Finite Group Databasebeta

← #20242413

Subgroups — #20242413

Order 6016.

236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689456C212yesmaximal, complemented
2#15689059C211yesmaximal, characteristic
3#15688860C212yesmaximal, complemented
4#15688847C211yesmaximal, characteristic
5C47×#543C211yesmaximal, characteristic
6C2×C4⋊Dic47C2211yescharacteristic
7C2×Dic47⋊C4—21no—
8C2×C22⋊Dic47—21no—
9#13093957—22no—
10#13093948—22no—
11C22⋊(C47⋊C8)C2212yes—
12C47⋊#95C2211yescharacteristic
13C22⋊Q8×C47—22no—
14C22⋊Q8×C47—21no—
15C22⋊Q8×C47—22no—
16C22⋊Q8×C47C2212yes—
17C2×C22⋊C4×C47—21no—
18C2×C22⋊C4×C47C2211yescharacteristic
19C24×C47D411yescharacteristic
20C2×Q8×C47—21no—
21C2×Q8×C47D412yes—
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47D411yescharacteristic
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—21no—
27C22×Dic47—21no—
28C4⋊C4×C47—21no—
29C4⋊C4×C47—22no—
30C4⋊C4×C47—22no—
31C4⋊C4×C47D412yes—
32C22⋊C4×C47—22no—
33C22⋊C4×C47—22no—
34C22⋊C4×C47—22no—
35C22⋊Dic47—42no—
36C4⋊Dic47—22no—
37Dic47⋊C4—42no—
38C2×C47⋊C8—22no—
39C23×C47—21no—
40C23×C47—21no—
41C23×C47—41no—
42C23×C47—41no—
43C23×C47Q1612yes—
44C23×C47C2×D411yescharacteristic
45Q8×C47—42no—
46Q8×C47—81no—
47C2×C4×C47—22no—
48C2×C4×C47—21no—
49C2×C4×C47—22no—
50C2×C4×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47—81no—
53C2×C4×C47—81no—
54C2×C4×C47C2×D412yes—
55C2×Dic47—22no—
56C2×Dic47—41no—
57C2×Dic47—41no—
58C2×Dic47—41no—
59C2×Dic47—41no—
60C2×Dic47—41no—
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—41no—
74C4×C47—42no—
75C4×C47—42no—
76Dic47—42no—
77Dic47—81no—
78#1614—471nomaximal, Sylow
79C2×C47—21no—
80C2×C47—21no—
81C2×C47—42no—
82C2×C47#45111yescharacteristic
83C2×C47#45311yescharacteristic
84C2×C47#45811yescharacteristic
85#543D4711yescharacteristic
86#484—472no—
87#399—471no—
88#328—472no—
89#323—471no—
90C47#161411yescharacteristic, complemented, Sylow
91C22⋊Q8—22no—
92C22⋊Q8—21no—
93C22⋊Q8—22no—
94C22⋊Q8C2×D4712yes—
95C2×C4⋊C4—471no—
96C2×C4⋊C4—941no—
97C2×C22⋊C4—21no—
98C2×C22⋊C4—941no—
99C2×C22⋊C4C2×D4711yescharacteristic
100#107—942no—
101#103—942no—
102C22⋊C8—472no—
103#95—471no—
104C24C22⋊D4711yescharacteristic
105C2×Q8—21no—
106C2×Q8C22⋊D4712yes—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—941no—
110C22×C4—941no—
111C22×C4C22⋊D4711yescharacteristic
112C22×C4C22×D4711yescharacteristic
113C2×C8—942no—
114C4⋊C4—21no—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—942no—
118C4⋊C4—1882no—
119C4⋊C4C22⋊D4712yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C22⋊C4—1882no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#1062533712yes—
129C23C2×C22⋊D4711yescharacteristic
130Q8—42no—
131Q8—81no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—81no—
139C2×C4—942no—
140C2×C4—1881no—
141C2×C4—1881no—
142C2×C4—1881no—
143C2×C4—1881no—
144C2×C4—1881no—
145C2×C4C2×C22⋊D4712yes—
146C8—1882no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1309399311yescharacteristic
155C22C2×#1062533711yescharacteristic
156C22#1309405511yescharacteristic
157C4—22no—
158C4—41no—
159C4—42no—
160C4—42no—
161C4—3761no—
162C4—1882no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1568927911yescharacteristic
167C2#1568929111yescharacteristic
168C2#1568931311yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#543C2
socleC22×C47#120
hypercenter#543D47
hypocenterC47#1614
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #15689456C2semidirect
3. #15688860C2semidirect
90. C47#1614semidirect