Finite Group Databasebeta

← #19139522

Subgroups — #19139522

Order 5504.

900 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 159 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×#13063310C212yesmaximal, complemented
2C2×#13063300C211yesmaximal, characteristic, complemented
3C2×#13063295C212yesmaximal, complemented
4C2×C22⋊C4×D43C211yesmaximal, characteristic, complemented
5#14582834C211yesmaximal, characteristic, complemented
6#14582809C211yesmaximal, characteristic, complemented
7#14582808C211yesmaximal, characteristic, complemented
8#14582800C212yesmaximal, complemented
9#14582799C212yesmaximal, complemented
10#14582746C211yesmaximal, characteristic, complemented
11C43×#399C211yesmaximal, characteristic, complemented
12C24×D43C2211yescharacteristic
13C22×D172C2212yes—
14C22×D172C2212yes—
15C22×D172C2211yescharacteristic, complemented
16C22×C22⋊D43C2212yes—
17C22×C4×D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19#13063310—28no—
20#13063300—24no—
21#13063295—28no—
22C2×Dic43⋊C4C2212yescomplemented
23C2×C22⋊Dic43C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2211yescharacteristic
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2212yescomplemented
29C2×(C2×D43)⋊C4C2212yescomplemented
30C2×(C2×D43)⋊C4C2212yescomplemented
31C22⋊C4×D43—24no—
32C2×C4×Dic43C2212yescomplemented
33C43⋊#95C2211yescharacteristic, complemented
34C2×C4⋊C4×C43C2212yescomplemented
35C2×C4⋊C4×C43C2211yescharacteristic, complemented
36C2×C22⋊C4×C43C2212yes—
37C2×C22⋊C4×C43C2211yescharacteristic
38#95×C43C2211yescharacteristic, complemented
39C24×C43C2311yescharacteristic
40C23×D43—22no—
41C23×D43—22no—
42C23×D43—22no—
43C23×D43—24no—
44C23×D43—42no—
45C23×D43C2312yes—
46C23×D43C2311yescharacteristic
47C23×D43C2311yescharacteristic
48C22×C4×C43C2311yescharacteristic
49C22×C4×C43C2312yes—
50C22×C4×C43C2311yescharacteristic
51C22×C4×C43C2312yes—
52C2×C22⋊D43—24no—
53C2×C22⋊D43—24no—
54C2×C22⋊D43—42no—
55C22×Dic43C2311yescharacteristic
56C22×Dic43C2312yes—
57C22×Dic43C2311yescharacteristic
58C2×D172—24no—
59C2×D172—22no—
60C2×D172—24no—
61C2×D172—24no—
62C2×D172—24no—
63C2×D172—24no—
64C2×D172—42no—
65C2×D172—42no—
66C2×C4×D43—22no—
67C2×C4×D43—24no—
68C2×C4×D43—42no—
69C2×C4×D43D414yescomplemented
70C4⋊C4×C43—22no—
71C4⋊C4×C43—24no—
72C22⋊C4×C43—22no—
73C22⋊C4×C43—24no—
74C22⋊Dic43—22no—
75(C2×D43)⋊C4—22no—
76(C2×D43)⋊C4—24no—
77(C2×D43)⋊C4—22no—
78(C2×D43)⋊C4—24no—
79(C2×D43)⋊C4—24no—
80(C2×D43)⋊C4—24no—
81(C2×D43)⋊C4D418yescomplemented
82Dic43⋊C4—24no—
83C4×Dic43—42no—
84C23×C43—21no—
85C23×C43—22no—
86C23×C43—21no—
87C23×C43—22no—
88C23×C43#4112yes—
89C23×C43C2411yescharacteristic
90C22×D43—21no—
91C22×D43—21no—
92C22×D43—22no—
93C22×D43—28no—
94C22×D43—21no—
95C22×D43—22no—
96C22×D43—21no—
