Finite Group Databasebeta

← #456×D43 #19143934

Subgroups — #456×D43 #19143934

Order 5504.

708 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 135 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
12−1+4×D43C211yesmaximal, characteristic
2#137×D43C212yesmaximal, complemented
3C4⋊Q8×D43C211yesmaximal, characteristic, complemented
4#14583084C211yesmaximal, characteristic, complemented
5#14583083C212yesmaximal, complemented
6#14583082C211yesmaximal, characteristic, complemented
7#14583081C211yesmaximal, characteristic, complemented
8#14583080C212yesmaximal, complemented
9#104×D43C212yesmaximal, complemented
10#101×D43C211yesmaximal, characteristic, complemented
11C43×#456C211yesmaximal, characteristic, complemented
12#13063373—22no—
13#13063373C2211yescharacteristic
14#13063372—22no—
15#13063372—22no—
16#13063372C2212yes—
17#41×D43—22no—
18#41×D43—22no—
19#41×D43C2212yes—
20C2×Q8×D43—22no—
21C2×Q8×D43C2211yescharacteristic
22C2×Q8×D43C2211yescharacteristic
23#13063358C2212yescomplemented
24#13063357—22no—
25#13063356C2212yescomplemented
26#13063355C2212yescomplemented
27#13063354—22no—
28Q16×D43—22no—
29SD16×D43—22no—
30M16×D43C2212yes—
31#13063325C2211yescharacteristic, complemented
32#13063324—22no—
33#13063323C2211yescharacteristic, complemented
34#13063323C2211yescharacteristic, complemented
35C4⋊C4×D43—22no—
36C42×D43C2211yescharacteristic
37#13063253C2212yescomplemented
38#13063252C2212yescomplemented
39#13063251C2212yescomplemented
40#13063244C2211yescharacteristic, complemented
41#13063243C2212yescomplemented
422−1+4×C43C2211yescharacteristic
43#137×C43C2212yescomplemented
44C4⋊Q8×C43C2211yescharacteristic, complemented
45#104×C43C2212yescomplemented
46#101×C43C2211yescharacteristic, complemented
47#41×C43—22no—
48#41×C43—22no—
49#41×C43C2312yes—
50C2×Q8×C43—22no—
51C2×Q8×C43C2311yescharacteristic
52C2×Q8×C43C2311yescharacteristic
53#10621902—22no—
54#10621902—22no—
55#10621902D412yes—
56Q8×D43—22no—
57Q8×D43—24no—
58Q8×D43—22no—
59Q8×D43—22no—
60Q8×D43—22no—
61Q8×D43—22no—
62Q8×D43—22no—
63Q8×D43—22no—
64Q8×D43D412yes—
65#10621900—22no—
66#10621900—24no—
67#10621900—22no—
68#10621900—24no—
69#10621900—22no—
70#10621900D412yes—
71D4×D43—22no—
72D4×D43—22no—
73D4×D43D412yes—
74#10621898—24no—
75#10621898—24no—
76#10621898—22no—
77#10621898—22no—
78#10621898—22no—
79#10621898C2312yes—
80C2×C4×D43—24no—
81C2×C4×D43—22no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43D412yes—
85C2×C4×D43C2311yescharacteristic
86C2×Dic86—24no—
87C2×Dic86—22no—
88C2×Dic86—21no—
89C2×Dic86D412yes—
90C2×Dic86C2311yescharacteristic
91C2×Dic86C2311yescharacteristic
92Q16×C43—22no—
93SD16×C43—22no—
94M16×C43C2312yes—
95C4⋊C4×C43—22no—
96C42×C43C2311yescharacteristic
97#10621885—22no—
98#10621885—22no—
99#10621884—22no—
100#10621883—22no—
101C4⋊Dic43—22no—
102Dic43⋊C4—22no—
103Dic43⋊C4—22no—
