Finite Group Databasebeta

← #19145347

Subgroups — #19145347

Order 5504.

468 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D43C211yesmaximal, characteristic, complemented
2#121×D43C211yesmaximal, characteristic
3#14583231C211yesmaximal, characteristic, complemented
4#14583228C211yesmaximal, characteristic, complemented
5#14583219C211yesmaximal, characteristic, complemented
6#14583216C211yesmaximal, characteristic, complemented
7#14583130C211yesmaximal, characteristic, complemented
8#14583128C211yesmaximal, characteristic, complemented
9#14583126C211yesmaximal, characteristic, complemented
10#14583051C211yesmaximal, characteristic, complemented
11#14583048C211yesmaximal, characteristic, complemented
12#14583039C211yesmaximal, characteristic, complemented
13#14583036C211yesmaximal, characteristic, complemented
14C2×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C43×#465C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic, complemented
17C2×D4×D43—21no—
18C2×D4×D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20C2×#10621873C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic, complemented
22C2×#10621884C2211yescharacteristic, complemented
23C22×C43⋊C8C2211yescharacteristic, complemented
24#13063305C2211yescharacteristic
25#13063304C2211yescharacteristic, complemented
26#13063303—21no—
27#13063302—21no—
28#13063301C2211yescharacteristic
29#13063300C2211yescharacteristic
30#13063299C2211yescharacteristic
31#13063298—21no—
32#13063297—21no—
33#13063296C2211yescharacteristic
34C4⋊C4×D43—21no—
35C4⋊C4×D43C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic, complemented
37C22⋊C4×D43—21no—
38C22⋊C4×D43—21no—
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic, complemented
54C22⋊Q8×C43C2211yescharacteristic, complemented
55#121×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C23×D43D411yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C22×Dic43D411yescharacteristic
69Q8×D43—41no—
70Q8×D43—41no—
71D4×D43—41no—
72D4×D43—41no—
73D4×D43—44no—
74C2×D172—21no—
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81C2×C4×D43D411yescharacteristic
82C2×C4×D43D411yescharacteristic
83C2×C4×D43C2311yescharacteristic
84C2×C4×D43C2311yescharacteristic
85C2×Dic86—21no—
86C2×Dic86C2311yescharacteristic
87SD16×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43C2311yescharacteristic
90C2×C8×C43C2311yescharacteristic
91C4⋊C4×C43—21no—
92C4⋊C4×C43C2311yescharacteristic
93C4⋊C4×C43C2311yescharacteristic
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43—21no—
98#10621884—41no—
99#10621883—41no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43C2311yescharacteristic
106C4⋊Dic43C2311yescharacteristic
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8C2311yescharacteristic
113C2×C43⋊C8C2311yescharacteristic
114#10621873—41no—
115C23×C43—21no—
116C23×C43C2×D411yescharacteristic
117C22×D43—21no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—42no—
121C22×D43—42no—
122C22×D43—42no—
123C22×D43SD1614yescomplemented
124C22×D43C2×D411yescharacteristic
125C22×D43C2×D411yescharacteristic
126Q8×C43—21no—
127Q8×C43—21no—
128D4×C43—21no—
129D4×C43—21no—
130D4×C43—42no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2411yescharacteristic
138C22⋊D43—42no—
139C22⋊D43—42no—
140C22⋊D43—42no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—41no—
145C2×Dic43C2×D411yescharacteristic
146C2×Dic43C2×D411yescharacteristic
147D172—21no—
148D172—21no—
149D172—42no—
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—21no—
153C4×D43—21no—
154C4×D43—41no—
155C4×D43—41no—
156C4×D43—42no—
157C4×D43—42no—
158C4×D43—42no—
159Dic86—21no—
160Dic86—21no—
161Dic86—42no—
162C8×C43—21no—
163C8×C43—21no—
164C43⋊C8—21no—
165C43⋊C8—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43C2×SD1612yes—
172C22×C43C22×D411yescharacteristic
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—44no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—84no—
182C2×D43C2×SD1612yes—
183C2×D43C2×SD1612yes—
184C4×C43—21no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43H(5,𝔽2)11yescharacteristic
189C4×C43H(5,𝔽2)11yescharacteristic
190Dic43—21no—
191Dic43—21no—
192Dic43—41no—
193Dic43—41no—
194Dic43—41no—
195#3187—431nomaximal, Sylow
196C2×C43—22no—
197C2×C43—81no—
198C2×C43#53411yescharacteristic
199C2×C43C22×SD1611yescharacteristic
200C2×C43#57511yescharacteristic
201D43—22no—
202D43—22no—
203D43—81no—
204C2×C22⋊Q8—431no—
205C2×#121—431no—
206#483—431no—
207#483—431no—
208#481—431no—
209#481—431no—
210#465—431no—
