Finite Group Databasebeta

← #19143991

Subgroups — #19143991

Order 5504.

800 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 145 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
2#14583458C212yesmaximal, complemented
3#14583088C214yesmaximal, complemented
4#14583085C214yesmaximal, complemented
5C2×#13063240C211yesmaximal, characteristic, complemented
6C2×#13063239C212yesmaximal, complemented
7C43×#534C211yesmaximal, characteristic, complemented
8#13063370—22no—
9#13063370—24no—
10#13063370C2214yes—
11C2×#10621898—21no—
12C2×#10621900—22no—
13C22×C22⋊D43—21no—
14C22×C22⋊D43C2212yes—
15C2×D4×D43—22no—
16#13063308C2214yescomplemented
17#13063306—22no—
18#13063297—24no—
19#13063294C2214yescomplemented
20#13063293—22no—
21C2×C22⋊Dic43C2212yescomplemented
22#13063240C2214yescomplemented
23#13063239C2218yescomplemented
24C22×D4×C43C2211yescharacteristic
25C22×D4×C43C2211yescharacteristic, complemented
26#123×C43—21no—
27#123×C43C2212yescomplemented
28#121×C43—22no—
29#120×C43—21no—
30#120×C43C2212yescomplemented
31C2×C22⋊C4×C43C2211yescharacteristic, complemented
32C24×C43D411yescharacteristic, complemented
33C24×C43C2311yescharacteristic
34C24×C43C2311yescharacteristic, complemented
35C23×D43—21no—
36C23×D43D412yescomplemented
37C2×D4×C43—22no—
38C2×D4×C43—22no—
39C2×D4×C43—21no—
40C2×D4×C43—21no—
41C2×D4×C43—22no—
42C2×D4×C43—22no—
43C2×D4×C43—22no—
44C2×D4×C43D412yescomplemented
45C2×D4×C43C2312yes—
46C22×C4×C43—21no—
47C22×C4×C43D411yescharacteristic, complemented
48C22×C4×C43C2311yescharacteristic, complemented
49C2×C22⋊D43—22no—
50C2×C22⋊D43—24no—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—24no—
54C2×C22⋊D43—22no—
55C2×C22⋊D43—22no—
56C2×C22⋊D43—24no—
57C2×C22⋊D43D414yescomplemented
58C2×C22⋊D43C2314yes—
59C22×Dic43—21no—
60C22×Dic43—22no—
61C22×Dic43D412yescomplemented
62#10621900—28no—
63#10621900—28no—
64D4×D43—28no—
65D4×D43—28no—
66#10621898—24no—
67#10621898—24no—
68C2×D172—21no—
69C2×C4×D43—22no—
70C2×Dic86—21no—
71C4⋊C4×C43—22no—
72C22⋊C4×C43—22no—
73C22⋊C4×C43—21no—
74C22⋊C4×C43—22no—
75C22⋊C4×C43C2312yescomplemented
76C22⋊Dic43—24no—
77C22⋊Dic43—22no—
78C22⋊Dic43C2314yescomplemented
79(C2×D43)⋊C4—24no—
80Dic43⋊C4—24no—
81C23×C43—21no—
82C23×C43—21no—
83C23×C43—22no—
84C23×C43—21no—
85C23×C43—81no—
86C23×C43—81no—
87C23×C43—81no—
88C23×C43C2×D412yes—
89C23×C43C2×D412yes—
90C23×C43C2×D412yes—
91C23×C43C2×D411yescharacteristic
92C23×C43C2×D411yescharacteristic
93C23×C43C2411yescharacteristic
94C22×D43—22no—
95C22×D43—24no—
96C22×D43—22no—
97C22×D43—82no—
98C22×D43—82no—
99C22×D43C2×D414yes—
100D4×C43—24no—
101D4×C43—24no—
102D4×C43—41no—
103D4×C43—42no—
104D4×C43—41no—
105D4×C43—82no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43—21no—
111C2×C4×C43—81no—
112C2×C4×C43C2×D412yes—
113C22⋊D43—28no—
114C22⋊D43—24no—
115C22⋊D43—24no—
116C22⋊D43—24no—
117C22⋊D43—24no—
118C22⋊D43—84no—
119C2×Dic43—24no—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—24no—
123C2×Dic43—82no—
124C2×Dic43C2×D414yes—
125D172—24no—
126C4×D43—28no—
127Dic86—24no—
128C22×C43—22no—
129C22×C43—42no—
130C22×C43—41no—
131C22×C43—41no—
132C22×C43—42no—
133C22×C43—41no—
134C22×C43—42no—
135C22×C43—42no—
136C22×C43—44no—
137C22×C43—42no—
138C22×C43—41no—
139C22×C43—81no—
140C22×C43#12011yescharacteristic
141C22×C43#12012yes—
142C22×C43#12011yescharacteristic
143C22×C43C22×D412yes—
144C22×C43C22×D411yescharacteristic
145C2×D43—24no—
146C2×D43—44no—
147C2×D43—44no—
148C2×D43—82no—
149C2×D43—84no—
150C4×C43—22no—
151C4×C43—42no—
152C4×C43—41no—
153Dic43—24no—
154Dic43—44no—
155#3026—431nomaximal, Sylow
156C2×C43—22no—
157C2×C43—21no—
158C2×C43—21no—
159C2×C43—22no—
160C2×C43—21no—
161C2×C43—42no—
162C2×C43—81no—
163C2×C43C2×#12011yescharacteristic
164D43—44no—
165C2×H(5,𝔽2)—431no—
166#534—432no—
167#534D4311yescharacteristic, complemented
168#458—434no—
169B(4,𝔽2)—434no—
170C2×#99—431no—
171C2×#99—432no—
172C43#302611yescharacteristic, complemented, Sylow
