Finite Group Databasebeta

← #20251432

Subgroups — #20251432

Order 6016.

580 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13094010C212yesmaximal, complemented
2#15689040C211yesmaximal, characteristic, complemented
3#15689039C212yesmaximal, complemented
4#15689036C212yesmaximal, complemented
5#15689035C212yesmaximal, complemented
6#15689032C212yesmaximal, complemented
7#15689031C212yesmaximal, complemented
8#15688988C211yesmaximal, characteristic, complemented
9C47×#394C211yesmaximal, characteristic, complemented
10C22×Dic94C2212yes—
11C22×D188C2211yescharacteristic
12C22×C22⋊D47C2212yes—
13C22×C22⋊D47C2212yes—
14#13094010—28no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2212yes—
27C22×D4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C22⋊C4×C47C2212yes—
30C2×C22⋊C4×C47C2212yes—
31#95×C47C2211yescharacteristic
32C24×C47C2312yes—
33C23×D47C2312yes—
34C2×D4×C47—42no—
35C2×D4×C47—41no—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—24no—
41C2×C22⋊D47—42no—
42C2×C22⋊D47—42no—
43C2×C22⋊D47—42no—
44C2×C22⋊D47—42no—
45C2×C22⋊D47—42no—
46C22×Dic47C2312yes—
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C2×D188—42no—
50C2×D188—41no—
51C2×Dic94—24no—
52C2×Dic94—42no—
53C2×Dic94—42no—
54C4⋊C4×C47—41no—
55C22⋊C4×C47—24no—
56C22⋊C4×C47—42no—
57C22⋊Dic47—24no—
58C22⋊Dic47—42no—
59(C2×D47)⋊C4—24no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4—42no—
62(C2×D47)⋊C4—42no—
63C4⋊Dic47—41no—
64C4×Dic47D414yescomplemented
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47C2411yescharacteristic
73C22×D47—22no—
74C22×D47—22no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47—22no—
78C22×D47—22no—
79C22×D47—22no—
80D4×C47—44no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47C2×D412yes—
91C22⋊D47—48no—
92C22⋊D47—48no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47C2×D414yes—
102D188—44no—
103Dic94—48no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47C22×D411yescharacteristic
112C22×C47H(5,𝔽2)12yes—
113C22×C47H(5,𝔽2)11yescharacteristic
114C22×C47H(5,𝔽2)12yes—
115C22×C472−1+411yescharacteristic
116C2×D47—42no—
117C2×D47—42no—
118C2×D47—42no—
119C2×D47—42no—
120C2×D47—42no—
121C2×D47—42no—
122C2×D47—42no—
123C4×C47—22no—
124C4×C47—42no—
125C4×C47—41no—
126C4×C47—41no—
127Dic47—24no—
128Dic47—42no—
129Dic47—42no—
130#2819—471nomaximal, Sylow
131C2×C47—82no—
132C2×C47#53512yes—
133C2×C47#53711yescharacteristic
134C2×C47H(3,𝔽4)11yescharacteristic
135C2×C47H(3,𝔽4)11yescharacteristic
136C2×C47#56212yes—
137D47—82no—
138C2×#124—472no—
139#394—471no—
140#394—472no—
141#394D4711yescharacteristic, complemented
142#393—472no—
143#393—472no—
144#392—472no—
145#392—472no—
146#382—471no—
147C47#281911yescharacteristic, complemented, Sylow
148C22×Q8—472no—
149C22×D4—472no—
150C22×D4—472no—
151C22×D4—471no—
152C22×D4C2×D4711yescharacteristic
153#124—948no—
154C2×C4⋊C4—471no—
155C2×C4⋊C4C2×D4711yescharacteristic
156C2×C22⋊C4—472no—
157C2×C22⋊C4—472no—
158C2×C22⋊C4—472no—
159C2×C22⋊C4—472no—
160C2×C22⋊C4—472no—
161C2×C22⋊C4—472no—
162C2×C22⋊C4C2×D4712yes—
163C2×C22⋊C4C2×D4712yes—
164C2×C42—471no—
165#95—472no—
166#95—472no—
167#95—472no—
168#95—471no—
169#95C2×D4711yescharacteristic
170C24—472no—
171C24C22×D4712yes—
172C2×Q8—944no—
173C2×Q8—1882no—
174C2×Q8—1882no—
175C2×D4—42no—
176C2×D4—41no—
177C2×D4—944no—
178C2×D4—1882no—
179C2×D4—1881no—
180C2×D4—1882no—
181C2×D4—1882no—
182C2×D4—1882no—
183C2×D4—1882no—
184C2×D4—1882no—
185C22×C4—472no—
186C22×C4—472no—
187C22×C4—472no—
188C22×C4C22×D4711yescharacteristic
189C22×C4C22×D4711yescharacteristic
190C22×C4C22×D4712yes—
191C22×C4C22×D4711yescharacteristic
192C4⋊C4—41no—
193C4⋊C4—1881no—
194C22⋊C4—24no—
195C22⋊C4—42no—
196C22⋊C4—944no—
197C22⋊C4—944no—
198C22⋊C4—944no—
199C22⋊C4—1882no—
200C22⋊C4—1882no—
201C22⋊C4—1882no—
202C42—474no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—942no—
211C23—942no—
212C23—942no—
213C23—942no—
214C23—942no—
215C23—942no—
216C23—942no—
217C23C23×D4711yescharacteristic
218Q8—1888no—
219D4—44no—
220D4—1884no—
221D4—1888no—
222D4—1888no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—474no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4D4×D4712yes—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—1882no—
250C22—1882no—
251C22—1882no—
252C22—1882no—
253C22—1882no—
254C22—1882no—
255C22—1882no—
256C22C2×D4×D4711yescharacteristic
257C22#1309406911yescharacteristic
258C22#1309406912yes—
259C22#1309407012yes—
260C22#1309407111yescharacteristic
261C4—22no—
262C4—41no—
263C4—41no—
264C4—42no—
265C4—944no—
266C4—1882no—
267C4—1882no—
268C2—82no—
269C2—3762no—
270C2#1568968912yes—
271C2#1568970011yescharacteristic
272C2#1568986511yescharacteristic
273C2#1568986611yescharacteristic
274C2#1568987012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2819
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13094010C2semidirect
2. #15689040C2semidirect
3. #15689039C2semidirect
4. #15689036C2semidirect
5. #15689035C2semidirect
6. #15689032C2semidirect
7. #15689031C2semidirect
8. #15688988C2semidirect
9. C47×#394C2semidirect
64. C4×Dic47D4semidirect
141. #394D47semidirect
147. C47#2819semidirect