Finite Group Databasebeta

← #19146295

Subgroups — #19146295

Order 5504.

504 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×#13063348C211yesmaximal, characteristic, complemented
2C22×#10621884C211yesmaximal, characteristic, complemented
3#14583560C211yesmaximal, characteristic, complemented
4#14583540C211yesmaximal, characteristic, complemented
5#14583284C211yesmaximal, characteristic, complemented
6#14583131C211yesmaximal, characteristic, complemented
7#14583130C211yesmaximal, characteristic, complemented
8#14583123C211yesmaximal, characteristic, complemented
9#14583117C211yesmaximal, characteristic, complemented
10#14583060C211yesmaximal, characteristic, complemented
11#14583047C211yesmaximal, characteristic, complemented
12#14583035C211yesmaximal, characteristic, complemented
13#14582984C211yesmaximal, characteristic, complemented
14(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
15C43×#451C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621902C2211yescharacteristic, complemented
18C22×D172C2211yescharacteristic
19#13063348—24no—
20C2×#10621884—24no—
21C2×#10621884C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23C2×#10621884C2211yescharacteristic
24C2×#10621884C2211yescharacteristic
25C2×#10621884C2211yescharacteristic, complemented
26C2×D344C2211yescharacteristic
27C2×D344C2211yescharacteristic
28C22×C43⋊C8C2211yescharacteristic
29C2×C8×D43C2211yescharacteristic, complemented
30#13063314—21no—
31#13063314C2211yescharacteristic
32#13063314C2211yescharacteristic, complemented
33#13063310—21no—
34#13063301—21no—
35#13063301C2211yescharacteristic, complemented
36#13063300—21no—
37#13063300C2211yescharacteristic
38#13063299—21no—
39#13063299C2211yescharacteristic
40#13063295—21no—
41Q8×Dic43C2211yescharacteristic, complemented
42#13063287C2211yescharacteristic
43C4×C22⋊D43—21no—
44C4×C22⋊D43C2211yescharacteristic
45C22⋊C4×D43—21no—
46#13063256C2211yescharacteristic, complemented
47Dic43⋊C8C2211yescharacteristic, complemented
48#13063249C2211yescharacteristic, complemented
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063245C2211yescharacteristic, complemented
52(C2×D43)⋊C8C2211yescharacteristic, complemented
53C8×Dic43C2211yescharacteristic, complemented
54C22×Q8×C43C2211yescharacteristic
55C2×Q16×C43C2211yescharacteristic, complemented
56C2×Q16×C43C2211yescharacteristic, complemented
57C22⋊Q8×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic, complemented
59#103×C43C2211yescharacteristic, complemented
60C22⋊C8×C43C2211yescharacteristic
61C23×D43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—22no—
64C2×Q8×C43—41no—
65C2×Q8×C43C2311yescharacteristic
66C2×Q8×C43C2311yescharacteristic
67C2×Q8×C43C2311yescharacteristic
68C22×C4×C43—21no—
69C22×C4×C43C2311yescharacteristic
70C2×C22⋊D43—21no—
71C2×C22⋊D43D411yescharacteristic
72#10621902—22no—
73#10621902—22no—
74#10621902—41no—
75#10621902—41no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—21no—
80C2×D172—22no—
81C2×D172—41no—
82C2×D172C2311yescharacteristic
83C2×D172C2311yescharacteristic
84C2×D172C2311yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43C2311yescharacteristic
89Q16×C43—22no—
90Q16×C43—41no—
91C2×C8×C43C2311yescharacteristic
92C2×C8×C43C2311yescharacteristic
93C4⋊C4×C43—21no—
