Finite Group Databasebeta

← #19137946

Subgroups — #19137946

Order 5504.

1232 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 171 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×#13063298C212yesmaximal, complemented
3C2×#13063295C212yesmaximal, complemented
4C2×#13063287C211yesmaximal, characteristic, complemented
5#14582816C211yesmaximal, characteristic, complemented
6#14582809C211yesmaximal, characteristic, complemented
7#14582807C211yesmaximal, characteristic, complemented
8#14582799C212yesmaximal, complemented
9#14582758C211yesmaximal, characteristic, complemented
10#14582754C212yesmaximal, complemented
11C43×#394C211yesmaximal, characteristic, complemented
12C24×D43C2212yes—
13C22×D172C2211yescharacteristic
14C22×D172C2211yescharacteristic
15C22×D172C2212yescomplemented
16C22×C22⋊D43C2212yes—
17C22×C22⋊D43C2212yescomplemented
18C2×D4×D43—28no—
19C2×D4×D43—24no—
20C22×C4×D43C2211yescharacteristic
21C22×C4×D43C2211yescharacteristic, complemented
22#13063298—28no—
23#13063295—28no—
24#13063287—24no—
25C2×Dic43⋊C4C2212yescomplemented
26C2×C22⋊Dic43C2212yescomplemented
27C2×(C2×D43)⋊C4C2211yescharacteristic
28C2×(C2×D43)⋊C4C2212yes—
29C2×(C2×D43)⋊C4C2212yescomplemented
30C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
31C2×(C2×D43)⋊C4C2212yescomplemented
32C2×(C2×D43)⋊C4C2212yescomplemented
33C2×C4×Dic43C2211yescharacteristic, complemented
34C43⋊#95C2211yescharacteristic, complemented
35C22×D4×C43C2211yescharacteristic
36C2×C4⋊C4×C43C2211yescharacteristic, complemented
37C2×C22⋊C4×C43C2212yescomplemented
38C2×C22⋊C4×C43C2212yescomplemented
39#95×C43C2211yescharacteristic, complemented
40C24×C43C2312yes—
41C23×D43—24no—
42C23×D43—24no—
43C23×D43—24no—
44C23×D43—24no—
45C23×D43—24no—
46C23×D43—42no—
47C23×D43—42no—
48C23×D43C2312yes—
49C23×D43C2311yescharacteristic
50C23×D43C2311yescharacteristic
51C2×D4×C43—22no—
52C2×D4×C43—24no—
53C22×C4×C43C2312yes—
54C22×C4×C43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C2×C22⋊D43—24no—
58C2×C22⋊D43—24no—
59C2×C22⋊D43—24no—
60C2×C22⋊D43—24no—
61C2×C22⋊D43—42no—
62C2×C22⋊D43D418yescomplemented
63C22×Dic43C2312yes—
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66D4×D43—232no—
67C2×D172—22no—
68C2×D172—22no—
69C2×D172—24no—
70C2×D172—24no—
71C2×D172—24no—
72C2×D172—22no—
73C2×D172—42no—
74C2×D172D414yescomplemented
75C2×C4×D43—24no—
76C2×C4×D43—22no—
77C2×C4×D43—24no—
78C2×C4×D43D414yescomplemented
79C4⋊C4×C43—22no—
80C22⋊C4×C43—24no—
81C22⋊C4×C43—24no—
82C22⋊Dic43—42no—
83(C2×D43)⋊C4—22no—
84(C2×D43)⋊C4—24no—
85(C2×D43)⋊C4—22no—
86(C2×D43)⋊C4—24no—
87(C2×D43)⋊C4—24no—
88(C2×D43)⋊C4—42no—
89Dic43⋊C4—24no—
90C4×Dic43—22no—
91C23×C43—22no—
92C23×C43—22no—
93C23×C43—22no—
94C23×C43—22no—
95C23×C43—22no—
96C23×C43—22no—
97C23×C43C2×D414yes—
98C23×C43C2411yescharacteristic
99C22×D43—22no—
100C22×D43—22no—
101C22×D43—216no—
102C22×D43—21no—
103C22×D43—22no—
104C22×D43—22no—
105C22×D43—22no—
106C22×D43—22no—
107C22×D43—21no—
108C22×D43—22no—
109C22×D43—22no—
110C22×D43—22no—
111C22×D43—22no—
112C22×D43—48no—
