Finite Group Databasebeta

← #20246708

Subgroups — #20246708

Order 6016.

1056 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1056 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
1C22×#10625354C211yesmaximal, characteristic, complemented
2C2×#13093994C212yesmaximal, complemented
3C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689034C211yesmaximal, characteristic, complemented
5#15689033C211yesmaximal, characteristic, complemented
6#15689032C211yesmaximal, characteristic, complemented
7#15689001C212yesmaximal, complemented
8#15689001C212yesmaximal, complemented
9#15688999C212yesmaximal, complemented
10#15688985C211yesmaximal, characteristic, complemented
11C47×#393C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C2×#10625354—28no—
14C2×#10625354—24no—
15C22×D188C2212yes—
16C22×D188C2212yes—
17C22×D188C2211yescharacteristic, complemented
18C22×C22⋊D47C2212yes—
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2212yescomplemented
22#13093994—28no—
23C2×C22⋊Dic47C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2212yescomplemented
29C2×(C2×D47)⋊C4C2212yescomplemented
30C22⋊C4×D47—24no—
31C47⋊#95C2212yescomplemented
32C47⋊#95C2211yescharacteristic, complemented
33C47⋊#95C2212yescomplemented
34C22×Q8×C47C2211yescharacteristic, complemented
35C2×C22⋊C4×C47C2212yes—
36C2×C22⋊C4×C47C2211yescharacteristic
37#95×C47C2211yescharacteristic, complemented
38#95×C47C2212yescomplemented
39C24×C47C2311yescharacteristic
40C23×D47—22no—
41C23×D47—22no—
42C23×D47—22no—
43C23×D47—24no—
44C23×D47—42no—
45C23×D47C2312yes—
46C23×D47C2311yescharacteristic
47C23×D47C2311yescharacteristic
48C2×Q8×C47—24no—
49C2×Q8×C47—22no—
50C22×C4×C47C2312yes—
51C22×C4×C47C2311yescharacteristic
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2312yes—
54C2×C22⋊D47—24no—
55C2×C22⋊D47—24no—
56C2×C22⋊D47—42no—
57C22×Dic47C2312yes—
58C22×Dic47C2311yescharacteristic
59C22×Dic47C2311yescharacteristic
60#10625354—232no—
61C2×D188—24no—
62C2×D188—24no—
63C2×D188—24no—
64C2×D188—22no—
65C2×D188—24no—
66C2×D188—24no—
67C2×D188—42no—
68C2×D188D418yescomplemented
69C2×C4×D47—24no—
70C2×C4×D47—24no—
71C2×C4×D47—24no—
72C2×C4×D47—24no—
73C2×C4×D47—22no—
74C2×C4×D47—42no—
75C2×C4×D47D414yescomplemented
76C22⋊C4×C47—22no—
77C22⋊C4×C47—24no—
78C22⋊Dic47—22no—
79(C2×D47)⋊C4—24no—
80(C2×D47)⋊C4—22no—
81(C2×D47)⋊C4—24no—
82(C2×D47)⋊C4—22no—
83(C2×D47)⋊C4—42no—
84(C2×D47)⋊C4—42no—
85C23×C47—21no—
86C23×C47—22no—
87C23×C47—21no—
88C23×C47—22no—
89C23×C47#4112yescomplemented
90C23×C47C2411yescharacteristic
91C22×D47—21no—
92C22×D47—21no—
93C22×D47—22no—
94C22×D47—28no—
95C22×D47—21no—
96C22×D47—22no—
97C22×D47—22no—
98C22×D47—22no—
99C22×D47—22no—
100C22×D47—22no—
101C22×D47—21no—
102C22×D47—22no—
103C22×D47—22no—
104C22×D47—22no—
105C22×D47—48no—
