Finite Group Databasebeta

← #19138227

Subgroups — #19138227

Order 5504.

1348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1348 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×D43C211yesmaximal, characteristic, complemented
2C2×#13063321C212yesmaximal, complemented
3C2×#13063298C211yesmaximal, characteristic, complemented
4C2×#13063295C212yesmaximal, complemented
5C2×#13063293C212yesmaximal, complemented
6#14582809C211yesmaximal, characteristic, complemented
7#14582808C211yesmaximal, characteristic, complemented
8#14582807C211yesmaximal, characteristic, complemented
9#14582799C212yesmaximal, complemented
10#14582746C211yesmaximal, characteristic, complemented
11C43×#392C211yesmaximal, characteristic, complemented
12C24×D43C2212yes—
13C22×D172C2211yescharacteristic
14C22×D172C2211yescharacteristic
15C22×D172C2212yescomplemented
16C22×C22⋊D43C2211yescharacteristic
17C22×C22⋊D43C2212yes—
18C22×C22⋊D43C2211yescharacteristic, complemented
19C22×C22⋊D43C2212yescomplemented
20C22×C22⋊D43C2212yescomplemented
21C2×D4×D43—28no—
22C2×D4×D43—24no—
23C22×C4×D43C2211yescharacteristic
24#13063321—28no—
25#13063298—24no—
26#13063295—28no—
27#13063293—28no—
28C2×Dic43⋊C4C2211yescharacteristic, complemented
29C2×C22⋊Dic43C2212yescomplemented
30C2×(C2×D43)⋊C4C2212yes—
31C2×(C2×D43)⋊C4C2212yescomplemented
32C2×(C2×D43)⋊C4C2212yescomplemented
33C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
34C2×C4×Dic43C2212yescomplemented
35C43⋊#95C2211yescharacteristic, complemented
36C22×D4×C43C2211yescharacteristic
37C22×D4×C43C2212yescomplemented
38C2×C22⋊C4×C43C2212yescomplemented
39C2×C22⋊C4×C43C2211yescharacteristic, complemented
40#95×C43C2211yescharacteristic, complemented
41C24×C43C2311yescharacteristic
42C24×C43C2312yes—
43C23×D43—24no—
44C23×D43—24no—
45C23×D43—24no—
46C23×D43—24no—
47C23×D43—24no—
48C23×D43—42no—
49C23×D43—42no—
50C23×D43C2311yescharacteristic
51C23×D43C2312yes—
52C23×D43C2311yescharacteristic
53C2×D4×C43—22no—
54C2×D4×C43—24no—
55C2×D4×C43—24no—
56C2×D4×C43—24no—
57C2×D4×C43—42no—
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2312yes—
61C2×C22⋊D43—24no—
62C2×C22⋊D43—24no—
63C2×C22⋊D43—22no—
64C2×C22⋊D43—24no—
65C2×C22⋊D43—24no—
66C2×C22⋊D43—24no—
67C2×C22⋊D43—24no—
68C2×C22⋊D43—24no—
69C2×C22⋊D43—22no—
70C2×C22⋊D43—24no—
71C2×C22⋊D43—42no—
72C2×C22⋊D43—42no—
73C2×C22⋊D43D418yescomplemented
74C22×Dic43C2311yescharacteristic
75C22×Dic43C2312yes—
76C22×Dic43C2311yescharacteristic
77D4×D43—232no—
78C2×D172—22no—
79C2×D172—24no—
80C2×D172—24no—
81C2×D172—24no—
82C2×D172—22no—
83C2×D172—24no—
84C2×D172—42no—
85C2×C4×D43—24no—
86C2×C4×D43D414yescomplemented
87C22⋊C4×C43—22no—
88C22⋊C4×C43—24no—
89C22⋊Dic43—24no—
90(C2×D43)⋊C4—22no—
91(C2×D43)⋊C4—24no—
92(C2×D43)⋊C4—24no—
93(C2×D43)⋊C4D418yescomplemented
94Dic43⋊C4—22no—
95C4×Dic43—24no—
96C23×C43—22no—
97C23×C43—22no—
98C23×C43—22no—
99C23×C43—22no—
100C23×C43—22no—
101C23×C43—22no—
102C23×C43—21no—
103C23×C43—22no—
104C23×C43—22no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43C2×D414yes—
108C23×C43C2411yescharacteristic
109C22×D43—22no—
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—216no—
113C22×D43—22no—
114C22×D43—22no—
115C22×D43—22no—
116C22×D43—22no—
117C22×D43—22no—
118C22×D43—22no—
