Finite Group Databasebeta

← #20247861

Subgroups — #20247861

Order 6016.

544 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 161 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
2C2×C4⋊C4×D47C211yesmaximal, characteristic
3#15689055C211yesmaximal, characteristic, complemented
4#15689054C211yesmaximal, characteristic, complemented
5#15689053C211yesmaximal, characteristic, complemented
6#15689027C212yesmaximal, complemented
7#15688997C212yesmaximal
8#15688994C212yesmaximal
9#15688992C212yesmaximal, complemented
10#15688970C211yesmaximal, characteristic
11C47×#398C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C22×C4×D47C2212yes—
15#13094002—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×Dic47⋊C4C2212yes—
23C4⋊C4×D47—24no—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×C4×Dic47C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C23×D47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2312yes—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2312yes—
47C22×Dic47C2311yescharacteristic
48C2×C4×D47—24no—
49C2×C4×D47—24no—
50C2×C4×D47—42no—
51C2×C4×D47—42no—
52C2×C4×D47D414yes—
53C2×Dic94—22no—
54C2×Dic94—24no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—22no—
57C4⋊C4×C47—42no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4Q818yescomplemented
61C4⋊Dic47—22no—
62C4⋊Dic47—42no—
63Dic47⋊C4—22no—
64Dic47⋊C4—24no—
65Dic47⋊C4—22no—
66Dic47⋊C4—42no—
67Dic47⋊C4—42no—
68C4×Dic47—24no—
69C23×C47C2411yescharacteristic
70C22×D47—22no—
71C22×D47—21no—
72C22×D47—21no—
73C22×D47C2×D412yes—
74C22×D47C2×Q814yes—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47C2×D412yes—
87C2×C4×C47C2×Q814yes—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—21no—
91C2×Dic47—22no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C2×Dic47—22no—
98C2×Dic47C2×D412yes—
99C2×Dic47C2×Q814yes—
100C2×Dic47#4114yes—
101C4×D47—28no—
102C4×D47—48no—
103Dic94—44no—
104C22×C47C22×D411yescharacteristic
105C22×C47C22×Q812yes—
106C22×C47C2×#4112yes—
107C22×C47H(5,𝔽2)11yescharacteristic
108C22×C47H(5,𝔽2)11yescharacteristic
109C2×D47—22no—
110C2×D47—22no—
111C2×D47—24no—
112C2×D47—24no—
113C2×D47C4⋊Q814yes—
114C4×C47—22no—
115C4×C47—24no—
116C4×C47—41no—
117C4×C47—42no—
118C4×C47—41no—
119Dic47—24no—
120Dic47—41no—
121Dic47—42no—
122Dic47—41no—
123Dic47#12314yes—
124#2502—471nomaximal, Sylow
125C2×C47C2×#12311yescharacteristic
126C2×C47C2×C4⋊Q811yescharacteristic
127C2×C47#53511yescharacteristic
128C2×C47#55412yes—
129C2×C47#55412yes—
130D47—24no—
131C2×C22⋊Q8—471no—
132C22×C4⋊C4—471no—
133#398—471no—
134#398—471no—
135#398—471no—
136#398D4711yescharacteristic, complemented
137#391—472no—
138#385—472no—
139#385—472no—
140#384—472no—
141C4×C22⋊C4—471no—
142C47#250211yescharacteristic, complemented, Sylow
143C22×Q8—471no—
144C23×C4—471no—
145C23×C4—472no—
146C22⋊Q8—944no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—471no—
150C2×C4⋊C4—471no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4—472no—
154C2×C4⋊C4—944no—
155C2×C4⋊C4C2×D4711yescharacteristic
156C2×C4⋊C4C2×D4711yescharacteristic
157C2×C4⋊C4C2×D4712yes—
158C2×C22⋊C4—472no—
159C2×C22⋊C4—471no—
160C2×C22⋊C4—471no—
161C2×C42—472no—
162#95—471no—
163#95—472no—
164#95—472no—
165#95—472no—
166#95C2×D4711yescharacteristic
167#95C2×D4712yes—
168C24—471no—
169C2×Q8—942no—
170C2×Q8—944no—
171C22×C4—471no—
172C22×C4—472no—
173C22×C4—474no—
174C22×C4—471no—
175C22×C4—472no—
176C22×C4—471no—
177C22×C4—944no—
178C22×C4—944no—
179C22×C4—1882no—
180C22×C4—1882no—
181C22×C4C22×D4711yescharacteristic
182C22×C4C22×D4712yes—
183C22×C4C22×D4711yescharacteristic
184C22×C4C22×D4711yescharacteristic
185C22×C4C22×D4712yes—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—944no—
190C4⋊C4—942no—
191C4⋊C4—942no—
192C4⋊C4—942no—
193C4⋊C4—1882no—
194C4⋊C4—1882no—
195C4⋊C4—1882no—
196C22⋊C4—478no—
197C22⋊C4—942no—
198C22⋊C4—942no—
199C42—944no—
200C23—472no—
201C23—474no—
202C23—942no—
203C23—941no—
204C23—941no—
205C23C23×D4711yescharacteristic
206Q8—1884no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—472no—
219C2×C4—474no—
220C2×C4—474no—
221C2×C4—948no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—941no—
225C2×C4—941no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—941no—
229C2×C4—942no—
230C2×C4—941no—
231C2×C4—942no—
232C2×C4—1888no—
233C2×C4D4×D4712yes—
234C2×C4Q8×D4714yes—
235C22—474no—
236C22—944no—
237C22—944no—
238C22—942no—
239C22—942no—
240C22C2×D4×D4711yescharacteristic
241C22C2×Q8×D4712yes—
242C22#41×D4712yes—
243C22#1309406911yescharacteristic
244C22#1309407011yescharacteristic
245C4—24no—
246C4—22no—
247C4—41no—
248C4—42no—
249C4—41no—
250C4—474no—
251C4—944no—
252C4—1881no—
253C4—1882no—
254C4—1881no—
255C2—944no—
256C2#123×D4711yescharacteristic
257C2C4⋊Q8×D4711yescharacteristic
258C2#1568968911yescharacteristic
259C2#1568982712yes—
260C2#1568982912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2502
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #15689055C2semidirect
4. #15689054C2semidirect
5. #15689053C2semidirect
6. #15689027C2semidirect
9. #15688992C2semidirect
11. C47×#398C2semidirect
60. (C2×D47)⋊C4Q8semidirect
136. #398D47semidirect
142. C47#2502semidirect