Finite Group Databasebeta

← #19143904

Subgroups — #19143904

Order 5504.

764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063370C211yesmaximal, characteristic, complemented
2C2×#13063351C211yesmaximal, characteristic, complemented
3C2×#13063347C211yesmaximal, characteristic, complemented
4#14583480C211yesmaximal, characteristic, complemented
5#14583062C212yesmaximal, complemented
6#14583051C212yesmaximal, complemented
7#14583045C212yesmaximal, complemented
8#14583034C212yesmaximal, complemented
9#14582898C211yesmaximal, characteristic, complemented
10#14582865C211yesmaximal, characteristic, complemented
11C2×#102×C43C211yesmaximal, characteristic, complemented
12#13063370—24no—
13#13063370—24no—
14C2×#10621898C2211yescharacteristic
15C2×#10621898C2211yescharacteristic
16C2×#10621898C2211yescharacteristic, complemented
17C2×#10621900—21no—
18C2×#10621900C2212yes—
19C22×C22⋊D43—22no—
20C2×D4×D43—21no—
21C2×D4×D43C2212yes—
22#13063351—24no—
23#13063347—24no—
24C2×Dic172C2211yescharacteristic, complemented
25C2×#10621873C2211yescharacteristic, complemented
26C2×#10621873C2211yescharacteristic, complemented
27C2×#10621883C2212yescomplemented
28C2×D344C2211yescharacteristic, complemented
29C2×#10621882C2212yescomplemented
30C2×#10621877C2211yescharacteristic, complemented
31#13063305—21no—
32#13063305C2212yescomplemented
33#13063300—21no—
34#13063300C2212yescomplemented
35#13063299—22no—
36#13063248C2212yescomplemented
37#13063245C2212yescomplemented
38(C2×D43)⋊C8C2212yescomplemented
39(C2×D43)⋊C8C2212yescomplemented
40C22×D4×C43C2211yescharacteristic
41C22×C8×C43C2211yescharacteristic, complemented
42C2×C4⋊C4×C43C2211yescharacteristic, complemented
43#102×C43C2212yescomplemented
44#102×C43C2212yescomplemented
45C24×C43—21no—
46C23×D43—22no—
47C2×D4×C43—21no—
48C2×D4×C43—22no—
49C2×D4×C43D414yescomplemented
50C2×D4×C43C2312yes—
51C22×C4×C43—21no—
52C22×C4×C43C2311yescharacteristic
53C2×C22⋊D43—216no—
54C2×C22⋊D43—22no—
55C2×C22⋊D43—21no—
56C2×C22⋊D43—21no—
57C2×C22⋊D43—22no—
58C2×C22⋊D43D412yes—
59C22×Dic43—22no—
60#10621900—28no—
61#10621900—24no—
62#10621900—24no—
63D4×D43—28no—
64D4×D43—24no—
65D4×D43—24no—
66#10621898—22no—
67#10621898—22no—
68#10621898—22no—
69#10621898—22no—
70#10621898—22no—
71#10621898D414yescomplemented
72C2×D172—22no—
73C2×D172D411yescharacteristic
74C2×D172C2311yescharacteristic
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2312yes—
79C2×Dic86D411yescharacteristic
80C2×Dic86C2311yescharacteristic
81C2×Dic86C2311yescharacteristic
82C2×C8×C43—22no—
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43—21no—
86C4⋊C4×C43C2312yes—
87#10621883—24no—
88#10621882—24no—
89(C2×D43)⋊C4—22no—
90(C2×D43)⋊C4—22no—
91C4⋊Dic43—22no—
92#10621877—22no—
93C2×C43⋊C8C2312yes—
94Dic172—22no—
95D344—22no—
96#10621873—22no—
97#10621873—22no—
98C23×C43—22no—
99C23×C43—24no—
100C23×C43—81no—
101C23×C43—81no—
