Finite Group Databasebeta

← #19144772

Subgroups — #19144772

Order 5504.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583516C211yesmaximal, characteristic, complemented
2#14583374C211yesmaximal, characteristic, complemented
3#14583241C211yesmaximal, characteristic, complemented
4#14583220C211yesmaximal, characteristic, complemented
5#14583187C211yesmaximal, characteristic, complemented
6#14583177C211yesmaximal, characteristic, complemented
7#14583112C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583050C211yesmaximal, characteristic, complemented
10#14583011C211yesmaximal, characteristic, complemented
11#14582996C211yesmaximal, characteristic, complemented
12#14582990C211yesmaximal, characteristic, complemented
13D8×Dic43C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#447C211yesmaximal, characteristic
16C2×#10621883C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18#13063324C2211yescharacteristic, complemented
19#13063318—21no—
20#13063312—21no—
21#13063312C2211yescharacteristic, complemented
22#13063306—21no—
23#13063304C2211yescharacteristic
24#13063302—21no—
25#13063290C2211yescharacteristic, complemented
26D4×Dic43—21no—
27D4×Dic43—21no—
28D4×Dic43C2211yescharacteristic
29D4×Dic43C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31D4×Dic43C2211yescharacteristic
32D4×Dic43C2211yescharacteristic, complemented
33#13063284C2211yescharacteristic
34#13063284C2211yescharacteristic
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic, complemented
48#13063246C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×D8×C43C2211yescharacteristic
54C2×D8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C24×C43—21no—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C2×Dic86—21no—
74C2×Dic86C2311yescharacteristic
75D8×C43—22no—
76D8×C43—22no—
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43D411yescharacteristic
91C22⋊Dic43D411yescharacteristic
92#10621883—22no—
93#10621883—22no—
94C4⋊Dic43D411yescharacteristic
95C4⋊Dic43D411yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—24no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—81no—
113C23×C43—81no—
114C23×C43C2×D411yescharacteristic
115D4×C43—24no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—81no—
121D4×C43#4112yes—
122D4×C43#4112yes—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141Dic86—21no—
142Dic86—21no—
143Dic86—81no—
144C8×C43—21no—
145C8×C43—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—21no—
149C22×C43—22no—
150C22×C43—22no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—84no—
161C22×C43C22×D411yescharacteristic
162C4×C43—21no—
163C4×C43—41no—
164C4×C43C2×#4111yescharacteristic
165C4×C43C2×#4111yescharacteristic
166Dic43—21no—
167Dic43—21no—
168Dic43—21no—
169Dic43—21no—
170Dic43—41no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3118—431nomaximal, Sylow
175C2×C43—41no—
176C2×C43—42no—
177C2×C43—42no—
178C2×C43—81no—
179C2×C43#52511yescharacteristic
180C2×C43#57611yescharacteristic
181C2×C43#57711yescharacteristic
182#542—431no—
183#518—431no—
184#485—431no—
185#482—431no—
186#476—431no—
187#474—431no—
188#463—431no—
189#463—431no—
190#450—431no—
191#447D4311yescharacteristic
192#442—431no—
193#440—431no—
194C4×SD16—431no—
195C4×D8—431no—
196#433—431no—
197C43#311811yescharacteristic, complemented, Sylow
198C22×D4C2×D4311yescharacteristic
199C2×SD16—431no—
200C2×SD16—431no—
201C2×D8C2×D4311yescharacteristic
202C2×D8C2×D4311yescharacteristic
203C4⋊Q8—431no—
204#126—861no—
205#124—431no—
206#124—861no—
207#123—861no—
208C22⋊Q8—431no—
209C22⋊Q8—861no—
210#121C2×D4311yescharacteristic
211C4×Q8—431no—
212C4×D4—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—431no—
217C4×D4—861no—
218C4×D4—861no—
219#117—431no—
220#117—431no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223#107—431no—
224#107—431no—
225#106—431no—
226#106—431no—
227C4⋊C8—431no—
228C4⋊C8—431no—
229#103—431no—
230#103—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102C2×D4311yescharacteristic
236#102C2×D4311yescharacteristic
237C22⋊C8—431no—
238C22⋊C8C2×D4311yescharacteristic
239#97—431no—
240C4×C8—431no—
241C24—21no—
242C2×Q8—431no—
243C2×Q8—861no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22×D4311yescharacteristic
249C2×D4C22×D4311yescharacteristic
250C2×D4C22×D4311yescharacteristic
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4C22×D4311yescharacteristic
257SD16—862no—
258SD16—862no—
259D8—22no—
260D8—22no—
261C2×C8—431no—
262C2×C8—431no—
263C2×C8C22×D4311yescharacteristic
264C2×C8C22×D4311yescharacteristic
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4C22×D4311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—431no—
276C22⋊C4—431no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—431no—
287C42—431no—
288C42—861no—
289C42—861no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23D4×D4311yescharacteristic
297Q8—861no—
298Q8—861no—
299Q8—3441no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#1062190012yes—
307D4#1062190012yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4D4×D4311yescharacteristic
325C2×C4C23×D4311yescharacteristic
326C8—21no—
327C8—21no—
328C8—861no—
329C8—861no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C2×D4×D4311yescharacteristic
344C4—21no—
345C4—41no—
346C4—861no—
347C4—861no—
348C4—861no—
349C4—861no—
350C4—1721no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4C2×#1062190011yescharacteristic
355C4C2×#1062190011yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#1458340511yescharacteristic
361C2#1458370011yescharacteristic
362C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#447C2
socleC22×C43C22×D4
hypercenter#447D43
hypocenterC43#3118
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14583516C2semidirect
2. #14583374C2semidirect
3. #14583241C2semidirect
4. #14583220C2semidirect
5. #14583187C2semidirect
6. #14583177C2semidirect
7. #14583112C2semidirect
8. #14583112C2semidirect
9. #14583050C2semidirect
10. #14583011C2semidirect
11. #14582996C2semidirect
12. #14582990C2semidirect
13. D8×Dic43C2semidirect
14. #14582957C2semidirect
18. #13063324C22semidirect
21. #13063312C22semidirect
25. #13063290C22semidirect
32. D4×Dic43C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063250C22semidirect
44. #13063250C22semidirect
47. #13063246C22semidirect
48. #13063246C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
197. C43#3118semidirect