Finite Group Databasebeta

← #19137904

Subgroups — #19137904

Order 5504.

1564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×D4×D43C212yesmaximal, complemented
2C2×#13063295C212yesmaximal, complemented
3C2×#13063293C212yesmaximal, complemented
4#14582808C211yesmaximal, characteristic, complemented
5#14582807C212yesmaximal, complemented
6#14582777C212yesmaximal, complemented
7#14582775C212yesmaximal, complemented
8#14582754C211yesmaximal, characteristic, complemented
9C43×#392C211yesmaximal, characteristic, complemented
10C24×D43C2211yescharacteristic
11C24×D43C2212yescomplemented
12C22×D172C2212yes—
13C22×D172C2211yescharacteristic, complemented
14C22×C22⋊D43C2212yes—
15C22×C22⋊D43C2212yescomplemented
16C22×C22⋊D43C2212yescomplemented
17C2×D4×D43—28no—
18C2×D4×D43—28no—
19C2×D4×D43—28no—
20C22×C4×D43C2212yescomplemented
21#13063295—28no—
22#13063293—28no—
23C2×C22⋊Dic43C2212yescomplemented
24C2×C22⋊Dic43C2211yescharacteristic, complemented
25C2×(C2×D43)⋊C4C2212yescomplemented
26C2×(C2×D43)⋊C4C2212yescomplemented
27C2×(C2×D43)⋊C4C2212yescomplemented
28C2×(C2×D43)⋊C4C2212yescomplemented
29C43⋊#95C2212yescomplemented
30C43⋊#95C2211yescharacteristic, complemented
31C22×D4×C43C2212yescomplemented
32C22×D4×C43C2211yescharacteristic, complemented
33C2×C22⋊C4×C43C2212yescomplemented
34C2×C22⋊C4×C43C2211yescharacteristic, complemented
35#95×C43C2211yescharacteristic, complemented
36C24×C43C2311yescharacteristic
37C24×C43C2312yes—
38C23×D43—24no—
39C23×D43—24no—
40C23×D43—24no—
41C23×D43—24no—
42C23×D43—24no—
43C23×D43—24no—
44C23×D43—24no—
45C23×D43—41no—
46C23×D43—41no—
47C23×D43—42no—
48C23×D43—42no—
49C23×D43D414yescomplemented
50C23×D43C2312yes—
51C23×D43C2312yes—
52C2×D4×C43—24no—
53C2×D4×C43—24no—
54C2×D4×C43—24no—
55C2×D4×C43—24no—
56C2×D4×C43—41no—
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2312yes—
60C2×C22⋊D43—24no—
61C2×C22⋊D43—24no—
62C2×C22⋊D43—24no—
63C2×C22⋊D43—24no—
64C2×C22⋊D43—24no—
65C2×C22⋊D43—24no—
66C2×C22⋊D43—24no—
67C2×C22⋊D43—42no—
68C2×C22⋊D43D418yescomplemented
69C22×Dic43C2312yes—
70C22×Dic43C2312yes—
71D4×D43—264no—
72C2×D172—24no—
73C2×D172—24no—
74C2×D172—24no—
75C2×D172—41no—
76C2×D172D418yescomplemented
77C2×C4×D43—24no—
78C2×C4×D43—24no—
79C2×C4×D43—24no—
80C22⋊C4×C43—24no—
81C22⋊C4×C43—41no—
82C22⋊Dic43—24no—
83C22⋊Dic43—41no—
84(C2×D43)⋊C4—24no—
85(C2×D43)⋊C4—24no—
86(C2×D43)⋊C4—24no—
87(C2×D43)⋊C4—24no—
88C23×C43—22no—
89C23×C43—22no—
90C23×C43—22no—
91C23×C43—22no—
92C23×C43—22no—
93C23×C43—22no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—22no—
97C23×C43—22no—
98C23×C43C2×D412yes—
99C23×C43C2×D414yescomplemented
100C23×C43C2411yescharacteristic
101C22×D43—22no—
102C22×D43—22no—
103C22×D43—22no—
104C22×D43—22no—
105C22×D43—216no—
106C22×D43—22no—
107C22×D43—22no—
108C22×D43—22no—
109C22×D43—22no—
110C22×D43—22no—
111C22×D43—22no—
112C22×D43—216no—
113C22×D43—44no—
114C22×D43—44no—
115C22×D43—48no—
116C22×D43—44no—
117C22×D43—48no—
118C22×D43—48no—
119C22×D43—48no—
120C22×D43—48no—
121C22×D43—48no—