94C4⋊C4×C43C2311yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊Dic43D411yescharacteristic
97#10621884—22no—
98#10621884—22no—
99#10621884—22no—
100#10621884—22no—
101#10621884D414yescomplemented
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4D411yescharacteristic
111C4⋊Dic43—21no—
112C4⋊Dic43C2311yescharacteristic
113Dic43⋊C4—21no—
114Dic43⋊C4D411yescharacteristic
115C4×Dic43—21no—
116C4×Dic43C2311yescharacteristic
117C2×C43⋊C8—22no—
118C2×C43⋊C8C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120D344—22no—
121D344—41no—
122C8×D43—22no—
123C23×C43C2×D411yescharacteristic
124C22×D43—21no—
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—81no—
130C22×D43C2×D411yescharacteristic
131Q8×C43—21no—
132Q8×C43—21no—
133Q8×C43—21no—
134Q8×C43—21no—
135Q8×C43—21no—
136Q8×C43—42no—
137Q8×C43C2×D412yes—
138C2×C4×C43—21no—
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—22no—
148C22⋊D43—42no—
149C2×Dic43—21no—
150C2×Dic43C2×D411yescharacteristic
151C2×Dic43C2×D411yescharacteristic
152C2×Dic43C2×D411yescharacteristic
153D172—21no—
154D172—21no—
155D172—21no—
156D172—21no—
157D172—21no—
158D172—42no—
159D172—42no—
160D172—42no—
161D172—81no—
162D172C2×D412yes—
163C4×D43—21no—
164C4×D43—21no—
165C4×D43—42no—
166C4×D43—42no—
167C4×D43—81no—
168C8×C43—21no—
169C8×C43—21no—
170C43⋊C8—21no—
171C43⋊C8C2×D412yes—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43#13512yescomplemented
175C22×C43C22×D411yescharacteristic
176C2×D43—22no—
177C2×D43—21no—
178C2×D43—21no—
179C2×D43—21no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—84no—
189C4×C43—22no—
190C4×C43—21no—
191C4×C43—41no—
192C4×C43—41no—
193C4×C43—41no—
194C4×C43C22×D411yescharacteristic
195C4×C43H(5,𝔽2)11yescharacteristic
196Dic43—21no—
197Dic43—21no—
198Dic43—21no—
199Dic43—41no—
200#3282—431nomaximal, Sylow
201C2×C43—22no—
202C2×C43D4211yescharacteristic
203C2×C43C2×#13511yescharacteristic
204C2×C43#57711yescharacteristic
205D43—41no—
206D43—42no—
207D43—81no—
208D43—81no—
209C2×#135—431no—
210C22×SD16—431no—
211#548—431no—
212#546—431no—
213#495—431no—
214#465—431no—
215#465—431no—
216#464—431no—
217#463—431no—
218#452—431no—
219#451D4311yescharacteristic, complemented
220#449—431no—
221#447—431no—
222C4×SD16—431no—
223C8×D4—431no—
224C43#328211yescharacteristic, complemented, Sylow
225C2×#41—431no—
226C2×#41—431no—
227C22×Q8C2×D4311yescharacteristic
228C22×D4—431no—
229#135—864no—
230C2×Q16C2×D4311yescharacteristic, complemented
231C2×Q16C2×D4311yescharacteristic, complemented
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—431no—
236C2×SD16—431no—
237C2×SD16—864no—
238C2×D8—431no—
239C2×D8—431no—
240C22×C8—431no—
241C22×C8—431no—
242#124—431no—
243#124—431no—
244#124—861no—
245#123—861no—
246C22⋊Q8—431no—
247C22⋊Q8—861no—
248C22⋊Q8C2×D4311yescharacteristic
249#121—431no—
250#121—431no—
251#121—861no—
252#121—861no—
253#120—861no—
254C4×Q8—431no—
255C4×D4—431no—
256C4×D4—431no—
257C4×D4—861no—
258C2×C22⋊C4—861no—
259#106—431no—
260C4⋊C8—431no—
261#103—431no—
262#103C2×D4311yescharacteristic, complemented
263#103C2×D4311yescharacteristic, complemented
264#102—431no—
265#102—431no—
266#102—431no—
267C22⋊C8—431no—
268C22⋊C8C2×D4311yescharacteristic
269C4×C8—431no—
270C24—861no—
271#41—862no—
272#41—862no—
273#41—1721no—
