Finite Group Databasebeta

← #19146679

Subgroups — #19146679

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#14583604C211yesmaximal, characteristic, complemented
2#14583546C211yesmaximal, characteristic
3#14583257C211yesmaximal, characteristic, complemented
4#14583236C211yesmaximal, characteristic, complemented
5#14583178C211yesmaximal, characteristic, complemented
6#14583143C211yesmaximal, characteristic, complemented
7#14583141C211yesmaximal, characteristic, complemented
8#14583120C211yesmaximal, characteristic, complemented
9#14583063C211yesmaximal, characteristic, complemented
10#14583051C211yesmaximal, characteristic, complemented
11#14582998C211yesmaximal, characteristic, complemented
12#14582973C211yesmaximal, characteristic, complemented
13#14582898C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#480C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×Dic172C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621877C2211yescharacteristic, complemented
22C2×C8×D43C2211yescharacteristic
23#13063324C2211yescharacteristic, complemented
24#13063315—21no—
25#13063312C2211yescharacteristic
26#13063307—21no—
27#13063305C2211yescharacteristic
28#13063305C2211yescharacteristic
29#13063304—21no—
30#13063304C2211yescharacteristic, complemented
31#13063303—21no—
32#13063296—21no—
33#13063293—21no—
34#13063290C2211yescharacteristic, complemented
35#13063287C2211yescharacteristic
36C4×C22⋊D43—21no—
37C4×C22⋊D43C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic
39C22⋊C4×D43—21no—
40#13063258C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063248C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic, complemented
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic, complemented
54#107×C43C2211yescharacteristic, complemented
55#107×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43D411yescharacteristic
67D4×D43—22no—
68D4×D43—41no—
69#10621898—22no—
70#10621898—41no—
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43C2311yescharacteristic
76C2×Dic86—21no—
77C2×Dic86C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621883—41no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105#10621877—41no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108Dic172—41no—
109#10621873—22no—
110C8×D43—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—81no—
117C22×D43C2×D411yescharacteristic
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—81no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—81no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—22no—
130C22⋊D43—42no—
131C22⋊D43—42no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138D172—21no—
139D172#4112yes—
140C4×D43—21no—
141C4×D43—21no—
142C4×D43—42no—
143C4×D43—81no—
144C4×D43—81no—
145Dic86—21no—
146Dic86—21no—
147Dic86—21no—
148Dic86—21no—
149Dic86—81no—
150C8×C43—21no—
151C8×C43—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—22no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—84no—
167C2×D43#13712yes—
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—
178Dic43—41no—
179Dic43—41no—
180#3314—431nomaximal, Sylow
181C2×C43—41no—
182C2×C43—81no—
183C2×C43#54611yescharacteristic
184C2×C43C2×#13711yescharacteristic
185C2×C43#57611yescharacteristic
186D43—22no—
187D43—42no—
188#554—431no—
189#546—431no—
190#489—431no—
191#484—431no—
192#480D4311yescharacteristic, complemented
193#474—431no—
194#468—431no—
195#467—431no—
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×Q16—431no—
207C2×SD16—431no—
208C2×SD16—431no—
209C2×M16—431no—
210C22×C8—431no—
211C4⋊Q8—431no—
212#125—861no—
213#124—431no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—431no—
218C22⋊Q8—861no—
219C22⋊Q8—861no—
220#121—861no—
221#121C2×D4311yescharacteristic
222#120—861no—
223C4×Q8—431no—
224C4×D4—431no—
225C4×D4—431no—
226C4×D4—861no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4C2×D4311yescharacteristic, complemented
229C2×C22⋊C4—861no—
230#107—431no—
231#107C2×D4311yescharacteristic, complemented
232#107C2×D4311yescharacteristic, complemented
233C4⋊C8—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#103—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102C2×D4311yescharacteristic
243#102C2×D4311yescharacteristic
244C22⋊C8—431no—
245C22⋊C8C2×D4311yescharacteristic, complemented
246#97—431no—
247C24—861no—
248#41—862no—
249#41—1721no—
250C2×Q8—431no—
251C2×Q8—431no—
252C2×Q8—861no—
253C2×D4—21no—
254C2×D4—431no—
255C2×D4—431no—
256C2×D4—861no—
257C2×D4—862no—
258C2×D4—861no—
259C2×D4—1721no—
260C2×D4C22×D4311yescharacteristic
261C22×C4—21no—
262C22×C4—431no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4C22×D4311yescharacteristic
267Q16—1721no—
268SD16—862no—
269SD16—1721no—
270M16—1721no—
271C2×C8—431no—
272C2×C8—431no—
273C2×C8—1721no—
274C2×C8C22×D4311yescharacteristic
275C2×C8C22×D4311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—431no—
278C4⋊C4—431no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4C22×D4311yescharacteristic
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—431no—
290C22⋊C4—431no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C42—431no—
298C42—861no—
299C23—21no—
300C23—431no—
301C23—861no—
302C23—3441no—
303C23—1722no—
304C23—1722no—
305C23D4×D4311yescharacteristic
306Q8—861no—
307Q8—861no—
308Q8—861no—
309Q8—861no—
310Q8—3441no—
311D4—21no—
312D4—21no—
313D4—81no—
314D4—432no—
315D4—862no—
316D4—861no—
317D4—1722no—
318D4—1722no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—81no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—431no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
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—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—432no—
349C22—861no—
350C22—861no—
351C22—862no—
352C22—3444no—
353C22—1721no—
354C22—1721no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—861no—
361C4—861no—
362C4—861no—
363C4—1721no—
364C4—1721no—
365C4—1721no—
366C4#41×D4311yescharacteristic
367C4#1306337111yescharacteristic
368C2—41no—
369C2—81no—
370C2—862no—
371C2—1722no—
372C2#1458354111yescharacteristic
373C2#137×D4311yescharacteristic
374C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#480C2
socleC22×C43C22×D4
hypercenter#480D43
hypocenterC43#3314
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14583604C2semidirect
3. #14583257C2semidirect
4. #14583236C2semidirect
5. #14583178C2semidirect
6. #14583143C2semidirect
7. #14583141C2semidirect
8. #14583120C2semidirect
9. #14583063C2semidirect
10. #14583051C2semidirect
11. #14582998C2semidirect
12. #14582973C2semidirect
13. #14582898C2semidirect
14. #102×D43C2semidirect
15. C43×#480C2semidirect
18. C2×Dic172C22semidirect
21. C2×#10621877C22semidirect
23. #13063324C22semidirect
30. #13063304C22semidirect
34. #13063290C22semidirect
40. #13063258C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063250C22semidirect
43. #13063248C22semidirect
44. #13063248C22semidirect
45. #13063248C22semidirect
51. #13063235C22semidirect
53. C2×C4⋊C4×C43C22semidirect
54. #107×C43C22semidirect
55. #107×C43C22semidirect
58. C22⋊C8×C43C22semidirect
192. #480D43semidirect
203. C43#3314semidirect
228. C2×C4⋊C4C2×D43semidirect
231. #107C2×D43semidirect
232. #107C2×D43semidirect
245. C22⋊C8C2×D43semidirect