113C22×D43—48no—
114C22×D43—48no—
115C22×D43—48no—
116C22×D43—48no—
117C22×D43—48no—
118C22×D43C2×D414yes—
119C22×D43C2×D412yes—
120C22×D43C2×D412yes—
121C22×D43C2×D412yescomplemented
122C22×D43#4112yes—
123D4×C43—28no—
124C2×C4×C43—21no—
125C2×C4×C43—22no—
126C2×C4×C43—21no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—21no—
131C2×C4×C43—22no—
132C2×C4×C43C2×D412yes—
133C2×C4×C43C2×D412yescomplemented
134C22⋊D43—216no—
135C22⋊D43—48no—
136C2×Dic43—21no—
137C2×Dic43—22no—
138C2×Dic43—22no—
139C2×Dic43—22no—
140C2×Dic43—22no—
141C2×Dic43C2×D412yes—
142C2×Dic43C2×D414yes—
143D172—28no—
144D172—28no—
145D172—48no—
146C4×D43—28no—
147C4×D43—44no—
148C22×C43—24no—
149C22×C43—24no—
150C22×C43—24no—
151C22×C43—42no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43C22×D411yescharacteristic
156C22×C43C22×D412yes—
157C22×C43C22×D411yescharacteristic
158C22×C43C2×#4111yescharacteristic
159C22×C43H(5,𝔽2)12yes—
160C2×D43—22no—
161C2×D43—22no—
162C2×D43—24no—
163C2×D43—24no—
164C2×D43—24no—
165C2×D43—22no—
166C2×D43—24no—
167C2×D43—24no—
168C2×D43—24no—
169C2×D43—432no—
170C2×D43—41no—
171C2×D43—42no—
172C2×D43—41no—
173C2×D43—42no—
174C2×D43—42no—
175C2×D43—42no—
176C2×D43—42no—
177C2×D43#12114yescomplemented
178C4×C43—22no—
179C4×C43—22no—
180C4×C43—41no—
181C4×C43—42no—
182Dic43—41no—
183Dic43—42no—
184Dic43#12014yescomplemented
185#2408—431nomaximal, Sylow
186C2×C43—44no—
187C2×C43C2×#12011yescharacteristic
188C2×C43C2×#12111yescharacteristic
189C2×C43#53511yescharacteristic
190C2×C43D4212yes—
191C2×C43#54612yes—
192D43—24no—
193D43—42no—
194D43—44no—
195C23×D4—431no—
196C2×#121—432no—
197C2×#120—432no—
198C2×C4×D4—431no—
199#394—431no—
200#394D4311yescharacteristic, complemented
201#392—431no—
202#392—431no—
203#390—432no—
204#380—431no—
205#379—432no—
206C43#240811yescharacteristic, complemented, Sylow
207C25—432no—
208C22×D4—432no—
209C22×D4—432no—
210C22×D4—431no—
211C22×D4—431no—
212C22×D4—432no—
213C22×D4—864no—
214C22×D4—868no—
215C22×D4C2×D4311yescharacteristic
216C23×C4—431no—
217C23×C4—431no—
218#121—868no—
219#120—868no—
220C4×D4—864no—
221C2×C4⋊C4—432no—
222C2×C4⋊C4C2×D4311yescharacteristic, complemented
223C2×C22⋊C4—431no—
224C2×C22⋊C4—431no—
225C2×C22⋊C4—432no—
226C2×C22⋊C4—432no—
227C2×C22⋊C4—432no—
228C2×C22⋊C4—432no—
229C2×C22⋊C4—432no—
230C2×C22⋊C4C2×D4312yescomplemented
231C2×C22⋊C4C2×D4312yescomplemented
232C2×C42—431no—
233#95—431no—
234#95C2×D4311yescharacteristic, complemented
235C24—431no—
236C24—432no—
237C24—431no—
238C24—864no—
239C24—864no—
240C24—864no—
241C24—864no—
242C24—864no—
243C24—1722no—
244C24—1722no—
245C24C22×D4312yes—
246C2×D4—24no—
247C2×D4—22no—
248C2×D4—438no—
249C2×D4—434no—
250C2×D4—862no—
251C2×D4—864no—
252C2×D4—862no—
253C2×D4—864no—
254C2×D4—864no—
255C2×D4—864no—
256C2×D4—864no—
257C2×D4—8632no—
258C2×D4—864no—
259C2×D4—864no—
260C2×D4—862no—
261C2×D4—1722no—
262C2×D4—1722no—
263C22×C4—431no—
264C22×C4—434no—
265C22×C4—432no—
266C22×C4—431no—
267C22×C4—864no—
268C22×C4—862no—
269C22×C4—864no—
270C22×C4C22×D4312yes—