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic
106#10621877C2312yes—
107Dic172—22no—
108#10621873—22no—
109#10621872—22no—
110C8×D43—22no—
111C22×D43—22no—
112C22×D43C2×D411yescharacteristic
113Q8×C43—22no—
114Q8×C43—22no—
115Q8×C43—22no—
116Q8×C43C2×D412yes—
117D4×C43—22no—
118D4×C43—22no—
119D4×C43C2×D412yes—
120C2×C4×C43—24no—
121C2×C4×C43—21no—
122C2×C4×C43—22no—
123C2×C4×C43—21no—
124C2×C4×C43C2×D412yes—
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—24no—
127C22⋊D43—22no—
128C22⋊D43—22no—
129C22⋊D43—22no—
130C2×Dic43—24no—
131C2×Dic43—21no—
132C2×Dic43—22no—
133C2×Dic43—21no—
134C2×Dic43C2×D412yes—
135C2×Dic43C2×D411yescharacteristic
136D172—22no—
137D172—22no—
138D172C2×D412yes—
139C4×D43—24no—
140C4×D43—24no—
141C4×D43—24no—
142C4×D43—22no—
143C4×D43—22no—
144C4×D43—22no—
145C4×D43—22no—
146C4×D43—22no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43C2×D412yes—
150C4×D43C2×D412yes—
151Dic86—24no—
152Dic86—22no—
153Dic86—22no—
154Dic86—22no—
155Dic86—24no—
156Dic86—22no—
157Dic86—42no—
158Dic86C2×D412yes—
159C8×C43—22no—
160C43⋊C8—22no—
161C22×C43—22no—
162C22×C43C22×D411yescharacteristic
163C2×D43—22no—
164C2×D43—22no—
165C2×D43—44no—
166C2×D43#12011yescharacteristic
167C2×D43#12011yescharacteristic
168C4×C43—22no—
169C4×C43—22no—
170C4×C43—22no—
171C4×C43—41no—
172C4×C43C22×D412yes—
173Dic43—22no—
174Dic43—22no—
175Dic43—22no—
176Dic43—41no—
177Dic43#12012yes—
178C2×#456—431nomaximal, Sylow
179C2×C43—21no—
180C2×C43—42no—
181C2×C43C2×#12011yescharacteristic
182D43—21no—
183D43—42no—
184D43#45612yesdirect product factor
185C2×2−1+4—431no—
186C2×#137—432no—
187C2×C4⋊Q8—431no—
188#456—431no—
189#456—432no—
190#456—431no—
191#456—432no—
192#456—431no—
193#456D4311yescharacteristic, direct product factor
194C2×#104—432no—
195C2×#101—431no—
196C43C2×#45611yescharacteristic, complemented, Sylow
1972−1+4—432no—
1982−1+4—431no—
1992−1+4—862no—
2002−1+4—862no—
2012−1+4—862no—
2022−1+4C2×D4311yescharacteristic
203C2×#41—432no—
204C2×#41—862no—
205C2×#41—862no—
206C22×Q8—431no—
207C22×Q8—431no—
208C22×Q8—862no—
209#137—432no—
210#137—432no—
211#137—432no—
212#137—862no—
213#137—862no—
214#137C2×D4312yescomplemented
215C2×Q16—862no—
216C2×SD16—862no—
217C2×M16—432no—
218C4⋊Q8—431no—
219C4⋊Q8—431no—
220C4⋊Q8—431no—
221C4⋊Q8—862no—
222C4⋊Q8C2×D4311yescharacteristic, complemented
223C2×C4⋊C4—862no—
224C2×C42—431no—
225#104—432no—
226#104—432no—
227#104—432no—
228#104C2×D4312yescomplemented
229#101—431no—
230#101—432no—
231#101C2×D4311yescharacteristic, complemented
232#41—22no—
233#41—22no—
234#41—432no—
235#41—432no—
236#41—432no—
237#41—862no—
238#41—862no—
239#41—864no—
240#41—864no—
241#41—862no—
242#41—864no—
243#41—862no—
244#41—864no—
245#41—862no—
246#41—862no—
247#41—862no—
248#41—862no—
249#41C22×D4312yes—
250C2×Q8—22no—
251C2×Q8—432no—
252C2×Q8—431no—
253C2×Q8—432no—
