Finite Group Databasebeta

← #19147616

Subgroups — #19147616

Order 5504.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583621C211yesmaximal, characteristic, complemented
2#14583570C211yesmaximal, characteristic, complemented
3#14583288C211yesmaximal, characteristic, complemented
4#14583285C211yesmaximal, characteristic, complemented
5#14583270C211yesmaximal, characteristic, complemented
6#14583117C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic, complemented
8#14583103C211yesmaximal, characteristic, complemented
9#14583099C211yesmaximal, characteristic, complemented
10#14583098C211yesmaximal, characteristic, complemented
11#14583093C211yesmaximal, characteristic, complemented
12#14583027C211yesmaximal, characteristic, complemented
13#14582998C211yesmaximal, characteristic, complemented
14#14582981C211yesmaximal, characteristic, complemented
15C43×#440C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621873C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×#10621884C2211yescharacteristic
22C2×D344C2211yescharacteristic
23C2×D344C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25#13063323C2211yescharacteristic
26#13063322C2211yescharacteristic
27#13063321C2211yescharacteristic
28#13063321C2211yescharacteristic
29#13063320—21no—
30#13063319—21no—
31#13063314C2211yescharacteristic
32#13063313C2211yescharacteristic
33#13063303—21no—
34#13063299—21no—
35#13063298—21no—
36#13063298—21no—
37C4×Dic86C2211yescharacteristic
38#13063290C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063287C2211yescharacteristic
41#13063287C2211yescharacteristic
42#13063282—21no—
43C4⋊(C43⋊C8)C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66#10621898—44no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172C2311yescharacteristic
70C2×D172C2311yescharacteristic
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×Dic86D411yescharacteristic
76C2×Dic86C2311yescharacteristic
77SD16×C43—22no—
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C42×C43—21no—
85C42×C43C2311yescharacteristic
86#10621884—41no—
87#10621884—41no—
88#10621883—41no—
89#10621882—41no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
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—
97C4⋊Dic43D411yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108D344—22no—
109D344—41no—
110#10621873—22no—
111#10621873—41no—
112C23×C43—21no—
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—42no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—42no—
128C22⋊D43—42no—
129C22⋊D43—81no—
130C22⋊D43—81no—
131C2×Dic43—21no—
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136D172—21no—
137D172—21no—
138D172—21no—
139D172—21no—
140D172—21no—
141D172—21no—
142D172—42no—
143D172—81no—
144C4×D43—42no—
145C4×D43—42no—
146C4×D43—42no—
147Dic86—22no—
148Dic86—21no—
149Dic86—21no—
150C8×C43—21no—
151C8×C43#4112yescomplemented
152C43⋊C8—21no—
153C43⋊C8—21no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43C22×D411yescharacteristic
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43C2×#4111yescharacteristic
173C4×C43H(5,𝔽2)11yescharacteristic
174Dic43—21no—
175Dic43—21no—
176Dic43—21no—
177Dic43—41no—
178Dic43AGL(1,ℤ/8)12yes—
179#3397—431nomaximal, Sylow
180C2×C43—81no—
181C2×C43#55011yescharacteristic
182C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C43#57711yescharacteristic
184D43—81no—
185D43—81no—
186D43—81no—
187#556—431no—
188#550—431no—
189#496—431no—
190#496—431no—
191#492—431no—
192#463—431no—
193#463—431no—
194#461—431no—
195#460—431no—
196#460—431no—
197#459—431no—
198#446—431no—
199#440—431no—
200#440D4311yescharacteristic, complemented
201C4×D8—431no—
202C43#339711yescharacteristic, complemented, Sylow
203C2×#41—861no—
204C2×SD16—431no—
205C2×SD16—431no—
206C2×SD16—431no—
207C2×SD16—431no—
208C2×SD16—431no—
209C2×SD16C2×D4311yescharacteristic
210C2×D8—431no—
211C2×D8—431no—
212C2×D8—431no—
213C4⋊Q8—431no—
214#127—431no—
215#127—431no—
216#127—431no—
217#126—861no—
218#126—861no—
219#124—431no—
220#124—431no—
221C22⋊Q8—861no—
222#121—861no—
223#121—861no—
224#121—861no—
225C4×Q8—431no—
226C4×Q8—431no—
227C4×Q8C2×D4311yescharacteristic
228C4×D4—431no—
229C4×D4—431no—
230C4×D4—431no—
231C4×D4C2×D4311yescharacteristic
232#117—861no—
233#107C2×D4311yescharacteristic
234C4⋊C8—431no—
235C4⋊C8—431no—
236C4⋊C8—431no—
237#103—431no—
238#103C2×D4311yescharacteristic
239#102—431no—
240#102—431no—
241#102—431no—
242#102C2×D4311yescharacteristic
243#97—431no—
244#97C2×D4311yescharacteristic
245C4×C8—431no—
246#41—1724no—
247C2×Q8—431no—
248C2×Q8—431no—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—431no—
251C2×D4—431no—
252C2×D4—431no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4C22×D4311yescharacteristic
260C22×C4—21no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264SD16—22no—
265SD16—862no—
266SD16—1721no—
267SD16—1721no—
268SD16—1721no—
269SD16—1721no—
270D8—862no—
271D8—1721no—
272D8—1721no—
273C2×C8—431no—
274C2×C8—431no—
275C2×C8C22×D4311yescharacteristic
276C2×C8C22×D4311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—431no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4C22×D4311yescharacteristic
285C4⋊C4C22×D4311yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—21no—
295C42—431no—
296C42—431no—
297C42—861no—
298C42C22×D4311yescharacteristic
299C23—21no—
300C23—861no—
301C23—861no—
302C23—861no—
303Q8—21no—
304Q8—21no—
305Q8—862no—
306Q8—861no—
307Q8—861no—
308D4—21no—
309D4—21no—
310D4—861no—
311D4—861no—
312D4—861no—
313D4—861no—
314D4—861no—
315D4—861no—
316D4—3441no—
317D4—3441no—
318D4—3441no—
319D4—1722no—
320D4—1722no—
321D4—1722no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—431no—
327C2×C4—431no—
328C2×C4—431no—
329C2×C4—431no—
330C2×C4—861no—
331C2×C4—1722no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4D4×D4311yescharacteristic
335C2×C4D4×D4311yescharacteristic
336C2×C4C23×D4311yescharacteristic
337C8—21no—
338C8—861no—
339C8—861no—
340C8#1062189812yescomplemented
341C22—41no—
342C22—41no—
343C22—41no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22—1721no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22C2×D4×D4311yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—432no—
360C4—861no—
361C4—861no—
362C4—861no—
363C4—1721no—
364C4C2×#1062189811yescharacteristic
365C4#1306337111yescharacteristic
366C2—81no—
367C2—3441no—
368C2—3441no—
369C2—3441no—
370C2#1458357011yescharacteristic
371C2AGL(1,ℤ/8)×D4311yescharacteristic
372C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#440C2
socleC22×C43C22×D4
hypercenter#440D43
hypocenterC43#3397
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14583621C2semidirect
2. #14583570C2semidirect
3. #14583288C2semidirect
4. #14583285C2semidirect
5. #14583270C2semidirect
6. #14583117C2semidirect
7. #14583114C2semidirect
8. #14583103C2semidirect
9. #14583099C2semidirect
10. #14583098C2semidirect
11. #14583093C2semidirect
12. #14583027C2semidirect
13. #14582998C2semidirect
14. #14582981C2semidirect
15. C43×#440C2semidirect
151. C8×C43#41semidirect
200. #440D43semidirect
202. C43#3397semidirect
340. C8#10621898semidirect