Finite Group Databasebeta

← #20254473

Subgroups — #20254473

Order 6016.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689735C211yesmaximal, characteristic, complemented
2#15689699C211yesmaximal, characteristic
3#15689517C211yesmaximal, characteristic, complemented
4#15689503C211yesmaximal, characteristic, complemented
5#15689492C211yesmaximal, characteristic, complemented
6#15689478C211yesmaximal, characteristic, complemented
7#15689346C212yesmaximal, complemented
8#15689334C212yesmaximal, complemented
9#15689287C212yesmaximal
10#15689281C212yesmaximal, complemented
11C47×#433C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14C2×Dic188C2212yes—
15C2×Dic188C2212yes—
16C2×Dic188C2212yes—
17C2×#10625325C2212yes—
18#13094024C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094017—22no—
22#13094016C2211yescharacteristic
23#13094014—22no—
24#13094012C2211yescharacteristic
25#13094012C2211yescharacteristic
26#13094008—22no—
27#13094004—22no—
28#13094003C2212yes—
29C4×Dic94C2212yes—
30#13093949C2212yes—
31#13093949C2212yes—
32#13093949C2212yes—
33#13093946C2212yes—
34#117×C47C2211yescharacteristic
35C4⋊C8×C47C2212yes—
36C22⋊C8×C47C2212yes—
37#97×C47C2211yescharacteristic
38C4×C8×C47C2211yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—21no—
41C22×Dic47—21no—
42#10625350—42no—
43C2×D188C2311yescharacteristic
44C2×C4×D47—21no—
45C2×Dic94—21no—
46C2×Dic94—42no—
47C2×Dic94C2311yescharacteristic
48C2×Dic94C2311yescharacteristic
49C2×Dic94C2311yescharacteristic
50C2×Dic94C2312yes—
51C2×C8×C47C2312yes—
52C2×C8×C47C2312yes—
53C4⋊C4×C47D412yes—
54C22⋊C4×C47D412yes—
55C42×C47C2311yescharacteristic
56C42×C47C2311yescharacteristic
57C22⋊Dic47—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47—22no—
62C4⋊Dic47—22no—
63C4⋊Dic47C2312yes—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67C4×Dic47—22no—
68Dic188—42no—
69Dic188—42no—
70Dic188—42no—
71#10625325—42no—
72C23×C47C2×D411yescharacteristic
73C22×D47—21no—
74C2×C4×C47—22no—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2411yescharacteristic
79C22⋊D47—42no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—42no—
86D188—22no—
87C4×D47—42no—
88Dic94—22no—
89Dic94—22no—
90Dic94—22no—
91Dic94—22no—
92Dic94—22no—
93Dic94—42no—
94C8×C47—22no—
95C8×C47—22no—
96C22×C47—21no—
97C22×C47—22no—
98C22×C47C22×D411yescharacteristic
99C2×D47—41no—
100C2×D47—42no—
101C4×C47—21no—
102C4×C47—22no—
103C4×C47—22no—
104C4×C47H(5,𝔽2)12yes—
105Dic47—41no—
106Dic47—41no—
107Dic47—41no—
108Dic47—42no—
109Dic47—42no—
110#3223—471nomaximal, Sylow
111C2×C47—41no—
112C2×C47#53511yescharacteristic
113C2×C47#57812yes—
114D47—81no—
115#541—471no—
116#536—471no—
117#497—471no—
118#494—471no—
119#491—471no—
120#488—471no—
121#464—472no—
122#462—472no—
123#452—472no—
124#451—472no—
125#433D4711yescharacteristic, complemented
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⋊Q8—471no—
136#126—942no—
137#125—471no—
138#125—942no—
139#124—471no—
140#124—471no—
141#123—942no—
142C22⋊Q8—472no—
143C22⋊Q8—942no—
144C4×Q8—472no—
145#117C2×D4711yescharacteristic
146C4⋊C8C2×D4712yes—
147#103—472no—
148#103—472no—
149#103—472no—
150#102—472no—
151C22⋊C8C2×D4712yes—
152#97C2×D4711yescharacteristic
153C4×C8C2×D4711yescharacteristic
154#41—1882no—
155C2×Q8—471no—
156C2×Q8—471no—
157C2×Q8—471no—
158C2×Q8—472no—
159C2×Q8—941no—
160C2×Q8—1882no—
161C2×D4—471no—
162C2×D4—941no—
163C22×C4—941no—
164C22×C4—941no—
165C22×C4C22×D4711yescharacteristic
166Q16—1882no—
167Q16—1882no—
168Q16—1882no—
169SD16—1882no—
170C2×C8C22×D4712yes—
171C2×C8C22×D4712yes—
172C4⋊C4—472no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4D18812yes—
180C22⋊C4—942no—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C22⋊C4D18812yes—
184C42—942no—
185C42C22×D4711yescharacteristic
186C42C22×D4711yescharacteristic
187C23—941no—
188C23C2×D18811yescharacteristic
189Q8—942no—
190Q8—942no—
191Q8—942no—
192Q8—942no—
193Q8—942no—
194Q8—1882no—
195D4—942no—
196D4—1882no—
197C2×C4—22no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—1882no—
204C2×C4—1882no—
205C2×C4C2×D18812yes—
206C2×C4C2×D18812yes—
207C2×C4C2×D18811yescharacteristic
208C2×C4C23×D4711yescharacteristic
209C8—22no—
210C8—22no—
211C22—22no—
212C22—21no—
213C22—1882no—
214C22—1881no—
215C22C22×D18811yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—1882no—
220C4—1881no—
221C4—1881no—
222C4—1881no—
223C4—1882no—
224C4#1309407012yes—
225C2—41no—
226C2—3761no—
227C2#1568969211yescharacteristic
228C2#1568994012yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3223
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #15689735C2semidirect
3. #15689517C2semidirect
4. #15689503C2semidirect
5. #15689492C2semidirect
6. #15689478C2semidirect
7. #15689346C2semidirect
8. #15689334C2semidirect
10. #15689281C2semidirect
11. C47×#433C2semidirect
125. #433D47semidirect
126. C47#3223semidirect