Finite Group Databasebeta

← C2×#15688858 #20241866

Subgroups — C2×#15688858 #20241866

Order 6016.

388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13093998C211yesmaximal, characteristic
2C2×C47⋊#95C211yesmaximal, characteristic, complemented
3#15688858C214yesmaximal, direct product factor
4C2×C22⋊C8×C47C211yesmaximal, characteristic, complemented
5C22×D188C411yescharacteristic, complemented
6C22×C22⋊D47—21no—
7C23×Dic47—21no—
8#13093998—21no—
9#13093998—21no—
10#13093998C412yescomplemented
11#13093998C2212yes—
12C2×C4⋊Dic47C411yescharacteristic, complemented
13C2×(C2×D47)⋊C4—21no—
14C47⋊#95—21no—
15C47⋊#95C2212yescomplemented
16C23×C4×C47C2211yescharacteristic
17C22×C8×C47—21no—
18C22⋊C8×C47—21no—
19C22⋊C8×C47C2212yescomplemented
20C24×C47D411yescharacteristic
21C23×D47—21no—
22C22×C4×C47—42no—
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47C2×C411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47C2311yescharacteristic
29C2×C22⋊D47—22no—
30C2×C22⋊D47—22no—
31C2×C22⋊D47—42no—
32C2×C22⋊D47—42no—
33C22×Dic47—24no—
34C22×Dic47—21no—
35C22×Dic47—22no—
36C22×Dic47—42no—
37C22×Dic47—42no—
38C2×D188—21no—
39C2×D188—42no—
40C2×D188C2×C412yescomplemented
41C2×C8×C47—22no—
42C2×C8×C47—42no—
43(C2×D47)⋊C4—22no—
44(C2×D47)⋊C4—22no—
45C4⋊Dic47—21no—
46C4⋊Dic47C2×C412yescomplemented
47C23×C47—22no—
48C23×C47—22no—
49C23×C47C22⋊C411yescharacteristic
50C23×C47C22⋊C411yescharacteristic
51C23×C47D812yes—
52C23×C47SD1612yes—
53C23×C47C2×D411yescharacteristic
54C22×D47—22no—
55C22×D47—42no—
56C22×D47—42no—
57C22×D47—42no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C22⋊C411yescharacteristic
65C2×C4×C47C22⋊C411yescharacteristic
66C2×C4×C47C22×C411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C22⋊D47—44no—
69C22⋊D47—42no—
70C22⋊D47—42no—
71C2×Dic47—24no—
72C2×Dic47—22no—
73C2×Dic47—48no—
74C2×Dic47—42no—
75C2×Dic47—42no—
76C2×Dic47—42no—
77D188—42no—
78D188—42no—
79C8×C47—42no—
80C22×C47—24no—
81C22×C47—24no—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47#9912yes—
87C22×C47#10212yes—
88C22×C47#10212yes—
89C22×C47#10412yes—
90C22×C47C2×C22⋊C411yescharacteristic
91C22×C47C2×D811yescharacteristic
92C22×C47C2×SD1611yescharacteristic
93C2×D47—42no—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—84no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101Dic47—44no—
102Dic47—42no—
103C2×#327—471nomaximal, Sylow
104C2×C47—21no—
105C2×C47—22no—
106C2×C47—21no—
107C2×C47#32714yescomplemented
108C2×C47C2×#9911yescharacteristic
109C2×C47C2×#10211yescharacteristic
110C2×C47C2×#10411yescharacteristic
111D47—82no—
112C2×#121—471no—
113C2×C22⋊C8D4711yescharacteristic, complemented
114C2×#95—471no—
115#327—474no—
116C47C2×#32711yescharacteristic, complemented, Sylow
117C22×D4—471no—
118C22×D4—941no—
119C23×C4—941no—
120C23×C4C2×D4711yescharacteristic
121C22×C8—21no—
122#121—472no—
123#121—472no—
124#121—941no—
125#121—941no—
126C2×C4⋊C4—471no—
127C2×C22⋊C4—941no—
128C22⋊C8—21no—
129C22⋊C8C2×D4712yescomplemented
130#95—472no—
131#95—941no—
132C24—941no—
133C24D18811yescharacteristic
134C2×D4—472no—
135C2×D4—942no—
136C2×D4—942no—
137C2×D4—941no—
138C2×D4—1882no—
139C2×D4—1882no—
140C2×D4—1882no—
141C22×C4—42no—
142C22×C4—944no—
143C22×C4—941no—
144C22×C4—942no—
145C22×C4—1882no—
146C22×C4—1882no—
147C22×C4C4×D4711yescharacteristic
148C22×C4C4×D4711yescharacteristic
149C22×C4D18811yescharacteristic
150C22×C4C22⋊D4711yescharacteristic
151C22×C4C22⋊D4711yescharacteristic
152C22×C4C22×D4711yescharacteristic
153C2×C8—22no—
154C2×C8—42no—
155C4⋊C4—472no—
156C4⋊C4—941no—
157C22⋊C4—942no—
158C22⋊C4—942no—
159C23—22no—
160C23—22no—
161C23—942no—
162C23—1882no—
163C23—1882no—
164C23—1882no—
165C23#1062532512yes—
166C23D37612yes—
167C23(C2×D47)⋊C411yescharacteristic
168C23(C2×D47)⋊C411yescharacteristic
169C23C2×D18811yescharacteristic
170D4—1882no—
171D4—1882no—
172D4—1884no—
173D4—1882no—
174D4—1882no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—944no—
182C2×C4—942no—
183C2×C4—1882no—
184C2×C4—1888no—
185C2×C4—1882no—
186C2×C4—1882no—
187C2×C4(C2×D47)⋊C411yescharacteristic
188C2×C4(C2×D47)⋊C411yescharacteristic
189C2×C4C2×C4×D4711yescharacteristic
190C2×C4C2×C22⋊D4711yescharacteristic
191C8—42no—
192C22—21no—
193C22—21no—
194C22—24no—
195C22—24no—
196C22—21no—
197C22—21no—
198C22—3764no—
199C22—1882no—
200C22—1882no—
201C22—1882no—
202C22#1309393812yes—
203C22#1309394612yes—
204C22#1309394612yes—
205C22#1309395012yes—
206C22C2×(C2×D47)⋊C411yescharacteristic
207C22C2×D37611yescharacteristic
208C22C2×#1062532511yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—1884no—
214C4—1882no—
215C2—21no—
216C2—22no—
217C2—21no—
218C2—3762no—
219C2#1568885814yesdirect product factor
220C2C2×#1309393811yescharacteristic
221C2C2×#1309394611yescharacteristic
222C2C2×#1309395011yescharacteristic
subgroupG/H
centerC23(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊C8×C47C2
socleC23×C47C22⋊C4
hypercenterC2×C22⋊C8D47
hypocenterC47C2×#327
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C47⋊#95C2semidirect
3. #15688858C2direct (N × H)
4. C2×C22⋊C8×C47C2semidirect
5. C22×D188C4semidirect
10. #13093998C4semidirect
12. C2×C4⋊Dic47C4semidirect
15. C47⋊#95C22semidirect
19. C22⋊C8×C47C22semidirect
40. C2×D188C2×C4semidirect
46. C4⋊Dic47C2×C4semidirect
107. C2×C47#327semidirect
113. C2×C22⋊C8D47semidirect
116. C47C2×#327semidirect
129. C22⋊C8C2×D47semidirect
219. C2#15688858direct (N × H)