Finite Group Databasebeta

← #19143970

Subgroups — #19143970

Order 5504.

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

normal subgroups only

This group has 704 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
2#137×D43C212yesmaximal, complemented
3#14583469C211yesmaximal, characteristic, complemented
4#14583083C212yesmaximal, complemented
5#14583080C212yesmaximal, complemented
6#14583079C211yesmaximal, characteristic, complemented
7#14583077C211yesmaximal, characteristic, complemented
8#14583076C211yesmaximal, characteristic, complemented
9#14582914C212yesmaximal, complemented
10#14582880C211yesmaximal, characteristic, complemented
11C43×#455C211yesmaximal, characteristic, complemented
12#13063372—22no—
13#13063372C2212yes—
14#13063370—22no—
15#13063370—22no—
16#13063370C2211yescharacteristic
17C2×#10621900—22no—
18C2×#10621900—22no—
19C2×#10621900C2211yescharacteristic
20#41×D43—22no—
21#41×D43C2212yes—
22C2×Q8×D43C2211yescharacteristic, complemented
23#13063358C2212yescomplemented
24#13063357—22no—
25#13063356C2212yescomplemented
26#13063355C2212yescomplemented
27#13063354—22no—
28Q16×D43—22no—
29SD16×D43—22no—
30M16×D43C2212yescomplemented
31#13063325C2211yescharacteristic, complemented
32#13063323C2211yescharacteristic, complemented
33#13063312C2211yescharacteristic, complemented
34#13063307—22no—
35#13063302—22no—
36#13063282C2211yescharacteristic, complemented
37#13063253C2212yescomplemented
38#13063252C2212yescomplemented
39#13063251C2212yescomplemented
40#13063243C2212yescomplemented
41#13063242C2211yescharacteristic, complemented
42H(5,𝔽2)×C43C2211yescharacteristic
43#137×C43C2212yescomplemented
44#124×C43C2211yescharacteristic, complemented
45#104×C43C2212yescomplemented
46#100×C43C2211yescharacteristic, complemented
47#41×C43—22no—
48#41×C43C2312yes—
49C2×Q8×C43C2311yescharacteristic
50C2×D4×C43—22no—
51C2×D4×C43—22no—
52C2×D4×C43C2311yescharacteristic
53C2×C22⋊D43—22no—
54C2×C22⋊D43—24no—
55C2×C22⋊D43—22no—
56C2×C22⋊D43D412yes—
57C22×Dic43—22no—
58C22×Dic43D412yes—
59#10621902D412yes—
60Q8×D43—22no—
61Q8×D43—22no—
62Q8×D43—22no—
63Q8×D43D412yes—
64#10621900—24no—
65#10621900—24no—
66#10621900—24no—
67#10621900—22no—
68#10621900—22no—
69#10621900—24no—
70#10621900—22no—
71#10621900—22no—
72#10621900—22no—
73#10621900D412yes—
74D4×D43—24no—
75D4×D43—22no—
76D4×D43—22no—
77D4×D43D412yes—
78#10621898—24no—
79#10621898—22no—
80#10621898—22no—
81#10621898C2312yes—
82C2×C4×D43—22no—
83C2×C4×D43—22no—
84C2×C4×D43—21no—
85C2×C4×D43C2311yescharacteristic
86C2×Dic86—22no—
87C2×Dic86—22no—
88C2×Dic86—21no—
89C2×Dic86C2311yescharacteristic
90C2×Dic86C2311yescharacteristic
91Q16×C43—22no—
92SD16×C43—22no—
93M16×C43C2312yes—
94C22⋊C4×C43—22no—
95C42×C43C2311yescharacteristic
96C22⋊Dic43—22no—
97#10621885—22no—
98#10621885—22no—
99#10621884—22no—
100#10621883—22no—
101(C2×D43)⋊C4—21no—