102C23×C43C2×D411yescharacteristic
103C22×D43—21no—
104C22×D43—28no—
105C22×D43—21no—
106C22×D43—82no—
107C22×D43—82no—
108C22×D43C2×D412yes—
109D4×C43—24no—
110D4×C43—22no—
111D4×C43C2×D414yes—
112C2×C4×C43—22no—
113C2×C4×C43—81no—
114C2×C4×C43C2×D412yes—
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2×D412yes—
117C2×C4×C43C2411yescharacteristic
118C22⋊D43—28no—
119C22⋊D43—28no—
120C22⋊D43—24no—
121C22⋊D43—24no—
122C22⋊D43—42no—
123C2×Dic43—28no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43C2×D412yes—
127D172—22no—
128D172—21no—
129D172—21no—
130D172—21no—
131D172—82no—
132D172C2×D412yes—
133C4×D43—24no—
134C4×D43—22no—
135C4×D43—22no—
136C4×D43—42no—
137Dic86—22no—
138Dic86—21no—
139Dic86—21no—
140Dic86—21no—
141Dic86C2×D412yes—
142C8×C43—21no—
143C8×C43—21no—
144C43⋊C8—22no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—24no—
148C22×C43—42no—
149C22×C43—42no—
150C22×C43—84no—
151C22×C43#12012yes—
152C22×C43C22×D411yescharacteristic
153C2×D43—22no—
154C2×D43—22no—
155C2×D43—22no—
156C2×D43—22no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—88no—
163C4×C43—42no—
164C4×C43#12012yes—
165C4×C43C22×D411yescharacteristic
166C4×C43C22×D411yescharacteristic
167Dic43—22no—
168Dic43—22no—
169Dic43—41no—
170#3012—431nomaximal, Sylow
171C2×C43—22no—
172C2×C43—44no—
173C2×C43C2×#12011yescharacteristic
174C2×C43#57611yescharacteristic
175C2×C43#57711yescharacteristic
176D43—42no—
177D43—42no—
178D43—81no—
179C2×H(5,𝔽2)—431no—
180C2×AGL(1,ℤ/8)—431no—
181C2×#135—431no—
182#537—431no—
183#452—432no—
184#450—432no—
185#449—432no—
186#447—432no—
187#417—431no—
188C2×#102D4311yescharacteristic, complemented
189#408—431no—
190C43#301211yescharacteristic, complemented, Sylow
191H(5,𝔽2)—864no—
192H(5,𝔽2)—864no—
193C2×#41—431no—
194C2×#41—432no—
195C2×#41—431no—
196C2×#41—431no—
197C2×#41—861no—
198C22×D4—432no—
199C22×D4—861no—
200C22×D4—862no—
201C22×D4C2×D4311yescharacteristic
202AGL(1,ℤ/8)—864no—
203#135—864no—
204C2×Q16—431no—
205C2×SD16—432no—
206C2×SD16—431no—
207C2×SD16—431no—
208C2×D8—432no—
209C2×D8—431no—
210C2×M16—431no—
211C22×C8C2×D4311yescharacteristic, complemented
212C22⋊Q8—432no—
213C22⋊Q8—861no—
214#121—432no—
215#121—861no—
216#121—862no—
217C2×C4⋊C4C2×D4311yescharacteristic, complemented
218#103—432no—
219#102—432no—
220#102C2×D4312yescomplemented
221#102C2×D4312yescomplemented
222C22⋊C8—432no—
223C22⋊C8—432no—
224C24—21no—
225C24—862no—
226#41—434no—
227#41—864no—
228#41—868no—
229#41—864no—
230#41—862no—
231#41—862no—
232#41—862no—
233#41—862no—
234#41—862no—
235C2×Q8—431no—
236C2×Q8—431no—
237C2×Q8—431no—
238C2×D4—21no—
239C2×D4—22no—
240C2×D4—432no—
241C2×D4—431no—
242C2×D4—431no—
243C2×D4—431no—
244C2×D4—862no—
245C2×D4—862no—
246C2×D4—864no—
247C2×D4—868no—
248C2×D4—862no—
249C2×D4—8616no—
250C2×D4—861no—
251C2×D4—864no—
252C2×D4—861no—
253C2×D4D17214yescomplemented
254C2×D4C22×D4312yes—
