Finite Group Databasebeta

← #19145652

Subgroups — #19145652

Order 5504.

388 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583502C211yesmaximal, characteristic, complemented
2#14583473C211yesmaximal, characteristic, complemented
3#14583285C211yesmaximal, characteristic, complemented
4#14583270C211yesmaximal, characteristic, complemented
5#14583266C211yesmaximal, characteristic, complemented
6#14583255C211yesmaximal, characteristic, complemented
7#14583117C211yesmaximal, characteristic, complemented
8#14583116C211yesmaximal, characteristic, complemented
9#14583103C211yesmaximal, characteristic, complemented
10#14583102C211yesmaximal, characteristic, complemented
11#14583046C211yesmaximal, characteristic, complemented
12#14583042C211yesmaximal, characteristic, complemented
13#14583038C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#448C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×D344C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23#13063323C2211yescharacteristic
24#13063323C2211yescharacteristic
25#13063321C2211yescharacteristic
26#13063316C2211yescharacteristic
27#13063314C2211yescharacteristic
28#13063314C2211yescharacteristic
29#13063309—21no—
30#13063308—21no—
31#13063308—21no—
32#13063307—21no—
33#13063301—21no—
34#13063301—21no—
35#13063299C2211yescharacteristic
36#13063297—21no—
37#13063296—21no—
38D4×Dic43C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063284C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C22×Q8×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43—21no—
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C22×Dic43—21no—
73#10621898—41no—
74#10621898—41no—
75C2×D172C2311yescharacteristic
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×Dic86C2311yescharacteristic
80SD16×C43—41no—
81SD16×C43—41no—
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43D411yescharacteristic
88C22⋊Dic43D411yescharacteristic
89#10621884—41no—
90#10621884—41no—
91#10621883—41no—
92#10621882—41no—
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)⋊C4—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43D411yescharacteristic
101C4⋊Dic43D411yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108C4×Dic43C2311yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112D344—41no—
113#10621873—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—21no—
117C22×D43—21no—
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122Q8×C43—42no—
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—81no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—42no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—42no—
135C22⋊D43—81no—
136C22⋊D43—81no—
137C22⋊D43—81no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—81no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144C2×Dic43C2×D411yescharacteristic
145D172—21no—
146D172—21no—
147D172—21no—
148D172—21no—
149C4×D43—42no—
150C4×D43—81no—
151Dic86—21no—
152Dic86—21no—
153C8×C43—21no—
154C8×C43—21no—
155C43⋊C8—21no—
156C43⋊C8—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43C22×D411yescharacteristic
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C4×C43—21no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43H(5,𝔽2)11yescharacteristic
175C4×C43H(5,𝔽2)11yescharacteristic
176Dic43—21no—
177Dic43—21no—
178Dic43—21no—
179Dic43—21no—
180Dic43—41no—
181Dic43—41no—
182#3221—431nomaximal, Sylow
183C2×C43—41no—
184C2×C43—81no—
185C2×C43#53511yescharacteristic
186C2×C43#57711yescharacteristic
187C2×C43#57711yescharacteristic
188D43—81no—
189D43—81no—
190#540—431no—
191#536—431no—
192#496—431no—
193#492—431no—
194#491—431no—
195#488—431no—
196#463—431no—
197#463—431no—
198#461—431no—
199#461—431no—
200#449—431no—
201#449—431no—
202#448—431no—
203#448D4311yescharacteristic, complemented
204#433—431no—
205C43#322111yescharacteristic, complemented, Sylow
206C2×#41—431no—
207C22×Q8C2×D4311yescharacteristic
208C2×SD16—431no—
209C2×SD16—431no—
210C2×SD16—431no—
211C2×SD16—431no—
212C2×SD16C2×D4311yescharacteristic
213C2×SD16C2×D4311yescharacteristic
214C2×D8—431no—
215C2×D8—431no—
216C4⋊Q8—431no—
217C4⋊Q8—431no—
218#127—431no—
219#125—431no—
220#124—431no—
221#124—431no—
222#123—861no—
223#123—861no—
224#123—861no—
225#123—861no—
226C22⋊Q8—861no—
227C22⋊Q8—861no—
228#121—431no—
229#121—861no—
230#121—861no—
231#121C2×D4311yescharacteristic
232C4×D4—431no—
233C4×D4—431no—
234#117—431no—
235C4⋊C8—431no—
236C4⋊C8—431no—
237#103—431no—
238#103—431no—
239#103—431no—
240#103—431no—
241#103C2×D4311yescharacteristic
242#103C2×D4311yescharacteristic
243#102—431no—
244#102—431no—
245C22⋊C8—431no—
246C22⋊C8C2×D4311yescharacteristic
247#97—431no—
248C4×C8—431no—
249#41—1721no—
250#41—1721no—
251C2×Q8—21no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—431no—
255C2×Q8C22×D4311yescharacteristic
256C2×Q8C22×D4311yescharacteristic
257C2×D4—21no—
258C2×D4—431no—
259C2×D4—431no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4C22×D4311yescharacteristic
265C22×C4—21no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4C22×D4311yescharacteristic
270SD16—41no—
271SD16—41no—
272SD16—1721no—
273SD16—1721no—
274SD16—1721no—
275SD16—1721no—
276D8—1721no—
277D8—1721no—
278C2×C8—431no—
279C2×C8—431no—
280C2×C8C22×D4311yescharacteristic
281C2×C8C22×D4311yescharacteristic
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—431no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4—861no—
291C4⋊C4C22×D4311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—431no—
294C22⋊C4—431no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C42—431no—
303C42—431no—
304C23—21no—
305C23—861no—
306C23—861no—
307C23D4×D4311yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—42no—
313Q8—861no—
314Q8—861no—
315D4—21no—
316D4—21no—
317D4—81no—
318D4—861no—
319D4—861no—
320D4—861no—
321D4—861no—
322D4—3441no—
323D4—3441no—
324D4—3441no—
325D4—1722no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—431no—
335C2×C4—431no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—3441no—
339C2×C4—3441no—
340C2×C4—1722no—
341C2×C4D4×D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—861no—
346C8—861no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—1721no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22C2×D4×D4311yescharacteristic
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—861no—
365C4—861no—
366C4—861no—
367C4—861no—
368C4—1721no—
369C4—1721no—
370C4#1306337011yescharacteristic
371C4#1306337011yescharacteristic
372C2—41no—
373C2—81no—
374C2—3441no—
375C2—3441no—
376C2#1458346411yescharacteristic
377C2#1458370511yescharacteristic
378C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#448C2
socleC22×C43C22×D4
hypercenter#448D43
hypocenterC43#3221
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #14583502C2semidirect
2. #14583473C2semidirect
3. #14583285C2semidirect
4. #14583270C2semidirect
5. #14583266C2semidirect
6. #14583255C2semidirect
7. #14583117C2semidirect
8. #14583116C2semidirect
9. #14583103C2semidirect
10. #14583102C2semidirect
11. #14583046C2semidirect
12. #14583042C2semidirect
13. #14583038C2semidirect
14. #14582957C2semidirect
15. C43×#448C2semidirect
203. #448D43semidirect
205. C43#3221semidirect