271C22×C4C22×D4311yescharacteristic
272C22×C4C22×D4311yescharacteristic
273C22×C4C22×D4311yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—864no—
276C22⋊C4—24no—
277C22⋊C4—24no—
278C22⋊C4—862no—
279C22⋊C4—864no—
280C22⋊C4—864no—
281C22⋊C4—862no—
282C22⋊C4—864no—
283C22⋊C4—1722no—
284C22⋊C4—1722no—
285C42—862no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—432no—
293C23—432no—
294C23—432no—
295C23—434no—
296C23—432no—
297C23—8616no—
298C23—862no—
299C23—862no—
300C23—861no—
301C23—862no—
302C23—862no—
303C23—862no—
304C23—862no—
305C23—861no—
306C23—862no—
307C23—862no—
308C23—862no—
309C23—862no—
310C23—1728no—
311C23—1728no—
312C23—1728no—
313C23—1728no—
314C23—1728no—
315C23—1728no—
316C23D4×D4314yes—
317C23C23×D4311yescharacteristic
318D4—28no—
319D4—868no—
320D4—868no—
321D4—8616no—
322D4—1728no—
323D4—1728no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—432no—
333C2×C4—434no—
334C2×C4—868no—
335C2×C4—861no—
336C2×C4—862no—
337C2×C4—862no—
338C2×C4—862no—
339C2×C4—862no—
340C2×C4—1724no—
341C2×C4D4×D4312yes—
342C2×C4D4×D4312yescomplemented
343C22—24no—
344C22—24no—
345C22—24no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—434no—
351C22—862no—
352C22—862no—
353C22—864no—
354C22—864no—
355C22—864no—
356C22—862no—
357C22—864no—
358C22—864no—
359C22—864no—
360C22—17232no—
361C22—1721no—
362C22—1722no—
363C22—1722no—
364C22—1721no—
365C22—1722no—
366C22—1722no—
367C22—1722no—
368C22C2×D4×D4311yescharacteristic
369C22C2×D4×D4312yes—
370C22C2×D4×D4311yescharacteristic
371C22#41×D4311yescharacteristic
372C22#1306337112yes—
373C4—22no—
374C4—22no—
375C4—41no—
376C4—42no—
377C4—434no—
378C4—1721no—
379C4—1722no—
380C2—44no—
381C2—864no—
382C2—1724no—
383C2—1722no—
384C2#120×D4311yescharacteristic
385C2#121×D4311yescharacteristic
386C2#1458346711yescharacteristic
387C2#1458353312yes—
388C2#1458354112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2408
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×#13063298C2semidirect
3. C2×#13063295C2semidirect
4. C2×#13063287C2semidirect
5. #14582816C2semidirect
6. #14582809C2semidirect
7. #14582807C2semidirect
8. #14582799C2semidirect
9. #14582758C2semidirect
10. #14582754C2semidirect
11. C43×#394C2semidirect
15. C22×D172C22semidirect
17. C22×C22⋊D43C22semidirect
21. C22×C4×D43C22semidirect
25. C2×Dic43⋊C4C22semidirect
26. C2×C22⋊Dic43C22semidirect
29. C2×(C2×D43)⋊C4C22semidirect
30. C2×(C2×D43)⋊C4C22semidirect
31. C2×(C2×D43)⋊C4C22semidirect
32. C2×(C2×D43)⋊C4C22semidirect
33. C2×C4×Dic43C22semidirect
34. C43⋊#95C22semidirect
36. C2×C4⋊C4×C43C22semidirect
37. C2×C22⋊C4×C43C22semidirect
38. C2×C22⋊C4×C43C22semidirect
39. #95×C43C22semidirect
62. C2×C22⋊D43D4semidirect
74. C2×D172D4semidirect
78. C2×C4×D43D4semidirect
121. C22×D43C2×D4semidirect
133. C2×C4×C43C2×D4semidirect
177. C2×D43#121semidirect
184. Dic43#120semidirect
200. #394D43semidirect
206. C43#2408semidirect
222. C2×C4⋊C4C2×D43semidirect
230. C2×C22⋊C4C2×D43semidirect
231. C2×C22⋊C4C2×D43semidirect
234. #95C2×D43semidirect
342. C2×C4D4×D43semidirect