Finite Group Databasebeta

← #19144775

Subgroups — #19144775

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#14583514C211yesmaximal, characteristic, complemented
2#14583371C211yesmaximal, characteristic, complemented
3#14583242C211yesmaximal, characteristic, complemented
4#14583222C211yesmaximal, characteristic, complemented
5#14583187C211yesmaximal, characteristic, complemented
6#14583178C211yesmaximal, characteristic, complemented
7#14583113C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583051C211yesmaximal, characteristic, complemented
10#14583031C211yesmaximal, characteristic
11#14583009C211yesmaximal, characteristic, complemented
12#14582999C211yesmaximal, characteristic, complemented
13C4×#10621873C211yesmaximal, characteristic, complemented
14#14582958C211yesmaximal, characteristic, complemented
15C4×D8×C43C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20#13063324C2211yescharacteristic, complemented
21#13063318—21no—
22#13063312C2211yescharacteristic, complemented
23#13063311—21no—
24#13063308—21no—
25#13063305C2211yescharacteristic
26#13063304—21no—
27#13063296C2211yescharacteristic
28C4×Dic86C2211yescharacteristic, complemented
29C4×D172C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31#13063287C2211yescharacteristic
32C4×C22⋊D43—21no—
33(C22⋊D43)⋊C4—21no—
34#13063283C2211yescharacteristic
35#13063282C2211yescharacteristic
36C2×(C2×D43)⋊C4—21no—
37C22⋊C4×D43—21no—
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic, complemented
52C2×D8×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic, complemented
55#107×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic, complemented
58C4×C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67D4×D43—22no—
68D4×D43—22no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43C2311yescharacteristic
73C2×Dic86—21no—
74C2×Dic86C2311yescharacteristic
75D8×C43—22no—
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C42×C43C2311yescharacteristic
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87#10621883—22no—
88#10621882—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4D411yescharacteristic
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107#10621873—22no—
108C23×C43—21no—
109C23×C43—21no—
110C22×D43—21no—
111C22×D43—24no—
112C22×D43—81no—
113C22×D43—81no—
114C22×D43C2×D411yescharacteristic
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43#4112yes—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—24no—
127C22⋊D43—81no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—81no—
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—21no—
136D172#4112yes—
137C4×D43—21no—
138C4×D43—21no—
139C4×D43—81no—
140C4×D43—81no—
141Dic86—21no—
142Dic86—21no—
143Dic86—81no—
144C8×C43—21no—
145C8×C43—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—22no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C2×D43—21no—
156C2×D43—22no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—84no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43C2×#4111yescharacteristic
167C4×C43C2×#4111yescharacteristic
168Dic43—21no—
169Dic43—21no—
170Dic43—21no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3118—431nomaximal, Sylow
175C2×C43—42no—
176C2×C43—81no—
177C2×C43#52511yescharacteristic
178C2×C43#57611yescharacteristic
179C2×C43#57711yescharacteristic
180D43—41no—
181D43—42no—
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#447—431no—
192#442—431no—
193#440—431no—
194C4×SD16—431no—
195C4×D8D4311yescharacteristic, complemented
196#433—431no—
197C43#311811yescharacteristic, complemented, Sylow
198C22×D4—431no—
199C2×SD16—431no—
200C2×SD16—431no—
201C2×D8—431no—
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#121—431no—
211C4×Q8—431no—
212C4×D4—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—861no—
216C4×D4—861no—
217C4×D4C2×D4311yescharacteristic
218C4×D4C2×D4311yescharacteristic, complemented
219#117—431no—
220#117—431no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223#107—431no—
224#107C2×D4311yescharacteristic, complemented
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, complemented
237C22⋊C8—431no—
238C22⋊C8—431no—
239#97—431no—
240C4×C8C2×D4311yescharacteristic, complemented
241C24—861no—
242C2×Q8—431no—
243C2×Q8—861no—
244C2×D4—431no—
245C2×D4—861no—
246C2×D4—862no—
247C2×D4—862no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C2×D4C22×D4311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—431no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257SD16—862no—
258SD16—862no—
259D8—22no—
260D8—862no—
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—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4C22×D4311yescharacteristic
273C4⋊C4C22×D4311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—431no—
277C22⋊C4—431no—
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—861no—
288C42—861no—
289C42C22×D4311yescharacteristic
290C23—21no—
291C23—21no—
292C23—431no—
293C23—864no—
294C23—861no—
295C23—3441no—
296C23—3441no—
297Q8—861no—
298Q8—861no—
299Q8—3441no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—432no—
304D4—864no—
305D4—861no—
306D4—3441no—
307D4#1062189812yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4D4×D4311yescharacteristic
324C2×C4D4×D4311yescharacteristic
325C2×C4C23×D4311yescharacteristic
326C8—21no—
327C8—21no—
328C8—861no—
329C8—861no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—861no—
337C22—862no—
338C22—861no—
339C22—861no—
340C22—3444no—
341C22—1721no—
342C22—1721no—
343C22C2×D4×D4311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—861no—
349C4—861no—
350C4—861no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4#41×D4311yescharacteristic
355C4C2×#1062189811yescharacteristic
356C2—42no—
357C2—81no—
358C2—1721no—
359C2—1722no—
360C2#1458340811yescharacteristic
361C2#1458370011yescharacteristic
362C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC4×D8×C43C2
socleC22×C43C22×D4
hypercenterC4×D8D43
hypocenterC43#3118
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14583514C2semidirect
2. #14583371C2semidirect
3. #14583242C2semidirect
4. #14583222C2semidirect
5. #14583187C2semidirect
6. #14583178C2semidirect
7. #14583113C2semidirect
8. #14583112C2semidirect
9. #14583051C2semidirect
11. #14583009C2semidirect
12. #14582999C2semidirect
13. C4×#10621873C2semidirect
14. #14582958C2semidirect
15. C4×D8×C43C2semidirect
20. #13063324C22semidirect
22. #13063312C22semidirect
28. C4×Dic86C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063250C22semidirect
44. #13063248C22semidirect
47. #13063246C22semidirect
51. #13063236C22semidirect
54. C4×D4×C43C22semidirect
55. #107×C43C22semidirect
57. #102×C43C22semidirect
58. C4×C8×C43C22semidirect
195. C4×D8D43semidirect
197. C43#3118semidirect
218. C4×D4C2×D43semidirect
224. #107C2×D43semidirect
236. #102C2×D43semidirect
240. C4×C8C2×D43semidirect