Finite Group Databasebeta

← #20242393

Subgroups — #20242393

Order 6016.

254 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689704C211yesmaximal, characteristic
2#15689437C212yesmaximal, complemented
3#15689053C211yesmaximal, characteristic, complemented
4#15688858C212yesmaximal, complemented
5C47×#324C211yesmaximal, characteristic, complemented
6C2×#10625350—21no—
7#13094004—22no—
8#13093999—22no—
9#13093998—21no—
10#13093998C2212yes—
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13#13093958—22no—
14#13093946—22no—
15C47⋊#95—21no—
16C47⋊#95C2211yescharacteristic
17C2×C4⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C22×C4×C47D411yescharacteristic
20C22×C4×C47D411yescharacteristic
21C22×C4×C47C2311yescharacteristic
22C2×C22⋊D47—22no—
23C22×Dic47—21no—
24C22×Dic47—21no—
25#10625350—42no—
26#10625350—42no—
27C2×D188—21no—
28C2×D188—21no—
29C2×D188D412yes—
30C2×C4×D47—22no—
31C2×Dic94—21no—
32C2×C8×C47—22no—
33C4⋊C4×C47—22no—
34(C2×D47)⋊C4—22no—
35(C2×D47)⋊C4—22no—
36C4⋊Dic47—21no—
37C4⋊Dic47—22no—
38C4⋊Dic47D412yes—
39Dic47⋊C4—42no—
40C23×C47C2×D411yescharacteristic
41C22×D47—22no—
42C2×C4×C47—21no—
43C2×C4×C47—21no—
44C2×C4×C47—21no—
45C2×C4×C47—41no—
46C2×C4×C47—41no—
47C2×C4×C47D812yes—
48C2×C4×C47C2×D412yes—
49C22⋊D47—42no—
50C22⋊D47—42no—
51C2×Dic47—22no—
52C2×Dic47—22no—
53C2×Dic47—41no—
54C2×Dic47—41no—
55C2×Dic47—41no—
56C2×Dic47—41no—
57C2×Dic47—41no—
58D188—42no—
59D188—42no—
60D188—81no—
61C4×D47—44no—
62Dic94—42no—
63C8×C47—42no—
64C22×C47—21no—
65C22×C47—21no—
66C22×C47#12011yescharacteristic
67C22×C47C2×D811yescharacteristic
68C22×C47AGL(1,ℤ/8)11yescharacteristic
69C2×D47—42no—
70C2×D47—42no—
71C2×D47—42no—
72C4×C47—22no—
73C4×C47—22no—
74C4×C47—41no—
75Dic47—42no—
76Dic47—42no—
77Dic47—81no—
78#1610—471nomaximal, Sylow
79C2×C47—21no—
80C2×C47—21no—
81C2×C47#44711yescharacteristic
82C2×C47#45611yescharacteristic
83C2×C47#45811yescharacteristic
84D47—82no—
85#537—471no—
86#480—472no—
87#398—471no—
88#327—472no—
89#324D4711yescharacteristic, complemented
90C47#161011yescharacteristic, complemented, Sylow
91C2×#41—941no—
92C22⋊Q8—942no—
93#121—472no—
94#121—942no—
95#121—941no—
96C2×C4⋊C4—471no—
97C2×C4⋊C4—941no—
98C2×C4⋊C4C2×D4711yescharacteristic
99#107—942no—
100#102—942no—
101C22⋊C8C2×D4712yes—
102#95—471no—
103#95—941no—
104#41—1882no—
105#41—1882no—
106C2×Q8—941no—
107C2×D4—472no—
108C2×D4—941no—
109C2×D4—941no—
110C2×D4—942no—
111C22×C4—942no—
112C22×C4—941no—
113C22×C4—941no—
114C22×C4D18811yescharacteristic
115C22×C4D18811yescharacteristic
116C22×C4C22×D4711yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—472no—
120C4⋊C4—941no—
121C4⋊C4—942no—
122C4⋊C4—1882no—
123C22⋊C4—942no—
124C22⋊C4—942no—
125C23—942no—
126C23C2×D18811yescharacteristic
127Q8—1882no—
128D4—3761no—
129D4—1882no—
130D4—1882no—
131D4—1882no—
132D4—1882no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—942no—
139C2×C4—942no—
140C2×C4—1884no—
141C2×C4—1881no—
142C2×C4—1881no—
143C2×C4—1881no—
144C2×C4—1881no—
145C2×C4—1881no—
146C2×C4D37612yes—
147C2×C4D4×D4712yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—1882no—
152C22—1882no—
153C22—1882no—
154C22#1309399411yescharacteristic
155C22C2×D37611yescharacteristic
156C22#1309405211yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—3761no—
161C4—1882no—
162C4—1882no—
163C2—21no—
164C2—21no—
165C2—3762no—
166C2#1568925911yescharacteristic
167C2#1568930811yescharacteristic
168C2#1568931411yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47#120
hypercenter#324D47
hypocenterC47#1610
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #15689437C2semidirect
3. #15689053C2semidirect
4. #15688858C2semidirect
5. C47×#324C2semidirect
89. #324D47semidirect
90. C47#1610semidirect