211#465—431no—
212#465—431no—
213#465D4311yescharacteristic, complemented
214#450—431no—
215#450—431no—
216#448—431no—
217#448—431no—
218C2×C22⋊C8—431no—
219C43#318711yescharacteristic, complemented, Sylow
220C22×Q8—431no—
221C22×D4—431no—
222C22×D4—861no—
223C23×C4—431no—
224C2×SD16—431no—
225C2×SD16—431no—
226C2×SD16—431no—
227C2×SD16C2×D4311yescharacteristic, complemented
228C22×C8—431no—
229C22×C8C2×D4311yescharacteristic, complemented
230C22⋊Q8—431no—
231C22⋊Q8—431no—
232C22⋊Q8—431no—
233C22⋊Q8—861no—
234C22⋊Q8—861no—
235C22⋊Q8C2×D4311yescharacteristic, complemented
236#121—431no—
237#121—431no—
238#121—431no—
239#121—861no—
240#121—861no—
241#121C2×D4311yescharacteristic
242C2×C4⋊C4—431no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247#106—431no—
248#106—431no—
249#106—431no—
250#106C2×D4311yescharacteristic, complemented
251#103—431no—
252#103—431no—
253#103—431no—
254#103C2×D4311yescharacteristic, complemented
255#102—431no—
256#102—431no—
257#102—431no—
258#102C2×D4311yescharacteristic, complemented
259C22⋊C8—431no—
260C22⋊C8—431no—
261C22⋊C8—431no—
262C22⋊C8—431no—
263C24—431no—
264C24—861no—
265C2×Q8—431no—
266C2×Q8—861no—
267C2×Q8—1721no—
268C2×Q8—1721no—
269C2×Q8C22×D4311yescharacteristic
270C2×D4—21no—
271C2×D4—431no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—1721no—
277C2×D4—1721no—
278C2×D4—1724no—
279C2×D4C22×D4311yescharacteristic
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—1721no—
289C22×C4—1721no—
290C22×C4C22×D4311yescharacteristic
291SD16—41no—
292SD16—1721no—
293SD16—1721no—
294SD16—1721no—
295C2×C8—41no—
296C2×C8—431no—
297C2×C8—431no—
298C2×C8—1721no—
299C2×C8C22×D4311yescharacteristic
300C2×C8C22×D4311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—431no—
303C4⋊C4—431no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4C22×D4311yescharacteristic
310C4⋊C4C22×D4311yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C23—21no—
320C23—431no—
321C23—431no—
322C23—434no—
323C23—861no—
324C23—1721no—
325C23—1721no—
326C23—1722no—
327C23—1722no—
328C23—1722no—
329C23D4×D4311yescharacteristic
330Q8—21no—
331Q8—21no—
332Q8—861no—
333Q8—861no—
334Q8—1722no—
335D4—21no—
336D4—21no—
337D4—42no—
338D4—861no—
339D4—861no—
340D4—1722no—
341D4—1722no—
342D4—1722no—
343D4—1722no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—431no—
350C2×C4—431no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4—1721no—
364C2×C4D4×D4311yescharacteristic
365C2×C4C23×D4311yescharacteristic
366C8—21no—
367C8—21no—
368C8—861no—
369C8—861no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—432no—
376C22—432no—
377C22—861no—
378C22—861no—
379C22—861no—
380C22—861no—
381C22—3444no—
382C22—1724no—
383C22—1721no—
384C22—1721no—
385C22—1721no—
386C22SD16×D4312yes—
387C22C2×D4×D4311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—861no—
393C4—861no—
394C4—1721no—
395C4—1721no—
396C4—1721no—
397C4#1306337011yescharacteristic
398C4#1306337111yescharacteristic
399C2—22no—
400C2—81no—
401C2—862no—
402C2—862no—
403C2—3441no—
404C2#1458345711yescharacteristic
405C2C2×SD16×D4311yescharacteristic
406C2#1458369611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#465C2
socleC22×C43C22×D4
hypercenter#465D43
hypocenterC43#3187
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×D43C2semidirect
3. #14583231C2semidirect
4. #14583228C2semidirect
5. #14583219C2semidirect
6. #14583216C2semidirect
7. #14583130C2semidirect
8. #14583128C2semidirect
9. #14583126C2semidirect
10. #14583051C2semidirect
11. #14583048C2semidirect
12. #14583039C2semidirect
13. #14583036C2semidirect
14. C2×(C2×D43)⋊C8C2semidirect
15. C43×#465C2semidirect
16. C2×Q8×D43C22semidirect
20. C2×#10621873C22semidirect
21. C2×#10621883C22semidirect
22. C2×#10621884C22semidirect
23. C22×C43⋊C8C22semidirect
25. #13063304C22semidirect
36. C4⋊C4×D43C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. #13063256C22semidirect
42. #13063250C22semidirect
43. #13063249C22semidirect
44. #13063248C22semidirect
45. #13063247C22semidirect
46. #13063246C22semidirect
47. #13063245C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
52. C2×SD16×C43C22semidirect
53. C22×C8×C43C22semidirect
54. C22⋊Q8×C43C22semidirect
56. #106×C43C22semidirect
57. #103×C43C22semidirect
58. #102×C43C22semidirect
123. C22×D43SD16semidirect
213. #465D43semidirect
219. C43#3187semidirect
227. C2×SD16C2×D43semidirect
229. C22×C8C2×D43semidirect
235. C22⋊Q8C2×D43semidirect
250. #106C2×D43semidirect
254. #103C2×D43semidirect
258. #102C2×D43semidirect