgroupG/H
centerC2#121×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#473C2
socleC2×C43C2×#121
hypercenter#473D43
hypocenterC43#3069
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
2. C2×#13063357C2semidirect
3. #137×D43C2semidirect
4. #14583664C2semidirect
5. #14583173C2semidirect
6. #14583172C2semidirect
7. #14583171C2semidirect
8. #14583165C2semidirect
9. #14583164C2semidirect
10. #14583163C2semidirect
11. #14583162C2semidirect
12. #14582946C2semidirect
13. #14582882C2semidirect
14. #101×D43C2semidirect
15. C43×#473C2semidirect
35. C2×#10621885C22semidirect
37. C2×#10621873C22semidirect
38. C2×#10621884C22semidirect
51. #13063261C22semidirect
52. #13063260C22semidirect
53. #13063260C22semidirect
54. #13063244C22semidirect
55. #13063244C22semidirect
56. #13063243C22semidirect
57. #13063243C22semidirect
58. #13063241C22semidirect
59. #13063241C22semidirect
62. C2×Q16×C43C22semidirect
64. #108×C43C22semidirect
65. #101×C43C22semidirect
66. #101×C43C22semidirect
230. #473D43semidirect
238. C43#3069semidirect
262. C2×Q16C2×D43semidirect
281. #108C2×D43semidirect
286. #101C2×D43semidirect
287. #101C2×D43semidirect