Finite Group Databasebeta

← #20256308

Subgroups — #20256308

Order 6016.

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

normal subgroups only

This group has 360 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
1#15689852C211yesmaximal, characteristic, complemented
2#15689788C211yesmaximal, characteristic
3#15689530C212yesmaximal, complemented
4#15689526C211yesmaximal, characteristic, complemented
5#15689422C212yesmaximal
6#15689416C212yesmaximal, complemented
7#15689404C211yesmaximal, characteristic
8#15689250C211yesmaximal, characteristic, complemented
9#15689226C212yesmaximal
10C4×#10625336C211yesmaximal, characteristic
11C47×#475C211yesmaximal, characteristic, complemented
12C2×Q8×D47—21no—
13C2×#10625336C2211yescharacteristic
14#13094024—21no—
15#13094024C2211yescharacteristic
16#13094023C2212yes—
17#13094015—22no—
18#13094015C2212yes—
19#13094002—22no—
20#13094000—21no—
21Q8×Dic47C2212yes—
22C4×Dic94—21no—
23C4×Dic94C2211yescharacteristic
24C4×D188C2211yescharacteristic
25#13093986C2212yes—
26#13093958C2212yes—
27#13093957C2212yes—
28#13093957C2212yes—
29#13093955C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093948C2211yescharacteristic
32#13093946C2212yes—
33#13093944C2211yescharacteristic
34#13093934C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43Q8×D47—44no—
44C2×D188C2311yescharacteristic
45C2×C4×D47—21no—
46C2×C4×D47—22no—
47C2×Dic94—21no—
48C2×Dic94—22no—
49C2×Dic94D411yescharacteristic
50C2×C8×C47C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2312yes—
54C4⋊C4×C47C2311yescharacteristic
55C42×C47—21no—
56C42×C47C2311yescharacteristic
57#10625336Q814yescomplemented
58(C2×D47)⋊C4—21no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47—22no—
63C4⋊Dic47D411yescharacteristic
64C4⋊Dic47C2312yes—
65C4⋊Dic47C2311yescharacteristic
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—22no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2311yescharacteristic
73C22×D47—21no—
74Q8×C47—21no—
75Q8×C47—42no—
76Q8×C47C2×Q812yescomplemented
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47C2×D412yes—
86C2×Dic47C2×D412yes—
87D188—21no—
88D188C2×Q812yes—
89C4×D47—44no—
90C4×D47—42no—
91Dic94—22no—
92Dic94—44no—
93Dic94—42no—
94C8×C47—22no—
95C47⋊C8—21no—
96C47⋊C8C2×Q812yescomplemented
97C22×C47C22×D411yescharacteristic
98C2×D47—22no—
99C2×D47—41no—
100C2×D47—41no—
101C4×C47—22no—
102C4×C47—21no—
103C4×C47—42no—
104C4×C47—41no—
105C4×C47AGL(1,ℤ/8)12yes—
106C4×C47C22×Q811yescharacteristic
107C4×C472−1+411yescharacteristic
108Dic47—22no—
109Dic47—22no—
110Dic47—41no—
111Dic47—42no—
112#3386—471nomaximal, Sylow
113C2×C47D4×Q811yescharacteristic
114C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
115C2×C47#57811yescharacteristic
116D47—42no—
117#557—471no—
118D4×Q8—471no—
119#501—472no—
120#500—471no—
121#478—472no—
122#477—472no—
123#475D4711yescharacteristic, complemented
124#474—471no—
125#446—471no—
126#440—472no—
127C4×SD16—471no—
128C47#338611yescharacteristic, complemented, Sylow
129C22×Q8—941no—
130C2×SD16—471no—
131C4⋊Q8—472no—
132C4⋊Q8—471no—
133C4⋊Q8—941no—
134C4⋊Q8C2×D4711yescharacteristic
135#125—472no—
136#125—942no—
137C22⋊Q8—942no—
138C22⋊Q8—941no—
139C4×Q8—471no—
140C4×Q8—472no—
141C4×Q8—941no—
142C4×Q8C2×D4711yescharacteristic
143C4×D4—472no—
144C4×D4—471no—
145#107—472no—
146#107—472no—
147#107—472no—
148#106—471no—
149#106C2×D4712yes—
150C4⋊C8—472no—
151C4⋊C8C2×D4711yescharacteristic
152#103—471no—
153#103C2×D4712yes—
154#102—472no—
155#102—471no—
156#97—472no—
157C4×C8—471no—
158C2×Q8—21no—
159C2×Q8—471no—
160C2×Q8—942no—
161C2×Q8—941no—
162C2×Q8—1884no—
163C2×Q8C22×D4711yescharacteristic
164C2×D4—471no—
165C22×C4—942no—
166C22×C4—941no—
167SD16—474no—
168C2×C8—471no—
169C2×C8—471no—
170C2×C8C22×D4712yes—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—472no—
174C4⋊C4—471no—
175C4⋊C4—472no—
176C4⋊C4—471no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—941no—
182C4⋊C4C22×D4711yescharacteristic
183C4⋊C4C22×D4712yes—
184C22⋊C4—942no—
185C22⋊C4—941no—
186C42—21no—
187C42—472no—
188C42—942no—
189C42C22×D4711yescharacteristic
190C23—941no—
191Q8—21no—
192Q8—42no—
193Q8—942no—
194Q8—1884no—
195Q8—1882no—
196Q8Q8×D4712yescomplemented
197D4—472no—
198D4—941no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—472no—
203C2×C4—472no—
204C2×C4—942no—
205C2×C4—941no—
206C2×C4—1884no—
207C2×C4—1882no—
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—472no—
213C8—941no—
214C22—942no—
215C22—1881no—
216C22—1881no—
217C22C2×D4×D4711yescharacteristic
218C4—22no—
219C4—21no—
220C4—42no—
221C4—41no—
222C4—942no—
223C4—942no—
224C4—1881no—
225C4—1882no—
226C4#1309405112yes—
227C4C2×Q8×D4711yescharacteristic
228C4#1309407111yescharacteristic
229C2—1882no—
230C2#1568978611yescharacteristic
231C2C2×#1309405111yescharacteristic
232C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3386
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #15689852C2semidirect
3. #15689530C2semidirect
4. #15689526C2semidirect
6. #15689416C2semidirect
8. #15689250C2semidirect
11. C47×#475C2semidirect
57. #10625336Q8semidirect
76. Q8×C47C2×Q8semidirect
96. C47⋊C8C2×Q8semidirect
123. #475D47semidirect
128. C47#3386semidirect
196. Q8Q8×D47semidirect