Finite Group Databasebeta

← #20248368

Subgroups — #20248368

Order 6016.

576 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13094024C211yesmaximal, characteristic, complemented
2C2×#13094012C211yesmaximal, characteristic
3C2×#13094012C211yesmaximal, characteristic
4C2×C4×Dic94C211yesmaximal, characteristic, complemented
5#15689045C214yesmaximal, complemented
6#15689029C211yesmaximal, characteristic, complemented
7#15689025C211yesmaximal, characteristic
8#15689015C214yesmaximal, complemented
9C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×Dic94C2211yescharacteristic
12C22×D188C2211yescharacteristic
13#13094024—24no—
14#13094012—24no—
15#13094012—24no—
16C4×Dic94—24no—
17C2×C4⋊Dic47C2214yes—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2214yes—
22C2×(C2×D47)⋊C4C2214yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×C4×Dic47C2212yes—
25C47⋊#95C2214yes—
26C2×C4⋊C4×C47C2212yes—
27C2×C42×C47C2211yescharacteristic
28C2×C42×C47C2211yescharacteristic
29C2×C42×C47C2211yescharacteristic
30#95×C47C2212yes—
31C23×D47C2312yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C2×D188—22no—
41C2×D188—22no—
42C2×D188—22no—
43C2×Dic94—22no—
44C2×Dic94—22no—
45C2×Dic94—22no—
46C2×Dic94—22no—
47C2×Dic94—22no—
48C2×Dic94D414yes—
49C4⋊C4×C47—24no—
50C42×C47—22no—
51C42×C47—22no—
52C42×C47D414yes—
53(C2×D47)⋊C4—24no—
54(C2×D47)⋊C4—24no—
55(C2×D47)⋊C4—28no—
56(C2×D47)⋊C4—28no—
57C4⋊Dic47—22no—
58C4⋊Dic47—28no—
59Dic47⋊C4—24no—
60C4×Dic47—24no—
61C23×C47C2411yescharacteristic
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—24no—
65C22×D47—22no—
66C22×D47—24no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D412yes—
78C2×C4×C47#4114yes—
79C2×C4×C47#4112yes—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—24no—
86C2×Dic47—22no—
87C2×Dic47C2×D414yes—
88D188—44no—
89Dic94—28no—
90Dic94—44no—
91C22×C47C22×D411yescharacteristic
92C22×C47C22×D411yescharacteristic
93C22×C47C2×#4112yes—
94C22×C47C2×#4111yescharacteristic
95C22×C472−1+412yes—
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—44no—
100C2×D47—44no—
101C4×C47—22no—
102C4×C47—22no—
103C4×C47—24no—
104C4×C47—42no—
105C4×C47#12114yes—
106Dic47—24no—
107Dic47—42no—
108Dic47—42no—
109#2545—471nomaximal, Sylow
110C2×C47C2×#12111yescharacteristic
111C2×C47#53211yescharacteristic
112C2×C47#53611yescharacteristic
113C2×C47#54812yes—
114C2×C47#55612yes—
115D47—82no—
116C2×C4⋊Q8—471no—
117C2×#124—471no—
118C2×#124—471no—
119C2×C4×Q8—471no—
120#396—474no—
121#391—471no—
122#390—471no—
123#388—474no—
124C4×C4⋊C4D4711yescharacteristic, complemented
125C47#254511yescharacteristic, complemented, Sylow
126C22×Q8—471no—
127C22×Q8—471no—
128C22×D4—471no—
129C4⋊Q8—944no—
130#124—944no—
131#124—944no—
132C4×Q8—944no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4—471no—
135C2×C4⋊C4—474no—
136C2×C4⋊C4C2×D4712yes—
137C2×C22⋊C4—472no—
138C2×C22⋊C4—474no—
139C2×C22⋊C4—472no—
140C2×C22⋊C4—474no—
141C2×C42—472no—
142C2×C42C2×D4711yescharacteristic
143C2×C42C2×D4711yescharacteristic
144C2×C42C2×D4711yescharacteristic
145#95—474no—
146#95C2×D4712yes—
147C24—472no—
148C2×Q8—474no—
149C2×Q8—942no—
150C2×Q8—942no—
151C2×Q8—942no—
152C2×Q8—942no—
153C2×Q8—942no—
154C2×D4—942no—
155C2×D4—942no—
156C2×D4—942no—
157C22×C4—472no—
158C22×C4—472no—
159C22×C4—472no—
160C22×C4C22×D4712yes—
161C22×C4C22×D4711yescharacteristic
162C22×C4C22×D4711yescharacteristic
163C22×C4C22×D4712yes—
164C22×C4C22×D4711yescharacteristic
165C4⋊C4—24no—
166C4⋊C4—948no—
167C4⋊C4—944no—
168C4⋊C4—942no—
169C22⋊C4—948no—
170C22⋊C4—944no—
171C22⋊C4—944no—
172C22⋊C4—948no—
173C42—22no—
174C42—22no—
175C42—944no—
176C42D18814yes—
177C23—942no—
178C23—942no—
179C23—944no—
180C23—942no—
181C23—944no—
182C23C23×D4711yescharacteristic
183Q8—948no—
184Q8—1884no—
185D4—1884no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—474no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—944no—
200C2×C4—942no—
201C2×C4C2×D18812yes—
202C2×C4C2×D18812yes—
203C2×C4C2×D18812yes—
204C2×C4#1062535014yes—
205C2×C4D4×D4712yes—
206C2×C4#1062535412yes—
207C22—1884no—
208C22—1884no—
209C22—1882no—
210C22—1882no—
211C22—1882no—
212C22C2×D4×D4711yescharacteristic
213C22C22×D18811yescharacteristic
214C22C2×#1062535012yes—
215C22C2×#1062535411yescharacteristic
216C22#1309407112yes—
217C4—24no—
218C4—22no—
219C4—22no—
220C4—42no—
221C4—944no—
222C4—1882no—
223C4—1882no—
224C4#1309399914yes—
225C2—3762no—
226C2C2×#1309399911yescharacteristic
227C2#1568967311yescharacteristic
228C2#1568969911yescharacteristic
229C2#1568978212yes—
230C2#1568984612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC4×C4⋊C4×C47C2
hypercenterC4×C4⋊C4D47
hypocenterC47#2545
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13094024C2semidirect
4. C2×C4×Dic94C2semidirect
5. #15689045C2semidirect
6. #15689029C2semidirect
8. #15689015C2semidirect
9. C4×C4⋊C4×C47C2semidirect
124. C4×C4⋊C4D47semidirect
125. C47#2545semidirect