Finite Group Databasebeta

← #19143940

Subgroups — #19143940

Order 5504.

724 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#14583734C211yesmaximal, characteristic, complemented
2#14583695C212yesmaximal, complemented
3#14583447C211yesmaximal, characteristic, complemented
4#14583083C212yesmaximal, complemented
5#14583079C211yesmaximal, characteristic, complemented
6#14583077C211yesmaximal, characteristic, complemented
7#14583070C212yesmaximal, complemented
8#14583066C211yesmaximal, characteristic, complemented
9#104×D43C212yesmaximal, complemented
10#14582880C211yesmaximal, characteristic, complemented
11C43×#453C211yesmaximal, characteristic, complemented
12#13063372—22no—
13#13063372C2212yes—
14#13063370—22no—
15#13063370—22no—
16#13063370C2211yescharacteristic
17C2×#10621900—22no—
18C2×#10621900—22no—
19C2×#10621900C2211yescharacteristic
20C2×#10621900C2211yescharacteristic, complemented
21#41×D43—22no—
22#41×D43C2212yes—
23#13063358C2212yescomplemented
24#13063355C2212yescomplemented
25#13063354—22no—
26#13063351C2212yescomplemented
27#13063349—22no—
28#13063346—22no—
29#13063344—22no—
30M16×D43C2212yescomplemented
31#13063325C2211yescharacteristic, complemented
32#13063312C2211yescharacteristic, complemented
33#13063312C2211yescharacteristic, complemented
34#13063296—22no—
35D4×Dic43—22no—
36C42×D43C2211yescharacteristic, complemented
37#13063253C2212yescomplemented
38#13063252C2212yescomplemented
39#13063251C2212yescomplemented
40#13063243C2212yescomplemented
41#13063242C2211yescharacteristic, complemented
42H(5,𝔽2)×C43C2211yescharacteristic
43AGL(1,ℤ/8)×C43C2212yescomplemented
44#127×C43C2211yescharacteristic, complemented
45#104×C43C2212yescomplemented
46#100×C43C2211yescharacteristic, complemented
47#41×C43—22no—
48#41×C43C2312yes—
49C2×D4×C43—22no—
50C2×D4×C43—22no—
51C2×D4×C43—22no—
52C2×D4×C43C2311yescharacteristic
53C2×D4×C43C2311yescharacteristic
54C2×C22⋊D43—22no—
55C2×C22⋊D43—24no—
56C2×C22⋊D43—22no—
57C2×C22⋊D43—21no—
58C2×C22⋊D43D412yes—
59C22×Dic43—22no—
60C22×Dic43—21no—
61C22×Dic43D412yes—
62#10621902D412yescomplemented
63Q8×D43—22no—
64Q8×D43D412yescomplemented
65#10621900—24no—
66#10621900—24no—
67#10621900—24no—
68#10621900—22no—
69#10621900—22no—
70#10621900—24no—
71#10621900—22no—
72#10621900—22no—
73#10621900—22no—
74#10621900—22no—
75#10621900—22no—
76#10621900D412yescomplemented
77D4×D43—24no—
78D4×D43—22no—
79D4×D43—22no—
80D4×D43D412yescomplemented
81#10621898—24no—
82#10621898—22no—
83#10621898—22no—
84#10621898C2312yes—
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—21no—
88C2×C4×D43C2311yescharacteristic
89C2×Dic86—22no—
90C2×Dic86—22no—
91C2×Dic86C2311yescharacteristic
92C2×Dic86C2311yescharacteristic
93SD16×C43—22no—
94D8×C43—22no—
95M16×C43C2312yes—
96C42×C43C2311yescharacteristic
97C22⋊Dic43—22no—
98C22⋊Dic43—22no—
99#10621885—22no—
100#10621883—22no—
101#10621883—22no—
102#10621882—22no—
103C4⋊Dic43—22no—
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic
