Finite Group Databasebeta

← #20241879

Subgroups — #20241879

Order 6016.

304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
2C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
3#15688860C212yesmaximal, complemented
4#15688857C212yesmaximal, complemented
5C47×#525C211yesmaximal, characteristic
6C22×C47⋊C8—21no—
7C2×C22⋊Dic47—21no—
8C2×C4×Dic47—21no—
9C22⋊(C47⋊C8)—21no—
10C22⋊(C47⋊C8)C2212yes—
11C47⋊#95C2212yes—
12C2×#41×C47C411yescharacteristic, complemented
13C23×C4×C47C2211yescharacteristic
14#123×C47—21no—
15C22⋊Q8×C47C411yescharacteristic, complemented
16C22⋊Q8×C47C2211yescharacteristic
17#121×C47C411yescharacteristic, complemented
18#121×C47C2211yescharacteristic
19#120×C47—21no—
20C4×D4×C47—21no—
21C4×D4×C47—21no—
22#117×C47C411yescharacteristic, complemented
23C24×C47D411yescharacteristic
24#41×C47—42no—
25C2×Q8×C47C2×C411yescharacteristic
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47C2×C411yescharacteristic
30C22×C4×C47—21no—
31C22×C4×C47—42no—
32C22×C4×C47C2×C411yescharacteristic
33C22×C4×C47C2×C411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×Dic47—22no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47C2×C411yescharacteristic
42C4⋊C4×C47C2×C411yescharacteristic
43C22⋊C4×C47—21no—
44C22⋊C4×C47—21no—
45C22⋊C4×C47—21no—
46C22⋊C4×C47—21no—
47C22⋊C4×C47—21no—
48C42×C47—21no—
49C22⋊Dic47—24no—
50C4×Dic47—42no—
51C2×C47⋊C8—22no—
52C2×C47⋊C8—42no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—21no—
56C23×C47—41no—
57C23×C47C22⋊C411yescharacteristic
58C23×C47C22⋊C411yescharacteristic
59C23×C47C2×D411yescharacteristic
60Q8×C47—41no—
61D4×C47—41no—
62D4×C47—42no—
63D4×C47—42no—
64D4×C47—42no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—42no—
75C2×C4×C47C22⋊C411yescharacteristic
76C2×C4×C47C22⋊C411yescharacteristic
77C2×C4×C47C22×C411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×Dic47—24no—
80C2×Dic47—42no—
81C2×Dic47—42no—
82C47⋊C8—42no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—44no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47—41no—
94C22×C47#10412yes—
95C22×C47C2×C22⋊C411yescharacteristic
96C22×C47#13512yes—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—41no—
101C4×C47—41no—
102C4×C47—41no—
103C4×C47#9912yes—
104Dic47—44no—
105#1501—471nomaximal, Sylow
106C2×C47—22no—
107C2×C47—22no—
108C2×C47—41no—
109C2×C47—81no—
110C2×C47C2×#9911yescharacteristic
111C2×C47#41611yescharacteristic
112C2×C47C2×#10411yescharacteristic
113#525D4711yescharacteristic
114C2×C22⋊C8—471no—
115C4×C22⋊C4—471no—
116#328—472no—
117#327—472no—
118C47#150111yescharacteristic, complemented, Sylow
119C2×#41Dic4711yescharacteristic, complemented
120C23×C4C2×D4711yescharacteristic
121C22×C8—941no—
122#123—21no—
123C22⋊Q8Dic4711yescharacteristic, complemented
124C22⋊Q8C2×D4711yescharacteristic
125#121Dic4711yescharacteristic, complemented
126#121C2×D4711yescharacteristic
127#120—21no—
128C4×D4—21no—
129C4×D4—21no—
130#117Dic4711yescharacteristic, complemented
131C2×C22⋊C4—941no—
132C2×C42—941no—
133C22⋊C8—472no—
134C22⋊C8—941no—
135#95—472no—
136C24C22⋊D4711yescharacteristic
137#41—42no—
138C2×Q8C2×Dic4711yescharacteristic
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4C2×Dic4711yescharacteristic
143C22×C4—21no—
144C22×C4—42no—
145C22×C4—942no—
146C22×C4C2×Dic4711yescharacteristic
147C22×C4C2×Dic4711yescharacteristic
148C22×C4C22⋊D4711yescharacteristic
149C22×C4C22⋊D4711yescharacteristic
150C22×C4C22⋊D4711yescharacteristic
151C22×C4C22×D4711yescharacteristic
152C2×C8—942no—
153C2×C8—1882no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4C2×Dic4711yescharacteristic
157C4⋊C4C2×Dic4711yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—21no—
163C22⋊C4—944no—
164C42—21no—
165C42—1882no—
166C23—22no—
167C23—22no—
168C23—21no—
169C23—41no—
170C23C22⋊Dic4711yescharacteristic
171C23C22⋊Dic4711yescharacteristic
172C23C2×C22⋊D4711yescharacteristic
173Q8—41no—
174D4—41no—
175D4—42no—
176D4—42no—
177D4—42no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—944no—
189C2×C4—1882no—
190C2×C4—1882no—
191C2×C4C22⋊Dic4711yescharacteristic
192C2×C4C22⋊Dic4711yescharacteristic
193C2×C4C22×Dic4711yescharacteristic
194C2×C4C2×C22⋊D4711yescharacteristic
195C8—1882no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22#1309395112yes—
208C22C2×C22⋊Dic4711yescharacteristic
209C22#1309404412yes—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—41no—
215C4—41no—
216C4—1884no—
217C4#1309393912yes—
218C2—22no—
219C2—22no—
220C2—41no—
221C2—81no—
222C2C2×#1309393911yescharacteristic
223C2#1568911911yescharacteristic
224C2C2×#1309395111yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#525C2
socleC22×C47C2×C22⋊C4
hypercenter#525D47
hypocenterC47#1501
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊(C47⋊C8)C2semidirect
2. C4×C22⋊Dic47C2semidirect
3. #15688860C2semidirect
4. #15688857C2semidirect
12. C2×#41×C47C4semidirect
15. C22⋊Q8×C47C4semidirect
17. #121×C47C4semidirect
22. #117×C47C4semidirect
118. C47#1501semidirect
119. C2×#41Dic47semidirect
123. C22⋊Q8Dic47semidirect
125. #121Dic47semidirect
130. #117Dic47semidirect