102C4⋊Dic43—22no—
103Dic43⋊C4—21no—
104Dic43⋊C4—22no—
105C4×Dic43C2311yescharacteristic
106#10621877C2312yes—
107Dic172—22no—
108#10621873—22no—
109#10621872—22no—
110C8×D43—22no—
111C23×C43—22no—
112C23×C43C2×D412yes—
113C22×D43—22no—
114C22×D43—22no—
115C22×D43C2×D411yescharacteristic
116Q8×C43—22no—
117Q8×C43C2×D412yes—
118D4×C43—24no—
119D4×C43—22no—
120D4×C43—22no—
121D4×C43C2×D412yes—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—24no—
128C22⋊D43—24no—
129C22⋊D43—22no—
130C22⋊D43—24no—
131C22⋊D43—22no—
132C22⋊D43—22no—
133C2×Dic43—24no—
134C2×Dic43—22no—
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43C2×D412yes—
141C2×Dic43C2×D411yescharacteristic
142D172—22no—
143D172C2×D412yes—
144C4×D43—24no—
145C4×D43—22no—
146C4×D43—22no—
147C4×D43—22no—
148C4×D43—42no—
149C4×D43C2×D412yes—
150C4×D43C2×D412yes—
151Dic86—24no—
152Dic86—22no—
153Dic86—22no—
154Dic86—22no—
155Dic86—41no—
156Dic86—41no—
157Dic86C2×D412yes—
158C8×C43—22no—
159C43⋊C8—22no—
160C22×C43—22no—
161C22×C43—22no—
162C22×C43—42no—
163C22×C43—82no—
164C22×C43C22×D411yescharacteristic
165C2×D43—22no—
166C2×D43—41no—
167C2×D43—82no—
168C2×D43—82no—
169C2×D43#12012yes—
170C4×C43—22no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43C22×D412yes—
174Dic43—22no—
175Dic43—22no—
176Dic43—41no—
177Dic43—41no—
178Dic43#12011yescharacteristic
179Dic43#12011yescharacteristic
180#3022—431nomaximal, Sylow
181C2×C43—21no—
182C2×C43—42no—
183C2×C43—42no—
184C2×C43C2×#12011yescharacteristic
185D43—22no—
186D43—42no—
187#585—431no—
188C2×#137—432no—
189#536—431no—
190#456—432no—
191#456—432no—
192#455—431no—
193#455—431no—
194#455—431no—
195#455D4311yescharacteristic, complemented
196#421—432no—
197#413—431no—
198C43#302211yescharacteristic, complemented, Sylow
1992−1+4—432no—
2002−1+4—862no—
201H(5,𝔽2)—431no—
202H(5,𝔽2)—862no—
203H(5,𝔽2)—862no—
204H(5,𝔽2)C2×D4311yescharacteristic
205C2×#41—431no—
206C2×#41—432no—
207C2×#41—862no—
208C2×#41—862no—
209C2×#41—862no—
210C22×Q8—431no—
211#137—432no—
212#137—432no—
213#137—432no—
214#137—862no—
215#137—862no—
216#137C2×D4312yescomplemented
217C2×Q16—862no—
218C2×SD16—862no—
219C2×M16—432no—
220C4⋊Q8—431no—
221C4⋊Q8—431no—
222#124—431no—
223#124C2×D4311yescharacteristic, complemented
224#123—862no—
225C22⋊Q8—862no—
226#117—431no—
227#104—432no—
228#104—432no—
229#104—432no—
230#104C2×D4312yescomplemented
231#101—432no—
232#100—431no—
233#100C2×D4311yescharacteristic, complemented
234#41—22no—
235#41—432no—
236#41—432no—
237#41—432no—
238#41—862no—
239#41—862no—
240#41—864no—
241#41—862no—
242#41—862no—
243#41—862no—
244#41—864no—
245#41—862no—
246#41—864no—
247#41—864no—
248#41—864no—
249#41—862no—
250#41C22×D4312yes—
251C2×Q8—431no—
252C2×Q8—432no—
253C2×Q8—431no—
254C2×Q8—861no—
255C2×Q8—862no—
256C2×Q8—862no—
257C2×Q8—862no—
258C2×Q8—862no—
259C2×Q8—862no—