274#41—1721no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D4311yescharacteristic
279C2×Q8C22×D4311yescharacteristic
280C2×Q8C22×D4311yescharacteristic
281C2×D4—431no—
282C2×D4—431no—
283C2×D4—431no—
284C2×D4—431no—
285C2×D4—862no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—1721no—
292C22×C4—21no—
293C22×C4—431no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4C22×D4311yescharacteristic
298Q16—22no—
299Q16—41no—
300SD16—434no—
301SD16—862no—
302SD16—862no—
303SD16—862no—
304SD16—862no—
305D8—862no—
306D8—1721no—
307C2×C8—431no—
308C2×C8—431no—
309C2×C8—862no—
310C2×C8—862no—
311C2×C8C22×D4311yescharacteristic
312C2×C8C22×D4311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—431no—
315C4⋊C4—431no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4C22×D4311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—431no—
321C22⋊C4—431no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4—861no—
329C22⋊C4—861no—
330C42—431no—
331C42—861no—
332C23—431no—
333C23—861no—
334C23—861no—
335C23—861no—
336C23—3441no—
337C23—1722no—
338C23—1722no—
339C23D4×D4311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8D4×D4312yes—
347D4—432no—
348D4—862no—
349D4—861no—
350D4—861no—
351D4—861no—
352D4—861no—
353D4—861no—
354D4—3441no—
355D4—1722no—
356D4—1722no—
357D4—1722no—
358D4—1722no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—431no—
367C2×C4—431no—
368C2×C4—431no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—3441no—
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—861no—
384C22—861no—
385C22—861no—
386C22—862no—
387C22—3444no—
388C22—1721no—
389C22—1721no—
390C22—1721no—
391C22—1721no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22—1721no—
396C22#1306334812yescomplemented
397C22C2×D4×D4311yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—861no—
404C4—861no—
405C4—861no—
406C4—1721no—
407C4C2×D4×D4311yescharacteristic
408C4#1306337011yescharacteristic
409C2—22no—
410C2—3441no—
411C2—3441no—
412C2—1721no—
413C2—1722no—
414C2#1458353111yescharacteristic
415C2C2×#1306334811yescharacteristic
416C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#451C2
socleC22×C43C22×D4
hypercenter#451D43
hypocenterC43#3282
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#13063348C2semidirect
2. C22×#10621884C2semidirect
3. #14583560C2semidirect
4. #14583540C2semidirect
5. #14583284C2semidirect
6. #14583131C2semidirect
7. #14583130C2semidirect
8. #14583123C2semidirect
9. #14583117C2semidirect
10. #14583060C2semidirect
11. #14583047C2semidirect
12. #14583035C2semidirect
13. #14582984C2semidirect
14. (C22⋊D43)⋊C8C2semidirect
15. C43×#451C2semidirect
17. C2×#10621902C22semidirect
25. C2×#10621884C22semidirect
29. C2×C8×D43C22semidirect
32. #13063314C22semidirect
35. #13063301C22semidirect
41. Q8×Dic43C22semidirect
46. #13063256C22semidirect
47. Dic43⋊C8C22semidirect
48. #13063249C22semidirect
51. #13063245C22semidirect
52. (C2×D43)⋊C8C22semidirect
53. C8×Dic43C22semidirect
55. C2×Q16×C43C22semidirect
56. C2×Q16×C43C22semidirect
58. #103×C43C22semidirect
59. #103×C43C22semidirect
101. #10621884D4semidirect
174. C22×C43#135semidirect
219. #451D43semidirect
224. C43#3282semidirect
230. C2×Q16C2×D43semidirect
231. C2×Q16C2×D43semidirect
262. #103C2×D43semidirect
263. #103C2×D43semidirect
396. C22#13063348semidirect