Finite Group Databasebeta

← #19146138

Subgroups — #19146138

Order 5504.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063350C211yesmaximal, characteristic, complemented
2C2×#13063348C211yesmaximal, characteristic, complemented
3#14583568C211yesmaximal, characteristic, complemented
4#14583540C211yesmaximal, characteristic, complemented
5#14583285C211yesmaximal, characteristic, complemented
6#14583147C211yesmaximal, characteristic, complemented
7#14583134C211yesmaximal, characteristic, complemented
8#14583123C211yesmaximal, characteristic, complemented
9#14583093C211yesmaximal, characteristic, complemented
10#14583047C211yesmaximal, characteristic, complemented
11#14583043C211yesmaximal, characteristic, complemented
12#14583035C211yesmaximal, characteristic, complemented
13#14583002C211yesmaximal, characteristic, complemented
14#14582973C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621902C2211yescharacteristic, complemented
18C22×D172C2211yescharacteristic
19#13063350—24no—
20#13063348—24no—
21C2×#10621884C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23C2×#10621884C2211yescharacteristic, complemented
24C2×D344C2211yescharacteristic
25C2×D344C2211yescharacteristic
26C2×#10621882C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621877C2211yescharacteristic
29C2×C8×D43C2211yescharacteristic, complemented
30#13063321—21no—
31#13063321C2211yescharacteristic, complemented
32#13063314C2211yescharacteristic
33#13063310—21no—
34#13063300—21no—
35#13063300C2211yescharacteristic
36#13063299—21no—
37#13063299C2211yescharacteristic
38#13063296—21no—
39#13063296C2211yescharacteristic, complemented
40#13063295—21no—
41Q8×Dic43C2211yescharacteristic, complemented
42#13063287C2211yescharacteristic
43C4×C22⋊D43—21no—
44C4×C22⋊D43C2211yescharacteristic
45C22⋊C4×D43—21no—
46#13063258C2211yescharacteristic, complemented
47Dic43⋊C8C2211yescharacteristic, complemented
48#13063249C2211yescharacteristic, complemented
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063245C2211yescharacteristic, complemented
52(C2×D43)⋊C8C2211yescharacteristic, complemented
53#13063235C2211yescharacteristic, complemented
54C2×#41×C43C2211yescharacteristic
55C2×Q16×C43C2211yescharacteristic, complemented
56C2×SD16×C43C2211yescharacteristic, complemented
57C22⋊Q8×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic, complemented
59#102×C43C2211yescharacteristic, complemented
60C22⋊C8×C43C2211yescharacteristic
61C23×D43—21no—
62#41×C43—22no—
63#41×C43—41no—
64C2×Q8×C43C2311yescharacteristic
65C2×Q8×C43C2311yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43C2311yescharacteristic
68C22×C4×C43—21no—
69C22×C4×C43C2311yescharacteristic
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43D411yescharacteristic
75#10621902—22no—
76#10621902—22no—
77#10621902—41no—
78#10621902—41no—
79C2×D172—21no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172—21no—
83C2×D172—22no—
84C2×D172—41no—
85C2×D172C2311yescharacteristic
86C2×D172C2311yescharacteristic
87C2×D172C2311yescharacteristic
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43C2311yescharacteristic
92Q16×C43—22no—
93SD16×C43—41no—
94C2×C8×C43C2311yescharacteristic
95C2×C8×C43C2311yescharacteristic
96C4⋊C4×C43—21no—
97C4⋊C4×C43C2311yescharacteristic
98C22⋊C4×C43—21no—
99C22⋊Dic43—21no—
100C22⋊Dic43D411yescharacteristic
