Finite Group Databasebeta

← #19146112

Subgroups — #19146112

Order 5504.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063358C211yesmaximal, characteristic, complemented
2C2×SD16×D43C211yesmaximal, characteristic, complemented
3#14583562C211yesmaximal, characteristic, complemented
4#14583546C211yesmaximal, characteristic
5#14583290C211yesmaximal, characteristic, complemented
6#14583141C211yesmaximal, characteristic, complemented
7#14583120C211yesmaximal, characteristic, complemented
8#14583103C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583056C211yesmaximal, characteristic, complemented
11#14583051C211yesmaximal, characteristic, complemented
12#14583037C211yesmaximal, characteristic, complemented
13#14582998C211yesmaximal, characteristic, complemented
14#14582968C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic, complemented
18C2×Q8×D43C2211yescharacteristic
19C2×D4×D43C2211yescharacteristic
20#13063358—24no—
21C2×Dic172C2211yescharacteristic, complemented
22C2×Dic172C2211yescharacteristic, complemented
23C2×#10621885C2211yescharacteristic, complemented
24C2×#10621873C2211yescharacteristic
25C2×#10621873C2211yescharacteristic
26C2×#10621883C2211yescharacteristic
27C2×#10621883C2211yescharacteristic
28C2×#10621884C2211yescharacteristic
29SD16×D43—24no—
30C2×C8×D43C2211yescharacteristic
31#13063324—21no—
32#13063323C2211yescharacteristic, complemented
33#13063312C2211yescharacteristic
34#13063307—21no—
35#13063305C2211yescharacteristic
36#13063305C2211yescharacteristic
37#13063303—21no—
38#13063302—21no—
39#13063296—21no—
40#13063293—21no—
41#13063290C2211yescharacteristic, complemented
42#13063287C2211yescharacteristic
43C4×C22⋊D43C2211yescharacteristic
44(C22⋊D43)⋊C4—21no—
45C22⋊C4×D43—21no—
46Dic43⋊C8C2211yescharacteristic, complemented
47#13063248C2211yescharacteristic, complemented
48#13063248C2211yescharacteristic, complemented
49#13063248C2211yescharacteristic, complemented
50#13063245C2211yescharacteristic
51C22⋊(C43⋊C8)C2211yescharacteristic, complemented
52(C2×D43)⋊C8C2211yescharacteristic
53#13063235C2211yescharacteristic, complemented
54C2×SD16×C43C2211yescharacteristic
55C2×M16×C43C2211yescharacteristic, complemented
56C22⋊Q8×C43C2211yescharacteristic, complemented
57#121×C43C2211yescharacteristic
58#107×C43C2211yescharacteristic, complemented
59#103×C43C2211yescharacteristic, complemented
60#102×C43C2211yescharacteristic
61C23×D43—21no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43D411yescharacteristic
69C22×Dic43—21no—
70Q8×D43—22no—
71Q8×D43—41no—
72D4×D43—22no—
73D4×D43—41no—
74#10621898—22no—
75#10621898—41no—
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43C2311yescharacteristic
81C2×Dic86—22no—
82C2×Dic86—21no—
83C2×Dic86—21no—
84C2×Dic86—41no—
85C2×Dic86C2311yescharacteristic
86C2×Dic86C2311yescharacteristic
87C2×Dic86C2311yescharacteristic
88SD16×C43—22no—
89M16×C43—22no—
90C2×C8×C43C2311yescharacteristic
91C2×C8×C43C2311yescharacteristic
92C4⋊C4×C43—21no—
93C4⋊C4×C43C2311yescharacteristic
94C4⋊C4×C43C2311yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊Dic43—21no—
98C22⋊Dic43—21no—
99C22⋊Dic43D411yescharacteristic
100#10621885—41no—
101#10621884—22no—
102#10621883—22no—
103#10621883—41no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4D411yescharacteristic
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113Dic43⋊C4D411yescharacteristic
114C4×Dic43—21no—
115C4×Dic43C2311yescharacteristic
116C2×C43⋊C8C2311yescharacteristic
117C2×C43⋊C8C2311yescharacteristic
118Dic172—22no—
119Dic172—22no—
120#10621873—22no—
121#10621873D414yescomplemented
122C8×D43—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—42no—
127C22×D43—42no—
128C22×D43—81no—
129C22×D43C2×D411yescharacteristic
130Q8×C43—21no—
131Q8×C43—21no—
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—81no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2411yescharacteristic
142C22⋊D43—22no—
143C22⋊D43—42no—
144C22⋊D43—42no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—42no—
149C2×Dic43C2×D411yescharacteristic
150C2×Dic43C2×D411yescharacteristic
151C2×Dic43C2×D411yescharacteristic
152D172—21no—
153D172C2×D412yes—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—42no—
157C4×D43—42no—
158C4×D43—81no—
159Dic86—21no—
160Dic86—21no—
161Dic86—21no—
162Dic86—21no—
163Dic86—21no—
164Dic86—42no—
165Dic86—42no—
166Dic86C2×D412yes—
167C8×C43—21no—
168C8×C43C2×D412yes—
169C43⋊C8—21no—
170C43⋊C8—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43C22×D411yescharacteristic
178C2×D43—21no—
179C2×D43—21no—
180C2×D43—22no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—84no—
184C2×D43#13712yescomplemented
185C4×C43—21no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43C22×D411yescharacteristic
190C4×C43H(5,𝔽2)11yescharacteristic
191Dic43—22no—
192Dic43—21no—
