Finite Group Databasebeta

← #19146426

Subgroups — #19146426

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583584C211yesmaximal, characteristic, complemented
2#14583543C211yesmaximal, characteristic
3#14583252C211yesmaximal, characteristic, complemented
4#14583229C211yesmaximal, characteristic, complemented
5#14583221C211yesmaximal, characteristic, complemented
6#14583197C211yesmaximal, characteristic, complemented
7#14583140C211yesmaximal, characteristic, complemented
8#14583127C211yesmaximal, characteristic, complemented
9#14583120C211yesmaximal, characteristic, complemented
10#14583062C211yesmaximal, characteristic, complemented
11#14583050C211yesmaximal, characteristic, complemented
12#14582990C211yesmaximal, characteristic, complemented
13C8×C22⋊D43C211yesmaximal, characteristic, complemented
14#14582892C211yesmaximal, characteristic, complemented
15C2×#102×C43C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×Dic172C2211yescharacteristic, complemented
18C2×#10621883C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic, complemented
21#13063320—21no—
22#13063316C2211yescharacteristic, complemented
23#13063315—21no—
24#13063312C2211yescharacteristic
25#13063308—21no—
26#13063306—21no—
27#13063305C2211yescharacteristic, complemented
28#13063304C2211yescharacteristic
29#13063304C2211yescharacteristic
30#13063297—21no—
31#13063296C2211yescharacteristic
32#13063294—21no—
33#13063290C2211yescharacteristic, complemented
34D4×Dic43C2211yescharacteristic
35C4×C22⋊D43C2211yescharacteristic
36#13063284—21no—
37#13063283C2211yescharacteristic, complemented
38C2×C22⋊Dic43—21no—
39#13063259C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063248C2211yescharacteristic, complemented
46#13063248C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54C2×C4⋊C4×C43C2211yescharacteristic
55#102×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C24×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—22no—
62C2×D4×C43—41no—
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72#10621900—22no—
73#10621900—41no—
74C2×C4×D43C2311yescharacteristic
75C2×Dic86C2311yescharacteristic
76C2×Dic86C2311yescharacteristic
77C2×C8×C43—41no—
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621883—22no—
91#10621883—41no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109Dic172—41no—
110C8×D43—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—81no—
116C23×C43C2×D411yescharacteristic
117C22×D43C2×D411yescharacteristic
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—42no—
122D4×C43#4112yes—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—42no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—22no—
131C22⋊D43—42no—
132C22⋊D43—81no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—42no—
138C2×Dic43—81no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142C4×D43—21no—
143C4×D43—21no—
144Dic86—21no—
145Dic86—21no—
146Dic86—21no—
147Dic86—21no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—22no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—84no—
161C22×C43#13512yes—
162C22×C43C22×D411yescharacteristic
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—21no—
172Dic43—21no—
173Dic43—21no—
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178#3296—431nomaximal, Sylow
179C2×C43—22no—
180C2×C43—42no—
181C2×C43—81no—
182C2×C43#54611yescharacteristic
183C2×C43C2×#13511yescharacteristic
184C2×C43#57711yescharacteristic
185D43—41no—
186#552—431no—
187#546—431no—
188#488—431no—
189#483—431no—
190#482—431no—
191#478—431no—
192#467—431no—
193#465—431no—
194#464—431no—
195#452—431no—
196#450—431no—
197C4×SD16—431no—
198C8×D4—431no—
199#416—431no—
200C2×#102D4311yescharacteristic, complemented
201C43#329611yescharacteristic, complemented, Sylow
202C2×#41—431no—
203C22×D4C2×D4311yescharacteristic
204C2×Q16—431no—
205C2×SD16—431no—
206C2×SD16—431no—
207C22×C8—431no—
208C22×C8C2×D4311yescharacteristic
209#126—861no—
210#125—431no—
211#125—861no—
212#124—431no—
213#123—861no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—431no—
218#121—431no—
219#121—861no—
220#120—861no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4—431no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4C2×D4311yescharacteristic
227C2×C22⋊C4—861no—
228#107—431no—
229#106—431no—
230#106—431no—
231C4⋊C8—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#102—431no—
237#102—431no—
238#102C2×D4311yescharacteristic
239#102C2×D4311yescharacteristic
240#102C2×D4311yescharacteristic
241#102C2×D4311yescharacteristic
242C22⋊C8—431no—
243C22⋊C8—431no—
244C4×C8—431no—
245C24—21no—
246#41—862no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8—431no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—431no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4C22×D4311yescharacteristic
257C2×D4C22×D4311yescharacteristic
258C22×C4—21no—
259C22×C4—431no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263Q16—1721no—
264SD16—862no—
265SD16—1721no—
266C2×C8—41no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—1721no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—431no—
285C22⋊C4—431no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—431no—
295C42—861no—
296C42—861no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—431no—
303C23D4×D4311yescharacteristic
304Q8—861no—
305Q8—861no—
306Q8—861no—
307Q8—861no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—862no—
313D4—3441no—
314D4—1722no—
315D4#1062189812yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—431no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—3441no—
331C2×C4—1722no—
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—861no—
348C22—861no—
349C22—861no—
350C22#1306334412yes—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—861no—
356C4—861no—
357C4—861no—
358C4—1721no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C4C2×#1062189811yescharacteristic
363C4#1306337011yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—1721no—
368C2#1458353911yescharacteristic
369C2C2×#1306334411yescharacteristic
370C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#102×C43C2
socleC22×C43C22×D4
hypercenterC2×#102D43
hypocenterC43#3296
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #14583584C2semidirect
3. #14583252C2semidirect
4. #14583229C2semidirect
5. #14583221C2semidirect
6. #14583197C2semidirect
7. #14583140C2semidirect
8. #14583127C2semidirect
9. #14583120C2semidirect
10. #14583062C2semidirect
11. #14583050C2semidirect
12. #14582990C2semidirect
13. C8×C22⋊D43C2semidirect
14. #14582892C2semidirect
15. C2×#102×C43C2semidirect
17. C2×Dic172C22semidirect
20. C2×C8×D43C22semidirect
22. #13063316C22semidirect
27. #13063305C22semidirect
33. #13063290C22semidirect
37. #13063283C22semidirect
39. #13063259C22semidirect
40. #13063256C22semidirect
41. #13063256C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063250C22semidirect
44. #13063250C22semidirect
45. #13063248C22semidirect
46. #13063248C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C8×Dic43C22semidirect
200. C2×#102D43semidirect
201. C43#3296semidirect