255C22×C4—21no—
256C22×C4—432no—
257C22×C4—862no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4C22×D4311yescharacteristic
261Q16—862no—
262SD16—862no—
263SD16—862no—
264SD16—864no—
265D8—862no—
266D8—864no—
267M16—862no—
268C2×C8—22no—
269C2×C8—432no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—862no—
274C4⋊C4C22×D4312yes—
275C22⋊C4—862no—
276C22⋊C4—862no—
277C23—22no—
278C23—24no—
279C23—81no—
280C23—81no—
281C23—432no—
282C23—868no—
283C23—861no—
284C23—861no—
285C23—3442no—
286C23—3442no—
287C23D4×D4311yescharacteristic
288Q8—432no—
289Q8—862no—
290Q8—861no—
291Q8—861no—
292Q8—861no—
293D4—24no—
294D4—22no—
295D4—432no—
296D4—868no—
297D4—868no—
298D4—864no—
299D4—864no—
300D4—862no—
301D4—861no—
302D4—861no—
303D4—861no—
304D4—3442no—
305D4—1722no—
306D4C2×D17214yes—
307C2×C4—22no—
308C2×C4—81no—
309C2×C4—432no—
310C2×C4—868no—
311C2×C4—861no—
312C2×C4—864no—
313C2×C4—862no—
314C2×C4—862no—
315C2×C4—861no—
316C2×C4—1722no—
317C2×C4C2×D17212yes—
318C2×C4D4×D4311yescharacteristic
319C2×C4D4×D4312yes—
320C2×C4C23×D4311yescharacteristic
321C8—21no—
322C8—21no—
323C8—862no—
324C22—21no—
325C22—21no—
326C22—24no—
327C22—42no—
328C22—42no—
329C22—84no—
330C22—862no—
331C22—862no—
332C22—862no—
333C22—862no—
334C22—3448no—
335C22—1721no—
336C22—1721no—
337C22—1721no—
338C22—1721no—
339C22—1721no—
340C22#1306329512yes—
341C22C2×D4×D4311yescharacteristic
342C4—42no—
343C4—862no—
344C4—862no—
345C4—1721no—
346C4#1306329512yes—
347C4C2×D4×D4311yescharacteristic
348C4C22×D17211yescharacteristic
349C2—22no—
350C2—44no—
351C2—3441no—
352C2—1722no—
353C2—1722no—
354C2C2×#1306329511yescharacteristic
355C2#1458370011yescharacteristic
356C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#102×C43C2
socleC22×C43C22×D4
hypercenterC2×#102D43
hypocenterC43#3012
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#13063370C2semidirect
2. C2×#13063351C2semidirect
3. C2×#13063347C2semidirect
4. #14583480C2semidirect
5. #14583062C2semidirect
6. #14583051C2semidirect
7. #14583045C2semidirect
8. #14583034C2semidirect
9. #14582898C2semidirect
10. #14582865C2semidirect
11. C2×#102×C43C2semidirect
16. C2×#10621898C22semidirect
24. C2×Dic172C22semidirect
25. C2×#10621873C22semidirect
26. C2×#10621873C22semidirect
27. C2×#10621883C22semidirect
28. C2×D344C22semidirect
29. C2×#10621882C22semidirect
30. C2×#10621877C22semidirect
32. #13063305C22semidirect
34. #13063300C22semidirect
36. #13063248C22semidirect
37. #13063245C22semidirect
38. (C2×D43)⋊C8C22semidirect
39. (C2×D43)⋊C8C22semidirect
41. C22×C8×C43C22semidirect
42. C2×C4⋊C4×C43C22semidirect
43. #102×C43C22semidirect
44. #102×C43C22semidirect
49. C2×D4×C43D4semidirect
71. #10621898D4semidirect
188. C2×#102D43semidirect
190. C43#3012semidirect
211. C22×C8C2×D43semidirect
217. C2×C4⋊C4C2×D43semidirect
220. #102C2×D43semidirect
221. #102C2×D43semidirect
253. C2×D4D172semidirect