106C22×D47—48no—
107C22×D47—44no—
108C22×D47—44no—
109C22×D47C2×D414yes—
110C22×D47C2×D414yes—
111C22×D47C2×D412yes—
112C22×D47#4112yescomplemented
113Q8×C47—28no—
114C2×C4×C47—22no—
115C2×C4×C47—22no—
116C2×C4×C47—22no—
117C2×C4×C47—21no—
118C2×C4×C47—22no—
119C2×C4×C47—22no—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47C2×D414yes—
123C2×C4×C47C2×D412yes—
124C22⋊D47—48no—
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—21no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47C2×D412yes—
132D188—28no—
133D188—216no—
134D188—48no—
135C4×D47—216no—
136C4×D47—28no—
137C4×D47—44no—
138C22×C47—22no—
139C22×C47—24no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47—42no—
143C22×C47C22×D411yescharacteristic
144C22×C47C22×D412yes—
145C22×C47C2×#4111yescharacteristic
146C22×C47C2×#4111yescharacteristic
147C22×C47H(5,𝔽2)12yes—
148C2×D47—22no—
149C2×D47—22no—
150C2×D47—24no—
151C2×D47—24no—
152C2×D47—24no—
153C2×D47—22no—
154C2×D47—24no—
155C2×D47—24no—
156C2×D47—24no—
157C2×D47—416no—
158C2×D47—41no—
159C2×D47—42no—
160C2×D47—42no—
161C2×D47—41no—
162C2×D47—42no—
163C2×D47—42no—
164C2×D47—42no—
165C2×D47#12014yes—
166C4×C47—24no—
167C4×C47—22no—
168C4×C47—41no—
169C4×C47—42no—
170Dic47—22no—
171Dic47—41no—
172Dic47—42no—
173#2404—471nomaximal, Sylow
174C2×C47—42no—
175C2×C47C2×#12011yescharacteristic
176C2×C47#52511yescharacteristic
177C2×C47#53511yescharacteristic
178C2×C47#54612yes—
179C2×C47#54612yes—
180D47—24no—
181D47—44no—
182D47—42no—
183C22×#41—471no—
184C2×#120—472no—
185C22×C22⋊C4—471no—
186#393—471no—
187#393D4711yescharacteristic, complemented
188#392—471no—
189#392—471no—
190#386—472no—
191#386—472no—
192#386—472no—
193#381—471no—
194C47#240411yescharacteristic, complemented, Sylow
195C25—471no—
196C2×#41—944no—
197C2×#41—948no—
198C22×Q8C2×D4711yescharacteristic, complemented
199C22×D4—472no—
200C22×D4—472no—
201C22×D4—471no—
202C22×D4—472no—
203C23×C4—471no—
204C23×C4—472no—
205C23×C4—471no—
206#120—948no—
207C2×C22⋊C4—471no—
208C2×C22⋊C4—471no—
209C2×C22⋊C4—471no—
210C2×C22⋊C4—472no—
211C2×C22⋊C4—472no—
212C2×C22⋊C4—472no—
213C2×C22⋊C4—472no—
214C2×C22⋊C4—944no—
215C2×C22⋊C4C2×D4711yescharacteristic
216C2×C22⋊C4C2×D4712yes—
217#95—472no—
218#95—471no—
219#95—472no—
220#95C2×D4711yescharacteristic, complemented
221#95C2×D4712yescomplemented
222C24—471no—
223C24—471no—
224C24—472no—
225C24—942no—
226C24—942no—
227C24—944no—
228C24—942no—
229C24—1882no—
230C24C22×D4711yescharacteristic
231#41—9432no—
232C2×Q8—22no—
233C2×Q8—24no—
234C2×D4—478no—
235C2×D4—944no—
236C2×D4—944no—
237C2×D4—944no—
238C2×D4—944no—
239C2×D4—944no—
240C2×D4—944no—
241C2×D4—944no—
242C2×D4—942no—
243C2×D4—1882no—
244C2×D4—1882no—
245C22×C4—471no—
246C22×C4—474no—
247C22×C4—472no—
248C22×C4—471no—
249C22×C4—944no—
250C22×C4—944no—