97C22×D43—22no—
98C22×D43—22no—
99C22×D43—22no—
100C22×D43—22no—
101C22×D43—22no—
102C22×D43—22no—
103C22×D43—22no—
104C22×D43—22no—
105C22×D43—48no—
106C22×D43—48no—
107C22×D43—44no—
108C22×D43—44no—
109C22×D43C2×D414yes—
110C22×D43C2×D412yes—
111C22×D43#4112yes—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—21no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43C2×D414yes—
121C2×C4×C43C2×D412yes—
122C22⋊D43—48no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43—21no—
128C2×Dic43C2×D414yes—
129C2×Dic43C2×D412yes—
130D172—48no—
131D172—44no—
132D172—48no—
133C4×D43—44no—
134C4×D43—44no—
135C22×C43—22no—
136C22×C43—24no—
137C22×C43—41no—
138C22×C43—41no—
139C22×C43—42no—
140C22×C43C22×D411yescharacteristic
141C22×C43C22×D412yes—
142C22×C43C2×#4111yescharacteristic
143C22×C43C2×#4111yescharacteristic
144C22×C43H(5,𝔽2)12yes—
145C2×D43—22no—
146C2×D43—22no—
147C2×D43—24no—
148C2×D43—24no—
149C2×D43—22no—
150C2×D43—24no—
151C2×D43—416no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—42no—
155C2×D43—42no—
156C2×D43—42no—
157C2×D43—42no—
158C2×D43—42no—
159C2×D43—42no—
160C2×D43—42no—
161C2×D43—42no—
162C2×D43#12714yes—
163C4×C43—22no—
164C4×C43—24no—
165C4×C43—41no—
166C4×C43—42no—
167Dic43—22no—
168Dic43—24no—
169Dic43—41no—
170#2539—431nomaximal, Sylow
171C2×C43—42no—
172C2×C43#52511yescharacteristic
173C2×C43C2×#12711yescharacteristic
174C2×C43#53411yescharacteristic
175C2×C43#54612yes—
176C2×C43#54612yes—
177D43—24no—
178D43—42no—
179D43—82no—
180C2×#123—432no—
181C2×#121—431no—
182C2×#120—432no—
183C22×C22⋊C4—431no—
184#399—431no—
185#399D4311yescharacteristic, complemented
186#392—431no—
187#392—431no—
188#390—432no—
189#390—432no—
190C4×C22⋊C4—431no—
191C43#253911yescharacteristic, complemented, Sylow
192C25—431no—
193C22×D4—432no—
194C22×D4—432no—
195C22×D4—432no—
196C22×D4—431no—
197C23×C4—431no—
198C23×C4—431no—
199#123—868no—
200#121—864no—
201#120—868no—
202C2×C4⋊C4—432no—
203C2×C4⋊C4C2×D4311yescharacteristic, complemented
204C2×C4⋊C4C2×D4312yescomplemented
205C2×C22⋊C4—432no—
206C2×C22⋊C4—431no—
207C2×C22⋊C4—431no—
208C2×C22⋊C4—431no—
209C2×C22⋊C4—432no—
210C2×C22⋊C4—432no—
211C2×C22⋊C4—432no—
212C2×C22⋊C4—432no—
213C2×C22⋊C4—864no—
214C2×C22⋊C4C2×D4311yescharacteristic
215C2×C22⋊C4C2×D4312yes—
216C2×C42—432no—
217#95—431no—
218#95C2×D4311yescharacteristic, complemented
219C24—431no—
220C24—431no—
221C24—432no—
222C24—862no—
223C24—862no—
224C24—864no—
225C24—862no—
226C24—1722no—
227C24C22×D4311yescharacteristic
228C2×D4—864no—
229C2×D4—864no—
230C2×D4—864no—
231C2×D4—864no—
232C2×D4—864no—
233C2×D4—864no—
234C2×D4—864no—
235C2×D4—862no—
236C2×D4—1722no—
237C2×D4—1722no—
238C2×D4—1722no—
239C22×C4—432no—
240C22×C4—431no—
241C22×C4—434no—
242C22×C4—431no—
