Finite Group Databasebeta

← #20249066

Subgroups — #20249066

Order 6016.

540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13093982C212yesmaximal, complemented
2#15689045C212yesmaximal, complemented
3#15689040C211yesmaximal, characteristic
4#15689013C212yesmaximal, complemented
5#15689010C212yesmaximal, complemented
6#15689001C212yesmaximal
7#15688997C212yesmaximal, complemented
8#15688988C211yesmaximal, characteristic, complemented
9C47×#398C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C4×D47C2212yes—
12#13093982—28no—
13C2×C4⋊Dic47C2212yes—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×(C2×D47)⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×C4×Dic47C2212yes—
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2212yes—
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30#95×C47C2211yescharacteristic
31#95×C47C2212yes—
32C23×D47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C2×D188—24no—
42C2×D188—41no—
43C2×C4×D47—24no—
44C2×C4×D47—24no—
45C2×C4×D47—24no—
46C4⋊C4×C47—24no—
47C4⋊C4×C47—41no—
48C4⋊C4×C47—41no—
49(C2×D47)⋊C4—24no—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—24no—
53(C2×D47)⋊C4—42no—
54C4⋊Dic47—24no—
55C4⋊Dic47—41no—
56Dic47⋊C4—24no—
57C4×Dic47—24no—
58C4×Dic47D414yescomplemented
59C23×C47C2411yescharacteristic
60C22×D47—22no—
61C22×D47—22no—
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—22no—
66C22×D47#4114yes—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47#4114yes—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47C2×D414yes—
89D188—44no—
90C4×D47—216no—
91C22×C47C22×D411yescharacteristic
92C22×C47C2×#4112yes—
93C22×C47C2×#4112yes—
94C22×C47H(5,𝔽2)11yescharacteristic
95C22×C472−1+411yescharacteristic
96C2×D47—24no—
97C2×D47—24no—
98C2×D47—24no—
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—42no—
103C4×C47—24no—
104C4×C47—22no—
105C4×C47—42no—
106C4×C47—41no—
107C4×C47—41no—
108Dic47—24no—
109Dic47—42no—
110Dic47—42no—
111#2609—471nomaximal, Sylow
112C2×C47#52512yes—
113C2×C47#53711yescharacteristic
114C2×C47#55111yescharacteristic
115C2×C47#55212yes—
116C2×C47#55511yescharacteristic
117D47—44no—
118C2×#117—472no—
119#398D4711yescharacteristic, complemented
120#396—472no—
121#394—471no—
122#388—472no—
123#387—472no—
124#386—472no—
125#385—472no—
126#382—471no—
127C47#260911yescharacteristic, complemented, Sylow
128C22×D4—471no—
129C23×C4—472no—
130#117—948no—
131C2×C4⋊C4—472no—
132C2×C4⋊C4—472no—
133C2×C4⋊C4—471no—
134C2×C4⋊C4C2×D4712yes—
135C2×C4⋊C4C2×D4711yescharacteristic
136C2×C4⋊C4C2×D4711yescharacteristic
137C2×C22⋊C4—472no—
138C2×C22⋊C4—472no—
139C2×C22⋊C4—472no—
140C2×C22⋊C4—472no—
141C2×C22⋊C4—472no—
142C2×C42—471no—
143C2×C42—472no—
144#95—472no—
145#95—472no—
146#95—471no—
147#95—472no—
148#95C2×D4711yescharacteristic
149#95C2×D4712yes—
150C24—472no—
151C2×D4—944no—
152C2×D4—1881no—
153C22×C4—472no—
154C22×C4—472no—
155C22×C4—472no—
156C22×C4—944no—
157C22×C4—944no—
158C22×C4—944no—
159C22×C4C22×D4711yescharacteristic
160C22×C4C22×D4711yescharacteristic
161C22×C4C22×D4712yes—
162C22×C4C22×D4711yescharacteristic
163C22×C4C22×D4712yes—
164C4⋊C4—24no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—944no—
168C4⋊C4—944no—
169C4⋊C4—1881no—
170C22⋊C4—944no—
171C22⋊C4—944no—
172C22⋊C4—944no—
173C22⋊C4—944no—
174C22⋊C4—1882no—
175C42—474no—
176C42—944no—
177C23—474no—
178C23—942no—
179C23—942no—
180C23—942no—
181C23—942no—
182C23—942no—
183C23—942no—
184C23C23×D4711yescharacteristic
185D4—1884no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—474no—
198C2×C4—9416no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4D4×D4712yes—
208C2×C4#1062535414yes—
209C22—944no—
210C22—944no—
211C22—944no—
212C22—1882no—
213C22—1882no—
214C22—1882no—
215C22—1882no—
216C22C2×D4×D4711yescharacteristic
217C22#41×D4712yes—
218C22C2×#1062535412yes—
219C22#1309406911yescharacteristic
220C22#1309407111yescharacteristic
221C4—24no—
222C4—22no—
223C4—41no—
224C4—41no—
225C4—42no—
226C4—944no—
227C4—1882no—
228C4—1882no—
229C2—1884no—
230C2#1568963612yes—
231C2#1568970011yescharacteristic
232C2#1568980111yescharacteristic
233C2#1568981112yes—
234C2#1568983911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2609
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13093982C2semidirect
2. #15689045C2semidirect
4. #15689013C2semidirect
5. #15689010C2semidirect
7. #15688997C2semidirect
8. #15688988C2semidirect
9. C47×#398C2semidirect
58. C4×Dic47D4semidirect
119. #398D47semidirect
127. C47#2609semidirect