122C22×D43—48no—
123C22×D43C2×D414yes—
124C22×D43C2×D414yes—
125C22×D43C2×D414yes—
126C22×D43C2×D414yescomplemented
127D4×C43—216no—
128D4×C43—44no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43C2×D414yescomplemented
136C22⋊D43—216no—
137C22⋊D43—216no—
138C22⋊D43—48no—
139C2×Dic43—22no—
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—22no—
143C2×Dic43—22no—
144C2×Dic43C2×D414yescomplemented
145D172—216no—
146D172—44no—
147C4×D43—216no—
148C22×C43—24no—
149C22×C43—24no—
150C22×C43—22no—
151C22×C43—24no—
152C22×C43—24no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43—41no—
156C22×C43—42no—
157C22×C43—42no—
158C22×C43—42no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C22×C43C22×D412yes—
162C22×C43C22×D412yes—
163C22×C43H(5,𝔽2)11yescharacteristic
164C22×C43H(5,𝔽2)11yescharacteristic
165C2×D43—24no—
166C2×D43—24no—
167C2×D43—24no—
168C2×D43—24no—
169C2×D43—24no—
170C2×D43—24no—
171C2×D43—24no—
172C2×D43—24no—
173C2×D43—24no—
174C2×D43—416no—
175C2×D43—432no—
176C2×D43—42no—
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—42no—
180C2×D43#12018yescomplemented
181C4×C43—24no—
182C4×C43—41no—
183C4×C43—41no—
184Dic43—24no—
185Dic43—42no—
186#2403—431nomaximal, Sylow
187C2×C43—42no—
188C2×C43—44no—
189C2×C43C2×#12012yes—
190C2×C43#53411yescharacteristic
191C2×C43D4211yescharacteristic
192C2×C43D4212yes—
193C2×C43D4211yescharacteristic
194D43—28no—
195D43—44no—
196C23×D4—432no—
197C2×#120—432no—
198C2×#120—432no—
199#392—432no—
200#392—431no—
201#392D4311yescharacteristic, complemented
202#386—432no—
203#386—432no—
204#379—431no—
205C43#240311yescharacteristic, complemented, Sylow
206C25—431no—
207C25—432no—
208C22×D4—432no—
209C22×D4—432no—
210C22×D4—432no—
211C22×D4—432no—
212C22×D4—431no—
213C22×D4—868no—
214C22×D4—868no—
215C22×D4—868no—
216C22×D4C2×D4312yescomplemented
217C22×D4C2×D4311yescharacteristic, complemented
218C23×C4—432no—
219#120—868no—
220#120—868no—
221C2×C22⋊C4—432no—
222C2×C22⋊C4—432no—
223C2×C22⋊C4—432no—
224C2×C22⋊C4—432no—
225C2×C22⋊C4—432no—
226C2×C22⋊C4—431no—
227C2×C22⋊C4C2×D4312yescomplemented
228C2×C22⋊C4C2×D4311yescharacteristic, complemented
229#95—431no—
230#95—432no—
231#95C2×D4311yescharacteristic, complemented
232C24—432no—
233C24—432no—
234C24—434no—
235C24—864no—
236C24—864no—
237C24—864no—
238C24—864no—
239C24—864no—
240C24—864no—
241C24—864no—
242C24—1721no—
243C24—1722no—
244C24—1721no—
245C24—1722no—
246C24C22×D4311yescharacteristic
247C24C22×D4312yes—
248C2×D4—24no—
249C2×D4—24no—
250C2×D4—24no—
251C2×D4—24no—
252C2×D4—41no—
253C2×D4—438no—
254C2×D4—438no—
255C2×D4—864no—
256C2×D4—864no—
257C2×D4—864no—
258C2×D4—864no—
259C2×D4—8664no—
260C2×D4—864no—
261C2×D4—864no—
262C2×D4—864no—
263C2×D4—864no—
264C2×D4—864no—
265C2×D4—864no—
266C2×D4—1721no—
267C2×D4—1722no—
268C22×C4—432no—
269C22×C4—432no—
270C22×C4—864no—
271C22×C4—864no—
272C22×C4—864no—
273C22×C4C22×D4311yescharacteristic
274C22×C4C22×D4311yescharacteristic
275C22×C4C22×D4312yes—
276C22⋊C4—24no—
277C22⋊C4—41no—