243C22×C4—862no—
244C22×C4—864no—
245C22×C4—1722no—
246C22×C4C22×D4311yescharacteristic
247C22×C4C22×D4312yes—
248C22×C4C22×D4311yescharacteristic
249C22×C4C22×D4312yes—
250C4⋊C4—22no—
251C4⋊C4—24no—
252C4⋊C4—864no—
253C22⋊C4—22no—
254C22⋊C4—24no—
255C22⋊C4—438no—
256C22⋊C4—862no—
257C22⋊C4—864no—
258C22⋊C4—864no—
259C22⋊C4—864no—
260C22⋊C4—862no—
261C22⋊C4—862no—
262C22⋊C4—864no—
263C42—1722no—
264C23—21no—
265C23—22no—
266C23—21no—
267C23—22no—
268C23—434no—
269C23—432no—
270C23—432no—
271C23—868no—
272C23—861no—
273C23—861no—
274C23—862no—
275C23—861no—
276C23—862no—
277C23—861no—
278C23—862no—
279C23—862no—
280C23—862no—
281C23—862no—
282C23—862no—
283C23—862no—
284C23—862no—
285C23—862no—
286C23—1728no—
287C23—1724no—
288C23—1728no—
289C23—1724no—
290C23#1062190212yes—
291C23C23×D4311yescharacteristic
292D4—1728no—
293D4—1724no—
294D4—1728no—
295D4—1728no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—434no—
305C2×C4—432no—
306C2×C4—862no—
307C2×C4—862no—
308C2×C4—862no—
309C2×C4—861no—
310C2×C4—862no—
311C2×C4—1724no—
312C2×C4—1724no—
313C2×C4D4×D4314yes—
314C2×C4D4×D4312yes—
315C22—22no—
316C22—24no—
317C22—41no—
318C22—41no—
319C22—42no—
320C22—434no—
321C22—862no—
322C22—862no—
323C22—864no—
324C22—864no—
325C22—862no—
326C22—864no—
327C22—17216no—
328C22—1722no—
329C22—1722no—
330C22—1722no—
331C22—1722no—
332C22—1722no—
333C22—1722no—
334C22—1722no—
335C22—1721no—
336C22—1721no—
337C22—1722no—
338C22C2×D4×D4311yescharacteristic
339C22C2×D4×D4312yes—
340C22#41×D4311yescharacteristic
341C22C2×#1062190211yescharacteristic
342C22#1306337112yes—
343C4—22no—
344C4—24no—
345C4—41no—
346C4—42no—
347C4—862no—
348C4—864no—
349C4—1721no—
350C2—42no—
351C2—864no—
352C2—3442no—
353C2—1722no—
354C2#1458341211yescharacteristic
355C2#127×D4311yescharacteristic
356C2#1458346011yescharacteristic
357C2#1458354012yes—
358C2#1458354112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2539
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13063310C2semidirect
2. C2×#13063300C2semidirect
3. C2×#13063295C2semidirect
4. C2×C22⋊C4×D43C2semidirect
5. #14582834C2semidirect
6. #14582809C2semidirect
7. #14582808C2semidirect
8. #14582800C2semidirect
9. #14582799C2semidirect
10. #14582746C2semidirect
11. C43×#399C2semidirect
15. C22×D172C22semidirect
22. C2×Dic43⋊C4C22semidirect
28. C2×(C2×D43)⋊C4C22semidirect
29. C2×(C2×D43)⋊C4C22semidirect
30. C2×(C2×D43)⋊C4C22semidirect
32. C2×C4×Dic43C22semidirect
33. C43⋊#95C22semidirect
34. C2×C4⋊C4×C43C22semidirect
35. C2×C4⋊C4×C43C22semidirect
38. #95×C43C22semidirect
69. C2×C4×D43D4semidirect
81. (C2×D43)⋊C4D4semidirect
185. #399D43semidirect
191. C43#2539semidirect
203. C2×C4⋊C4C2×D43semidirect
204. C2×C4⋊C4C2×D43semidirect
218. #95C2×D43semidirect