Finite Group Databasebeta

← #20241945

Subgroups — #20241945

Order 6016.

284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689634C211yesmaximal, characteristic
2#15688986C211yesmaximal, characteristic, complemented
3#15688861C212yesmaximal, complemented
4#15688858C212yesmaximal, complemented
5C2×C22⋊C8×C47C211yesmaximal, characteristic, complemented
6C2×#10625350C411yescharacteristic, complemented
7#13094007—21no—
8#13094003C411yescharacteristic, complemented
9#13094003C2211yescharacteristic
10#13093998C411yescharacteristic, complemented
11#13093998C2211yescharacteristic
12#13093993—21no—
13C4×C22⋊D47—21no—
14C4×C22⋊D47—21no—
15#13093983C411yescharacteristic, complemented
16C2×C22⋊Dic47—21no—
17C47⋊#95—21no—
18C47⋊#95C2212yes—
19C23×C4×C47C2211yescharacteristic
20C22×C8×C47—21no—
21C22⋊C8×C47—21no—
22C22⋊C8×C47C2212yes—
23C24×C47D411yescharacteristic
24C22×C4×C47—42no—
25C22×C4×C47C2×C411yescharacteristic
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47—21no—
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C22×Dic47—22no—
35#10625350—42no—
36C2×D188C2×C411yescharacteristic
37C2×C4×D47—21no—
38C2×Dic94C2×C411yescharacteristic
39C2×C8×C47—22no—
40C2×C8×C47—42no—
41C22⋊Dic47—21no—
42C22⋊Dic47—21no—
43C22⋊Dic47—21no—
44C22⋊Dic47—42no—
45(C2×D47)⋊C4—21no—
46(C2×D47)⋊C4—21no—
47C4⋊Dic47C2×C411yescharacteristic
48C4⋊Dic47C2×C411yescharacteristic
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51C4×Dic47—21no—
52C23×C47—22no—
53C23×C47—22no—
54C23×C47—41no—
55C23×C47C22⋊C411yescharacteristic
56C23×C47C22⋊C411yescharacteristic
57C23×C47C2×D411yescharacteristic
58C22×D47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47C22⋊C411yescharacteristic
66C2×C4×C47C22⋊C411yescharacteristic
67C2×C4×C47C22×C411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C22⋊D47—42no—
70C22⋊D47—42no—
71C22⋊D47—42no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—42no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78D188—41no—
79C4×D47—42no—
80Dic94—41no—
81C8×C47—42no—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—44no—
90C22×C47#9912yes—
91C22×C47C2×C22⋊C411yescharacteristic
92C22×C47#13512yes—
93C2×D47—41no—
94C2×D47—41no—
95C2×D47—41no—
96C4×C47—21no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—21no—
100Dic47—41no—
101Dic47—41no—
102Dic47—41no—
103Dic47—82no—
104#1516—471nomaximal, Sylow
105C2×C47—22no—
106C2×C47—22no—
107C2×C47—41no—
108C2×C47C2×#9911yescharacteristic
109C2×C47#41611yescharacteristic
110C2×C47#42111yescharacteristic
111D47—81no—
112#525—471no—
113C2×C22⋊C8D4711yescharacteristic, complemented
114#381—471no—
115#328—472no—
116#327—472no—
117C47#151611yescharacteristic, complemented, Sylow
118C2×#41—471no—
119C23×C4C2×D4711yescharacteristic
120C22×C8—21no—
121#123—941no—
122C22⋊Q8—471no—
123C22⋊Q8—471no—
124#121—471no—
125#121—471no—
126#120—941no—
127C4×D4—941no—
128C4×D4—941no—
129#117—471no—
130C2×C22⋊C4—941no—
131C22⋊C8—21no—
132C22⋊C8C2×D4712yes—
133#95—472no—
134#95—941no—
135C24D18811yescharacteristic
136#41—1882no—
137C2×Q8—471no—
138C2×D4—471no—
139C2×D4—941no—
140C2×D4—941no—
141C2×D4—941no—
142C22×C4—42no—
143C22×C4—941no—
144C22×C4—942no—
145C22×C4C4×D4711yescharacteristic
146C22×C4C4×D4711yescharacteristic
147C22×C4D18811yescharacteristic
148C22×C4C22⋊D4711yescharacteristic
149C22×C4C22⋊D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151C2×C8—22no—
152C2×C8—42no—
153C4⋊C4—471no—
154C4⋊C4—471no—
155C4⋊C4—941no—
156C4⋊C4—941no—
157C22⋊C4—941no—
158C22⋊C4—941no—
159C22⋊C4—941no—
160C22⋊C4—941no—
161C22⋊C4—941no—
162C22⋊C4—1882no—
163C42—941no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—941no—
168C23(C2×D47)⋊C411yescharacteristic
169C23(C2×D47)⋊C411yescharacteristic
170C23C2×D18811yescharacteristic
171Q8—1881no—
172D4—1881no—
173D4—1882no—
174D4—1882no—
175D4—1882no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—941no—
185C2×C4—1882no—
186C2×C4—1882no—
187C2×C4—1882no—
188C2×C4—1882no—
189C2×C4(C2×D47)⋊C411yescharacteristic
190C2×C4(C2×D47)⋊C411yescharacteristic
191C2×C4C2×C4×D4711yescharacteristic
192C2×C4C2×C22⋊D4711yescharacteristic
193C8—42no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—1881no—
203C22—1881no—
204C22—1881no—
205C22#1309393812yes—
206C22C2×(C2×D47)⋊C411yescharacteristic
207C22#1309404612yes—
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—3762no—
213C4—1881no—
214C4—1881no—
215C4—1881no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—3761no—
220C2C2×#1309393811yescharacteristic
221C2#1568912011yescharacteristic
222C2#1568913911yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊C8×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×C22⋊C8D47
hypocenterC47#1516
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #15688986C2semidirect
3. #15688861C2semidirect
4. #15688858C2semidirect
5. C2×C22⋊C8×C47C2semidirect
6. C2×#10625350C4semidirect
8. #13094003C4semidirect
10. #13093998C4semidirect
15. #13093983C4semidirect
113. C2×C22⋊C8D47semidirect
117. C47#1516semidirect