Finite Group Databasebeta

← #20243347

Subgroups — #20243347

Order 6016.

552 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13093951C212yesmaximal, complemented
2#15689124C212yesmaximal, complemented
3C2×#13093943C211yesmaximal, characteristic, complemented
4#15689030C211yesmaximal, characteristic, complemented
5C2×2−1+4×C47C211yesmaximal, characteristic
6C2×#10625329C2212yes—
7C2×C4⋊Dic47C2211yescharacteristic
8C2×C4×Dic47C2211yescharacteristic
9#13093951—24no—
10#13093948—22no—
11#13093945—22no—
12#13093943—22no—
13C47⋊#95—22no—
142−1+4×C47—24no—
152−1+4×C47—22no—
162−1+4×C47C414yescomplemented
17C2×#41×C47—22no—
18C2×#41×C47—22no—
19C2×#41×C47C2212yes—
20C22×Q8×C47—22no—
21C22×Q8×C47C2211yescharacteristic
22#41×C47—28no—
23#41×C47—28no—
24#41×C47—28no—
25#41×C47—28no—
26#41×C47—22no—
27#41×C47—22no—
28#41×C47C2×C414yes—
29#41×C47D414yes—
30C2×Q8×C47—22no—
31C2×Q8×C47—28no—
32C2×Q8×C47—28no—
33C2×Q8×C47—22no—
34C2×Q8×C47—22no—
35C2×Q8×C47C2×C412yes—
36C2×Q8×C47D412yes—
37C2×Q8×C47D412yes—
38C2×D4×C47—22no—
39C2×D4×C47—22no—
40C2×D4×C47D412yes—
41C22×C4×C47—24no—
42C22×C4×C47—22no—
43C22×C4×C47D412yes—
44C22×C4×C47C2311yescharacteristic
45C22×Dic47—21no—
46C22×Dic47—21no—
47C4⋊Dic47—22no—
48C4×Dic47—22no—
49#10625329—22no—
50#10625329—22no—
51C2×C47⋊C8—22no—
52C23×C47—22no—
53C23×C47C2×D411yescharacteristic
54Q8×C47—28no—
55Q8×C47—24no—
56Q8×C47—22no—
57Q8×C47—24no—
58Q8×C47C22⋊C414yes—
59D4×C47—28no—
60D4×C47—24no—
61D4×C47—24no—
62D4×C47—22no—
63D4×C47C22⋊C414yes—
64C2×C4×C47—216no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—24no—
69C2×C4×C47—24no—
70C2×C4×C47C22⋊C414yes—
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D412yes—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D411yescharacteristic
75C2×Dic47—22no—
76C2×Dic47—41no—
77C2×Dic47—41no—
78C2×Dic47—42no—
79C2×Dic47—41no—
80C47⋊C8—42no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47—24no—
84C22×C47—42no—
85C22×C47—42no—
86C22×C47C2×C22⋊C411yescharacteristic
87C22×C47#12011yescharacteristic
88C22×C47#12011yescharacteristic
89C4×C47—24no—
90C4×C47—24no—
91C4×C47C2×C22⋊C412yes—
92C4×C47#12012yes—
93Dic47—42no—
94Dic47—81no—
95#1793—471nomaximal, Sylow
96C2×C47—21no—
97C2×C47—21no—
98C2×C47—44no—
99C2×C47#37911yescharacteristic
100C2×C47#45411yescharacteristic
101C2×C47#45611yescharacteristic
102C2×2−1+4D4711yescharacteristic
103C2×#104—472no—
104#417—472no—
105C2×#101—471no—
106#391—471no—
107C47#179311yescharacteristic, complemented, Sylow
1082−1+4—24no—
1092−1+4—22no—
1102−1+4Dic4714yescomplemented
111C2×#41—22no—
112C2×#41—22no—
113C2×#41C2×D4712yes—
114C22×Q8—22no—
115C22×Q8C2×D4711yescharacteristic
116C2×M16—472no—
117C2×C4⋊C4—471no—
118C2×C42—471no—
119#104—944no—
120#103—942no—
121#102—942no—
122#101—942no—
123#95—942no—
124#41—28no—
125#41—28no—
126#41—28no—
127#41—28no—
128#41—22no—
129#41—22no—
130#41C2×Dic4714yes—
131#41C22⋊D4714yes—
132C2×Q8—22no—
133C2×Q8—28no—
134C2×Q8—28no—
135C2×Q8—22no—
136C2×Q8—22no—
137C2×Q8C2×Dic4712yes—
138C2×Q8C22⋊D4712yes—
139C2×Q8C22⋊D4712yes—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22⋊D4712yes—
143C22×C4—24no—
144C22×C4—22no—
145C22×C4—941no—
146C22×C4—941no—
147C22×C4C22⋊D4712yes—
148C22×C4C22×D4711yescharacteristic
149M16—942no—
150M16—942no—
151C2×C8—942no—
152C4⋊C4—942no—
153C42—942no—
154C23—22no—
155C23C2×C22⋊D4711yescharacteristic
156Q8—28no—
157Q8—24no—
158Q8—22no—
159Q8—24no—
160Q8C22⋊Dic4714yes—
161D4—28no—
162D4—24no—
163D4—24no—
164D4—22no—
165D4C22⋊Dic4714yes—
166C2×C4—216no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—942no—
173C2×C4—1882no—
174C2×C4—1881no—
175C2×C4—1881no—
176C2×C4—1881no—
177C2×C4C22⋊Dic4714yes—
178C2×C4C22×Dic4711yescharacteristic
179C2×C4C2×C22⋊D4712yes—
180C2×C4C2×C22⋊D4712yes—
181C2×C4C2×C22⋊D4711yescharacteristic
182C8—1882no—
183C22—21no—
184C22—21no—
185C22—24no—
186C22—42no—
187C22—42no—
188C22C2×C22⋊Dic4711yescharacteristic
189C22#1309399311yescharacteristic
190C22#1309399311yescharacteristic
191C4—24no—
192C4—24no—
193C4—3761no—
194C4—1882no—
195C4C2×C22⋊Dic4712yes—
196C4#1309399312yes—
197C2—21no—
198C2—21no—
199C2—44no—
200C2#1568897911yescharacteristic
201C2#1568929611yescharacteristic
202C2#1568930611yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×2−1+4×C47C2
socleC22×C47#120
hypercenterC2×2−1+4D47
hypocenterC47#1793
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#13093951C2semidirect
2. #15689124C2semidirect
3. C2×#13093943C2semidirect
4. #15689030C2semidirect
16. 2−1+4×C47C4semidirect
107. C47#1793semidirect
110. 2−1+4Dic47semidirect