Finite Group Databasebeta

← #19146682

Subgroups — #19146682

Order 5504.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583607C211yesmaximal, characteristic, complemented
2#14583540C211yesmaximal, characteristic
3#14583260C211yesmaximal, characteristic, complemented
4#14583232C211yesmaximal, characteristic, complemented
5#14583214C211yesmaximal, characteristic, complemented
6#14583178C211yesmaximal, characteristic, complemented
7#14583148C211yesmaximal, characteristic, complemented
8#14583123C211yesmaximal, characteristic, complemented
9#14583060C211yesmaximal, characteristic, complemented
10#14583049C211yesmaximal, characteristic, complemented
11#14583002C211yesmaximal, characteristic, complemented
12#14582970C211yesmaximal, characteristic, complemented
13#14582899C211yesmaximal, characteristic, complemented
14C2×#13063247C211yesmaximal, characteristic, complemented
15C43×#467C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621872C2211yescharacteristic, complemented
21#13063324C2211yescharacteristic, complemented
22#13063315—21no—
23#13063314C2211yescharacteristic
24#13063310—21no—
25#13063305—21no—
26#13063302—21no—
27#13063301C2211yescharacteristic, complemented
28#13063300—21no—
29#13063300C2211yescharacteristic
30#13063295—21no—
31Q8×Dic43C2211yescharacteristic, complemented
32#13063287C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34(C22⋊D43)⋊C4—21no—
35C2×C4⋊Dic43C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic, complemented
37C22⋊C4×D43—21no—
38#13063258C2211yescharacteristic, complemented
39#13063258C2211yescharacteristic, complemented
40Dic43⋊C8C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51#13063235C2211yescharacteristic, complemented
52C2×Q16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#103×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43D411yescharacteristic
64C22×Dic43—21no—
65#10621902—22no—
66#10621902—41no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172—22no—
71C2×D172—41no—
72C2×D172C2311yescharacteristic
73C2×D172C2311yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78C2×Dic86—21no—
79Q16×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621884—22no—
91#10621884—41no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4D411yescharacteristic
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4D411yescharacteristic
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621872—41no—
111C23×C43C2×D411yescharacteristic
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—81no—
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—22no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—81no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137D172—21no—
138D172—21no—
139D172—21no—
140D172—42no—
141D172—42no—
142D172—81no—
143D172#4112yes—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—42no—
147C4×D43—81no—
148C4×D43—81no—
149Dic86—81no—
150C8×C43—21no—
151C8×C43—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43#13712yes—
157C22×C43C22×D411yescharacteristic
158C2×D43—22no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—84no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43C2×#4111yescharacteristic
174C4×C43H(5,𝔽2)11yescharacteristic
175Dic43—21no—
176Dic43—21no—
177Dic43—21no—
178Dic43—41no—
179Dic43—41no—
180#3314—431nomaximal, Sylow
181C2×C43—22no—
182C2×C43#54611yescharacteristic
183C2×C43C2×#13711yescharacteristic
184C2×C43#57611yescharacteristic
185D43—41no—
186D43—42no—
187D43—81no—
188#554—431no—
189#546—431no—
190#489—431no—
191#484—431no—
192#480—431no—
193#474—431no—
194#468—431no—
195#467D4311yescharacteristic, complemented
196#464—431no—
197#452—431no—
198#450—431no—
199#440—431no—
200#435—431no—
201#417—431no—
202C2×#102—431no—
203C43#331411yescharacteristic, complemented, Sylow
204C2×#41—431no—
205C22×D4—431no—
206C2×Q16C2×D4311yescharacteristic, complemented
207C2×SD16—431no—
208C2×SD16—431no—
209C2×M16—431no—
210C22×C8C2×D4311yescharacteristic
211C4⋊Q8—431no—
212#125—861no—
213#124—431no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—861no—
217C22⋊Q8—861no—
218C22⋊Q8C2×D4311yescharacteristic
219C22⋊Q8C2×D4311yescharacteristic
220#121—431no—
221#121—861no—
222#120—861no—
223C4×Q8—431no—
224C4×D4—431no—
225C4×D4—431no—
226C4×D4—861no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C22⋊C4—861no—
230#107—431no—
231#107—431no—
232#107C2×D4311yescharacteristic, complemented
233C4⋊C8—431no—
234#103—431no—
235#103—431no—
236#103C2×D4311yescharacteristic, complemented
237#103C2×D4311yescharacteristic, complemented
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244C22⋊C8—431no—
245C22⋊C8—431no—
246#97—431no—
247C24—861no—
248#41—862no—
249#41—1721no—
250C2×Q8—861no—
251C2×Q8C22×D4311yescharacteristic
252C2×Q8C22×D4311yescharacteristic
253C2×D4—431no—
254C2×D4—431no—
255C2×D4—431no—
256C2×D4—862no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—1721no—
261C22×C4—431no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4C22×D4311yescharacteristic
267Q16—41no—
268SD16—862no—
269SD16—1721no—
270M16—1721no—
271C2×C8—41no—
272C2×C8—431no—
273C2×C8—431no—
274C2×C8C22×D4311yescharacteristic
275C2×C8C22×D4311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—431no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—431no—
291C22⋊C4—431no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C42—431no—
298C42—861no—
299C23—431no—
300C23—861no—
301C23—861no—
302C23—3441no—
303C23—1722no—
304C23—1722no—
305C23D4×D4311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—3441no—
311D4—432no—
312D4—862no—
313D4—861no—
314D4—861no—
315D4—861no—
316D4—3441no—
317D4—1722no—
318D4—1722no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—431no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4—1722no—
336C2×C4D4×D4311yescharacteristic
337C2×C4C23×D4311yescharacteristic
338C8—21no—
339C8—21no—
340C8—861no—
341C8—861no—
342C22—21no—
343C22—21no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—862no—
348C22—3444no—
349C22—1721no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22—1721no—
354C22#1306335712yes—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—861no—
362C4—861no—
363C4—861no—
364C4—1721no—
365C4—1721no—
366C4#41×D4311yescharacteristic
367C4#1306337011yescharacteristic
368C2—22no—
369C2—3441no—
370C2—1721no—
371C2—1722no—
372C2#1458353811yescharacteristic
373C2C2×#1306335711yescharacteristic
374C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#467C2
socleC22×C43C22×D4
hypercenter#467D43
hypocenterC43#3314
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #14583607C2semidirect
3. #14583260C2semidirect
4. #14583232C2semidirect
5. #14583214C2semidirect
6. #14583178C2semidirect
7. #14583148C2semidirect
8. #14583123C2semidirect
9. #14583060C2semidirect
10. #14583049C2semidirect
11. #14583002C2semidirect
12. #14582970C2semidirect
13. #14582899C2semidirect
14. C2×#13063247C2semidirect
15. C43×#467C2semidirect
20. C2×#10621872C22semidirect
21. #13063324C22semidirect
27. #13063301C22semidirect
31. Q8×Dic43C22semidirect
36. C4⋊C4×D43C22semidirect
38. #13063258C22semidirect
39. #13063258C22semidirect
40. Dic43⋊C8C22semidirect
41. #13063249C22semidirect
42. #13063249C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. #13063235C22semidirect
52. C2×Q16×C43C22semidirect
56. #107×C43C22semidirect
57. #103×C43C22semidirect
58. #103×C43C22semidirect
195. #467D43semidirect
203. C43#3314semidirect
206. C2×Q16C2×D43semidirect
232. #107C2×D43semidirect
236. #103C2×D43semidirect
237. #103C2×D43semidirect