Finite Group Databasebeta

← #20249532

Subgroups — #20249532

Order 6016.

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

normal subgroups only

This group has 534 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×#13094019C211yesmaximal, characteristic, complemented
2C2×#13094013C211yesmaximal, characteristic, complemented
3#15689045C212yesmaximal, complemented
4#15689041C212yesmaximal, complemented
5#15689040C211yesmaximal, characteristic, complemented
6#15689034C211yesmaximal, characteristic, complemented
7#15689033C211yesmaximal, characteristic
8#15689024C212yesmaximal, complemented
9#15689012C212yesmaximal, complemented
10#15688974C211yesmaximal, characteristic, complemented
11C47×#395C211yesmaximal, characteristic, complemented
12C22×D188C2212yes—
13C22×D188C2211yescharacteristic
14#13094019—24no—
15#13094013—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×C4×Dic47C2212yes—
29C2×C4×Dic47C2211yescharacteristic
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C23×D47C2311yescharacteristic
38C23×D47C2312yes—
39C2×Q8×C47—22no—
40C2×Q8×C47—42no—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2312yes—
46C22×Dic47C2312yes—
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×D188—22no—
51C2×D188—24no—
52C2×D188—42no—
53C2×D188—42no—
54C2×D188—42no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—42no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—24no—
59(C2×D47)⋊C4—24no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—42no—
64(C2×D47)⋊C4—42no—
65(C2×D47)⋊C4—42no—
66C4⋊Dic47—22no—
67Dic47⋊C4—24no—
68Dic47⋊C4—22no—
69C4×Dic47—42no—
70C4×Dic47D414yescomplemented
71C23×C47C2411yescharacteristic
72C22×D47—21no—
73C22×D47—22no—
74C22×D47—22no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47—22no—
78C22×D47—22no—
79C22×D47—22no—
80C22×D47—22no—
81C22×D47—21no—
82C22×D47—21no—
83C22×D47—22no—
84Q8×C47—44no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—21no—
96C2×C4×C47C2×D412yes—
97C2×C4×C47#4114yes—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—21no—
101C2×Dic47—21no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47C2×D412yes—
107C2×Dic47C2×D412yes—
108D188—44no—
109D188—48no—
110C22×C47C22×D411yescharacteristic
111C22×C47C2×#4112yes—
112C22×C47H(5,𝔽2)12yes—
113C22×C47H(5,𝔽2)11yescharacteristic
114C22×C472−1+411yescharacteristic
115C2×D47—41no—
116C2×D47—42no—
117C2×D47—42no—
118C2×D47—41no—
119C2×D47—41no—
120C2×D47—42no—
121C2×D47—42no—
122C2×D47—42no—
123C2×D47—42no—
124C2×D47—42no—
125C2×D47—42no—
126C2×D47—42no—
127C4×C47—22no—
128C4×C47—24no—
129C4×C47—41no—
130C4×C47—42no—
131C4×C47—41no—
132Dic47—22no—
133Dic47—22no—
134Dic47—41no—
135Dic47—42no—
136#2662—471nomaximal, Sylow
137C2×C47#53211yescharacteristic
138C2×C47#53511yescharacteristic
139C2×C47#53711yescharacteristic
140C2×C47#53812yes—
141C2×C47#54212yes—
142D47—82no—
143D47—81no—
144C2×#126—471no—
145C2×#124—471no—
146#396—472no—
147#395D4711yescharacteristic, complemented
148#394—471no—
149#394—472no—
150#393—471no—
151#392—471no—
152#390—472no—
153#388—472no—
154C4×C4⋊C4—471no—
155C47#266211yescharacteristic, complemented, Sylow
156C22×Q8C2×D4711yescharacteristic
157C22×D4—471no—
158C22×D4—472no—
159#126—944no—
160#124—944no—
161C2×C4⋊C4—471no—
162C2×C4⋊C4—471no—
163C2×C4⋊C4—472no—
164C2×C4⋊C4C2×D4711yescharacteristic
165C2×C4⋊C4C2×D4712yes—
166C2×C22⋊C4—472no—
167C2×C22⋊C4—472no—
168C2×C22⋊C4—471no—
169C2×C22⋊C4—471no—
170C2×C22⋊C4—471no—
171C2×C22⋊C4—472no—
172C2×C22⋊C4—472no—
173C2×C22⋊C4—472no—
174C2×C22⋊C4—472no—
175C2×C42—471no—
176C2×C42—472no—
177#95—471no—
178#95—472no—
179#95C2×D4711yescharacteristic
180#95C2×D4712yes—
181C24—471no—
182C24—472no—
183C2×Q8—22no—
184C2×Q8—42no—
185C2×D4—942no—
186C2×D4—944no—
187C2×D4—1882no—
188C2×D4—1882no—
189C2×D4—1882no—
190C22×C4—471no—
191C22×C4—471no—
192C22×C4—472no—
193C22×C4—471no—
194C22×C4C22×D4712yes—
195C22×C4C22×D4711yescharacteristic
196C22×C4C22×D4711yescharacteristic
197C22×C4C22×D4711yescharacteristic
198C22×C4C22×D4712yes—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—942no—
202C4⋊C4—942no—
203C4⋊C4—944no—
204C22⋊C4—944no—
205C22⋊C4—944no—
206C22⋊C4—942no—
207C22⋊C4—942no—
208C22⋊C4—942no—
209C22⋊C4—944no—
210C22⋊C4—1882no—
211C22⋊C4—1882no—
212C22⋊C4—1882no—
213C42—474no—
214C42—1882no—
215C23—941no—
216C23—942no—
217C23—942no—
218C23—942no—
219C23—942no—
220C23—942no—
221C23—942no—
222C23—942no—
223C23—942no—
224C23—941no—
225C23—942no—
226C23—941no—
227C23C23×D4711yescharacteristic
228Q8—44no—
229D4—1884no—
230D4—1888no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—472no—
243C2×C4—472no—
244C2×C4—942no—
245C2×C4—941no—
246C2×C4—941no—
247C2×C4—941no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—942no—
251C2×C4—942no—
252C2×C4D4×D4712yes—
253C2×C4#1062535414yes—
254C22—1882no—
255C22—1882no—
256C22—1882no—
257C22—1881no—
258C22—1882no—
259C22—1882no—
260C22—1881no—
261C22—1881no—
262C22—1882no—
263C22—1882no—
264C22—1882no—
265C22—1882no—
266C22C2×D4×D4711yescharacteristic
267C22C2×#1062535412yes—
268C22#1309406912yes—
269C22#1309407011yescharacteristic
270C22#1309407211yescharacteristic
271C4—22no—
272C4—24no—
273C4—42no—
274C4—41no—
275C4—41no—
276C4—942no—
277C4—942no—
278C4—1881no—
279C4—1882no—
280C2—3762no—
281C2—3761no—
282C2#1568967411yescharacteristic
283C2#1568968811yescharacteristic
284C2#1568970311yescharacteristic
285C2#1568971312yes—
286C2#1568974712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2662
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#13094019C2semidirect
2. C2×#13094013C2semidirect
3. #15689045C2semidirect
4. #15689041C2semidirect
5. #15689040C2semidirect
6. #15689034C2semidirect
8. #15689024C2semidirect
9. #15689012C2semidirect
10. #15688974C2semidirect
11. C47×#395C2semidirect
70. C4×Dic47D4semidirect
147. #395D47semidirect
155. C47#2662semidirect