Finite Group Databasebeta

← #20246724

Subgroups — #20246724

Order 6016.

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

normal subgroups only

This group has 864 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
2C2×#13094009C212yesmaximal, complemented
3C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689042C211yesmaximal, characteristic, complemented
5#15689041C211yesmaximal, characteristic, complemented
6#15689040C211yesmaximal, characteristic, complemented
7#15689001C212yesmaximal, complemented
8#15688997C212yesmaximal, complemented
9#15688994C212yesmaximal, complemented
10#15688985C211yesmaximal, characteristic, complemented
11C47×#395C211yesmaximal, characteristic, complemented
12C2×#10625354—28no—
13C2×#10625354—24no—
14C22×D188C2211yescharacteristic
15C22×D188C2212yes—
16C22×C4×D47C2212yes—
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13094009—28no—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2212yes—
24C2×Dic47⋊C4C2211yescharacteristic
25C4⋊C4×D47—24no—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2212yes—
29C2×(C2×D47)⋊C4C2212yes—
30C2×(C2×D47)⋊C4C2212yes—
31C47⋊#95C2212yes—
32C47⋊#95C2211yescharacteristic
33C47⋊#95C2212yes—
34C22×Q8×C47C2211yescharacteristic
35C2×C4⋊C4×C47C2212yes—
36C2×C4⋊C4×C47C2211yescharacteristic
37#95×C47C2211yescharacteristic
38#95×C47C2212yes—
39C23×D47C2312yes—
40C23×D47C2311yescharacteristic
41C2×Q8×C47—24no—
42C2×Q8×C47—22no—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C22×C4×C47C2312yes—
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2311yescharacteristic
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2311yescharacteristic
52#10625354—232no—
53C2×D188—24no—
54C2×D188—24no—
55C2×D188—24no—
56C2×D188—22no—
57C2×D188D418yes—
58C2×C4×D47—22no—
59C2×C4×D47—24no—
60C2×C4×D47—24no—
61C2×C4×D47—24no—
62C2×C4×D47—22no—
63C2×C4×D47—24no—
64C2×C4×D47—22no—
65C2×C4×D47—22no—
66C2×C4×D47—24no—
67C2×C4×D47D414yes—
68C4⋊C4×C47—22no—
69C4⋊C4×C47—24no—
70(C2×D47)⋊C4—24no—
71(C2×D47)⋊C4—24no—
72(C2×D47)⋊C4—24no—
73(C2×D47)⋊C4—24no—
74(C2×D47)⋊C4—24no—
75C4⋊Dic47—22no—
76Dic47⋊C4—22no—
77Dic47⋊C4—24no—
78Dic47⋊C4—22no—
79C23×C47C2411yescharacteristic
80C22×D47—21no—
81C22×D47—21no—
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—22no—
89C22×D47C2×D414yes—
90C22×D47C2×D414yes—
91C22×D47C2×D412yes—
92Q8×C47—28no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47C2×D414yes—
104C2×C4×C47C2×D412yes—
105C2×C4×C47#4112yescomplemented
106C2×Dic47—21no—
107C2×Dic47—22no—
108C2×Dic47—21no—
109C2×Dic47—21no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47C2×D412yes—
115C2×Dic47#4112yescomplemented
116D188—28no—
117D188—216no—
118C4×D47—28no—
119C4×D47—216no—
120C4×D47—28no—
121C4×D47—44no—
122C22×C47C22×D411yescharacteristic
123C22×C47C22×D412yes—
124C22×C47C2×#4111yescharacteristic
125C22×C47C2×#4111yescharacteristic
126C22×C472−1+412yes—
127C2×D47—22no—
128C2×D47—22no—
129C2×D47—24no—
130C2×D47—24no—
131C2×D47—24no—
132C2×D47—24no—
133C2×D47—24no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—42no—
137C2×D47—42no—
138C2×D47#12014yes—
139C4×C47—24no—
140C4×C47—22no—
141C4×C47—22no—
142C4×C47—41no—
143C4×C47—42no—
144Dic47—22no—
145Dic47—22no—
146Dic47—41no—
147Dic47—42no—
148#2406—471nomaximal, Sylow
149C2×C47C2×#12011yescharacteristic
150C2×C47#52511yescharacteristic
