Finite Group Databasebeta

← #20254472

Subgroups — #20254472

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#15689736C211yesmaximal, characteristic, complemented
2#15689698C211yesmaximal, characteristic
3#15689517C211yesmaximal, characteristic, complemented
4#15689502C211yesmaximal, characteristic, complemented
5#15689480C211yesmaximal, characteristic, complemented
6#15689348C212yesmaximal, complemented
7#15689332C212yesmaximal, complemented
8#15689288C212yesmaximal
9#15689280C212yesmaximal, complemented
10#15689185C211yesmaximal, characteristic, complemented
11C47×#491C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic
13C2×Q8×D47C2211yescharacteristic
14C2×Dic188C2212yes—
15C2×#10625337C2212yes—
16C2×#10625337C2212yes—
17C2×#10625325C2212yes—
18#13094024C2211yescharacteristic
19#13094022C2211yescharacteristic
20#13094019—22no—
21#13094015—22no—
22#13094013C2211yescharacteristic
23#13094012C2211yescharacteristic
24#13094009—22no—
25#13094004C2212yes—
26#13094002—22no—
27#13093989C2212yes—
28#13093981C2211yescharacteristic
29Dic47⋊C8C2212yes—
30#13093947C2212yes—
31#13093944C2212yes—
32(C2×D47)⋊C8C2212yes—
33C4×C47⋊C8C2211yescharacteristic
34C4⋊Q8×C47C2211yescharacteristic
35#125×C47C2211yescharacteristic
36#103×C47C2212yes—
37#103×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×Q8×C47C2311yescharacteristic
40C2×Q8×C47C2311yescharacteristic
41#10625354—42no—
42Q8×D47—42no—
43C2×D188—21no—
44C2×D188C2311yescharacteristic
45C2×C4×D47—21no—
46C2×C4×D47—21no—
47C2×C4×D47C2311yescharacteristic
48C2×Dic94—21no—
49C2×Dic94C2311yescharacteristic
50C2×Dic94C2312yes—
51C2×C8×C47C2312yes—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—22no—
54C4⋊C4×C47C2312yes—
55C42×C47C2311yescharacteristic
56#10625337—42no—
57#10625337—42no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4D412yes—
62C4⋊Dic47—22no—
63C4⋊Dic47—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4D412yes—
67C4×Dic47—22no—
68C4×Dic47C2311yescharacteristic
69C2×C47⋊C8C2312yes—
70Dic188—42no—
71#10625325—42no—
72C22×D47—21no—
73C22×D47C2×D411yescharacteristic
74Q8×C47—22no—
75Q8×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2411yescharacteristic
81C2×Dic47—22no—
82C2×Dic47—21no—
83C2×Dic47C2×D412yes—
84C2×Dic47C2×D411yescharacteristic
85D188—22no—
86D188—42no—
87C4×D47—22no—
88C4×D47—42no—
89C4×D47—42no—
90Dic94—22no—
91Dic94—22no—
92Dic94—22no—
93Dic94—42no—
94C8×C47—22no—
95C47⋊C8—22no—
96C22×C47C22×D411yescharacteristic
97C2×D47—21no—
98C2×D47—22no—
99C2×D47—41no—
100C2×D47—42no—
101C4×C47—22no—
102C4×C47—41no—
103C4×C47—41no—
104C4×C47—42no—
105C4×C47H(5,𝔽2)12yes—
106Dic47—21no—
107Dic47—22no—
108Dic47—41no—
109Dic47—42no—
110#3223—471nomaximal, Sylow
111C2×C47#53511yescharacteristic
112C2×C47#57812yes—
113D47—41no—
114D47—81no—
115#541—471no—
116#536—471no—
117#497—471no—
118#494—471no—
119#491D4711yescharacteristic, complemented
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×Q16—472no—
132C2×SD16—472no—
133C4⋊Q8—471no—
134C4⋊Q8—471no—
135C4⋊Q8C2×D4711yescharacteristic
136#126—942no—
137#125—942no—
138#125C2×D4711yescharacteristic
139#124—471no—
140#124—471no—
141#123—942no—
142C22⋊Q8—472no—
143C22⋊Q8—942no—
144C4×Q8—472no—
145#117—471no—
146C4⋊C8—472no—
147#103—472no—
148#103C2×D4712yes—
149#103C2×D4712yes—
150#102—472no—
151C22⋊C8—472no—
152#97C2×D4711yescharacteristic
153C4×C8—471no—
154#41—1882no—
155C2×Q8—471no—
156C2×Q8—472no—
157C2×Q8—941no—
158C2×Q8—1882no—
159C2×Q8C22×D4711yescharacteristic
160C2×Q8C22×D4711yescharacteristic
161C2×D4—471no—
162C2×D4—941no—
163C22×C4—471no—
164C22×C4—941no—
165C22×C4—941no—
166Q16—1882no—
167Q16—1882no—
168Q16—1882no—
169SD16—1882no—
170C2×C8—472no—
171C2×C8C22×D4712yes—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—472no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4C22×D4712yes—
180C22⋊C4—472no—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C42—471no—
185C42—942no—
186C42C22×D4711yescharacteristic
187C23—471no—
188C23—941no—
189Q8—22no—
190Q8—22no—
191Q8—942no—
192Q8—942no—
193Q8—942no—
194Q8—1882no—
195D4—942no—
196D4—1882no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—472no—
201C2×C4—471no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—941no—
205C2×C4—1882no—
206C2×C4—1882no—
207C2×C4D4×D4712yes—
208C2×C4C23×D4711yescharacteristic
209C8—22no—
210C8—942no—
211C22—942no—
212C22—941no—
213C22—1882no—
214C22—1881no—
215C22C2×D4×D4711yescharacteristic
216C4—22no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—942no—
221C4—941no—
222C4—1881no—
223C4—1882no—
224C4#1309407012yes—
225C2—3761no—
226C2—1881no—
227C2#1568969111yescharacteristic
228C2#1568993912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#491C2
socleC22×C47C22×D4
hypercenter#491D47
hypocenterC47#3223
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #15689736C2semidirect
3. #15689517C2semidirect
4. #15689502C2semidirect
5. #15689480C2semidirect
6. #15689348C2semidirect
7. #15689332C2semidirect
9. #15689280C2semidirect
10. #15689185C2semidirect
11. C47×#491C2semidirect
119. #491D47semidirect
126. C47#3223semidirect