Finite Group Databasebeta

← #20243769

Subgroups — #20243769

Order 6016.

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

normal subgroups only

This group has 332 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
1#15689890C211yesmaximal, characteristic, complemented
2#15689669C211yesmaximal, characteristic
3#15689141C212yesmaximal, complemented
4#15688882C212yesmaximal, complemented
5C47×#410C211yesmaximal, characteristic, complemented
6C2×#10625350C2211yescharacteristic
7#13094031—24no—
8C2×#10625329—22no—
9C2×#10625329C2212yes—
10#13094022C411yescharacteristic, complemented
11#13094020C411yescharacteristic, complemented
12#13094013C411yescharacteristic, complemented
13#13094011C411yescharacteristic, complemented
14#13093996—22no—
15C4×C22⋊D47—22no—
16C2×C4×Dic47C2211yescharacteristic
17#13093952—24no—
18C2×#41×C47C2211yescharacteristic
19#117×C47C2212yes—
20#99×C47—22no—
21#41×C47—22no—
22#41×C47—22no—
23C2×Q8×C47C2×C411yescharacteristic
24C2×D4×C47C2×C411yescharacteristic
25C2×D4×C47D412yes—
26C22×C4×C47D412yes—
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—22no—
29C2×C22⋊D47—21no—
30C22×Dic47—21no—
31#10625350—22no—
32#10625350—22no—
33C2×D188C2×C411yescharacteristic
34C2×C4×D47—21no—
35C2×Dic94C2×C411yescharacteristic
36C4⋊C4×C47—22no—
37C22⋊C4×C47—22no—
38C42×C47—22no—
39C22⋊Dic47—22no—
40(C2×D47)⋊C4—22no—
41Dic47⋊C4—22no—
42C4×Dic47—21no—
43C4×Dic47C2×C411yescharacteristic
44C4×Dic47C2×C411yescharacteristic
45#10625329—24no—
46#10625329—22no—
47#10625329D414yescomplemented
48C2×C47⋊C8—24no—
49C2×C47⋊C8—22no—
50C23×C47C22⋊C412yes—
51C23×C47C2×D411yescharacteristic
52C22×D47—21no—
53Q8×C47—22no—
54D4×C47—24no—
55D4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—42no—
59C2×C4×C47C22⋊C412yes—
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D412yes—
63C2×C4×C47#4112yes—
64C22⋊D47—44no—
65C22⋊D47—42no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47—42no—
70D188—22no—
71C4×D47—41no—
72C4×D47—41no—
73Dic94—22no—
74C47⋊C8—24no—
75C22×C47—22no—
76C22×C47—41no—
77C22×C47—42no—
78C22×C47C2×C22⋊C411yescharacteristic
79C22×C47#12112yes—
80C2×D47—42no—
81C2×D47—41no—
82C4×C47—22no—
83C4×C47—82no—
84C4×C47C4×D412yes—
85C4×C47#12011yescharacteristic
86C4×C47#12311yescharacteristic
87Dic47—22no—
88Dic47—41no—
89Dic47—41no—
90#1884—471nomaximal, Sylow
91C2×C47—21no—
92C2×C47—22no—
93C2×C47—42no—
94C2×C47#38611yescharacteristic
95D47—81no—
96#568—471no—
97#532—471no—
98#421—472no—
99#410D4711yescharacteristic, complemented
100#339—472no—
101C47#188411yescharacteristic, complemented, Sylow
102C2×#41—471no—
103C2×#41C2×D4711yescharacteristic
104#131—944no—
105C2×M16—472no—
106C2×M16—942no—
107C4⋊Q8—471no—
108#127—471no—
109#124—471no—
110#124—471no—
111#121—942no—
112C4×D4—942no—
113#117C2×D4712yes—
114C2×C42—471no—
115#104—944no—
116#99—22no—
117#41—22no—
118#41—22no—
119#41—942no—
120#41—942no—
121C2×Q8—471no—
122C2×Q8C4×D4711yescharacteristic
123C2×D4—471no—
124C2×D4—942no—
125C2×D4—941no—
126C2×D4C4×D4711yescharacteristic
127C2×D4C22⋊D4712yes—
128C22×C4—941no—
129C22×C4—941no—
130C22×C4D18812yes—
131C22×C4C22×D4711yescharacteristic
132M16—474no—
133M16—944no—
134M16—942no—
135C2×C8—944no—
136C2×C8—942no—
137C4⋊C4—22no—
138C4⋊C4—942no—
139C22⋊C4—22no—
140C22⋊C4—942no—
141C22⋊C4—942no—
142C42—22no—
143C42—471no—
144C42—471no—
145C42—941no—
146C23—941no—
147C23(C2×D47)⋊C412yes—
148C23C2×C22⋊D4711yescharacteristic
149Q8—22no—
150Q8—942no—
151D4—24no—
152D4—22no—
153D4—942no—
154D4—1884no—
155D4—1882no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—941no—
160C2×C4—941no—
161C2×C4—941no—
162C2×C4—1882no—
163C2×C4—1881no—
164C2×C4—1881no—
165C2×C4(C2×D47)⋊C412yes—
166C2×C4C2×C4×D4711yescharacteristic
167C2×C4C2×D18811yescharacteristic
168C2×C4D4×D4712yes—
169C2×C4#1062535212yes—
170C8—944no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—1882no—
175C22—1881no—
176C22C2×(C2×D47)⋊C411yescharacteristic
177C22#1309399612yes—
178C4—22no—
179C4—82no—
180C4—942no—
181C4—1881no—
182C4—1881no—
183C4(C22⋊D47)⋊C412yes—
184C4#1309399411yescharacteristic
185C4#1309400811yescharacteristic
186C2—22no—
187C2—21no—
188C2—42no—
189C2—3761no—
190C2#1568900011yescharacteristic
subgroupG/H
centerC4#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#410C2
socleC2×C47#386
hypercenter#410D47
hypocenterC47#1884
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #15689890C2semidirect
3. #15689141C2semidirect
4. #15688882C2semidirect
5. C47×#410C2semidirect
10. #13094022C4semidirect
11. #13094020C4semidirect
12. #13094013C4semidirect
13. #13094011C4semidirect
47. #10625329D4semidirect
99. #410D47semidirect
101. C47#1884semidirect