Finite Group Databasebeta

← #20254466

Subgroups — #20254466

Order 6016.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#15689734C211yesmaximal, characteristic, complemented
2#15689693C211yesmaximal, characteristic
3#15689502C211yesmaximal, characteristic, complemented
4#15689492C211yesmaximal, characteristic, complemented
5#15689477C211yesmaximal, characteristic, complemented
6#15689343C212yesmaximal, complemented
7#15689331C212yesmaximal, complemented
8#15689282C212yesmaximal
9#15689277C212yesmaximal, complemented
10#15689185C211yesmaximal, characteristic, complemented
11C47×#497C211yesmaximal, characteristic, complemented
12C2×#10625352C2211yescharacteristic
13C2×Q8×D47C2211yescharacteristic
14C2×#10625337C2212yes—
15C2×#10625337C2212yes—
16#13094024C2211yescharacteristic
17#13094022C2211yescharacteristic
18#13094019—22no—
19#13094016C2211yescharacteristic
20#13094014—22no—
21#13094011C2211yescharacteristic
22#13094006—22no—
23#13094001—22no—
24#13094000C2212yes—
25Q8×Dic47C2212yes—
26#13093981C2211yescharacteristic
27Dic47⋊C8C2212yes—
28#13093949C2212yes—
29#13093949C2212yes—
30#13093948C2212yes—
31#13093945C2212yes—
32(C2×D47)⋊C8C2212yes—
33C4×C47⋊C8C2211yescharacteristic
34C2×Q16×C47C2212yes—
35C2×SD16×C47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37#124×C47C2211yescharacteristic
38#97×C47C2211yescharacteristic
39C2×Q8×C47C2311yescharacteristic
40C2×Q8×C47C2312yes—
41C2×D4×C47C2311yescharacteristic
42C2×C22⋊D47—21no—
43C22×Dic47—21no—
44Q8×D47—42no—
45#10625352—42no—
46C2×C4×D47—21no—
47C2×C4×D47C2311yescharacteristic
48C2×Dic94—21no—
49C2×Dic94C2311yescharacteristic
50C2×Dic94C2311yescharacteristic
51Q16×C47—42no—
52SD16×C47—42no—
53C2×C8×C47C2312yes—
54C4⋊C4×C47—22no—
55C22⋊C4×C47—22no—
56C42×C47C2311yescharacteristic
57C22⋊Dic47—22no—
58#10625337—42no—
59#10625337—42no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4D412yes—
62C4⋊Dic47—22no—
63C4⋊Dic47—22no—
64C4⋊Dic47C2312yes—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—22no—
70C4×Dic47C2311yescharacteristic
71C2×C47⋊C8C2312yes—
72C23×C47—21no—
73C22×D47C2×D411yescharacteristic
74Q8×C47—22no—
75Q8×C47—22no—
76Q8×C47—22no—
77D4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2411yescharacteristic
82C22⋊D47—42no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—42no—
87C2×Dic47C2×D412yes—
88C2×Dic47C2×D411yescharacteristic
89C4×D47—22no—
90C4×D47—42no—
91Dic94—22no—
92Dic94—22no—
93Dic94—42no—
94C8×C47—22no—
95C47⋊C8—22no—
96C22×C47—41no—
97C22×C47—42no—
98C22×C47C22×D411yescharacteristic
99C2×D47—21no—
100C2×D47—22no—
101C4×C47—22no—
102C4×C47—41no—
103C4×C47—42no—
104C4×C47H(5,𝔽2)12yes—
105Dic47—21no—
106Dic47—22no—
107Dic47—41no—
108Dic47—41no—
109Dic47—42no—
110#3223—471nomaximal, Sylow
111C2×C47—81no—
112C2×C47#53511yescharacteristic
113C2×C47#57812yes—
114D47—41no—
115#541—471no—
116#536—471no—
117#497D4711yescharacteristic, complemented
118#494—471no—
119#491—471no—
120#488—471no—
121#464—472no—
122#462—472no—
123#452—472no—
124#451—472no—
125#433—471no—
126C47#322311yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C22×Q8—471no—
129C2×Q16—472no—
130C2×Q16—472no—
131C2×Q16C2×D4712yes—
132C2×SD16C2×D4712yes—
133C4⋊Q8—471no—
134C4⋊Q8—471no—
135C4⋊Q8C2×D4711yescharacteristic
136#126—942no—
137#125—471no—
138#125—942no—
139#124—471no—
140#124C2×D4711yescharacteristic
141#123—942no—
142C22⋊Q8—472no—
143C22⋊Q8—942no—
144C4×Q8—472no—
145#117—471no—
146C4⋊C8—472no—
147#103—472no—
148#103—472no—
149#103—472no—
150#102—472no—
151C22⋊C8—472no—
152#97C2×D4711yescharacteristic
153C4×C8—471no—
154#41—1882no—
155C2×Q8—471no—
156C2×Q8—471no—
157C2×Q8—941no—
158C2×Q8—1882no—
159C2×Q8C22×D4711yescharacteristic
160C2×Q8C22×D4712yes—
161C2×D4—941no—
162C2×D4C22×D4711yescharacteristic
163C22×C4—471no—
164C22×C4—941no—
165C22×C4—941no—
166Q16—42no—
167Q16—1882no—
168Q16—1882no—
169SD16—42no—
170C2×C8—472no—
171C2×C8C22×D4712yes—
172C4⋊C4—22no—
173C4⋊C4—472no—
174C4⋊C4—472no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C22⋊C4—22no—
181C22⋊C4—472no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C42—471no—
185C42—942no—
186C42C22×D4711yescharacteristic
187C23—21no—
188C23—471no—
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—942no—
193Q8—942no—
194Q8—1882no—
195D4—22no—
196D4—1882no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—472no—
200C2×C4—471no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—941no—
204C2×C4—941no—
205C2×C4—1882no—
206C2×C4—1882no—
207C2×C4D4×D4712yes—
208C2×C4C23×D4711yescharacteristic
209C8—22no—
210C8—942no—
211C22—42no—
212C22—41no—
213C22—942no—
214C22—941no—
215C22C2×D4×D4711yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—942no—
220C4—941no—
221C4—1882no—
222C4—1881no—
223C4—1881no—
224C4#1309406912yes—
225C2—81no—
226C2—1881no—
227C2#1568968611yescharacteristic
228C2#1568993912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#497C2
socleC22×C47C22×D4
hypercenter#497D47
hypocenterC47#3223
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #15689734C2semidirect
3. #15689502C2semidirect
4. #15689492C2semidirect
5. #15689477C2semidirect
6. #15689343C2semidirect
7. #15689331C2semidirect
9. #15689277C2semidirect
10. #15689185C2semidirect
11. C47×#497C2semidirect
117. #497D47semidirect
126. C47#3223semidirect