260C2×Q8C22×D4311yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—432no—
264C2×D4—432no—
265C2×D4—862no—
266C2×D4—862no—
267C2×D4—864no—
268C2×D4—862no—
269C2×D4—864no—
270C2×D4—862no—
271C2×D4C22×D4311yescharacteristic
272C22×C4—431no—
273C22×C4—432no—
274C22×C4—862no—
275C22×C4—862no—
276C22×C4—861no—
277C22×C4—862no—
278Q16—22no—
279Q16—862no—
280Q16—862no—
281Q16—862no—
282SD16—22no—
283SD16—862no—
284SD16—862no—
285SD16—862no—
286M16—432no—
287M16—862no—
288M16C22×D4312yes—
289C2×C8—862no—
290C4⋊C4—861no—
291C4⋊C4—862no—
292C4⋊C4—862no—
293C22⋊C4—22no—
294C22⋊C4—861no—
295C22⋊C4—862no—
296C42—431no—
297C42C22×D4311yescharacteristic
298C23—22no—
299C23—431no—
300C23—862no—
301C23—862no—
302C23D4×D4312yes—
303Q8—22no—
304Q8—432no—
305Q8—862no—
306Q8—864no—
307Q8—862no—
308Q8—862no—
309Q8—1721no—
310Q8—1721no—
311Q8D4×D4312yes—
312D4—24no—
313D4—22no—
314D4—22no—
315D4—432no—
316D4—862no—
317D4—862no—
318D4—864no—
319D4—862no—
320D4—864no—
321D4—864no—
322D4—862no—
323D4D4×D4312yes—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—431no—
329C2×C4—432no—
330C2×C4—432no—
331C2×C4—432no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—864no—
335C2×C4—862no—
336C2×C4—862no—
337C2×C4—862no—
338C2×C4—864no—
339C2×C4—862no—
340C2×C4—862no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—1722no—
344C2×C4C23×D4311yescharacteristic
345C8—22no—
346C8—862no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—82no—
351C22—432no—
352C22—862no—
353C22—3442no—
354C22—3442no—
355C22—1721no—
356C22C2×D4×D4311yescharacteristic
357C4—22no—
358C4—41no—
359C4—41no—
360C4—431no—
361C4—431no—
362C4—862no—
363C4—862no—
364C4—1721no—
365C4—1721no—
366C4C2×D4×D4312yes—
367C2—21no—
368C2—42no—
369C2—42no—
370C2—862no—
371C2—1722no—
372C2#120×D4311yescharacteristic
subgroupG/H
centerC2#120×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#455C2
socleC2×C43C2×#120
hypercenter#455D43
hypocenterC43#3022
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
2. #137×D43C2semidirect
3. #14583469C2semidirect
4. #14583083C2semidirect
5. #14583080C2semidirect
6. #14583079C2semidirect
7. #14583077C2semidirect
8. #14583076C2semidirect
9. #14582914C2semidirect
10. #14582880C2semidirect
11. C43×#455C2semidirect
22. C2×Q8×D43C22semidirect
23. #13063358C22semidirect
25. #13063356C22semidirect
26. #13063355C22semidirect
30. M16×D43C22semidirect
31. #13063325C22semidirect
32. #13063323C22semidirect
33. #13063312C22semidirect
36. #13063282C22semidirect
37. #13063253C22semidirect
38. #13063252C22semidirect
39. #13063251C22semidirect
40. #13063243C22semidirect
41. #13063242C22semidirect
43. #137×C43C22semidirect
44. #124×C43C22semidirect
45. #104×C43C22semidirect
46. #100×C43C22semidirect
195. #455D43semidirect
198. C43#3022semidirect
216. #137C2×D43semidirect
223. #124C2×D43semidirect
230. #104C2×D43semidirect
233. #100C2×D43semidirect