Finite Group Databasebeta

← #20245051

Subgroups — #20245051

Order 6016.

258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689669C211yesmaximal, characteristic
2#15689097C211yesmaximal, characteristic, complemented
3#15688917C212yesmaximal, complemented
4#15688915C212yesmaximal, complemented
5C47×#410C211yesmaximal, characteristic, complemented
6C2×#10625350C411yescharacteristic, complemented
7#13094022C411yescharacteristic, complemented
8#13094020C2211yescharacteristic
9#13094013C411yescharacteristic, complemented
10#13094011C2211yescharacteristic
11#13093996—21no—
12#13093996—21no—
13C4×C22⋊D47—21no—
14C4×C22⋊D47—21no—
15#13093983—21no—
16C2×C4×Dic47C411yescharacteristic, complemented
17#13093939—21no—
18#13093939C2212yes—
19C2×#41×C47C2211yescharacteristic
20#117×C47—21no—
21#99×C47—21no—
22#99×C47C2212yes—
23#41×C47—41no—
24#41×C47—41no—
25C2×Q8×C47C2×C411yescharacteristic
26C2×D4×C47D411yescharacteristic
27C2×D4×C47D411yescharacteristic
28C2×D4×C47C2311yescharacteristic
29C22×C4×C47C2×C411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D411yescharacteristic
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C2×C22⋊D47—21no—
35C22×Dic47—21no—
36#10625350—41no—
37#10625350—41no—
38C2×D188C2×C411yescharacteristic
39C2×C4×D47—21no—
40C2×Dic94C2×C411yescharacteristic
41C4⋊C4×C47—41no—
42C22⋊C4×C47—22no—
43C42×C47—41no—
44C22⋊Dic47—21no—
45C22⋊Dic47—21no—
46C22⋊Dic47—22no—
47(C2×D47)⋊C4—21no—
48(C2×D47)⋊C4—21no—
49C4⋊Dic47—41no—
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52C4×Dic47—21no—
53C4×Dic47—41no—
54C4×Dic47C2×C411yescharacteristic
55C4×Dic47C2×C411yescharacteristic
56C23×C47C22⋊C411yescharacteristic
57C23×C47C2×D411yescharacteristic
58C23×C47C2×D411yescharacteristic
59C22×D47—21no—
60Q8×C47—41no—
61D4×C47—41no—
62D4×C47—41no—
63D4×C47—41no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—42no—
71C2×C4×C47C22⋊C411yescharacteristic
72C2×C4×C47C22⋊C411yescharacteristic
73C2×C4×C47C22⋊C411yescharacteristic
74C2×C4×C47C22×C411yescharacteristic
75C22⋊D47—42no—
76C22⋊D47—42no—
77C22⋊D47—42no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81C2×Dic47—42no—
82C2×Dic47—42no—
83D188—41no—
84C4×D47—41no—
85C4×D47—41no—
86Dic94—41no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47C2×C22⋊C411yescharacteristic
94C2×D47—41no—
95C2×D47—41no—
96C2×D47—41no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—82no—
101C4×C47#9911yescharacteristic
102C4×C47#9911yescharacteristic
103Dic47—22no—
104Dic47—41no—
105Dic47—41no—
106Dic47—82no—
107#2126—471nomaximal, Sylow
108C2×C47—21no—
109C2×C47—41no—
110C2×C47—41no—
111C2×C47—41no—
112C2×C47C2×#9911yescharacteristic
113D47—81no—
114#532—471no—
115#410—471no—
116#410D4711yescharacteristic, complemented
117#354—472no—
118#353—472no—
119C47#212611yescharacteristic, complemented, Sylow
120C2×#41—471no—
121C2×#41C2×D4711yescharacteristic
122C4⋊Q8—471no—
123#127—471no—
124#124—471no—
125#124—471no—
126#121—941no—
127#121—941no—
128C4×D4—941no—
129C4×D4—941no—
130#117—21no—
131#117—941no—
132C2×C42—471no—
133#99—21no—
134#99—472no—
135#99—941no—
136#99C2×D4712yes—
137#41—41no—
138#41—41no—
139#41—1881no—
140#41—1881no—
141C2×Q8—471no—
142C2×Q8C4×D4711yescharacteristic
143C2×D4—471no—
144C2×D4—941no—
145C2×D4—941no—
146C2×D4—941no—
147C2×D4D18811yescharacteristic
148C2×D4C22⋊D4711yescharacteristic
149C2×D4C22×D4711yescharacteristic
150C22×C4—941no—
151C22×C4—941no—
152C22×C4C4×D4711yescharacteristic
153C22×C4D18811yescharacteristic
154C22×C4C22⋊D4711yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—941no—
157C4⋊C4—941no—
158C4⋊C4—1881no—
159C22⋊C4—22no—
160C22⋊C4—941no—
161C22⋊C4—941no—
162C22⋊C4—941no—
163C22⋊C4—941no—
164C22⋊C4—942no—
165C42—41no—
166C42—471no—
167C42—471no—
168C42—941no—
169C42—1881no—
170C23—941no—
171C23(C2×D47)⋊C411yescharacteristic
172C23C2×D18811yescharacteristic
173C23C2×C22⋊D4711yescharacteristic
174Q8—41no—
175Q8—1881no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—1881no—
180D4—1882no—
181D4—1882no—
182D4—1882no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—1882no—
194C2×C4—1882no—
195C2×C4—1881no—
196C2×C4—1881no—
197C2×C4(C2×D47)⋊C411yescharacteristic
198C2×C4(C2×D47)⋊C411yescharacteristic
199C2×C4(C2×D47)⋊C411yescharacteristic
200C2×C4C2×C4×D4711yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—1881no—
208C22—1881no—
209C22—1881no—
210C22C2×(C2×D47)⋊C411yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—942no—
216C4—3762no—
217C4—1881no—
218C4—1881no—
219C4#1309393811yescharacteristic
220C4#1309393811yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—3761no—
226C2C2×#1309393811yescharacteristic
subgroupG/H
centerC4#13093938
commutatorC2×C4×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#410C2
socleC2×C47C2×#99
hypercenter#410D47
hypocenterC47#2126
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #15689097C2semidirect
3. #15688917C2semidirect
4. #15688915C2semidirect
5. C47×#410C2semidirect
6. C2×#10625350C4semidirect
7. #13094022C4semidirect
9. #13094013C4semidirect
16. C2×C4×Dic47C4semidirect
116. #410D47semidirect
119. C47#2126semidirect