119C22×D43—21no—
120C22×D43—22no—
121C22×D43—22no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—48no—
125C22×D43—48no—
126C22×D43—48no—
127C22×D43—48no—
128C22×D43—48no—
129C22×D43—48no—
130C22×D43C2×D414yes—
131C22×D43C2×D414yes—
132C22×D43C2×D412yes—
133D4×C43—28no—
134D4×C43—48no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—21no—
139C2×C4×C43—22no—
140C2×C4×C43C2×D412yes—
141C2×C4×C43C2×D414yescomplemented
142C22⋊D43—216no—
143C22⋊D43—48no—
144C22⋊D43—48no—
145C22⋊D43—44no—
146C22⋊D43—44no—
147C2×Dic43—22no—
148C2×Dic43—22no—
149C2×Dic43—21no—
150C2×Dic43—22no—
151C2×Dic43C2×D414yes—
152C2×Dic43C2×D412yes—
153C2×Dic43C2×D414yescomplemented
154D172—28no—
155D172—48no—
156D172—44no—
157C4×D43—28no—
158C22×C43—24no—
159C22×C43—24no—
160C22×C43—24no—
161C22×C43—42no—
162C22×C43—42no—
163C22×C43—42no—
164C22×C43—42no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—42no—
169C22×C43—42no—
170C22×C43C22×D411yescharacteristic
171C22×C43C22×D412yes—
172C22×C43C22×D412yes—
173C22×C43H(5,𝔽2)11yescharacteristic
174C22×C43H(5,𝔽2)11yescharacteristic
175C2×D43—22no—
176C2×D43—22no—
177C2×D43—24no—
178C2×D43—24no—
179C2×D43—24no—
180C2×D43—24no—
181C2×D43—24no—
182C2×D43—432no—
183C2×D43—42no—
184C2×D43—42no—
185C2×D43—42no—
186C2×D43—42no—
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—41no—
190C2×D43—42no—
191C2×D43—42no—
192C2×D43#12714yescomplemented
193C4×C43—22no—
194C4×C43—24no—
195C4×C43—41no—
196Dic43—24no—
197Dic43—41no—
198Dic43#12014yescomplemented
199#2433—431nomaximal, Sylow
200C2×C43—44no—
201C2×C43—81no—
202C2×C43C2×#12011yescharacteristic
203C2×C43C2×#12711yescharacteristic
204C2×C43#53511yescharacteristic
205C2×C43D4212yes—
206C2×C43D4212yes—
207D43—24no—
208D43—44no—
209D43—81no—
210C23×D4—431no—
211C2×#127—432no—
212C2×#121—431no—
213C2×#120—432no—
214C2×#120—432no—
215#392—431no—
216#392—431no—
217#392—431no—
218#392D4311yescharacteristic, complemented
219#390—432no—
220C4×C22⋊C4—431no—
221C43#243311yescharacteristic, complemented, Sylow
222C25—432no—
223C22×D4—432no—
224C22×D4—431no—
225C22×D4—431no—
226C22×D4—432no—
227C22×D4—432no—
228C22×D4—431no—
229C22×D4—431no—
230C22×D4—432no—
231C22×D4—864no—
232C22×D4—868no—
233C22×D4C2×D4311yescharacteristic
234C22×D4C2×D4312yescomplemented
235C23×C4—431no—
236#127—868no—
237#121—864no—
238#120—868no—
239#120—868no—
240C2×C4⋊C4—431no—
241C2×C22⋊C4—432no—
242C2×C22⋊C4—432no—
243C2×C22⋊C4—432no—
244C2×C22⋊C4—432no—
245C2×C22⋊C4—431no—
246C2×C22⋊C4C2×D4312yescomplemented
247C2×C22⋊C4C2×D4311yescharacteristic, complemented
248C2×C42—432no—
249#95—431no—
250#95C2×D4311yescharacteristic, complemented
251C24—431no—
252C24—432no—
253C24—431no—
254C24—864no—
255C24—864no—
256C24—864no—
257C24—864no—
258C24—864no—
259C24—1722no—
260C24—1722no—
261C24C22×D4311yescharacteristic
262C24C22×D4312yes—
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—22no—
266C2×D4—24no—
267C2×D4—42no—
268C2×D4—438no—
269C2×D4—864no—
270C2×D4—864no—
271C2×D4—862no—
272C2×D4—864no—
273C2×D4—864no—
274C2×D4—864no—
275C2×D4—864no—
276C2×D4—864no—
277C2×D4—862no—
278C2×D4—864no—
279C2×D4—8632no—
280C2×D4—864no—
281C2×D4—862no—
282C2×D4—864no—
283C2×D4—864no—
284C2×D4—862no—
285C2×D4—864no—
286C2×D4—1722no—
287C2×D4—1722no—
288C2×D4—1722no—