173H(5,𝔽2)—434no—
174H(5,𝔽2)—864no—
175H(5,𝔽2)—862no—
176C2×#41—862no—
177C2×#41—861no—
178C22×D4—432no—
179C22×D4—862no—
180C22×D4—861no—
181C22×D4C2×D4311yescharacteristic
182C22×D4C2×D4311yescharacteristic, complemented
183#123—21no—
184#123—434no—
185#123—862no—
186#123C2×D4312yescomplemented
187#121—22no—
188#121—864no—
189#120—21no—
190#120—434no—
191#120—862no—
192#120C2×D4312yescomplemented
193C2×C22⋊C4—432no—
194C2×C22⋊C4C2×D4311yescharacteristic, complemented
195#99—434no—
196#99—438no—
197C24—432no—
198C24—861no—
199C24C22⋊D4311yescharacteristic, complemented
200C24C22×D4311yescharacteristic
201C24C22×D4311yescharacteristic, complemented
202#41—864no—
203#41—868no—
204#41—868no—
205#41—864no—
206C2×Q8—861no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—22no—
214C2×D4—434no—
215C2×D4—434no—
216C2×D4—861no—
217C2×D4—868no—
218C2×D4—868no—
219C2×D4—862no—
220C2×D4—864no—
221C2×D4—862no—
222C2×D4—862no—
223C2×D4—862no—
224C2×D4—862no—
225C2×D4—864no—
226C2×D4—864no—
227C2×D4C22⋊D4312yescomplemented
228C2×D4C22×D4312yes—
229C22×C4—21no—
230C22×C4—432no—
231C22×C4—862no—
232C22×C4—861no—
233C22×C4—862no—
234C22×C4C22⋊D4311yescharacteristic, complemented
235C22×C4C22×D4311yescharacteristic, complemented
236C4⋊C4—22no—
237C4⋊C4—864no—
238C22⋊C4—21no—
239C22⋊C4—22no—
240C22⋊C4—22no—
241C22⋊C4—434no—
242C22⋊C4—864no—
243C22⋊C4—864no—
244C22⋊C4—862no—
245C22⋊C4C22×D4312yescomplemented
246C23—21no—
247C23—21no—
248C23—22no—
249C23—21no—
250C23—81no—
251C23—81no—
252C23—81no—
253C23—434no—
254C23—864no—
255C23—862no—
256C23—862no—
257C23—3442no—
258C23—3442no—
259C23D4×D4312yes—
260C23D4×D4312yes—
261C23C2×C22⋊D4312yes—
262C23C2×C22⋊D4311yescharacteristic
263C23C2×C22⋊D4311yescharacteristic
264C23C23×D4311yescharacteristic
265Q8—864no—
266D4—24no—
267D4—24no—
268D4—41no—
269D4—41no—
270D4—42no—
271D4—82no—
272D4—864no—
273D4—868no—
274D4—864no—
275D4—864no—
276D4—864no—
277D4—864no—
278D4—3444no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—434no—
286C2×C4—868no—
287C2×C4—864no—
288C2×C4—862no—
289C2×C4—862no—
290C2×C4—864no—
291C2×C4—3442no—
292C2×C4C2×C22⋊D4312yes—
293C22—22no—
294C22—41no—
295C22—42no—
296C22—41no—
297C22—41no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—44no—
303C22—41no—
304C22—81no—
305C22—864no—
306C22—3442no—
307C22—3444no—
308C22—1724no—
309C22—1724no—
310C22#1306329311yescharacteristic
311C22#1306329311yescharacteristic
312C22#1306329312yes—
313C22C2×D4×D4312yes—
314C22C22×C22⋊D4311yescharacteristic
315C4—22no—
316C4—42no—
317C4—41no—
318C4—864no—
319C4—1724no—
320C2—21no—
321C2—22no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—42no—
326C2—81no—
327C2—1724no—
328C2C2×#1306329311yescharacteristic
subgroupG/H
centerC2C2×#13063293
commutatorC23×C43C24
FrattiniC23C23×D43
FittingC43×#534C2
socleC2×C43C2×#120
hypercenter#534D43
hypocenterC43#3026
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#13063370C2semidirect
2. #14583458C2semidirect
3. #14583088C2semidirect
4. #14583085C2semidirect
5. C2×#13063240C2semidirect
6. C2×#13063239C2semidirect
7. C43×#534C2semidirect
16. #13063308C22semidirect
19. #13063294C22semidirect
21. C2×C22⋊Dic43C22semidirect
22. #13063240C22semidirect
23. #13063239C22semidirect
25. C22×D4×C43C22semidirect
27. #123×C43C22semidirect
30. #120×C43C22semidirect
31. C2×C22⋊C4×C43C22semidirect
32. C24×C43D4semidirect
34. C24×C43C23semidirect
36. C23×D43D4semidirect
44. C2×D4×C43D4semidirect
47. C22×C4×C43D4semidirect
48. C22×C4×C43C23semidirect
57. C2×C22⋊D43D4semidirect
61. C22×Dic43D4semidirect
75. C22⋊C4×C43C23semidirect
78. C22⋊Dic43C23semidirect
167. #534D43semidirect
172. C43#3026semidirect
182. C22×D4C2×D43semidirect
186. #123C2×D43semidirect
192. #120C2×D43semidirect
194. C2×C22⋊C4C2×D43semidirect
199. C24C22⋊D43semidirect
201. C24C22×D43semidirect
227. C2×D4C22⋊D43semidirect
234. C22×C4C22⋊D43semidirect
235. C22×C4C22×D43semidirect
245. C22⋊C4C22×D43semidirect