Finite Group Databasebeta

← #20242415

Subgroups — #20242415

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#15689459C212yesmaximal, complemented
3#15689059C211yesmaximal, characteristic
4#15688861C212yesmaximal, complemented
5C47×#323C211yesmaximal, characteristic
6#13094003—21no—
7#13094003C2212yes—
8#13094001—22no—
9#13094001—22no—
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—21no—
12C2×C22⋊Dic47—21no—
13C2×C22⋊Dic47—21no—
14#13093958—22no—
15#13093949—22no—
16C47⋊#95C2211yescharacteristic
17C2×C22⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C24×C47D411yescharacteristic
20C22×C4×C47D411yescharacteristic
21C22×C4×C47C2311yescharacteristic
22C22×Dic47—21no—
23C22×Dic47—21no—
24C22×Dic47—21no—
25C22×Dic47—21no—
26C2×Dic94—21no—
27C2×Dic94D412yes—
28C2×C8×C47—22no—
29C22⋊C4×C47—22no—
30C22⋊Dic47—22no—
31C22⋊Dic47—22no—
32C22⋊Dic47—42no—
33C4⋊Dic47—21no—
34C4⋊Dic47—22no—
35C4⋊Dic47D412yes—
36Dic47⋊C4—22no—
37Dic47⋊C4—22no—
38Dic47⋊C4—42no—
39C23×C47—21no—
40C23×C47—21no—
41C23×C47—41no—
42C23×C47—41no—
43C23×C47Q1612yes—
44C23×C47C2×D411yescharacteristic
45C2×C4×C47—21no—
46C2×C4×C47—41no—
47C2×C4×C47—41no—
48C2×C4×C47C2×D412yes—
49C2×Dic47—22no—
50C2×Dic47—22no—
51C2×Dic47—22no—
52C2×Dic47—41no—
53C2×Dic47—41no—
54C2×Dic47—41no—
55C2×Dic47—41no—
56C2×Dic47—41no—
57C2×Dic47—81no—
58C2×Dic47—81no—
59Dic94—42no—
60Dic94—81no—
61C8×C47—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—
74Dic47—42no—
75Dic47—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#543—471no—
86#484—472no—
87#399—471no—
88#328—472no—
89#323D4711yescharacteristic
90C47#161411yescharacteristic, complemented, Sylow
91C22⋊Q8—472no—
92C22⋊Q8—942no—
93C22⋊Q8—942no—
94C22⋊Q8—941no—
95C2×C4⋊C4—471no—
96C2×C4⋊C4—941no—
97C2×C22⋊C4—941no—
98C2×C22⋊C4—941no—
99C2×C22⋊C4C2×D4711yescharacteristic
100#107—942no—
101#103—942no—
102C22⋊C8C2×D4712yes—
103#95—471no—
104C24D18811yescharacteristic
105C2×Q8—472no—
106C2×Q8—941no—
107C22×C4—941no—
108C22×C4—941no—
109C22×C4—941no—
110C22×C4—941no—
111C22×C4D18811yescharacteristic
112C22×C4C22×D4711yescharacteristic
113C2×C8—22no—
114C4⋊C4—472no—
115C4⋊C4—942no—
116C4⋊C4—941no—
117C4⋊C4—942no—
118C4⋊C4—942no—
119C4⋊C4—1882no—
120C22⋊C4—22no—
121C22⋊C4—942no—
122C22⋊C4—942no—
123C22⋊C4—1882no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23Dic18812yes—
129C23C2×D18811yescharacteristic
130Q8—3761no—
131Q8—1882no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—942no—
136C2×C4—942no—
137C2×C4—942no—
138C2×C4—3761no—
139C2×C4—3761no—
140C2×C4—1881no—
141C2×C4—1881no—
142C2×C4—1881no—
143C2×C4—1881no—
144C2×C4—1881no—
145C2×C4D4×D4712yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1309399411yescharacteristic
155C22C2×Dic18811yescharacteristic
156C22#1309405711yescharacteristic
157C4—22no—
158C4—41no—
159C4—3761no—
160C4—1882no—
161C4—1882no—
162C4—1882no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1568928111yescharacteristic
167C2#1568929311yescharacteristic
168C2#1568931411yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#323C2
socleC22×C47#120
hypercenter#323D47
hypocenterC47#1614
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #15689459C2semidirect
4. #15688861C2semidirect
90. C47#1614semidirect