106#10621877C2312yes—
107Dic172—22no—
108#10621873—22no—
109#10621872—22no—
110C8×D43—22no—
111C23×C43—22no—
112C23×C43—21no—
113C23×C43C2×D412yes—
114C22×D43—22no—
115C22×D43—22no—
116C22×D43C2×D411yescharacteristic
117Q8×C43C2×D412yes—
118D4×C43—24no—
119D4×C43—22no—
120D4×C43—22no—
121D4×C43—22no—
122D4×C43—44no—
123D4×C43C2×D412yes—
124C2×C4×C43—22no—
125C2×C4×C43—21no—
126C2×C4×C43—22no—
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—24no—
129C22⋊D43—24no—
130C22⋊D43—22no—
131C22⋊D43—24no—
132C22⋊D43—22no—
133C22⋊D43—22no—
134C22⋊D43—42no—
135C2×Dic43—24no—
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43—22no—
139C2×Dic43—22no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43C2×D412yes—
145C2×Dic43C2×D411yescharacteristic
146D172—22no—
147D172C2×D412yes—
148C4×D43—24no—
149C4×D43—22no—
150C4×D43—22no—
151C4×D43—22no—
152C4×D43—42no—
153C4×D43C2×D412yes—
154C4×D43C2×D412yes—
155Dic86—24no—
156Dic86—22no—
157Dic86—22no—
158Dic86—22no—
159Dic86C2×D412yes—
160C8×C43—22no—
161C43⋊C8—22no—
162C22×C43—22no—
163C22×C43—22no—
164C22×C43—42no—
165C22×C43—42no—
166C22×C43—41no—
167C22×C43—82no—
168C22×C43C22×D411yescharacteristic
169C2×D43—22no—
170C2×D43—41no—
171C2×D43—82no—
172C2×D43—82no—
173C2×D43#12012yes—
174C4×C43—22no—
175C4×C43—22no—
176C4×C43C22×D412yes—
177Dic43—22no—
178Dic43—22no—
179Dic43—41no—
180Dic43—41no—
181Dic43#12011yescharacteristic
182Dic43#12011yescharacteristic
183#3018—431nomaximal, Sylow
184C2×C43—21no—
185C2×C43—42no—
186C2×C43—42no—
187C2×C43—81no—
188C2×C43C2×#12011yescharacteristic
189D43—22no—
190D43—42no—
191#585—431no—
192#575—432no—
193#532—431no—
194#456—432no—
195#455—431no—
196#455—431no—
197#454—432no—
198#453—431no—
199#453D4311yescharacteristic, complemented
200C2×#104—432no—
201#413—431no—
202C43#301811yescharacteristic, complemented, Sylow
2032−1+4—432no—
2042−1+4—862no—
205H(5,𝔽2)—431no—
206H(5,𝔽2)—862no—
207H(5,𝔽2)—862no—
208H(5,𝔽2)C2×D4311yescharacteristic
209C2×#41—431no—
210C2×#41—432no—
211C2×#41—431no—
212C2×#41—862no—
213C2×#41—862no—
214C2×#41—862no—
215#137—432no—
216#137—432no—
217#137—862no—
218AGL(1,ℤ/8)—432no—
219AGL(1,ℤ/8)—862no—
220AGL(1,ℤ/8)C2×D4312yescomplemented
221#135—862no—
222#135—862no—
223C2×M16—432no—
224C4⋊Q8—431no—
225#127C2×D4311yescharacteristic, complemented
226#124—431no—
227#124—431no—
228#121—862no—
229C4×D4—862no—
230C2×C42—431no—
231#104—432no—
232#104—432no—
233#104—432no—
234#104C2×D4312yescomplemented
235#101—432no—
236#100—431no—
237#100C2×D4311yescharacteristic, complemented
238#41—22no—
239#41—432no—
240#41—432no—
241#41—432no—
242#41—862no—
243#41—862no—
244#41—864no—
245#41—862no—
246#41—862no—
247#41—862no—
248#41—864no—
249#41—862no—
250#41—862no—
251#41—862no—
252#41—864no—
253#41—864no—
254#41—864no—
255#41—862no—
256#41C22×D4312yes—
257C2×Q8—431no—
258C2×Q8—432no—
259C2×Q8—431no—
260C2×Q8—862no—
261C2×Q8—862no—
262C2×Q8—862no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—432no—
267C2×D4—432no—