193Dic43—21no—
194Dic43—21no—
195Dic43—41no—
196Dic43—41no—
197#3266—431nomaximal, Sylow
198C2×C43—41no—
199C2×C43—81no—
200C2×C43D4211yescharacteristic
201C2×C43C2×#13711yescharacteristic
202C2×C43#57711yescharacteristic
203D43—22no—
204D43—42no—
205C2×#137—431no—
206C22×SD16—431no—
207D4×Q8—431no—
208#546—431no—
209#497—431no—
210#468D4311yescharacteristic, complemented
211#467—431no—
212#464—431no—
213#461—431no—
214#452—431no—
215#451—431no—
216#450—431no—
217#448—431no—
218#440—431no—
219#435—431no—
220C43#326611yescharacteristic, complemented, Sylow
221C2×#41—431no—
222C22×Q8—431no—
223C22×Q8—431no—
224C22×D4—431no—
225#137—864no—
226C2×Q16—431no—
227C2×Q16—431no—
228C2×Q16—431no—
229C2×SD16—431no—
230C2×SD16—431no—
231C2×SD16—431no—
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—864no—
235C2×SD16C2×D4311yescharacteristic
236C2×M16C2×D4311yescharacteristic, complemented
237C22×C8—431no—
238C4⋊Q8—431no—
239C4⋊Q8—861no—
240#124—431no—
241#123—861no—
242C22⋊Q8—431no—
243C22⋊Q8—431no—
244C22⋊Q8—861no—
245C22⋊Q8—861no—
246C22⋊Q8C2×D4311yescharacteristic, complemented
247#121—861no—
248#121C2×D4311yescharacteristic
249#120—861no—
250C4×Q8—431no—
251C4×D4—431no—
252C4×D4—431no—
253C4×D4—861no—
254C2×C22⋊C4—861no—
255#107C2×D4311yescharacteristic, complemented
256C4⋊C8—431no—
257#103—431no—
258#103—431no—
259#103—431no—
260#103C2×D4311yescharacteristic, complemented
261#102—431no—
262#102C2×D4311yescharacteristic
263C22⋊C8—431no—
264C22⋊C8—431no—
265#97—431no—
266C24—861no—
267#41—862no—
268#41—1721no—
269C2×Q8—431no—
270C2×Q8—431no—
271C2×Q8—431no—
272C2×Q8—861no—
273C2×Q8—862no—
274C2×Q8—861no—
275C2×Q8—862no—
276C2×Q8—1721no—
277C2×Q8—1721no—
278C2×Q8C22×D4311yescharacteristic
279C2×D4—21no—
280C2×D4—431no—
281C2×D4—431no—
282C2×D4—861no—
283C2×D4—862no—
284C2×D4—861no—
285C2×D4—1721no—
286C2×D4C22×D4311yescharacteristic
287C22×C4—431no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4C22×D4311yescharacteristic
293Q16—862no—
294Q16—862no—
295Q16—1721no—
296SD16—22no—
297SD16—434no—
298SD16—862no—
299SD16—862no—
300SD16—862no—
301SD16—1721no—
302M16—22no—
303C2×C8—431no—
304C2×C8—431no—
305C2×C8—862no—
306C2×C8C22×D4311yescharacteristic
307C2×C8C22×D4311yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—431no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4C22×D4311yescharacteristic
316C4⋊C4C22×D4311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—431no—
320C22⋊C4—431no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C42—431no—
327C42—861no—
328C23—21no—
329C23—431no—
330C23—861no—
331C23—3441no—
332C23—1722no—
333C23—1722no—
334C23D4×D4311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—432no—
338Q8—861no—
339Q8—861no—
340Q8—861no—
341Q8—861no—
342Q8—861no—
343Q8—1722no—
344Q8—1722no—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—432no—
349D4—862no—
350D4—861no—
351D4—1722no—
352D4—1722no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—431no—
359C2×C4—431no—
360C2×C4—431no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—3441no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4D4×D4311yescharacteristic
371C2×C4C23×D4311yescharacteristic
372C8—21no—
373C8—861no—
374C8—861no—
375C8D4×D4312yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—432no—
383C22—861no—
384C22—861no—
385C22—862no—
386C22—3444no—
387C22—1721no—
388C22—1721no—
389C22C2×D4×D4311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—861no—
395C4—861no—
396C4—861no—
397C4—862no—
398C4—1721no—
399C4—1721no—
400C4C2×D4×D4311yescharacteristic
401C4#1306337111yescharacteristic
402C2—41no—
403C2—81no—
404C2—862no—
405C2—1722no—
406C2#1458353311yescharacteristic
407C2#137×D4311yescharacteristic
408C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3266
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#13063358C2semidirect
2. C2×SD16×D43C2semidirect
3. #14583562C2semidirect
5. #14583290C2semidirect
6. #14583141C2semidirect
7. #14583120C2semidirect
8. #14583103C2semidirect
9. #14583059C2semidirect
10. #14583056C2semidirect
11. #14583051C2semidirect
12. #14583037C2semidirect
13. #14582998C2semidirect
14. #14582968C2semidirect
15. C43×#468C2semidirect
17. C22×Dic86C22semidirect
21. C2×Dic172C22semidirect
22. C2×Dic172C22semidirect
23. C2×#10621885C22semidirect
32. #13063323C22semidirect
41. #13063290C22semidirect
46. Dic43⋊C8C22semidirect
47. #13063248C22semidirect
48. #13063248C22semidirect
49. #13063248C22semidirect
51. C22⋊(C43⋊C8)C22semidirect
53. #13063235C22semidirect
55. C2×M16×C43C22semidirect
56. C22⋊Q8×C43C22semidirect
58. #107×C43C22semidirect
59. #103×C43C22semidirect
121. #10621873D4semidirect
184. C2×D43#137semidirect
210. #468D43semidirect
220. C43#3266semidirect
236. C2×M16C2×D43semidirect
246. C22⋊Q8C2×D43semidirect
255. #107C2×D43semidirect
260. #103C2×D43semidirect