Finite Group Databasebeta

← #20242412

Subgroups — #20242412

Order 6016.

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

normal subgroups only

This group has 236 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#15689749C211yesmaximal, characteristic
2#15689458C212yesmaximal, complemented
3#15688859C212yesmaximal, complemented
4#15688847C211yesmaximal, characteristic
5C47×#399C211yesmaximal, characteristic
6#13094003—21no—
7#13094003C2212yes—
8#13094001—22no—
9#13094001—22no—
10C2×C22⋊Dic47—21no—
11#13093957—22no—
12#13093947—22no—
13C22⋊(C47⋊C8)C2212yes—
14C2×C4⋊C4×C47—21no—
15C2×C4⋊C4×C47C2211yescharacteristic
16C2×C22⋊C4×C47—21no—
17C2×C22⋊C4×C47C2211yescharacteristic
18#95×C47C2211yescharacteristic
19C24×C47D411yescharacteristic
20C22×C4×C47—21no—
21C22×C4×C47—21no—
22C22×C4×C47D411yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—21no—
25C22×Dic47—21no—
26C2×Dic94—21no—
27C2×Dic94D412yes—
28C4⋊C4×C47—22no—
29C4⋊C4×C47—42no—
30C22⋊C4×C47—22no—
31C22⋊C4×C47—42no—
32C22⋊Dic47—22no—
33C22⋊Dic47—22no—
34C4⋊Dic47—21no—
35C4⋊Dic47D412yes—
36Dic47⋊C4—22no—
37Dic47⋊C4—22no—
38C2×C47⋊C8—22no—
39C23×C47—21no—
40C23×C47—21no—
41C23×C47—41no—
42C23×C47—41no—
43C23×C47Q1612yes—
44C23×C47C2×D411yescharacteristic
45C2×C4×C47—22no—
46C2×C4×C47—21no—
47C2×C4×C47—41no—
48C2×C4×C47—41no—
49C2×C4×C47—41no—
50C2×C4×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47C2×D412yes—
55C2×Dic47—22no—
56C2×Dic47—22no—
57C2×Dic47—81no—
58C2×Dic47—81no—
59Dic94—42no—
60Dic94—81no—
61C47⋊C8—42no—
62C22×C47—21no—
63C22×C47—21no—
64C22×C47—22no—
65C22×C47—42no—
66C22×C47—41no—
67C22×C47—41no—
68C22×C47—81no—
69C22×C47#12011yescharacteristic
70C22×C47C2×Q1611yescharacteristic
71C22×C47#13711yescharacteristic
72C4×C47—22no—
73C4×C47—42no—
74C4×C47—41no—
75C4×C47—81no—
76Dic47—42no—
77Dic47—42no—
78#1614—471nomaximal, Sylow
79C2×C47—21no—
80C2×C47—21no—
81C2×C47—42no—
82C2×C47#45111yescharacteristic
83C2×C47#45311yescharacteristic
84C2×C47#45811yescharacteristic
85#543—471no—
86#484—472no—
87#399D4711yescharacteristic
88#328—472no—
89#323—471no—
90C47#161411yescharacteristic, complemented, Sylow
91C22⋊Q8—472no—
92C22⋊Q8—942no—
93C22⋊Q8—942no—
94C22⋊Q8—941no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4C2×D4711yescharacteristic
97C2×C22⋊C4—21no—
98C2×C22⋊C4—941no—
99C2×C22⋊C4C2×D4711yescharacteristic
100#107—942no—
101#103—942no—
102C22⋊C8—472no—
103#95C2×D4711yescharacteristic
104C24C22⋊D4711yescharacteristic
105C2×Q8—472no—
106C2×Q8—941no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—941no—
110C22×C4—941no—
111C22×C4C22⋊D4711yescharacteristic
112C22×C4C22×D4711yescharacteristic
113C2×C8—942no—
114C4⋊C4—22no—
115C4⋊C4—42no—
116C4⋊C4—472no—
117C4⋊C4—942no—
118C4⋊C4—941no—
119C4⋊C4—942no—
120C22⋊C4—22no—
121C22⋊C4—42no—
122C22⋊C4—942no—
123C22⋊C4—942no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#1062533712yes—
129C23C2×C22⋊D4711yescharacteristic
130Q8—3761no—
131Q8—1882no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—942no—
142C2×C4—942no—
143C2×C4—3761no—
144C2×C4—3761no—
145C2×C4D4×D4712yes—
146C8—1882no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1309399211yescharacteristic
155C22C2×#1062533711yescharacteristic
156C22#1309405411yescharacteristic
157C4—22no—
158C4—42no—
159C4—41no—
160C4—81no—
161C4—1882no—
162C4—1882no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1568927811yescharacteristic
167C2#1568929011yescharacteristic
168C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#399C2
socleC22×C47#120
hypercenter#399D47
hypocenterC47#1614
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #15689458C2semidirect
3. #15688859C2semidirect
90. C47#1614semidirect