Finite Group Databasebeta

← #19145603

Subgroups — #19145603

Order 5504.

390 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#14583451C211yesmaximal, characteristic, complemented
2#14583445C211yesmaximal, characteristic
3#14583292C211yesmaximal, characteristic, complemented
4#14583290C211yesmaximal, characteristic, complemented
5#14583260C211yesmaximal, characteristic, complemented
6#14583257C211yesmaximal, characteristic, complemented
7#14583108C211yesmaximal, characteristic, complemented
8#14583107C211yesmaximal, characteristic, complemented
9#14583098C211yesmaximal, characteristic, complemented
10#14583097C211yesmaximal, characteristic, complemented
11#14583063C211yesmaximal, characteristic, complemented
12#14583061C211yesmaximal, characteristic, complemented
13#14583059C211yesmaximal, characteristic, complemented
14#14582953C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23#13063324C2211yescharacteristic
24#13063323C2211yescharacteristic
25#13063323C2211yescharacteristic
26#13063321C2211yescharacteristic
27#13063315—21no—
28#13063314C2211yescharacteristic
29#13063312C2211yescharacteristic
30#13063304C2211yescharacteristic
31#13063302—21no—
32#13063297—21no—
33#13063297—21no—
34Q8×Dic43C2211yescharacteristic
35#13063290—21no—
36#13063290C2211yescharacteristic
37C4×C22⋊D43—21no—
38C4×C22⋊D43—21no—
39#13063281—21no—
40C2×C4×Dic43C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic
51#13063235C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C2×Q16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59#41×C43—41no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C22×Dic43D411yescharacteristic
71C22×Dic43D411yescharacteristic
72#10621898—41no—
73#10621898—41no—
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×Dic86—21no—
77C2×Dic86C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79Q16×C43—41no—
80SD16×C43—41no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89#10621885—41no—
90#10621885—41no—
91#10621884—41no—
92#10621883—41no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43D411yescharacteristic
107C4×Dic43D411yescharacteristic
108C4×Dic43C2311yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112Dic172—41no—
113#10621873—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—21no—
117Q8×C43—21no—
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—42no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—42no—
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—42no—
133C22⋊D43—42no—
134C22⋊D43—42no—
135C2×Dic43—22no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—41no—
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144D172—21no—
145D172—21no—
146C4×D43—42no—
147Dic86—21no—
148Dic86—21no—
149Dic86—21no—
150Dic86—21no—
151Dic86—42no—
152C8×C43—21no—
153C8×C43—21no—
154C43⋊C8—21no—
155C43⋊C8—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43C22×D411yescharacteristic
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43H(5,𝔽2)11yescharacteristic
171C4×C43H(5,𝔽2)11yescharacteristic
172Dic43—21no—
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178Dic43#13712yes—
179#3216—431nomaximal, Sylow
180C2×C43—41no—
181C2×C43—81no—
182C2×C43#53511yescharacteristic
183C2×C43C2×#13711yescharacteristic
184C2×C43#57511yescharacteristic
185D43—81no—
186#533—431no—
187#532—431no—
188#497—431no—
189#497—431no—
190#489—431no—
191#489—431no—
192#462—431no—
193#462—431no—
194#460—431no—
195#460—431no—
196#452—431no—
197#452—431no—
198#452—431no—
199#452D4311yescharacteristic, complemented
200#432—431no—
201C43#321611yescharacteristic, complemented, Sylow
202C2×#41—431no—
203C2×#41C2×D4311yescharacteristic
204C2×Q16—431no—
205C2×Q16—431no—
206C2×Q16—431no—
207C2×Q16C2×D4311yescharacteristic
208C2×SD16—431no—
209C2×SD16—431no—
210C2×SD16—431no—
211C2×SD16C2×D4311yescharacteristic
212C4⋊Q8—431no—
213C4⋊Q8—431no—
214C4⋊Q8—431no—
215#127—431no—
216#125—861no—
217#124—431no—
218#124—431no—
219C22⋊Q8—431no—
220C22⋊Q8—861no—
221C22⋊Q8C2×D4311yescharacteristic
222#121—861no—
223#121—861no—
224C4×Q8—431no—
225C4×Q8—431no—
226C4×Q8—861no—
227C4×D4—861no—
228C4×D4—861no—
229#117—861no—
230C2×C42—431no—
231C4⋊C8—431no—
232C4⋊C8—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103C2×D4311yescharacteristic
237#102—431no—
238#102—431no—
239#102—431no—
240#102C2×D4311yescharacteristic
241C22⋊C8—431no—
242C22⋊C8C2×D4311yescharacteristic
243#97—431no—
244#97—431no—
245#41—41no—
246#41—41no—
247#41—1721no—
248#41—1721no—
249C2×Q8—431no—
250C2×Q8—431no—
251C2×Q8—861no—
252C2×Q8C22×D4311yescharacteristic
253C2×Q8C22×D4311yescharacteristic
254C2×D4—21no—
255C2×D4—431no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4C22×D4311yescharacteristic
260C22×C4—21no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—861no—
264C22×C4C22×D4311yescharacteristic
265Q16—41no—
266Q16—1721no—
267Q16—1721no—
268Q16—1721no—
269SD16—41no—
270SD16—1721no—
271SD16—1721no—
272SD16—1721no—
273C2×C8—431no—
274C2×C8—431no—
275C2×C8C22×D4311yescharacteristic
276C2×C8C22×D4311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—431no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—431no—
295C42—431no—
296C42—431no—
297C42—431no—
298C42—861no—
299C42—861no—
300C23—21no—
301C23—861no—
302C23D4×D4311yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—861no—
308Q8—861no—
309Q8—861no—
310Q8—861no—
311Q8—1722no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—861no—
316D4—861no—
317D4—1722no—
318D4—1722no—
319D4—1722no—
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—431no—
330C2×C4—862no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—1722no—
335C2×C4—1721no—
336C2×C4D4×D4311yescharacteristic
337C2×C4C23×D4311yescharacteristic
338C8—21no—
339C8—21no—
340C8—861no—
341C8—861no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—1721no—
349C22—1721no—
350C22—1721no—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—432no—
357C4—861no—
358C4—861no—
359C4—861no—
360C4—1721no—
361C4—1721no—
362C4—1721no—
363C4#1306337011yescharacteristic
364C4#1306337011yescharacteristic
365C2—41no—
366C2—81no—
367C2—3441no—
368C2#1458346411yescharacteristic
369C2#137×D4311yescharacteristic
370C2#1458369611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3216
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #14583451C2semidirect
3. #14583292C2semidirect
4. #14583290C2semidirect
5. #14583260C2semidirect
6. #14583257C2semidirect
7. #14583108C2semidirect
8. #14583107C2semidirect
9. #14583098C2semidirect
10. #14583097C2semidirect
11. #14583063C2semidirect
12. #14583061C2semidirect
13. #14583059C2semidirect
14. #14582953C2semidirect
15. C43×#452C2semidirect
199. #452D43semidirect
201. C43#3216semidirect