101#10621884—22no—
102#10621884—22no—
103#10621884D414yescomplemented
104#10621882—22no—
105#10621882—22no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4D411yescharacteristic
112C4⋊Dic43—21no—
113C4⋊Dic43C2311yescharacteristic
114Dic43⋊C4D411yescharacteristic
115C4×Dic43—21no—
116C4×Dic43C2311yescharacteristic
117#10621877—22no—
118C2×C43⋊C8C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120D344—22no—
121D344—41no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—42no—
129C22×D43—42no—
130C22×D43—81no—
131C22×D43C2×D411yescharacteristic
132Q8×C43—21no—
133Q8×C43—21no—
134Q8×C43—21no—
135Q8×C43C2×D412yes—
136D4×C43—21no—
137D4×C43—21no—
138D4×C43—42no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—42no—
145C2×C4×C43C2×D411yescharacteristic
146C2×C4×C43C2411yescharacteristic
147C22⋊D43—41no—
148C22⋊D43—42no—
149C22⋊D43—81no—
150C22⋊D43—81no—
151C22⋊D43—81no—
152C2×Dic43—21no—
153C2×Dic43C2×D411yescharacteristic
154C2×Dic43C2×D411yescharacteristic
155C2×Dic43C2×D411yescharacteristic
156D172—21no—
157D172—21no—
158D172—21no—
159D172—21no—
160D172—21no—
161D172—42no—
162D172—42no—
163D172—42no—
164D172—81no—
165D172C2×D412yes—
166C4×D43—21no—
167C4×D43—21no—
168C4×D43—42no—
169C4×D43—42no—
170C4×D43—81no—
171C8×C43—21no—
172C8×C43—21no—
173C43⋊C8—21no—
174C43⋊C8C2×D412yes—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
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—41no—
189C2×D43—41no—
190C2×D43—41no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—84no—
195C4×C43—22no—
196C4×C43—21no—
197C4×C43—41no—
198C4×C43—41no—
199C4×C43C22×D411yescharacteristic
200C4×C43H(5,𝔽2)11yescharacteristic
201Dic43—21no—
202Dic43—21no—
203Dic43—21no—
204Dic43—41no—
205#3268—431nomaximal, Sylow
206C2×C43—41no—
207C2×C43—81no—
208C2×C43D4211yescharacteristic
209C2×C43#57511yescharacteristic
210C2×C43#57611yescharacteristic
211D43—41no—
212D43—42no—
213D43—81no—
214D43—81no—
215C2×AGL(1,ℤ/8)—431no—
216C2×#135—431no—
217#550—431no—
218#546—431no—
219#496—431no—
220#468—431no—
221#466—431no—
222#464—431no—
223#459—431no—
224#452D4311yescharacteristic, complemented
225#449—431no—
226#449—431no—
227#447—431no—
228#440—431no—
229#435—431no—
230C43#326811yescharacteristic, complemented, Sylow
231C2×#41—431no—
232C2×#41—431no—
233C2×#41C2×D4311yescharacteristic
234C22×D4—431no—
235AGL(1,ℤ/8)—864no—
236#135—864no—
237C2×Q16C2×D4311yescharacteristic, complemented
238C2×SD16—431no—
239C2×SD16—431no—
240C2×SD16—431no—
241C2×SD16C2×D4311yescharacteristic, complemented
242C2×D8—431no—
243C2×D8—431no—
244C2×D8—431no—
245C2×D8—431no—
246C2×M16—431no—
247C22×C8—431no—
248#127—431no—
249#127—861no—
250#124—431no—
251#123—861no—
252C22⋊Q8C2×D4311yescharacteristic
253#121—431no—
254#121—431no—
255#121—431no—
256#121—861no—
257#121—861no—
258#121—861no—
259#120—861no—
260C4×Q8—431no—
261C4×D4—431no—
262C4×D4—431no—
263C4×D4—861no—
264C2×C22⋊C4—861no—
265#107—431no—
266C4⋊C8—431no—
267#103—431no—
268#103C2×D4311yescharacteristic, complemented
269#102—431no—
270#102—431no—
271#102—431no—
272#102C2×D4311yescharacteristic, complemented
273C22⋊C8—431no—
274C22⋊C8C2×D4311yescharacteristic
275#97—431no—
276C24—861no—
277#41—22no—
278#41—41no—
279#41—862no—
280#41—862no—
281#41—1721no—
282#41—1721no—
283C2×Q8C22×D4311yescharacteristic
284C2×Q8C22×D4311yescharacteristic
285C2×D4—21no—