251C22×C4—944no—
252C22×C4—942no—
253C22×C4—944no—
254C22×C4—1882no—
255C22×C4C22×D4712yes—
256C22×C4C22×D4711yescharacteristic
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4712yes—
259C22⋊C4—22no—
260C22⋊C4—24no—
261C22⋊C4—942no—
262C22⋊C4—944no—
263C22⋊C4—942no—
264C22⋊C4—942no—
265C22⋊C4—944no—
266C22⋊C4—1882no—
267C22⋊C4—1882no—
268C23—21no—
269C23—22no—
270C23—21no—
271C23—22no—
272C23—474no—
273C23—472no—
274C23—474no—
275C23—472no—
276C23—948no—
277C23—941no—
278C23—941no—
279C23—942no—
280C23—941no—
281C23—942no—
282C23—942no—
283C23—942no—
284C23—942no—
285C23—942no—
286C23—941no—
287C23—942no—
288C23—942no—
289C23—942no—
290C23—1888no—
291C23—1884no—
292C23—1888no—
293C23—1884no—
294C23#1062535412yescomplemented
295C23C23×D4711yescharacteristic
296Q8—28no—
297D4—9416no—
298D4—948no—
299D4—1888no—
300D4—1888no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—472no—
310C2×C4—948no—
311C2×C4—9416no—
312C2×C4—942no—
313C2×C4—941no—
314C2×C4—942no—
315C2×C4—942no—
316C2×C4—942no—
317C2×C4—942no—
318C2×C4—1884no—
319C2×C4D4×D4712yes—
320C2×C4D4×D4714yes—
321C22—24no—
322C22—22no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—474no—
327C22—944no—
328C22—944no—
329C22—942no—
330C22—942no—
331C22—944no—
332C22—944no—
333C22—944no—
334C22—944no—
335C22—942no—
336C22—18816no—
337C22—1882no—
338C22—1882no—
339C22—1882no—
340C22—1881no—
341C22—1882no—
342C22—1881no—
343C22—1882no—
344C22C2×D4×D4712yes—
345C22C2×D4×D4711yescharacteristic
346C22#41×D4711yescharacteristic
347C22C2×#1062535411yescharacteristic
348C22#1309407012yes—
349C4—22no—
350C4—24no—
351C4—42no—
352C4—41no—
353C4—942no—
354C4—1882no—
355C4—1881no—
356C2—42no—
357C2—944no—
358C2—1882no—
359C2—1884no—
360C2#120×D4711yescharacteristic
361C2#1568963611yescharacteristic
362C2#1568969111yescharacteristic
363C2#1568976412yes—
364C2#1568976612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2404
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×#10625354C2semidirect
2. C2×#13093994C2semidirect
3. C2×C22⋊C4×D47C2semidirect
4. #15689034C2semidirect
5. #15689033C2semidirect
6. #15689032C2semidirect
7. #15689001C2semidirect
8. #15689001C2semidirect
9. #15688999C2semidirect
10. #15688985C2semidirect
11. C47×#393C2semidirect
17. C22×D188C22semidirect
21. C22×C4×D47C22semidirect
28. C2×(C2×D47)⋊C4C22semidirect
29. C2×(C2×D47)⋊C4C22semidirect
31. C47⋊#95C22semidirect
32. C47⋊#95C22semidirect
33. C47⋊#95C22semidirect
34. C22×Q8×C47C22semidirect
37. #95×C47C22semidirect
38. #95×C47C22semidirect
68. C2×D188D4semidirect
75. C2×C4×D47D4semidirect
89. C23×C47#41semidirect
112. C22×D47#41semidirect
187. #393D47semidirect
194. C47#2404semidirect
198. C22×Q8C2×D47semidirect
220. #95C2×D47semidirect
221. #95C2×D47semidirect
294. C23#10625354semidirect