254C2×Q8—431no—
255C2×Q8—861no—
256C2×Q8—862no—
257C2×Q8—864no—
258C2×Q8—862no—
259C2×Q8—862no—
260C2×Q8—862no—
261C2×Q8—862no—
262C2×Q8—862no—
263C2×Q8—862no—
264C2×Q8—864no—
265C2×Q8—862no—
266C2×Q8C22×D4311yescharacteristic
267C2×Q8C22×D4311yescharacteristic
268C2×D4—432no—
269C2×D4—862no—
270C2×D4—862no—
271C22×C4—431no—
272C22×C4—432no—
273C22×C4—862no—
274C22×C4—861no—
275C22×C4—864no—
276C22×C4—861no—
277Q16—22no—
278Q16—862no—
279Q16—862no—
280Q16—862no—
281SD16—22no—
282SD16—862no—
283SD16—862no—
284SD16—862no—
285M16—432no—
286M16—862no—
287M16C22×D4312yes—
288C2×C8—862no—
289C4⋊C4—22no—
290C4⋊C4—862no—
291C4⋊C4—862no—
292C4⋊C4—862no—
293C42—431no—
294C42—861no—
295C42C22×D4311yescharacteristic
296C23—431no—
297C23—862no—
298Q8—22no—
299Q8—22no—
300Q8—22no—
301Q8—432no—
302Q8—862no—
303Q8—864no—
304Q8—864no—
305Q8—862no—
306Q8—862no—
307Q8—862no—
308Q8—1722no—
309Q8D4×D4312yes—
310D4—22no—
311D4—22no—
312D4—432no—
313D4—862no—
314D4—862no—
315D4—862no—
316D4—862no—
317D4—864no—
318D4—862no—
319D4D4×D4312yes—
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—431no—
325C2×C4—432no—
326C2×C4—432no—
327C2×C4—432no—
328C2×C4—862no—
329C2×C4—862no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—864no—
333C2×C4—864no—
334C2×C4—864no—
335C2×C4—862no—
336C2×C4—864no—
337C2×C4—861no—
338C2×C4—862no—
339C2×C4—861no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4D4×D4312yes—
343C2×C4C23×D4311yescharacteristic
344C8—22no—
345C8—862no—
346C22—22no—
347C22—431no—
348C22—431no—
349C22—862no—
350C22—862no—
351C22—1724no—
352C22C2×D4×D4311yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—41no—
357C4—432no—
358C4—862no—
359C4—862no—
360C4—862no—
361C4—1721no—
362C4C2×D4×D4312yes—
363C2—21no—
364C2—42no—
365C2—432no—
366C2—861no—
367C2—1722no—
368C2#120×D4311yescharacteristic
subgroupG/H
centerC2#120×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#456C2
socleC2×C43C2×#120
hypercenter#456D43
hypocenterC43C2×#456
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
2. #137×D43C2semidirect
3. C4⋊Q8×D43C2semidirect
4. #14583084C2semidirect
5. #14583083C2semidirect
6. #14583082C2semidirect
7. #14583081C2semidirect
8. #14583080C2semidirect
9. #104×D43C2semidirect
10. #101×D43C2semidirect
11. C43×#456C2semidirect
23. #13063358C22semidirect
25. #13063356C22semidirect
26. #13063355C22semidirect
31. #13063325C22semidirect
33. #13063323C22semidirect
34. #13063323C22semidirect
37. #13063253C22semidirect
38. #13063252C22semidirect
39. #13063251C22semidirect
40. #13063244C22semidirect
41. #13063243C22semidirect
43. #137×C43C22semidirect
44. C4⋊Q8×C43C22semidirect
45. #104×C43C22semidirect
46. #101×C43C22semidirect
184. D43#456direct (N × H)
193. #456D43direct (N × H)
196. C43C2×#456semidirect
214. #137C2×D43semidirect
222. C4⋊Q8C2×D43semidirect
228. #104C2×D43semidirect
231. #101C2×D43semidirect