Finite Group Databasebeta

← #20253193

Subgroups — #20253193

Order 6016.

376 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 153 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#15689680C211yesmaximal, characteristic
2#15689430C214yesmaximal, complemented
3#15689418C212yesmaximal, complemented
4#15689408C212yesmaximal, complemented
5#15689163C212yesmaximal
6#15689147C211yesmaximal, characteristic
7#15689132C212yesmaximal
8C2×C4×Q8×C47C211yesmaximal, characteristic
9C2×#10625329C2212yes—
10#13094024C2211yescharacteristic
11#13094024C2211yescharacteristic
12#13094016C2212yes—
13#13094003—21no—
14#13094003—21no—
15C4×Dic94—21no—
16C4×Dic94—21no—
17#13093983C2212yes—
18#13093957C2214yes—
19#13093955C2214yes—
20C4⋊(C47⋊C8)C2212yes—
21C4⋊(C47⋊C8)C2212yes—
22#13093948C2214yes—
23#13093948C2214yes—
24C22×Q8×C47C2211yescharacteristic
25C4×Q8×C47—21no—
26C4×Q8×C47—21no—
27C4×Q8×C47C2212yes—
28C4×Q8×C47C2212yes—
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47C2211yescharacteristic
31C2×C42×C47—21no—
32C2×C42×C47C2211yescharacteristic
33C2×Q8×C47—21no—
34C2×Q8×C47—22no—
35C2×Q8×C47Q814yescomplemented
36C2×Q8×C47C2312yes—
37C22×C4×C47—21no—
38C22×C4×C47—21no—
39C22×C4×C47D411yescharacteristic
40C22×C4×C47D411yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C2×Dic94—21no—
43C2×Dic94—21no—
44C4⋊C4×C47—22no—
45C4⋊C4×C47—22no—
46C4⋊C4×C47—21no—
47C4⋊C4×C47C2312yes—
48C42×C47—22no—
49C42×C47—22no—
50C42×C47D411yescharacteristic
51C42×C47D411yescharacteristic
52C42×C47C2311yescharacteristic
53C42×C47C2311yescharacteristic
54C22⋊Dic47—22no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47C2312yes—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62#10625329—24no—
63C2×C47⋊C8C2314yes—
64C23×C47C2×D411yescharacteristic
65Q8×C47—24no—
66Q8×C47—22no—
67Q8×C47C2×Q814yes—
68C2×C4×C47—24no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—41no—
73C2×C4×C47—42no—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×Q812yes—
80C2×C4×C47#4112yes—
81C2×C4×C47C2411yescharacteristic
82C2×Dic47—22no—
83C2×Dic47—22no—
84Dic94—42no—
85Dic94—42no—
86C47⋊C8—24no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47C22⋊Q812yes—
90C22×C47C22×D411yescharacteristic
91C4×C47—24no—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—21no—
95C4×C47—42no—
96C4×C47C22⋊Q812yes—
97C4×C47#13712yes—
98C4×C47C22×Q811yescharacteristic
99C4×C47C2×#4111yescharacteristic
100Dic47—42no—
101Dic47—42no—
102#3078—471nomaximal, Sylow
103C2×C47—22no—
104C2×C47C2×C22⋊Q811yescharacteristic
105C2×C47C2×#13711yescharacteristic
106C2×C47#57511yescharacteristic
107#533—471no—
108C2×C4×Q8D4711yescharacteristic
109#479—474no—
110#477—472no—
111#475—472no—
112#428—472no—
113#423—471no—
114#419—472no—
115C47#307811yescharacteristic, complemented, Sylow
116C22×Q8C2×D4711yescharacteristic
117C2×M16—472no—
118C4⋊Q8—471no—
119C4⋊Q8—471no—
120#125—472no—
121C22⋊Q8—941no—
122C22⋊Q8—941no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—941no—
126C4×Q8—941no—
127C4×Q8C2×D4712yes—
128C4×Q8C2×D4712yes—
129#117—472no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C42—21no—
133C2×C42C2×D4711yescharacteristic
134#107—474no—
135#106—474no—
136C4⋊C8—472no—
137C4⋊C8—472no—
138#103—474no—
139#103—474no—
140C2×Q8—22no—
141C2×Q8—21no—
142C2×Q8—941no—
143C2×Q8—941no—
144C2×Q8Dic9414yescomplemented
145C2×Q8C22×D4712yes—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4C22⋊D4711yescharacteristic
149C22×C4C22⋊D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151M16—944no—
152C2×C8—474no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—472no—
157C4⋊C4—472no—
158C4⋊C4—942no—
159C4⋊C4—942no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C4⋊C4C22×D4712yes—
163C22⋊C4—942no—
164C42—22no—
165C42—22no—
166C42—942no—
167C42C22⋊D4711yescharacteristic
168C42C22⋊D4711yescharacteristic
169C42C22×D4711yescharacteristic
170C42C22×D4711yescharacteristic
171C23C2×C22⋊D4711yescharacteristic
172Q8—24no—
173Q8—22no—
174Q8—1882no—
175Q8—1882no—
176Q8C2×Dic9414yes—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4C2×Dic9412yes—
186C2×C4#1062535012yes—
187C2×C4C2×C22⋊D4711yescharacteristic
188C2×C4C2×C22⋊D4711yescharacteristic
189C2×C4C2×C22⋊D4711yescharacteristic
190C2×C4C2×C22⋊D4711yescharacteristic
191C2×C4C2×C22⋊D4711yescharacteristic
192C2×C4C23×D4711yescharacteristic
193C8—944no—
194C22—21no—
195C22—21no—
196C22#1309400312yes—
197C22C22×C22⋊D4711yescharacteristic
198C4—24no—
199C4—21no—
200C4—21no—
201C4—21no—
202C4—42no—
203C4—1882no—
204C4—1882no—
205C4#1309400312yes—
206C4#1309405512yes—
207C4C22×Dic9411yescharacteristic
208C4C2×#1062535011yescharacteristic
209C2—22no—
210C2C2×#1309400311yescharacteristic
211C2C2×#1309405511yescharacteristic
212C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C4×Q8×C47C2
socleC22×C47C22×D4
hypercenterC2×C4×Q8D47
hypocenterC47#3078
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #15689430C2semidirect
3. #15689418C2semidirect
4. #15689408C2semidirect
35. C2×Q8×C47Q8semidirect
115. C47#3078semidirect
144. C2×Q8Dic94semidirect