Finite Group Databasebeta

← #19146589

Subgroups — #19146589

Order 5504.

420 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#14583559C211yesmaximal, characteristic, complemented
2#14583550C211yesmaximal, characteristic, complemented
3#14583260C211yesmaximal, characteristic, complemented
4#14583214C211yesmaximal, characteristic, complemented
5#14583193C211yesmaximal, characteristic, complemented
6#14583147C211yesmaximal, characteristic, complemented
7#14583136C211yesmaximal, characteristic, complemented
8#14583117C211yesmaximal, characteristic, complemented
9#14583046C211yesmaximal, characteristic, complemented
10#14583039C211yesmaximal, characteristic, complemented
11#14582998C211yesmaximal, characteristic, complemented
12#14582973C211yesmaximal, characteristic, complemented
13#14582898C211yesmaximal, characteristic, complemented
14#103×D43C211yesmaximal, characteristic, complemented
15C43×#484C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621898C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×D344C2211yescharacteristic
22C2×#10621877C2211yescharacteristic
23C2×C8×D43C2211yescharacteristic
24#13063324C2211yescharacteristic
25#13063314C2211yescharacteristic
26#13063311—21no—
27#13063310—21no—
28#13063308—21no—
29#13063303—21no—
30#13063303—21no—
31#13063300C2211yescharacteristic
32#13063300C2211yescharacteristic
33#13063299C2211yescharacteristic
34#13063298—21no—
35#13063290C2211yescharacteristic
36#13063287—21no—
37#13063287C2211yescharacteristic
38C4×C22⋊D43C2211yescharacteristic
39C4⋊C4×D43C2211yescharacteristic
40#13063258C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C22×C4×C43—21no—
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43D411yescharacteristic
65Q8×D43—22no—
66Q8×D43—41no—
67#10621898—22no—
68#10621898—41no—
69#10621898—44no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172C2311yescharacteristic
73C2×D172C2311yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×Dic86—21no—
80C2×Dic86—21no—
81C2×Dic86C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C22⋊Dic43D411yescharacteristic
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)⋊C4—21no—
98(C2×D43)⋊C4D411yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic
106#10621877—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109D344—41no—
110#10621873—22no—
111C8×D43—41no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43C2×D411yescharacteristic
116Q8×C43—21no—
117Q8×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—42no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—22no—
128C22⋊D43—42no—
129C22⋊D43—42no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—21no—
136D172—21no—
137D172—21no—
138D172—21no—
139D172—42no—
140D172—42no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—42no—
144C4×D43—42no—
145C4×D43—42no—
146C4×D43—42no—
147Dic86—21no—
148Dic86—42no—
149Dic86—42no—
150Dic86#4112yescomplemented
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43C22×D411yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43AGL(1,ℤ/8)12yes—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43C2×#4111yescharacteristic
174C4×C43H(5,𝔽2)11yescharacteristic
175Dic43—22no—
176Dic43—21no—
177Dic43—21no—
178Dic43—21no—
179Dic43—41no—
180#3308—431nomaximal, Sylow
181C2×C43—41no—
182C2×C43#54611yescharacteristic
183C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C43#57811yescharacteristic
185D43—22no—
186D43—81no—
187D43—81no—
188#548—431no—
189#547—431no—
190#489—431no—
191#484D4311yescharacteristic, complemented
192#480—431no—
193#477—431no—
194#468—431no—
195#466—431no—
196#463—431no—
197#449—431no—
198#448—431no—
199#440—431no—
200#435—431no—
201#417—431no—
202C2×#103—431no—
203C43#330811yescharacteristic, complemented, Sylow
204C2×#41—431no—
205C2×#41—861no—
206C22×Q8—431no—
207C2×SD16—431no—
208C2×SD16—431no—
209C2×D8—431no—
210C2×M16—431no—
211C22×C8—431no—
212C4⋊Q8—431no—
213#124—431no—
214#124—861no—
215#123—861no—
216#123—861no—
217C22⋊Q8—861no—
218C22⋊Q8—861no—
219C22⋊Q8C2×D4311yescharacteristic
220#121—431no—
221#121—431no—
222#121—431no—
223#121—861no—
224C4×Q8—431no—
225C4×D4—431no—
226C4×D4—431no—
227C4×D4—861no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4C2×D4311yescharacteristic
230#107—431no—
231#107C2×D4311yescharacteristic
232#107C2×D4311yescharacteristic
233C4⋊C8—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#103—431no—
238#103C2×D4311yescharacteristic
239#103C2×D4311yescharacteristic
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244C22⋊C8—431no—
245C22⋊C8C2×D4311yescharacteristic
246#97—431no—
247#41—862no—
248#41—1721no—
249#41—1724no—
250C2×Q8—431no—
251C2×Q8—861no—
252C2×Q8—861no—
253C2×Q8—862no—
254C2×Q8—1721no—
255C2×Q8C22×D4311yescharacteristic
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C22×C4—21no—
264C22×C4—431no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4C22×D4311yescharacteristic
270SD16—862no—
271SD16—1721no—
272D8—1721no—
273M16—1721no—
274C2×C8—431no—
275C2×C8—431no—
276C2×C8—1721no—
277C2×C8C22×D4311yescharacteristic
278C2×C8C22×D4311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—431no—
282C4⋊C4—431no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—431no—
291C22⋊C4—431no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C42—431no—
299C42—861no—
300C23—431no—
301C23—861no—
302C23—861no—
303C23D4×D4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—432no—
307Q8—861no—
308Q8—1722no—
309Q8—1722no—
310D4—862no—
311D4—861no—
312D4—861no—
313D4—861no—
314D4—861no—
315D4—1722no—
316D4—1722no—
317D4—1722no—
318D4—1722no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—431no—
327C2×C4—431no—
328C2×C4—431no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4D4×D4311yescharacteristic
338C2×C4C23×D4311yescharacteristic
339C8—21no—
340C8—21no—
341C8—861no—
342C8—861no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—432no—
347C22—861no—
348C22—861no—
349C22—1721no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22—1721no—
354C22—1721no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—861no—
362C4—861no—
363C4—861no—
364C4—862no—
365C4—1721no—
366C4#41×D4311yescharacteristic
367C4#1306337111yescharacteristic
368C2—41no—
369C2—862no—
370C2—3441no—
371C2—3441no—
372C2#1458354111yescharacteristic
373C2AGL(1,ℤ/8)×D4311yescharacteristic
374C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#484C2
socleC22×C43C22×D4
hypercenter#484D43
hypocenterC43#3308
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #14583559C2semidirect
2. #14583550C2semidirect
3. #14583260C2semidirect
4. #14583214C2semidirect
5. #14583193C2semidirect
6. #14583147C2semidirect
7. #14583136C2semidirect
8. #14583117C2semidirect
9. #14583046C2semidirect
10. #14583039C2semidirect
11. #14582998C2semidirect
12. #14582973C2semidirect
13. #14582898C2semidirect
14. #103×D43C2semidirect
15. C43×#484C2semidirect
150. Dic86#41semidirect
191. #484D43semidirect
203. C43#3308semidirect