151C2×C47#53611yescharacteristic
152C2×C47#54712yes—
153C2×C47#54712yes—
154D47—24no—
155D47—44no—
156C22×#41—471no—
157C2×#123—472no—
158C22×C4⋊C4—471no—
159#395—471no—
160#395D4711yescharacteristic, complemented
161#394—471no—
162#394—471no—
163#386—472no—
164#385—472no—
165#385—472no—
166#381—471no—
167C47#240611yescharacteristic, complemented, Sylow
168C2×#41—944no—
169C2×#41—948no—
170C22×Q8C2×D4711yescharacteristic
171C22×D4—472no—
172C22×D4—471no—
173C23×C4—471no—
174C23×C4—471no—
175C23×C4—471no—
176C23×C4—472no—
177#123—948no—
178C2×C4⋊C4—471no—
179C2×C4⋊C4—471no—
180C2×C4⋊C4—471no—
181C2×C4⋊C4—472no—
182C2×C4⋊C4—944no—
183C2×C4⋊C4C2×D4711yescharacteristic
184C2×C4⋊C4C2×D4712yes—
185C2×C22⋊C4—472no—
186C2×C22⋊C4—472no—
187C2×C22⋊C4—472no—
188C2×C22⋊C4—472no—
189C2×C22⋊C4—472no—
190#95—472no—
191#95—471no—
192#95—472no—
193#95C2×D4711yescharacteristic
194#95C2×D4712yes—
195C24—471no—
196C24—472no—
197#41—9432no—
198C2×Q8—22no—
199C2×Q8—24no—
200C2×D4—478no—
201C2×D4—944no—
202C2×D4—944no—
203C2×D4—944no—
204C2×D4—942no—
205C22×C4—471no—
206C22×C4—471no—
207C22×C4—474no—
208C22×C4—472no—
209C22×C4—471no—
210C22×C4—942no—
211C22×C4—944no—
212C22×C4—942no—
213C22×C4—944no—
214C22×C4—944no—
215C22×C4—942no—
216C22×C4—944no—
217C22×C4—944no—
218C22×C4—942no—
219C22×C4C22×D4712yes—
220C22×C4C22×D4711yescharacteristic
221C22×C4C22×D4711yescharacteristic
222C22×C4C22×D4712yes—
223C22×C4C22×D4711yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—24no—
226C4⋊C4—942no—
227C4⋊C4—942no—
228C4⋊C4—942no—
229C4⋊C4—944no—
230C22⋊C4—944no—
231C22⋊C4—944no—
232C22⋊C4—944no—
233C22⋊C4—944no—
234C22⋊C4—944no—
235C23—474no—
236C23—472no—
237C23—474no—
238C23—941no—
239C23—941no—
240C23—942no—
241C23—942no—
242C23—942no—
243C23—942no—
244C23—942no—
245C23—942no—
246C23—942no—
247C23C23×D4711yescharacteristic
248Q8—28no—
249D4—9416no—
250D4—948no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—472no—
262C2×C4—472no—
263C2×C4—948no—
264C2×C4—948no—
265C2×C4—9416no—
266C2×C4—941no—
267C2×C4—942no—
268C2×C4—941no—
269C2×C4—942no—
270C2×C4—942no—
271C2×C4—941no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4—1884no—
275C2×C4D4×D4712yes—
276C2×C4D4×D4714yes—
277C2×C4#1062535412yescomplemented
278C22—474no—
279C22—944no—
280C22—944no—
281C22—942no—
282C22—942no—
283C22—944no—
284C22—944no—
285C22—944no—
286C22—1882no—
287C22—1882no—
288C22—1882no—
289C22—1882no—
290C22C2×D4×D4712yes—
291C22C2×D4×D4711yescharacteristic
292C22#41×D4711yescharacteristic
293C22C2×#1062535411yescharacteristic
294C22#1309407212yes—
295C4—22no—
296C4—24no—
297C4—22no—
298C4—42no—
299C4—41no—
300C4—942no—
301C4—942no—
302C4—1882no—
303C4—1881no—
304C2—944no—
305C2—1884no—
306C2#120×D4711yescharacteristic
307C2#1568963611yescharacteristic
308C2#1568969811yescharacteristic
309C2#1568977512yes—
310C2#1568977612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2406
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#13094009C2semidirect
3. C2×C4⋊C4×D47C2semidirect
4. #15689042C2semidirect
5. #15689041C2semidirect
6. #15689040C2semidirect
7. #15689001C2semidirect
8. #15688997C2semidirect
9. #15688994C2semidirect
10. #15688985C2semidirect
11. C47×#395C2semidirect
105. C2×C4×C47#41semidirect
115. C2×Dic47#41semidirect
160. #395D47semidirect
167. C47#2406semidirect
277. C2×C4#10625354semidirect