278C22⋊C4—864no—
279C22⋊C4—864no—
280C22⋊C4—864no—
281C22⋊C4—864no—
282C22⋊C4—864no—
283C22⋊C4—1721no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—21no—
291C23—22no—
292C23—21no—
293C23—22no—
294C23—434no—
295C23—434no—
296C23—434no—
297C23—434no—
298C23—8616no—
299C23—8616no—
300C23—862no—
301C23—862no—
302C23—862no—
303C23—862no—
304C23—862no—
305C23—862no—
306C23—862no—
307C23—862no—
308C23—862no—
309C23—862no—
310C23—1724no—
311C23—1728no—
312C23—1728no—
313C23—1728no—
314C23—1724no—
315C23—1728no—
316C23—1728no—
317C23—1724no—
318C23—1728no—
319C23—1728no—
320C23D4×D4312yes—
321C23D4×D4314yescomplemented
322C23C23×D4311yescharacteristic
323D4—216no—
324D4—44no—
325D4—8616no—
326D4—8616no—
327D4—8616no—
328D4—1724no—
329D4—1728no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—434no—
337C2×C4—8616no—
338C2×C4—862no—
339C2×C4—862no—
340C2×C4—862no—
341C2×C4—862no—
342C2×C4—862no—
343C2×C4D4×D4314yescomplemented
344C22—24no—
345C22—24no—
346C22—22no—
347C22—24no—
348C22—24no—
349C22—42no—
350C22—42no—
351C22—41no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22—41no—
356C22—438no—
357C22—864no—
358C22—864no—
359C22—864no—
360C22—864no—
361C22—864no—
362C22—864no—
363C22—864no—
364C22—864no—
365C22—864no—
366C22—17216no—
367C22—17232no—
368C22—1722no—
369C22—1722no—
370C22—1722no—
371C22—1722no—
372C22C2×D4×D4311yescharacteristic
373C22C2×D4×D4312yes—
374C22C2×D4×D4312yes—
375C22#1306337011yescharacteristic
376C22#1306337111yescharacteristic
377C4—24no—
378C4—41no—
379C4—41no—
380C4—864no—
381C4—1722no—
382C2—42no—
383C2—44no—
384C2—868no—
385C2—1724no—
386C2#120×D4312yes—
387C2#1458345711yescharacteristic
388C2#1458353111yescharacteristic
389C2#1458353312yes—
390C2#1458353411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2403
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×#13063295C2semidirect
3. C2×#13063293C2semidirect
4. #14582808C2semidirect
5. #14582807C2semidirect
6. #14582777C2semidirect
7. #14582775C2semidirect
8. #14582754C2semidirect
9. C43×#392C2semidirect
11. C24×D43C22semidirect
13. C22×D172C22semidirect
15. C22×C22⋊D43C22semidirect
16. C22×C22⋊D43C22semidirect
20. C22×C4×D43C22semidirect
23. C2×C22⋊Dic43C22semidirect
24. C2×C22⋊Dic43C22semidirect
25. C2×(C2×D43)⋊C4C22semidirect
26. C2×(C2×D43)⋊C4C22semidirect
27. C2×(C2×D43)⋊C4C22semidirect
28. C2×(C2×D43)⋊C4C22semidirect
29. C43⋊#95C22semidirect
30. C43⋊#95C22semidirect
31. C22×D4×C43C22semidirect
32. C22×D4×C43C22semidirect
33. C2×C22⋊C4×C43C22semidirect
34. C2×C22⋊C4×C43C22semidirect
35. #95×C43C22semidirect
49. C23×D43D4semidirect
68. C2×C22⋊D43D4semidirect
76. C2×D172D4semidirect
99. C23×C43C2×D4semidirect
126. C22×D43C2×D4semidirect
135. C2×C4×C43C2×D4semidirect
144. C2×Dic43C2×D4semidirect
180. C2×D43#120semidirect
201. #392D43semidirect
205. C43#2403semidirect
216. C22×D4C2×D43semidirect
217. C22×D4C2×D43semidirect
227. C2×C22⋊C4C2×D43semidirect
228. C2×C22⋊C4C2×D43semidirect
231. #95C2×D43semidirect
321. C23D4×D43semidirect
343. C2×C4D4×D43semidirect