Finite Group Databasebeta

← #20249319

Subgroups — #20249319

Order 6016.

576 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094002C211yesmaximal, characteristic, complemented
2C2×#13093995C211yesmaximal, characteristic
3#15689063C211yesmaximal, characteristic, complemented
4#15689062C211yesmaximal, characteristic, complemented
5#15689051C212yesmaximal, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689035C212yesmaximal, complemented
8#15688999C212yesmaximal, complemented
9#15688999C212yesmaximal, complemented
10#95×D47C211yesmaximal, characteristic, complemented
11C47×#394C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C22×C4×D47C2212yes—
15C22×C4×D47C2211yescharacteristic
16#13094002—24no—
17#13093995—24no—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2212yes—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×D4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2312yes—
38C23×D47C2311yescharacteristic
39C2×D4×C47—22no—
40C2×D4×C47—42no—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—24no—
46C2×C22⋊D47—24no—
47C2×C22⋊D47—24no—
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2311yescharacteristic
52C22×Dic47C2311yescharacteristic
53C2×C4×D47—24no—
54C2×C4×D47—42no—
55C2×C4×D47—42no—
56C2×C4×D47—42no—
57C2×C4×D47D414yes—
58C2×Dic94—22no—
59C2×Dic94—42no—
60C4⋊C4×C47—22no—
61C22⋊C4×C47—42no—
62C22⋊C4×C47—42no—
63C22⋊Dic47—24no—
64C22⋊Dic47—42no—
65C22⋊Dic47—42no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—22no—
68C4⋊Dic47—22no—
69Dic47⋊C4—22no—
70Dic47⋊C4—22no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47C2411yescharacteristic
79C22×D47—22no—
80C22×D47—21no—
81C22×D47—21no—
82C22×D47C2×D412yes—
83C22×D47#4114yes—
84D4×C47—44no—
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—22no—
89C2×C4×C47—21no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47C2×D412yes—
95C22⋊D47—48no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—21no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—21no—
108C2×Dic47C2×D412yes—
109C4×D47—44no—
110C4×D47—48no—
111Dic94—44no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47—42no—
117C22×C47—42no—
118C22×C47—42no—
119C22×C47C22×D411yescharacteristic
120C22×C47C2×#4112yes—
121C22×C47H(5,𝔽2)12yes—
122C22×C47H(5,𝔽2)11yescharacteristic
123C22×C472−1+411yescharacteristic
124C2×D47—22no—
125C2×D47—22no—
126C2×D47—24no—
127C2×D47—24no—
128C2×D47#12414yes—
129C4×C47—22no—
130C4×C47—41no—
131C4×C47—41no—
132C4×C47—42no—
133Dic47—22no—
134Dic47—42no—
135Dic47—41no—
136Dic47—41no—
137Dic47—42no—
138#2639—471nomaximal, Sylow
139C2×C47—82no—
140C2×C47C2×#12411yescharacteristic
141C2×C47#53411yescharacteristic
142C2×C47#53711yescharacteristic
143C2×C47#53812yes—
144C2×C47#53912yes—
145D47—24no—
146C2×C22⋊Q8—471no—
147C2×#121—471no—
148#400—471no—
149#400—471no—
150#397—472no—
151#394—471no—
152#394D4711yescharacteristic, complemented
153#393—472no—
154#386—472no—
155#386—472no—
156C2×#95—471no—
157C47#263911yescharacteristic, complemented, Sylow
158C22×Q8—471no—
159C22×D4—472no—
160C22×D4C2×D4711yescharacteristic
161C23×C4—471no—
162C23×C4—472no—
163C22⋊Q8—944no—
164#121—944no—
165C2×C4⋊C4—471no—
166C2×C4⋊C4—471no—
167C2×C4⋊C4—471no—
168C2×C4⋊C4C2×D4711yescharacteristic
169C2×C22⋊C4—472no—
170C2×C22⋊C4—471no—
171C2×C22⋊C4—471no—
172C2×C22⋊C4—472no—
173C2×C22⋊C4—472no—
174C2×C22⋊C4C2×D4712yes—
175C2×C22⋊C4C2×D4712yes—
176#95—472no—
177#95—471no—
178#95—472no—
179#95—472no—
180#95—472no—
181#95—472no—
182#95C2×D4711yescharacteristic
183C24—471no—
184C24C22×D4712yes—
185C2×Q8—942no—
186C2×Q8—1882no—
187C2×D4—22no—
188C2×D4—42no—
189C2×D4—944no—
190C2×D4—944no—
191C2×D4—944no—
192C22×C4—471no—
193C22×C4—474no—
194C22×C4—472no—
195C22×C4—472no—
196C22×C4—471no—
197C22×C4—471no—
198C22×C4—944no—
199C22×C4—1882no—
200C22×C4—1882no—
201C22×C4—1882no—
202C22×C4C22×D4712yes—
203C22×C4C22×D4711yescharacteristic
204C22×C4C22×D4711yescharacteristic
205C22×C4C22×D4711yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—942no—
208C4⋊C4—942no—
209C4⋊C4—942no—
210C22⋊C4—42no—
211C22⋊C4—42no—
212C22⋊C4—942no—
213C22⋊C4—942no—
214C22⋊C4—944no—
215C22⋊C4—1882no—
216C22⋊C4—1882no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—472no—
225C23—474no—
226C23—942no—
227C23—941no—
228C23—941no—
229C23C23×D4711yescharacteristic
230Q8—1884no—
231D4—44no—
232D4—1888no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—472no—
243C2×C4—942no—
244C2×C4—941no—
245C2×C4—942no—
246C2×C4—941no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—941no—
251C2×C4—942no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—941no—
255C2×C4—1884no—
256C2×C4—1888no—
257C2×C4D4×D4712yes—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—474no—
266C22—942no—
267C22—942no—
268C22—944no—
269C22—944no—
270C22C2×D4×D4711yescharacteristic
271C22#41×D4712yes—
272C22#1309406912yes—
273C22#1309406911yescharacteristic
274C22#1309407111yescharacteristic
275C4—22no—
276C4—41no—
277C4—41no—
278C4—42no—
279C4—942no—
280C4—1882no—
281C4—1881no—
282C4—1881no—
283C4—1882no—
284C2—82no—
285C2—944no—
286C2#124×D4711yescharacteristic
287C2#1568968311yescharacteristic
288C2#1568970211yescharacteristic
289C2#1568970512yes—
290C2#1568971612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2639
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13094002C2semidirect
3. #15689063C2semidirect
4. #15689062C2semidirect
5. #15689051C2semidirect
6. #15689037C2semidirect
7. #15689035C2semidirect
8. #15688999C2semidirect
9. #15688999C2semidirect
10. #95×D47C2semidirect
11. C47×#394C2semidirect
152. #394D47semidirect
157. C47#2639semidirect