289C22×C4—431no—
290C22×C4—432no—
291C22×C4—434no—
292C22×C4—431no—
293C22×C4—864no—
294C22×C4C22×D4311yescharacteristic
295C22×C4C22×D4311yescharacteristic
296C22×C4C22×D4312yes—
297C4⋊C4—862no—
298C22⋊C4—22no—
299C22⋊C4—24no—
300C22⋊C4—438no—
301C22⋊C4—864no—
302C22⋊C4—864no—
303C22⋊C4—862no—
304C22⋊C4—864no—
305C42—864no—
306C23—22no—
307C23—22no—
308C23—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—21no—
313C23—22no—
314C23—22no—
315C23—21no—
316C23—21no—
317C23—434no—
318C23—432no—
319C23—434no—
320C23—8616no—
321C23—862no—
322C23—861no—
323C23—861no—
324C23—862no—
325C23—862no—
326C23—862no—
327C23—862no—
328C23—862no—
329C23—862no—
330C23—861no—
331C23—862no—
332C23—862no—
333C23—861no—
334C23—861no—
335C23—1728no—
336C23—1728no—
337C23—1728no—
338C23—1728no—
339C23—1728no—
340C23—1728no—
341C23D4×D4314yes—
342C23C23×D4311yescharacteristic
343D4—28no—
344D4—48no—
345D4—868no—
346D4—8616no—
347D4—1728no—
348D4—1724no—
349D4—1724no—
350D4—1728no—
351D4—1728no—
352D4—1724no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—21no—
358C2×C4—434no—
359C2×C4—432no—
360C2×C4—434no—
361C2×C4—868no—
362C2×C4—862no—
363C2×C4—862no—
364C2×C4—862no—
365C2×C4—861no—
366C2×C4D4×D4312yes—
367C2×C4D4×D4314yescomplemented
368C22—24no—
369C22—24no—
370C22—24no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—42no—
379C22—42no—
380C22—434no—
381C22—862no—
382C22—862no—
383C22—864no—
384C22—864no—
385C22—864no—
386C22—864no—
387C22—864no—
388C22—17232no—
389C22—1721no—
390C22—1721no—
391C22—1721no—
392C22—1722no—
393C22—1722no—
394C22—1722no—
395C22—1722no—
396C22—1722no—
397C22—1722no—
398C22C2×D4×D4311yescharacteristic
399C22C2×D4×D4312yes—
400C22C2×D4×D4312yes—
401C22#1306337011yescharacteristic
402C22#1306337111yescharacteristic
403C4—22no—
404C4—24no—
405C4—41no—
406C4—434no—
407C4—864no—
408C4—1721no—
409C2—44no—
410C2—81no—
411C2—864no—
412C2—3441no—
413C2—1724no—
414C2#120×D4311yescharacteristic
415C2#127×D4311yescharacteristic
416C2#1458346511yescharacteristic
417C2#1458353112yes—
418C2#1458353312yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2433
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×#13063321C2semidirect
3. C2×#13063298C2semidirect
4. C2×#13063295C2semidirect
5. C2×#13063293C2semidirect
6. #14582809C2semidirect
7. #14582808C2semidirect
8. #14582807C2semidirect
9. #14582799C2semidirect
10. #14582746C2semidirect
11. C43×#392C2semidirect
15. C22×D172C22semidirect
18. C22×C22⋊D43C22semidirect
19. C22×C22⋊D43C22semidirect
20. C22×C22⋊D43C22semidirect
28. C2×Dic43⋊C4C22semidirect
29. C2×C22⋊Dic43C22semidirect
31. C2×(C2×D43)⋊C4C22semidirect
32. C2×(C2×D43)⋊C4C22semidirect
33. C2×(C2×D43)⋊C4C22semidirect
34. C2×C4×Dic43C22semidirect
35. C43⋊#95C22semidirect
37. C22×D4×C43C22semidirect
38. C2×C22⋊C4×C43C22semidirect
39. C2×C22⋊C4×C43C22semidirect
40. #95×C43C22semidirect
73. C2×C22⋊D43D4semidirect
86. C2×C4×D43D4semidirect
93. (C2×D43)⋊C4D4semidirect
141. C2×C4×C43C2×D4semidirect
153. C2×Dic43C2×D4semidirect
192. C2×D43#127semidirect
198. Dic43#120semidirect
218. #392D43semidirect
221. C43#2433semidirect
234. C22×D4C2×D43semidirect
246. C2×C22⋊C4C2×D43semidirect
247. C2×C22⋊C4C2×D43semidirect
250. #95C2×D43semidirect
367. C2×C4D4×D43semidirect