268C2×D4—862no—
269C2×D4—862no—
270C2×D4—864no—
271C2×D4—862no—
272C2×D4—864no—
273C2×D4—862no—
274C2×D4—861no—
275C2×D4C22×D4311yescharacteristic
276C2×D4C22×D4311yescharacteristic
277C22×C4—431no—
278C22×C4—432no—
279C22×C4—862no—
280C22×C4—862no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—862no—
284Q16—862no—
285Q16—862no—
286SD16—22no—
287SD16—862no—
288SD16—862no—
289SD16—862no—
290D8—22no—
291D8—862no—
292M16—432no—
293M16—862no—
294M16C22×D4312yes—
295C2×C8—862no—
296C4⋊C4—862no—
297C22⋊C4—862no—
298C22⋊C4—862no—
299C42—431no—
300C42—861no—
301C42C22×D4311yescharacteristic
302C23—22no—
303C23—21no—
304C23—431no—
305C23—862no—
306C23—862no—
307C23D4×D4312yes—
308Q8—432no—
309Q8—862no—
310Q8—864no—
311Q8—862no—
312Q8—862no—
313Q8D4×D4312yes—
314D4—24no—
315D4—22no—
316D4—22no—
317D4—22no—
318D4—44no—
319D4—432no—
320D4—862no—
321D4—862no—
322D4—864no—
323D4—862no—
324D4—864no—
325D4—864no—
326D4—862no—
327D4—1722no—
328D4D4×D4312yes—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—431no—
333C2×C4—432no—
334C2×C4—432no—
335C2×C4—432no—
336C2×C4—862no—
337C2×C4—862no—
338C2×C4—864no—
339C2×C4—862no—
340C2×C4—862no—
341C2×C4—862no—
342C2×C4—864no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—1722no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4C23×D4311yescharacteristic
351C8—22no—
352C8—862no—
353C22—22no—
354C22—22no—
355C22—42no—
356C22—42no—
357C22—41no—
358C22—82no—
359C22—432no—
360C22—862no—
361C22—3442no—
362C22—3442no—
363C22—1721no—
364C22C2×D4×D4311yescharacteristic
365C4—22no—
366C4—22no—
367C4—431no—
368C4—431no—
369C4—862no—
370C4—862no—
371C4—1721no—
372C4—1721no—
373C4C2×D4×D4312yes—
374C2—21no—
375C2—42no—
376C2—42no—
377C2—81no—
378C2—862no—
379C2—1722no—
380C2#120×D4311yescharacteristic
subgroupG/H
centerC2#120×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#453C2
socleC2×C43C2×#120
hypercenter#453D43
hypocenterC43#3018
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14583734C2semidirect
2. #14583695C2semidirect
3. #14583447C2semidirect
4. #14583083C2semidirect
5. #14583079C2semidirect
6. #14583077C2semidirect
7. #14583070C2semidirect
8. #14583066C2semidirect
9. #104×D43C2semidirect
10. #14582880C2semidirect
11. C43×#453C2semidirect
20. C2×#10621900C22semidirect
23. #13063358C22semidirect
24. #13063355C22semidirect
26. #13063351C22semidirect
30. M16×D43C22semidirect
31. #13063325C22semidirect
32. #13063312C22semidirect
33. #13063312C22semidirect
36. C42×D43C22semidirect
37. #13063253C22semidirect
38. #13063252C22semidirect
39. #13063251C22semidirect
40. #13063243C22semidirect
41. #13063242C22semidirect
43. AGL(1,ℤ/8)×C43C22semidirect
44. #127×C43C22semidirect
45. #104×C43C22semidirect
46. #100×C43C22semidirect
62. #10621902D4semidirect
64. Q8×D43D4semidirect
76. #10621900D4semidirect
80. D4×D43D4semidirect
199. #453D43semidirect
202. C43#3018semidirect
220. AGL(1,ℤ/8)C2×D43semidirect
225. #127C2×D43semidirect
234. #104C2×D43semidirect
237. #100C2×D43semidirect