286C2×D4—431no—
287C2×D4—431no—
288C2×D4—431no—
289C2×D4—431no—
290C2×D4—862no—
291C2×D4—861no—
292C2×D4—861no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—861no—
298C2×D4—861no—
299C2×D4—1721no—
300C2×D4C22×D4311yescharacteristic
301C22×C4—21no—
302C22×C4—431no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4C22×D4311yescharacteristic
307Q16—22no—
308SD16—41no—
309SD16—434no—
310SD16—862no—
311SD16—862no—
312D8—862no—
313D8—862no—
314D8—862no—
315D8—1721no—
316M16—862no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8—862no—
320C2×C8C22×D4311yescharacteristic
321C2×C8C22×D4311yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—431no—
324C4⋊C4—431no—
325C4⋊C4—861no—
326C4⋊C4C22×D4311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—431no—
329C22⋊C4—431no—
330C22⋊C4—861no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C42—431no—
337C42—861no—
338C23—21no—
339C23—431no—
340C23—861no—
341C23—861no—
342C23—861no—
343C23—3441no—
344C23—1722no—
345C23—1722no—
346C23D4×D4311yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8D4×D4312yes—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—432no—
355D4—861no—
356D4—861no—
357D4—861no—
358D4—861no—
359D4—861no—
360D4—3441no—
361D4—3441no—
362D4—3441no—
363D4—3441no—
364D4—1722no—
365D4—1722no—
366D4—1722no—
367D4—1721no—
368D4—1722no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—431no—
376C2×C4—431no—
377C2×C4—431no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—3441no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4D4×D4311yescharacteristic
385C2×C4C23×D4311yescharacteristic
386C8—21no—
387C8—21no—
388C8—432no—
389C8—861no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—861no—
397C22—861no—
398C22—861no—
399C22—862no—
400C22—3444no—
401C22—1721no—
402C22—1721no—
403C22—1721no—
404C22—1721no—
405C22—1721no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22C2×D4×D4311yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—861no—
415C4—861no—
416C4—861no—
417C4—1721no—
418C4C2×D4×D4311yescharacteristic
419C4#1306337011yescharacteristic
420C2—41no—
421C2—81no—
422C2—3441no—
423C2—3441no—
424C2—1721no—
425C2—1722no—
426C2#1458353111yescharacteristic
427C2#1458369811yescharacteristic
428C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3268
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#13063350C2semidirect
2. C2×#13063348C2semidirect
3. #14583568C2semidirect
4. #14583540C2semidirect
5. #14583285C2semidirect
6. #14583147C2semidirect
7. #14583134C2semidirect
8. #14583123C2semidirect
9. #14583093C2semidirect
10. #14583047C2semidirect
11. #14583043C2semidirect
12. #14583035C2semidirect
13. #14583002C2semidirect
14. #14582973C2semidirect
15. C43×#452C2semidirect
17. C2×#10621902C22semidirect
23. C2×#10621884C22semidirect
29. C2×C8×D43C22semidirect
31. #13063321C22semidirect
39. #13063296C22semidirect
41. Q8×Dic43C22semidirect
46. #13063258C22semidirect
47. Dic43⋊C8C22semidirect
48. #13063249C22semidirect
51. #13063245C22semidirect
52. (C2×D43)⋊C8C22semidirect
53. #13063235C22semidirect
55. C2×Q16×C43C22semidirect
56. C2×SD16×C43C22semidirect
58. #103×C43C22semidirect
59. #102×C43C22semidirect
103. #10621884D4semidirect
224. #452D43semidirect
230. C43#3268semidirect
237. C2×Q16C2×D43semidirect
241. C2×SD16C2×D43semidirect
268. #103C2×D43semidirect
272. #102C2×D43semidirect